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

Percentage Accurate: 73.6% → 79.9%

Time: 33.8s

Alternatives: 22

Speedup: 0.5×

• 58.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 79.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := a \cdot c - y \cdot i\\ t_3 := t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_4 := t\_3 + j \cdot t\_2\\ t_5 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;t\_4 \leq 2 \cdot 10^{+216}:\\ \;\;\;\;\mathsf{fma}\left(j, t\_2, t\_3\right)\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;\left(\left(t\_1 + a \cdot \left(c \cdot j\right)\right) + t\_5\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (- (* a c) (* y i)))
        (t_3 (+ t_1 (* b (- (* t i) (* z c)))))
        (t_4 (+ t_3 (* j t_2)))
        (t_5 (* i (- (* t b) (* y j)))))
   (if (<= t_4 2e+216)
     (fma j t_2 t_3)
     (if (<= t_4 INFINITY)
       (- (+ (+ t_1 (* a (* c j))) t_5) (* b (* z c)))
       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 = x * ((y * z) - (t * a));
	double t_2 = (a * c) - (y * i);
	double t_3 = t_1 + (b * ((t * i) - (z * c)));
	double t_4 = t_3 + (j * t_2);
	double t_5 = i * ((t * b) - (y * j));
	double tmp;
	if (t_4 <= 2e+216) {
		tmp = fma(j, t_2, t_3);
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = ((t_1 + (a * (c * j))) + t_5) - (b * (z * c));
	} else {
		tmp = t_5;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(Float64(a * c) - Float64(y * i))
	t_3 = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_4 = Float64(t_3 + Float64(j * t_2))
	t_5 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (t_4 <= 2e+216)
		tmp = fma(j, t_2, t_3);
	elseif (t_4 <= Inf)
		tmp = Float64(Float64(Float64(t_1 + Float64(a * Float64(c * j))) + t_5) - Float64(b * Float64(z * c)));
	else
		tmp = t_5;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + N[(j * t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, 2e+216], N[(j * t$95$2 + t$95$3), $MachinePrecision], If[LessEqual[t$95$4, Infinity], N[(N[(N[(t$95$1 + N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$5]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < 2e216

   1. Initial program 91.3%

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

      1. +-commutative 91.3%

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

      2. fma-define 91.3%

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

      3. *-commutative 91.3%

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

      4. *-commutative 91.3%

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

   3. Simplified 91.3%

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

   if 2e216 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 83.5%

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

   3. Taylor expanded in i around -inf 91.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around inf 54.0%

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

      1. distribute-lft-out-- 54.0%

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

   5. Simplified 54.0%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq 2 \cdot 10^{+216}:\\ \;\;\;\;\mathsf{fma}\left(j, a \cdot c - y \cdot i, x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right)\\ \mathbf{elif}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z - t \cdot a\right) + a \cdot \left(c \cdot j\right)\right) + i \cdot \left(t \cdot b - y \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 79.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := \left(t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;t\_2 \leq 2 \cdot 10^{+216}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\left(\left(t\_1 + a \cdot \left(c \cdot j\right)\right) + t\_3\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ (+ t_1 (* b (- (* t i) (* z c)))) (* j (- (* a c) (* y i)))))
        (t_3 (* i (- (* t b) (* y j)))))
   (if (<= t_2 2e+216)
     t_2
     (if (<= t_2 INFINITY)
       (- (+ (+ t_1 (* a (* c j))) t_3) (* b (* z c)))
       t_3))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (t_1 + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (t_2 <= 2e+216) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = ((t_1 + (a * (c * j))) + t_3) - (b * (z * c));
	} else {
		tmp = t_3;
	}
	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));
	double t_2 = (t_1 + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (t_2 <= 2e+216) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = ((t_1 + (a * (c * j))) + t_3) - (b * (z * c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = (t_1 + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)))
	t_3 = i * ((t * b) - (y * j))
	tmp = 0
	if t_2 <= 2e+216:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = ((t_1 + (a * (c * j))) + t_3) - (b * (z * c))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	t_3 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (t_2 <= 2e+216)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(Float64(t_1 + Float64(a * Float64(c * j))) + t_3) - Float64(b * Float64(z * c)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = (t_1 + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	t_3 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (t_2 <= 2e+216)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = ((t_1 + (a * (c * j))) + t_3) - (b * (z * c));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, 2e+216], t$95$2, If[LessEqual[t$95$2, Infinity], N[(N[(N[(t$95$1 + N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < 2e216

   1. Initial program 91.3%

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

   if 2e216 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 83.5%

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

   3. Taylor expanded in i around -inf 91.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around inf 54.0%

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

      1. distribute-lft-out-- 54.0%

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

   5. Simplified 54.0%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq 2 \cdot 10^{+216}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z - t \cdot a\right) + a \cdot \left(c \cdot j\right)\right) + i \cdot \left(t \cdot b - y \cdot j\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 88.7%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in i around inf 54.0%

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

      1. distribute-lft-out-- 54.0%

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

   5. Simplified 54.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.9%

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

Alternative 4: 29.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := i \cdot \left(t \cdot b\right)\\ t_3 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+168}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-10}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-125}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-280}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-83}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+23}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))) (t_2 (* i (* t b))) (t_3 (* a (* c j))))
   (if (<= t -1.6e+168)
     t_2
     (if (<= t -1.55e-10)
       (* a (* t (- x)))
       (if (<= t -3.4e-91)
         t_2
         (if (<= t -3.8e-125)
           (* c (* a j))
           (if (<= t 8.8e-280)
             t_1
             (if (<= t 1.7e-83)
               t_3
               (if (<= t 3.7e-28)
                 t_1
                 (if (<= t 8.5e+23) t_3 (* b (* t i))))))))))))

