Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 74.6% → 82.6%

Time: 38.4s

Alternatives: 30

Speedup: 0.5×

• 58.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 74.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.6% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.2%

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

      1. +-commutative 93.2%

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

      2. fma-def 93.2%

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

      3. *-commutative 93.2%

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

      4. *-commutative 93.2%

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

      5. cancel-sign-sub-inv 93.2%

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

      6. cancel-sign-sub 93.2%

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

      7. remove-double-neg 93.2%

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

      8. *-commutative 93.2%

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

      9. *-commutative 93.2%

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

   3. Simplified 93.2%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in t around inf 53.6%

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

      1. *-commutative 53.6%

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

      2. mul-1-neg 53.6%

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

      3. unsub-neg 53.6%

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

   4. Simplified 53.6%

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

4. Final simplification 85.9%

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

Alternative 2: 82.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.2%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in t around inf 53.6%

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

      1. *-commutative 53.6%

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

      2. mul-1-neg 53.6%

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

      3. unsub-neg 53.6%

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

   4. Simplified 53.6%

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

4. Final simplification 85.9%

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

Alternative 3: 67.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_4 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_5 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -4.85 \cdot 10^{+92}:\\ \;\;\;\;t_5 + t_2\\ \mathbf{elif}\;x \leq -880000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-17}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+96}:\\ \;\;\;\;t_2 + t_3\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+143}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+153}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* y (- (* x z) (* i j))) (* c (- (* t j) (* z b)))))
        (t_2 (* j (- (* t c) (* y i))))
        (t_3 (* b (- (* a i) (* z c))))
        (t_4 (* t (- (* c j) (* x a))))
        (t_5 (* x (- (* y z) (* t a)))))
   (if (<= x -4.85e+92)
     (+ t_5 t_2)
     (if (<= x -880000000000.0)
       t_1
       (if (<= x -2e-17)
         t_4
         (if (<= x -3e-171)
           t_1
           (if (<= x 3.7e+96)
             (+ t_2 t_3)
             (if (<= x 7.2e+143) t_4 (if (<= x 2e+153) t_3 t_5)))))))))

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 * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = b * ((a * i) - (z * c));
	double t_4 = t * ((c * j) - (x * a));
	double t_5 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4.85e+92) {
		tmp = t_5 + t_2;
	} else if (x <= -880000000000.0) {
		tmp = t_1;
	} else if (x <= -2e-17) {
		tmp = t_4;
	} else if (x <= -3e-171) {
		tmp = t_1;
	} else if (x <= 3.7e+96) {
		tmp = t_2 + t_3;
	} else if (x <= 7.2e+143) {
		tmp = t_4;
	} else if (x <= 2e+153) {
		tmp = t_3;
	} else {
		tmp = t_5;
	}
	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 = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)))
    t_2 = j * ((t * c) - (y * i))
    t_3 = b * ((a * i) - (z * c))
    t_4 = t * ((c * j) - (x * a))
    t_5 = x * ((y * z) - (t * a))
    if (x <= (-4.85d+92)) then
        tmp = t_5 + t_2
    else if (x <= (-880000000000.0d0)) then
        tmp = t_1
    else if (x <= (-2d-17)) then
        tmp = t_4
    else if (x <= (-3d-171)) then
        tmp = t_1
    else if (x <= 3.7d+96) then
        tmp = t_2 + t_3
    else if (x <= 7.2d+143) then
        tmp = t_4
    else if (x <= 2d+153) then
        tmp = t_3
    else
        tmp = t_5
    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 = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = b * ((a * i) - (z * c));
	double t_4 = t * ((c * j) - (x * a));
	double t_5 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4.85e+92) {
		tmp = t_5 + t_2;
	} else if (x <= -880000000000.0) {
		tmp = t_1;
	} else if (x <= -2e-17) {
		tmp = t_4;
	} else if (x <= -3e-171) {
		tmp = t_1;
	} else if (x <= 3.7e+96) {
		tmp = t_2 + t_3;
	} else if (x <= 7.2e+143) {
		tmp = t_4;
	} else if (x <= 2e+153) {
		tmp = t_3;
	} else {
		tmp = t_5;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)))
	t_2 = j * ((t * c) - (y * i))
	t_3 = b * ((a * i) - (z * c))
	t_4 = t * ((c * j) - (x * a))
	t_5 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -4.85e+92:
		tmp = t_5 + t_2
	elif x <= -880000000000.0:
		tmp = t_1
	elif x <= -2e-17:
		tmp = t_4
	elif x <= -3e-171:
		tmp = t_1
	elif x <= 3.7e+96:
		tmp = t_2 + t_3
	elif x <= 7.2e+143:
		tmp = t_4
	elif x <= 2e+153:
		tmp = t_3
	else:
		tmp = t_5
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(c * Float64(Float64(t * j) - Float64(z * b))))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_3 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_4 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_5 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -4.85e+92)
		tmp = Float64(t_5 + t_2);
	elseif (x <= -880000000000.0)
		tmp = t_1;
	elseif (x <= -2e-17)
		tmp = t_4;
	elseif (x <= -3e-171)
		tmp = t_1;
	elseif (x <= 3.7e+96)
		tmp = Float64(t_2 + t_3);
	elseif (x <= 7.2e+143)
		tmp = t_4;
	elseif (x <= 2e+153)
		tmp = t_3;
	else
		tmp = t_5;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)));
	t_2 = j * ((t * c) - (y * i));
	t_3 = b * ((a * i) - (z * c));
	t_4 = t * ((c * j) - (x * a));
	t_5 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -4.85e+92)
		tmp = t_5 + t_2;
	elseif (x <= -880000000000.0)
		tmp = t_1;
	elseif (x <= -2e-17)
		tmp = t_4;
	elseif (x <= -3e-171)
		tmp = t_1;
	elseif (x <= 3.7e+96)
		tmp = t_2 + t_3;
	elseif (x <= 7.2e+143)
		tmp = t_4;
	elseif (x <= 2e+153)
		tmp = t_3;
	else
		tmp = t_5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.85e+92], N[(t$95$5 + t$95$2), $MachinePrecision], If[LessEqual[x, -880000000000.0], t$95$1, If[LessEqual[x, -2e-17], t$95$4, If[LessEqual[x, -3e-171], t$95$1, If[LessEqual[x, 3.7e+96], N[(t$95$2 + t$95$3), $MachinePrecision], If[LessEqual[x, 7.2e+143], t$95$4, If[LessEqual[x, 2e+153], t$95$3, t$95$5]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -4.84999999999999983e92

   1. Initial program 70.3%

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

   2. Taylor expanded in b around 0 77.9%

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

   if -4.84999999999999983e92 < x < -8.8e11 or -2.00000000000000014e-17 < x < -3e-171

   1. Initial program 80.0%

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

   2. Taylor expanded in t around 0 82.0%

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

   3. Taylor expanded in a around 0 90.9%

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

      1. cancel-sign-sub-inv 90.9%

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

      2. +-commutative 90.9%

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

      3. associate-+l+ 90.9%

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

      4. mul-1-neg 90.9%

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

      5. distribute-rgt-neg-in 90.9%

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

      6. mul-1-neg 90.9%

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

      7. distribute-lft-in 90.9%

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

      8. mul-1-neg 90.9%

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

      9. unsub-neg 90.9%

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

      10. *-commutative 90.9%

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

      11. *-commutative 90.9%

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

      12. distribute-lft-neg-in 90.9%

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

      13. distribute-rgt-neg-in 90.9%

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

      14. mul-1-neg 90.9%

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

      15. distribute-lft-in 92.8%

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

   5. Simplified 92.8%

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

   if -8.8e11 < x < -2.00000000000000014e-17 or 3.69999999999999991e96 < x < 7.1999999999999998e143

   1. Initial program 65.7%

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

   2. Taylor expanded in t around inf 94.1%

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

      1. *-commutative 94.1%

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

      2. mul-1-neg 94.1%

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

      3. unsub-neg 94.1%

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

   4. Simplified 94.1%

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

   if -3e-171 < x < 3.69999999999999991e96

   1. Initial program 81.1%

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

   2. Taylor expanded in x around 0 79.3%

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

   if 7.1999999999999998e143 < x < 2e153

   1. Initial program 75.0%

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

      1. associate-+l- 75.0%

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

      2. sub-neg 75.0%

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

      3. sub-neg 75.0%

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

      4. *-commutative 75.0%

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

      5. fma-neg 75.0%

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

      6. *-commutative 75.0%

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

      7. *-commutative 75.0%

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

      8. fma-neg 75.0%

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

      9. distribute-lft-neg-out 75.0%

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

      10. *-commutative 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in b around inf 100.0%

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

   if 2e153 < x

   1. Initial program 64.9%

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

   2. Taylor expanded in x around inf 75.9%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.85 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -880000000000:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-17}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+96}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+143}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+153}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]

Alternative 4: 65.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.4 \cdot 10^{+99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -0.0027:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+220}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* y (- (* x z) (* i j))) (* c (- (* t j) (* z b)))))
        (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -3.4e+99)
     t_2
     (if (<= a -0.0027)
       t_1
       (if (<= a -1.8e-32)
         t_2
         (if (<= a 1.05e+63)
           t_1
           (if (<= a 3.6e+220)
             (- (* x (- (* y z) (* t a))) (* c (* z b)))
             t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -3.4e+99) {
		tmp = t_2;
	} else if (a <= -0.0027) {
		tmp = t_1;
	} else if (a <= -1.8e-32) {
		tmp = t_2;
	} else if (a <= 1.05e+63) {
		tmp = t_1;
	} else if (a <= 3.6e+220) {
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-3.4d+99)) then
        tmp = t_2
    else if (a <= (-0.0027d0)) then
        tmp = t_1
    else if (a <= (-1.8d-32)) then
        tmp = t_2
    else if (a <= 1.05d+63) then
        tmp = t_1
    else if (a <= 3.6d+220) then
        tmp = (x * ((y * z) - (t * a))) - (c * (z * b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -3.4e+99) {
		tmp = t_2;
	} else if (a <= -0.0027) {
		tmp = t_1;
	} else if (a <= -1.8e-32) {
		tmp = t_2;
	} else if (a <= 1.05e+63) {
		tmp = t_1;
	} else if (a <= 3.6e+220) {
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -3.4e+99:
		tmp = t_2
	elif a <= -0.0027:
		tmp = t_1
	elif a <= -1.8e-32:
		tmp = t_2
	elif a <= 1.05e+63:
		tmp = t_1
	elif a <= 3.6e+220:
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(c * Float64(Float64(t * j) - Float64(z * b))))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.4e+99)
		tmp = t_2;
	elseif (a <= -0.0027)
		tmp = t_1;
	elseif (a <= -1.8e-32)
		tmp = t_2;
	elseif (a <= 1.05e+63)
		tmp = t_1;
	elseif (a <= 3.6e+220)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(c * Float64(z * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -3.4e+99)
		tmp = t_2;
	elseif (a <= -0.0027)
		tmp = t_1;
	elseif (a <= -1.8e-32)
		tmp = t_2;
	elseif (a <= 1.05e+63)
		tmp = t_1;
	elseif (a <= 3.6e+220)
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.4e+99], t$95$2, If[LessEqual[a, -0.0027], t$95$1, If[LessEqual[a, -1.8e-32], t$95$2, If[LessEqual[a, 1.05e+63], t$95$1, If[LessEqual[a, 3.6e+220], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.39999999999999984e99 or -0.0027000000000000001 < a < -1.79999999999999996e-32 or 3.60000000000000019e220 < a

   1. Initial program 70.4%

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

   2. Taylor expanded in a around inf 78.1%

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

      1. associate-*r* 78.1%

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

      2. neg-mul-1 78.1%

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

      3. cancel-sign-sub 78.1%

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

      4. +-commutative 78.1%

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

      5. mul-1-neg 78.1%

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

      6. unsub-neg 78.1%

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

   4. Simplified 78.1%

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

   if -3.39999999999999984e99 < a < -0.0027000000000000001 or -1.79999999999999996e-32 < a < 1.0500000000000001e63

   1. Initial program 81.1%

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

   2. Taylor expanded in t around 0 80.0%

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

   3. Taylor expanded in a around 0 75.1%

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

      1. cancel-sign-sub-inv 75.1%

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

      2. +-commutative 75.1%

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

      3. associate-+l+ 75.1%

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

      4. mul-1-neg 75.1%

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

      5. distribute-rgt-neg-in 75.1%

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

      6. mul-1-neg 75.1%

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

      7. distribute-lft-in 75.7%

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

      8. mul-1-neg 75.7%

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

      9. unsub-neg 75.7%

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

      10. *-commutative 75.7%

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

      11. *-commutative 75.7%

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

      12. distribute-lft-neg-in 75.7%

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

      13. distribute-rgt-neg-in 75.7%

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

      14. mul-1-neg 75.7%

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

      15. distribute-lft-in 76.3%

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

   5. Simplified 76.3%

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

   if 1.0500000000000001e63 < a < 3.60000000000000019e220

   1. Initial program 60.7%

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

   2. Taylor expanded in a around -inf 54.8%

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

   3. Taylor expanded in x around inf 61.9%

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

      1. *-commutative 61.9%

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

      2. mul-1-neg 61.9%

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

      3. distribute-lft-neg-out 61.9%

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

      4. cancel-sign-sub-inv 61.9%

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

      5. *-commutative 61.9%

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

      6. *-commutative 61.9%

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

   5. Simplified 61.9%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+99}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -0.0027:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-32}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+63}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+220}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 5: 70.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_2 + t_1\\ \mathbf{if}\;j \leq -9.2 \cdot 10^{+107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-80}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{-72}:\\ \;\;\;\;t_2 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{+107}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1 - c \cdot \left(z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (+ t_2 t_1)))
   (if (<= j -9.2e+107)
     t_3
     (if (<= j -9.5e-80)
       (+ (* y (- (* x z) (* i j))) (* c (- (* t j) (* z b))))
       (if (<= j 6.4e-72)
         (+ t_2 (* b (- (* a i) (* z c))))
         (if (<= j 5.6e+107) t_3 (- t_1 (* c (* z 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 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + t_1;
	double tmp;
	if (j <= -9.2e+107) {
		tmp = t_3;
	} else if (j <= -9.5e-80) {
		tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)));
	} else if (j <= 6.4e-72) {
		tmp = t_2 + (b * ((a * i) - (z * c)));
	} else if (j <= 5.6e+107) {
		tmp = t_3;
	} else {
		tmp = t_1 - (c * (z * 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    t_3 = t_2 + t_1
    if (j <= (-9.2d+107)) then
        tmp = t_3
    else if (j <= (-9.5d-80)) then
        tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)))
    else if (j <= 6.4d-72) then
        tmp = t_2 + (b * ((a * i) - (z * c)))
    else if (j <= 5.6d+107) then
        tmp = t_3
    else
        tmp = t_1 - (c * (z * 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 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + t_1;
	double tmp;
	if (j <= -9.2e+107) {
		tmp = t_3;
	} else if (j <= -9.5e-80) {
		tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)));
	} else if (j <= 6.4e-72) {
		tmp = t_2 + (b * ((a * i) - (z * c)));
	} else if (j <= 5.6e+107) {
		tmp = t_3;
	} else {
		tmp = t_1 - (c * (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	t_3 = t_2 + t_1
	tmp = 0
	if j <= -9.2e+107:
		tmp = t_3
	elif j <= -9.5e-80:
		tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)))
	elif j <= 6.4e-72:
		tmp = t_2 + (b * ((a * i) - (z * c)))
	elif j <= 5.6e+107:
		tmp = t_3
	else:
		tmp = t_1 - (c * (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(t_2 + t_1)
	tmp = 0.0
	if (j <= -9.2e+107)
		tmp = t_3;
	elseif (j <= -9.5e-80)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(c * Float64(Float64(t * j) - Float64(z * b))));
	elseif (j <= 6.4e-72)
		tmp = Float64(t_2 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (j <= 5.6e+107)
		tmp = t_3;
	else
		tmp = Float64(t_1 - Float64(c * Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	t_3 = t_2 + t_1;
	tmp = 0.0;
	if (j <= -9.2e+107)
		tmp = t_3;
	elseif (j <= -9.5e-80)
		tmp = (y * ((x * z) - (i * j))) + (c * ((t * j) - (z * b)));
	elseif (j <= 6.4e-72)
		tmp = t_2 + (b * ((a * i) - (z * c)));
	elseif (j <= 5.6e+107)
		tmp = t_3;
	else
		tmp = t_1 - (c * (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + t$95$1), $MachinePrecision]}, If[LessEqual[j, -9.2e+107], t$95$3, If[LessEqual[j, -9.5e-80], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.4e-72], N[(t$95$2 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.6e+107], t$95$3, N[(t$95$1 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -9.2000000000000001e107 or 6.39999999999999998e-72 < j < 5.59999999999999969e107

