Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.1% → 83.1%

Time: 21.7s

Alternatives: 22

Speedup: 0.5×

• 58.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
  (* j (- (* c t) (* i y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
  (* j (- (* c t) (* i y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 83.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot j - x \cdot a\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \sqrt[3]{t_1 \cdot \left(t_1 \cdot t_1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* c j) (* x a)))
        (t_2
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
          (* j (- (* t c) (* y i))))))
   (if (<= t_2 INFINITY) t_2 (* t (cbrt (* t_1 (* t_1 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * j) - (x * a);
	double t_2 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = t * cbrt((t_1 * (t_1 * t_1)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (c * j) - (x * a);
	double t_2 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = t * Math.cbrt((t_1 * (t_1 * t_1)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(c * j) - Float64(x * a))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(t * cbrt(Float64(t_1 * Float64(t_1 * t_1))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(t * N[Power[N[(t$95$1 * N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 92.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 0.0%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 0.0%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in t around inf 54.3%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 54.3%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 54.3%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 54.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   8. Simplified 54.3%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]
   9. Step-by-step derivation

      1. add-cbrt-cube 60.5%

         \[\leadsto t \cdot \color{blue}{\sqrt[3]{\left(\left(c \cdot j - a \cdot x\right) \cdot \left(c \cdot j - a \cdot x\right)\right) \cdot \left(c \cdot j - a \cdot x\right)}} \]

      2. *-commutative 60.5%

         \[\leadsto t \cdot \sqrt[3]{\left(\left(c \cdot j - \color{blue}{x \cdot a}\right) \cdot \left(c \cdot j - a \cdot x\right)\right) \cdot \left(c \cdot j - a \cdot x\right)} \]

      3. *-commutative 60.5%

         \[\leadsto t \cdot \sqrt[3]{\left(\left(c \cdot j - x \cdot a\right) \cdot \left(c \cdot j - \color{blue}{x \cdot a}\right)\right) \cdot \left(c \cdot j - a \cdot x\right)} \]

      4. *-commutative 60.5%

         \[\leadsto t \cdot \sqrt[3]{\left(\left(c \cdot j - x \cdot a\right) \cdot \left(c \cdot j - x \cdot a\right)\right) \cdot \left(c \cdot j - \color{blue}{x \cdot a}\right)} \]

   10. Applied egg-rr 60.5%

       \[\leadsto t \cdot \color{blue}{\sqrt[3]{\left(\left(c \cdot j - x \cdot a\right) \cdot \left(c \cdot j - x \cdot a\right)\right) \cdot \left(c \cdot j - x \cdot a\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \sqrt[3]{\left(c \cdot j - x \cdot a\right) \cdot \left(\left(c \cdot j - x \cdot a\right) \cdot \left(c \cdot j - x \cdot a\right)\right)}\\ \end{array} \]

Alternative 2: 81.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
          (* j (- (* t c) (* y i))))))
   (if (<= t_1 INFINITY) t_1 (* t (- (* c j) (* x a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = t * ((c * j) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = t * ((c * j) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 92.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 0.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 0.0%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 0.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 0.0%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in t around inf 54.3%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 54.3%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 54.3%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 54.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   8. Simplified 54.3%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 3: 57.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;z \leq -3.35 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-111} \lor \neg \left(z \leq 1.05 \cdot 10^{+68}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (* y z)) (* b (- (* a i) (* z c))))))
   (if (<= z -3.35e+38)
     t_1
     (if (<= z -6.6e-34)
       (* t (- (* c j) (* x a)))
       (if (or (<= z -2.35e-111) (not (<= z 1.05e+68)))
         t_1
         (- (* b (* a i)) (* j (- (* y i) (* t c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * (y * z)) + (b * ((a * i) - (z * c)));
	double tmp;
	if (z <= -3.35e+38) {
		tmp = t_1;
	} else if (z <= -6.6e-34) {
		tmp = t * ((c * j) - (x * a));
	} else if ((z <= -2.35e-111) || !(z <= 1.05e+68)) {
		tmp = t_1;
	} else {
		tmp = (b * (a * i)) - (j * ((y * i) - (t * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (y * z)) + (b * ((a * i) - (z * c)))
    if (z <= (-3.35d+38)) then
        tmp = t_1
    else if (z <= (-6.6d-34)) then
        tmp = t * ((c * j) - (x * a))
    else if ((z <= (-2.35d-111)) .or. (.not. (z <= 1.05d+68))) then
        tmp = t_1
    else
        tmp = (b * (a * i)) - (j * ((y * i) - (t * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * (y * z)) + (b * ((a * i) - (z * c)));
	double tmp;
	if (z <= -3.35e+38) {
		tmp = t_1;
	} else if (z <= -6.6e-34) {
		tmp = t * ((c * j) - (x * a));
	} else if ((z <= -2.35e-111) || !(z <= 1.05e+68)) {
		tmp = t_1;
	} else {
		tmp = (b * (a * i)) - (j * ((y * i) - (t * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * (y * z)) + (b * ((a * i) - (z * c)))
	tmp = 0
	if z <= -3.35e+38:
		tmp = t_1
	elif z <= -6.6e-34:
		tmp = t * ((c * j) - (x * a))
	elif (z <= -2.35e-111) or not (z <= 1.05e+68):
		tmp = t_1
	else:
		tmp = (b * (a * i)) - (j * ((y * i) - (t * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	tmp = 0.0
	if (z <= -3.35e+38)
		tmp = t_1;
	elseif (z <= -6.6e-34)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif ((z <= -2.35e-111) || !(z <= 1.05e+68))
		tmp = t_1;
	else
		tmp = Float64(Float64(b * Float64(a * i)) - Float64(j * Float64(Float64(y * i) - Float64(t * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * (y * z)) + (b * ((a * i) - (z * c)));
	tmp = 0.0;
	if (z <= -3.35e+38)
		tmp = t_1;
	elseif (z <= -6.6e-34)
		tmp = t * ((c * j) - (x * a));
	elseif ((z <= -2.35e-111) || ~((z <= 1.05e+68)))
		tmp = t_1;
	else
		tmp = (b * (a * i)) - (j * ((y * i) - (t * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.35e+38], t$95$1, If[LessEqual[z, -6.6e-34], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.35e-111], N[Not[LessEqual[z, 1.05e+68]], $MachinePrecision]], t$95$1, N[(N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.35000000000000012e38 or -6.59999999999999965e-34 < z < -2.35000000000000003e-111 or 1.05e68 < z

   1. Initial program 70.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 70.7%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 72.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 72.2%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 72.2%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 72.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 72.2%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 72.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 73.2%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   5. Taylor expanded in y around inf 72.5%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b \]
   6. Step-by-step derivation

      1. *-commutative 72.5%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b \]

   7. Simplified 72.5%

      \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b \]

   if -3.35000000000000012e38 < z < -6.59999999999999965e-34

   1. Initial program 72.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 72.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 72.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 72.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 72.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 72.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 72.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 72.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 72.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 72.4%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 72.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 72.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 72.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 72.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 72.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 72.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 72.4%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in t around inf 67.9%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 67.9%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 67.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 67.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   8. Simplified 67.9%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -2.35000000000000003e-111 < z < 1.05e68

   1. Initial program 82.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 82.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 82.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 82.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 82.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 82.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 82.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 82.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 82.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 67.9%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. associate-*r* 68.8%

         \[\leadsto \color{blue}{\left(a \cdot i\right) \cdot b} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 68.8%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 68.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.35 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-111} \lor \neg \left(z \leq 1.05 \cdot 10^{+68}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \end{array} \]

Alternative 4: 66.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -4 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(a \cdot i\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;j \leq 1.32 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -4e+53)
   (- (* b (* a i)) (* j (- (* y i) (* t c))))
   (if (<= j 1.32e+170)
     (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
     (* j (- (* t c) (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -4e+53) {
		tmp = (b * (a * i)) - (j * ((y * i) - (t * c)));
	} else if (j <= 1.32e+170) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = j * ((t * c) - (y * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-4d+53)) then
        tmp = (b * (a * i)) - (j * ((y * i) - (t * c)))
    else if (j <= 1.32d+170) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    else
        tmp = j * ((t * c) - (y * i))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -4e+53) {
		tmp = (b * (a * i)) - (j * ((y * i) - (t * c)));
	} else if (j <= 1.32e+170) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = j * ((t * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -4e+53:
		tmp = (b * (a * i)) - (j * ((y * i) - (t * c)))
	elif j <= 1.32e+170:
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	else:
		tmp = j * ((t * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -4e+53)
		tmp = Float64(Float64(b * Float64(a * i)) - Float64(j * Float64(Float64(y * i) - Float64(t * c))));
	elseif (j <= 1.32e+170)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -4e+53)
		tmp = (b * (a * i)) - (j * ((y * i) - (t * c)));
	elseif (j <= 1.32e+170)
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	else
		tmp = j * ((t * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -4e+53], N[(N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.32e+170], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -4e53