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 = i * (t * b);
	double t_3 = a * (c * j);
	double tmp;
	if (t <= -1.6e+168) {
		tmp = t_2;
	} else if (t <= -1.55e-10) {
		tmp = a * (t * -x);
	} else if (t <= -3.4e-91) {
		tmp = t_2;
	} else if (t <= -3.8e-125) {
		tmp = c * (a * j);
	} else if (t <= 8.8e-280) {
		tmp = t_1;
	} else if (t <= 1.7e-83) {
		tmp = t_3;
	} else if (t <= 3.7e-28) {
		tmp = t_1;
	} else if (t <= 8.5e+23) {
		tmp = t_3;
	} else {
		tmp = b * (t * 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * (x * z)
    t_2 = i * (t * b)
    t_3 = a * (c * j)
    if (t <= (-1.6d+168)) then
        tmp = t_2
    else if (t <= (-1.55d-10)) then
        tmp = a * (t * -x)
    else if (t <= (-3.4d-91)) then
        tmp = t_2
    else if (t <= (-3.8d-125)) then
        tmp = c * (a * j)
    else if (t <= 8.8d-280) then
        tmp = t_1
    else if (t <= 1.7d-83) then
        tmp = t_3
    else if (t <= 3.7d-28) then
        tmp = t_1
    else if (t <= 8.5d+23) then
        tmp = t_3
    else
        tmp = b * (t * 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 t_1 = y * (x * z);
	double t_2 = i * (t * b);
	double t_3 = a * (c * j);
	double tmp;
	if (t <= -1.6e+168) {
		tmp = t_2;
	} else if (t <= -1.55e-10) {
		tmp = a * (t * -x);
	} else if (t <= -3.4e-91) {
		tmp = t_2;
	} else if (t <= -3.8e-125) {
		tmp = c * (a * j);
	} else if (t <= 8.8e-280) {
		tmp = t_1;
	} else if (t <= 1.7e-83) {
		tmp = t_3;
	} else if (t <= 3.7e-28) {
		tmp = t_1;
	} else if (t <= 8.5e+23) {
		tmp = t_3;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	t_2 = i * (t * b)
	t_3 = a * (c * j)
	tmp = 0
	if t <= -1.6e+168:
		tmp = t_2
	elif t <= -1.55e-10:
		tmp = a * (t * -x)
	elif t <= -3.4e-91:
		tmp = t_2
	elif t <= -3.8e-125:
		tmp = c * (a * j)
	elif t <= 8.8e-280:
		tmp = t_1
	elif t <= 1.7e-83:
		tmp = t_3
	elif t <= 3.7e-28:
		tmp = t_1
	elif t <= 8.5e+23:
		tmp = t_3
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	t_2 = Float64(i * Float64(t * b))
	t_3 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (t <= -1.6e+168)
		tmp = t_2;
	elseif (t <= -1.55e-10)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (t <= -3.4e-91)
		tmp = t_2;
	elseif (t <= -3.8e-125)
		tmp = Float64(c * Float64(a * j));
	elseif (t <= 8.8e-280)
		tmp = t_1;
	elseif (t <= 1.7e-83)
		tmp = t_3;
	elseif (t <= 3.7e-28)
		tmp = t_1;
	elseif (t <= 8.5e+23)
		tmp = t_3;
	else
		tmp = Float64(b * Float64(t * i));
	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 = i * (t * b);
	t_3 = a * (c * j);
	tmp = 0.0;
	if (t <= -1.6e+168)
		tmp = t_2;
	elseif (t <= -1.55e-10)
		tmp = a * (t * -x);
	elseif (t <= -3.4e-91)
		tmp = t_2;
	elseif (t <= -3.8e-125)
		tmp = c * (a * j);
	elseif (t <= 8.8e-280)
		tmp = t_1;
	elseif (t <= 1.7e-83)
		tmp = t_3;
	elseif (t <= 3.7e-28)
		tmp = t_1;
	elseif (t <= 8.5e+23)
		tmp = t_3;
	else
		tmp = b * (t * i);
	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[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+168], t$95$2, If[LessEqual[t, -1.55e-10], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.4e-91], t$95$2, If[LessEqual[t, -3.8e-125], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.8e-280], t$95$1, If[LessEqual[t, 1.7e-83], t$95$3, If[LessEqual[t, 3.7e-28], t$95$1, If[LessEqual[t, 8.5e+23], t$95$3, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.6000000000000001e168 or -1.55000000000000008e-10 < t < -3.40000000000000027e-91

   1. Initial program 65.2%

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

   3. Taylor expanded in t around inf 58.8%

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

      1. distribute-lft-out-- 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in a around 0 42.2%

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

      1. neg-mul-1 42.2%

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

      2. distribute-rgt-neg-in 42.2%

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

   8. Simplified 42.2%

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

   9. Taylor expanded in t around 0 43.2%

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

       1. *-commutative 43.2%

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

       2. associate-*l* 46.9%

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

   11. Simplified 46.9%

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

   if -1.6000000000000001e168 < t < -1.55000000000000008e-10

   1. Initial program 65.4%

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

   3. Taylor expanded in a around inf 49.3%

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

      1. +-commutative 49.3%

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

      2. mul-1-neg 49.3%

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

      3. unsub-neg 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in c around 0 35.9%

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

      1. mul-1-neg 35.9%

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

      2. distribute-lft-neg-out 35.9%

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

      3. *-commutative 35.9%

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

   8. Simplified 35.9%

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

   if -3.40000000000000027e-91 < t < -3.8000000000000001e-125

   1. Initial program 78.3%

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

   3. Taylor expanded in a around inf 57.2%

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

      1. +-commutative 57.2%

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

      2. mul-1-neg 57.2%

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

      3. unsub-neg 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in c around inf 36.3%

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

      1. *-commutative 36.3%

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

      2. associate-*l* 67.4%

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

      3. *-commutative 67.4%

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

   8. Simplified 67.4%

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

   if -3.8000000000000001e-125 < t < 8.8000000000000004e-280 or 1.6999999999999999e-83 < t < 3.7000000000000002e-28

   1. Initial program 77.1%

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

   3. Taylor expanded in y around inf 59.2%

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

      1. +-commutative 59.2%

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

      2. mul-1-neg 59.2%

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

      3. unsub-neg 59.2%

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

      4. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in z around inf 34.0%

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

      1. *-commutative 34.0%

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

      2. associate-*l* 41.7%

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

   8. Simplified 41.7%

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

   if 8.8000000000000004e-280 < t < 1.6999999999999999e-83 or 3.7000000000000002e-28 < t < 8.5000000000000001e23

   1. Initial program 80.5%

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

   3. Taylor expanded in a around inf 52.2%

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

      1. +-commutative 52.2%

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

      2. mul-1-neg 52.2%

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

      3. unsub-neg 52.2%

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

   5. Simplified 52.2%

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

   6. Taylor expanded in c around inf 43.7%

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

      1. *-commutative 43.7%

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

   8. Simplified 43.7%

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

   if 8.5000000000000001e23 < t

   1. Initial program 76.7%

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

   3. Taylor expanded in t around inf 65.4%

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

      1. distribute-lft-out-- 65.4%

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

   5. Simplified 65.4%

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

   6. Taylor expanded in a around 0 49.0%

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

      1. *-commutative 49.0%

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

   8. Simplified 49.0%

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

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+168}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-10}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-91}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-125}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-280}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-28}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+23}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 29.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -0.005:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-125}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-95}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-7}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* t b))))
   (if (<= t -1.45e+169)
     t_1
     (if (<= t -0.005)
       (* a (* t (- x)))
       (if (<= t -3.8e-91)
         t_1
         (if (<= t -3.5e-125)
           (* c (* a j))
           (if (<= t 1.62e-279)
             (* y (* x z))
             (if (<= t 1.25e-95)
               (* a (* c j))
               (if (<= t 3.8e-7) (* c (* z (- b))) (* b (* t i)))))))))))

