Data.Colour.Matrix:determinant from colour-2.3.3, A

Percentage Accurate: 72.8% → 79.5%

Time: 44.5s

Alternatives: 26

Speedup: 0.5×

• 58.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

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) - (t * i)))) + (j * ((c * a) - (y * 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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * 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 ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

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

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(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
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[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 72.8% accurate, 1.0× speedup

Math

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

FPCore

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

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) - (t * i)))) + (j * ((c * a) - (y * 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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * 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 ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

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

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(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
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[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 79.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - t \cdot a\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;t_2 + \left(x \cdot t_1 + t_3\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(x, t_1, t_3\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;t_2 - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y z) (* t a)))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= (+ t_2 (+ (* x t_1) t_3)) INFINITY)
     (+ (fma x t_1 t_3) t_2)
     (- t_2 (* b (* z 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 = (y * z) - (t * a);
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if ((t_2 + ((x * t_1) + t_3)) <= ((double) INFINITY)) {
		tmp = fma(x, t_1, t_3) + t_2;
	} else {
		tmp = t_2 - (b * (z * c));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * z) - Float64(t * a))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (Float64(t_2 + Float64(Float64(x * t_1) + t_3)) <= Inf)
		tmp = Float64(fma(x, t_1, t_3) + t_2);
	else
		tmp = Float64(t_2 - Float64(b * Float64(z * c)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 + N[(N[(x * t$95$1), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(x * t$95$1 + t$95$3), $MachinePrecision] + t$95$2), $MachinePrecision], N[(t$95$2 - N[(b * N[(z * c), $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 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 90.2%

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

      1. fma-neg 90.2%

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

      2. distribute-lft-neg-out 90.2%

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

      3. *-commutative 90.2%

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

      4. *-commutative 90.2%

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

      5. sub-neg 90.2%

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

      6. sub-neg 90.2%

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

      7. *-commutative 90.2%

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

   3. Simplified 90.2%

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

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

   1. Initial program 0.0%

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

      1. fma-neg 10.0%

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

      2. distribute-lft-neg-out 10.0%

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

      3. *-commutative 10.0%

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

      4. *-commutative 10.0%

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

      5. sub-neg 10.0%

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

      6. sub-neg 10.0%

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

      7. *-commutative 10.0%

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

   3. Simplified 10.0%

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

   4. Taylor expanded in c around inf 58.4%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 58.4%

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

      2. *-commutative 58.4%

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

      3. distribute-rgt-neg-out 58.4%

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

   6. Simplified 58.4%

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

4. Final simplification 84.0%

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

Alternative 2: 79.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (+ t_1 (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c)))))))
   (if (<= t_2 INFINITY) t_2 (- t_1 (* b (* z 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 = j * ((a * c) - (y * i));
	double t_2 = t_1 + ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c))));
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = t_1 - (b * (z * c));
	}
	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 = j * ((a * c) - (y * i));
	double t_2 = t_1 + ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c))));
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = t_1 - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t_1 + ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c))))
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = t_1 - (b * (z * c))
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t_1 + ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c))));
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = t_1 - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(t$95$1 - N[(b * N[(z * c), $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 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 90.2%

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

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

   1. Initial program 0.0%

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

      1. fma-neg 10.0%

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

      2. distribute-lft-neg-out 10.0%

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

      3. *-commutative 10.0%

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

      4. *-commutative 10.0%

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

      5. sub-neg 10.0%

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

      6. sub-neg 10.0%

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

      7. *-commutative 10.0%

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

   3. Simplified 10.0%

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

   4. Taylor expanded in c around inf 58.4%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 58.4%

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

      2. *-commutative 58.4%

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

      3. distribute-rgt-neg-out 58.4%

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

   6. Simplified 58.4%

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

4. Final simplification 84.0%

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

Alternative 3: 68.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{x}{\frac{1}{y \cdot z - t \cdot a}} + b \cdot \left(t \cdot i - z \cdot c\right)\right) + a \cdot \left(c \cdot j\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;i \leq -1.4 \cdot 10^{+166}:\\ \;\;\;\;t_2 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{-5}:\\ \;\;\;\;t_2 + t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;i \leq -5.6 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-166}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (/ x (/ 1.0 (- (* y z) (* t a)))) (* b (- (* t i) (* z c))))
          (* a (* c j))))
        (t_2 (* j (- (* a c) (* y i)))))
   (if (<= i -1.4e+166)
     (- t_2 (* b (* z c)))
     (if (<= i -3.5e-5)
       (+ t_2 (* t (- (* b i) (* x a))))
       (if (<= i -5.6e-143)
         t_1
         (if (<= i -1.1e-166)
           (+ (- (* z (- (* x y) (* b c))) (* a (* x t))) (* b (* t i)))
           (if (<= i 1.5e+153) t_1 (* i (- (* t b) (* y j))))))))))

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 / (1.0 / ((y * z) - (t * a)))) + (b * ((t * i) - (z * c)))) + (a * (c * j));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (i <= -1.4e+166) {
		tmp = t_2 - (b * (z * c));
	} else if (i <= -3.5e-5) {
		tmp = t_2 + (t * ((b * i) - (x * a)));
	} else if (i <= -5.6e-143) {
		tmp = t_1;
	} else if (i <= -1.1e-166) {
		tmp = ((z * ((x * y) - (b * c))) - (a * (x * t))) + (b * (t * i));
	} else if (i <= 1.5e+153) {
		tmp = t_1;
	} else {
		tmp = i * ((t * b) - (y * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x / (1.0d0 / ((y * z) - (t * a)))) + (b * ((t * i) - (z * c)))) + (a * (c * j))
    t_2 = j * ((a * c) - (y * i))
    if (i <= (-1.4d+166)) then
        tmp = t_2 - (b * (z * c))
    else if (i <= (-3.5d-5)) then
        tmp = t_2 + (t * ((b * i) - (x * a)))
    else if (i <= (-5.6d-143)) then
        tmp = t_1
    else if (i <= (-1.1d-166)) then
        tmp = ((z * ((x * y) - (b * c))) - (a * (x * t))) + (b * (t * i))
    else if (i <= 1.5d+153) then
        tmp = t_1
    else
        tmp = i * ((t * b) - (y * 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 t_1 = ((x / (1.0 / ((y * z) - (t * a)))) + (b * ((t * i) - (z * c)))) + (a * (c * j));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (i <= -1.4e+166) {
		tmp = t_2 - (b * (z * c));
	} else if (i <= -3.5e-5) {
		tmp = t_2 + (t * ((b * i) - (x * a)));
	} else if (i <= -5.6e-143) {
		tmp = t_1;
	} else if (i <= -1.1e-166) {
		tmp = ((z * ((x * y) - (b * c))) - (a * (x * t))) + (b * (t * i));
	} else if (i <= 1.5e+153) {
		tmp = t_1;
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x / (1.0 / ((y * z) - (t * a)))) + (b * ((t * i) - (z * c)))) + (a * (c * j))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if i <= -1.4e+166:
		tmp = t_2 - (b * (z * c))
	elif i <= -3.5e-5:
		tmp = t_2 + (t * ((b * i) - (x * a)))
	elif i <= -5.6e-143:
		tmp = t_1
	elif i <= -1.1e-166:
		tmp = ((z * ((x * y) - (b * c))) - (a * (x * t))) + (b * (t * i))
	elif i <= 1.5e+153:
		tmp = t_1
	else:
		tmp = i * ((t * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x / Float64(1.0 / Float64(Float64(y * z) - Float64(t * a)))) + Float64(b * Float64(Float64(t * i) - Float64(z * c)))) + Float64(a * Float64(c * j)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (i <= -1.4e+166)
		tmp = Float64(t_2 - Float64(b * Float64(z * c)));
	elseif (i <= -3.5e-5)
		tmp = Float64(t_2 + Float64(t * Float64(Float64(b * i) - Float64(x * a))));
	elseif (i <= -5.6e-143)
		tmp = t_1;
	elseif (i <= -1.1e-166)
		tmp = Float64(Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(a * Float64(x * t))) + Float64(b * Float64(t * i)));
	elseif (i <= 1.5e+153)
		tmp = t_1;
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x / (1.0 / ((y * z) - (t * a)))) + (b * ((t * i) - (z * c)))) + (a * (c * j));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (i <= -1.4e+166)
		tmp = t_2 - (b * (z * c));
	elseif (i <= -3.5e-5)
		tmp = t_2 + (t * ((b * i) - (x * a)));
	elseif (i <= -5.6e-143)
		tmp = t_1;
	elseif (i <= -1.1e-166)
		tmp = ((z * ((x * y) - (b * c))) - (a * (x * t))) + (b * (t * i));
	elseif (i <= 1.5e+153)
		tmp = t_1;
	else
		tmp = i * ((t * b) - (y * j));
	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[(1.0 / N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.4e+166], N[(t$95$2 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.5e-5], N[(t$95$2 + N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.6e-143], t$95$1, If[LessEqual[i, -1.1e-166], N[(N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.5e+153], t$95$1, N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.39999999999999998e166

   1. Initial program 44.1%

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

      1. fma-neg 47.7%

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

      2. distribute-lft-neg-out 47.7%

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

      3. *-commutative 47.7%

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

      4. *-commutative 47.7%

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

      5. sub-neg 47.7%

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

      6. sub-neg 47.7%

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

      7. *-commutative 47.7%

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

   3. Simplified 47.7%

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

   4. Taylor expanded in c around inf 75.2%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 75.2%

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

      2. *-commutative 75.2%

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

      3. distribute-rgt-neg-out 75.2%

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

   6. Simplified 75.2%

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

   if -1.39999999999999998e166 < i < -3.4999999999999997e-5

   1. Initial program 63.7%

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

      1. fma-neg 63.7%

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

      2. distribute-lft-neg-out 63.7%

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

      3. *-commutative 63.7%

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

      4. *-commutative 63.7%

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

      5. sub-neg 63.7%

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

      6. sub-neg 63.7%

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

      7. *-commutative 63.7%

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

   3. Simplified 63.7%

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

   4. Taylor expanded in t around inf 74.5%

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

   if -3.4999999999999997e-5 < i < -5.5999999999999997e-143 or -1.1000000000000001e-166 < i < 1.50000000000000009e153

   1. Initial program 85.1%

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

      1. flip-- 65.1%

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

      2. clear-num 65.1%

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

      3. un-div-inv 65.1%

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

      4. clear-num 65.1%

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

      5. flip-- 85.1%

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

      6. *-commutative 85.1%

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

   3. Applied egg-rr 85.1%

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

   4. Taylor expanded in c around inf 81.8%

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

      1. *-commutative 81.8%

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

   6. Simplified 81.8%

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

   if -5.5999999999999997e-143 < i < -1.1000000000000001e-166

   1. Initial program 45.5%

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

      1. flip-- 44.1%

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

      2. clear-num 44.1%

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

      3. un-div-inv 44.1%

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

      4. clear-num 44.1%

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

      5. flip-- 45.5%

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

      6. *-commutative 45.5%

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

   3. Applied egg-rr 45.5%

      \[\leadsto \left(\color{blue}{\frac{x}{\frac{1}{y \cdot z - a \cdot t}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-/r/ 45.5%

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

      2. /-rgt-identity 45.5%

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

      3. *-commutative 45.5%

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

      4. sub-neg 45.5%

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

      5. distribute-rgt-in 45.5%

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

      6. *-commutative 45.5%

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

      7. distribute-rgt-neg-in 45.5%

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

   5. Applied egg-rr 45.5%

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

   6. Taylor expanded in j around 0 64.4%

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

   7. Taylor expanded in z around 0 86.6%

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

   if 1.50000000000000009e153 < i

   1. Initial program 59.0%

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

   2. Taylor expanded in i around -inf 83.4%

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

      1. associate-*r* 83.4%

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

      2. neg-mul-1 83.4%

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

   4. Simplified 83.4%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(j \cdot y - b \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+166}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{-5}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;i \leq -5.6 \cdot 10^{-143}:\\ \;\;\;\;\left(\frac{x}{\frac{1}{y \cdot z - t \cdot a}} + b \cdot \left(t \cdot i - z \cdot c\right)\right) + a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-166}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 1.5 \cdot 10^{+153}:\\ \;\;\;\;\left(\frac{x}{\frac{1}{y \cdot z - t \cdot a}} + b \cdot \left(t \cdot i - z \cdot c\right)\right) + a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 4: 66.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot c - y \cdot i\\ t_2 := b \cdot \left(z \cdot c\right)\\ t_3 := j \cdot t_1\\ \mathbf{if}\;i \leq -3.6 \cdot 10^{+165}:\\ \;\;\;\;t_3 - t_2\\ \mathbf{elif}\;i \leq -1.4 \cdot 10^{-133}:\\ \;\;\;\;t_3 + t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;i \leq -4.6 \cdot 10^{-190}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+152}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - t_2\right) + \frac{j}{\frac{1}{t_1}}\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* a c) (* y i))) (t_2 (* b (* z c))) (t_3 (* j t_1)))
   (if (<= i -3.6e+165)
     (- t_3 t_2)
     (if (<= i -1.4e-133)
       (+ t_3 (* t (- (* b i) (* x a))))
       (if (<= i -4.6e-190)
         (+ (- (* z (- (* x y) (* b c))) (* a (* x t))) (* b (* t i)))
         (if (<= i 5.2e+152)
           (+ (- (* x (- (* y z) (* t a))) t_2) (/ j (/ 1.0 t_1)))
           (* i (- (* t b) (* y j)))))))))

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 * c) - (y * i);
	double t_2 = b * (z * c);
	double t_3 = j * t_1;
	double tmp;
	if (i <= -3.6e+165) {
		tmp = t_3 - t_2;
	} else if (i <= -1.4e-133) {
		tmp = t_3 + (t * ((b * i) - (x * a)));
	} else if (i <= -4.6e-190) {
		tmp = ((z * ((x * y) - (b * c))) - (a * (x * t))) + (b * (t * i));
	} else if (i <= 5.2e+152) {
		tmp = ((x * ((y * z) - (t * a))) - t_2) + (j / (1.0 / t_1));
	} else {
		tmp = i * ((t * b) - (y * 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a * c) - (y * i)
    t_2 = b * (z * c)
    t_3 = j * t_1
    if (i <= (-3.6d+165)) then
        tmp = t_3 - t_2
    else if (i <= (-1.4d-133)) then
        tmp = t_3 + (t * ((b * i) - (x * a)))
    else if (i <= (-4.6d-190)) then
        tmp = ((z * ((x * y) - (b * c))) - (a * (x * t))) + (b * (t * i))
    else if (i <= 5.2d+152) then
        tmp = ((x * ((y * z) - (t * a))) - t_2) + (j / (1.0d0 / t_1))
    else
        tmp = i * ((t * b) - (y * 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 t_1 = (a * c) - (y * i);
	double t_2 = b * (z * c);
	double t_3 = j * t_1;
	double tmp;
	if (i <= -3.6e+165) {
		tmp = t_3 - t_2;
	} else if (i <= -1.4e-133) {
		tmp = t_3 + (t * ((b * i) - (x * a)));
	} else if (i <= -4.6e-190) {
		tmp = ((z * ((x * y) - (b * c))) - (a * (x * t))) + (b * (t * i));
	} else if (i <= 5.2e+152) {
		tmp = ((x * ((y * z) - (t * a))) - t_2) + (j / (1.0 / t_1));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (a * c) - (y * i)
	t_2 = b * (z * c)
	t_3 = j * t_1
	tmp = 0
	if i <= -3.6e+165:
		tmp = t_3 - t_2
	elif i <= -1.4e-133:
		tmp = t_3 + (t * ((b * i) - (x * a)))
	elif i <= -4.6e-190:
		tmp = ((z * ((x * y) - (b * c))) - (a * (x * t))) + (b * (t * i))
	elif i <= 5.2e+152:
		tmp = ((x * ((y * z) - (t * a))) - t_2) + (j / (1.0 / t_1))
	else:
		tmp = i * ((t * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(a * c) - Float64(y * i))
	t_2 = Float64(b * Float64(z * c))
	t_3 = Float64(j * t_1)
	tmp = 0.0
	if (i <= -3.6e+165)
		tmp = Float64(t_3 - t_2);
	elseif (i <= -1.4e-133)
		tmp = Float64(t_3 + Float64(t * Float64(Float64(b * i) - Float64(x * a))));
	elseif (i <= -4.6e-190)
		tmp = Float64(Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - Float64(a * Float64(x * t))) + Float64(b * Float64(t * i)));
	elseif (i <= 5.2e+152)
		tmp = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - t_2) + Float64(j / Float64(1.0 / t_1)));
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (a * c) - (y * i);
	t_2 = b * (z * c);
	t_3 = j * t_1;
	tmp = 0.0;
	if (i <= -3.6e+165)
		tmp = t_3 - t_2;
	elseif (i <= -1.4e-133)
		tmp = t_3 + (t * ((b * i) - (x * a)));
	elseif (i <= -4.6e-190)
		tmp = ((z * ((x * y) - (b * c))) - (a * (x * t))) + (b * (t * i));
	elseif (i <= 5.2e+152)
		tmp = ((x * ((y * z) - (t * a))) - t_2) + (j / (1.0 / t_1));
	else
		tmp = i * ((t * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * t$95$1), $MachinePrecision]}, If[LessEqual[i, -3.6e+165], N[(t$95$3 - t$95$2), $MachinePrecision], If[LessEqual[i, -1.4e-133], N[(t$95$3 + N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -4.6e-190], N[(N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.2e+152], N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] + N[(j / N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -3.5999999999999998e165