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 79.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 79.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 79.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 76.9%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. associate-*r* 83.7%

         \[\leadsto \color{blue}{\left(a \cdot i\right) \cdot b} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 83.7%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 83.7%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   if -4e53 < j < 1.3199999999999999e170

   1. Initial program 76.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. +-commutative 76.2%

         \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      2. fma-def 78.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right)} \]

      3. *-commutative 78.0%

         \[\leadsto \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      4. *-commutative 78.0%

         \[\leadsto \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) \]

      5. *-commutative 78.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) \]

      6. *-commutative 78.0%

         \[\leadsto \mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) \]

   3. Simplified 78.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, t \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right)} \]

   4. Taylor expanded in j around 0 72.3%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x - \left(c \cdot z - i \cdot a\right) \cdot b} \]

   if 1.3199999999999999e170 < j

   1. Initial program 67.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 67.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 67.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 67.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 67.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 67.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 67.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 67.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 67.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around inf 67.9%

      \[\leadsto \color{blue}{\left(c \cdot t - i \cdot y\right) \cdot j} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(a \cdot i\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;j \leq 1.32 \cdot 10^{+170}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 5: 44.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -2100000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-247}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-302}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-242}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+122}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))))
   (if (<= t -2100000000000.0)
     t_1
     (if (<= t -5e-83)
       (* a (- (* b i) (* x t)))
       (if (<= t -6.5e-247)
         (* x (* y z))
         (if (<= t -1.55e-302)
           (* i (* a b))
           (if (<= t 5.5e-242)
             (* y (* i (- j)))
             (if (<= t 9.2e+122) (* c (- (* t j) (* z b))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2100000000000.0) {
		tmp = t_1;
	} else if (t <= -5e-83) {
		tmp = a * ((b * i) - (x * t));
	} else if (t <= -6.5e-247) {
		tmp = x * (y * z);
	} else if (t <= -1.55e-302) {
		tmp = i * (a * b);
	} else if (t <= 5.5e-242) {
		tmp = y * (i * -j);
	} else if (t <= 9.2e+122) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    if (t <= (-2100000000000.0d0)) then
        tmp = t_1
    else if (t <= (-5d-83)) then
        tmp = a * ((b * i) - (x * t))
    else if (t <= (-6.5d-247)) then
        tmp = x * (y * z)
    else if (t <= (-1.55d-302)) then
        tmp = i * (a * b)
    else if (t <= 5.5d-242) then
        tmp = y * (i * -j)
    else if (t <= 9.2d+122) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2100000000000.0) {
		tmp = t_1;
	} else if (t <= -5e-83) {
		tmp = a * ((b * i) - (x * t));
	} else if (t <= -6.5e-247) {
		tmp = x * (y * z);
	} else if (t <= -1.55e-302) {
		tmp = i * (a * b);
	} else if (t <= 5.5e-242) {
		tmp = y * (i * -j);
	} else if (t <= 9.2e+122) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -2100000000000.0:
		tmp = t_1
	elif t <= -5e-83:
		tmp = a * ((b * i) - (x * t))
	elif t <= -6.5e-247:
		tmp = x * (y * z)
	elif t <= -1.55e-302:
		tmp = i * (a * b)
	elif t <= 5.5e-242:
		tmp = y * (i * -j)
	elif t <= 9.2e+122:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2100000000000.0)
		tmp = t_1;
	elseif (t <= -5e-83)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (t <= -6.5e-247)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= -1.55e-302)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 5.5e-242)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (t <= 9.2e+122)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -2100000000000.0)
		tmp = t_1;
	elseif (t <= -5e-83)
		tmp = a * ((b * i) - (x * t));
	elseif (t <= -6.5e-247)
		tmp = x * (y * z);
	elseif (t <= -1.55e-302)
		tmp = i * (a * b);
	elseif (t <= 5.5e-242)
		tmp = y * (i * -j);
	elseif (t <= 9.2e+122)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2100000000000.0], t$95$1, If[LessEqual[t, -5e-83], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.5e-247], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.55e-302], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-242], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e+122], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.1e12 or 9.2000000000000002e122 < t

   1. Initial program 62.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 62.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 62.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 62.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 62.5%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 62.5%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 62.5%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 62.5%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 62.5%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 62.5%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 62.5%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 62.5%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in t around inf 75.3%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 75.3%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 75.3%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 75.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   8. Simplified 75.3%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -2.1e12 < t < -5e-83

   1. Initial program 78.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 78.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 78.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 78.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 78.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 41.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 41.1%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 41.1%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 41.1%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 41.1%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 41.1%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 41.1%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 41.1%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 41.1%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   if -5e-83 < t < -6.4999999999999996e-247

   1. Initial program 97.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 97.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 97.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 97.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 97.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 97.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 97.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 97.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 97.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 69.5%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 40.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 50.2%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

   7. Simplified 50.2%

      \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

   if -6.4999999999999996e-247 < t < -1.54999999999999992e-302

   1. Initial program 87.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 87.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 87.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 87.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 87.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 87.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 87.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 87.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 87.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 81.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 81.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 81.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 81.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 81.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 81.8%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 81.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 81.8%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 81.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 82.0%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if -1.54999999999999992e-302 < t < 5.4999999999999998e-242

   1. Initial program 85.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 85.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 85.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 85.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 85.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 85.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. *-commutative 85.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. *-commutative 85.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. distribute-rgt-neg-in 85.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      9. sub-neg 85.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      10. +-commutative 85.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(\left(-i \cdot a\right) + c \cdot z\right)}\right)\right)\right) \]

      11. distribute-neg-in 85.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)\right)}\right)\right) \]

      12. unsub-neg 85.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) - c \cdot z\right)}\right)\right) \]

      13. remove-double-neg 85.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right)\right)\right) \]

      14. *-commutative 85.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{a \cdot i} - c \cdot z\right)\right)\right) \]

      15. *-commutative 85.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right)\right)\right) \]

   3. Simplified 85.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around inf 78.1%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]

   5. Taylor expanded in z around 0 55.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \cdot y \]
   6. Step-by-step derivation

      1. neg-mul-1 55.1%

         \[\leadsto \color{blue}{\left(-i \cdot j\right)} \cdot y \]

      2. distribute-rgt-neg-in 55.1%

         \[\leadsto \color{blue}{\left(i \cdot \left(-j\right)\right)} \cdot y \]

   7. Simplified 55.1%

      \[\leadsto \color{blue}{\left(i \cdot \left(-j\right)\right)} \cdot y \]

   if 5.4999999999999998e-242 < t < 9.2000000000000002e122

   1. Initial program 79.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 79.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 79.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 79.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 79.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 79.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 79.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 79.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 49.8%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2100000000000:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-247}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-302}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-242}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{+122}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 6: 49.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -5400000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.06 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-175}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+122}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -5400000000000.0)
     t_2
     (if (<= t -1.06e-89)
       t_1
       (if (<= t -3.9e-175)
         (* x (* y z))
         (if (<= t 1.25e-82)
           t_1
           (if (<= t 1.4e+122) (* c (- (* t j) (* z b))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -5400000000000.0) {
		tmp = t_2;
	} else if (t <= -1.06e-89) {
		tmp = t_1;
	} else if (t <= -3.9e-175) {
		tmp = x * (y * z);
	} else if (t <= 1.25e-82) {
		tmp = t_1;
	} else if (t <= 1.4e+122) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-5400000000000.0d0)) then
        tmp = t_2
    else if (t <= (-1.06d-89)) then
        tmp = t_1
    else if (t <= (-3.9d-175)) then
        tmp = x * (y * z)
    else if (t <= 1.25d-82) then
        tmp = t_1
    else if (t <= 1.4d+122) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -5400000000000.0) {
		tmp = t_2;
	} else if (t <= -1.06e-89) {
		tmp = t_1;
	} else if (t <= -3.9e-175) {
		tmp = x * (y * z);
	} else if (t <= 1.25e-82) {
		tmp = t_1;
	} else if (t <= 1.4e+122) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -5400000000000.0:
		tmp = t_2
	elif t <= -1.06e-89:
		tmp = t_1
	elif t <= -3.9e-175:
		tmp = x * (y * z)
	elif t <= 1.25e-82:
		tmp = t_1
	elif t <= 1.4e+122:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -5400000000000.0)
		tmp = t_2;
	elseif (t <= -1.06e-89)
		tmp = t_1;
	elseif (t <= -3.9e-175)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= 1.25e-82)
		tmp = t_1;
	elseif (t <= 1.4e+122)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -5400000000000.0)
		tmp = t_2;
	elseif (t <= -1.06e-89)
		tmp = t_1;
	elseif (t <= -3.9e-175)
		tmp = x * (y * z);
	elseif (t <= 1.25e-82)
		tmp = t_1;
	elseif (t <= 1.4e+122)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5400000000000.0], t$95$2, If[LessEqual[t, -1.06e-89], t$95$1, If[LessEqual[t, -3.9e-175], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-82], t$95$1, If[LessEqual[t, 1.4e+122], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.4e12 or 1.4e122 < t