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 * (t * b);
	double tmp;
	if (t <= -1.45e+169) {
		tmp = t_1;
	} else if (t <= -0.005) {
		tmp = a * (t * -x);
	} else if (t <= -3.8e-91) {
		tmp = t_1;
	} else if (t <= -3.5e-125) {
		tmp = c * (a * j);
	} else if (t <= 1.62e-279) {
		tmp = y * (x * z);
	} else if (t <= 1.25e-95) {
		tmp = a * (c * j);
	} else if (t <= 3.8e-7) {
		tmp = c * (z * -b);
	} else {
		tmp = b * (t * 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) :: t_1
    real(8) :: tmp
    t_1 = i * (t * b)
    if (t <= (-1.45d+169)) then
        tmp = t_1
    else if (t <= (-0.005d0)) then
        tmp = a * (t * -x)
    else if (t <= (-3.8d-91)) then
        tmp = t_1
    else if (t <= (-3.5d-125)) then
        tmp = c * (a * j)
    else if (t <= 1.62d-279) then
        tmp = y * (x * z)
    else if (t <= 1.25d-95) then
        tmp = a * (c * j)
    else if (t <= 3.8d-7) then
        tmp = c * (z * -b)
    else
        tmp = b * (t * 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 t_1 = i * (t * b);
	double tmp;
	if (t <= -1.45e+169) {
		tmp = t_1;
	} else if (t <= -0.005) {
		tmp = a * (t * -x);
	} else if (t <= -3.8e-91) {
		tmp = t_1;
	} else if (t <= -3.5e-125) {
		tmp = c * (a * j);
	} else if (t <= 1.62e-279) {
		tmp = y * (x * z);
	} else if (t <= 1.25e-95) {
		tmp = a * (c * j);
	} else if (t <= 3.8e-7) {
		tmp = c * (z * -b);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (t * b)
	tmp = 0
	if t <= -1.45e+169:
		tmp = t_1
	elif t <= -0.005:
		tmp = a * (t * -x)
	elif t <= -3.8e-91:
		tmp = t_1
	elif t <= -3.5e-125:
		tmp = c * (a * j)
	elif t <= 1.62e-279:
		tmp = y * (x * z)
	elif t <= 1.25e-95:
		tmp = a * (c * j)
	elif t <= 3.8e-7:
		tmp = c * (z * -b)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (t <= -1.45e+169)
		tmp = t_1;
	elseif (t <= -0.005)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (t <= -3.8e-91)
		tmp = t_1;
	elseif (t <= -3.5e-125)
		tmp = Float64(c * Float64(a * j));
	elseif (t <= 1.62e-279)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 1.25e-95)
		tmp = Float64(a * Float64(c * j));
	elseif (t <= 3.8e-7)
		tmp = Float64(c * Float64(z * Float64(-b)));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (t * b);
	tmp = 0.0;
	if (t <= -1.45e+169)
		tmp = t_1;
	elseif (t <= -0.005)
		tmp = a * (t * -x);
	elseif (t <= -3.8e-91)
		tmp = t_1;
	elseif (t <= -3.5e-125)
		tmp = c * (a * j);
	elseif (t <= 1.62e-279)
		tmp = y * (x * z);
	elseif (t <= 1.25e-95)
		tmp = a * (c * j);
	elseif (t <= 3.8e-7)
		tmp = c * (z * -b);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.45e+169], t$95$1, If[LessEqual[t, -0.005], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e-91], t$95$1, If[LessEqual[t, -3.5e-125], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.62e-279], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-95], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e-7], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.45e169 or -0.0050000000000000001 < t < -3.79999999999999978e-91

   1. Initial program 65.2%

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

   3. Taylor expanded in t around inf 58.8%

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

      1. distribute-lft-out-- 58.8%

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

   5. Simplified 58.8%

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

   6. Taylor expanded in a around 0 42.2%

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

      1. neg-mul-1 42.2%

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

      2. distribute-rgt-neg-in 42.2%

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

   8. Simplified 42.2%

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

   9. Taylor expanded in t around 0 43.2%

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

       1. *-commutative 43.2%

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

       2. associate-*l* 46.9%

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

   11. Simplified 46.9%

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

   if -1.45e169 < t < -0.0050000000000000001

   1. Initial program 65.4%

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

   3. Taylor expanded in a around inf 49.3%

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

      1. +-commutative 49.3%

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

      2. mul-1-neg 49.3%

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

      3. unsub-neg 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in c around 0 35.9%

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

      1. mul-1-neg 35.9%

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

      2. distribute-lft-neg-out 35.9%

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

      3. *-commutative 35.9%

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

   8. Simplified 35.9%

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

   if -3.79999999999999978e-91 < t < -3.49999999999999998e-125

   1. Initial program 78.3%

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

   3. Taylor expanded in a around inf 57.2%

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

      1. +-commutative 57.2%

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

      2. mul-1-neg 57.2%

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

      3. unsub-neg 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in c around inf 36.3%

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

      1. *-commutative 36.3%

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

      2. associate-*l* 67.4%

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

      3. *-commutative 67.4%

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

   8. Simplified 67.4%

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

   if -3.49999999999999998e-125 < t < 1.62e-279

   1. Initial program 75.0%

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

   3. Taylor expanded in y around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. mul-1-neg 59.1%

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

      3. unsub-neg 59.1%

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

      4. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in z around inf 34.4%

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

      1. *-commutative 34.4%

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

      2. associate-*l* 42.2%

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

   8. Simplified 42.2%

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

   if 1.62e-279 < t < 1.2499999999999999e-95

   1. Initial program 85.9%

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

   3. Taylor expanded in a around inf 51.1%

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

      1. +-commutative 51.1%

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

      2. mul-1-neg 51.1%

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

      3. unsub-neg 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in c around inf 48.3%

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

      1. *-commutative 48.3%

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

   8. Simplified 48.3%

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

   if 1.2499999999999999e-95 < t < 3.80000000000000015e-7

   1. Initial program 84.1%

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

   3. Taylor expanded in c around inf 38.9%

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

      1. *-commutative 38.9%

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

   5. Simplified 38.9%

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

   6. Taylor expanded in j around 0 34.0%

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

      1. neg-mul-1 34.0%

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

      2. distribute-rgt-neg-in 34.0%

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

   8. Simplified 34.0%

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

   if 3.80000000000000015e-7 < t

   1. Initial program 73.9%

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

   3. Taylor expanded in t around inf 65.1%

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

      1. distribute-lft-out-- 65.1%

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

   5. Simplified 65.1%

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

   6. Taylor expanded in a around 0 46.8%

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

      1. *-commutative 46.8%

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

   8. Simplified 46.8%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+169}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq -0.005:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-91}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-125}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq 1.62 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-95}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-7}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 28.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;t \leq -3 \cdot 10^{+168}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-125}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq 10^{-277}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))) (t_2 (* i (* t b))))
   (if (<= t -3e+168)
     t_2
     (if (<= t -1.02e+17)
       t_1
       (if (<= t -4e-91)
         t_2
         (if (<= t -2.4e-125)
           (* c (* a j))
           (if (<= t 1e-277)
             t_1
             (if (<= t 2.5e-83)
               (* a (* c j))
               (if (<= t 1e+34) t_1 (* b (* t i)))))))))))