   1. Initial program 44.1%

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

      1. fma-neg 47.7%

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

      2. distribute-lft-neg-out 47.7%

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

      3. *-commutative 47.7%

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

      4. *-commutative 47.7%

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

      5. sub-neg 47.7%

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

      6. sub-neg 47.7%

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

      7. *-commutative 47.7%

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

   3. Simplified 47.7%

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

   4. Taylor expanded in c around inf 75.2%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 75.2%

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

      2. *-commutative 75.2%

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

      3. distribute-rgt-neg-out 75.2%

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

   6. Simplified 75.2%

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

   if -3.5999999999999998e165 < i < -1.3999999999999999e-133

   1. Initial program 75.7%

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

      1. fma-neg 75.7%

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

      2. distribute-lft-neg-out 75.7%

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

      3. *-commutative 75.7%

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

      4. *-commutative 75.7%

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

      5. sub-neg 75.7%

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

      6. sub-neg 75.7%

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

      7. *-commutative 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in t around inf 77.0%

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

   if -1.3999999999999999e-133 < i < -4.59999999999999984e-190

   1. Initial program 69.1%

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

      1. flip-- 53.1%

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

      2. clear-num 53.1%

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

      3. un-div-inv 53.2%

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

      4. clear-num 53.0%

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

      5. flip-- 69.0%

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

      6. *-commutative 69.0%

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

   3. Applied egg-rr 69.0%

      \[\leadsto \left(\color{blue}{\frac{x}{\frac{1}{y \cdot z - a \cdot t}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-/r/ 69.1%

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

      2. /-rgt-identity 69.1%

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

      3. *-commutative 69.1%

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

      4. sub-neg 69.1%

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

      5. distribute-rgt-in 69.2%

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

      6. *-commutative 69.2%

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

      7. distribute-rgt-neg-in 69.2%

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

   5. Applied egg-rr 69.2%

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

   6. Taylor expanded in j around 0 78.0%

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

   7. Taylor expanded in z around 0 93.6%

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

   if -4.59999999999999984e-190 < i < 5.2000000000000001e152

   1. Initial program 82.6%

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

      1. *-commutative 82.6%

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

      2. flip-- 56.7%

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

      3. clear-num 56.7%

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

      4. un-div-inv 56.7%

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

      5. clear-num 56.7%

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

      6. flip-- 82.6%

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

      7. *-commutative 82.6%

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

   3. Applied egg-rr 82.6%

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

   4. Taylor expanded in c around inf 76.0%

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

   if 5.2000000000000001e152 < i

   1. Initial program 59.0%

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

   2. Taylor expanded in i around -inf 83.4%

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

      1. associate-*r* 83.4%

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

      2. neg-mul-1 83.4%

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

   4. Simplified 83.4%

      \[\leadsto \color{blue}{\left(-i\right) \cdot \left(j \cdot y - b \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.6 \cdot 10^{+165}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;i \leq -1.4 \cdot 10^{-133}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;i \leq -4.6 \cdot 10^{-190}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+152}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\right) + \frac{j}{\frac{1}{a \cdot c - y \cdot i}}\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 5: 66.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot t\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := t_2 + t \cdot \left(b \cdot i - x \cdot a\right)\\ t_4 := t_2 - b \cdot \left(z \cdot c\right)\\ \mathbf{if}\;j \leq -2 \cdot 10^{+225}:\\ \;\;\;\;t_2 + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq -4.3 \cdot 10^{+120}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -4.4 \cdot 10^{-52}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-83}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - \left(t_1 - x \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{+36}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - y \cdot \left(i \cdot j - x \cdot z\right)\right) - t_1\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{+195}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+241}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x t)))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (+ t_2 (* t (- (* b i) (* x a)))))
        (t_4 (- t_2 (* b (* z c)))))
   (if (<= j -2e+225)
     (+ t_2 (* b (* t i)))
     (if (<= j -4.3e+120)
       t_4
       (if (<= j -4.4e-52)
         t_3
         (if (<= j 5.8e-83)
           (- (* b (- (* t i) (* z c))) (- t_1 (* x (* y z))))
           (if (<= j 4.7e+36)
             (- (- (* a (* c j)) (* y (- (* i j) (* x z)))) t_1)
             (if (<= j 3.5e+195) t_4 (if (<= j 3.4e+241) t_3 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 = a * (x * t);
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t_2 + (t * ((b * i) - (x * a)));
	double t_4 = t_2 - (b * (z * c));
	double tmp;
	if (j <= -2e+225) {
		tmp = t_2 + (b * (t * i));
	} else if (j <= -4.3e+120) {
		tmp = t_4;
	} else if (j <= -4.4e-52) {
		tmp = t_3;
	} else if (j <= 5.8e-83) {
		tmp = (b * ((t * i) - (z * c))) - (t_1 - (x * (y * z)));
	} else if (j <= 4.7e+36) {
		tmp = ((a * (c * j)) - (y * ((i * j) - (x * z)))) - t_1;
	} else if (j <= 3.5e+195) {
		tmp = t_4;
	} else if (j <= 3.4e+241) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = a * (x * t)
    t_2 = j * ((a * c) - (y * i))
    t_3 = t_2 + (t * ((b * i) - (x * a)))
    t_4 = t_2 - (b * (z * c))
    if (j <= (-2d+225)) then
        tmp = t_2 + (b * (t * i))
    else if (j <= (-4.3d+120)) then
        tmp = t_4
    else if (j <= (-4.4d-52)) then
        tmp = t_3
    else if (j <= 5.8d-83) then
        tmp = (b * ((t * i) - (z * c))) - (t_1 - (x * (y * z)))
    else if (j <= 4.7d+36) then
        tmp = ((a * (c * j)) - (y * ((i * j) - (x * z)))) - t_1
    else if (j <= 3.5d+195) then
        tmp = t_4
    else if (j <= 3.4d+241) then
        tmp = t_3
    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 = a * (x * t);
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t_2 + (t * ((b * i) - (x * a)));
	double t_4 = t_2 - (b * (z * c));
	double tmp;
	if (j <= -2e+225) {
		tmp = t_2 + (b * (t * i));
	} else if (j <= -4.3e+120) {
		tmp = t_4;
	} else if (j <= -4.4e-52) {
		tmp = t_3;
	} else if (j <= 5.8e-83) {
		tmp = (b * ((t * i) - (z * c))) - (t_1 - (x * (y * z)));
	} else if (j <= 4.7e+36) {
		tmp = ((a * (c * j)) - (y * ((i * j) - (x * z)))) - t_1;
	} else if (j <= 3.5e+195) {
		tmp = t_4;
	} else if (j <= 3.4e+241) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * t)
	t_2 = j * ((a * c) - (y * i))
	t_3 = t_2 + (t * ((b * i) - (x * a)))
	t_4 = t_2 - (b * (z * c))
	tmp = 0
	if j <= -2e+225:
		tmp = t_2 + (b * (t * i))
	elif j <= -4.3e+120:
		tmp = t_4
	elif j <= -4.4e-52:
		tmp = t_3
	elif j <= 5.8e-83:
		tmp = (b * ((t * i) - (z * c))) - (t_1 - (x * (y * z)))
	elif j <= 4.7e+36:
		tmp = ((a * (c * j)) - (y * ((i * j) - (x * z)))) - t_1
	elif j <= 3.5e+195:
		tmp = t_4
	elif j <= 3.4e+241:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * t))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(t_2 + Float64(t * Float64(Float64(b * i) - Float64(x * a))))
	t_4 = Float64(t_2 - Float64(b * Float64(z * c)))
	tmp = 0.0
	if (j <= -2e+225)
		tmp = Float64(t_2 + Float64(b * Float64(t * i)));
	elseif (j <= -4.3e+120)
		tmp = t_4;
	elseif (j <= -4.4e-52)
		tmp = t_3;
	elseif (j <= 5.8e-83)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(t_1 - Float64(x * Float64(y * z))));
	elseif (j <= 4.7e+36)
		tmp = Float64(Float64(Float64(a * Float64(c * j)) - Float64(y * Float64(Float64(i * j) - Float64(x * z)))) - t_1);
	elseif (j <= 3.5e+195)
		tmp = t_4;
	elseif (j <= 3.4e+241)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (x * t);
	t_2 = j * ((a * c) - (y * i));
	t_3 = t_2 + (t * ((b * i) - (x * a)));
	t_4 = t_2 - (b * (z * c));
	tmp = 0.0;
	if (j <= -2e+225)
		tmp = t_2 + (b * (t * i));
	elseif (j <= -4.3e+120)
		tmp = t_4;
	elseif (j <= -4.4e-52)
		tmp = t_3;
	elseif (j <= 5.8e-83)
		tmp = (b * ((t * i) - (z * c))) - (t_1 - (x * (y * z)));
	elseif (j <= 4.7e+36)
		tmp = ((a * (c * j)) - (y * ((i * j) - (x * z)))) - t_1;
	elseif (j <= 3.5e+195)
		tmp = t_4;
	elseif (j <= 3.4e+241)
		tmp = t_3;
	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[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2e+225], N[(t$95$2 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.3e+120], t$95$4, If[LessEqual[j, -4.4e-52], t$95$3, If[LessEqual[j, 5.8e-83], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 - N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.7e+36], N[(N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[j, 3.5e+195], t$95$4, If[LessEqual[j, 3.4e+241], t$95$3, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.99999999999999986e225

   1. Initial program 76.1%

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

      1. fma-neg 76.1%

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

      2. distribute-lft-neg-out 76.1%

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

      3. *-commutative 76.1%

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

      4. *-commutative 76.1%

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

      5. sub-neg 76.1%

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

      6. sub-neg 76.1%

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

      7. *-commutative 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in i around inf 90.8%

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

   if -1.99999999999999986e225 < j < -4.3000000000000002e120 or 4.69999999999999989e36 < j < 3.5000000000000002e195

   1. Initial program 72.9%

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

      1. fma-neg 74.6%

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

      2. distribute-lft-neg-out 74.6%

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

      3. *-commutative 74.6%

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

      4. *-commutative 74.6%

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

      5. sub-neg 74.6%

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

      6. sub-neg 74.6%

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

      7. *-commutative 74.6%

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

   3. Simplified 74.6%

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

   4. Taylor expanded in c around inf 81.0%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 81.0%

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

      2. *-commutative 81.0%

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

      3. distribute-rgt-neg-out 81.0%

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

   6. Simplified 81.0%

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

   if -4.3000000000000002e120 < j < -4.40000000000000018e-52 or 3.5000000000000002e195 < j < 3.39999999999999994e241

   1. Initial program 74.3%

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

      1. fma-neg 82.8%

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

      2. distribute-lft-neg-out 82.8%

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

      3. *-commutative 82.8%

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

      4. *-commutative 82.8%

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

      5. sub-neg 82.8%

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

      6. sub-neg 82.8%

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

      7. *-commutative 82.8%

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

   3. Simplified 82.8%

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

   4. Taylor expanded in t around inf 85.7%

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

   if -4.40000000000000018e-52 < j < 5.7999999999999998e-83

   1. Initial program 73.9%

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

      1. flip-- 55.3%

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

      2. clear-num 55.2%

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

      3. un-div-inv 55.3%

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

      4. clear-num 55.3%

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

      5. flip-- 73.8%

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

      6. *-commutative 73.8%

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

   3. Applied egg-rr 73.8%

      \[\leadsto \left(\color{blue}{\frac{x}{\frac{1}{y \cdot z - a \cdot t}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-/r/ 73.9%

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

      2. /-rgt-identity 73.9%

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

      3. *-commutative 73.9%

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

      4. sub-neg 73.9%

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

      5. distribute-rgt-in 73.9%

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

      6. *-commutative 73.9%

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

      7. distribute-rgt-neg-in 73.9%

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

   5. Applied egg-rr 73.9%

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

   6. Taylor expanded in j around 0 75.9%

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

   if 5.7999999999999998e-83 < j < 4.69999999999999989e36

   1. Initial program 72.4%

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

   2. Taylor expanded in b around 0 60.1%

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

   3. Taylor expanded in y around 0 73.3%

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

   if 3.39999999999999994e241 < j

   1. Initial program 50.0%

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

      1. flip-- 50.0%

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

      2. clear-num 50.0%

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

      3. un-div-inv 50.0%

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

      4. clear-num 50.0%

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

      5. flip-- 50.0%

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

      6. *-commutative 50.0%

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

   3. Applied egg-rr 50.0%

      \[\leadsto \left(\color{blue}{\frac{x}{\frac{1}{y \cdot z - a \cdot t}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-/r/ 50.0%

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

      2. /-rgt-identity 50.0%

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

      3. *-commutative 50.0%

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

      4. sub-neg 50.0%

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

      5. distribute-rgt-in 50.0%

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

      6. *-commutative 50.0%

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

      7. distribute-rgt-neg-in 50.0%

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

   5. Applied egg-rr 50.0%

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

   6. Taylor expanded in j around inf 83.3%

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

      1. *-commutative 83.3%

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

   8. Simplified 83.3%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2 \cdot 10^{+225}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq -4.3 \cdot 10^{+120}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq -4.4 \cdot 10^{-52}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-83}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - \left(a \cdot \left(x \cdot t\right) - x \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{+36}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - y \cdot \left(i \cdot j - x \cdot z\right)\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{+195}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.4 \cdot 10^{+241}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 6: 66.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := t_3 + t \cdot \left(b \cdot i - x \cdot a\right)\\ t_5 := t_3 - b \cdot \left(z \cdot c\right)\\ \mathbf{if}\;j \leq -2.45 \cdot 10^{+218}:\\ \;\;\;\;t_3 + t_2\\ \mathbf{elif}\;j \leq -9 \cdot 10^{+119}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq -8.6 \cdot 10^{-50}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-82}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y - b \cdot c\right) - t_1\right) + t_2\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{+36}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - y \cdot \left(i \cdot j - x \cdot z\right)\right) - t_1\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+197}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{+241}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x t)))
        (t_2 (* b (* t i)))
        (t_3 (* j (- (* a c) (* y i))))
        (t_4 (+ t_3 (* t (- (* b i) (* x a)))))
        (t_5 (- t_3 (* b (* z c)))))
   (if (<= j -2.45e+218)
     (+ t_3 t_2)
     (if (<= j -9e+119)
       t_5
       (if (<= j -8.6e-50)
         t_4
         (if (<= j 4.8e-82)
           (+ (- (* z (- (* x y) (* b c))) t_1) t_2)
           (if (<= j 5.5e+36)
             (- (- (* a (* c j)) (* y (- (* i j) (* x z)))) t_1)
             (if (<= j 3.2e+197) t_5 (if (<= j 5.2e+241) t_4 t_3)))))))))

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 * (x * t);
	double t_2 = b * (t * i);
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = t_3 + (t * ((b * i) - (x * a)));
	double t_5 = t_3 - (b * (z * c));
	double tmp;
	if (j <= -2.45e+218) {
		tmp = t_3 + t_2;
	} else if (j <= -9e+119) {
		tmp = t_5;
	} else if (j <= -8.6e-50) {
		tmp = t_4;
	} else if (j <= 4.8e-82) {
		tmp = ((z * ((x * y) - (b * c))) - t_1) + t_2;
	} else if (j <= 5.5e+36) {
		tmp = ((a * (c * j)) - (y * ((i * j) - (x * z)))) - t_1;
	} else if (j <= 3.2e+197) {
		tmp = t_5;
	} else if (j <= 5.2e+241) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = a * (x * t)
    t_2 = b * (t * i)
    t_3 = j * ((a * c) - (y * i))
    t_4 = t_3 + (t * ((b * i) - (x * a)))
    t_5 = t_3 - (b * (z * c))
    if (j <= (-2.45d+218)) then
        tmp = t_3 + t_2
    else if (j <= (-9d+119)) then
        tmp = t_5
    else if (j <= (-8.6d-50)) then
        tmp = t_4
    else if (j <= 4.8d-82) then
        tmp = ((z * ((x * y) - (b * c))) - t_1) + t_2
    else if (j <= 5.5d+36) then
        tmp = ((a * (c * j)) - (y * ((i * j) - (x * z)))) - t_1
    else if (j <= 3.2d+197) then
        tmp = t_5
    else if (j <= 5.2d+241) then
        tmp = t_4
    else
        tmp = t_3
    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 * (x * t);
	double t_2 = b * (t * i);
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = t_3 + (t * ((b * i) - (x * a)));
	double t_5 = t_3 - (b * (z * c));
	double tmp;
	if (j <= -2.45e+218) {
		tmp = t_3 + t_2;
	} else if (j <= -9e+119) {
		tmp = t_5;
	} else if (j <= -8.6e-50) {
		tmp = t_4;
	} else if (j <= 4.8e-82) {
		tmp = ((z * ((x * y) - (b * c))) - t_1) + t_2;
	} else if (j <= 5.5e+36) {
		tmp = ((a * (c * j)) - (y * ((i * j) - (x * z)))) - t_1;
	} else if (j <= 3.2e+197) {
		tmp = t_5;
	} else if (j <= 5.2e+241) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * t)
	t_2 = b * (t * i)
	t_3 = j * ((a * c) - (y * i))
	t_4 = t_3 + (t * ((b * i) - (x * a)))
	t_5 = t_3 - (b * (z * c))
	tmp = 0
	if j <= -2.45e+218:
		tmp = t_3 + t_2
	elif j <= -9e+119:
		tmp = t_5
	elif j <= -8.6e-50:
		tmp = t_4
	elif j <= 4.8e-82:
		tmp = ((z * ((x * y) - (b * c))) - t_1) + t_2
	elif j <= 5.5e+36:
		tmp = ((a * (c * j)) - (y * ((i * j) - (x * z)))) - t_1
	elif j <= 3.2e+197:
		tmp = t_5
	elif j <= 5.2e+241:
		tmp = t_4
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * t))
	t_2 = Float64(b * Float64(t * i))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_4 = Float64(t_3 + Float64(t * Float64(Float64(b * i) - Float64(x * a))))
	t_5 = Float64(t_3 - Float64(b * Float64(z * c)))
	tmp = 0.0
	if (j <= -2.45e+218)
		tmp = Float64(t_3 + t_2);
	elseif (j <= -9e+119)
		tmp = t_5;
	elseif (j <= -8.6e-50)
		tmp = t_4;
	elseif (j <= 4.8e-82)
		tmp = Float64(Float64(Float64(z * Float64(Float64(x * y) - Float64(b * c))) - t_1) + t_2);
	elseif (j <= 5.5e+36)
		tmp = Float64(Float64(Float64(a * Float64(c * j)) - Float64(y * Float64(Float64(i * j) - Float64(x * z)))) - t_1);
	elseif (j <= 3.2e+197)
		tmp = t_5;
	elseif (j <= 5.2e+241)
		tmp = t_4;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (x * t);
	t_2 = b * (t * i);
	t_3 = j * ((a * c) - (y * i));
	t_4 = t_3 + (t * ((b * i) - (x * a)));
	t_5 = t_3 - (b * (z * c));
	tmp = 0.0;
	if (j <= -2.45e+218)
		tmp = t_3 + t_2;
	elseif (j <= -9e+119)
		tmp = t_5;
	elseif (j <= -8.6e-50)
		tmp = t_4;
	elseif (j <= 4.8e-82)
		tmp = ((z * ((x * y) - (b * c))) - t_1) + t_2;
	elseif (j <= 5.5e+36)
		tmp = ((a * (c * j)) - (y * ((i * j) - (x * z)))) - t_1;
	elseif (j <= 3.2e+197)
		tmp = t_5;
	elseif (j <= 5.2e+241)
		tmp = t_4;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.45e+218], N[(t$95$3 + t$95$2), $MachinePrecision], If[LessEqual[j, -9e+119], t$95$5, If[LessEqual[j, -8.6e-50], t$95$4, If[LessEqual[j, 4.8e-82], N[(N[(N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[j, 5.5e+36], N[(N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(i * j), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[j, 3.2e+197], t$95$5, If[LessEqual[j, 5.2e+241], t$95$4, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -2.4499999999999999e218