   1. Initial program 62.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 62.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 62.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 62.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 62.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 62.5%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 62.5%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 62.5%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 62.5%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 62.5%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 62.5%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 62.5%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 62.5%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in t around inf 75.3%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 75.3%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 75.3%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 75.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   8. Simplified 75.3%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -5.4e12 < t < -1.0600000000000001e-89 or -3.89999999999999998e-175 < t < 1.25e-82

   1. Initial program 84.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 84.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 84.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 84.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 84.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 84.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 84.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 84.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 84.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 53.1%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   if -1.0600000000000001e-89 < t < -3.89999999999999998e-175

   1. Initial program 99.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 99.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 99.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 99.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 99.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 99.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 99.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 99.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 60.5%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 46.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 55.6%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

   7. Simplified 55.6%

      \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

   if 1.25e-82 < t < 1.4e122

   1. Initial program 73.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 73.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 73.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 73.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 73.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 73.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 73.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 73.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 73.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 57.8%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5400000000000:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.06 \cdot 10^{-89}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-175}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-82}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+122}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 7: 50.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-302}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -3.8e+104)
     t_2
     (if (<= b 3.2e-302)
       (* t (- (* c j) (* x a)))
       (if (<= b 3.2e+59)
         t_1
         (if (<= b 1.9e+79) (* y (* x z)) (if (<= b 1e+102) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.8e+104) {
		tmp = t_2;
	} else if (b <= 3.2e-302) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 3.2e+59) {
		tmp = t_1;
	} else if (b <= 1.9e+79) {
		tmp = y * (x * z);
	} else if (b <= 1e+102) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-3.8d+104)) then
        tmp = t_2
    else if (b <= 3.2d-302) then
        tmp = t * ((c * j) - (x * a))
    else if (b <= 3.2d+59) then
        tmp = t_1
    else if (b <= 1.9d+79) then
        tmp = y * (x * z)
    else if (b <= 1d+102) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.8e+104) {
		tmp = t_2;
	} else if (b <= 3.2e-302) {
		tmp = t * ((c * j) - (x * a));
	} else if (b <= 3.2e+59) {
		tmp = t_1;
	} else if (b <= 1.9e+79) {
		tmp = y * (x * z);
	} else if (b <= 1e+102) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -3.8e+104:
		tmp = t_2
	elif b <= 3.2e-302:
		tmp = t * ((c * j) - (x * a))
	elif b <= 3.2e+59:
		tmp = t_1
	elif b <= 1.9e+79:
		tmp = y * (x * z)
	elif b <= 1e+102:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.8e+104)
		tmp = t_2;
	elseif (b <= 3.2e-302)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (b <= 3.2e+59)
		tmp = t_1;
	elseif (b <= 1.9e+79)
		tmp = Float64(y * Float64(x * z));
	elseif (b <= 1e+102)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.8e+104)
		tmp = t_2;
	elseif (b <= 3.2e-302)
		tmp = t * ((c * j) - (x * a));
	elseif (b <= 3.2e+59)
		tmp = t_1;
	elseif (b <= 1.9e+79)
		tmp = y * (x * z);
	elseif (b <= 1e+102)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.8e+104], t$95$2, If[LessEqual[b, 3.2e-302], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.2e+59], t$95$1, If[LessEqual[b, 1.9e+79], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e+102], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.79999999999999969e104 or 9.99999999999999977e101 < b

   1. Initial program 76.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 76.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 76.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 76.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 76.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 76.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 76.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 76.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in b around inf 72.3%

      \[\leadsto \color{blue}{\left(a \cdot i - c \cdot z\right) \cdot b} \]

   if -3.79999999999999969e104 < b < 3.19999999999999978e-302

   1. Initial program 69.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 69.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 69.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 69.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 69.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 69.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 69.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 69.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 69.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 69.3%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 69.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 69.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 69.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 69.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 69.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 69.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 69.3%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in t around inf 60.3%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 60.3%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 60.3%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 60.3%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   8. Simplified 60.3%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if 3.19999999999999978e-302 < b < 3.19999999999999982e59 or 1.9000000000000001e79 < b < 9.99999999999999977e101

   1. Initial program 79.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 79.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 79.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 79.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 79.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 79.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 79.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 79.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around inf 55.8%

      \[\leadsto \color{blue}{\left(c \cdot t - i \cdot y\right) \cdot j} \]

   if 3.19999999999999982e59 < b < 1.9000000000000001e79

   1. Initial program 89.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 89.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 89.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 89.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 89.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 89.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. *-commutative 89.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. *-commutative 89.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. distribute-rgt-neg-in 89.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      9. sub-neg 89.7%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      10. +-commutative 89.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(\left(-i \cdot a\right) + c \cdot z\right)}\right)\right)\right) \]

      11. distribute-neg-in 89.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)\right)}\right)\right) \]

      12. unsub-neg 89.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) - c \cdot z\right)}\right)\right) \]

      13. remove-double-neg 89.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right)\right)\right) \]

      14. *-commutative 89.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{a \cdot i} - c \cdot z\right)\right)\right) \]

      15. *-commutative 89.7%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right)\right)\right) \]

   3. Simplified 89.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around inf 61.1%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]

   5. Taylor expanded in z around inf 61.1%

      \[\leadsto \color{blue}{\left(z \cdot x\right)} \cdot y \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+104}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-302}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+59}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+79}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq 10^{+102}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 8: 51.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-134}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -5e+41)
     t_2
     (if (<= z -3.2e-34)
       t_1
       (if (<= z 1.9e-134)
         (* j (- (* t c) (* y i)))
         (if (<= z 8.8e-82)
           (* a (- (* b i) (* x t)))
           (if (<= z 1.45e+68) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -5e+41) {
		tmp = t_2;
	} else if (z <= -3.2e-34) {
		tmp = t_1;
	} else if (z <= 1.9e-134) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 8.8e-82) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 1.45e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-5d+41)) then
        tmp = t_2
    else if (z <= (-3.2d-34)) then
        tmp = t_1
    else if (z <= 1.9d-134) then
        tmp = j * ((t * c) - (y * i))
    else if (z <= 8.8d-82) then
        tmp = a * ((b * i) - (x * t))
    else if (z <= 1.45d+68) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -5e+41) {
		tmp = t_2;
	} else if (z <= -3.2e-34) {
		tmp = t_1;
	} else if (z <= 1.9e-134) {
		tmp = j * ((t * c) - (y * i));
	} else if (z <= 8.8e-82) {
		tmp = a * ((b * i) - (x * t));
	} else if (z <= 1.45e+68) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -5e+41:
		tmp = t_2
	elif z <= -3.2e-34:
		tmp = t_1
	elif z <= 1.9e-134:
		tmp = j * ((t * c) - (y * i))
	elif z <= 8.8e-82:
		tmp = a * ((b * i) - (x * t))
	elif z <= 1.45e+68:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -5e+41)
		tmp = t_2;
	elseif (z <= -3.2e-34)
		tmp = t_1;
	elseif (z <= 1.9e-134)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (z <= 8.8e-82)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (z <= 1.45e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -5e+41)
		tmp = t_2;
	elseif (z <= -3.2e-34)
		tmp = t_1;
	elseif (z <= 1.9e-134)
		tmp = j * ((t * c) - (y * i));
	elseif (z <= 8.8e-82)
		tmp = a * ((b * i) - (x * t));
	elseif (z <= 1.45e+68)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+41], t$95$2, If[LessEqual[z, -3.2e-34], t$95$1, If[LessEqual[z, 1.9e-134], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e-82], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+68], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.00000000000000022e41 or 1.45000000000000006e68 < z

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 72.8%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   if -5.00000000000000022e41 < z < -3.20000000000000003e-34 or 8.79999999999999943e-82 < z < 1.45000000000000006e68

   1. Initial program 64.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 64.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 64.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 64.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 64.7%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 64.7%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 64.7%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 64.7%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 64.7%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 64.7%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 64.7%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 64.7%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in t around inf 63.1%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 63.1%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 63.1%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 63.1%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   8. Simplified 63.1%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   if -3.20000000000000003e-34 < z < 1.90000000000000001e-134