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 = i * (t * b);
	double tmp;
	if (t <= -3e+168) {
		tmp = t_2;
	} else if (t <= -1.02e+17) {
		tmp = t_1;
	} else if (t <= -4e-91) {
		tmp = t_2;
	} else if (t <= -2.4e-125) {
		tmp = c * (a * j);
	} else if (t <= 1e-277) {
		tmp = t_1;
	} else if (t <= 2.5e-83) {
		tmp = a * (c * j);
	} else if (t <= 1e+34) {
		tmp = t_1;
	} else {
		tmp = b * (t * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (x * z)
    t_2 = i * (t * b)
    if (t <= (-3d+168)) then
        tmp = t_2
    else if (t <= (-1.02d+17)) then
        tmp = t_1
    else if (t <= (-4d-91)) then
        tmp = t_2
    else if (t <= (-2.4d-125)) then
        tmp = c * (a * j)
    else if (t <= 1d-277) then
        tmp = t_1
    else if (t <= 2.5d-83) then
        tmp = a * (c * j)
    else if (t <= 1d+34) then
        tmp = t_1
    else
        tmp = b * (t * 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 t_1 = y * (x * z);
	double t_2 = i * (t * b);
	double tmp;
	if (t <= -3e+168) {
		tmp = t_2;
	} else if (t <= -1.02e+17) {
		tmp = t_1;
	} else if (t <= -4e-91) {
		tmp = t_2;
	} else if (t <= -2.4e-125) {
		tmp = c * (a * j);
	} else if (t <= 1e-277) {
		tmp = t_1;
	} else if (t <= 2.5e-83) {
		tmp = a * (c * j);
	} else if (t <= 1e+34) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	t_2 = i * (t * b)
	tmp = 0
	if t <= -3e+168:
		tmp = t_2
	elif t <= -1.02e+17:
		tmp = t_1
	elif t <= -4e-91:
		tmp = t_2
	elif t <= -2.4e-125:
		tmp = c * (a * j)
	elif t <= 1e-277:
		tmp = t_1
	elif t <= 2.5e-83:
		tmp = a * (c * j)
	elif t <= 1e+34:
		tmp = t_1
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	t_2 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (t <= -3e+168)
		tmp = t_2;
	elseif (t <= -1.02e+17)
		tmp = t_1;
	elseif (t <= -4e-91)
		tmp = t_2;
	elseif (t <= -2.4e-125)
		tmp = Float64(c * Float64(a * j));
	elseif (t <= 1e-277)
		tmp = t_1;
	elseif (t <= 2.5e-83)
		tmp = Float64(a * Float64(c * j));
	elseif (t <= 1e+34)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(t * i));
	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 = i * (t * b);
	tmp = 0.0;
	if (t <= -3e+168)
		tmp = t_2;
	elseif (t <= -1.02e+17)
		tmp = t_1;
	elseif (t <= -4e-91)
		tmp = t_2;
	elseif (t <= -2.4e-125)
		tmp = c * (a * j);
	elseif (t <= 1e-277)
		tmp = t_1;
	elseif (t <= 2.5e-83)
		tmp = a * (c * j);
	elseif (t <= 1e+34)
		tmp = t_1;
	else
		tmp = b * (t * i);
	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[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3e+168], t$95$2, If[LessEqual[t, -1.02e+17], t$95$1, If[LessEqual[t, -4e-91], t$95$2, If[LessEqual[t, -2.4e-125], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-277], t$95$1, If[LessEqual[t, 2.5e-83], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+34], t$95$1, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.9999999999999998e168 or -1.02e17 < t < -4.00000000000000009e-91

   1. Initial program 65.9%

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

   3. Taylor expanded in t around inf 58.3%

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

      1. distribute-lft-out-- 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in a around 0 41.2%

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

      1. neg-mul-1 41.2%

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

      2. distribute-rgt-neg-in 41.2%

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

   8. Simplified 41.2%

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

   9. Taylor expanded in t around 0 42.1%

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

       1. *-commutative 42.1%

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

       2. associate-*l* 45.5%

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

   11. Simplified 45.5%

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

   if -2.9999999999999998e168 < t < -1.02e17 or -2.4000000000000001e-125 < t < 9.99999999999999969e-278 or 2.5e-83 < t < 9.99999999999999946e33

   1. Initial program 71.9%

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

   3. Taylor expanded in y around inf 49.9%

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

      1. +-commutative 49.9%

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

      2. mul-1-neg 49.9%

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

      3. unsub-neg 49.9%

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

      4. *-commutative 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in z around inf 28.7%

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

      1. *-commutative 28.7%

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

      2. associate-*l* 33.3%

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

   8. Simplified 33.3%

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

   if -4.00000000000000009e-91 < t < -2.4000000000000001e-125

   1. Initial program 78.3%

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

   3. Taylor expanded in a around inf 57.2%

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

      1. +-commutative 57.2%

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

      2. mul-1-neg 57.2%

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

      3. unsub-neg 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in c around inf 36.3%