   1. Initial program 76.1%

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

      1. fma-neg 76.1%

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

      2. distribute-lft-neg-out 76.1%

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

      3. *-commutative 76.1%

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

      4. *-commutative 76.1%

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

      5. sub-neg 76.1%

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

      6. sub-neg 76.1%

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

      7. *-commutative 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in i around inf 90.8%

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

   if -2.4499999999999999e218 < j < -9.00000000000000039e119 or 5.5000000000000002e36 < j < 3.1999999999999998e197

   1. Initial program 72.9%

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

      1. fma-neg 74.6%

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

      2. distribute-lft-neg-out 74.6%

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

      3. *-commutative 74.6%

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

      4. *-commutative 74.6%

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

      5. sub-neg 74.6%

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

      6. sub-neg 74.6%

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

      7. *-commutative 74.6%

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

   3. Simplified 74.6%

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

   4. Taylor expanded in c around inf 81.0%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 81.0%

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

      2. *-commutative 81.0%

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

      3. distribute-rgt-neg-out 81.0%

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

   6. Simplified 81.0%

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

   if -9.00000000000000039e119 < j < -8.59999999999999995e-50 or 3.1999999999999998e197 < j < 5.20000000000000015e241

   1. Initial program 76.4%

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

      1. fma-neg 82.3%

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

      2. distribute-lft-neg-out 82.3%

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

      3. *-commutative 82.3%

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

      4. *-commutative 82.3%

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

      5. sub-neg 82.3%

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

      6. sub-neg 82.3%

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

      7. *-commutative 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in t around inf 88.2%

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

   if -8.59999999999999995e-50 < j < 4.80000000000000017e-82

   1. Initial program 72.4%

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

      1. flip-- 54.2%

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

      2. clear-num 54.2%

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

      3. un-div-inv 54.2%

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

      4. clear-num 54.2%

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

      5. flip-- 72.4%

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

      6. *-commutative 72.4%

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

   3. Applied egg-rr 72.4%

      \[\leadsto \left(\color{blue}{\frac{x}{\frac{1}{y \cdot z - a \cdot t}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-/r/ 72.4%

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

      2. /-rgt-identity 72.4%

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

      3. *-commutative 72.4%

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

      4. sub-neg 72.4%

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

      5. distribute-rgt-in 72.4%

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

      6. *-commutative 72.4%

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

      7. distribute-rgt-neg-in 72.4%

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

   5. Applied egg-rr 72.4%

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

   6. Taylor expanded in j around 0 74.4%

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

   7. Taylor expanded in z around 0 80.2%

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

   if 4.80000000000000017e-82 < j < 5.5000000000000002e36

   1. Initial program 75.1%

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

   2. Taylor expanded in b around 0 62.3%

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

   3. Taylor expanded in y around 0 76.0%

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

   if 5.20000000000000015e241 < j

   1. Initial program 50.0%

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

      1. flip-- 50.0%

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

      2. clear-num 50.0%

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

      3. un-div-inv 50.0%

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

      4. clear-num 50.0%

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

      5. flip-- 50.0%

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

      6. *-commutative 50.0%

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

   3. Applied egg-rr 50.0%

      \[\leadsto \left(\color{blue}{\frac{x}{\frac{1}{y \cdot z - a \cdot t}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-/r/ 50.0%

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

      2. /-rgt-identity 50.0%

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

      3. *-commutative 50.0%

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

      4. sub-neg 50.0%

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

      5. distribute-rgt-in 50.0%

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

      6. *-commutative 50.0%

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

      7. distribute-rgt-neg-in 50.0%

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

   5. Applied egg-rr 50.0%

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

   6. Taylor expanded in j around inf 83.3%

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

      1. *-commutative 83.3%

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

   8. Simplified 83.3%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.45 \cdot 10^{+218}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq -9 \cdot 10^{+119}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq -8.6 \cdot 10^{-50}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-82}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y - b \cdot c\right) - a \cdot \left(x \cdot t\right)\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{+36}:\\ \;\;\;\;\left(a \cdot \left(c \cdot j\right) - y \cdot \left(i \cdot j - x \cdot z\right)\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+197}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{+241}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 7: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right) + t_2\\ \mathbf{if}\;j \leq -1.3 \cdot 10^{+223}:\\ \;\;\;\;t_2 + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{+143}:\\ \;\;\;\;t_2 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{+37}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 3.25 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (- (* t i) (* z c))) (* a (* x t))))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (+ (* x (- (* y z) (* t a))) t_2)))
   (if (<= j -1.3e+223)
     (+ t_2 (* b (* t i)))
     (if (<= j -1.6e+143)
       (- t_2 (* b (* z c)))
       (if (<= j -4.5e-49)
         t_3
         (if (<= j 1.15e-68)
           t_1
           (if (<= j 6.8e+37) t_3 (if (<= j 3.25e+56) 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 = (b * ((t * i) - (z * c))) - (a * (x * t));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = (x * ((y * z) - (t * a))) + t_2;
	double tmp;
	if (j <= -1.3e+223) {
		tmp = t_2 + (b * (t * i));
	} else if (j <= -1.6e+143) {
		tmp = t_2 - (b * (z * c));
	} else if (j <= -4.5e-49) {
		tmp = t_3;
	} else if (j <= 1.15e-68) {
		tmp = t_1;
	} else if (j <= 6.8e+37) {
		tmp = t_3;
	} else if (j <= 3.25e+56) {
		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) :: t_3
    real(8) :: tmp
    t_1 = (b * ((t * i) - (z * c))) - (a * (x * t))
    t_2 = j * ((a * c) - (y * i))
    t_3 = (x * ((y * z) - (t * a))) + t_2
    if (j <= (-1.3d+223)) then
        tmp = t_2 + (b * (t * i))
    else if (j <= (-1.6d+143)) then
        tmp = t_2 - (b * (z * c))
    else if (j <= (-4.5d-49)) then
        tmp = t_3
    else if (j <= 1.15d-68) then
        tmp = t_1
    else if (j <= 6.8d+37) then
        tmp = t_3
    else if (j <= 3.25d+56) 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 = (b * ((t * i) - (z * c))) - (a * (x * t));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = (x * ((y * z) - (t * a))) + t_2;
	double tmp;
	if (j <= -1.3e+223) {
		tmp = t_2 + (b * (t * i));
	} else if (j <= -1.6e+143) {
		tmp = t_2 - (b * (z * c));
	} else if (j <= -4.5e-49) {
		tmp = t_3;
	} else if (j <= 1.15e-68) {
		tmp = t_1;
	} else if (j <= 6.8e+37) {
		tmp = t_3;
	} else if (j <= 3.25e+56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * ((t * i) - (z * c))) - (a * (x * t))
	t_2 = j * ((a * c) - (y * i))
	t_3 = (x * ((y * z) - (t * a))) + t_2
	tmp = 0
	if j <= -1.3e+223:
		tmp = t_2 + (b * (t * i))
	elif j <= -1.6e+143:
		tmp = t_2 - (b * (z * c))
	elif j <= -4.5e-49:
		tmp = t_3
	elif j <= 1.15e-68:
		tmp = t_1
	elif j <= 6.8e+37:
		tmp = t_3
	elif j <= 3.25e+56:
		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(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(a * Float64(x * t)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_2)
	tmp = 0.0
	if (j <= -1.3e+223)
		tmp = Float64(t_2 + Float64(b * Float64(t * i)));
	elseif (j <= -1.6e+143)
		tmp = Float64(t_2 - Float64(b * Float64(z * c)));
	elseif (j <= -4.5e-49)
		tmp = t_3;
	elseif (j <= 1.15e-68)
		tmp = t_1;
	elseif (j <= 6.8e+37)
		tmp = t_3;
	elseif (j <= 3.25e+56)
		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 = (b * ((t * i) - (z * c))) - (a * (x * t));
	t_2 = j * ((a * c) - (y * i));
	t_3 = (x * ((y * z) - (t * a))) + t_2;
	tmp = 0.0;
	if (j <= -1.3e+223)
		tmp = t_2 + (b * (t * i));
	elseif (j <= -1.6e+143)
		tmp = t_2 - (b * (z * c));
	elseif (j <= -4.5e-49)
		tmp = t_3;
	elseif (j <= 1.15e-68)
		tmp = t_1;
	elseif (j <= 6.8e+37)
		tmp = t_3;
	elseif (j <= 3.25e+56)
		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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[j, -1.3e+223], N[(t$95$2 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.6e+143], N[(t$95$2 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -4.5e-49], t$95$3, If[LessEqual[j, 1.15e-68], t$95$1, If[LessEqual[j, 6.8e+37], t$95$3, If[LessEqual[j, 3.25e+56], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.3000000000000001e223

   1. Initial program 76.1%

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

      1. fma-neg 76.1%

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

      2. distribute-lft-neg-out 76.1%

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

      3. *-commutative 76.1%

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

      4. *-commutative 76.1%

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

      5. sub-neg 76.1%

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

      6. sub-neg 76.1%

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

      7. *-commutative 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in i around inf 90.8%

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

   if -1.3000000000000001e223 < j < -1.60000000000000008e143

   1. Initial program 79.8%

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

      1. fma-neg 84.8%

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

      2. distribute-lft-neg-out 84.8%

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

      3. *-commutative 84.8%

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

      4. *-commutative 84.8%

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

      5. sub-neg 84.8%

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

      6. sub-neg 84.8%

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

      7. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in c around inf 85.1%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 85.1%

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

      2. *-commutative 85.1%

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

      3. distribute-rgt-neg-out 85.1%

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

   6. Simplified 85.1%

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

   if -1.60000000000000008e143 < j < -4.5000000000000002e-49 or 1.14999999999999998e-68 < j < 6.80000000000000011e37

   1. Initial program 80.3%

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

   2. Taylor expanded in b around 0 78.0%

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

   if -4.5000000000000002e-49 < j < 1.14999999999999998e-68 or 6.80000000000000011e37 < j < 3.25e56

   1. Initial program 72.5%

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

      1. flip-- 53.4%

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

      2. clear-num 53.4%

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

      3. un-div-inv 53.4%

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

      4. clear-num 53.4%

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

      5. flip-- 72.5%

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

      6. *-commutative 72.5%

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

   3. Applied egg-rr 72.5%

      \[\leadsto \left(\color{blue}{\frac{x}{\frac{1}{y \cdot z - a \cdot t}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-/r/ 72.5%

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

      2. /-rgt-identity 72.5%

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

      3. *-commutative 72.5%

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

      4. sub-neg 72.5%

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

      5. distribute-rgt-in 72.5%

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

      6. *-commutative 72.5%

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

      7. distribute-rgt-neg-in 72.5%

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

   5. Applied egg-rr 72.5%

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

   6. Taylor expanded in j around 0 73.1%

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

   7. Taylor expanded in y around 0 66.0%

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

      1. mul-1-neg 66.0%

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

      2. *-commutative 66.0%

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

      3. distribute-lft-neg-in 66.0%

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

   9. Simplified 66.0%

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

   if 3.25e56 < j

   1. Initial program 58.8%

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

      1. flip-- 56.6%

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

      2. clear-num 56.6%

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

      3. un-div-inv 56.6%

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

      4. clear-num 56.6%

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

      5. flip-- 58.8%

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

      6. *-commutative 58.8%

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

   3. Applied egg-rr 58.8%

      \[\leadsto \left(\color{blue}{\frac{x}{\frac{1}{y \cdot z - a \cdot t}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-/r/ 58.8%

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

      2. /-rgt-identity 58.8%

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

      3. *-commutative 58.8%

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

      4. sub-neg 58.8%

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

      5. distribute-rgt-in 58.8%

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

      6. *-commutative 58.8%

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

      7. distribute-rgt-neg-in 58.8%

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

   5. Applied egg-rr 58.8%

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

   6. Taylor expanded in j around inf 80.2%

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

      1. *-commutative 80.2%

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

   8. Simplified 80.2%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.3 \cdot 10^{+223}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq -1.6 \cdot 10^{+143}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{-68}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 3.25 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 8: 66.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := t_1 + t_2\\ t_4 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -2.5 \cdot 10^{+223}:\\ \;\;\;\;t_2 + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{+143}:\\ \;\;\;\;t_2 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{-68}:\\ \;\;\;\;t_1 + t_4\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+37}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{+54}:\\ \;\;\;\;t_4 - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (+ t_1 t_2))
        (t_4 (* b (- (* t i) (* z c)))))
   (if (<= j -2.5e+223)
     (+ t_2 (* b (* t i)))
     (if (<= j -1.75e+143)
       (- t_2 (* b (* z c)))
       (if (<= j -3.5e-50)
         t_3
         (if (<= j 2.1e-68)
           (+ t_1 t_4)
           (if (<= j 2e+37)
             t_3
             (if (<= j 5.5e+54) (- t_4 (* a (* x t))) 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));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t_1 + t_2;
	double t_4 = b * ((t * i) - (z * c));
	double tmp;
	if (j <= -2.5e+223) {
		tmp = t_2 + (b * (t * i));
	} else if (j <= -1.75e+143) {
		tmp = t_2 - (b * (z * c));
	} else if (j <= -3.5e-50) {
		tmp = t_3;
	} else if (j <= 2.1e-68) {
		tmp = t_1 + t_4;
	} else if (j <= 2e+37) {
		tmp = t_3;
	} else if (j <= 5.5e+54) {
		tmp = t_4 - (a * (x * t));
	} 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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = j * ((a * c) - (y * i))
    t_3 = t_1 + t_2
    t_4 = b * ((t * i) - (z * c))
    if (j <= (-2.5d+223)) then
        tmp = t_2 + (b * (t * i))
    else if (j <= (-1.75d+143)) then
        tmp = t_2 - (b * (z * c))
    else if (j <= (-3.5d-50)) then
        tmp = t_3
    else if (j <= 2.1d-68) then
        tmp = t_1 + t_4
    else if (j <= 2d+37) then
        tmp = t_3
    else if (j <= 5.5d+54) then
        tmp = t_4 - (a * (x * t))
    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));
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t_1 + t_2;
	double t_4 = b * ((t * i) - (z * c));
	double tmp;
	if (j <= -2.5e+223) {
		tmp = t_2 + (b * (t * i));
	} else if (j <= -1.75e+143) {
		tmp = t_2 - (b * (z * c));
	} else if (j <= -3.5e-50) {
		tmp = t_3;
	} else if (j <= 2.1e-68) {
		tmp = t_1 + t_4;
	} else if (j <= 2e+37) {
		tmp = t_3;
	} else if (j <= 5.5e+54) {
		tmp = t_4 - (a * (x * t));
	} 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))
	t_2 = j * ((a * c) - (y * i))
	t_3 = t_1 + t_2
	t_4 = b * ((t * i) - (z * c))
	tmp = 0
	if j <= -2.5e+223:
		tmp = t_2 + (b * (t * i))
	elif j <= -1.75e+143:
		tmp = t_2 - (b * (z * c))
	elif j <= -3.5e-50:
		tmp = t_3
	elif j <= 2.1e-68:
		tmp = t_1 + t_4
	elif j <= 2e+37:
		tmp = t_3
	elif j <= 5.5e+54:
		tmp = t_4 - (a * (x * t))
	else:
		tmp = t_2
	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)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(t_1 + t_2)
	t_4 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (j <= -2.5e+223)
		tmp = Float64(t_2 + Float64(b * Float64(t * i)));
	elseif (j <= -1.75e+143)
		tmp = Float64(t_2 - Float64(b * Float64(z * c)));
	elseif (j <= -3.5e-50)
		tmp = t_3;
	elseif (j <= 2.1e-68)
		tmp = Float64(t_1 + t_4);
	elseif (j <= 2e+37)
		tmp = t_3;
	elseif (j <= 5.5e+54)
		tmp = Float64(t_4 - Float64(a * Float64(x * t)));
	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));
	t_2 = j * ((a * c) - (y * i));
	t_3 = t_1 + t_2;
	t_4 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (j <= -2.5e+223)
		tmp = t_2 + (b * (t * i));
	elseif (j <= -1.75e+143)
		tmp = t_2 - (b * (z * c));
	elseif (j <= -3.5e-50)
		tmp = t_3;
	elseif (j <= 2.1e-68)
		tmp = t_1 + t_4;
	elseif (j <= 2e+37)
		tmp = t_3;
	elseif (j <= 5.5e+54)
		tmp = t_4 - (a * (x * t));
	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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.5e+223], N[(t$95$2 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.75e+143], N[(t$95$2 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.5e-50], t$95$3, If[LessEqual[j, 2.1e-68], N[(t$95$1 + t$95$4), $MachinePrecision], If[LessEqual[j, 2e+37], t$95$3, If[LessEqual[j, 5.5e+54], N[(t$95$4 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -2.49999999999999992e223