   1. Initial program 80.3%

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

   2. Taylor expanded in b around 0 79.4%

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

   if -9.2000000000000001e107 < j < -9.5000000000000003e-80

   1. Initial program 72.0%

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

   2. Taylor expanded in t around 0 78.0%

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

   3. Taylor expanded in a around 0 74.3%

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

      1. cancel-sign-sub-inv 74.3%

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

      2. +-commutative 74.3%

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

      3. associate-+l+ 74.3%

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

      4. mul-1-neg 74.3%

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

      5. distribute-rgt-neg-in 74.3%

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

      6. mul-1-neg 74.3%

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

      7. distribute-lft-in 74.3%

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

      8. mul-1-neg 74.3%

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

      9. unsub-neg 74.3%

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

      10. *-commutative 74.3%

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

      11. *-commutative 74.3%

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

      12. distribute-lft-neg-in 74.3%

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

      13. distribute-rgt-neg-in 74.3%

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

      14. mul-1-neg 74.3%

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

      15. distribute-lft-in 74.3%

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

   5. Simplified 74.3%

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

   if -9.5000000000000003e-80 < j < 6.39999999999999998e-72

   1. Initial program 79.5%

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

   2. Taylor expanded in j around 0 80.3%

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

   if 5.59999999999999969e107 < j

   1. Initial program 64.8%

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

   2. Taylor expanded in a around -inf 72.9%

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

   3. Taylor expanded in j around -inf 73.3%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -9.2 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-80}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 6.4 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{+107}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \end{array} \]

Alternative 6: 51.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.16 \cdot 10^{+39}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{-216}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 6.3 \cdot 10^{-167}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.9 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq 8.6 \cdot 10^{+91}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a))))
        (t_2 (* c (- (* t j) (* z b))))
        (t_3 (* i (- (* a b) (* y j)))))
   (if (<= i -1.16e+39)
     t_3
     (if (<= i -3.5e-216)
       t_2
       (if (<= i -3.5e-295)
         t_1
         (if (<= i 6.3e-167)
           t_2
           (if (<= i 2.2e-8)
             t_1
             (if (<= i 2.9e+38)
               (* y (- (* x z) (* i j)))
               (if (<= i 8.6e+91) (* a (- (* b i) (* x t))) 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 = t * ((c * j) - (x * a));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.16e+39) {
		tmp = t_3;
	} else if (i <= -3.5e-216) {
		tmp = t_2;
	} else if (i <= -3.5e-295) {
		tmp = t_1;
	} else if (i <= 6.3e-167) {
		tmp = t_2;
	} else if (i <= 2.2e-8) {
		tmp = t_1;
	} else if (i <= 2.9e+38) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= 8.6e+91) {
		tmp = a * ((b * i) - (x * t));
	} 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 = t * ((c * j) - (x * a))
    t_2 = c * ((t * j) - (z * b))
    t_3 = i * ((a * b) - (y * j))
    if (i <= (-1.16d+39)) then
        tmp = t_3
    else if (i <= (-3.5d-216)) then
        tmp = t_2
    else if (i <= (-3.5d-295)) then
        tmp = t_1
    else if (i <= 6.3d-167) then
        tmp = t_2
    else if (i <= 2.2d-8) then
        tmp = t_1
    else if (i <= 2.9d+38) then
        tmp = y * ((x * z) - (i * j))
    else if (i <= 8.6d+91) then
        tmp = a * ((b * i) - (x * t))
    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 = t * ((c * j) - (x * a));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -1.16e+39) {
		tmp = t_3;
	} else if (i <= -3.5e-216) {
		tmp = t_2;
	} else if (i <= -3.5e-295) {
		tmp = t_1;
	} else if (i <= 6.3e-167) {
		tmp = t_2;
	} else if (i <= 2.2e-8) {
		tmp = t_1;
	} else if (i <= 2.9e+38) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= 8.6e+91) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = c * ((t * j) - (z * b))
	t_3 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -1.16e+39:
		tmp = t_3
	elif i <= -3.5e-216:
		tmp = t_2
	elif i <= -3.5e-295:
		tmp = t_1
	elif i <= 6.3e-167:
		tmp = t_2
	elif i <= 2.2e-8:
		tmp = t_1
	elif i <= 2.9e+38:
		tmp = y * ((x * z) - (i * j))
	elif i <= 8.6e+91:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_3 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.16e+39)
		tmp = t_3;
	elseif (i <= -3.5e-216)
		tmp = t_2;
	elseif (i <= -3.5e-295)
		tmp = t_1;
	elseif (i <= 6.3e-167)
		tmp = t_2;
	elseif (i <= 2.2e-8)
		tmp = t_1;
	elseif (i <= 2.9e+38)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (i <= 8.6e+91)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = c * ((t * j) - (z * b));
	t_3 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.16e+39)
		tmp = t_3;
	elseif (i <= -3.5e-216)
		tmp = t_2;
	elseif (i <= -3.5e-295)
		tmp = t_1;
	elseif (i <= 6.3e-167)
		tmp = t_2;
	elseif (i <= 2.2e-8)
		tmp = t_1;
	elseif (i <= 2.9e+38)
		tmp = y * ((x * z) - (i * j));
	elseif (i <= 8.6e+91)
		tmp = a * ((b * i) - (x * t));
	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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.16e+39], t$95$3, If[LessEqual[i, -3.5e-216], t$95$2, If[LessEqual[i, -3.5e-295], t$95$1, If[LessEqual[i, 6.3e-167], t$95$2, If[LessEqual[i, 2.2e-8], t$95$1, If[LessEqual[i, 2.9e+38], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.6e+91], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.16000000000000003e39 or 8.6000000000000001e91 < i

   1. Initial program 60.7%

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

   2. Taylor expanded in i around inf 66.2%

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

      1. *-commutative 66.2%

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

      2. cancel-sign-sub-inv 66.2%

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

      3. metadata-eval 66.2%

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

      4. *-lft-identity 66.2%

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

      5. +-commutative 66.2%

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

      6. mul-1-neg 66.2%

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

      7. unsub-neg 66.2%

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

   4. Simplified 66.2%

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

   if -1.16000000000000003e39 < i < -3.49999999999999982e-216 or -3.49999999999999988e-295 < i < 6.3000000000000001e-167

   1. Initial program 86.2%

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

   2. Taylor expanded in c around inf 56.9%

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

      1. *-commutative 56.9%

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

   4. Simplified 56.9%

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

   if -3.49999999999999982e-216 < i < -3.49999999999999988e-295 or 6.3000000000000001e-167 < i < 2.1999999999999998e-8

   1. Initial program 91.0%

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

   2. Taylor expanded in t around inf 64.4%

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

      1. *-commutative 64.4%

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

      2. mul-1-neg 64.4%

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

      3. unsub-neg 64.4%

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

   4. Simplified 64.4%

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

   if 2.1999999999999998e-8 < i < 2.90000000000000007e38

   1. Initial program 70.0%

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

   2. Taylor expanded in y around inf 80.3%

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

      1. +-commutative 80.3%

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

      2. mul-1-neg 80.3%

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

      3. unsub-neg 80.3%

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

   4. Simplified 80.3%

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

   if 2.90000000000000007e38 < i < 8.6000000000000001e91

   1. Initial program 83.3%

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

   2. Taylor expanded in a around inf 83.9%

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

      1. associate-*r* 83.9%

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

      2. neg-mul-1 83.9%

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

      3. cancel-sign-sub 83.9%

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

      4. +-commutative 83.9%

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

      5. mul-1-neg 83.9%

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

      6. unsub-neg 83.9%

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

   4. Simplified 83.9%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.16 \cdot 10^{+39}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{-216}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{-295}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 6.3 \cdot 10^{-167}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 2.9 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq 8.6 \cdot 10^{+91}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 7: 67.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+62} \lor \neg \left(b \leq 1.16 \cdot 10^{+148}\right):\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.3e+62) (not (<= b 1.16e+148)))
   (+ (* j (* t c)) (* b (- (* a i) (* z c))))
   (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.3e+62) || !(b <= 1.16e+148)) {
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.3d+62)) .or. (.not. (b <= 1.16d+148))) then
        tmp = (j * (t * c)) + (b * ((a * i) - (z * c)))
    else
        tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.3e+62) || !(b <= 1.16e+148)) {
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.3e+62) or not (b <= 1.16e+148):
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)))
	else:
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.3e+62) || !(b <= 1.16e+148))
		tmp = Float64(Float64(j * Float64(t * c)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.3e+62) || ~((b <= 1.16e+148)))
		tmp = (j * (t * c)) + (b * ((a * i) - (z * c)));
	else
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.3e+62], N[Not[LessEqual[b, 1.16e+148]], $MachinePrecision]], N[(N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.29999999999999992e62 or 1.1599999999999999e148 < b

   1. Initial program 74.5%

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

   2. Taylor expanded in x around 0 72.6%

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

   3. Taylor expanded in c around inf 72.6%

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

   if -1.29999999999999992e62 < b < 1.1599999999999999e148

   1. Initial program 77.0%

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

   2. Taylor expanded in b around 0 72.0%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{+62} \lor \neg \left(b \leq 1.16 \cdot 10^{+148}\right):\\ \;\;\;\;j \cdot \left(t \cdot c\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 8: 43.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-226}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-292}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-128}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -2.9e-44)
     t_2
     (if (<= a -2.5e-226)
       (* j (* i (- y)))
       (if (<= a 2.9e-304)
         t_1
         (if (<= a 6.2e-292)
           (* i (* y (- j)))
           (if (<= a 5.4e-128) (* t (* c j)) (if (<= a 4.9e-55) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -2.9e-44) {
		tmp = t_2;
	} else if (a <= -2.5e-226) {
		tmp = j * (i * -y);
	} else if (a <= 2.9e-304) {
		tmp = t_1;
	} else if (a <= 6.2e-292) {
		tmp = i * (y * -j);
	} else if (a <= 5.4e-128) {
		tmp = t * (c * j);
	} else if (a <= 4.9e-55) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-2.9d-44)) then
        tmp = t_2
    else if (a <= (-2.5d-226)) then
        tmp = j * (i * -y)
    else if (a <= 2.9d-304) then
        tmp = t_1
    else if (a <= 6.2d-292) then
        tmp = i * (y * -j)
    else if (a <= 5.4d-128) then
        tmp = t * (c * j)
    else if (a <= 4.9d-55) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -2.9e-44) {
		tmp = t_2;
	} else if (a <= -2.5e-226) {
		tmp = j * (i * -y);
	} else if (a <= 2.9e-304) {
		tmp = t_1;
	} else if (a <= 6.2e-292) {
		tmp = i * (y * -j);
	} else if (a <= 5.4e-128) {
		tmp = t * (c * j);
	} else if (a <= 4.9e-55) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -2.9e-44:
		tmp = t_2
	elif a <= -2.5e-226:
		tmp = j * (i * -y)
	elif a <= 2.9e-304:
		tmp = t_1
	elif a <= 6.2e-292:
		tmp = i * (y * -j)
	elif a <= 5.4e-128:
		tmp = t * (c * j)
	elif a <= 4.9e-55:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.9e-44)
		tmp = t_2;
	elseif (a <= -2.5e-226)
		tmp = Float64(j * Float64(i * Float64(-y)));
	elseif (a <= 2.9e-304)
		tmp = t_1;
	elseif (a <= 6.2e-292)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (a <= 5.4e-128)
		tmp = Float64(t * Float64(c * j));
	elseif (a <= 4.9e-55)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -2.9e-44)
		tmp = t_2;
	elseif (a <= -2.5e-226)
		tmp = j * (i * -y);
	elseif (a <= 2.9e-304)
		tmp = t_1;
	elseif (a <= 6.2e-292)
		tmp = i * (y * -j);
	elseif (a <= 5.4e-128)
		tmp = t * (c * j);
	elseif (a <= 4.9e-55)
		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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.9e-44], t$95$2, If[LessEqual[a, -2.5e-226], N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.9e-304], t$95$1, If[LessEqual[a, 6.2e-292], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.4e-128], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.9e-55], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.9000000000000001e-44 or 4.90000000000000035e-55 < a

   1. Initial program 69.6%

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

   2. Taylor expanded in a around inf 53.5%

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

      1. associate-*r* 53.5%

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

      2. neg-mul-1 53.5%

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

      3. cancel-sign-sub 53.5%

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

      4. +-commutative 53.5%

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

      5. mul-1-neg 53.5%

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

      6. unsub-neg 53.5%

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

   4. Simplified 53.5%

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

   if -2.9000000000000001e-44 < a < -2.4999999999999999e-226

   1. Initial program 91.5%

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

   2. Taylor expanded in j around inf 58.1%

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

   3. Taylor expanded in c around 0 39.2%

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

      1. mul-1-neg 39.2%

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

      2. distribute-lft-neg-out 39.2%

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

      3. *-commutative 39.2%

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

   5. Simplified 39.2%

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

   if -2.4999999999999999e-226 < a < 2.9e-304 or 5.40000000000000011e-128 < a < 4.90000000000000035e-55