   1. Initial program 85.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 85.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 85.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 85.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 85.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 85.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 85.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 85.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 85.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around inf 60.4%

      \[\leadsto \color{blue}{\left(c \cdot t - i \cdot y\right) \cdot j} \]

   if 1.90000000000000001e-134 < z < 8.79999999999999943e-82

   1. Initial program 85.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 85.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 85.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 85.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 85.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 85.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 85.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 85.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 85.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 58.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 58.5%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 58.5%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 58.5%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 58.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 58.5%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 58.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 58.5%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 58.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+41}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-134}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-82}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 9: 60.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+38} \lor \neg \left(z \leq 10^{+68}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= z -2.8e+38) (not (<= z 1e+68)))
   (* z (- (* x y) (* b c)))
   (- (* b (* a i)) (* j (- (* y i) (* t c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -2.8e+38) || !(z <= 1e+68)) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = (b * (a * i)) - (j * ((y * i) - (t * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((z <= (-2.8d+38)) .or. (.not. (z <= 1d+68))) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = (b * (a * i)) - (j * ((y * i) - (t * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((z <= -2.8e+38) || !(z <= 1e+68)) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = (b * (a * i)) - (j * ((y * i) - (t * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (z <= -2.8e+38) or not (z <= 1e+68):
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = (b * (a * i)) - (j * ((y * i) - (t * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((z <= -2.8e+38) || !(z <= 1e+68))
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = Float64(Float64(b * Float64(a * i)) - Float64(j * Float64(Float64(y * i) - Float64(t * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((z <= -2.8e+38) || ~((z <= 1e+68)))
		tmp = z * ((x * y) - (b * c));
	else
		tmp = (b * (a * i)) - (j * ((y * i) - (t * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[z, -2.8e+38], N[Not[LessEqual[z, 1e+68]], $MachinePrecision]], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8e38 or 9.99999999999999953e67 < z

   1. Initial program 71.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 72.2%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   if -2.8e38 < z < 9.99999999999999953e67

   1. Initial program 79.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 79.3%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 79.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 79.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 79.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 79.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 79.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 79.3%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in i around inf 62.1%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. associate-*r* 62.0%

         \[\leadsto \color{blue}{\left(a \cdot i\right) \cdot b} + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 62.0%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Simplified 62.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} + j \cdot \left(t \cdot c - y \cdot i\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+38} \lor \neg \left(z \leq 10^{+68}\right):\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \end{array} \]

Alternative 10: 41.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.4 \cdot 10^{-74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-248}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-98}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+42}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -4.4e-74)
     t_1
     (if (<= a 6.8e-248)
       (* z (* x y))
       (if (<= a 2.8e-98)
         (* b (* c (- z)))
         (if (<= a 2.7e+42) (* t (* c j)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4.4e-74) {
		tmp = t_1;
	} else if (a <= 6.8e-248) {
		tmp = z * (x * y);
	} else if (a <= 2.8e-98) {
		tmp = b * (c * -z);
	} else if (a <= 2.7e+42) {
		tmp = t * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (a <= (-4.4d-74)) then
        tmp = t_1
    else if (a <= 6.8d-248) then
        tmp = z * (x * y)
    else if (a <= 2.8d-98) then
        tmp = b * (c * -z)
    else if (a <= 2.7d+42) then
        tmp = t * (c * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4.4e-74) {
		tmp = t_1;
	} else if (a <= 6.8e-248) {
		tmp = z * (x * y);
	} else if (a <= 2.8e-98) {
		tmp = b * (c * -z);
	} else if (a <= 2.7e+42) {
		tmp = t * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -4.4e-74:
		tmp = t_1
	elif a <= 6.8e-248:
		tmp = z * (x * y)
	elif a <= 2.8e-98:
		tmp = b * (c * -z)
	elif a <= 2.7e+42:
		tmp = t * (c * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.4e-74)
		tmp = t_1;
	elseif (a <= 6.8e-248)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 2.8e-98)
		tmp = Float64(b * Float64(c * Float64(-z)));
	elseif (a <= 2.7e+42)
		tmp = Float64(t * Float64(c * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -4.4e-74)
		tmp = t_1;
	elseif (a <= 6.8e-248)
		tmp = z * (x * y);
	elseif (a <= 2.8e-98)
		tmp = b * (c * -z);
	elseif (a <= 2.7e+42)
		tmp = t * (c * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.4e-74], t$95$1, If[LessEqual[a, 6.8e-248], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-98], N[(b * N[(c * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e+42], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.40000000000000021e-74 or 2.7000000000000001e42 < a

   1. Initial program 67.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 67.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 67.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 67.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 67.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 67.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 67.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 67.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 67.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 53.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 53.6%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 53.6%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 53.6%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 53.6%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 53.6%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 53.6%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 53.6%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 53.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   if -4.40000000000000021e-74 < a < 6.7999999999999996e-248

   1. Initial program 91.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 91.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 91.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 91.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 91.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 91.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 91.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 91.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 91.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 51.8%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 40.7%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if 6.7999999999999996e-248 < a < 2.7999999999999999e-98

   1. Initial program 85.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 85.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 85.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 85.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 85.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 85.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 85.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 85.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 85.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 51.9%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around 0 37.0%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 37.0%

         \[\leadsto \color{blue}{-c \cdot \left(z \cdot b\right)} \]

      2. associate-*r* 42.6%

         \[\leadsto -\color{blue}{\left(c \cdot z\right) \cdot b} \]

      3. distribute-lft-neg-in 42.6%

         \[\leadsto \color{blue}{\left(-c \cdot z\right) \cdot b} \]

      4. *-commutative 42.6%

         \[\leadsto \left(-\color{blue}{z \cdot c}\right) \cdot b \]

   7. Simplified 42.6%

      \[\leadsto \color{blue}{\left(-z \cdot c\right) \cdot b} \]

   if 2.7999999999999999e-98 < a < 2.7000000000000001e42

   1. Initial program 75.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 75.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 75.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 75.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 75.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 75.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 75.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 75.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 75.0%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 75.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 75.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 75.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 75.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 75.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 75.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 75.0%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in t around inf 56.6%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 56.6%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 56.6%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 56.6%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   8. Simplified 56.6%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   9. Taylor expanded in c around inf 51.4%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.4 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-248}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-98}:\\ \;\;\;\;b \cdot \left(c \cdot \left(-z\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+42}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 11: 29.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-249}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-301}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-243}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+122}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4.2e+80)
   (* t (* c j))
   (if (<= t -3.6e-249)
     (* x (* y z))
     (if (<= t -1.45e-301)
       (* i (* a b))
       (if (<= t 1.25e-243)
         (* i (* y (- j)))
         (if (<= t 4.9e+122) (* c (* b (- z))) (* c (* t j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4.2e+80) {
		tmp = t * (c * j);
	} else if (t <= -3.6e-249) {
		tmp = x * (y * z);
	} else if (t <= -1.45e-301) {
		tmp = i * (a * b);
	} else if (t <= 1.25e-243) {
		tmp = i * (y * -j);
	} else if (t <= 4.9e+122) {
		tmp = c * (b * -z);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-4.2d+80)) then
        tmp = t * (c * j)
    else if (t <= (-3.6d-249)) then
        tmp = x * (y * z)
    else if (t <= (-1.45d-301)) then
        tmp = i * (a * b)
    else if (t <= 1.25d-243) then
        tmp = i * (y * -j)
    else if (t <= 4.9d+122) then
        tmp = c * (b * -z)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4.2e+80) {
		tmp = t * (c * j);
	} else if (t <= -3.6e-249) {
		tmp = x * (y * z);
	} else if (t <= -1.45e-301) {
		tmp = i * (a * b);
	} else if (t <= 1.25e-243) {
		tmp = i * (y * -j);
	} else if (t <= 4.9e+122) {
		tmp = c * (b * -z);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -4.2e+80:
		tmp = t * (c * j)
	elif t <= -3.6e-249:
		tmp = x * (y * z)
	elif t <= -1.45e-301:
		tmp = i * (a * b)
	elif t <= 1.25e-243:
		tmp = i * (y * -j)
	elif t <= 4.9e+122:
		tmp = c * (b * -z)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4.2e+80)
		tmp = Float64(t * Float64(c * j));
	elseif (t <= -3.6e-249)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= -1.45e-301)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 1.25e-243)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (t <= 4.9e+122)
		tmp = Float64(c * Float64(b * Float64(-z)));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -4.2e+80)
		tmp = t * (c * j);
	elseif (t <= -3.6e-249)
		tmp = x * (y * z);
	elseif (t <= -1.45e-301)
		tmp = i * (a * b);
	elseif (t <= 1.25e-243)
		tmp = i * (y * -j);
	elseif (t <= 4.9e+122)
		tmp = c * (b * -z);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4.2e+80], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.6e-249], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.45e-301], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-243], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.9e+122], N[(c * N[(b * (-z)), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -4.20000000000000003e80

   1. Initial program 66.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 66.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 66.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 66.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 66.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 66.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 66.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 66.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 66.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 66.3%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 66.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 66.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 66.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 66.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 66.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 66.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 66.3%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in t around inf 73.6%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 73.6%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 73.6%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 73.6%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   8. Simplified 73.6%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   9. Taylor expanded in c around inf 47.0%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]

   if -4.20000000000000003e80 < t < -3.59999999999999995e-249

   1. Initial program 86.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 86.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 86.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 86.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 86.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 86.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 86.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 86.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 86.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 58.6%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 34.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 38.0%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