   1. Initial program 76.1%

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

      1. fma-neg 76.1%

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

      2. distribute-lft-neg-out 76.1%

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

      3. *-commutative 76.1%

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

      4. *-commutative 76.1%

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

      5. sub-neg 76.1%

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

      6. sub-neg 76.1%

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

      7. *-commutative 76.1%

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

   3. Simplified 76.1%

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

   4. Taylor expanded in i around inf 90.8%

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

   if -2.49999999999999992e223 < j < -1.75000000000000004e143

   1. Initial program 79.8%

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

      1. fma-neg 84.8%

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

      2. distribute-lft-neg-out 84.8%

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

      3. *-commutative 84.8%

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

      4. *-commutative 84.8%

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

      5. sub-neg 84.8%

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

      6. sub-neg 84.8%

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

      7. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in c around inf 85.1%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 85.1%

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

      2. *-commutative 85.1%

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

      3. distribute-rgt-neg-out 85.1%

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

   6. Simplified 85.1%

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

   if -1.75000000000000004e143 < j < -3.49999999999999997e-50 or 2.10000000000000008e-68 < j < 1.99999999999999991e37

   1. Initial program 78.9%

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

   2. Taylor expanded in b around 0 76.6%

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

   if -3.49999999999999997e-50 < j < 2.10000000000000008e-68

   1. Initial program 71.7%

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

   2. Taylor expanded in j around 0 72.6%

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

   if 1.99999999999999991e37 < j < 5.50000000000000026e54

   1. Initial program 100.0%

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

      1. flip-- 68.2%

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

      2. clear-num 68.2%

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

      3. un-div-inv 68.2%

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

      4. clear-num 68.2%

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

      5. flip-- 100.0%

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

      6. *-commutative 100.0%

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

   3. Applied egg-rr 100.0%

      \[\leadsto \left(\color{blue}{\frac{x}{\frac{1}{y \cdot z - a \cdot t}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-/r/ 100.0%

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

      2. /-rgt-identity 100.0%

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

      3. *-commutative 100.0%

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

      4. sub-neg 100.0%

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

      5. distribute-rgt-in 100.0%

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

      6. *-commutative 100.0%

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

      7. distribute-rgt-neg-in 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in j around 0 84.3%

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

   7. Taylor expanded in y around 0 84.3%

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

      1. mul-1-neg 84.3%

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

      2. *-commutative 84.3%

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

      3. distribute-lft-neg-in 84.3%

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

   9. Simplified 84.3%

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

   if 5.50000000000000026e54 < j

   1. Initial program 58.8%

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

      1. flip-- 56.6%

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

      2. clear-num 56.6%

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

      3. un-div-inv 56.6%

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

      4. clear-num 56.6%

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

      5. flip-- 58.8%

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

      6. *-commutative 58.8%

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

   3. Applied egg-rr 58.8%

      \[\leadsto \left(\color{blue}{\frac{x}{\frac{1}{y \cdot z - a \cdot t}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-/r/ 58.8%

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

      2. /-rgt-identity 58.8%

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

      3. *-commutative 58.8%

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

      4. sub-neg 58.8%

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

      5. distribute-rgt-in 58.8%

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

      6. *-commutative 58.8%

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

      7. distribute-rgt-neg-in 58.8%

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

   5. Applied egg-rr 58.8%

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

   6. Taylor expanded in j around inf 80.2%

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

      1. *-commutative 80.2%

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

   8. Simplified 80.2%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.5 \cdot 10^{+223}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{+143}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq -3.5 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{+54}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 9: 64.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+226}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+164}:\\ \;\;\;\;t_2 + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{+18}:\\ \;\;\;\;t_1 + t_3\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-123}:\\ \;\;\;\;t_1 + t_2\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+159}:\\ \;\;\;\;t_2 + t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -4.8e+226)
     t_3
     (if (<= b -2.5e+164)
       (+ t_2 (* b (* t i)))
       (if (<= b -1.55e+18)
         (+ t_1 t_3)
         (if (<= b -9.5e-123)
           (+ t_1 t_2)
           (if (<= b 3.2e+159) (+ t_2 (* t (- (* b i) (* x a)))) t_3)))))))

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 t_2 = j * ((a * c) - (y * i));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.8e+226) {
		tmp = t_3;
	} else if (b <= -2.5e+164) {
		tmp = t_2 + (b * (t * i));
	} else if (b <= -1.55e+18) {
		tmp = t_1 + t_3;
	} else if (b <= -9.5e-123) {
		tmp = t_1 + t_2;
	} else if (b <= 3.2e+159) {
		tmp = t_2 + (t * ((b * i) - (x * a)));
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = j * ((a * c) - (y * i))
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-4.8d+226)) then
        tmp = t_3
    else if (b <= (-2.5d+164)) then
        tmp = t_2 + (b * (t * i))
    else if (b <= (-1.55d+18)) then
        tmp = t_1 + t_3
    else if (b <= (-9.5d-123)) then
        tmp = t_1 + t_2
    else if (b <= 3.2d+159) then
        tmp = t_2 + (t * ((b * i) - (x * a)))
    else
        tmp = t_3
    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 t_2 = j * ((a * c) - (y * i));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.8e+226) {
		tmp = t_3;
	} else if (b <= -2.5e+164) {
		tmp = t_2 + (b * (t * i));
	} else if (b <= -1.55e+18) {
		tmp = t_1 + t_3;
	} else if (b <= -9.5e-123) {
		tmp = t_1 + t_2;
	} else if (b <= 3.2e+159) {
		tmp = t_2 + (t * ((b * i) - (x * a)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((a * c) - (y * i))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -4.8e+226:
		tmp = t_3
	elif b <= -2.5e+164:
		tmp = t_2 + (b * (t * i))
	elif b <= -1.55e+18:
		tmp = t_1 + t_3
	elif b <= -9.5e-123:
		tmp = t_1 + t_2
	elif b <= 3.2e+159:
		tmp = t_2 + (t * ((b * i) - (x * a)))
	else:
		tmp = t_3
	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)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.8e+226)
		tmp = t_3;
	elseif (b <= -2.5e+164)
		tmp = Float64(t_2 + Float64(b * Float64(t * i)));
	elseif (b <= -1.55e+18)
		tmp = Float64(t_1 + t_3);
	elseif (b <= -9.5e-123)
		tmp = Float64(t_1 + t_2);
	elseif (b <= 3.2e+159)
		tmp = Float64(t_2 + Float64(t * Float64(Float64(b * i) - Float64(x * a))));
	else
		tmp = t_3;
	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));
	t_2 = j * ((a * c) - (y * i));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.8e+226)
		tmp = t_3;
	elseif (b <= -2.5e+164)
		tmp = t_2 + (b * (t * i));
	elseif (b <= -1.55e+18)
		tmp = t_1 + t_3;
	elseif (b <= -9.5e-123)
		tmp = t_1 + t_2;
	elseif (b <= 3.2e+159)
		tmp = t_2 + (t * ((b * i) - (x * a)));
	else
		tmp = t_3;
	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]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.8e+226], t$95$3, If[LessEqual[b, -2.5e+164], N[(t$95$2 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.55e+18], N[(t$95$1 + t$95$3), $MachinePrecision], If[LessEqual[b, -9.5e-123], N[(t$95$1 + t$95$2), $MachinePrecision], If[LessEqual[b, 3.2e+159], N[(t$95$2 + N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.8e226 or 3.19999999999999985e159 < b

   1. Initial program 81.0%

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

   2. Taylor expanded in b around inf 79.4%

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

   if -4.8e226 < b < -2.49999999999999975e164

   1. Initial program 77.0%

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

      1. fma-neg 77.0%

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

      2. distribute-lft-neg-out 77.0%

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

      3. *-commutative 77.0%

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

      4. *-commutative 77.0%

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

      5. sub-neg 77.0%

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

      6. sub-neg 77.0%

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

      7. *-commutative 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in i around inf 97.1%

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

   if -2.49999999999999975e164 < b < -1.55e18

   1. Initial program 72.4%

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

   2. Taylor expanded in j around 0 69.2%

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

   if -1.55e18 < b < -9.5000000000000002e-123

   1. Initial program 70.8%

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

   2. Taylor expanded in b around 0 74.7%

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

   if -9.5000000000000002e-123 < b < 3.19999999999999985e159

   1. Initial program 69.1%

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

      1. fma-neg 71.4%

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

      2. distribute-lft-neg-out 71.4%

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

      3. *-commutative 71.4%

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

      4. *-commutative 71.4%

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

      5. sub-neg 71.4%

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

      6. sub-neg 71.4%

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

      7. *-commutative 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in t around inf 73.3%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+226}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+164}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+159}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 10: 64.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+226}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{+167}:\\ \;\;\;\;t_1 + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{+17}:\\ \;\;\;\;t_2 - \left(a \cdot \left(x \cdot t\right) - x \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t_1\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+163}:\\ \;\;\;\;t_1 + t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -1.25e+226)
     t_2
     (if (<= b -2.05e+167)
       (+ t_1 (* b (* t i)))
       (if (<= b -4.6e+17)
         (- t_2 (- (* a (* x t)) (* x (* y z))))
         (if (<= b -1.2e-121)
           (+ (* x (- (* y z) (* t a))) t_1)
           (if (<= b 1.05e+163) (+ t_1 (* t (- (* b i) (* x a)))) 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 * ((a * c) - (y * i));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.25e+226) {
		tmp = t_2;
	} else if (b <= -2.05e+167) {
		tmp = t_1 + (b * (t * i));
	} else if (b <= -4.6e+17) {
		tmp = t_2 - ((a * (x * t)) - (x * (y * z)));
	} else if (b <= -1.2e-121) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else if (b <= 1.05e+163) {
		tmp = t_1 + (t * ((b * i) - (x * a)));
	} 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 * ((a * c) - (y * i))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-1.25d+226)) then
        tmp = t_2
    else if (b <= (-2.05d+167)) then
        tmp = t_1 + (b * (t * i))
    else if (b <= (-4.6d+17)) then
        tmp = t_2 - ((a * (x * t)) - (x * (y * z)))
    else if (b <= (-1.2d-121)) then
        tmp = (x * ((y * z) - (t * a))) + t_1
    else if (b <= 1.05d+163) then
        tmp = t_1 + (t * ((b * i) - (x * a)))
    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 * ((a * c) - (y * i));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.25e+226) {
		tmp = t_2;
	} else if (b <= -2.05e+167) {
		tmp = t_1 + (b * (t * i));
	} else if (b <= -4.6e+17) {
		tmp = t_2 - ((a * (x * t)) - (x * (y * z)));
	} else if (b <= -1.2e-121) {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	} else if (b <= 1.05e+163) {
		tmp = t_1 + (t * ((b * i) - (x * a)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1.25e+226:
		tmp = t_2
	elif b <= -2.05e+167:
		tmp = t_1 + (b * (t * i))
	elif b <= -4.6e+17:
		tmp = t_2 - ((a * (x * t)) - (x * (y * z)))
	elif b <= -1.2e-121:
		tmp = (x * ((y * z) - (t * a))) + t_1
	elif b <= 1.05e+163:
		tmp = t_1 + (t * ((b * i) - (x * a)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.25e+226)
		tmp = t_2;
	elseif (b <= -2.05e+167)
		tmp = Float64(t_1 + Float64(b * Float64(t * i)));
	elseif (b <= -4.6e+17)
		tmp = Float64(t_2 - Float64(Float64(a * Float64(x * t)) - Float64(x * Float64(y * z))));
	elseif (b <= -1.2e-121)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	elseif (b <= 1.05e+163)
		tmp = Float64(t_1 + Float64(t * Float64(Float64(b * i) - Float64(x * a))));
	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 * ((a * c) - (y * i));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.25e+226)
		tmp = t_2;
	elseif (b <= -2.05e+167)
		tmp = t_1 + (b * (t * i));
	elseif (b <= -4.6e+17)
		tmp = t_2 - ((a * (x * t)) - (x * (y * z)));
	elseif (b <= -1.2e-121)
		tmp = (x * ((y * z) - (t * a))) + t_1;
	elseif (b <= 1.05e+163)
		tmp = t_1 + (t * ((b * i) - (x * a)));
	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[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e+226], t$95$2, If[LessEqual[b, -2.05e+167], N[(t$95$1 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.6e+17], N[(t$95$2 - N[(N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision] - N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.2e-121], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 1.05e+163], N[(t$95$1 + N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.2500000000000001e226 or 1.05e163 < b

   1. Initial program 81.0%

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

   2. Taylor expanded in b around inf 79.4%

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

   if -1.2500000000000001e226 < b < -2.05e167

   1. Initial program 77.0%

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

      1. fma-neg 77.0%

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

      2. distribute-lft-neg-out 77.0%

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

      3. *-commutative 77.0%

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

      4. *-commutative 77.0%

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

      5. sub-neg 77.0%

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

      6. sub-neg 77.0%

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

      7. *-commutative 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in i around inf 97.1%

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

   if -2.05e167 < b < -4.6e17

   1. Initial program 72.4%

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

      1. flip-- 47.9%

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

      2. clear-num 47.9%

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

      3. un-div-inv 47.9%

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

      4. clear-num 47.9%

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

      5. flip-- 72.5%

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

      6. *-commutative 72.5%

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

   3. Applied egg-rr 72.5%

      \[\leadsto \left(\color{blue}{\frac{x}{\frac{1}{y \cdot z - a \cdot t}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-/r/ 72.4%

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

      2. /-rgt-identity 72.4%

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

      3. *-commutative 72.4%

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

      4. sub-neg 72.4%

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

      5. distribute-rgt-in 72.4%

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

      6. *-commutative 72.4%

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

      7. distribute-rgt-neg-in 72.4%

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

   5. Applied egg-rr 72.4%

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

   6. Taylor expanded in j around 0 71.9%

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

   if -4.6e17 < b < -1.20000000000000002e-121

   1. Initial program 70.8%

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

   2. Taylor expanded in b around 0 74.7%

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

   if -1.20000000000000002e-121 < b < 1.05e163

   1. Initial program 69.1%

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

      1. fma-neg 71.4%

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

      2. distribute-lft-neg-out 71.4%

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

      3. *-commutative 71.4%

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

      4. *-commutative 71.4%

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

      5. sub-neg 71.4%

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

      6. sub-neg 71.4%

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

      7. *-commutative 71.4%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in t around inf 73.3%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+226}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.05 \cdot 10^{+167}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - \left(a \cdot \left(x \cdot t\right) - x \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-121}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{+163}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 11: 58.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+71}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+65} \lor \neg \left(t \leq 1.95 \cdot 10^{+108}\right) \land t \leq 7.7 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* j (- (* a c) (* y i))) (* b (* z c))))
        (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -1.15e+152)
     t_2
     (if (<= t -2e+91)
       t_1
       (if (<= t -7e+71)
         (- (* b (* t i)) (* a (* x t)))
         (if (or (<= t 7.5e+65) (and (not (<= t 1.95e+108)) (<= t 7.7e+174)))
           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 * ((a * c) - (y * i))) - (b * (z * c));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.15e+152) {
		tmp = t_2;
	} else if (t <= -2e+91) {
		tmp = t_1;
	} else if (t <= -7e+71) {
		tmp = (b * (t * i)) - (a * (x * t));
	} else if ((t <= 7.5e+65) || (!(t <= 1.95e+108) && (t <= 7.7e+174))) {
		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 * ((a * c) - (y * i))) - (b * (z * c))
    t_2 = t * ((b * i) - (x * a))
    if (t <= (-1.15d+152)) then
        tmp = t_2
    else if (t <= (-2d+91)) then
        tmp = t_1
    else if (t <= (-7d+71)) then
        tmp = (b * (t * i)) - (a * (x * t))
    else if ((t <= 7.5d+65) .or. (.not. (t <= 1.95d+108)) .and. (t <= 7.7d+174)) 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 * ((a * c) - (y * i))) - (b * (z * c));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.15e+152) {
		tmp = t_2;
	} else if (t <= -2e+91) {
		tmp = t_1;
	} else if (t <= -7e+71) {
		tmp = (b * (t * i)) - (a * (x * t));
	} else if ((t <= 7.5e+65) || (!(t <= 1.95e+108) && (t <= 7.7e+174))) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (y * i))) - (b * (z * c))
	t_2 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -1.15e+152:
		tmp = t_2
	elif t <= -2e+91:
		tmp = t_1
	elif t <= -7e+71:
		tmp = (b * (t * i)) - (a * (x * t))
	elif (t <= 7.5e+65) or (not (t <= 1.95e+108) and (t <= 7.7e+174)):
		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(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(b * Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.15e+152)
		tmp = t_2;
	elseif (t <= -2e+91)
		tmp = t_1;
	elseif (t <= -7e+71)
		tmp = Float64(Float64(b * Float64(t * i)) - Float64(a * Float64(x * t)));
	elseif ((t <= 7.5e+65) || (!(t <= 1.95e+108) && (t <= 7.7e+174)))
		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 * ((a * c) - (y * i))) - (b * (z * c));
	t_2 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -1.15e+152)
		tmp = t_2;
	elseif (t <= -2e+91)
		tmp = t_1;
	elseif (t <= -7e+71)
		tmp = (b * (t * i)) - (a * (x * t));
	elseif ((t <= 7.5e+65) || (~((t <= 1.95e+108)) && (t <= 7.7e+174)))
		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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+152], t$95$2, If[LessEqual[t, -2e+91], t$95$1, If[LessEqual[t, -7e+71], N[(N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 7.5e+65], And[N[Not[LessEqual[t, 1.95e+108]], $MachinePrecision], LessEqual[t, 7.7e+174]]], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.14999999999999993e152 or 7.50000000000000006e65 < t < 1.94999999999999992e108 or 7.69999999999999959e174 < t