   1. Initial program 71.4%

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

   2. Taylor expanded in x around inf 45.4%

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

   3. Taylor expanded in y around inf 45.5%

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

   if 2.9e-304 < a < 6.1999999999999999e-292

   1. Initial program 99.4%

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

   2. Taylor expanded in x around 0 79.5%

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

   3. Taylor expanded in y around inf 61.0%

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

      1. associate-*r* 60.4%

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

      2. *-commutative 60.4%

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

      3. associate-*r* 61.1%

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

      4. associate-*r* 61.1%

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

      5. neg-mul-1 61.1%

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

   5. Simplified 61.1%

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

   if 6.1999999999999999e-292 < a < 5.40000000000000011e-128

   1. Initial program 82.6%

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

   2. Taylor expanded in t around inf 47.2%

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

      1. *-commutative 47.2%

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

      2. mul-1-neg 47.2%

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

      3. unsub-neg 47.2%

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

   4. Simplified 47.2%

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

   5. Taylor expanded in c around inf 44.0%

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

      1. *-commutative 44.0%

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

      2. associate-*l* 47.2%

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

   7. Simplified 47.2%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.9 \cdot 10^{-44}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-226}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-304}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-292}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-128}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-55}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]

Alternative 9: 60.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(z \cdot b\right)\\ t_2 := y \cdot \left(x \cdot z\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{if}\;j \leq -1.7 \cdot 10^{-114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 7.6 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - t_1\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+99}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* z b))) (t_2 (- (* y (* x z)) (* j (- (* y i) (* t c))))))
   (if (<= j -1.7e-114)
     t_2
     (if (<= j 7.6e-83)
       (- (* x (- (* y z) (* t a))) t_1)
       (if (<= j 4.2e+99) t_2 (- (* j (- (* t c) (* y i))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (z * b);
	double t_2 = (y * (x * z)) - (j * ((y * i) - (t * c)));
	double tmp;
	if (j <= -1.7e-114) {
		tmp = t_2;
	} else if (j <= 7.6e-83) {
		tmp = (x * ((y * z) - (t * a))) - t_1;
	} else if (j <= 4.2e+99) {
		tmp = t_2;
	} else {
		tmp = (j * ((t * c) - (y * i))) - 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) :: t_2
    real(8) :: tmp
    t_1 = c * (z * b)
    t_2 = (y * (x * z)) - (j * ((y * i) - (t * c)))
    if (j <= (-1.7d-114)) then
        tmp = t_2
    else if (j <= 7.6d-83) then
        tmp = (x * ((y * z) - (t * a))) - t_1
    else if (j <= 4.2d+99) then
        tmp = t_2
    else
        tmp = (j * ((t * c) - (y * i))) - 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 = c * (z * b);
	double t_2 = (y * (x * z)) - (j * ((y * i) - (t * c)));
	double tmp;
	if (j <= -1.7e-114) {
		tmp = t_2;
	} else if (j <= 7.6e-83) {
		tmp = (x * ((y * z) - (t * a))) - t_1;
	} else if (j <= 4.2e+99) {
		tmp = t_2;
	} else {
		tmp = (j * ((t * c) - (y * i))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (z * b)
	t_2 = (y * (x * z)) - (j * ((y * i) - (t * c)))
	tmp = 0
	if j <= -1.7e-114:
		tmp = t_2
	elif j <= 7.6e-83:
		tmp = (x * ((y * z) - (t * a))) - t_1
	elif j <= 4.2e+99:
		tmp = t_2
	else:
		tmp = (j * ((t * c) - (y * i))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(z * b))
	t_2 = Float64(Float64(y * Float64(x * z)) - Float64(j * Float64(Float64(y * i) - Float64(t * c))))
	tmp = 0.0
	if (j <= -1.7e-114)
		tmp = t_2;
	elseif (j <= 7.6e-83)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - t_1);
	elseif (j <= 4.2e+99)
		tmp = t_2;
	else
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (z * b);
	t_2 = (y * (x * z)) - (j * ((y * i) - (t * c)));
	tmp = 0.0;
	if (j <= -1.7e-114)
		tmp = t_2;
	elseif (j <= 7.6e-83)
		tmp = (x * ((y * z) - (t * a))) - t_1;
	elseif (j <= 4.2e+99)
		tmp = t_2;
	else
		tmp = (j * ((t * c) - (y * i))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.7e-114], t$95$2, If[LessEqual[j, 7.6e-83], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[j, 4.2e+99], t$95$2, N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.69999999999999991e-114 or 7.59999999999999953e-83 < j < 4.2000000000000002e99

   1. Initial program 79.9%

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

   2. Taylor expanded in b around 0 73.0%

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

   3. Taylor expanded in a around 0 65.5%

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

   if -1.69999999999999991e-114 < j < 7.59999999999999953e-83

   1. Initial program 77.9%

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

   2. Taylor expanded in a around -inf 70.2%

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

   3. Taylor expanded in x around inf 67.1%

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

      1. *-commutative 67.1%

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

      2. mul-1-neg 67.1%

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

      3. distribute-lft-neg-out 67.1%

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

      4. cancel-sign-sub-inv 67.1%

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

      5. *-commutative 67.1%

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

      6. *-commutative 67.1%

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

   5. Simplified 67.1%

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

   if 4.2000000000000002e99 < j

   1. Initial program 63.5%

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

   2. Taylor expanded in a around -inf 73.4%

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

   3. Taylor expanded in j around -inf 71.8%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;j \leq 7.6 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq 4.2 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - c \cdot \left(z \cdot b\right)\\ \end{array} \]

Alternative 10: 29.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ t_3 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -2.45 \cdot 10^{+90}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -1.42 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{-119}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.85 \cdot 10^{-258}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-129}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))) (t_2 (* x (* y z))) (t_3 (* t (* c j))))
   (if (<= c -2.45e+90)
     t_3
     (if (<= c -1.42e-8)
       t_1
       (if (<= c -4.4e-119)
         (* z (* x y))
         (if (<= c -3.8e-177)
           t_1
           (if (<= c -2.85e-258)
             t_2
             (if (<= c 1.6e-129)
               (* i (* a b))
               (if (<= c 5.2e+53) t_2 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 * (b * i);
	double t_2 = x * (y * z);
	double t_3 = t * (c * j);
	double tmp;
	if (c <= -2.45e+90) {
		tmp = t_3;
	} else if (c <= -1.42e-8) {
		tmp = t_1;
	} else if (c <= -4.4e-119) {
		tmp = z * (x * y);
	} else if (c <= -3.8e-177) {
		tmp = t_1;
	} else if (c <= -2.85e-258) {
		tmp = t_2;
	} else if (c <= 1.6e-129) {
		tmp = i * (a * b);
	} else if (c <= 5.2e+53) {
		tmp = t_2;
	} 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 = a * (b * i)
    t_2 = x * (y * z)
    t_3 = t * (c * j)
    if (c <= (-2.45d+90)) then
        tmp = t_3
    else if (c <= (-1.42d-8)) then
        tmp = t_1
    else if (c <= (-4.4d-119)) then
        tmp = z * (x * y)
    else if (c <= (-3.8d-177)) then
        tmp = t_1
    else if (c <= (-2.85d-258)) then
        tmp = t_2
    else if (c <= 1.6d-129) then
        tmp = i * (a * b)
    else if (c <= 5.2d+53) then
        tmp = t_2
    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 * (b * i);
	double t_2 = x * (y * z);
	double t_3 = t * (c * j);
	double tmp;
	if (c <= -2.45e+90) {
		tmp = t_3;
	} else if (c <= -1.42e-8) {
		tmp = t_1;
	} else if (c <= -4.4e-119) {
		tmp = z * (x * y);
	} else if (c <= -3.8e-177) {
		tmp = t_1;
	} else if (c <= -2.85e-258) {
		tmp = t_2;
	} else if (c <= 1.6e-129) {
		tmp = i * (a * b);
	} else if (c <= 5.2e+53) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	t_2 = x * (y * z)
	t_3 = t * (c * j)
	tmp = 0
	if c <= -2.45e+90:
		tmp = t_3
	elif c <= -1.42e-8:
		tmp = t_1
	elif c <= -4.4e-119:
		tmp = z * (x * y)
	elif c <= -3.8e-177:
		tmp = t_1
	elif c <= -2.85e-258:
		tmp = t_2
	elif c <= 1.6e-129:
		tmp = i * (a * b)
	elif c <= 5.2e+53:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	t_2 = Float64(x * Float64(y * z))
	t_3 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (c <= -2.45e+90)
		tmp = t_3;
	elseif (c <= -1.42e-8)
		tmp = t_1;
	elseif (c <= -4.4e-119)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= -3.8e-177)
		tmp = t_1;
	elseif (c <= -2.85e-258)
		tmp = t_2;
	elseif (c <= 1.6e-129)
		tmp = Float64(i * Float64(a * b));
	elseif (c <= 5.2e+53)
		tmp = t_2;
	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 * (b * i);
	t_2 = x * (y * z);
	t_3 = t * (c * j);
	tmp = 0.0;
	if (c <= -2.45e+90)
		tmp = t_3;
	elseif (c <= -1.42e-8)
		tmp = t_1;
	elseif (c <= -4.4e-119)
		tmp = z * (x * y);
	elseif (c <= -3.8e-177)
		tmp = t_1;
	elseif (c <= -2.85e-258)
		tmp = t_2;
	elseif (c <= 1.6e-129)
		tmp = i * (a * b);
	elseif (c <= 5.2e+53)
		tmp = t_2;
	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[(b * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.45e+90], t$95$3, If[LessEqual[c, -1.42e-8], t$95$1, If[LessEqual[c, -4.4e-119], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.8e-177], t$95$1, If[LessEqual[c, -2.85e-258], t$95$2, If[LessEqual[c, 1.6e-129], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.2e+53], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -2.4500000000000001e90 or 5.19999999999999996e53 < c

   1. Initial program 67.5%

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

   2. Taylor expanded in t around inf 48.4%

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

      1. *-commutative 48.4%

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

      2. mul-1-neg 48.4%

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

      3. unsub-neg 48.4%

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

   4. Simplified 48.4%

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

   5. Taylor expanded in c around inf 39.7%

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

      1. *-commutative 39.7%

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

      2. associate-*l* 41.7%

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

   7. Simplified 41.7%

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

   if -2.4500000000000001e90 < c < -1.41999999999999998e-8 or -4.4000000000000001e-119 < c < -3.80000000000000004e-177

   1. Initial program 70.6%

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

   2. Taylor expanded in a around inf 41.1%

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

      1. associate-*r* 41.1%

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

      2. neg-mul-1 41.1%

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

      3. cancel-sign-sub 41.1%

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

      4. +-commutative 41.1%

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

      5. mul-1-neg 41.1%

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

      6. unsub-neg 41.1%

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

   4. Simplified 41.1%

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

   5. Taylor expanded in i around inf 44.6%

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

   if -1.41999999999999998e-8 < c < -4.4000000000000001e-119

   1. Initial program 88.4%

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

   2. Taylor expanded in x around inf 47.1%

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

   3. Taylor expanded in y around inf 31.9%

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

   4. Taylor expanded in y around 0 31.9%

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

      1. *-commutative 31.9%

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

      2. associate-*l* 39.2%

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

   6. Simplified 39.2%

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

   if -3.80000000000000004e-177 < c < -2.8500000000000001e-258 or 1.6000000000000001e-129 < c < 5.19999999999999996e53

   1. Initial program 85.6%

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

   2. Taylor expanded in x around inf 63.0%

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

   3. Taylor expanded in y around inf 41.5%

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

   if -2.8500000000000001e-258 < c < 1.6000000000000001e-129

   1. Initial program 80.3%

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

   2. Taylor expanded in a around inf 52.4%

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

      1. associate-*r* 52.4%

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

      2. neg-mul-1 52.4%

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

      3. cancel-sign-sub 52.4%

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

      4. +-commutative 52.4%

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

      5. mul-1-neg 52.4%

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

      6. unsub-neg 52.4%

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

   4. Simplified 52.4%

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

   5. Taylor expanded in i around inf 28.3%

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

      1. associate-*r* 30.5%

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

      2. *-commutative 30.5%

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

      3. associate-*r* 34.5%

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

   7. Simplified 34.5%

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

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.45 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -1.42 \cdot 10^{-8}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq -4.4 \cdot 10^{-119}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{-177}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq -2.85 \cdot 10^{-258}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-129}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 11: 47.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -6.8 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-154}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -6.8e-23)
     t_2
     (if (<= c -1e-154)
       (* (* i j) (- y))
       (if (<= c 2e-129)
         t_1
         (if (<= c 2.1e+41) (* x (* y z)) (if (<= c 2.4e+107) 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 * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -6.8e-23) {
		tmp = t_2;
	} else if (c <= -1e-154) {
		tmp = (i * j) * -y;
	} else if (c <= 2e-129) {
		tmp = t_1;
	} else if (c <= 2.1e+41) {
		tmp = x * (y * z);
	} else if (c <= 2.4e+107) {
		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 * ((b * i) - (x * t))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-6.8d-23)) then
        tmp = t_2
    else if (c <= (-1d-154)) then
        tmp = (i * j) * -y
    else if (c <= 2d-129) then
        tmp = t_1
    else if (c <= 2.1d+41) then
        tmp = x * (y * z)
    else if (c <= 2.4d+107) 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 * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -6.8e-23) {
		tmp = t_2;
	} else if (c <= -1e-154) {
		tmp = (i * j) * -y;
	} else if (c <= 2e-129) {
		tmp = t_1;
	} else if (c <= 2.1e+41) {
		tmp = x * (y * z);
	} else if (c <= 2.4e+107) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -6.8e-23:
		tmp = t_2
	elif c <= -1e-154:
		tmp = (i * j) * -y
	elif c <= 2e-129:
		tmp = t_1
	elif c <= 2.1e+41:
		tmp = x * (y * z)
	elif c <= 2.4e+107:
		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(b * i) - Float64(x * t)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -6.8e-23)
		tmp = t_2;
	elseif (c <= -1e-154)
		tmp = Float64(Float64(i * j) * Float64(-y));
	elseif (c <= 2e-129)
		tmp = t_1;
	elseif (c <= 2.1e+41)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 2.4e+107)
		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 * ((b * i) - (x * t));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -6.8e-23)
		tmp = t_2;
	elseif (c <= -1e-154)
		tmp = (i * j) * -y;
	elseif (c <= 2e-129)
		tmp = t_1;
	elseif (c <= 2.1e+41)
		tmp = x * (y * z);
	elseif (c <= 2.4e+107)
		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[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -6.8e-23], t$95$2, If[LessEqual[c, -1e-154], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[c, 2e-129], t$95$1, If[LessEqual[c, 2.1e+41], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.4e+107], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -6.8000000000000001e-23 or 2.4000000000000001e107 < c