   7. Simplified 38.0%

      \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

   if -3.59999999999999995e-249 < t < -1.44999999999999992e-301

   1. Initial program 87.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 87.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 87.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 87.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 87.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 87.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 87.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 87.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 87.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 81.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 81.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 81.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 81.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 81.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 81.8%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 81.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 81.8%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 81.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 82.0%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if -1.44999999999999992e-301 < t < 1.25e-243

   1. Initial program 85.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 85.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 85.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 85.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 85.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 85.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. *-commutative 85.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. *-commutative 85.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. distribute-rgt-neg-in 85.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      9. sub-neg 85.1%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      10. +-commutative 85.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(\left(-i \cdot a\right) + c \cdot z\right)}\right)\right)\right) \]

      11. distribute-neg-in 85.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)\right)}\right)\right) \]

      12. unsub-neg 85.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) - c \cdot z\right)}\right)\right) \]

      13. remove-double-neg 85.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right)\right)\right) \]

      14. *-commutative 85.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{a \cdot i} - c \cdot z\right)\right)\right) \]

      15. *-commutative 85.1%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right)\right)\right) \]

   3. Simplified 85.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around inf 78.1%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]

   5. Taylor expanded in z around 0 55.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(i \cdot j\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 55.1%

         \[\leadsto -1 \cdot \color{blue}{\left(\left(y \cdot i\right) \cdot j\right)} \]

      2. *-commutative 55.1%

         \[\leadsto -1 \cdot \left(\color{blue}{\left(i \cdot y\right)} \cdot j\right) \]

      3. associate-*r* 55.0%

         \[\leadsto -1 \cdot \color{blue}{\left(i \cdot \left(y \cdot j\right)\right)} \]

      4. associate-*r* 55.0%

         \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(y \cdot j\right)} \]

      5. neg-mul-1 55.0%

         \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(y \cdot j\right) \]

   7. Simplified 55.0%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(y \cdot j\right)} \]

   if 1.25e-243 < t < 4.8999999999999998e122

   1. Initial program 79.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 79.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 79.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 79.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 79.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 79.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 79.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 79.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 79.0%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 79.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 79.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 79.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 79.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 79.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 79.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 79.0%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in z around inf 72.2%

      \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) - \color{blue}{c \cdot \left(z \cdot b\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in b around inf 36.5%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 36.5%

         \[\leadsto \color{blue}{-c \cdot \left(z \cdot b\right)} \]

      2. *-commutative 36.5%

         \[\leadsto -c \cdot \color{blue}{\left(b \cdot z\right)} \]

   9. Simplified 36.5%

      \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

   if 4.8999999999999998e122 < t

   1. Initial program 57.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 57.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 57.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 57.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 57.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 57.0%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 57.0%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in t around inf 84.1%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 84.1%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 84.1%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 84.1%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   8. Simplified 84.1%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   9. Taylor expanded in c around inf 51.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-249}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-301}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-243}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+122}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 12: 29.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-243}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-300}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+122}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -6.8e+80)
   (* t (* c j))
   (if (<= t -4.7e-243)
     (* x (* y z))
     (if (<= t -1.15e-300)
       (* i (* a b))
       (if (<= t 9.2e-158)
         (* y (* i (- j)))
         (if (<= t 1.85e+122) (* c (* b (- z))) (* c (* t j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -6.8e+80) {
		tmp = t * (c * j);
	} else if (t <= -4.7e-243) {
		tmp = x * (y * z);
	} else if (t <= -1.15e-300) {
		tmp = i * (a * b);
	} else if (t <= 9.2e-158) {
		tmp = y * (i * -j);
	} else if (t <= 1.85e+122) {
		tmp = c * (b * -z);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-6.8d+80)) then
        tmp = t * (c * j)
    else if (t <= (-4.7d-243)) then
        tmp = x * (y * z)
    else if (t <= (-1.15d-300)) then
        tmp = i * (a * b)
    else if (t <= 9.2d-158) then
        tmp = y * (i * -j)
    else if (t <= 1.85d+122) then
        tmp = c * (b * -z)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -6.8e+80) {
		tmp = t * (c * j);
	} else if (t <= -4.7e-243) {
		tmp = x * (y * z);
	} else if (t <= -1.15e-300) {
		tmp = i * (a * b);
	} else if (t <= 9.2e-158) {
		tmp = y * (i * -j);
	} else if (t <= 1.85e+122) {
		tmp = c * (b * -z);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -6.8e+80:
		tmp = t * (c * j)
	elif t <= -4.7e-243:
		tmp = x * (y * z)
	elif t <= -1.15e-300:
		tmp = i * (a * b)
	elif t <= 9.2e-158:
		tmp = y * (i * -j)
	elif t <= 1.85e+122:
		tmp = c * (b * -z)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -6.8e+80)
		tmp = Float64(t * Float64(c * j));
	elseif (t <= -4.7e-243)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= -1.15e-300)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 9.2e-158)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (t <= 1.85e+122)
		tmp = Float64(c * Float64(b * Float64(-z)));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -6.8e+80)
		tmp = t * (c * j);
	elseif (t <= -4.7e-243)
		tmp = x * (y * z);
	elseif (t <= -1.15e-300)
		tmp = i * (a * b);
	elseif (t <= 9.2e-158)
		tmp = y * (i * -j);
	elseif (t <= 1.85e+122)
		tmp = c * (b * -z);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -6.8e+80], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.7e-243], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.15e-300], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-158], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e+122], N[(c * N[(b * (-z)), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -6.79999999999999984e80

   1. Initial program 66.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 66.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 66.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 66.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 66.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 66.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 66.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 66.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 66.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 66.3%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 66.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 66.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 66.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 66.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 66.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 66.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 66.3%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in t around inf 73.6%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 73.6%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 73.6%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 73.6%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   8. Simplified 73.6%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   9. Taylor expanded in c around inf 47.0%

      \[\leadsto t \cdot \color{blue}{\left(c \cdot j\right)} \]

   if -6.79999999999999984e80 < t < -4.7000000000000004e-243

   1. Initial program 86.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 86.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 86.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 86.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 86.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 86.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 86.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 86.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 86.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 58.6%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 34.3%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 38.0%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

   7. Simplified 38.0%

      \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

   if -4.7000000000000004e-243 < t < -1.15e-300

   1. Initial program 87.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 87.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 87.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 87.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 87.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 87.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 87.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 87.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 87.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 81.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 81.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 81.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 81.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 81.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 81.8%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 81.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 81.8%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 81.8%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 82.0%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if -1.15e-300 < t < 9.1999999999999995e-158

   1. Initial program 80.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 80.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 80.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 83.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. *-commutative 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. *-commutative 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. distribute-rgt-neg-in 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      9. sub-neg 83.4%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      10. +-commutative 83.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(\left(-i \cdot a\right) + c \cdot z\right)}\right)\right)\right) \]

      11. distribute-neg-in 83.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)\right)}\right)\right) \]

      12. unsub-neg 83.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) - c \cdot z\right)}\right)\right) \]

      13. remove-double-neg 83.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right)\right)\right) \]

      14. *-commutative 83.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{a \cdot i} - c \cdot z\right)\right)\right) \]

      15. *-commutative 83.4%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right)\right)\right) \]

   3. Simplified 83.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around inf 58.3%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]

   5. Taylor expanded in z around 0 41.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \cdot y \]
   6. Step-by-step derivation

      1. neg-mul-1 41.7%

         \[\leadsto \color{blue}{\left(-i \cdot j\right)} \cdot y \]

      2. distribute-rgt-neg-in 41.7%

         \[\leadsto \color{blue}{\left(i \cdot \left(-j\right)\right)} \cdot y \]

   7. Simplified 41.7%

      \[\leadsto \color{blue}{\left(i \cdot \left(-j\right)\right)} \cdot y \]

   if 9.1999999999999995e-158 < t < 1.8499999999999998e122

   1. Initial program 79.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 79.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 79.8%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 79.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 79.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 79.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 79.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 79.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 79.8%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 79.7%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 79.7%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 79.7%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in z around inf 69.6%

      \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) - \color{blue}{c \cdot \left(z \cdot b\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in b around inf 38.0%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 38.0%

         \[\leadsto \color{blue}{-c \cdot \left(z \cdot b\right)} \]

      2. *-commutative 38.0%

         \[\leadsto -c \cdot \color{blue}{\left(b \cdot z\right)} \]