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

      1. *-commutative 36.3%

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

      2. associate-*l* 67.4%

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

      3. *-commutative 67.4%

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

   8. Simplified 67.4%

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

   if 9.99999999999999969e-278 < t < 2.5e-83

   1. Initial program 86.3%

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

   3. Taylor expanded in a around inf 49.8%

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

      1. +-commutative 49.8%

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

      2. mul-1-neg 49.8%

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

      3. unsub-neg 49.8%

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

   5. Simplified 49.8%

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

   6. Taylor expanded in c around inf 47.0%

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

      1. *-commutative 47.0%

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

   8. Simplified 47.0%

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

   if 9.99999999999999946e33 < t

   1. Initial program 76.9%

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

   3. Taylor expanded in t around inf 64.7%

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

      1. distribute-lft-out-- 64.7%

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

   5. Simplified 64.7%

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

   6. Taylor expanded in a around 0 50.6%

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

      1. *-commutative 50.6%

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

   8. Simplified 50.6%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{+168}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-91}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-125}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq 10^{-277}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 10^{+34}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 28.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+170}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-92}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-125}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-84}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* i (* t b))))
   (if (<= t -3.4e+170)
     t_2
     (if (<= t -9.8e+16)
       t_1
       (if (<= t -5e-92)
         t_2
         (if (<= t -8e-125)
           (* c (* a j))
           (if (<= t 1.06e-277)
             (* y (* x z))
             (if (<= t 7.8e-84)
               (* a (* c j))
               (if (<= t 2.3e+33) t_1 (* b (* t i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double t_2 = i * (t * b);
	double tmp;
	if (t <= -3.4e+170) {
		tmp = t_2;
	} else if (t <= -9.8e+16) {
		tmp = t_1;
	} else if (t <= -5e-92) {
		tmp = t_2;
	} else if (t <= -8e-125) {
		tmp = c * (a * j);
	} else if (t <= 1.06e-277) {
		tmp = y * (x * z);
	} else if (t <= 7.8e-84) {
		tmp = a * (c * j);
	} else if (t <= 2.3e+33) {
		tmp = t_1;
	} else {
		tmp = b * (t * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * (x * y)
    t_2 = i * (t * b)
    if (t <= (-3.4d+170)) then
        tmp = t_2
    else if (t <= (-9.8d+16)) then
        tmp = t_1
    else if (t <= (-5d-92)) then
        tmp = t_2
    else if (t <= (-8d-125)) then
        tmp = c * (a * j)
    else if (t <= 1.06d-277) then
        tmp = y * (x * z)
    else if (t <= 7.8d-84) then
        tmp = a * (c * j)
    else if (t <= 2.3d+33) then
        tmp = t_1
    else
        tmp = b * (t * 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 t_1 = z * (x * y);
	double t_2 = i * (t * b);
	double tmp;
	if (t <= -3.4e+170) {
		tmp = t_2;
	} else if (t <= -9.8e+16) {
		tmp = t_1;
	} else if (t <= -5e-92) {
		tmp = t_2;
	} else if (t <= -8e-125) {
		tmp = c * (a * j);
	} else if (t <= 1.06e-277) {
		tmp = y * (x * z);
	} else if (t <= 7.8e-84) {
		tmp = a * (c * j);
	} else if (t <= 2.3e+33) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = i * (t * b)
	tmp = 0
	if t <= -3.4e+170:
		tmp = t_2
	elif t <= -9.8e+16:
		tmp = t_1
	elif t <= -5e-92:
		tmp = t_2
	elif t <= -8e-125:
		tmp = c * (a * j)
	elif t <= 1.06e-277:
		tmp = y * (x * z)
	elif t <= 7.8e-84:
		tmp = a * (c * j)
	elif t <= 2.3e+33:
		tmp = t_1
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (t <= -3.4e+170)
		tmp = t_2;
	elseif (t <= -9.8e+16)
		tmp = t_1;
	elseif (t <= -5e-92)
		tmp = t_2;
	elseif (t <= -8e-125)
		tmp = Float64(c * Float64(a * j));
	elseif (t <= 1.06e-277)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 7.8e-84)
		tmp = Float64(a * Float64(c * j));
	elseif (t <= 2.3e+33)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	t_2 = i * (t * b);
	tmp = 0.0;
	if (t <= -3.4e+170)
		tmp = t_2;
	elseif (t <= -9.8e+16)
		tmp = t_1;
	elseif (t <= -5e-92)
		tmp = t_2;
	elseif (t <= -8e-125)
		tmp = c * (a * j);
	elseif (t <= 1.06e-277)
		tmp = y * (x * z);
	elseif (t <= 7.8e-84)
		tmp = a * (c * j);
	elseif (t <= 2.3e+33)
		tmp = t_1;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e+170], t$95$2, If[LessEqual[t, -9.8e+16], t$95$1, If[LessEqual[t, -5e-92], t$95$2, If[LessEqual[t, -8e-125], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.06e-277], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e-84], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+33], t$95$1, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -3.4000000000000001e170 or -9.8e16 < t < -5.00000000000000011e-92

   1. Initial program 65.9%

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

   3. Taylor expanded in t around inf 58.3%

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

      1. distribute-lft-out-- 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in a around 0 41.2%

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

      1. neg-mul-1 41.2%

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

      2. distribute-rgt-neg-in 41.2%

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

   8. Simplified 41.2%

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

   9. Taylor expanded in t around 0 42.1%

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

       1. *-commutative 42.1%

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

       2. associate-*l* 45.5%

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

   11. Simplified 45.5%

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

   if -3.4000000000000001e170 < t < -9.8e16 or 7.80000000000000045e-84 < t < 2.30000000000000011e33