   1. Initial program 70.3%

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

   2. Taylor expanded in c around inf 61.4%

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

      1. *-commutative 61.4%

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

   4. Simplified 61.4%

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

   if -6.8000000000000001e-23 < c < -9.9999999999999997e-155

   1. Initial program 87.5%

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

   2. Taylor expanded in j around inf 64.5%

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

   3. Taylor expanded in c around 0 47.9%

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

      1. associate-*r* 48.0%

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

      2. *-commutative 48.0%

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

      3. associate-*r* 51.8%

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

      4. associate-*r* 51.8%

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

      5. neg-mul-1 51.8%

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

   5. Simplified 51.8%

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

   if -9.9999999999999997e-155 < c < 1.9999999999999999e-129 or 2.1e41 < c < 2.4000000000000001e107

   1. Initial program 78.8%

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

   2. Taylor expanded in a around inf 48.9%

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

      1. associate-*r* 48.9%

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

      2. neg-mul-1 48.9%

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

      3. cancel-sign-sub 48.9%

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

      4. +-commutative 48.9%

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

      5. mul-1-neg 48.9%

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

      6. unsub-neg 48.9%

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

   4. Simplified 48.9%

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

   if 1.9999999999999999e-129 < c < 2.1e41

   1. Initial program 81.3%

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

   2. Taylor expanded in x around inf 67.0%

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

   3. Taylor expanded in y around inf 48.7%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.8 \cdot 10^{-23}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -1 \cdot 10^{-154}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-129}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{+107}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 12: 51.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.8 \cdot 10^{+37}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{-218}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -6.5 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-166}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a))))
        (t_2 (* c (- (* t j) (* z b))))
        (t_3 (* i (- (* a b) (* y j)))))
   (if (<= i -2.8e+37)
     t_3
     (if (<= i -7.2e-218)
       t_2
       (if (<= i -6.5e-297)
         t_1
         (if (<= i 2e-166) t_2 (if (<= i 8.2e-14) 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 = t * ((c * j) - (x * a));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.8e+37) {
		tmp = t_3;
	} else if (i <= -7.2e-218) {
		tmp = t_2;
	} else if (i <= -6.5e-297) {
		tmp = t_1;
	} else if (i <= 2e-166) {
		tmp = t_2;
	} else if (i <= 8.2e-14) {
		tmp = 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) :: tmp
    t_1 = t * ((c * j) - (x * a))
    t_2 = c * ((t * j) - (z * b))
    t_3 = i * ((a * b) - (y * j))
    if (i <= (-2.8d+37)) then
        tmp = t_3
    else if (i <= (-7.2d-218)) then
        tmp = t_2
    else if (i <= (-6.5d-297)) then
        tmp = t_1
    else if (i <= 2d-166) then
        tmp = t_2
    else if (i <= 8.2d-14) then
        tmp = 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 = t * ((c * j) - (x * a));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.8e+37) {
		tmp = t_3;
	} else if (i <= -7.2e-218) {
		tmp = t_2;
	} else if (i <= -6.5e-297) {
		tmp = t_1;
	} else if (i <= 2e-166) {
		tmp = t_2;
	} else if (i <= 8.2e-14) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = c * ((t * j) - (z * b))
	t_3 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -2.8e+37:
		tmp = t_3
	elif i <= -7.2e-218:
		tmp = t_2
	elif i <= -6.5e-297:
		tmp = t_1
	elif i <= 2e-166:
		tmp = t_2
	elif i <= 8.2e-14:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_3 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.8e+37)
		tmp = t_3;
	elseif (i <= -7.2e-218)
		tmp = t_2;
	elseif (i <= -6.5e-297)
		tmp = t_1;
	elseif (i <= 2e-166)
		tmp = t_2;
	elseif (i <= 8.2e-14)
		tmp = 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 = t * ((c * j) - (x * a));
	t_2 = c * ((t * j) - (z * b));
	t_3 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.8e+37)
		tmp = t_3;
	elseif (i <= -7.2e-218)
		tmp = t_2;
	elseif (i <= -6.5e-297)
		tmp = t_1;
	elseif (i <= 2e-166)
		tmp = t_2;
	elseif (i <= 8.2e-14)
		tmp = 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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.8e+37], t$95$3, If[LessEqual[i, -7.2e-218], t$95$2, If[LessEqual[i, -6.5e-297], t$95$1, If[LessEqual[i, 2e-166], t$95$2, If[LessEqual[i, 8.2e-14], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -2.7999999999999998e37 or 8.2000000000000004e-14 < i

   1. Initial program 62.6%

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

   2. Taylor expanded in i around inf 63.4%

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

      1. *-commutative 63.4%

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

      2. cancel-sign-sub-inv 63.4%

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

      3. metadata-eval 63.4%

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

      4. *-lft-identity 63.4%

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

      5. +-commutative 63.4%

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

      6. mul-1-neg 63.4%

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

      7. unsub-neg 63.4%

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

   4. Simplified 63.4%

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

   if -2.7999999999999998e37 < i < -7.20000000000000023e-218 or -6.5000000000000002e-297 < i < 2.00000000000000008e-166

   1. Initial program 86.2%

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

   2. Taylor expanded in c around inf 56.9%

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

      1. *-commutative 56.9%

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

   4. Simplified 56.9%

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

   if -7.20000000000000023e-218 < i < -6.5000000000000002e-297 or 2.00000000000000008e-166 < i < 8.2000000000000004e-14

   1. Initial program 91.0%

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

   2. Taylor expanded in t around inf 64.4%

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

      1. *-commutative 64.4%

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

      2. mul-1-neg 64.4%

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

      3. unsub-neg 64.4%

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

   4. Simplified 64.4%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.8 \cdot 10^{+37}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{-218}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -6.5 \cdot 10^{-297}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-166}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 8.2 \cdot 10^{-14}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 13: 60.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.15 \cdot 10^{-114} \lor \neg \left(j \leq 1.12 \cdot 10^{-82}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.15e-114) (not (<= j 1.12e-82)))
   (- (* y (* x z)) (* j (- (* y i) (* t c))))
   (- (* x (- (* y z) (* t a))) (* c (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.15e-114) || !(j <= 1.12e-82)) {
		tmp = (y * (x * z)) - (j * ((y * i) - (t * c)));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (c * (z * 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) :: tmp
    if ((j <= (-1.15d-114)) .or. (.not. (j <= 1.12d-82))) then
        tmp = (y * (x * z)) - (j * ((y * i) - (t * c)))
    else
        tmp = (x * ((y * z) - (t * a))) - (c * (z * 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 tmp;
	if ((j <= -1.15e-114) || !(j <= 1.12e-82)) {
		tmp = (y * (x * z)) - (j * ((y * i) - (t * c)));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1.15e-114) or not (j <= 1.12e-82):
		tmp = (y * (x * z)) - (j * ((y * i) - (t * c)))
	else:
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.15e-114) || !(j <= 1.12e-82))
		tmp = Float64(Float64(y * Float64(x * z)) - Float64(j * Float64(Float64(y * i) - Float64(t * c))));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(c * Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -1.15e-114) || ~((j <= 1.12e-82)))
		tmp = (y * (x * z)) - (j * ((y * i) - (t * c)));
	else
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1.15e-114], N[Not[LessEqual[j, 1.12e-82]], $MachinePrecision]], N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.15e-114 or 1.12e-82 < j

   1. Initial program 75.1%

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

   2. Taylor expanded in b around 0 69.1%

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

   3. Taylor expanded in a around 0 63.9%

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

   if -1.15e-114 < j < 1.12e-82

   1. Initial program 77.9%

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

   2. Taylor expanded in a around -inf 70.2%

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

   3. Taylor expanded in x around inf 67.1%

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

      1. *-commutative 67.1%

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

      2. mul-1-neg 67.1%

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

      3. distribute-lft-neg-out 67.1%

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

      4. cancel-sign-sub-inv 67.1%

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

      5. *-commutative 67.1%

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

      6. *-commutative 67.1%

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

   5. Simplified 67.1%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.15 \cdot 10^{-114} \lor \neg \left(j \leq 1.12 \cdot 10^{-82}\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \end{array} \]

Alternative 14: 58.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.75 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+153}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -1.75e+126)
     t_1
     (if (<= b 1.12e+89)
       (- (* y (* x z)) (* j (- (* y i) (* t c))))
       (if (<= b 3.4e+153) (* i (- (* a b) (* 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 * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.75e+126) {
		tmp = t_1;
	} else if (b <= 1.12e+89) {
		tmp = (y * (x * z)) - (j * ((y * i) - (t * c)));
	} else if (b <= 3.4e+153) {
		tmp = i * ((a * b) - (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 * ((a * i) - (z * c))
    if (b <= (-1.75d+126)) then
        tmp = t_1
    else if (b <= 1.12d+89) then
        tmp = (y * (x * z)) - (j * ((y * i) - (t * c)))
    else if (b <= 3.4d+153) then
        tmp = i * ((a * b) - (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 * ((a * i) - (z * c));
	double tmp;
	if (b <= -1.75e+126) {
		tmp = t_1;
	} else if (b <= 1.12e+89) {
		tmp = (y * (x * z)) - (j * ((y * i) - (t * c)));
	} else if (b <= 3.4e+153) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -1.75e+126:
		tmp = t_1
	elif b <= 1.12e+89:
		tmp = (y * (x * z)) - (j * ((y * i) - (t * c)))
	elif b <= 3.4e+153:
		tmp = i * ((a * b) - (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(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.75e+126)
		tmp = t_1;
	elseif (b <= 1.12e+89)
		tmp = Float64(Float64(y * Float64(x * z)) - Float64(j * Float64(Float64(y * i) - Float64(t * c))));
	elseif (b <= 3.4e+153)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * 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 * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.75e+126)
		tmp = t_1;
	elseif (b <= 1.12e+89)
		tmp = (y * (x * z)) - (j * ((y * i) - (t * c)));
	elseif (b <= 3.4e+153)
		tmp = i * ((a * b) - (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[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.75e+126], t$95$1, If[LessEqual[b, 1.12e+89], N[(N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.4e+153], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.7500000000000001e126 or 3.3999999999999997e153 < b

   1. Initial program 76.5%

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

      1. associate-+l- 76.5%

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

      2. sub-neg 76.5%

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

      3. sub-neg 76.5%

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

      4. *-commutative 76.5%

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

      5. fma-neg 76.5%

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

      6. *-commutative 76.5%

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

      7. *-commutative 76.5%

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

      8. fma-neg 76.5%

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

      9. distribute-lft-neg-out 76.5%

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

      10. *-commutative 76.5%

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

   3. Simplified 76.5%

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

   4. Taylor expanded in b around inf 71.1%

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

   if -1.7500000000000001e126 < b < 1.11999999999999995e89

   1. Initial program 75.1%

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

   2. Taylor expanded in b around 0 71.6%

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

   3. Taylor expanded in a around 0 62.0%

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

   if 1.11999999999999995e89 < b < 3.3999999999999997e153

   1. Initial program 83.2%

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

   2. Taylor expanded in i around inf 73.8%

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

      1. *-commutative 73.8%

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

      2. cancel-sign-sub-inv 73.8%

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

      3. metadata-eval 73.8%

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

      4. *-lft-identity 73.8%

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

      5. +-commutative 73.8%

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

      6. mul-1-neg 73.8%

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

      7. unsub-neg 73.8%

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

   4. Simplified 73.8%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+126}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(x \cdot z\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+153}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 15: 30.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;c \leq -4200000000:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-120}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-177}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq -6.2 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= c -4200000000.0)
     (* z (* c (- b)))
     (if (<= c -2.8e-120)
       (* z (* x y))
       (if (<= c -4e-177)
         (* a (* b i))
         (if (<= c -6.2e-257)
           t_1
           (if (<= c 2.9e-130)
             (* i (* a b))
             (if (<= c 5.8e+54) t_1 (* t (* c 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 * (y * z);
	double tmp;
	if (c <= -4200000000.0) {
		tmp = z * (c * -b);
	} else if (c <= -2.8e-120) {
		tmp = z * (x * y);
	} else if (c <= -4e-177) {
		tmp = a * (b * i);
	} else if (c <= -6.2e-257) {
		tmp = t_1;
	} else if (c <= 2.9e-130) {
		tmp = i * (a * b);
	} else if (c <= 5.8e+54) {
		tmp = t_1;
	} else {
		tmp = t * (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) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (c <= (-4200000000.0d0)) then
        tmp = z * (c * -b)
    else if (c <= (-2.8d-120)) then
        tmp = z * (x * y)
    else if (c <= (-4d-177)) then
        tmp = a * (b * i)
    else if (c <= (-6.2d-257)) then
        tmp = t_1
    else if (c <= 2.9d-130) then
        tmp = i * (a * b)
    else if (c <= 5.8d+54) then
        tmp = t_1
    else
        tmp = t * (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 t_1 = x * (y * z);
	double tmp;
	if (c <= -4200000000.0) {
		tmp = z * (c * -b);
	} else if (c <= -2.8e-120) {
		tmp = z * (x * y);
	} else if (c <= -4e-177) {
		tmp = a * (b * i);
	} else if (c <= -6.2e-257) {
		tmp = t_1;
	} else if (c <= 2.9e-130) {
		tmp = i * (a * b);
	} else if (c <= 5.8e+54) {
		tmp = t_1;
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if c <= -4200000000.0:
		tmp = z * (c * -b)
	elif c <= -2.8e-120:
		tmp = z * (x * y)
	elif c <= -4e-177:
		tmp = a * (b * i)
	elif c <= -6.2e-257:
		tmp = t_1
	elif c <= 2.9e-130:
		tmp = i * (a * b)
	elif c <= 5.8e+54:
		tmp = t_1
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (c <= -4200000000.0)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (c <= -2.8e-120)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= -4e-177)
		tmp = Float64(a * Float64(b * i));
	elseif (c <= -6.2e-257)
		tmp = t_1;
	elseif (c <= 2.9e-130)
		tmp = Float64(i * Float64(a * b));
	elseif (c <= 5.8e+54)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (c <= -4200000000.0)
		tmp = z * (c * -b);
	elseif (c <= -2.8e-120)
		tmp = z * (x * y);
	elseif (c <= -4e-177)
		tmp = a * (b * i);
	elseif (c <= -6.2e-257)
		tmp = t_1;
	elseif (c <= 2.9e-130)
		tmp = i * (a * b);
	elseif (c <= 5.8e+54)
		tmp = t_1;
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4200000000.0], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.8e-120], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -4e-177], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -6.2e-257], t$95$1, If[LessEqual[c, 2.9e-130], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.8e+54], t$95$1, N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -4.2e9