   1. Initial program 65.2%

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

   2. Taylor expanded in t around -inf 77.1%

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

      1. associate-*r* 77.1%

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

      2. neg-mul-1 77.1%

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

      3. *-commutative 77.1%

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

   4. Simplified 77.1%

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

   if -1.14999999999999993e152 < t < -2.00000000000000016e91 or -6.9999999999999998e71 < t < 7.50000000000000006e65 or 1.94999999999999992e108 < t < 7.69999999999999959e174

   1. Initial program 75.3%

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

      1. fma-neg 77.7%

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

      2. distribute-lft-neg-out 77.7%

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

      3. *-commutative 77.7%

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

      4. *-commutative 77.7%

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

      5. sub-neg 77.7%

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

      6. sub-neg 77.7%

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

      7. *-commutative 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in c around inf 68.3%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 68.3%

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

      2. *-commutative 68.3%

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

      3. distribute-rgt-neg-out 68.3%

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

   6. Simplified 68.3%

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

   if -2.00000000000000016e91 < t < -6.9999999999999998e71

   1. Initial program 86.4%

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

      1. flip-- 71.4%

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

      2. clear-num 71.4%

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

      3. un-div-inv 71.4%

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

      4. clear-num 71.4%

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

      5. flip-- 86.4%

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

      6. *-commutative 86.4%

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

   3. Applied egg-rr 86.4%

      \[\leadsto \left(\color{blue}{\frac{x}{\frac{1}{y \cdot z - a \cdot t}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-/r/ 86.4%

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

      2. /-rgt-identity 86.4%

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

      3. *-commutative 86.4%

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

      4. sub-neg 86.4%

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

      5. distribute-rgt-in 86.4%

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

      6. *-commutative 86.4%

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

      7. distribute-rgt-neg-in 86.4%

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

   5. Applied egg-rr 86.4%

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

   6. Taylor expanded in j around 0 100.0%

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

   7. Taylor expanded in z around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*r* 100.0%

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

      3. neg-mul-1 100.0%

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

      4. cancel-sign-sub 100.0%

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

      5. mul-1-neg 100.0%

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

      6. *-commutative 100.0%

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

      7. distribute-lft-neg-in 100.0%

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

      8. *-commutative 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+152}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+91}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+71}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+65} \lor \neg \left(t \leq 1.95 \cdot 10^{+108}\right) \land t \leq 7.7 \cdot 10^{+174}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]

Alternative 12: 53.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := t_2 + t_1\\ t_4 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+226}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{+163}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{+17}:\\ \;\;\;\;t_1 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-130}:\\ \;\;\;\;t_2 + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-251}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+151}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 10^{+304}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i)))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (+ t_2 t_1))
        (t_4 (* b (- (* t i) (* z c)))))
   (if (<= b -1.25e+226)
     t_4
     (if (<= b -4.6e+163)
       t_3
       (if (<= b -2.1e+17)
         (- t_1 (* c (* z b)))
         (if (<= b -2.2e-130)
           (+ t_2 (* x (* y z)))
           (if (<= b 8.5e-251)
             (* a (- (* c j) (* x t)))
             (if (<= b 1.7e+151)
               t_3
               (if (<= b 1e+304) t_4 (* i (* y (- j))))))))))))

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 * (t * i);
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t_2 + t_1;
	double t_4 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.25e+226) {
		tmp = t_4;
	} else if (b <= -4.6e+163) {
		tmp = t_3;
	} else if (b <= -2.1e+17) {
		tmp = t_1 - (c * (z * b));
	} else if (b <= -2.2e-130) {
		tmp = t_2 + (x * (y * z));
	} else if (b <= 8.5e-251) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 1.7e+151) {
		tmp = t_3;
	} else if (b <= 1e+304) {
		tmp = t_4;
	} else {
		tmp = i * (y * -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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * (t * i)
    t_2 = j * ((a * c) - (y * i))
    t_3 = t_2 + t_1
    t_4 = b * ((t * i) - (z * c))
    if (b <= (-1.25d+226)) then
        tmp = t_4
    else if (b <= (-4.6d+163)) then
        tmp = t_3
    else if (b <= (-2.1d+17)) then
        tmp = t_1 - (c * (z * b))
    else if (b <= (-2.2d-130)) then
        tmp = t_2 + (x * (y * z))
    else if (b <= 8.5d-251) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 1.7d+151) then
        tmp = t_3
    else if (b <= 1d+304) then
        tmp = t_4
    else
        tmp = i * (y * -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 t_1 = b * (t * i);
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t_2 + t_1;
	double t_4 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.25e+226) {
		tmp = t_4;
	} else if (b <= -4.6e+163) {
		tmp = t_3;
	} else if (b <= -2.1e+17) {
		tmp = t_1 - (c * (z * b));
	} else if (b <= -2.2e-130) {
		tmp = t_2 + (x * (y * z));
	} else if (b <= 8.5e-251) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 1.7e+151) {
		tmp = t_3;
	} else if (b <= 1e+304) {
		tmp = t_4;
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	t_2 = j * ((a * c) - (y * i))
	t_3 = t_2 + t_1
	t_4 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1.25e+226:
		tmp = t_4
	elif b <= -4.6e+163:
		tmp = t_3
	elif b <= -2.1e+17:
		tmp = t_1 - (c * (z * b))
	elif b <= -2.2e-130:
		tmp = t_2 + (x * (y * z))
	elif b <= 8.5e-251:
		tmp = a * ((c * j) - (x * t))
	elif b <= 1.7e+151:
		tmp = t_3
	elif b <= 1e+304:
		tmp = t_4
	else:
		tmp = i * (y * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(t_2 + t_1)
	t_4 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.25e+226)
		tmp = t_4;
	elseif (b <= -4.6e+163)
		tmp = t_3;
	elseif (b <= -2.1e+17)
		tmp = Float64(t_1 - Float64(c * Float64(z * b)));
	elseif (b <= -2.2e-130)
		tmp = Float64(t_2 + Float64(x * Float64(y * z)));
	elseif (b <= 8.5e-251)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 1.7e+151)
		tmp = t_3;
	elseif (b <= 1e+304)
		tmp = t_4;
	else
		tmp = Float64(i * Float64(y * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	t_2 = j * ((a * c) - (y * i));
	t_3 = t_2 + t_1;
	t_4 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.25e+226)
		tmp = t_4;
	elseif (b <= -4.6e+163)
		tmp = t_3;
	elseif (b <= -2.1e+17)
		tmp = t_1 - (c * (z * b));
	elseif (b <= -2.2e-130)
		tmp = t_2 + (x * (y * z));
	elseif (b <= 8.5e-251)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 1.7e+151)
		tmp = t_3;
	elseif (b <= 1e+304)
		tmp = t_4;
	else
		tmp = i * (y * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e+226], t$95$4, If[LessEqual[b, -4.6e+163], t$95$3, If[LessEqual[b, -2.1e+17], N[(t$95$1 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.2e-130], N[(t$95$2 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e-251], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e+151], t$95$3, If[LessEqual[b, 1e+304], t$95$4, N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.2500000000000001e226 or 1.7e151 < b < 9.9999999999999994e303

   1. Initial program 80.3%

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

   2. Taylor expanded in b around inf 82.5%

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

   if -1.2500000000000001e226 < b < -4.60000000000000003e163 or 8.49999999999999984e-251 < b < 1.7e151

   1. Initial program 70.8%

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

      1. fma-neg 73.0%

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

      2. distribute-lft-neg-out 73.0%

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

      3. *-commutative 73.0%

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

      4. *-commutative 73.0%

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

      5. sub-neg 73.0%

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

      6. sub-neg 73.0%

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

      7. *-commutative 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in i around inf 62.0%

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

   if -4.60000000000000003e163 < b < -2.1e17

   1. Initial program 72.4%

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

   2. Taylor expanded in b around inf 61.5%

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

      1. sub-neg 61.5%

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

      2. distribute-rgt-in 61.5%

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

      3. distribute-lft-neg-in 61.5%

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

      4. distribute-rgt-neg-out 61.5%

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

      5. associate-*l* 66.8%

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

      6. distribute-rgt-neg-out 66.8%

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

   4. Applied egg-rr 66.8%

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

   if -2.1e17 < b < -2.1999999999999999e-130

   1. Initial program 69.3%

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

   2. Taylor expanded in b around 0 75.5%

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

   3. Taylor expanded in t around 0 69.0%

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

   if -2.1999999999999999e-130 < b < 8.49999999999999984e-251

   1. Initial program 68.8%

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

   2. Taylor expanded in a around inf 70.6%

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

   3. Taylor expanded in t around 0 70.6%

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

      1. mul-1-neg 70.6%

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

      2. *-commutative 70.6%

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

      3. distribute-rgt-neg-in 70.6%

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

      4. mul-1-neg 70.6%

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

      5. *-commutative 70.6%

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

      6. distribute-lft-in 70.6%

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

      7. +-commutative 70.6%

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

      8. associate-*r* 70.6%

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

      9. neg-mul-1 70.6%

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

      10. cancel-sign-sub-inv 70.6%

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

      11. *-commutative 70.6%

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

   5. Simplified 70.6%

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

   if 9.9999999999999994e303 < b

   1. Initial program 99.2%

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

   2. Taylor expanded in y around inf 100.0%

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

   3. Taylor expanded in i around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-*r* 100.0%

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

      3. distribute-rgt-neg-out 100.0%

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

      4. associate-*l* 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+226}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{+163}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{+17}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-130}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-251}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{+151}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 10^{+304}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 13: 52.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right) + t_1\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+226}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{+163}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.05 \cdot 10^{+28}:\\ \;\;\;\;t_1 - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;b \leq 10^{-250}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.04 \cdot 10^{+158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 10^{+304}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i)))
        (t_2 (+ (* j (- (* a c) (* y i))) t_1))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -4.8e+226)
     t_3
     (if (<= b -2.7e+163)
       t_2
       (if (<= b -3.05e+28)
         (- t_1 (* c (* z b)))
         (if (<= b 1e-250)
           (* a (- (* c j) (* x t)))
           (if (<= b 1.04e+158)
             t_2
             (if (<= b 1e+304) t_3 (* i (* y (- j)))))))))))

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 * (t * i);
	double t_2 = (j * ((a * c) - (y * i))) + t_1;
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.8e+226) {
		tmp = t_3;
	} else if (b <= -2.7e+163) {
		tmp = t_2;
	} else if (b <= -3.05e+28) {
		tmp = t_1 - (c * (z * b));
	} else if (b <= 1e-250) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 1.04e+158) {
		tmp = t_2;
	} else if (b <= 1e+304) {
		tmp = t_3;
	} else {
		tmp = i * (y * -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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * (t * i)
    t_2 = (j * ((a * c) - (y * i))) + t_1
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-4.8d+226)) then
        tmp = t_3
    else if (b <= (-2.7d+163)) then
        tmp = t_2
    else if (b <= (-3.05d+28)) then
        tmp = t_1 - (c * (z * b))
    else if (b <= 1d-250) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 1.04d+158) then
        tmp = t_2
    else if (b <= 1d+304) then
        tmp = t_3
    else
        tmp = i * (y * -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 t_1 = b * (t * i);
	double t_2 = (j * ((a * c) - (y * i))) + t_1;
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.8e+226) {
		tmp = t_3;
	} else if (b <= -2.7e+163) {
		tmp = t_2;
	} else if (b <= -3.05e+28) {
		tmp = t_1 - (c * (z * b));
	} else if (b <= 1e-250) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 1.04e+158) {
		tmp = t_2;
	} else if (b <= 1e+304) {
		tmp = t_3;
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	t_2 = (j * ((a * c) - (y * i))) + t_1
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -4.8e+226:
		tmp = t_3
	elif b <= -2.7e+163:
		tmp = t_2
	elif b <= -3.05e+28:
		tmp = t_1 - (c * (z * b))
	elif b <= 1e-250:
		tmp = a * ((c * j) - (x * t))
	elif b <= 1.04e+158:
		tmp = t_2
	elif b <= 1e+304:
		tmp = t_3
	else:
		tmp = i * (y * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	t_2 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + t_1)
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.8e+226)
		tmp = t_3;
	elseif (b <= -2.7e+163)
		tmp = t_2;
	elseif (b <= -3.05e+28)
		tmp = Float64(t_1 - Float64(c * Float64(z * b)));
	elseif (b <= 1e-250)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 1.04e+158)
		tmp = t_2;
	elseif (b <= 1e+304)
		tmp = t_3;
	else
		tmp = Float64(i * Float64(y * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	t_2 = (j * ((a * c) - (y * i))) + t_1;
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.8e+226)
		tmp = t_3;
	elseif (b <= -2.7e+163)
		tmp = t_2;
	elseif (b <= -3.05e+28)
		tmp = t_1 - (c * (z * b));
	elseif (b <= 1e-250)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 1.04e+158)
		tmp = t_2;
	elseif (b <= 1e+304)
		tmp = t_3;
	else
		tmp = i * (y * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.8e+226], t$95$3, If[LessEqual[b, -2.7e+163], t$95$2, If[LessEqual[b, -3.05e+28], N[(t$95$1 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e-250], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.04e+158], t$95$2, If[LessEqual[b, 1e+304], t$95$3, N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -4.8e226 or 1.04000000000000004e158 < b < 9.9999999999999994e303

   1. Initial program 80.3%

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

   2. Taylor expanded in b around inf 82.5%

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

   if -4.8e226 < b < -2.69999999999999999e163 or 1.0000000000000001e-250 < b < 1.04000000000000004e158

   1. Initial program 70.8%

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

      1. fma-neg 73.0%

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

      2. distribute-lft-neg-out 73.0%

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

      3. *-commutative 73.0%

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

      4. *-commutative 73.0%

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

      5. sub-neg 73.0%

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

      6. sub-neg 73.0%

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

      7. *-commutative 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in i around inf 62.0%

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

   if -2.69999999999999999e163 < b < -3.0500000000000001e28

   1. Initial program 71.7%

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

   2. Taylor expanded in b around inf 66.6%

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

      1. sub-neg 66.6%

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

      2. distribute-rgt-in 66.6%

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

      3. distribute-lft-neg-in 66.6%

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

      4. distribute-rgt-neg-out 66.6%

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

      5. associate-*l* 69.5%

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

      6. distribute-rgt-neg-out 69.5%

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

   4. Applied egg-rr 69.5%

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

   if -3.0500000000000001e28 < b < 1.0000000000000001e-250

   1. Initial program 69.5%

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

   2. Taylor expanded in a around inf 59.4%

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

   3. Taylor expanded in t around 0 58.2%

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

      1. mul-1-neg 58.2%

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

      2. *-commutative 58.2%

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

      3. distribute-rgt-neg-in 58.2%

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

      4. mul-1-neg 58.2%

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

      5. *-commutative 58.2%

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

      6. distribute-lft-in 59.4%

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

      7. +-commutative 59.4%

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

      8. associate-*r* 59.4%

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

      9. neg-mul-1 59.4%

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

      10. cancel-sign-sub-inv 59.4%

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

      11. *-commutative 59.4%

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

   5. Simplified 59.4%

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

   if 9.9999999999999994e303 < b

   1. Initial program 99.2%

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

   2. Taylor expanded in y around inf 100.0%

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

   3. Taylor expanded in i around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. associate-*r* 100.0%

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

      3. distribute-rgt-neg-out 100.0%

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

      4. associate-*l* 100.0%

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

   5. Simplified 100.0%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(-y\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+226}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{+163}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -3.05 \cdot 10^{+28}:\\ \;\;\;\;b \cdot \left(t \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;b \leq 10^{-250}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.04 \cdot 10^{+158}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 10^{+304}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]