   9. Simplified 38.0%

      \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

   if 1.8499999999999998e122 < t

   1. Initial program 57.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 57.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 57.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 57.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 57.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 57.0%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 57.0%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 57.0%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in t around inf 84.1%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 84.1%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 84.1%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 84.1%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   8. Simplified 84.1%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   9. Taylor expanded in c around inf 51.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-243}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-300}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{+122}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 13: 43.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+265}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+80}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+83}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -3.5e+265)
   (* t (* x (- a)))
   (if (<= x -2.1e+80)
     (* z (* x y))
     (if (<= x 6.2e+83) (* c (- (* t j) (* z b))) (* a (- (* b i) (* x t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -3.5e+265) {
		tmp = t * (x * -a);
	} else if (x <= -2.1e+80) {
		tmp = z * (x * y);
	} else if (x <= 6.2e+83) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (x <= (-3.5d+265)) then
        tmp = t * (x * -a)
    else if (x <= (-2.1d+80)) then
        tmp = z * (x * y)
    else if (x <= 6.2d+83) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = a * ((b * i) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -3.5e+265) {
		tmp = t * (x * -a);
	} else if (x <= -2.1e+80) {
		tmp = z * (x * y);
	} else if (x <= 6.2e+83) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if x <= -3.5e+265:
		tmp = t * (x * -a)
	elif x <= -2.1e+80:
		tmp = z * (x * y)
	elif x <= 6.2e+83:
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -3.5e+265)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (x <= -2.1e+80)
		tmp = Float64(z * Float64(x * y));
	elseif (x <= 6.2e+83)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (x <= -3.5e+265)
		tmp = t * (x * -a);
	elseif (x <= -2.1e+80)
		tmp = z * (x * y);
	elseif (x <= 6.2e+83)
		tmp = c * ((t * j) - (z * b));
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -3.5e+265], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.1e+80], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+83], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.5e265

   1. Initial program 76.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 76.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 76.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 76.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 76.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 76.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 76.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 76.9%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 76.9%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 76.9%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 76.9%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 76.9%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 76.9%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 76.9%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 76.9%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in t around inf 62.2%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 62.2%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 62.2%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 62.2%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   8. Simplified 62.2%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   9. Taylor expanded in c around 0 62.3%

      \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 62.3%

          \[\leadsto t \cdot \left(-1 \cdot \color{blue}{\left(x \cdot a\right)}\right) \]

       2. associate-*r* 62.3%

          \[\leadsto t \cdot \color{blue}{\left(\left(-1 \cdot x\right) \cdot a\right)} \]

       3. neg-mul-1 62.3%

          \[\leadsto t \cdot \left(\color{blue}{\left(-x\right)} \cdot a\right) \]

   11. Simplified 62.3%

       \[\leadsto t \cdot \color{blue}{\left(\left(-x\right) \cdot a\right)} \]

   if -3.5e265 < x < -2.10000000000000001e80

   1. Initial program 64.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 64.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 64.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 64.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 64.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 64.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 64.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 64.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 64.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 68.1%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 57.6%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if -2.10000000000000001e80 < x < 6.19999999999999984e83

   1. Initial program 80.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 80.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 80.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 53.7%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if 6.19999999999999984e83 < x

   1. Initial program 69.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 69.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 69.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 69.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 69.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 69.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 69.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 69.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 69.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 51.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 51.9%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 51.9%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 51.9%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 51.9%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 51.9%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 51.9%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 51.9%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 51.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+265}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+80}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+83}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 14: 51.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.95 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-98}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+66}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -1.95e+80)
     t_1
     (if (<= x 4.9e-98)
       (* c (- (* t j) (* z b)))
       (if (<= x 2.7e+66) (* j (- (* t c) (* y i))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.95e+80) {
		tmp = t_1;
	} else if (x <= 4.9e-98) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 2.7e+66) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-1.95d+80)) then
        tmp = t_1
    else if (x <= 4.9d-98) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 2.7d+66) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.95e+80) {
		tmp = t_1;
	} else if (x <= 4.9e-98) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 2.7e+66) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.95e+80:
		tmp = t_1
	elif x <= 4.9e-98:
		tmp = c * ((t * j) - (z * b))
	elif x <= 2.7e+66:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.95e+80)
		tmp = t_1;
	elseif (x <= 4.9e-98)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 2.7e+66)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.95e+80)
		tmp = t_1;
	elseif (x <= 4.9e-98)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 2.7e+66)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.95e+80], t$95$1, If[LessEqual[x, 4.9e-98], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e+66], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.94999999999999999e80 or 2.7e66 < x

   1. Initial program 69.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 69.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 69.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 69.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 69.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 69.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 69.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 69.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 69.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in x around inf 71.7%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   if -1.94999999999999999e80 < x < 4.90000000000000014e-98

   1. Initial program 76.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 76.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 76.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 76.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 76.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 76.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 76.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 76.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in c around inf 56.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if 4.90000000000000014e-98 < x < 2.7e66

   1. Initial program 90.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 90.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 90.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 90.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 90.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 90.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 90.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 90.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 90.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in j around inf 65.0%

      \[\leadsto \color{blue}{\left(c \cdot t - i \cdot y\right) \cdot j} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{-98}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+66}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 15: 29.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-138}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+86}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))))
   (if (<= z -2.6e+38)
     t_1
     (if (<= z 1.35e-138)
       (* c (* t j))
       (if (<= z 1.05e+86) (* i (* a b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (z <= -2.6e+38) {
		tmp = t_1;
	} else if (z <= 1.35e-138) {
		tmp = c * (t * j);
	} else if (z <= 1.05e+86) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x * y)
    if (z <= (-2.6d+38)) then
        tmp = t_1
    else if (z <= 1.35d-138) then
        tmp = c * (t * j)
    else if (z <= 1.05d+86) then
        tmp = i * (a * b)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (z <= -2.6e+38) {
		tmp = t_1;
	} else if (z <= 1.35e-138) {
		tmp = c * (t * j);
	} else if (z <= 1.05e+86) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	tmp = 0
	if z <= -2.6e+38:
		tmp = t_1
	elif z <= 1.35e-138:
		tmp = c * (t * j)
	elif z <= 1.05e+86:
		tmp = i * (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (z <= -2.6e+38)
		tmp = t_1;
	elseif (z <= 1.35e-138)
		tmp = Float64(c * Float64(t * j));
	elseif (z <= 1.05e+86)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	tmp = 0.0;
	if (z <= -2.6e+38)
		tmp = t_1;
	elseif (z <= 1.35e-138)
		tmp = c * (t * j);
	elseif (z <= 1.05e+86)
		tmp = i * (a * b);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+38], t$95$1, If[LessEqual[z, 1.35e-138], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+86], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5999999999999999e38 or 1.0499999999999999e86 < z

   1. Initial program 72.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 72.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 72.2%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 72.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 72.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 72.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 72.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 72.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 72.2%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 72.9%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 43.9%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   if -2.5999999999999999e38 < z < 1.35000000000000014e-138

   1. Initial program 82.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 82.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 82.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 82.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 82.4%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 82.4%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in t around inf 48.5%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 48.5%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 48.5%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 48.5%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   8. Simplified 48.5%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   9. Taylor expanded in c around inf 34.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if 1.35000000000000014e-138 < z < 1.0499999999999999e86

   1. Initial program 68.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 68.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 68.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 68.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 50.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 50.6%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 50.6%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 50.6%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 50.6%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 50.6%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 50.6%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 50.6%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 50.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 35.1%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-138}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+86}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 16: 29.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-140}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+77}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.7e+38)
   (* x (* y z))
   (if (<= z 9e-140)
     (* c (* t j))
     (if (<= z 2.5e+77) (* i (* a b)) (* z (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.7e+38) {
		tmp = x * (y * z);
	} else if (z <= 9e-140) {
		tmp = c * (t * j);
	} else if (z <= 2.5e+77) {
		tmp = i * (a * b);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-2.7d+38)) then
        tmp = x * (y * z)
    else if (z <= 9d-140) then
        tmp = c * (t * j)
    else if (z <= 2.5d+77) then
        tmp = i * (a * b)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.7e+38) {
		tmp = x * (y * z);
	} else if (z <= 9e-140) {
		tmp = c * (t * j);
	} else if (z <= 2.5e+77) {
		tmp = i * (a * b);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.7e+38:
		tmp = x * (y * z)
	elif z <= 9e-140:
		tmp = c * (t * j)
	elif z <= 2.5e+77:
		tmp = i * (a * b)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.7e+38)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 9e-140)
		tmp = Float64(c * Float64(t * j));
	elseif (z <= 2.5e+77)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.7e+38)
		tmp = x * (y * z);
	elseif (z <= 9e-140)
		tmp = c * (t * j);
	elseif (z <= 2.5e+77)
		tmp = i * (a * b);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.7e+38], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-140], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+77], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.69999999999999996e38

   1. Initial program 73.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 73.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 73.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 73.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 71.3%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 37.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 39.6%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

   7. Simplified 39.6%

      \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

   if -2.69999999999999996e38 < z < 9.00000000000000008e-140

   1. Initial program 82.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 82.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 82.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 82.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 82.4%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 82.4%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in t around inf 48.5%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 48.5%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 48.5%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 48.5%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   8. Simplified 48.5%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   9. Taylor expanded in c around inf 34.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if 9.00000000000000008e-140 < z < 2.50000000000000002e77