   1. Initial program 66.7%

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

   2. Taylor expanded in c around inf 59.5%

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

      1. *-commutative 59.5%

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

   4. Simplified 59.5%

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

   5. Taylor expanded in t around 0 37.0%

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

      1. mul-1-neg 37.0%

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

      2. *-commutative 37.0%

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

      3. *-commutative 37.0%

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

      4. *-commutative 37.0%

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

      5. associate-*l* 34.3%

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

   7. Simplified 34.3%

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

   if -4.2e9 < c < -2.79999999999999994e-120

   1. Initial program 86.2%

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

   2. Taylor expanded in x around inf 49.2%

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

   3. Taylor expanded in y around inf 35.6%

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

   4. Taylor expanded in y around 0 32.3%

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

      1. *-commutative 32.3%

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

      2. associate-*l* 38.9%

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

   6. Simplified 38.9%

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

   if -2.79999999999999994e-120 < c < -3.99999999999999981e-177

   1. Initial program 64.5%

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

   2. Taylor expanded in a around inf 30.6%

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

      1. associate-*r* 30.6%

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

      2. neg-mul-1 30.6%

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

      3. cancel-sign-sub 30.6%

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

      4. +-commutative 30.6%

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

      5. mul-1-neg 30.6%

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

      6. unsub-neg 30.6%

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

   4. Simplified 30.6%

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

   5. Taylor expanded in i around inf 37.6%

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

   if -3.99999999999999981e-177 < c < -6.20000000000000016e-257 or 2.9e-130 < c < 5.7999999999999997e54

   1. Initial program 85.6%

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

   2. Taylor expanded in x around inf 63.0%

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

   3. Taylor expanded in y around inf 41.5%

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

   if -6.20000000000000016e-257 < c < 2.9e-130

   1. Initial program 80.3%

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

   2. Taylor expanded in a around inf 52.4%

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

      1. associate-*r* 52.4%

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

      2. neg-mul-1 52.4%

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

      3. cancel-sign-sub 52.4%

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

      4. +-commutative 52.4%

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

      5. mul-1-neg 52.4%

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

      6. unsub-neg 52.4%

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

   4. Simplified 52.4%

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

   5. Taylor expanded in i around inf 28.3%

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

      1. associate-*r* 30.5%

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

      2. *-commutative 30.5%

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

      3. associate-*r* 34.5%

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

   7. Simplified 34.5%

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

   if 5.7999999999999997e54 < c

   1. Initial program 71.9%

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

   2. Taylor expanded in t around inf 59.4%

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

      1. *-commutative 59.4%

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

      2. mul-1-neg 59.4%

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

      3. unsub-neg 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in c around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. associate-*l* 52.5%

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

   7. Simplified 52.5%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4200000000:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-120}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-177}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq -6.2 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 16: 51.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -9 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.65 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -9e+36)
     t_2
     (if (<= i -1.65e-223)
       t_1
       (if (<= i -3.5e-257)
         (* a (- (* b i) (* x t)))
         (if (<= i 3e-41) 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 = c * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -9e+36) {
		tmp = t_2;
	} else if (i <= -1.65e-223) {
		tmp = t_1;
	} else if (i <= -3.5e-257) {
		tmp = a * ((b * i) - (x * t));
	} else if (i <= 3e-41) {
		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 = c * ((t * j) - (z * b))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-9d+36)) then
        tmp = t_2
    else if (i <= (-1.65d-223)) then
        tmp = t_1
    else if (i <= (-3.5d-257)) then
        tmp = a * ((b * i) - (x * t))
    else if (i <= 3d-41) 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 = c * ((t * j) - (z * b));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -9e+36) {
		tmp = t_2;
	} else if (i <= -1.65e-223) {
		tmp = t_1;
	} else if (i <= -3.5e-257) {
		tmp = a * ((b * i) - (x * t));
	} else if (i <= 3e-41) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -9e+36:
		tmp = t_2
	elif i <= -1.65e-223:
		tmp = t_1
	elif i <= -3.5e-257:
		tmp = a * ((b * i) - (x * t))
	elif i <= 3e-41:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -9e+36)
		tmp = t_2;
	elseif (i <= -1.65e-223)
		tmp = t_1;
	elseif (i <= -3.5e-257)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (i <= 3e-41)
		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 = c * ((t * j) - (z * b));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -9e+36)
		tmp = t_2;
	elseif (i <= -1.65e-223)
		tmp = t_1;
	elseif (i <= -3.5e-257)
		tmp = a * ((b * i) - (x * t));
	elseif (i <= 3e-41)
		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[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -9e+36], t$95$2, If[LessEqual[i, -1.65e-223], t$95$1, If[LessEqual[i, -3.5e-257], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3e-41], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -8.99999999999999994e36 or 2.99999999999999989e-41 < i

   1. Initial program 64.7%

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

   2. Taylor expanded in i around inf 61.1%

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

      1. *-commutative 61.1%

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

      2. cancel-sign-sub-inv 61.1%

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

      3. metadata-eval 61.1%

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

      4. *-lft-identity 61.1%

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

      5. +-commutative 61.1%

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

      6. mul-1-neg 61.1%

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

      7. unsub-neg 61.1%

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

   4. Simplified 61.1%

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

   if -8.99999999999999994e36 < i < -1.64999999999999997e-223 or -3.50000000000000029e-257 < i < 2.99999999999999989e-41

   1. Initial program 88.0%

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

   2. Taylor expanded in c around inf 53.8%

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

      1. *-commutative 53.8%

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

   4. Simplified 53.8%

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

   if -1.64999999999999997e-223 < i < -3.50000000000000029e-257

   1. Initial program 99.7%

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

   2. Taylor expanded in a around inf 83.4%

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

      1. associate-*r* 83.4%

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

      2. neg-mul-1 83.4%

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

      3. cancel-sign-sub 83.4%

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

      4. +-commutative 83.4%

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

      5. mul-1-neg 83.4%

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

      6. unsub-neg 83.4%

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

   4. Simplified 83.4%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9 \cdot 10^{+36}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.65 \cdot 10^{-223}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{-257}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-41}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]

Alternative 17: 30.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-176}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-60}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))) (t_2 (* t (* c j))))
   (if (<= t -2.2e+94)
     t_2
     (if (<= t -9.8e-176)
       (* a (* b i))
       (if (<= t 1.35e-276)
         t_1
         (if (<= t 5.2e-60) (* i (* a b)) (if (<= t 6.9e+72) 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 = y * (x * z);
	double t_2 = t * (c * j);
	double tmp;
	if (t <= -2.2e+94) {
		tmp = t_2;
	} else if (t <= -9.8e-176) {
		tmp = a * (b * i);
	} else if (t <= 1.35e-276) {
		tmp = t_1;
	} else if (t <= 5.2e-60) {
		tmp = i * (a * b);
	} else if (t <= 6.9e+72) {
		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 = y * (x * z)
    t_2 = t * (c * j)
    if (t <= (-2.2d+94)) then
        tmp = t_2
    else if (t <= (-9.8d-176)) then
        tmp = a * (b * i)
    else if (t <= 1.35d-276) then
        tmp = t_1
    else if (t <= 5.2d-60) then
        tmp = i * (a * b)
    else if (t <= 6.9d+72) 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 = y * (x * z);
	double t_2 = t * (c * j);
	double tmp;
	if (t <= -2.2e+94) {
		tmp = t_2;
	} else if (t <= -9.8e-176) {
		tmp = a * (b * i);
	} else if (t <= 1.35e-276) {
		tmp = t_1;
	} else if (t <= 5.2e-60) {
		tmp = i * (a * b);
	} else if (t <= 6.9e+72) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	t_2 = t * (c * j)
	tmp = 0
	if t <= -2.2e+94:
		tmp = t_2
	elif t <= -9.8e-176:
		tmp = a * (b * i)
	elif t <= 1.35e-276:
		tmp = t_1
	elif t <= 5.2e-60:
		tmp = i * (a * b)
	elif t <= 6.9e+72:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	t_2 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (t <= -2.2e+94)
		tmp = t_2;
	elseif (t <= -9.8e-176)
		tmp = Float64(a * Float64(b * i));
	elseif (t <= 1.35e-276)
		tmp = t_1;
	elseif (t <= 5.2e-60)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 6.9e+72)
		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 = y * (x * z);
	t_2 = t * (c * j);
	tmp = 0.0;
	if (t <= -2.2e+94)
		tmp = t_2;
	elseif (t <= -9.8e-176)
		tmp = a * (b * i);
	elseif (t <= 1.35e-276)
		tmp = t_1;
	elseif (t <= 5.2e-60)
		tmp = i * (a * b);
	elseif (t <= 6.9e+72)
		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[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.2e+94], t$95$2, If[LessEqual[t, -9.8e-176], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.35e-276], t$95$1, If[LessEqual[t, 5.2e-60], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.9e+72], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.20000000000000012e94 or 6.90000000000000034e72 < t

   1. Initial program 72.2%

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

   2. Taylor expanded in t around inf 72.2%

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

      1. *-commutative 72.2%

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

      2. mul-1-neg 72.2%

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

      3. unsub-neg 72.2%

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

   4. Simplified 72.2%

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

   5. Taylor expanded in c around inf 46.6%

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

      1. *-commutative 46.6%

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

      2. associate-*l* 48.3%

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

   7. Simplified 48.3%

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

   if -2.20000000000000012e94 < t < -9.7999999999999994e-176

   1. Initial program 81.5%

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

   2. Taylor expanded in a around inf 47.1%

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

      1. associate-*r* 47.1%

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

      2. neg-mul-1 47.1%

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

      3. cancel-sign-sub 47.1%

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

      4. +-commutative 47.1%

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

      5. mul-1-neg 47.1%

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

      6. unsub-neg 47.1%

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

   4. Simplified 47.1%

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

   5. Taylor expanded in i around inf 28.5%

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

   if -9.7999999999999994e-176 < t < 1.34999999999999993e-276 or 5.1999999999999995e-60 < t < 6.90000000000000034e72

   1. Initial program 75.4%

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

   2. Taylor expanded in x around inf 35.5%

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

   3. Taylor expanded in y around inf 30.8%

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

   if 1.34999999999999993e-276 < t < 5.1999999999999995e-60

   1. Initial program 78.3%

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

   2. Taylor expanded in a around inf 29.0%

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

      1. associate-*r* 29.0%

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

      2. neg-mul-1 29.0%

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

      3. cancel-sign-sub 29.0%

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

      4. +-commutative 29.0%

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

      5. mul-1-neg 29.0%

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

      6. unsub-neg 29.0%

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

   4. Simplified 29.0%

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

   5. Taylor expanded in i around inf 25.7%

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

      1. associate-*r* 29.7%

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

      2. *-commutative 29.7%

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

      3. associate-*r* 34.3%

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

   7. Simplified 34.3%

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

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+94}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-176}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-276}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-60}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 18: 30.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;c \leq -1.05 \cdot 10^{-18}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-195}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))))
   (if (<= c -1.05e-18)
     (* b (* z (- c)))
     (if (<= c 1.15e-285)
       t_1
       (if (<= c 1.4e-195)
         (* a (* x (- t)))
         (if (<= c 6.5e-130)
           t_1
           (if (<= c 7.5e+57) (* x (* y z)) (* t (* c 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 = i * (y * -j);
	double tmp;
	if (c <= -1.05e-18) {
		tmp = b * (z * -c);
	} else if (c <= 1.15e-285) {
		tmp = t_1;
	} else if (c <= 1.4e-195) {
		tmp = a * (x * -t);
	} else if (c <= 6.5e-130) {
		tmp = t_1;
	} else if (c <= 7.5e+57) {
		tmp = x * (y * z);
	} else {
		tmp = t * (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) :: t_1
    real(8) :: tmp
    t_1 = i * (y * -j)
    if (c <= (-1.05d-18)) then
        tmp = b * (z * -c)
    else if (c <= 1.15d-285) then
        tmp = t_1
    else if (c <= 1.4d-195) then
        tmp = a * (x * -t)
    else if (c <= 6.5d-130) then
        tmp = t_1
    else if (c <= 7.5d+57) then
        tmp = x * (y * z)
    else
        tmp = t * (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 t_1 = i * (y * -j);
	double tmp;
	if (c <= -1.05e-18) {
		tmp = b * (z * -c);
	} else if (c <= 1.15e-285) {
		tmp = t_1;
	} else if (c <= 1.4e-195) {
		tmp = a * (x * -t);
	} else if (c <= 6.5e-130) {
		tmp = t_1;
	} else if (c <= 7.5e+57) {
		tmp = x * (y * z);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	tmp = 0
	if c <= -1.05e-18:
		tmp = b * (z * -c)
	elif c <= 1.15e-285:
		tmp = t_1
	elif c <= 1.4e-195:
		tmp = a * (x * -t)
	elif c <= 6.5e-130:
		tmp = t_1
	elif c <= 7.5e+57:
		tmp = x * (y * z)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (c <= -1.05e-18)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (c <= 1.15e-285)
		tmp = t_1;
	elseif (c <= 1.4e-195)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (c <= 6.5e-130)
		tmp = t_1;
	elseif (c <= 7.5e+57)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(t * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (y * -j);
	tmp = 0.0;
	if (c <= -1.05e-18)
		tmp = b * (z * -c);
	elseif (c <= 1.15e-285)
		tmp = t_1;
	elseif (c <= 1.4e-195)
		tmp = a * (x * -t);
	elseif (c <= 6.5e-130)
		tmp = t_1;
	elseif (c <= 7.5e+57)
		tmp = x * (y * z);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.05e-18], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.15e-285], t$95$1, If[LessEqual[c, 1.4e-195], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.5e-130], t$95$1, If[LessEqual[c, 7.5e+57], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.05e-18

   1. Initial program 67.5%

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

   2. Taylor expanded in x around 0 62.1%

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

   3. Taylor expanded in z around inf 35.7%

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

      1. associate-*r* 35.7%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(b \cdot z\right)} \]

      2. neg-mul-1 35.7%

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

      3. *-commutative 35.7%

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

      4. *-commutative 35.7%

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

      5. *-commutative 35.7%

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

      6. associate-*l* 35.7%

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

      7. distribute-rgt-neg-in 35.7%

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

      8. *-commutative 35.7%

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

      9. distribute-rgt-neg-in 35.7%

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

   5. Simplified 35.7%

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

   if -1.05e-18 < c < 1.14999999999999998e-285 or 1.40000000000000002e-195 < c < 6.5000000000000002e-130