Alternative 14: 59.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t_1 + b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;j \leq -7.2 \cdot 10^{+221}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -5 \cdot 10^{+99}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-48}:\\ \;\;\;\;t_1 + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 8.4 \cdot 10^{+24}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (+ t_1 (* b (* t i)))))
   (if (<= j -7.2e+221)
     t_2
     (if (<= j -5e+99)
       (- t_1 (* b (* z c)))
       (if (<= j -1.75e+48)
         (* a (- (* c j) (* x t)))
         (if (<= j -6e-48)
           (+ t_1 (* x (* y z)))
           (if (<= j 8.4e+24)
             (- (* b (- (* t i) (* z c))) (* a (* x t)))
             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 * ((a * c) - (y * i));
	double t_2 = t_1 + (b * (t * i));
	double tmp;
	if (j <= -7.2e+221) {
		tmp = t_2;
	} else if (j <= -5e+99) {
		tmp = t_1 - (b * (z * c));
	} else if (j <= -1.75e+48) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -6e-48) {
		tmp = t_1 + (x * (y * z));
	} else if (j <= 8.4e+24) {
		tmp = (b * ((t * i) - (z * c))) - (a * (x * t));
	} 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 * ((a * c) - (y * i))
    t_2 = t_1 + (b * (t * i))
    if (j <= (-7.2d+221)) then
        tmp = t_2
    else if (j <= (-5d+99)) then
        tmp = t_1 - (b * (z * c))
    else if (j <= (-1.75d+48)) then
        tmp = a * ((c * j) - (x * t))
    else if (j <= (-6d-48)) then
        tmp = t_1 + (x * (y * z))
    else if (j <= 8.4d+24) then
        tmp = (b * ((t * i) - (z * c))) - (a * (x * t))
    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 * ((a * c) - (y * i));
	double t_2 = t_1 + (b * (t * i));
	double tmp;
	if (j <= -7.2e+221) {
		tmp = t_2;
	} else if (j <= -5e+99) {
		tmp = t_1 - (b * (z * c));
	} else if (j <= -1.75e+48) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -6e-48) {
		tmp = t_1 + (x * (y * z));
	} else if (j <= 8.4e+24) {
		tmp = (b * ((t * i) - (z * c))) - (a * (x * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t_1 + (b * (t * i))
	tmp = 0
	if j <= -7.2e+221:
		tmp = t_2
	elif j <= -5e+99:
		tmp = t_1 - (b * (z * c))
	elif j <= -1.75e+48:
		tmp = a * ((c * j) - (x * t))
	elif j <= -6e-48:
		tmp = t_1 + (x * (y * z))
	elif j <= 8.4e+24:
		tmp = (b * ((t * i) - (z * c))) - (a * (x * t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(t_1 + Float64(b * Float64(t * i)))
	tmp = 0.0
	if (j <= -7.2e+221)
		tmp = t_2;
	elseif (j <= -5e+99)
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	elseif (j <= -1.75e+48)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (j <= -6e-48)
		tmp = Float64(t_1 + Float64(x * Float64(y * z)));
	elseif (j <= 8.4e+24)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(a * Float64(x * t)));
	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 * ((a * c) - (y * i));
	t_2 = t_1 + (b * (t * i));
	tmp = 0.0;
	if (j <= -7.2e+221)
		tmp = t_2;
	elseif (j <= -5e+99)
		tmp = t_1 - (b * (z * c));
	elseif (j <= -1.75e+48)
		tmp = a * ((c * j) - (x * t));
	elseif (j <= -6e-48)
		tmp = t_1 + (x * (y * z));
	elseif (j <= 8.4e+24)
		tmp = (b * ((t * i) - (z * c))) - (a * (x * t));
	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[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.2e+221], t$95$2, If[LessEqual[j, -5e+99], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.75e+48], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6e-48], N[(t$95$1 + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.4e+24], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -7.20000000000000018e221 or 8.4000000000000005e24 < j

   1. Initial program 66.3%

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

      1. fma-neg 67.6%

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

      2. distribute-lft-neg-out 67.6%

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

      3. *-commutative 67.6%

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

      4. *-commutative 67.6%

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

      5. sub-neg 67.6%

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

      6. sub-neg 67.6%

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

      7. *-commutative 67.6%

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

   3. Simplified 67.6%

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

   4. Taylor expanded in i around inf 79.5%

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

   if -7.20000000000000018e221 < j < -5.00000000000000008e99

   1. Initial program 80.5%

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

      1. fma-neg 84.3%

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

      2. distribute-lft-neg-out 84.3%

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

      3. *-commutative 84.3%

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

      4. *-commutative 84.3%

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

      5. sub-neg 84.3%

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

      6. sub-neg 84.3%

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

      7. *-commutative 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in c around inf 83.1%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 83.1%

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

      2. *-commutative 83.1%

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

      3. distribute-rgt-neg-out 83.1%

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

   6. Simplified 83.1%

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

   if -5.00000000000000008e99 < j < -1.7499999999999999e48

   1. Initial program 91.1%

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

   2. Taylor expanded in a around inf 73.4%

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

   3. Taylor expanded in t around 0 73.4%

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

      1. mul-1-neg 73.4%

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

      2. *-commutative 73.4%

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

      3. distribute-rgt-neg-in 73.4%

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

      4. mul-1-neg 73.4%

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

      5. *-commutative 73.4%

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

      6. distribute-lft-in 73.4%

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

      7. +-commutative 73.4%

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

      8. associate-*r* 73.4%

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

      9. neg-mul-1 73.4%

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

      10. cancel-sign-sub-inv 73.4%

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

      11. *-commutative 73.4%

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

   5. Simplified 73.4%

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

   if -1.7499999999999999e48 < j < -5.9999999999999998e-48

   1. Initial program 73.2%

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

   2. Taylor expanded in b around 0 80.4%

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

   3. Taylor expanded in t around 0 74.3%

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

   if -5.9999999999999998e-48 < j < 8.4000000000000005e24

   1. Initial program 73.1%

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

      1. flip-- 52.8%

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

      2. clear-num 52.7%

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

      3. un-div-inv 52.8%

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

      4. clear-num 52.8%

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

      5. flip-- 73.1%

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

      6. *-commutative 73.1%

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

   3. Applied egg-rr 73.1%

      \[\leadsto \left(\color{blue}{\frac{x}{\frac{1}{y \cdot z - a \cdot t}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-/r/ 73.1%

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

      2. /-rgt-identity 73.1%

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

      3. *-commutative 73.1%

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

      4. sub-neg 73.1%

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

      5. distribute-rgt-in 73.1%

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

      6. *-commutative 73.1%

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

      7. distribute-rgt-neg-in 73.1%

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

   5. Applied egg-rr 73.1%

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

   6. Taylor expanded in j around 0 71.2%

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

   7. Taylor expanded in y around 0 63.3%

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

      1. mul-1-neg 63.3%

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

      2. *-commutative 63.3%

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

      3. distribute-lft-neg-in 63.3%

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

   9. Simplified 63.3%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.2 \cdot 10^{+221}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{+99}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{+48}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -6 \cdot 10^{-48}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 8.4 \cdot 10^{+24}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 15: 60.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot t\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := t_2 + b \cdot \left(t \cdot i\right)\\ t_4 := b \cdot \left(z \cdot c\right)\\ \mathbf{if}\;j \leq -1.3 \cdot 10^{+222}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.9 \cdot 10^{+101}:\\ \;\;\;\;t_2 - t_4\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-81}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y\right) - t_1\right) - t_4\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{+21}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x t)))
        (t_2 (* j (- (* a c) (* y i))))
        (t_3 (+ t_2 (* b (* t i))))
        (t_4 (* b (* z c))))
   (if (<= j -1.3e+222)
     t_3
     (if (<= j -1.9e+101)
       (- t_2 t_4)
       (if (<= j -1.8e+38)
         (* a (- (* c j) (* x t)))
         (if (<= j -1.25e-81)
           (- (- (* z (* x y)) t_1) t_4)
           (if (<= j 1.65e+21) (- (* b (- (* t i) (* z c))) t_1) t_3)))))))

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 * (x * t);
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t_2 + (b * (t * i));
	double t_4 = b * (z * c);
	double tmp;
	if (j <= -1.3e+222) {
		tmp = t_3;
	} else if (j <= -1.9e+101) {
		tmp = t_2 - t_4;
	} else if (j <= -1.8e+38) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -1.25e-81) {
		tmp = ((z * (x * y)) - t_1) - t_4;
	} else if (j <= 1.65e+21) {
		tmp = (b * ((t * i) - (z * c))) - t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = a * (x * t)
    t_2 = j * ((a * c) - (y * i))
    t_3 = t_2 + (b * (t * i))
    t_4 = b * (z * c)
    if (j <= (-1.3d+222)) then
        tmp = t_3
    else if (j <= (-1.9d+101)) then
        tmp = t_2 - t_4
    else if (j <= (-1.8d+38)) then
        tmp = a * ((c * j) - (x * t))
    else if (j <= (-1.25d-81)) then
        tmp = ((z * (x * y)) - t_1) - t_4
    else if (j <= 1.65d+21) then
        tmp = (b * ((t * i) - (z * c))) - t_1
    else
        tmp = t_3
    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 * (x * t);
	double t_2 = j * ((a * c) - (y * i));
	double t_3 = t_2 + (b * (t * i));
	double t_4 = b * (z * c);
	double tmp;
	if (j <= -1.3e+222) {
		tmp = t_3;
	} else if (j <= -1.9e+101) {
		tmp = t_2 - t_4;
	} else if (j <= -1.8e+38) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -1.25e-81) {
		tmp = ((z * (x * y)) - t_1) - t_4;
	} else if (j <= 1.65e+21) {
		tmp = (b * ((t * i) - (z * c))) - t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * t)
	t_2 = j * ((a * c) - (y * i))
	t_3 = t_2 + (b * (t * i))
	t_4 = b * (z * c)
	tmp = 0
	if j <= -1.3e+222:
		tmp = t_3
	elif j <= -1.9e+101:
		tmp = t_2 - t_4
	elif j <= -1.8e+38:
		tmp = a * ((c * j) - (x * t))
	elif j <= -1.25e-81:
		tmp = ((z * (x * y)) - t_1) - t_4
	elif j <= 1.65e+21:
		tmp = (b * ((t * i) - (z * c))) - t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * t))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_3 = Float64(t_2 + Float64(b * Float64(t * i)))
	t_4 = Float64(b * Float64(z * c))
	tmp = 0.0
	if (j <= -1.3e+222)
		tmp = t_3;
	elseif (j <= -1.9e+101)
		tmp = Float64(t_2 - t_4);
	elseif (j <= -1.8e+38)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (j <= -1.25e-81)
		tmp = Float64(Float64(Float64(z * Float64(x * y)) - t_1) - t_4);
	elseif (j <= 1.65e+21)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - t_1);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (x * t);
	t_2 = j * ((a * c) - (y * i));
	t_3 = t_2 + (b * (t * i));
	t_4 = b * (z * c);
	tmp = 0.0;
	if (j <= -1.3e+222)
		tmp = t_3;
	elseif (j <= -1.9e+101)
		tmp = t_2 - t_4;
	elseif (j <= -1.8e+38)
		tmp = a * ((c * j) - (x * t));
	elseif (j <= -1.25e-81)
		tmp = ((z * (x * y)) - t_1) - t_4;
	elseif (j <= 1.65e+21)
		tmp = (b * ((t * i) - (z * c))) - t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.3e+222], t$95$3, If[LessEqual[j, -1.9e+101], N[(t$95$2 - t$95$4), $MachinePrecision], If[LessEqual[j, -1.8e+38], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.25e-81], N[(N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] - t$95$4), $MachinePrecision], If[LessEqual[j, 1.65e+21], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.3000000000000001e222 or 1.65e21 < j

   1. Initial program 66.3%

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

      1. fma-neg 67.6%

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

      2. distribute-lft-neg-out 67.6%

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

      3. *-commutative 67.6%

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

      4. *-commutative 67.6%

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

      5. sub-neg 67.6%

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

      6. sub-neg 67.6%

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

      7. *-commutative 67.6%

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

   3. Simplified 67.6%

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

   4. Taylor expanded in i around inf 79.5%

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

   if -1.3000000000000001e222 < j < -1.8999999999999999e101

   1. Initial program 80.5%

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

      1. fma-neg 84.3%

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

      2. distribute-lft-neg-out 84.3%

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

      3. *-commutative 84.3%

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

      4. *-commutative 84.3%

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

      5. sub-neg 84.3%

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

      6. sub-neg 84.3%

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

      7. *-commutative 84.3%

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

   3. Simplified 84.3%

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

   4. Taylor expanded in c around inf 83.1%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} + j \cdot \left(a \cdot c - y \cdot i\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 83.1%

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

      2. *-commutative 83.1%

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

      3. distribute-rgt-neg-out 83.1%

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

   6. Simplified 83.1%

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

   if -1.8999999999999999e101 < j < -1.79999999999999985e38

   1. Initial program 84.8%

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

   2. Taylor expanded in a around inf 77.5%

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

   3. Taylor expanded in t around 0 69.8%

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

      1. mul-1-neg 69.8%

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

      2. *-commutative 69.8%

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

      3. distribute-rgt-neg-in 69.8%

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

      4. mul-1-neg 69.8%

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

      5. *-commutative 69.8%

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

      6. distribute-lft-in 77.5%

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

      7. +-commutative 77.5%

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

      8. associate-*r* 77.5%

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

      9. neg-mul-1 77.5%

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

      10. cancel-sign-sub-inv 77.5%

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

      11. *-commutative 77.5%

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

   5. Simplified 77.5%

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

   if -1.79999999999999985e38 < j < -1.24999999999999995e-81

   1. Initial program 79.1%

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

      1. flip-- 46.4%

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

      2. clear-num 46.4%

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

      3. un-div-inv 46.4%

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

      4. clear-num 46.4%

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

      5. flip-- 79.0%

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

      6. *-commutative 79.0%

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

   3. Applied egg-rr 79.0%

      \[\leadsto \left(\color{blue}{\frac{x}{\frac{1}{y \cdot z - a \cdot t}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-/r/ 79.1%

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

      2. /-rgt-identity 79.1%

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

      3. *-commutative 79.1%

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

      4. sub-neg 79.1%

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

      5. distribute-rgt-in 79.1%

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

      6. *-commutative 79.1%

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

      7. distribute-rgt-neg-in 79.1%

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

   5. Applied egg-rr 79.1%

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

   6. Taylor expanded in j around 0 67.3%

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

   7. Taylor expanded in i around 0 75.7%

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

      1. +-commutative 75.7%

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

      2. mul-1-neg 75.7%

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

      3. *-commutative 75.7%

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

      4. sub-neg 75.7%

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

      5. associate-*r* 75.7%

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

      6. *-commutative 75.7%

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

   9. Simplified 75.7%

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

   if -1.24999999999999995e-81 < j < 1.65e21

   1. Initial program 72.3%

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

      1. flip-- 54.2%

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

      2. clear-num 54.2%

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

      3. un-div-inv 54.2%

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

      4. clear-num 54.2%

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

      5. flip-- 72.3%

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

      6. *-commutative 72.3%

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

   3. Applied egg-rr 72.3%

      \[\leadsto \left(\color{blue}{\frac{x}{\frac{1}{y \cdot z - a \cdot t}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-/r/ 72.3%

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

      2. /-rgt-identity 72.3%

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

      3. *-commutative 72.3%

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

      4. sub-neg 72.3%

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

      5. distribute-rgt-in 72.3%

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

      6. *-commutative 72.3%

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

      7. distribute-rgt-neg-in 72.3%

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

   5. Applied egg-rr 72.3%

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

   6. Taylor expanded in j around 0 70.1%

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

   7. Taylor expanded in y around 0 63.1%

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

      1. mul-1-neg 63.1%

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

      2. *-commutative 63.1%

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

      3. distribute-lft-neg-in 63.1%

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

   9. Simplified 63.1%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(x \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.3 \cdot 10^{+222}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq -1.9 \cdot 10^{+101}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-81}:\\ \;\;\;\;\left(z \cdot \left(x \cdot y\right) - a \cdot \left(x \cdot t\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{+21}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 16: 30.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+152}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+92}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-220}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* b (* t i))))
   (if (<= t -1.15e+152)
     (* a (* t (- x)))
     (if (<= t -1.25e+92)
       (* c (* a j))
       (if (<= t -9.8e+50)
         t_2
         (if (<= t -2.7e-254)
           t_1
           (if (<= t 2.15e-220)
             (* y (* x z))
             (if (<= t 4.4e+58) 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 = a * (c * j);
	double t_2 = b * (t * i);
	double tmp;
	if (t <= -1.15e+152) {
		tmp = a * (t * -x);
	} else if (t <= -1.25e+92) {
		tmp = c * (a * j);
	} else if (t <= -9.8e+50) {
		tmp = t_2;
	} else if (t <= -2.7e-254) {
		tmp = t_1;
	} else if (t <= 2.15e-220) {
		tmp = y * (x * z);
	} else if (t <= 4.4e+58) {
		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 = a * (c * j)
    t_2 = b * (t * i)
    if (t <= (-1.15d+152)) then
        tmp = a * (t * -x)
    else if (t <= (-1.25d+92)) then
        tmp = c * (a * j)
    else if (t <= (-9.8d+50)) then
        tmp = t_2
    else if (t <= (-2.7d-254)) then
        tmp = t_1
    else if (t <= 2.15d-220) then
        tmp = y * (x * z)
    else if (t <= 4.4d+58) 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 = a * (c * j);
	double t_2 = b * (t * i);
	double tmp;
	if (t <= -1.15e+152) {
		tmp = a * (t * -x);
	} else if (t <= -1.25e+92) {
		tmp = c * (a * j);
	} else if (t <= -9.8e+50) {
		tmp = t_2;
	} else if (t <= -2.7e-254) {
		tmp = t_1;
	} else if (t <= 2.15e-220) {
		tmp = y * (x * z);
	} else if (t <= 4.4e+58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = b * (t * i)
	tmp = 0
	if t <= -1.15e+152:
		tmp = a * (t * -x)
	elif t <= -1.25e+92:
		tmp = c * (a * j)
	elif t <= -9.8e+50:
		tmp = t_2
	elif t <= -2.7e-254:
		tmp = t_1
	elif t <= 2.15e-220:
		tmp = y * (x * z)
	elif t <= 4.4e+58:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (t <= -1.15e+152)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (t <= -1.25e+92)
		tmp = Float64(c * Float64(a * j));
	elseif (t <= -9.8e+50)
		tmp = t_2;
	elseif (t <= -2.7e-254)
		tmp = t_1;
	elseif (t <= 2.15e-220)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 4.4e+58)
		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 = a * (c * j);
	t_2 = b * (t * i);
	tmp = 0.0;
	if (t <= -1.15e+152)
		tmp = a * (t * -x);
	elseif (t <= -1.25e+92)
		tmp = c * (a * j);
	elseif (t <= -9.8e+50)
		tmp = t_2;
	elseif (t <= -2.7e-254)
		tmp = t_1;
	elseif (t <= 2.15e-220)
		tmp = y * (x * z);
	elseif (t <= 4.4e+58)
		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[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.15e+152], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.25e+92], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.8e+50], t$95$2, If[LessEqual[t, -2.7e-254], t$95$1, If[LessEqual[t, 2.15e-220], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e+58], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.14999999999999993e152