   1. Initial program 68.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 68.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 68.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 68.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 50.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 50.6%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 50.6%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 50.6%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 50.6%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 50.6%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 50.6%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 50.6%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 50.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 35.1%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if 2.50000000000000002e77 < z

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 74.5%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 50.3%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-140}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+77}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 17: 29.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-139}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+82}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -3.1e+38)
   (* x (* y z))
   (if (<= z 5.2e-139)
     (* c (* t j))
     (if (<= z 1.25e+82) (* i (* a b)) (* y (* x z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3.1e+38) {
		tmp = x * (y * z);
	} else if (z <= 5.2e-139) {
		tmp = c * (t * j);
	} else if (z <= 1.25e+82) {
		tmp = i * (a * b);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-3.1d+38)) then
        tmp = x * (y * z)
    else if (z <= 5.2d-139) then
        tmp = c * (t * j)
    else if (z <= 1.25d+82) then
        tmp = i * (a * b)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3.1e+38) {
		tmp = x * (y * z);
	} else if (z <= 5.2e-139) {
		tmp = c * (t * j);
	} else if (z <= 1.25e+82) {
		tmp = i * (a * b);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -3.1e+38:
		tmp = x * (y * z)
	elif z <= 5.2e-139:
		tmp = c * (t * j)
	elif z <= 1.25e+82:
		tmp = i * (a * b)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -3.1e+38)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 5.2e-139)
		tmp = Float64(c * Float64(t * j));
	elseif (z <= 1.25e+82)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -3.1e+38)
		tmp = x * (y * z);
	elseif (z <= 5.2e-139)
		tmp = c * (t * j);
	elseif (z <= 1.25e+82)
		tmp = i * (a * b);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -3.1e+38], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-139], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+82], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.10000000000000018e38

   1. Initial program 73.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 73.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 73.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 73.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in z around inf 71.3%

      \[\leadsto \color{blue}{\left(y \cdot x - c \cdot b\right) \cdot z} \]

   5. Taylor expanded in y around inf 37.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 39.6%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

   7. Simplified 39.6%

      \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

   if -3.10000000000000018e38 < z < 5.1999999999999996e-139

   1. Initial program 82.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 82.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 82.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 82.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 82.4%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 82.4%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in t around inf 48.5%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 48.5%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 48.5%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 48.5%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   8. Simplified 48.5%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   9. Taylor expanded in c around inf 34.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if 5.1999999999999996e-139 < z < 1.25000000000000004e82

   1. Initial program 68.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 68.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 68.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 68.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 50.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 50.6%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 50.6%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 50.6%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 50.6%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 50.6%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 50.6%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 50.6%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 50.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 35.1%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if 1.25000000000000004e82 < z

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 71.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 73.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 73.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 73.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. *-commutative 73.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. *-commutative 73.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. distribute-rgt-neg-in 73.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      9. sub-neg 73.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      10. +-commutative 73.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(\left(-i \cdot a\right) + c \cdot z\right)}\right)\right)\right) \]

      11. distribute-neg-in 73.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)\right)}\right)\right) \]

      12. unsub-neg 73.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) - c \cdot z\right)}\right)\right) \]

      13. remove-double-neg 73.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right)\right)\right) \]

      14. *-commutative 73.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{a \cdot i} - c \cdot z\right)\right)\right) \]

      15. *-commutative 73.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right)\right)\right) \]

   3. Simplified 73.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around inf 58.4%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]

   5. Taylor expanded in z around inf 54.7%

      \[\leadsto \color{blue}{\left(z \cdot x\right)} \cdot y \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-139}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+82}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 18: 29.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+38}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-140}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+78}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -2.7e+38)
   (* c (* b (- z)))
   (if (<= z 6.8e-140)
     (* c (* t j))
     (if (<= z 5.2e+78) (* i (* a b)) (* y (* x z))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.7e+38) {
		tmp = c * (b * -z);
	} else if (z <= 6.8e-140) {
		tmp = c * (t * j);
	} else if (z <= 5.2e+78) {
		tmp = i * (a * b);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-2.7d+38)) then
        tmp = c * (b * -z)
    else if (z <= 6.8d-140) then
        tmp = c * (t * j)
    else if (z <= 5.2d+78) then
        tmp = i * (a * b)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -2.7e+38) {
		tmp = c * (b * -z);
	} else if (z <= 6.8e-140) {
		tmp = c * (t * j);
	} else if (z <= 5.2e+78) {
		tmp = i * (a * b);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -2.7e+38:
		tmp = c * (b * -z)
	elif z <= 6.8e-140:
		tmp = c * (t * j)
	elif z <= 5.2e+78:
		tmp = i * (a * b)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -2.7e+38)
		tmp = Float64(c * Float64(b * Float64(-z)));
	elseif (z <= 6.8e-140)
		tmp = Float64(c * Float64(t * j));
	elseif (z <= 5.2e+78)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -2.7e+38)
		tmp = c * (b * -z);
	elseif (z <= 6.8e-140)
		tmp = c * (t * j);
	elseif (z <= 5.2e+78)
		tmp = i * (a * b);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -2.7e+38], N[(c * N[(b * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e-140], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e+78], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.69999999999999996e38

   1. Initial program 73.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 73.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 73.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 73.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 73.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 73.3%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 73.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 73.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 73.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 73.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 73.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 73.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 73.3%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in z around inf 67.4%

      \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) - \color{blue}{c \cdot \left(z \cdot b\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   7. Taylor expanded in b around inf 49.3%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(z \cdot b\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 49.3%

         \[\leadsto \color{blue}{-c \cdot \left(z \cdot b\right)} \]

      2. *-commutative 49.3%

         \[\leadsto -c \cdot \color{blue}{\left(b \cdot z\right)} \]

   9. Simplified 49.3%

      \[\leadsto \color{blue}{-c \cdot \left(b \cdot z\right)} \]

   if -2.69999999999999996e38 < z < 6.80000000000000017e-140

   1. Initial program 82.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 82.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 82.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 82.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 82.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 82.4%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 82.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 82.4%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in t around inf 48.5%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 48.5%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 48.5%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 48.5%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   8. Simplified 48.5%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   9. Taylor expanded in c around inf 34.9%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if 6.80000000000000017e-140 < z < 5.2e78

   1. Initial program 68.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 68.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 68.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 68.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 68.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 50.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 50.6%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 50.6%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 50.6%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 50.6%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 50.6%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 50.6%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 50.6%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 50.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 35.1%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if 5.2e78 < z

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. sub-neg 71.1%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)\right)} + j \cdot \left(c \cdot t - i \cdot y\right) \]

      2. associate-+l+ 71.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) + \left(\left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      3. fma-def 73.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\right)} \]

      4. +-commutative 73.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + \left(-b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      5. fma-def 73.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \color{blue}{\mathsf{fma}\left(j, c \cdot t - i \cdot y, -b \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) \]

      6. *-commutative 73.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, c \cdot t - \color{blue}{y \cdot i}, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      7. *-commutative 73.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, \color{blue}{t \cdot c} - y \cdot i, -b \cdot \left(c \cdot z - i \cdot a\right)\right)\right) \]

      8. distribute-rgt-neg-in 73.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, \color{blue}{b \cdot \left(-\left(c \cdot z - i \cdot a\right)\right)}\right)\right) \]

      9. sub-neg 73.0%

         \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right)\right) \]

      10. +-commutative 73.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(-\color{blue}{\left(\left(-i \cdot a\right) + c \cdot z\right)}\right)\right)\right) \]

      11. distribute-neg-in 73.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) + \left(-c \cdot z\right)\right)}\right)\right) \]

      12. unsub-neg 73.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \color{blue}{\left(\left(-\left(-i \cdot a\right)\right) - c \cdot z\right)}\right)\right) \]

      13. remove-double-neg 73.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right)\right)\right) \]

      14. *-commutative 73.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(\color{blue}{a \cdot i} - c \cdot z\right)\right)\right) \]

      15. *-commutative 73.0%

          \[\leadsto \mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right)\right)\right) \]

   3. Simplified 73.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y \cdot z - t \cdot a, \mathsf{fma}\left(j, t \cdot c - y \cdot i, b \cdot \left(a \cdot i - z \cdot c\right)\right)\right)} \]

   4. Taylor expanded in y around inf 58.4%

      \[\leadsto \color{blue}{\left(z \cdot x + -1 \cdot \left(i \cdot j\right)\right) \cdot y} \]