   1. Initial program 69.2%

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

   3. Taylor expanded in z around inf 45.9%

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

      1. *-commutative 45.9%

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

   5. Simplified 45.9%

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

   6. Taylor expanded in y around inf 27.1%

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

   if -5.00000000000000011e-92 < t < -8.0000000000000001e-125

   1. Initial program 78.3%

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

   3. Taylor expanded in a around inf 57.2%

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

      1. +-commutative 57.2%

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

      2. mul-1-neg 57.2%

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

      3. unsub-neg 57.2%

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

   5. Simplified 57.2%

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

   6. Taylor expanded in c around inf 36.3%

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

      1. *-commutative 36.3%

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

      2. associate-*l* 67.4%

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

      3. *-commutative 67.4%

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

   8. Simplified 67.4%

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

   if -8.0000000000000001e-125 < t < 1.06e-277

   1. Initial program 75.0%

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

   3. Taylor expanded in y around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. mul-1-neg 59.1%

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

      3. unsub-neg 59.1%

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

      4. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in z around inf 34.4%

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

      1. *-commutative 34.4%

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

      2. associate-*l* 42.2%

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

   8. Simplified 42.2%

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

   if 1.06e-277 < t < 7.80000000000000045e-84

   1. Initial program 86.3%

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

   3. Taylor expanded in a around inf 49.8%

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

      1. +-commutative 49.8%

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

      2. mul-1-neg 49.8%

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

      3. unsub-neg 49.8%

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

   5. Simplified 49.8%

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

   6. Taylor expanded in c around inf 47.0%

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

      1. *-commutative 47.0%

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

   8. Simplified 47.0%

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

   if 2.30000000000000011e33 < t

   1. Initial program 76.9%

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

   3. Taylor expanded in t around inf 64.7%

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

      1. distribute-lft-out-- 64.7%

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

   5. Simplified 64.7%

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

   6. Taylor expanded in a around 0 50.6%

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

      1. *-commutative 50.6%

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

   8. Simplified 50.6%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+170}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-92}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-125}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;t \leq 1.06 \cdot 10^{-277}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-84}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+33}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.72 \cdot 10^{+198}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{+147}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{+55}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.25 \cdot 10^{-223}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.66 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* a (- (* c j) (* x t))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -1.72e+198)
     t_3
     (if (<= b -6.6e+147)
       t_2
       (if (<= b -2.6e+55)
         t_3
         (if (<= b -1.85e-147)
           t_1
           (if (<= b -2.25e-223) t_2 (if (<= b 1.66e-9) 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 = y * ((x * z) - (i * j));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.72e+198) {
		tmp = t_3;
	} else if (b <= -6.6e+147) {
		tmp = t_2;
	} else if (b <= -2.6e+55) {
		tmp = t_3;
	} else if (b <= -1.85e-147) {
		tmp = t_1;
	} else if (b <= -2.25e-223) {
		tmp = t_2;
	} else if (b <= 1.66e-9) {
		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 = y * ((x * z) - (i * j))
    t_2 = a * ((c * j) - (x * t))
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-1.72d+198)) then
        tmp = t_3
    else if (b <= (-6.6d+147)) then
        tmp = t_2
    else if (b <= (-2.6d+55)) then
        tmp = t_3
    else if (b <= (-1.85d-147)) then
        tmp = t_1
    else if (b <= (-2.25d-223)) then
        tmp = t_2
    else if (b <= 1.66d-9) 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 = y * ((x * z) - (i * j));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.72e+198) {
		tmp = t_3;
	} else if (b <= -6.6e+147) {
		tmp = t_2;
	} else if (b <= -2.6e+55) {
		tmp = t_3;
	} else if (b <= -1.85e-147) {
		tmp = t_1;
	} else if (b <= -2.25e-223) {
		tmp = t_2;
	} else if (b <= 1.66e-9) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = a * ((c * j) - (x * t))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1.72e+198:
		tmp = t_3
	elif b <= -6.6e+147:
		tmp = t_2
	elif b <= -2.6e+55:
		tmp = t_3
	elif b <= -1.85e-147:
		tmp = t_1
	elif b <= -2.25e-223:
		tmp = t_2
	elif b <= 1.66e-9:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.72e+198)
		tmp = t_3;
	elseif (b <= -6.6e+147)
		tmp = t_2;
	elseif (b <= -2.6e+55)
		tmp = t_3;
	elseif (b <= -1.85e-147)
		tmp = t_1;
	elseif (b <= -2.25e-223)
		tmp = t_2;
	elseif (b <= 1.66e-9)
		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 = y * ((x * z) - (i * j));
	t_2 = a * ((c * j) - (x * t));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.72e+198)
		tmp = t_3;
	elseif (b <= -6.6e+147)
		tmp = t_2;
	elseif (b <= -2.6e+55)
		tmp = t_3;
	elseif (b <= -1.85e-147)
		tmp = t_1;
	elseif (b <= -2.25e-223)
		tmp = t_2;
	elseif (b <= 1.66e-9)
		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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.72e+198], t$95$3, If[LessEqual[b, -6.6e+147], t$95$2, If[LessEqual[b, -2.6e+55], t$95$3, If[LessEqual[b, -1.85e-147], t$95$1, If[LessEqual[b, -2.25e-223], t$95$2, If[LessEqual[b, 1.66e-9], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.71999999999999998e198 or -6.60000000000000049e147 < b < -2.6e55 or 1.6600000000000001e-9 < b

   1. Initial program 76.2%

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

   3. Taylor expanded in b around inf 66.5%

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

   if -1.71999999999999998e198 < b < -6.60000000000000049e147 or -1.8500000000000001e-147 < b < -2.24999999999999984e-223

   1. Initial program 79.4%

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

   3. Taylor expanded in a around inf 66.1%

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

      1. +-commutative 66.1%

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

      2. mul-1-neg 66.1%

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

      3. unsub-neg 66.1%

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

   5. Simplified 66.1%

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

   if -2.6e55 < b < -1.8500000000000001e-147 or -2.24999999999999984e-223 < b < 1.6600000000000001e-9

   1. Initial program 70.3%

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

   3. Taylor expanded in y around inf 58.5%

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

      1. +-commutative 58.5%

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

      2. mul-1-neg 58.5%

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

      3. unsub-neg 58.5%

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

      4. *-commutative 58.5%

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

   5. Simplified 58.5%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.72 \cdot 10^{+198}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{+147}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.85 \cdot 10^{-147}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq -2.25 \cdot 10^{-223}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.66 \cdot 10^{-9}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -4.4 \cdot 10^{+120}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-293}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 9.8 \cdot 10^{-139}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i)))))
        (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -4.4e+120)
     t_2
     (if (<= i 3.5e-293)
       t_1
       (if (<= i 9.8e-139)
         (* z (- (* x y) (* b c)))
         (if (<= i 5e+38) 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))) + (j * ((a * c) - (y * i)));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -4.4e+120) {
		tmp = t_2;
	} else if (i <= 3.5e-293) {
		tmp = t_1;
	} else if (i <= 9.8e-139) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 5e+38) {
		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))) + (j * ((a * c) - (y * i)))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-4.4d+120)) then
        tmp = t_2
    else if (i <= 3.5d-293) then
        tmp = t_1
    else if (i <= 9.8d-139) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= 5d+38) 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))) + (j * ((a * c) - (y * i)));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -4.4e+120) {
		tmp = t_2;
	} else if (i <= 3.5e-293) {
		tmp = t_1;
	} else if (i <= 9.8e-139) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 5e+38) {
		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))) + (j * ((a * c) - (y * i)))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -4.4e+120:
		tmp = t_2
	elif i <= 3.5e-293:
		tmp = t_1
	elif i <= 9.8e-139:
		tmp = z * ((x * y) - (b * c))
	elif i <= 5e+38:
		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(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -4.4e+120)
		tmp = t_2;
	elseif (i <= 3.5e-293)
		tmp = t_1;
	elseif (i <= 9.8e-139)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= 5e+38)
		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))) + (j * ((a * c) - (y * i)));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -4.4e+120)
		tmp = t_2;
	elseif (i <= 3.5e-293)
		tmp = t_1;
	elseif (i <= 9.8e-139)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= 5e+38)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.4e+120], t$95$2, If[LessEqual[i, 3.5e-293], t$95$1, If[LessEqual[i, 9.8e-139], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5e+38], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -4.4000000000000003e120 or 4.9999999999999997e38 < i

   1. Initial program 63.5%

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

   3. Taylor expanded in i around inf 74.7%

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

      1. distribute-lft-out-- 74.7%

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

   5. Simplified 74.7%

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

   if -4.4000000000000003e120 < i < 3.5000000000000002e-293 or 9.80000000000000063e-139 < i < 4.9999999999999997e38