   1. Initial program 82.1%

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

   2. Taylor expanded in x around 0 66.1%

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

   3. Taylor expanded in y around inf 42.8%

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

      1. associate-*r* 41.7%

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

      2. *-commutative 41.7%

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

      3. associate-*r* 41.9%

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

      4. associate-*r* 41.9%

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

      5. neg-mul-1 41.9%

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

   5. Simplified 41.9%

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

   if 1.14999999999999998e-285 < c < 1.40000000000000002e-195

   1. Initial program 86.4%

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

   2. Taylor expanded in a around inf 72.6%

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

      1. associate-*r* 72.6%

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

      2. neg-mul-1 72.6%

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

      3. cancel-sign-sub 72.6%

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

      4. +-commutative 72.6%

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

      5. mul-1-neg 72.6%

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

      6. unsub-neg 72.6%

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

   4. Simplified 72.6%

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

   5. Taylor expanded in i around 0 58.7%

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

      1. associate-*r* 58.7%

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

      2. neg-mul-1 58.7%

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

   7. Simplified 58.7%

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

   if 6.5000000000000002e-130 < c < 7.5000000000000006e57

   1. Initial program 82.9%

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

   2. Taylor expanded in x around inf 69.8%

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

   3. Taylor expanded in y around inf 47.5%

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

   if 7.5000000000000006e57 < c

   1. Initial program 71.9%

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

   2. Taylor expanded in t around inf 59.4%

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

      1. *-commutative 59.4%

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

      2. mul-1-neg 59.4%

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

      3. unsub-neg 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in c around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. associate-*l* 52.5%

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

   7. Simplified 52.5%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{-18}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-285}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-195}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 19: 29.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6 \cdot 10^{-19}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-275}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-196}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -6e-19)
   (* b (* z (- c)))
   (if (<= c 1.7e-275)
     (* (* i j) (- y))
     (if (<= c 1.4e-196)
       (* a (* x (- t)))
       (if (<= c 4.4e-130)
         (* i (* y (- j)))
         (if (<= c 2.4e+55) (* x (* y z)) (* t (* 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 (c <= -6e-19) {
		tmp = b * (z * -c);
	} else if (c <= 1.7e-275) {
		tmp = (i * j) * -y;
	} else if (c <= 1.4e-196) {
		tmp = a * (x * -t);
	} else if (c <= 4.4e-130) {
		tmp = i * (y * -j);
	} else if (c <= 2.4e+55) {
		tmp = x * (y * z);
	} else {
		tmp = t * (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 (c <= (-6d-19)) then
        tmp = b * (z * -c)
    else if (c <= 1.7d-275) then
        tmp = (i * j) * -y
    else if (c <= 1.4d-196) then
        tmp = a * (x * -t)
    else if (c <= 4.4d-130) then
        tmp = i * (y * -j)
    else if (c <= 2.4d+55) then
        tmp = x * (y * z)
    else
        tmp = t * (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 (c <= -6e-19) {
		tmp = b * (z * -c);
	} else if (c <= 1.7e-275) {
		tmp = (i * j) * -y;
	} else if (c <= 1.4e-196) {
		tmp = a * (x * -t);
	} else if (c <= 4.4e-130) {
		tmp = i * (y * -j);
	} else if (c <= 2.4e+55) {
		tmp = x * (y * z);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -6e-19:
		tmp = b * (z * -c)
	elif c <= 1.7e-275:
		tmp = (i * j) * -y
	elif c <= 1.4e-196:
		tmp = a * (x * -t)
	elif c <= 4.4e-130:
		tmp = i * (y * -j)
	elif c <= 2.4e+55:
		tmp = x * (y * z)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -6e-19)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (c <= 1.7e-275)
		tmp = Float64(Float64(i * j) * Float64(-y));
	elseif (c <= 1.4e-196)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (c <= 4.4e-130)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (c <= 2.4e+55)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(t * 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 (c <= -6e-19)
		tmp = b * (z * -c);
	elseif (c <= 1.7e-275)
		tmp = (i * j) * -y;
	elseif (c <= 1.4e-196)
		tmp = a * (x * -t);
	elseif (c <= 4.4e-130)
		tmp = i * (y * -j);
	elseif (c <= 2.4e+55)
		tmp = x * (y * z);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -6e-19], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.7e-275], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[c, 1.4e-196], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.4e-130], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.4e+55], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -5.99999999999999985e-19

   1. Initial program 67.5%

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

   2. Taylor expanded in x around 0 62.1%

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

   3. Taylor expanded in z around inf 35.7%

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

      1. associate-*r* 35.7%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(b \cdot z\right)} \]

      2. neg-mul-1 35.7%

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

      3. *-commutative 35.7%

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

      4. *-commutative 35.7%

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

      5. *-commutative 35.7%

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

      6. associate-*l* 35.7%

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

      7. distribute-rgt-neg-in 35.7%

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

      8. *-commutative 35.7%

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

      9. distribute-rgt-neg-in 35.7%

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

   5. Simplified 35.7%

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

   if -5.99999999999999985e-19 < c < 1.69999999999999984e-275

   1. Initial program 85.2%

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

   2. Taylor expanded in j around inf 50.4%

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

   3. Taylor expanded in c around 0 39.6%

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

      1. associate-*r* 40.8%

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

      2. *-commutative 40.8%

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

      3. associate-*r* 42.2%

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

      4. associate-*r* 42.2%

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

      5. neg-mul-1 42.2%

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

   5. Simplified 42.2%

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

   if 1.69999999999999984e-275 < c < 1.3999999999999999e-196

   1. Initial program 86.4%

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

   2. Taylor expanded in a around inf 72.6%

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

      1. associate-*r* 72.6%

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

      2. neg-mul-1 72.6%

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

      3. cancel-sign-sub 72.6%

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

      4. +-commutative 72.6%

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

      5. mul-1-neg 72.6%

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

      6. unsub-neg 72.6%

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

   4. Simplified 72.6%

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

   5. Taylor expanded in i around 0 58.7%

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

      1. associate-*r* 58.7%

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

      2. neg-mul-1 58.7%

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

   7. Simplified 58.7%

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

   if 1.3999999999999999e-196 < c < 4.3999999999999997e-130

   1. Initial program 69.3%

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

   2. Taylor expanded in x around 0 57.7%

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

   3. Taylor expanded in y around inf 45.4%

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

      1. associate-*r* 45.7%

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

      2. *-commutative 45.7%

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

      3. associate-*r* 51.3%

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

      4. associate-*r* 51.3%

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

      5. neg-mul-1 51.3%

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

   5. Simplified 51.3%

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

   if 4.3999999999999997e-130 < c < 2.3999999999999999e55

   1. Initial program 82.9%

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

   2. Taylor expanded in x around inf 69.8%

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

   3. Taylor expanded in y around inf 47.5%

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

   if 2.3999999999999999e55 < c

   1. Initial program 71.9%

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

   2. Taylor expanded in t around inf 59.4%

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

      1. *-commutative 59.4%

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

      2. mul-1-neg 59.4%

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

      3. unsub-neg 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in c around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. associate-*l* 52.5%

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

   7. Simplified 52.5%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6 \cdot 10^{-19}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-275}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-196}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 20: 30.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{-18}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-277}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-195}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 10^{-129}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1e-18)
   (* b (* z (- c)))
   (if (<= c 6.8e-277)
     (* (* i j) (- y))
     (if (<= c 2.5e-195)
       (* t (* x (- a)))
       (if (<= c 1e-129)
         (* i (* y (- j)))
         (if (<= c 7.6e+53) (* x (* y z)) (* t (* 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 (c <= -1e-18) {
		tmp = b * (z * -c);
	} else if (c <= 6.8e-277) {
		tmp = (i * j) * -y;
	} else if (c <= 2.5e-195) {
		tmp = t * (x * -a);
	} else if (c <= 1e-129) {
		tmp = i * (y * -j);
	} else if (c <= 7.6e+53) {
		tmp = x * (y * z);
	} else {
		tmp = t * (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 (c <= (-1d-18)) then
        tmp = b * (z * -c)
    else if (c <= 6.8d-277) then
        tmp = (i * j) * -y
    else if (c <= 2.5d-195) then
        tmp = t * (x * -a)
    else if (c <= 1d-129) then
        tmp = i * (y * -j)
    else if (c <= 7.6d+53) then
        tmp = x * (y * z)
    else
        tmp = t * (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 (c <= -1e-18) {
		tmp = b * (z * -c);
	} else if (c <= 6.8e-277) {
		tmp = (i * j) * -y;
	} else if (c <= 2.5e-195) {
		tmp = t * (x * -a);
	} else if (c <= 1e-129) {
		tmp = i * (y * -j);
	} else if (c <= 7.6e+53) {
		tmp = x * (y * z);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1e-18:
		tmp = b * (z * -c)
	elif c <= 6.8e-277:
		tmp = (i * j) * -y
	elif c <= 2.5e-195:
		tmp = t * (x * -a)
	elif c <= 1e-129:
		tmp = i * (y * -j)
	elif c <= 7.6e+53:
		tmp = x * (y * z)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1e-18)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (c <= 6.8e-277)
		tmp = Float64(Float64(i * j) * Float64(-y));
	elseif (c <= 2.5e-195)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (c <= 1e-129)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (c <= 7.6e+53)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(t * 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 (c <= -1e-18)
		tmp = b * (z * -c);
	elseif (c <= 6.8e-277)
		tmp = (i * j) * -y;
	elseif (c <= 2.5e-195)
		tmp = t * (x * -a);
	elseif (c <= 1e-129)
		tmp = i * (y * -j);
	elseif (c <= 7.6e+53)
		tmp = x * (y * z);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1e-18], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.8e-277], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[c, 2.5e-195], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1e-129], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.6e+53], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.0000000000000001e-18

   1. Initial program 67.5%

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

   2. Taylor expanded in x around 0 62.1%

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

   3. Taylor expanded in z around inf 35.7%

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

      1. associate-*r* 35.7%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(b \cdot z\right)} \]

      2. neg-mul-1 35.7%

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

      3. *-commutative 35.7%

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

      4. *-commutative 35.7%

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

      5. *-commutative 35.7%

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

      6. associate-*l* 35.7%

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

      7. distribute-rgt-neg-in 35.7%

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

      8. *-commutative 35.7%

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

      9. distribute-rgt-neg-in 35.7%

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

   5. Simplified 35.7%

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

   if -1.0000000000000001e-18 < c < 6.79999999999999964e-277

   1. Initial program 85.2%

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

   2. Taylor expanded in j around inf 50.4%

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

   3. Taylor expanded in c around 0 39.6%

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

      1. associate-*r* 40.8%

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

      2. *-commutative 40.8%

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

      3. associate-*r* 42.2%

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

      4. associate-*r* 42.2%

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

      5. neg-mul-1 42.2%

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

   5. Simplified 42.2%

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

   if 6.79999999999999964e-277 < c < 2.50000000000000004e-195

   1. Initial program 86.4%

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

   2. Taylor expanded in a around inf 72.6%

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

      1. associate-*r* 72.6%

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

      2. neg-mul-1 72.6%

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

      3. cancel-sign-sub 72.6%

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

      4. +-commutative 72.6%

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

      5. mul-1-neg 72.6%

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

      6. unsub-neg 72.6%

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

   4. Simplified 72.6%

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

   5. Taylor expanded in i around 0 58.7%

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

      1. *-commutative 58.7%

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

      2. associate-*r* 58.7%

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

      3. neg-mul-1 58.7%

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

      4. associate-*r* 65.4%

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

      5. distribute-lft-neg-out 65.4%

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

      6. distribute-rgt-neg-in 65.4%

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

   7. Simplified 65.4%

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

   if 2.50000000000000004e-195 < c < 9.9999999999999993e-130

   1. Initial program 69.3%

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

   2. Taylor expanded in x around 0 57.7%

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

   3. Taylor expanded in y around inf 45.4%

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

      1. associate-*r* 45.7%

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

      2. *-commutative 45.7%

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

      3. associate-*r* 51.3%

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

      4. associate-*r* 51.3%

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

      5. neg-mul-1 51.3%

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

   5. Simplified 51.3%

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

   if 9.9999999999999993e-130 < c < 7.59999999999999995e53

   1. Initial program 82.9%

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

   2. Taylor expanded in x around inf 69.8%

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

   3. Taylor expanded in y around inf 47.5%

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

   if 7.59999999999999995e53 < c

   1. Initial program 71.9%

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

   2. Taylor expanded in t around inf 59.4%

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

      1. *-commutative 59.4%

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

      2. mul-1-neg 59.4%

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

      3. unsub-neg 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in c around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. associate-*l* 52.5%

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

   7. Simplified 52.5%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1 \cdot 10^{-18}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-277}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-195}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 10^{-129}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 21: 29.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{-18}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-282}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-196}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-129}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1.15e-18)
   (* c (* z (- b)))
   (if (<= c 1.4e-282)
     (* (* i j) (- y))
     (if (<= c 1.05e-196)
       (* t (* x (- a)))
       (if (<= c 1.8e-129)
         (* i (* y (- j)))
         (if (<= c 1.95e+56) (* x (* y z)) (* t (* 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 (c <= -1.15e-18) {
		tmp = c * (z * -b);
	} else if (c <= 1.4e-282) {
		tmp = (i * j) * -y;
	} else if (c <= 1.05e-196) {
		tmp = t * (x * -a);
	} else if (c <= 1.8e-129) {
		tmp = i * (y * -j);
	} else if (c <= 1.95e+56) {
		tmp = x * (y * z);
	} else {
		tmp = t * (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 (c <= (-1.15d-18)) then
        tmp = c * (z * -b)
    else if (c <= 1.4d-282) then
        tmp = (i * j) * -y
    else if (c <= 1.05d-196) then
        tmp = t * (x * -a)
    else if (c <= 1.8d-129) then
        tmp = i * (y * -j)
    else if (c <= 1.95d+56) then
        tmp = x * (y * z)
    else
        tmp = t * (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 (c <= -1.15e-18) {
		tmp = c * (z * -b);
	} else if (c <= 1.4e-282) {
		tmp = (i * j) * -y;
	} else if (c <= 1.05e-196) {
		tmp = t * (x * -a);
	} else if (c <= 1.8e-129) {
		tmp = i * (y * -j);
	} else if (c <= 1.95e+56) {
		tmp = x * (y * z);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1.15e-18:
		tmp = c * (z * -b)
	elif c <= 1.4e-282:
		tmp = (i * j) * -y
	elif c <= 1.05e-196:
		tmp = t * (x * -a)
	elif c <= 1.8e-129:
		tmp = i * (y * -j)
	elif c <= 1.95e+56:
		tmp = x * (y * z)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1.15e-18)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (c <= 1.4e-282)
		tmp = Float64(Float64(i * j) * Float64(-y));
	elseif (c <= 1.05e-196)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (c <= 1.8e-129)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (c <= 1.95e+56)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(t * 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 (c <= -1.15e-18)
		tmp = c * (z * -b);
	elseif (c <= 1.4e-282)
		tmp = (i * j) * -y;
	elseif (c <= 1.05e-196)
		tmp = t * (x * -a);
	elseif (c <= 1.8e-129)
		tmp = i * (y * -j);
	elseif (c <= 1.95e+56)
		tmp = x * (y * z);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1.15e-18], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.4e-282], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[c, 1.05e-196], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.8e-129], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.95e+56], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.15e-18