   1. Initial program 60.3%

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

   2. Taylor expanded in t around -inf 73.6%

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

      1. associate-*r* 73.6%

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

      2. neg-mul-1 73.6%

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

      3. *-commutative 73.6%

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

   4. Simplified 73.6%

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

   5. Taylor expanded in a around inf 46.5%

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

      1. mul-1-neg 46.5%

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

   7. Simplified 46.5%

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

   if -1.14999999999999993e152 < t < -1.25000000000000005e92

   1. Initial program 59.8%

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

   2. Taylor expanded in a around inf 50.9%

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

   3. Taylor expanded in t around 0 45.2%

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

      1. associate-*r* 45.5%

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

      2. *-commutative 45.5%

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

      3. associate-*r* 45.4%

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

   5. Simplified 45.4%

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

   if -1.25000000000000005e92 < t < -9.8000000000000003e50 or 4.4000000000000001e58 < t

   1. Initial program 68.7%

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

   2. Taylor expanded in b around inf 63.9%

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

   3. Taylor expanded in i around inf 50.5%

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

   if -9.8000000000000003e50 < t < -2.70000000000000007e-254 or 2.1499999999999999e-220 < t < 4.4000000000000001e58

   1. Initial program 76.2%

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

   2. Taylor expanded in a around inf 43.6%

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

   3. Taylor expanded in t around 0 36.7%

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

   if -2.70000000000000007e-254 < t < 2.1499999999999999e-220

   1. Initial program 87.0%

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

   2. Taylor expanded in y around inf 54.1%

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

   3. Taylor expanded in i around 0 34.9%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+152}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+92}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{+50}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-254}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-220}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+58}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 17: 41.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;b \leq -7.4 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-155}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= b -7.4e+147)
     (* b (* t i))
     (if (<= b 8.2e-197)
       t_1
       (if (<= b 3.3e-155)
         (* y (* i (- j)))
         (if (<= b 6.5e+152) t_1 (* (* z c) (- b))))))))

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 * ((c * j) - (x * t));
	double tmp;
	if (b <= -7.4e+147) {
		tmp = b * (t * i);
	} else if (b <= 8.2e-197) {
		tmp = t_1;
	} else if (b <= 3.3e-155) {
		tmp = y * (i * -j);
	} else if (b <= 6.5e+152) {
		tmp = t_1;
	} else {
		tmp = (z * c) * -b;
	}
	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 * ((c * j) - (x * t))
    if (b <= (-7.4d+147)) then
        tmp = b * (t * i)
    else if (b <= 8.2d-197) then
        tmp = t_1
    else if (b <= 3.3d-155) then
        tmp = y * (i * -j)
    else if (b <= 6.5d+152) then
        tmp = t_1
    else
        tmp = (z * c) * -b
    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 * ((c * j) - (x * t));
	double tmp;
	if (b <= -7.4e+147) {
		tmp = b * (t * i);
	} else if (b <= 8.2e-197) {
		tmp = t_1;
	} else if (b <= 3.3e-155) {
		tmp = y * (i * -j);
	} else if (b <= 6.5e+152) {
		tmp = t_1;
	} else {
		tmp = (z * c) * -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if b <= -7.4e+147:
		tmp = b * (t * i)
	elif b <= 8.2e-197:
		tmp = t_1
	elif b <= 3.3e-155:
		tmp = y * (i * -j)
	elif b <= 6.5e+152:
		tmp = t_1
	else:
		tmp = (z * c) * -b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (b <= -7.4e+147)
		tmp = Float64(b * Float64(t * i));
	elseif (b <= 8.2e-197)
		tmp = t_1;
	elseif (b <= 3.3e-155)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (b <= 6.5e+152)
		tmp = t_1;
	else
		tmp = Float64(Float64(z * c) * Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (b <= -7.4e+147)
		tmp = b * (t * i);
	elseif (b <= 8.2e-197)
		tmp = t_1;
	elseif (b <= 3.3e-155)
		tmp = y * (i * -j);
	elseif (b <= 6.5e+152)
		tmp = t_1;
	else
		tmp = (z * c) * -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.4e+147], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e-197], t$95$1, If[LessEqual[b, 3.3e-155], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.5e+152], t$95$1, N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.3999999999999999e147

   1. Initial program 71.4%

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

   2. Taylor expanded in b around inf 76.9%

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

   3. Taylor expanded in i around inf 52.4%

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

   if -7.3999999999999999e147 < b < 8.2e-197 or 3.29999999999999986e-155 < b < 6.4999999999999997e152

   1. Initial program 70.7%

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

   2. Taylor expanded in a around inf 52.9%

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

   3. Taylor expanded in t around 0 51.8%

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

      1. mul-1-neg 51.8%

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

      2. *-commutative 51.8%

         \[\leadsto \left(-a \cdot \color{blue}{\left(x \cdot t\right)}\right) + a \cdot \left(c \cdot j\right) \]

      3. distribute-rgt-neg-in 51.8%

         \[\leadsto \color{blue}{a \cdot \left(-x \cdot t\right)} + a \cdot \left(c \cdot j\right) \]

      4. mul-1-neg 51.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(x \cdot t\right)\right)} + a \cdot \left(c \cdot j\right) \]

      5. *-commutative 51.8%

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(t \cdot x\right)}\right) + a \cdot \left(c \cdot j\right) \]

      6. distribute-lft-in 52.9%

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

      7. +-commutative 52.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      8. associate-*r* 52.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-1 \cdot t\right) \cdot x}\right) \]

      9. neg-mul-1 52.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t\right)} \cdot x\right) \]

      10. cancel-sign-sub-inv 52.9%

          \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      11. *-commutative 52.9%

          \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 52.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   if 8.2e-197 < b < 3.29999999999999986e-155

   1. Initial program 71.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf 93.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

   3. Taylor expanded in i around inf 79.2%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 79.2%

         \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

      2. distribute-rgt-neg-out 79.2%

         \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]

   5. Simplified 79.2%

      \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]

   if 6.4999999999999997e152 < b

   1. Initial program 86.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 72.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   3. Taylor expanded in i around 0 41.7%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 41.7%

         \[\leadsto b \cdot \color{blue}{\left(-c \cdot z\right)} \]

      2. distribute-rgt-neg-out 41.7%

         \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(-z\right)\right)} \]

   5. Simplified 41.7%

      \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(-z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-197}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-155}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+152}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \]

Alternative 18: 50.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -3.4e+28)
     t_2
     (if (<= b 6e-197)
       t_1
       (if (<= b 1.8e-150) (* y (* i (- j))) (if (<= b 4.1e+92) 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 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.4e+28) {
		tmp = t_2;
	} else if (b <= 6e-197) {
		tmp = t_1;
	} else if (b <= 1.8e-150) {
		tmp = y * (i * -j);
	} else if (b <= 4.1e+92) {
		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 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-3.4d+28)) then
        tmp = t_2
    else if (b <= 6d-197) then
        tmp = t_1
    else if (b <= 1.8d-150) then
        tmp = y * (i * -j)
    else if (b <= 4.1d+92) 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 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3.4e+28) {
		tmp = t_2;
	} else if (b <= 6e-197) {
		tmp = t_1;
	} else if (b <= 1.8e-150) {
		tmp = y * (i * -j);
	} else if (b <= 4.1e+92) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -3.4e+28:
		tmp = t_2
	elif b <= 6e-197:
		tmp = t_1
	elif b <= 1.8e-150:
		tmp = y * (i * -j)
	elif b <= 4.1e+92:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.4e+28)
		tmp = t_2;
	elseif (b <= 6e-197)
		tmp = t_1;
	elseif (b <= 1.8e-150)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (b <= 4.1e+92)
		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 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.4e+28)
		tmp = t_2;
	elseif (b <= 6e-197)
		tmp = t_1;
	elseif (b <= 1.8e-150)
		tmp = y * (i * -j);
	elseif (b <= 4.1e+92)
		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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.4e+28], t$95$2, If[LessEqual[b, 6e-197], t$95$1, If[LessEqual[b, 1.8e-150], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.1e+92], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.4e28 or 4.10000000000000024e92 < b

   1. Initial program 76.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 69.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -3.4e28 < b < 6.00000000000000051e-197 or 1.8000000000000001e-150 < b < 4.10000000000000024e92

   1. Initial program 69.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 55.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

   3. Taylor expanded in t around 0 54.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 54.3%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + a \cdot \left(c \cdot j\right) \]

      2. *-commutative 54.3%

         \[\leadsto \left(-a \cdot \color{blue}{\left(x \cdot t\right)}\right) + a \cdot \left(c \cdot j\right) \]

      3. distribute-rgt-neg-in 54.3%

         \[\leadsto \color{blue}{a \cdot \left(-x \cdot t\right)} + a \cdot \left(c \cdot j\right) \]

      4. mul-1-neg 54.3%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(x \cdot t\right)\right)} + a \cdot \left(c \cdot j\right) \]

      5. *-commutative 54.3%

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(t \cdot x\right)}\right) + a \cdot \left(c \cdot j\right) \]

      6. distribute-lft-in 55.0%

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

      7. +-commutative 55.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      8. associate-*r* 55.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-1 \cdot t\right) \cdot x}\right) \]

      9. neg-mul-1 55.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t\right)} \cdot x\right) \]

      10. cancel-sign-sub-inv 55.0%

          \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      11. *-commutative 55.0%

          \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 55.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   if 6.00000000000000051e-197 < b < 1.8000000000000001e-150

   1. Initial program 71.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf 93.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

   3. Taylor expanded in i around inf 79.2%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 79.2%

         \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

      2. distribute-rgt-neg-out 79.2%

         \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]

   5. Simplified 79.2%

      \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+28}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-197}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{+92}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 19: 29.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+152}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{+91}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-262}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+44}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= t -2.4e+152)
     (* a (* t (- x)))
     (if (<= t -2.75e+91)
       (* c (* a j))
       (if (<= t -2.5e+43)
         t_1
         (if (<= t -2e-262)
           (* a (* c j))
           (if (<= t 8e+44) (* i (* y (- 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 = b * (t * i);
	double tmp;
	if (t <= -2.4e+152) {
		tmp = a * (t * -x);
	} else if (t <= -2.75e+91) {
		tmp = c * (a * j);
	} else if (t <= -2.5e+43) {
		tmp = t_1;
	} else if (t <= -2e-262) {
		tmp = a * (c * j);
	} else if (t <= 8e+44) {
		tmp = i * (y * -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 = b * (t * i)
    if (t <= (-2.4d+152)) then
        tmp = a * (t * -x)
    else if (t <= (-2.75d+91)) then
        tmp = c * (a * j)
    else if (t <= (-2.5d+43)) then
        tmp = t_1
    else if (t <= (-2d-262)) then
        tmp = a * (c * j)
    else if (t <= 8d+44) then
        tmp = i * (y * -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 = b * (t * i);
	double tmp;
	if (t <= -2.4e+152) {
		tmp = a * (t * -x);
	} else if (t <= -2.75e+91) {
		tmp = c * (a * j);
	} else if (t <= -2.5e+43) {
		tmp = t_1;
	} else if (t <= -2e-262) {
		tmp = a * (c * j);
	} else if (t <= 8e+44) {
		tmp = i * (y * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	tmp = 0
	if t <= -2.4e+152:
		tmp = a * (t * -x)
	elif t <= -2.75e+91:
		tmp = c * (a * j)
	elif t <= -2.5e+43:
		tmp = t_1
	elif t <= -2e-262:
		tmp = a * (c * j)
	elif t <= 8e+44:
		tmp = i * (y * -j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (t <= -2.4e+152)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (t <= -2.75e+91)
		tmp = Float64(c * Float64(a * j));
	elseif (t <= -2.5e+43)
		tmp = t_1;
	elseif (t <= -2e-262)
		tmp = Float64(a * Float64(c * j));
	elseif (t <= 8e+44)
		tmp = Float64(i * Float64(y * Float64(-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 = b * (t * i);
	tmp = 0.0;
	if (t <= -2.4e+152)
		tmp = a * (t * -x);
	elseif (t <= -2.75e+91)
		tmp = c * (a * j);
	elseif (t <= -2.5e+43)
		tmp = t_1;
	elseif (t <= -2e-262)
		tmp = a * (c * j);
	elseif (t <= 8e+44)
		tmp = i * (y * -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[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e+152], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.75e+91], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.5e+43], t$95$1, If[LessEqual[t, -2e-262], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+44], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.3999999999999999e152

   1. Initial program 60.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in t around -inf 73.6%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 73.6%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(a \cdot x - b \cdot i\right)} \]

      2. neg-mul-1 73.6%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(a \cdot x - b \cdot i\right) \]

      3. *-commutative 73.6%

         \[\leadsto \left(-t\right) \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right) \]

   4. Simplified 73.6%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(a \cdot x - i \cdot b\right)} \]

   5. Taylor expanded in a around inf 46.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 46.5%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

   7. Simplified 46.5%

      \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

   if -2.3999999999999999e152 < t < -2.7499999999999999e91

   1. Initial program 59.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 50.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

   3. Taylor expanded in t around 0 45.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 45.5%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

      2. *-commutative 45.5%

         \[\leadsto \color{blue}{\left(c \cdot a\right)} \cdot j \]

      3. associate-*r* 45.4%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   5. Simplified 45.4%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if -2.7499999999999999e91 < t < -2.5000000000000002e43 or 8.0000000000000007e44 < t

   1. Initial program 70.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 61.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   3. Taylor expanded in i around inf 47.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if -2.5000000000000002e43 < t < -2.00000000000000002e-262

   1. Initial program 84.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 46.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

   3. Taylor expanded in t around 0 41.6%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -2.00000000000000002e-262 < t < 8.0000000000000007e44

   1. Initial program 74.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf 47.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

   3. Taylor expanded in i around inf 35.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 35.6%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. associate-*r* 38.4%

         \[\leadsto -\color{blue}{\left(i \cdot j\right) \cdot y} \]

      3. distribute-rgt-neg-out 38.4%

         \[\leadsto \color{blue}{\left(i \cdot j\right) \cdot \left(-y\right)} \]

      4. associate-*l* 35.6%

         \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(-y\right)\right)} \]

   5. Simplified 35.6%

      \[\leadsto \color{blue}{i \cdot \left(j \cdot \left(-y\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+152}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{+91}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-262}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+44}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 20: 29.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+153}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{+92}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-262}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 1.66 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= t -1.7e+153)
     (* a (* t (- x)))
     (if (<= t -1.6e+92)
       (* c (* a j))
       (if (<= t -2.7e+46)
         t_1
         (if (<= t -2.15e-262)
           (* a (* c j))
           (if (<= t 1.66e+56) (* y (* i (- 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 = b * (t * i);
	double tmp;
	if (t <= -1.7e+153) {
		tmp = a * (t * -x);
	} else if (t <= -1.6e+92) {
		tmp = c * (a * j);
	} else if (t <= -2.7e+46) {
		tmp = t_1;
	} else if (t <= -2.15e-262) {
		tmp = a * (c * j);
	} else if (t <= 1.66e+56) {
		tmp = y * (i * -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 = b * (t * i)
    if (t <= (-1.7d+153)) then
        tmp = a * (t * -x)
    else if (t <= (-1.6d+92)) then
        tmp = c * (a * j)
    else if (t <= (-2.7d+46)) then
        tmp = t_1
    else if (t <= (-2.15d-262)) then
        tmp = a * (c * j)
    else if (t <= 1.66d+56) then
        tmp = y * (i * -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 = b * (t * i);
	double tmp;
	if (t <= -1.7e+153) {
		tmp = a * (t * -x);
	} else if (t <= -1.6e+92) {
		tmp = c * (a * j);
	} else if (t <= -2.7e+46) {
		tmp = t_1;
	} else if (t <= -2.15e-262) {
		tmp = a * (c * j);
	} else if (t <= 1.66e+56) {
		tmp = y * (i * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	tmp = 0
	if t <= -1.7e+153:
		tmp = a * (t * -x)
	elif t <= -1.6e+92:
		tmp = c * (a * j)
	elif t <= -2.7e+46:
		tmp = t_1
	elif t <= -2.15e-262:
		tmp = a * (c * j)
	elif t <= 1.66e+56:
		tmp = y * (i * -j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (t <= -1.7e+153)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (t <= -1.6e+92)
		tmp = Float64(c * Float64(a * j));
	elseif (t <= -2.7e+46)
		tmp = t_1;
	elseif (t <= -2.15e-262)
		tmp = Float64(a * Float64(c * j));
	elseif (t <= 1.66e+56)
		tmp = Float64(y * Float64(i * Float64(-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 = b * (t * i);
	tmp = 0.0;
	if (t <= -1.7e+153)
		tmp = a * (t * -x);
	elseif (t <= -1.6e+92)
		tmp = c * (a * j);
	elseif (t <= -2.7e+46)
		tmp = t_1;
	elseif (t <= -2.15e-262)
		tmp = a * (c * j);
	elseif (t <= 1.66e+56)
		tmp = y * (i * -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[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.7e+153], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.6e+92], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.7e+46], t$95$1, If[LessEqual[t, -2.15e-262], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.66e+56], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.6999999999999999e153

   1. Initial program 60.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in t around -inf 73.6%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 73.6%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(a \cdot x - b \cdot i\right)} \]

      2. neg-mul-1 73.6%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(a \cdot x - b \cdot i\right) \]

      3. *-commutative 73.6%

         \[\leadsto \left(-t\right) \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right) \]

   4. Simplified 73.6%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(a \cdot x - i \cdot b\right)} \]

   5. Taylor expanded in a around inf 46.5%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 46.5%

         \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

   7. Simplified 46.5%

      \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]

   if -1.6999999999999999e153 < t < -1.60000000000000013e92

   1. Initial program 59.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 50.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

   3. Taylor expanded in t around 0 45.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 45.5%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

      2. *-commutative 45.5%

         \[\leadsto \color{blue}{\left(c \cdot a\right)} \cdot j \]