   5. Taylor expanded in z around inf 54.7%

      \[\leadsto \color{blue}{\left(z \cdot x\right)} \cdot y \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+38}:\\ \;\;\;\;c \cdot \left(b \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-140}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+78}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 19: 30.2% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+104} \lor \neg \left(b \leq 3.4 \cdot 10^{+81}\right):\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -7.2e+104) (not (<= b 3.4e+81))) (* i (* a b)) (* c (* t j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -7.2e+104) || !(b <= 3.4e+81)) {
		tmp = i * (a * b);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-7.2d+104)) .or. (.not. (b <= 3.4d+81))) then
        tmp = i * (a * b)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -7.2e+104) || !(b <= 3.4e+81)) {
		tmp = i * (a * b);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -7.2e+104) or not (b <= 3.4e+81):
		tmp = i * (a * b)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -7.2e+104) || !(b <= 3.4e+81))
		tmp = Float64(i * Float64(a * b));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -7.2e+104) || ~((b <= 3.4e+81)))
		tmp = i * (a * b);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -7.2e+104], N[Not[LessEqual[b, 3.4e+81]], $MachinePrecision]], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.20000000000000001e104 or 3.40000000000000003e81 < b

   1. Initial program 76.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 76.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 76.9%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 76.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 76.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 76.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 76.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 76.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 76.9%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 45.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 45.9%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 45.9%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 45.9%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 45.9%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 45.9%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 45.9%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 45.9%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 45.9%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 40.4%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if -7.20000000000000001e104 < b < 3.40000000000000003e81

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 75.5%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 75.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 75.3%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 75.3%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 75.3%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in t around inf 47.1%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 47.1%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 47.1%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 47.1%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   8. Simplified 47.1%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   9. Taylor expanded in c around inf 30.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+104} \lor \neg \left(b \leq 3.4 \cdot 10^{+81}\right):\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 20: 29.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+145}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+81}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -4e+145)
   (* b (* a i))
   (if (<= b 4.5e+81) (* c (* t j)) (* a (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -4e+145) {
		tmp = b * (a * i);
	} else if (b <= 4.5e+81) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-4d+145)) then
        tmp = b * (a * i)
    else if (b <= 4.5d+81) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -4e+145) {
		tmp = b * (a * i);
	} else if (b <= 4.5e+81) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -4e+145:
		tmp = b * (a * i)
	elif b <= 4.5e+81:
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -4e+145)
		tmp = Float64(b * Float64(a * i));
	elseif (b <= 4.5e+81)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -4e+145)
		tmp = b * (a * i);
	elseif (b <= 4.5e+81)
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -4e+145], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e+81], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4e145

   1. Initial program 84.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 84.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 84.7%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 84.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 84.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 84.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 84.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 84.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 84.7%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 38.7%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 38.7%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 38.7%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 38.7%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 38.7%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 38.7%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 38.7%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 38.7%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 38.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 35.7%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 32.8%

         \[\leadsto \color{blue}{\left(i \cdot a\right) \cdot b} \]

      2. *-commutative 32.8%

         \[\leadsto \color{blue}{\left(a \cdot i\right)} \cdot b \]

      3. associate-*r* 27.3%

         \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   9. Simplified 27.3%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   10. Taylor expanded in a around 0 35.7%

       \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 32.8%

          \[\leadsto \color{blue}{\left(i \cdot a\right) \cdot b} \]

       2. *-commutative 32.8%

          \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} \]

   12. Simplified 32.8%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} \]

   if -4e145 < b < 4.50000000000000017e81

   1. Initial program 75.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 75.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 75.6%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 75.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 75.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 75.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 75.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 75.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 75.6%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 75.4%

         \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      2. *-commutative 75.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{\color{blue}{z \cdot y} - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      3. *-commutative 75.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - \color{blue}{a \cdot t}} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      4. *-commutative 75.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      5. *-commutative 75.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      6. *-commutative 75.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{\color{blue}{z \cdot y} - t \cdot a}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

      7. *-commutative 75.4%

         \[\leadsto \left(x \cdot \left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - \color{blue}{a \cdot t}}\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   5. Applied egg-rr 75.4%

      \[\leadsto \left(x \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot y - a \cdot t} \cdot \sqrt[3]{z \cdot y - a \cdot t}\right) \cdot \sqrt[3]{z \cdot y - a \cdot t}\right)} - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right) \]

   6. Taylor expanded in t around inf 45.9%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 45.9%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 45.9%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 45.9%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   8. Simplified 45.9%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   9. Taylor expanded in c around inf 30.2%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if 4.50000000000000017e81 < b

   1. Initial program 71.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Step-by-step derivation

      1. cancel-sign-sub 71.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      2. cancel-sign-sub-inv 71.4%

         \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

      3. *-commutative 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      4. *-commutative 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

      5. remove-double-neg 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

      6. *-commutative 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

      7. *-commutative 71.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

   4. Taylor expanded in a around inf 54.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 54.5%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 54.5%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 54.5%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 54.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 54.5%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 54.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

      7. *-commutative 54.5%

         \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

   6. Simplified 54.5%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

   7. Taylor expanded in b around inf 46.4%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 40.8%

         \[\leadsto \color{blue}{\left(i \cdot a\right) \cdot b} \]

      2. *-commutative 40.8%

         \[\leadsto \color{blue}{\left(a \cdot i\right)} \cdot b \]

      3. associate-*r* 42.7%

         \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   9. Simplified 42.7%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+145}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+81}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 21: 22.5% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.0%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Step-by-step derivation

   1. cancel-sign-sub 76.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

   2. cancel-sign-sub-inv 76.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

   3. *-commutative 76.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

   4. *-commutative 76.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

   5. remove-double-neg 76.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

   6. *-commutative 76.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

   7. *-commutative 76.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

3. Simplified 76.0%

   \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

4. Taylor expanded in a around inf 32.6%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
5. Step-by-step derivation

   1. associate-*r* 32.6%

      \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

   2. neg-mul-1 32.6%

      \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

   3. cancel-sign-sub 32.6%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

   4. +-commutative 32.6%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

   5. mul-1-neg 32.6%

      \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

   6. unsub-neg 32.6%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   7. *-commutative 32.6%

      \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

6. Simplified 32.6%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

7. Taylor expanded in b around inf 19.8%

   \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
8. Step-by-step derivation

   1. associate-*r* 18.8%

      \[\leadsto \color{blue}{\left(i \cdot a\right) \cdot b} \]

   2. *-commutative 18.8%

      \[\leadsto \color{blue}{\left(a \cdot i\right)} \cdot b \]

   3. associate-*r* 17.4%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

9. Simplified 17.4%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

10. Final simplification 17.4%

    \[\leadsto a \cdot \left(b \cdot i\right) \]

Alternative 22: 22.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ b \cdot \left(a \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* b (* a i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return b * (a * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = b * (a * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return b * (a * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return b * (a * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(b * Float64(a * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = b * (a * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.0%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Step-by-step derivation

   1. cancel-sign-sub 76.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) - \left(-j\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

   2. cancel-sign-sub-inv 76.0%

      \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right)} \]

   3. *-commutative 76.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - \color{blue}{a \cdot i}\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

   4. *-commutative 76.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right)\right) + \left(-\left(-j\right)\right) \cdot \left(c \cdot t - i \cdot y\right) \]

   5. remove-double-neg 76.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + \color{blue}{j} \cdot \left(c \cdot t - i \cdot y\right) \]

   6. *-commutative 76.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(\color{blue}{t \cdot c} - i \cdot y\right) \]

   7. *-commutative 76.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - \color{blue}{y \cdot i}\right) \]

3. Simplified 76.0%

   \[\leadsto \color{blue}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\right) + j \cdot \left(t \cdot c - y \cdot i\right)} \]

4. Taylor expanded in a around inf 32.6%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
5. Step-by-step derivation

   1. associate-*r* 32.6%

      \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

   2. neg-mul-1 32.6%

      \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

   3. cancel-sign-sub 32.6%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

   4. +-commutative 32.6%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

   5. mul-1-neg 32.6%

      \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

   6. unsub-neg 32.6%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   7. *-commutative 32.6%

      \[\leadsto a \cdot \left(\color{blue}{b \cdot i} - t \cdot x\right) \]

6. Simplified 32.6%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i - t \cdot x\right)} \]

7. Taylor expanded in b around inf 19.8%

   \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
8. Step-by-step derivation

   1. associate-*r* 18.8%

      \[\leadsto \color{blue}{\left(i \cdot a\right) \cdot b} \]

   2. *-commutative 18.8%

      \[\leadsto \color{blue}{\left(a \cdot i\right)} \cdot b \]

   3. associate-*r* 17.4%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

9. Simplified 17.4%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

10. Taylor expanded in a around 0 19.8%

    \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
11. Step-by-step derivation

    1. associate-*r* 18.8%

       \[\leadsto \color{blue}{\left(i \cdot a\right) \cdot b} \]

    2. *-commutative 18.8%

       \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} \]

12. Simplified 18.8%

    \[\leadsto \color{blue}{b \cdot \left(i \cdot a\right)} \]

13. Final simplification 18.8%

    \[\leadsto b \cdot \left(a \cdot i\right) \]

Developer target: 68.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2023195 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))