   1. Initial program 67.5%

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

   2. Taylor expanded in c around inf 55.2%

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

      1. *-commutative 55.2%

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

   4. Simplified 55.2%

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

   5. Taylor expanded in t around 0 35.7%

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

      1. mul-1-neg 35.7%

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

      2. *-commutative 35.7%

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

      3. *-commutative 35.7%

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

      4. distribute-rgt-neg-in 35.7%

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

   7. Simplified 35.7%

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

   if -1.15e-18 < c < 1.3999999999999999e-282

   1. Initial program 85.2%

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

   2. Taylor expanded in j around inf 50.4%

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

   3. Taylor expanded in c around 0 39.6%

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

      1. associate-*r* 40.8%

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

      2. *-commutative 40.8%

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

      3. associate-*r* 42.2%

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

      4. associate-*r* 42.2%

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

      5. neg-mul-1 42.2%

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

   5. Simplified 42.2%

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

   if 1.3999999999999999e-282 < c < 1.04999999999999994e-196

   1. Initial program 86.4%

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

   2. Taylor expanded in a around inf 72.6%

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

      1. associate-*r* 72.6%

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

      2. neg-mul-1 72.6%

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

      3. cancel-sign-sub 72.6%

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

      4. +-commutative 72.6%

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

      5. mul-1-neg 72.6%

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

      6. unsub-neg 72.6%

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

   4. Simplified 72.6%

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

   5. Taylor expanded in i around 0 58.7%

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

      1. *-commutative 58.7%

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

      2. associate-*r* 58.7%

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

      3. neg-mul-1 58.7%

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

      4. associate-*r* 65.4%

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

      5. distribute-lft-neg-out 65.4%

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

      6. distribute-rgt-neg-in 65.4%

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

   7. Simplified 65.4%

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

   if 1.04999999999999994e-196 < c < 1.8e-129

   1. Initial program 69.3%

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

   2. Taylor expanded in x around 0 57.7%

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

   3. Taylor expanded in y around inf 45.4%

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

      1. associate-*r* 45.7%

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

      2. *-commutative 45.7%

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

      3. associate-*r* 51.3%

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

      4. associate-*r* 51.3%

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

      5. neg-mul-1 51.3%

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

   5. Simplified 51.3%

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

   if 1.8e-129 < c < 1.94999999999999997e56

   1. Initial program 82.9%

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

   2. Taylor expanded in x around inf 69.8%

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

   3. Taylor expanded in y around inf 47.5%

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

   if 1.94999999999999997e56 < c

   1. Initial program 71.9%

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

   2. Taylor expanded in t around inf 59.4%

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

      1. *-commutative 59.4%

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

      2. mul-1-neg 59.4%

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

      3. unsub-neg 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in c around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. associate-*l* 52.5%

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

   7. Simplified 52.5%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{-18}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{-282}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;c \leq 1.05 \cdot 10^{-196}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{-129}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 22: 50.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -3.2 \cdot 10^{+189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{-114}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{-72}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -3.2e+189)
     t_1
     (if (<= j -1.15e-114)
       (* i (- (* a b) (* y j)))
       (if (<= j 1.3e-72) (* b (- (* a i) (* z c))) 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 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -3.2e+189) {
		tmp = t_1;
	} else if (j <= -1.15e-114) {
		tmp = i * ((a * b) - (y * j));
	} else if (j <= 1.3e-72) {
		tmp = b * ((a * i) - (z * c));
	} 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 = j * ((t * c) - (y * i))
    if (j <= (-3.2d+189)) then
        tmp = t_1
    else if (j <= (-1.15d-114)) then
        tmp = i * ((a * b) - (y * j))
    else if (j <= 1.3d-72) then
        tmp = b * ((a * i) - (z * c))
    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 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -3.2e+189) {
		tmp = t_1;
	} else if (j <= -1.15e-114) {
		tmp = i * ((a * b) - (y * j));
	} else if (j <= 1.3e-72) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -3.2e+189:
		tmp = t_1
	elif j <= -1.15e-114:
		tmp = i * ((a * b) - (y * j))
	elif j <= 1.3e-72:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -3.2e+189)
		tmp = t_1;
	elseif (j <= -1.15e-114)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (j <= 1.3e-72)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -3.2e+189)
		tmp = t_1;
	elseif (j <= -1.15e-114)
		tmp = i * ((a * b) - (y * j));
	elseif (j <= 1.3e-72)
		tmp = b * ((a * i) - (z * c));
	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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.2e+189], t$95$1, If[LessEqual[j, -1.15e-114], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.3e-72], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.2000000000000001e189 or 1.29999999999999998e-72 < j

   1. Initial program 74.2%

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

   2. Taylor expanded in j around inf 65.0%

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

   if -3.2000000000000001e189 < j < -1.15e-114

   1. Initial program 76.3%

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

   2. Taylor expanded in i around inf 55.7%

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

      1. *-commutative 55.7%

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

      2. cancel-sign-sub-inv 55.7%

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

      3. metadata-eval 55.7%

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

      4. *-lft-identity 55.7%

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

      5. +-commutative 55.7%

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

      6. mul-1-neg 55.7%

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

      7. unsub-neg 55.7%

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

   4. Simplified 55.7%

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

   if -1.15e-114 < j < 1.29999999999999998e-72

   1. Initial program 78.2%

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

      1. associate-+l- 78.2%

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

      2. sub-neg 78.2%

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

      3. sub-neg 78.2%

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

      4. *-commutative 78.2%

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

      5. fma-neg 78.2%

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

      6. *-commutative 78.2%

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

      7. *-commutative 78.2%

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

      8. fma-neg 78.2%

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

      9. distribute-lft-neg-out 78.2%

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

      10. *-commutative 78.2%

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

   3. Simplified 78.2%

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

   4. Taylor expanded in b around inf 54.1%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.2 \cdot 10^{+189}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{-114}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{-72}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 23: 30.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -800000:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -7 \cdot 10^{-248}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -800000.0)
   (* b (* z (- c)))
   (if (<= c -7e-248)
     (* z (* x y))
     (if (<= c 5.8e-130)
       (* i (* a b))
       (if (<= c 3.5e+57) (* x (* y z)) (* t (* 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 (c <= -800000.0) {
		tmp = b * (z * -c);
	} else if (c <= -7e-248) {
		tmp = z * (x * y);
	} else if (c <= 5.8e-130) {
		tmp = i * (a * b);
	} else if (c <= 3.5e+57) {
		tmp = x * (y * z);
	} else {
		tmp = t * (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 (c <= (-800000.0d0)) then
        tmp = b * (z * -c)
    else if (c <= (-7d-248)) then
        tmp = z * (x * y)
    else if (c <= 5.8d-130) then
        tmp = i * (a * b)
    else if (c <= 3.5d+57) then
        tmp = x * (y * z)
    else
        tmp = t * (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 (c <= -800000.0) {
		tmp = b * (z * -c);
	} else if (c <= -7e-248) {
		tmp = z * (x * y);
	} else if (c <= 5.8e-130) {
		tmp = i * (a * b);
	} else if (c <= 3.5e+57) {
		tmp = x * (y * z);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -800000.0:
		tmp = b * (z * -c)
	elif c <= -7e-248:
		tmp = z * (x * y)
	elif c <= 5.8e-130:
		tmp = i * (a * b)
	elif c <= 3.5e+57:
		tmp = x * (y * z)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -800000.0)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (c <= -7e-248)
		tmp = Float64(z * Float64(x * y));
	elseif (c <= 5.8e-130)
		tmp = Float64(i * Float64(a * b));
	elseif (c <= 3.5e+57)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(t * 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 (c <= -800000.0)
		tmp = b * (z * -c);
	elseif (c <= -7e-248)
		tmp = z * (x * y);
	elseif (c <= 5.8e-130)
		tmp = i * (a * b);
	elseif (c <= 3.5e+57)
		tmp = x * (y * z);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -800000.0], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -7e-248], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.8e-130], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.5e+57], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -8e5

   1. Initial program 66.7%

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

   2. Taylor expanded in x around 0 65.9%

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

   3. Taylor expanded in z around inf 37.0%

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

      1. associate-*r* 37.0%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(b \cdot z\right)} \]

      2. neg-mul-1 37.0%

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

      3. *-commutative 37.0%

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

      4. *-commutative 37.0%

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

      5. *-commutative 37.0%

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

      6. associate-*l* 36.9%

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

      7. distribute-rgt-neg-in 36.9%

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

      8. *-commutative 36.9%

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

      9. distribute-rgt-neg-in 36.9%

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

   5. Simplified 36.9%

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

   if -8e5 < c < -6.99999999999999966e-248

   1. Initial program 81.8%

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

   2. Taylor expanded in x around inf 42.9%

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

   3. Taylor expanded in y around inf 26.3%

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

   4. Taylor expanded in y around 0 26.3%

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

      1. *-commutative 26.3%

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

      2. associate-*l* 29.4%

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

   6. Simplified 29.4%

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

   if -6.99999999999999966e-248 < c < 5.8e-130

   1. Initial program 81.5%

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

   2. Taylor expanded in a around inf 51.3%

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

      1. associate-*r* 51.3%

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

      2. neg-mul-1 51.3%

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

      3. cancel-sign-sub 51.3%

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

      4. +-commutative 51.3%

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

      5. mul-1-neg 51.3%

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

      6. unsub-neg 51.3%

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

   4. Simplified 51.3%

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

   5. Taylor expanded in i around inf 28.7%

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

      1. associate-*r* 30.7%

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

      2. *-commutative 30.7%

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

      3. associate-*r* 34.5%

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

   7. Simplified 34.5%

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

   if 5.8e-130 < c < 3.4999999999999997e57

   1. Initial program 82.9%

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

   2. Taylor expanded in x around inf 69.8%

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

   3. Taylor expanded in y around inf 47.5%

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

   if 3.4999999999999997e57 < c

   1. Initial program 71.9%

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

   2. Taylor expanded in t around inf 59.4%

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

      1. *-commutative 59.4%

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

      2. mul-1-neg 59.4%

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

      3. unsub-neg 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in c around inf 50.2%

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

      1. *-commutative 50.2%

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

      2. associate-*l* 52.5%

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

   7. Simplified 52.5%

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

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -800000:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -7 \cdot 10^{-248}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-130}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 24: 30.4% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{+91}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -5.4 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-187}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -3.2e+91)
   (* b (* z (- c)))
   (if (<= c -5.4e-308)
     (* a (* b i))
     (if (<= c 1.55e-187)
       (* a (* x (- t)))
       (if (<= c 8e+54) (* x (* y z)) (* t (* 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 (c <= -3.2e+91) {
		tmp = b * (z * -c);
	} else if (c <= -5.4e-308) {
		tmp = a * (b * i);
	} else if (c <= 1.55e-187) {
		tmp = a * (x * -t);
	} else if (c <= 8e+54) {
		tmp = x * (y * z);
	} else {
		tmp = t * (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 (c <= (-3.2d+91)) then
        tmp = b * (z * -c)
    else if (c <= (-5.4d-308)) then
        tmp = a * (b * i)
    else if (c <= 1.55d-187) then
        tmp = a * (x * -t)
    else if (c <= 8d+54) then
        tmp = x * (y * z)
    else
        tmp = t * (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 (c <= -3.2e+91) {
		tmp = b * (z * -c);
	} else if (c <= -5.4e-308) {
		tmp = a * (b * i);
	} else if (c <= 1.55e-187) {
		tmp = a * (x * -t);
	} else if (c <= 8e+54) {
		tmp = x * (y * z);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -3.2e+91:
		tmp = b * (z * -c)
	elif c <= -5.4e-308:
		tmp = a * (b * i)
	elif c <= 1.55e-187:
		tmp = a * (x * -t)
	elif c <= 8e+54:
		tmp = x * (y * z)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -3.2e+91)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (c <= -5.4e-308)
		tmp = Float64(a * Float64(b * i));
	elseif (c <= 1.55e-187)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (c <= 8e+54)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(t * 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 (c <= -3.2e+91)
		tmp = b * (z * -c);
	elseif (c <= -5.4e-308)
		tmp = a * (b * i);
	elseif (c <= 1.55e-187)
		tmp = a * (x * -t);
	elseif (c <= 8e+54)
		tmp = x * (y * z);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -3.2e+91], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.4e-308], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.55e-187], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8e+54], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -3.19999999999999989e91

   1. Initial program 63.9%

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

   2. Taylor expanded in x around 0 64.5%

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

   3. Taylor expanded in z around inf 40.0%

      \[\leadsto \color{blue}{-1 \cdot \left(c \cdot \left(b \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 40.0%

         \[\leadsto \color{blue}{\left(-1 \cdot c\right) \cdot \left(b \cdot z\right)} \]

      2. neg-mul-1 40.0%

         \[\leadsto \color{blue}{\left(-c\right)} \cdot \left(b \cdot z\right) \]

      3. *-commutative 40.0%

         \[\leadsto \left(-c\right) \cdot \color{blue}{\left(z \cdot b\right)} \]

      4. *-commutative 40.0%

         \[\leadsto \color{blue}{\left(z \cdot b\right) \cdot \left(-c\right)} \]

      5. *-commutative 40.0%

         \[\leadsto \color{blue}{\left(b \cdot z\right)} \cdot \left(-c\right) \]

      6. associate-*l* 39.9%

         \[\leadsto \color{blue}{b \cdot \left(z \cdot \left(-c\right)\right)} \]

      7. distribute-rgt-neg-in 39.9%

         \[\leadsto b \cdot \color{blue}{\left(-z \cdot c\right)} \]

      8. *-commutative 39.9%

         \[\leadsto b \cdot \left(-\color{blue}{c \cdot z}\right) \]

      9. distribute-rgt-neg-in 39.9%

         \[\leadsto b \cdot \color{blue}{\left(c \cdot \left(-z\right)\right)} \]

   5. Simplified 39.9%

      \[\leadsto \color{blue}{b \cdot \left(c \cdot \left(-z\right)\right)} \]

   if -3.19999999999999989e91 < c < -5.4000000000000003e-308

   1. Initial program 83.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in a around inf 36.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 36.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 36.8%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 36.8%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 36.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 36.8%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 36.8%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   4. Simplified 36.8%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   5. Taylor expanded in i around inf 28.5%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

   if -5.4000000000000003e-308 < c < 1.5500000000000001e-187

   1. Initial program 82.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in a around inf 60.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 60.0%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 60.0%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 60.0%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 60.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 60.0%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 60.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   4. Simplified 60.0%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   5. Taylor expanded in i around 0 46.9%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot \left(t \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 46.9%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot \left(t \cdot x\right)} \]

      2. neg-mul-1 46.9%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot \left(t \cdot x\right) \]