      3. associate-*r* 45.4%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   5. Simplified 45.4%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if -1.60000000000000013e92 < t < -2.7000000000000002e46 or 1.6600000000000001e56 < t

   1. Initial program 68.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 63.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   3. Taylor expanded in i around inf 49.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if -2.7000000000000002e46 < t < -2.1500000000000001e-262

   1. Initial program 84.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 46.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

   3. Taylor expanded in t around 0 41.6%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -2.1500000000000001e-262 < t < 1.6600000000000001e56

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf 47.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

   3. Taylor expanded in i around inf 38.9%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 38.9%

         \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

      2. distribute-rgt-neg-out 38.9%

         \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]

   5. Simplified 38.9%

      \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+153}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{+92}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-262}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 1.66 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 21: 29.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+153}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{+92}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-261}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= t -3.3e+153)
     (* t (* a (- x)))
     (if (<= t -1.12e+92)
       (* c (* a j))
       (if (<= t -3.4e+66)
         t_1
         (if (<= t -3.6e-261)
           (* a (* c j))
           (if (<= t 1.02e+56) (* y (* i (- 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 = b * (t * i);
	double tmp;
	if (t <= -3.3e+153) {
		tmp = t * (a * -x);
	} else if (t <= -1.12e+92) {
		tmp = c * (a * j);
	} else if (t <= -3.4e+66) {
		tmp = t_1;
	} else if (t <= -3.6e-261) {
		tmp = a * (c * j);
	} else if (t <= 1.02e+56) {
		tmp = y * (i * -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 = b * (t * i)
    if (t <= (-3.3d+153)) then
        tmp = t * (a * -x)
    else if (t <= (-1.12d+92)) then
        tmp = c * (a * j)
    else if (t <= (-3.4d+66)) then
        tmp = t_1
    else if (t <= (-3.6d-261)) then
        tmp = a * (c * j)
    else if (t <= 1.02d+56) then
        tmp = y * (i * -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 = b * (t * i);
	double tmp;
	if (t <= -3.3e+153) {
		tmp = t * (a * -x);
	} else if (t <= -1.12e+92) {
		tmp = c * (a * j);
	} else if (t <= -3.4e+66) {
		tmp = t_1;
	} else if (t <= -3.6e-261) {
		tmp = a * (c * j);
	} else if (t <= 1.02e+56) {
		tmp = y * (i * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	tmp = 0
	if t <= -3.3e+153:
		tmp = t * (a * -x)
	elif t <= -1.12e+92:
		tmp = c * (a * j)
	elif t <= -3.4e+66:
		tmp = t_1
	elif t <= -3.6e-261:
		tmp = a * (c * j)
	elif t <= 1.02e+56:
		tmp = y * (i * -j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (t <= -3.3e+153)
		tmp = Float64(t * Float64(a * Float64(-x)));
	elseif (t <= -1.12e+92)
		tmp = Float64(c * Float64(a * j));
	elseif (t <= -3.4e+66)
		tmp = t_1;
	elseif (t <= -3.6e-261)
		tmp = Float64(a * Float64(c * j));
	elseif (t <= 1.02e+56)
		tmp = Float64(y * Float64(i * Float64(-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 = b * (t * i);
	tmp = 0.0;
	if (t <= -3.3e+153)
		tmp = t * (a * -x);
	elseif (t <= -1.12e+92)
		tmp = c * (a * j);
	elseif (t <= -3.4e+66)
		tmp = t_1;
	elseif (t <= -3.6e-261)
		tmp = a * (c * j);
	elseif (t <= 1.02e+56)
		tmp = y * (i * -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[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e+153], N[(t * N[(a * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.12e+92], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.4e+66], t$95$1, If[LessEqual[t, -3.6e-261], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e+56], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.29999999999999994e153

   1. Initial program 60.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in t around -inf 73.6%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 73.6%

         \[\leadsto \color{blue}{\left(-1 \cdot t\right) \cdot \left(a \cdot x - b \cdot i\right)} \]

      2. neg-mul-1 73.6%

         \[\leadsto \color{blue}{\left(-t\right)} \cdot \left(a \cdot x - b \cdot i\right) \]

      3. *-commutative 73.6%

         \[\leadsto \left(-t\right) \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right) \]

   4. Simplified 73.6%

      \[\leadsto \color{blue}{\left(-t\right) \cdot \left(a \cdot x - i \cdot b\right)} \]

   5. Taylor expanded in a around inf 48.7%

      \[\leadsto \left(-t\right) \cdot \color{blue}{\left(a \cdot x\right)} \]

   if -3.29999999999999994e153 < t < -1.1199999999999999e92

   1. Initial program 59.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 50.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

   3. Taylor expanded in t around 0 45.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 45.5%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

      2. *-commutative 45.5%

         \[\leadsto \color{blue}{\left(c \cdot a\right)} \cdot j \]

      3. associate-*r* 45.4%

         \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   5. Simplified 45.4%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j\right)} \]

   if -1.1199999999999999e92 < t < -3.4000000000000003e66 or 1.02e56 < t

   1. Initial program 68.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 63.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   3. Taylor expanded in i around inf 49.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if -3.4000000000000003e66 < t < -3.59999999999999999e-261

   1. Initial program 82.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 44.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

   3. Taylor expanded in t around 0 38.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -3.59999999999999999e-261 < t < 1.02e56

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf 47.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

   3. Taylor expanded in i around inf 38.9%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 38.9%

         \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

      2. distribute-rgt-neg-out 38.9%

         \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]

   5. Simplified 38.9%

      \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+153}:\\ \;\;\;\;t \cdot \left(a \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{+92}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{+66}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-261}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 22: 52.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-250}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+59}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -7.5e+28)
     t_1
     (if (<= b 1.25e-250)
       (* a (- (* c j) (* x t)))
       (if (<= b 6.8e+59) (* j (- (* a 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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7.5e+28) {
		tmp = t_1;
	} else if (b <= 1.25e-250) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 6.8e+59) {
		tmp = j * ((a * 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 = b * ((t * i) - (z * c))
    if (b <= (-7.5d+28)) then
        tmp = t_1
    else if (b <= 1.25d-250) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 6.8d+59) then
        tmp = j * ((a * 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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -7.5e+28) {
		tmp = t_1;
	} else if (b <= 1.25e-250) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 6.8e+59) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -7.5e+28:
		tmp = t_1
	elif b <= 1.25e-250:
		tmp = a * ((c * j) - (x * t))
	elif b <= 6.8e+59:
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -7.5e+28)
		tmp = t_1;
	elseif (b <= 1.25e-250)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 6.8e+59)
		tmp = Float64(j * Float64(Float64(a * 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 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -7.5e+28)
		tmp = t_1;
	elseif (b <= 1.25e-250)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 6.8e+59)
		tmp = j * ((a * 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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.5e+28], t$95$1, If[LessEqual[b, 1.25e-250], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.8e+59], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.4999999999999998e28 or 6.80000000000000012e59 < b

   1. Initial program 77.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 68.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -7.4999999999999998e28 < b < 1.25000000000000007e-250

   1. Initial program 69.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 59.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

   3. Taylor expanded in t around 0 58.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right) + a \cdot \left(c \cdot j\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 58.2%

         \[\leadsto \color{blue}{\left(-a \cdot \left(t \cdot x\right)\right)} + a \cdot \left(c \cdot j\right) \]

      2. *-commutative 58.2%

         \[\leadsto \left(-a \cdot \color{blue}{\left(x \cdot t\right)}\right) + a \cdot \left(c \cdot j\right) \]

      3. distribute-rgt-neg-in 58.2%

         \[\leadsto \color{blue}{a \cdot \left(-x \cdot t\right)} + a \cdot \left(c \cdot j\right) \]

      4. mul-1-neg 58.2%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(x \cdot t\right)\right)} + a \cdot \left(c \cdot j\right) \]

      5. *-commutative 58.2%

         \[\leadsto a \cdot \left(-1 \cdot \color{blue}{\left(t \cdot x\right)}\right) + a \cdot \left(c \cdot j\right) \]

      6. distribute-lft-in 59.4%

         \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

      7. +-commutative 59.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      8. associate-*r* 59.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-1 \cdot t\right) \cdot x}\right) \]

      9. neg-mul-1 59.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t\right)} \cdot x\right) \]

      10. cancel-sign-sub-inv 59.4%

          \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      11. *-commutative 59.4%

          \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 59.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   if 1.25000000000000007e-250 < b < 6.80000000000000012e59

   1. Initial program 68.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. flip-- 58.4%

         \[\leadsto \left(x \cdot \color{blue}{\frac{\left(y \cdot z\right) \cdot \left(y \cdot z\right) - \left(t \cdot a\right) \cdot \left(t \cdot a\right)}{y \cdot z + t \cdot a}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. clear-num 58.4%

         \[\leadsto \left(x \cdot \color{blue}{\frac{1}{\frac{y \cdot z + t \cdot a}{\left(y \cdot z\right) \cdot \left(y \cdot z\right) - \left(t \cdot a\right) \cdot \left(t \cdot a\right)}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. un-div-inv 58.5%

         \[\leadsto \left(\color{blue}{\frac{x}{\frac{y \cdot z + t \cdot a}{\left(y \cdot z\right) \cdot \left(y \cdot z\right) - \left(t \cdot a\right) \cdot \left(t \cdot a\right)}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. clear-num 58.4%

         \[\leadsto \left(\frac{x}{\color{blue}{\frac{1}{\frac{\left(y \cdot z\right) \cdot \left(y \cdot z\right) - \left(t \cdot a\right) \cdot \left(t \cdot a\right)}{y \cdot z + t \cdot a}}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. flip-- 68.2%

         \[\leadsto \left(\frac{x}{\frac{1}{\color{blue}{y \cdot z - t \cdot a}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. *-commutative 68.2%

         \[\leadsto \left(\frac{x}{\frac{1}{y \cdot z - \color{blue}{a \cdot t}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. Applied egg-rr 68.2%

      \[\leadsto \left(\color{blue}{\frac{x}{\frac{1}{y \cdot z - a \cdot t}}} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-/r/ 68.3%

         \[\leadsto \left(\color{blue}{\frac{x}{1} \cdot \left(y \cdot z - a \cdot t\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. /-rgt-identity 68.3%

         \[\leadsto \left(\color{blue}{x} \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 68.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - \color{blue}{t \cdot a}\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. sub-neg 68.3%

         \[\leadsto \left(x \cdot \color{blue}{\left(y \cdot z + \left(-t \cdot a\right)\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. distribute-rgt-in 68.3%

         \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(-t \cdot a\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. *-commutative 68.3%

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x + \left(-\color{blue}{a \cdot t}\right) \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. distribute-rgt-neg-in 68.3%

         \[\leadsto \left(\left(\left(y \cdot z\right) \cdot x + \color{blue}{\left(a \cdot \left(-t\right)\right)} \cdot x\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Applied egg-rr 68.3%

      \[\leadsto \left(\color{blue}{\left(\left(y \cdot z\right) \cdot x + \left(a \cdot \left(-t\right)\right) \cdot x\right)} - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in j around inf 54.1%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   7. Step-by-step derivation

      1. *-commutative 54.1%

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{y \cdot i}\right) \]

   8. Simplified 54.1%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+28}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-250}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+59}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 23: 30.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{-220}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* b (* t i))))
   (if (<= t -4.1e+46)
     t_2
     (if (<= t -1.3e-253)
       t_1
       (if (<= t 6.3e-220) (* y (* x z)) (if (<= t 7e+57) 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 = a * (c * j);
	double t_2 = b * (t * i);
	double tmp;
	if (t <= -4.1e+46) {
		tmp = t_2;
	} else if (t <= -1.3e-253) {
		tmp = t_1;
	} else if (t <= 6.3e-220) {
		tmp = y * (x * z);
	} else if (t <= 7e+57) {
		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 = a * (c * j)
    t_2 = b * (t * i)
    if (t <= (-4.1d+46)) then
        tmp = t_2
    else if (t <= (-1.3d-253)) then
        tmp = t_1
    else if (t <= 6.3d-220) then
        tmp = y * (x * z)
    else if (t <= 7d+57) 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 = a * (c * j);
	double t_2 = b * (t * i);
	double tmp;
	if (t <= -4.1e+46) {
		tmp = t_2;
	} else if (t <= -1.3e-253) {
		tmp = t_1;
	} else if (t <= 6.3e-220) {
		tmp = y * (x * z);
	} else if (t <= 7e+57) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	t_2 = b * (t * i)
	tmp = 0
	if t <= -4.1e+46:
		tmp = t_2
	elif t <= -1.3e-253:
		tmp = t_1
	elif t <= 6.3e-220:
		tmp = y * (x * z)
	elif t <= 7e+57:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	t_2 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (t <= -4.1e+46)
		tmp = t_2;
	elseif (t <= -1.3e-253)
		tmp = t_1;
	elseif (t <= 6.3e-220)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 7e+57)
		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 = a * (c * j);
	t_2 = b * (t * i);
	tmp = 0.0;
	if (t <= -4.1e+46)
		tmp = t_2;
	elseif (t <= -1.3e-253)
		tmp = t_1;
	elseif (t <= 6.3e-220)
		tmp = y * (x * z);
	elseif (t <= 7e+57)
		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[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.1e+46], t$95$2, If[LessEqual[t, -1.3e-253], t$95$1, If[LessEqual[t, 6.3e-220], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+57], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.1e46 or 6.9999999999999995e57 < t

   1. Initial program 64.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 54.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   3. Taylor expanded in i around inf 41.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if -4.1e46 < t < -1.3e-253 or 6.30000000000000017e-220 < t < 6.9999999999999995e57

   1. Initial program 76.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 43.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

   3. Taylor expanded in t around 0 36.7%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -1.3e-253 < t < 6.30000000000000017e-220

   1. Initial program 87.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in y around inf 54.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]

   3. Taylor expanded in i around 0 34.9%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+46}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-253}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{-220}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+57}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 24: 30.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+121}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -740000000 \lor \neg \left(b \leq 7.2 \cdot 10^{+57}\right):\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -3.4e+121)
   (* b (* t i))
   (if (or (<= b -740000000.0) (not (<= b 7.2e+57)))
     (* (* z c) (- b))
     (* a (* c 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 <= -3.4e+121) {
		tmp = b * (t * i);
	} else if ((b <= -740000000.0) || !(b <= 7.2e+57)) {
		tmp = (z * c) * -b;
	} else {
		tmp = a * (c * 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 <= (-3.4d+121)) then
        tmp = b * (t * i)
    else if ((b <= (-740000000.0d0)) .or. (.not. (b <= 7.2d+57))) then
        tmp = (z * c) * -b
    else
        tmp = a * (c * 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 <= -3.4e+121) {
		tmp = b * (t * i);
	} else if ((b <= -740000000.0) || !(b <= 7.2e+57)) {
		tmp = (z * c) * -b;
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -3.4e+121:
		tmp = b * (t * i)
	elif (b <= -740000000.0) or not (b <= 7.2e+57):
		tmp = (z * c) * -b
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -3.4e+121)
		tmp = Float64(b * Float64(t * i));
	elseif ((b <= -740000000.0) || !(b <= 7.2e+57))
		tmp = Float64(Float64(z * c) * Float64(-b));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -3.4e+121)
		tmp = b * (t * i);
	elseif ((b <= -740000000.0) || ~((b <= 7.2e+57)))
		tmp = (z * c) * -b;
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -3.4e+121], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -740000000.0], N[Not[LessEqual[b, 7.2e+57]], $MachinePrecision]], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.4000000000000001e121

   1. Initial program 74.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 71.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   3. Taylor expanded in i around inf 48.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if -3.4000000000000001e121 < b < -7.4e8 or 7.2000000000000005e57 < b

   1. Initial program 79.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 63.1%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   3. Taylor expanded in i around 0 40.7%

      \[\leadsto b \cdot \color{blue}{\left(-1 \cdot \left(c \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg 40.7%

         \[\leadsto b \cdot \color{blue}{\left(-c \cdot z\right)} \]

      2. distribute-rgt-neg-out 40.7%

         \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(-z\right)\right)} \]

   5. Simplified 40.7%

      \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(-z\right)\right)} \]

   if -7.4e8 < b < 7.2000000000000005e57

   1. Initial program 68.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 52.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

   3. Taylor expanded in t around 0 33.7%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+121}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -740000000 \lor \neg \left(b \leq 7.2 \cdot 10^{+57}\right):\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 25: 31.1% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+43} \lor \neg \left(t \leq 3.1 \cdot 10^{+59}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -4.3e+43) (not (<= t 3.1e+59))) (* b (* t i)) (* a (* c 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 <= -4.3e+43) || !(t <= 3.1e+59)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * 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 <= (-4.3d+43)) .or. (.not. (t <= 3.1d+59))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * 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 <= -4.3e+43) || !(t <= 3.1e+59)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -4.3e+43) or not (t <= 3.1e+59):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -4.3e+43) || !(t <= 3.1e+59))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -4.3e+43) || ~((t <= 3.1e+59)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -4.3e+43], N[Not[LessEqual[t, 3.1e+59]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.3e43 or 3.10000000000000015e59 < t

   1. Initial program 64.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in b around inf 54.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   3. Taylor expanded in i around inf 41.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if -4.3e43 < t < 3.10000000000000015e59

   1. Initial program 78.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. Taylor expanded in a around inf 39.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

   3. Taylor expanded in t around 0 33.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+43} \lor \neg \left(t \leq 3.1 \cdot 10^{+59}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 26: 23.2% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

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 * (c * j)
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 * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.6%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

2. Taylor expanded in a around inf 40.5%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]

3. Taylor expanded in t around 0 25.6%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

4. Final simplification 25.6%

   \[\leadsto a \cdot \left(c \cdot j\right) \]

Developer target: 59.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) 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 * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - 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 * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - 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 * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - 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(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - 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 * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - 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[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))