   1. Initial program 80.1%

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

   3. Taylor expanded in b around 0 70.3%

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

   if 3.5000000000000002e-293 < i < 9.80000000000000063e-139

   1. Initial program 77.2%

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

   3. Taylor expanded in z around inf 70.2%

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

      1. *-commutative 70.2%

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

   5. Simplified 70.2%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.4 \cdot 10^{+120}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-293}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq 9.8 \cdot 10^{-139}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 5 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 27.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+230}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{+177}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq -6500000000000:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-298}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+47}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -5.8e+230)
   (* a (* t (- x)))
   (if (<= a -1.95e+177)
     (* y (* i (- j)))
     (if (<= a -6500000000000.0)
       (* b (* t i))
       (if (<= a -1e-65)
         (* x (* y z))
         (if (<= a 4.8e-298)
           (* t (* b i))
           (if (<= a 6e+47) (* z (* x y)) (* a (* c j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -5.8e+230) {
		tmp = a * (t * -x);
	} else if (a <= -1.95e+177) {
		tmp = y * (i * -j);
	} else if (a <= -6500000000000.0) {
		tmp = b * (t * i);
	} else if (a <= -1e-65) {
		tmp = x * (y * z);
	} else if (a <= 4.8e-298) {
		tmp = t * (b * i);
	} else if (a <= 6e+47) {
		tmp = z * (x * y);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-5.8d+230)) then
        tmp = a * (t * -x)
    else if (a <= (-1.95d+177)) then
        tmp = y * (i * -j)
    else if (a <= (-6500000000000.0d0)) then
        tmp = b * (t * i)
    else if (a <= (-1d-65)) then
        tmp = x * (y * z)
    else if (a <= 4.8d-298) then
        tmp = t * (b * i)
    else if (a <= 6d+47) then
        tmp = z * (x * y)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -5.8e+230) {
		tmp = a * (t * -x);
	} else if (a <= -1.95e+177) {
		tmp = y * (i * -j);
	} else if (a <= -6500000000000.0) {
		tmp = b * (t * i);
	} else if (a <= -1e-65) {
		tmp = x * (y * z);
	} else if (a <= 4.8e-298) {
		tmp = t * (b * i);
	} else if (a <= 6e+47) {
		tmp = z * (x * y);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -5.8e+230:
		tmp = a * (t * -x)
	elif a <= -1.95e+177:
		tmp = y * (i * -j)
	elif a <= -6500000000000.0:
		tmp = b * (t * i)
	elif a <= -1e-65:
		tmp = x * (y * z)
	elif a <= 4.8e-298:
		tmp = t * (b * i)
	elif a <= 6e+47:
		tmp = z * (x * y)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -5.8e+230)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (a <= -1.95e+177)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (a <= -6500000000000.0)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= -1e-65)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 4.8e-298)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 6e+47)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -5.8e+230)
		tmp = a * (t * -x);
	elseif (a <= -1.95e+177)
		tmp = y * (i * -j);
	elseif (a <= -6500000000000.0)
		tmp = b * (t * i);
	elseif (a <= -1e-65)
		tmp = x * (y * z);
	elseif (a <= 4.8e-298)
		tmp = t * (b * i);
	elseif (a <= 6e+47)
		tmp = z * (x * y);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -5.8e+230], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.95e+177], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6500000000000.0], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1e-65], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e-298], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e+47], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -5.7999999999999998e230

   1. Initial program 56.3%

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

   3. Taylor expanded in a around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. mul-1-neg 99.9%

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

      3. unsub-neg 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in c around 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. distribute-lft-neg-out 75.7%

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

      3. *-commutative 75.7%

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

   8. Simplified 75.7%

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

   if -5.7999999999999998e230 < a < -1.95e177

   1. Initial program 61.4%

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

   3. Taylor expanded in y around inf 62.4%

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

      1. +-commutative 62.4%

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

      2. mul-1-neg 62.4%

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

      3. unsub-neg 62.4%

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

      4. *-commutative 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in z around 0 56.4%

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

      1. associate-*r* 56.4%

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

      2. neg-mul-1 56.4%

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

   8. Simplified 56.4%

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

   if -1.95e177 < a < -6.5e12

   1. Initial program 71.3%

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

   3. Taylor expanded in t around inf 43.6%

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

      1. distribute-lft-out-- 43.6%

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

   5. Simplified 43.6%

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

   6. Taylor expanded in a around 0 40.6%

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

      1. *-commutative 40.6%

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

   8. Simplified 40.6%

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

   if -6.5e12 < a < -9.99999999999999923e-66

   1. Initial program 72.6%

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

   3. Taylor expanded in y around inf 55.6%

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

      1. +-commutative 55.6%

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

      2. mul-1-neg 55.6%

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

      3. unsub-neg 55.6%

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

      4. *-commutative 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in z around inf 51.8%

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

      1. *-commutative 51.8%

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

   8. Simplified 51.8%

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

   if -9.99999999999999923e-66 < a < 4.79999999999999975e-298

   1. Initial program 81.0%

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

   3. Taylor expanded in t around inf 49.2%

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

      1. distribute-lft-out-- 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in a around 0 42.1%

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

      1. neg-mul-1 42.1%

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

      2. distribute-rgt-neg-in 42.1%

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

   8. Simplified 42.1%

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

   9. Taylor expanded in t around 0 38.9%

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

       1. *-commutative 38.9%

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

       2. *-commutative 38.9%

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

       3. associate-*r* 42.1%

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

   11. Simplified 42.1%

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

   if 4.79999999999999975e-298 < a < 6.0000000000000003e47

   1. Initial program 79.9%

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

   3. Taylor expanded in z around inf 50.7%

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

      1. *-commutative 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y around inf 35.3%

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

   if 6.0000000000000003e47 < a

   1. Initial program 68.5%

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

   3. Taylor expanded in a around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. mul-1-neg 59.1%

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

      3. unsub-neg 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in c around inf 45.5%