   7. Simplified 46.9%

      \[\leadsto \color{blue}{\left(-a\right) \cdot \left(t \cdot x\right)} \]

   if 1.5500000000000001e-187 < c < 8.0000000000000006e54

   1. Initial program 79.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in x around inf 59.8%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   3. Taylor expanded in y around inf 41.3%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x \]

   if 8.0000000000000006e54 < c

   1. Initial program 71.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in t around inf 59.4%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   3. Step-by-step derivation

      1. *-commutative 59.4%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 59.4%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 59.4%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   4. Simplified 59.4%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   5. Taylor expanded in c around inf 50.2%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 50.2%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot c} \]

      2. associate-*l* 52.5%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

   7. Simplified 52.5%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.2 \cdot 10^{+91}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;c \leq -5.4 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{-187}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 25: 30.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -7.7 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-59}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+72}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* c j))))
   (if (<= t -7.7e+89)
     t_1
     (if (<= t 2.8e-59) (* i (* a b)) (if (<= t 5.4e+72) (* z (* x y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (t <= -7.7e+89) {
		tmp = t_1;
	} else if (t <= 2.8e-59) {
		tmp = i * (a * b);
	} else if (t <= 5.4e+72) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (c * j)
    if (t <= (-7.7d+89)) then
        tmp = t_1
    else if (t <= 2.8d-59) then
        tmp = i * (a * b)
    else if (t <= 5.4d+72) then
        tmp = z * (x * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (t <= -7.7e+89) {
		tmp = t_1;
	} else if (t <= 2.8e-59) {
		tmp = i * (a * b);
	} else if (t <= 5.4e+72) {
		tmp = z * (x * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (c * j)
	tmp = 0
	if t <= -7.7e+89:
		tmp = t_1
	elif t <= 2.8e-59:
		tmp = i * (a * b)
	elif t <= 5.4e+72:
		tmp = z * (x * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (t <= -7.7e+89)
		tmp = t_1;
	elseif (t <= 2.8e-59)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 5.4e+72)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (c * j);
	tmp = 0.0;
	if (t <= -7.7e+89)
		tmp = t_1;
	elseif (t <= 2.8e-59)
		tmp = i * (a * b);
	elseif (t <= 5.4e+72)
		tmp = z * (x * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.7e+89], t$95$1, If[LessEqual[t, 2.8e-59], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e+72], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.7000000000000003e89 or 5.4000000000000001e72 < t

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in t around inf 72.5%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   3. Step-by-step derivation

      1. *-commutative 72.5%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 72.5%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 72.5%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   4. Simplified 72.5%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   5. Taylor expanded in c around inf 46.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 46.0%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot c} \]

      2. associate-*l* 47.8%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

   7. Simplified 47.8%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

   if -7.7000000000000003e89 < t < 2.79999999999999981e-59

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in a around inf 31.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 31.2%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 31.2%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 31.2%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 31.2%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 31.2%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 31.2%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   4. Simplified 31.2%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   5. Taylor expanded in i around inf 24.2%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 24.4%

         \[\leadsto \color{blue}{\left(a \cdot i\right) \cdot b} \]

      2. *-commutative 24.4%

         \[\leadsto \color{blue}{\left(i \cdot a\right)} \cdot b \]

      3. associate-*r* 26.8%

         \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   7. Simplified 26.8%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if 2.79999999999999981e-59 < t < 5.4000000000000001e72

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in x around inf 42.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   3. Taylor expanded in y around inf 28.5%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x \]

   4. Taylor expanded in y around 0 31.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   5. Step-by-step derivation

      1. *-commutative 31.6%

         \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot y} \]

      2. associate-*l* 31.7%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

   6. Simplified 31.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.7 \cdot 10^{+89}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-59}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+72}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 26: 30.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+87}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-58}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -3.6e+87)
   (* j (* t c))
   (if (<= t 1.4e-58)
     (* i (* a b))
     (if (<= t 1.12e+73) (* z (* x y)) (* t (* 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 <= -3.6e+87) {
		tmp = j * (t * c);
	} else if (t <= 1.4e-58) {
		tmp = i * (a * b);
	} else if (t <= 1.12e+73) {
		tmp = z * (x * y);
	} else {
		tmp = t * (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 <= (-3.6d+87)) then
        tmp = j * (t * c)
    else if (t <= 1.4d-58) then
        tmp = i * (a * b)
    else if (t <= 1.12d+73) then
        tmp = z * (x * y)
    else
        tmp = t * (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 <= -3.6e+87) {
		tmp = j * (t * c);
	} else if (t <= 1.4e-58) {
		tmp = i * (a * b);
	} else if (t <= 1.12e+73) {
		tmp = z * (x * y);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -3.6e+87:
		tmp = j * (t * c)
	elif t <= 1.4e-58:
		tmp = i * (a * b)
	elif t <= 1.12e+73:
		tmp = z * (x * y)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -3.6e+87)
		tmp = Float64(j * Float64(t * c));
	elseif (t <= 1.4e-58)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 1.12e+73)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(t * 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 <= -3.6e+87)
		tmp = j * (t * c);
	elseif (t <= 1.4e-58)
		tmp = i * (a * b);
	elseif (t <= 1.12e+73)
		tmp = z * (x * y);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -3.6e+87], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-58], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.12e+73], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.59999999999999994e87

   1. Initial program 75.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in j around inf 47.5%

      \[\leadsto \color{blue}{\left(c \cdot t - y \cdot i\right) \cdot j} \]

   3. Taylor expanded in c around inf 45.0%

      \[\leadsto \color{blue}{\left(c \cdot t\right)} \cdot j \]
   4. Step-by-step derivation

      1. *-commutative 45.0%

         \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot j \]

   5. Simplified 45.0%

      \[\leadsto \color{blue}{\left(t \cdot c\right)} \cdot j \]

   if -3.59999999999999994e87 < t < 1.4e-58

   1. Initial program 78.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in a around inf 31.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 31.2%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 31.2%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 31.2%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 31.2%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 31.2%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 31.2%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   4. Simplified 31.2%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   5. Taylor expanded in i around inf 24.2%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 24.4%

         \[\leadsto \color{blue}{\left(a \cdot i\right) \cdot b} \]

      2. *-commutative 24.4%

         \[\leadsto \color{blue}{\left(i \cdot a\right)} \cdot b \]

      3. associate-*r* 26.8%

         \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   7. Simplified 26.8%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   if 1.4e-58 < t < 1.12e73

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in x around inf 42.0%

      \[\leadsto \color{blue}{\left(y \cdot z - a \cdot t\right) \cdot x} \]

   3. Taylor expanded in y around inf 28.5%

      \[\leadsto \color{blue}{\left(y \cdot z\right)} \cdot x \]

   4. Taylor expanded in y around 0 31.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   5. Step-by-step derivation

      1. *-commutative 31.6%

         \[\leadsto \color{blue}{\left(z \cdot x\right) \cdot y} \]

      2. associate-*l* 31.7%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

   6. Simplified 31.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y\right)} \]

   if 1.12e73 < t

   1. Initial program 69.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in t around inf 69.5%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   3. Step-by-step derivation

      1. *-commutative 69.5%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 69.5%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 69.5%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   4. Simplified 69.5%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   5. Taylor expanded in c around inf 49.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 49.0%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot c} \]

      2. associate-*l* 50.2%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

   7. Simplified 50.2%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+87}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-58}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 27: 30.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.85 \cdot 10^{+94} \lor \neg \left(t \leq 1.06 \cdot 10^{+73}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -2.85e+94) (not (<= t 1.06e+73))) (* c (* t j)) (* a (* b i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -2.85e+94) || !(t <= 1.06e+73)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-2.85d+94)) .or. (.not. (t <= 1.06d+73))) then
        tmp = c * (t * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -2.85e+94) || !(t <= 1.06e+73)) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -2.85e+94) or not (t <= 1.06e+73):
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -2.85e+94) || !(t <= 1.06e+73))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -2.85e+94) || ~((t <= 1.06e+73)))
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -2.85e+94], N[Not[LessEqual[t, 1.06e+73]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8500000000000001e94 or 1.0600000000000001e73 < t

   1. Initial program 72.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in t around inf 72.2%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   3. Step-by-step derivation

      1. *-commutative 72.2%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 72.2%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 72.2%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   4. Simplified 72.2%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   5. Taylor expanded in c around inf 46.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -2.8500000000000001e94 < t < 1.0600000000000001e73

   1. Initial program 78.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in a around inf 31.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 31.5%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 31.5%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 31.5%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 31.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 31.5%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 31.5%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   4. Simplified 31.5%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   5. Taylor expanded in i around inf 23.4%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.85 \cdot 10^{+94} \lor \neg \left(t \leq 1.06 \cdot 10^{+73}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 28: 30.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+86} \lor \neg \left(t \leq 8.6 \cdot 10^{+72}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -4.8e+86) (not (<= t 8.6e+72))) (* c (* t j)) (* i (* a b))))

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 <= -4.8e+86) || !(t <= 8.6e+72)) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * 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) :: tmp
    if ((t <= (-4.8d+86)) .or. (.not. (t <= 8.6d+72))) then
        tmp = c * (t * j)
    else
        tmp = i * (a * 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 tmp;
	if ((t <= -4.8e+86) || !(t <= 8.6e+72)) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -4.8e+86) or not (t <= 8.6e+72):
		tmp = c * (t * j)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -4.8e+86) || !(t <= 8.6e+72))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -4.8e+86) || ~((t <= 8.6e+72)))
		tmp = c * (t * j);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -4.8e+86], N[Not[LessEqual[t, 8.6e+72]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.8000000000000001e86 or 8.6000000000000003e72 < t

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in t around inf 72.5%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   3. Step-by-step derivation

      1. *-commutative 72.5%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 72.5%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 72.5%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   4. Simplified 72.5%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   5. Taylor expanded in c around inf 46.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]

   if -4.8000000000000001e86 < t < 8.6000000000000003e72

   1. Initial program 77.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in a around inf 31.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 31.0%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 31.0%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 31.0%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 31.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 31.0%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 31.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   4. Simplified 31.0%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   5. Taylor expanded in i around inf 23.5%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 23.7%

         \[\leadsto \color{blue}{\left(a \cdot i\right) \cdot b} \]

      2. *-commutative 23.7%

         \[\leadsto \color{blue}{\left(i \cdot a\right)} \cdot b \]

      3. associate-*r* 25.2%

         \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   7. Simplified 25.2%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+86} \lor \neg \left(t \leq 8.6 \cdot 10^{+72}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 29: 29.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+88} \lor \neg \left(t \leq 5.4 \cdot 10^{+72}\right):\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.22e+88) (not (<= t 5.4e+72))) (* t (* c j)) (* i (* a b))))

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 <= -1.22e+88) || !(t <= 5.4e+72)) {
		tmp = t * (c * j);
	} else {
		tmp = i * (a * 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) :: tmp
    if ((t <= (-1.22d+88)) .or. (.not. (t <= 5.4d+72))) then
        tmp = t * (c * j)
    else
        tmp = i * (a * 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 tmp;
	if ((t <= -1.22e+88) || !(t <= 5.4e+72)) {
		tmp = t * (c * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.22e+88) or not (t <= 5.4e+72):
		tmp = t * (c * j)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.22e+88) || !(t <= 5.4e+72))
		tmp = Float64(t * Float64(c * j));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.22e+88) || ~((t <= 5.4e+72)))
		tmp = t * (c * j);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.22e+88], N[Not[LessEqual[t, 5.4e+72]], $MachinePrecision]], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.22e88 or 5.4000000000000001e72 < t

   1. Initial program 72.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in t around inf 72.5%

      \[\leadsto \color{blue}{\left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right) \cdot t} \]
   3. Step-by-step derivation

      1. *-commutative 72.5%

         \[\leadsto \color{blue}{t \cdot \left(c \cdot j + -1 \cdot \left(a \cdot x\right)\right)} \]

      2. mul-1-neg 72.5%

         \[\leadsto t \cdot \left(c \cdot j + \color{blue}{\left(-a \cdot x\right)}\right) \]

      3. unsub-neg 72.5%

         \[\leadsto t \cdot \color{blue}{\left(c \cdot j - a \cdot x\right)} \]

   4. Simplified 72.5%

      \[\leadsto \color{blue}{t \cdot \left(c \cdot j - a \cdot x\right)} \]

   5. Taylor expanded in c around inf 46.0%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j\right)} \]
   6. Step-by-step derivation

      1. *-commutative 46.0%

         \[\leadsto \color{blue}{\left(t \cdot j\right) \cdot c} \]

      2. associate-*l* 47.8%

         \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

   7. Simplified 47.8%

      \[\leadsto \color{blue}{t \cdot \left(j \cdot c\right)} \]

   if -1.22e88 < t < 5.4000000000000001e72

   1. Initial program 77.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in a around inf 31.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 31.0%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

      2. neg-mul-1 31.0%

         \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

      3. cancel-sign-sub 31.0%

         \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

      4. +-commutative 31.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

      5. mul-1-neg 31.0%

         \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

      6. unsub-neg 31.0%

         \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

   4. Simplified 31.0%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

   5. Taylor expanded in i around inf 23.5%

      \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 23.7%

         \[\leadsto \color{blue}{\left(a \cdot i\right) \cdot b} \]

      2. *-commutative 23.7%

         \[\leadsto \color{blue}{\left(i \cdot a\right)} \cdot b \]

      3. associate-*r* 25.2%

         \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]

   7. Simplified 25.2%

      \[\leadsto \color{blue}{i \cdot \left(a \cdot b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+88} \lor \neg \left(t \leq 5.4 \cdot 10^{+72}\right):\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]

Alternative 30: 23.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.1%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

2. Taylor expanded in a around inf 34.2%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) - -1 \cdot \left(i \cdot b\right)\right)} \]
3. Step-by-step derivation

   1. associate-*r* 34.2%

      \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-1 \cdot i\right) \cdot b}\right) \]

   2. neg-mul-1 34.2%

      \[\leadsto a \cdot \left(-1 \cdot \left(t \cdot x\right) - \color{blue}{\left(-i\right)} \cdot b\right) \]

   3. cancel-sign-sub 34.2%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right) + i \cdot b\right)} \]

   4. +-commutative 34.2%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b + -1 \cdot \left(t \cdot x\right)\right)} \]

   5. mul-1-neg 34.2%

      \[\leadsto a \cdot \left(i \cdot b + \color{blue}{\left(-t \cdot x\right)}\right) \]

   6. unsub-neg 34.2%

      \[\leadsto a \cdot \color{blue}{\left(i \cdot b - t \cdot x\right)} \]

4. Simplified 34.2%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b - t \cdot x\right)} \]

5. Taylor expanded in i around inf 20.0%

   \[\leadsto \color{blue}{a \cdot \left(i \cdot b\right)} \]

6. Final simplification 20.0%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Developer target: 70.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2023274 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))