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

      1. *-commutative 45.5%

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

   8. Simplified 45.5%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+230}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq -1.95 \cdot 10^{+177}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq -6500000000000:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-298}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+47}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 27.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+230}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{+177}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq -13200000000000:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-297}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+47}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -5.8e+230)
   (* a (* t (- x)))
   (if (<= a -1.85e+177)
     (* i (* y (- j)))
     (if (<= a -13200000000000.0)
       (* b (* t i))
       (if (<= a -1.25e-65)
         (* x (* y z))
         (if (<= a 4.2e-297)
           (* t (* b i))
           (if (<= a 6e+47) (* z (* x y)) (* a (* c j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -5.8e+230) {
		tmp = a * (t * -x);
	} else if (a <= -1.85e+177) {
		tmp = i * (y * -j);
	} else if (a <= -13200000000000.0) {
		tmp = b * (t * i);
	} else if (a <= -1.25e-65) {
		tmp = x * (y * z);
	} else if (a <= 4.2e-297) {
		tmp = t * (b * i);
	} else if (a <= 6e+47) {
		tmp = z * (x * y);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-5.8d+230)) then
        tmp = a * (t * -x)
    else if (a <= (-1.85d+177)) then
        tmp = i * (y * -j)
    else if (a <= (-13200000000000.0d0)) then
        tmp = b * (t * i)
    else if (a <= (-1.25d-65)) then
        tmp = x * (y * z)
    else if (a <= 4.2d-297) then
        tmp = t * (b * i)
    else if (a <= 6d+47) then
        tmp = z * (x * y)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -5.8e+230) {
		tmp = a * (t * -x);
	} else if (a <= -1.85e+177) {
		tmp = i * (y * -j);
	} else if (a <= -13200000000000.0) {
		tmp = b * (t * i);
	} else if (a <= -1.25e-65) {
		tmp = x * (y * z);
	} else if (a <= 4.2e-297) {
		tmp = t * (b * i);
	} else if (a <= 6e+47) {
		tmp = z * (x * y);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -5.8e+230:
		tmp = a * (t * -x)
	elif a <= -1.85e+177:
		tmp = i * (y * -j)
	elif a <= -13200000000000.0:
		tmp = b * (t * i)
	elif a <= -1.25e-65:
		tmp = x * (y * z)
	elif a <= 4.2e-297:
		tmp = t * (b * i)
	elif a <= 6e+47:
		tmp = z * (x * y)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -5.8e+230)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (a <= -1.85e+177)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (a <= -13200000000000.0)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= -1.25e-65)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 4.2e-297)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 6e+47)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -5.8e+230)
		tmp = a * (t * -x);
	elseif (a <= -1.85e+177)
		tmp = i * (y * -j);
	elseif (a <= -13200000000000.0)
		tmp = b * (t * i);
	elseif (a <= -1.25e-65)
		tmp = x * (y * z);
	elseif (a <= 4.2e-297)
		tmp = t * (b * i);
	elseif (a <= 6e+47)
		tmp = z * (x * y);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -5.8e+230], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.85e+177], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -13200000000000.0], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.25e-65], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e-297], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e+47], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -5.7999999999999998e230

   1. Initial program 56.3%

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

   3. Taylor expanded in a around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. mul-1-neg 99.9%

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

      3. unsub-neg 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in c around 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. distribute-lft-neg-out 75.7%

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

      3. *-commutative 75.7%

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

   8. Simplified 75.7%

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

   if -5.7999999999999998e230 < a < -1.85000000000000007e177

   1. Initial program 61.4%

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

   3. Taylor expanded in y around inf 62.4%

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

      1. +-commutative 62.4%

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

      2. mul-1-neg 62.4%

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

      3. unsub-neg 62.4%

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

      4. *-commutative 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in z around 0 70.2%

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

      1. associate-*r* 70.2%

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

      2. neg-mul-1 70.2%

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

   8. Simplified 70.2%

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

   if -1.85000000000000007e177 < a < -1.32e13

   1. Initial program 71.3%

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

   3. Taylor expanded in t around inf 43.6%

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

      1. distribute-lft-out-- 43.6%

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

   5. Simplified 43.6%

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

   6. Taylor expanded in a around 0 40.6%

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

      1. *-commutative 40.6%

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

   8. Simplified 40.6%

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

   if -1.32e13 < a < -1.24999999999999996e-65

   1. Initial program 72.6%

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

   3. Taylor expanded in y around inf 55.6%

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

      1. +-commutative 55.6%

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

      2. mul-1-neg 55.6%

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

      3. unsub-neg 55.6%

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

      4. *-commutative 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in z around inf 51.8%

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

      1. *-commutative 51.8%

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

   8. Simplified 51.8%

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

   if -1.24999999999999996e-65 < a < 4.20000000000000027e-297

   1. Initial program 81.0%

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

   3. Taylor expanded in t around inf 49.2%

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

      1. distribute-lft-out-- 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in a around 0 42.1%

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

      1. neg-mul-1 42.1%

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

      2. distribute-rgt-neg-in 42.1%

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

   8. Simplified 42.1%

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

   9. Taylor expanded in t around 0 38.9%

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

       1. *-commutative 38.9%

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

       2. *-commutative 38.9%

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

       3. associate-*r* 42.1%

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

   11. Simplified 42.1%

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

   if 4.20000000000000027e-297 < a < 6.0000000000000003e47

   1. Initial program 79.9%

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

   3. Taylor expanded in z around inf 50.7%

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

      1. *-commutative 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y around inf 35.3%

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

   if 6.0000000000000003e47 < a

   1. Initial program 68.5%

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

   3. Taylor expanded in a around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. mul-1-neg 59.1%

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

      3. unsub-neg 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in c around inf 45.5%

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

      1. *-commutative 45.5%

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

   8. Simplified 45.5%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+230}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{+177}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq -13200000000000:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-297}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+47}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 27.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+230}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+177}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-298}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+47}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -7.2e+230)
   (* t (* x (- a)))
   (if (<= a -2.7e+177)
     (* i (* y (- j)))
     (if (<= a -3.5e+14)
       (* b (* t i))
       (if (<= a -6e-64)
         (* x (* y z))
         (if (<= a 1.02e-298)
           (* t (* b i))
           (if (<= a 2.8e+47) (* z (* x y)) (* a (* c j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -7.2e+230) {
		tmp = t * (x * -a);
	} else if (a <= -2.7e+177) {
		tmp = i * (y * -j);
	} else if (a <= -3.5e+14) {
		tmp = b * (t * i);
	} else if (a <= -6e-64) {
		tmp = x * (y * z);
	} else if (a <= 1.02e-298) {
		tmp = t * (b * i);
	} else if (a <= 2.8e+47) {
		tmp = z * (x * y);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-7.2d+230)) then
        tmp = t * (x * -a)
    else if (a <= (-2.7d+177)) then
        tmp = i * (y * -j)
    else if (a <= (-3.5d+14)) then
        tmp = b * (t * i)
    else if (a <= (-6d-64)) then
        tmp = x * (y * z)
    else if (a <= 1.02d-298) then
        tmp = t * (b * i)
    else if (a <= 2.8d+47) then
        tmp = z * (x * y)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -7.2e+230) {
		tmp = t * (x * -a);
	} else if (a <= -2.7e+177) {
		tmp = i * (y * -j);
	} else if (a <= -3.5e+14) {
		tmp = b * (t * i);
	} else if (a <= -6e-64) {
		tmp = x * (y * z);
	} else if (a <= 1.02e-298) {
		tmp = t * (b * i);
	} else if (a <= 2.8e+47) {
		tmp = z * (x * y);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -7.2e+230:
		tmp = t * (x * -a)
	elif a <= -2.7e+177:
		tmp = i * (y * -j)
	elif a <= -3.5e+14:
		tmp = b * (t * i)
	elif a <= -6e-64:
		tmp = x * (y * z)
	elif a <= 1.02e-298:
		tmp = t * (b * i)
	elif a <= 2.8e+47:
		tmp = z * (x * y)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -7.2e+230)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (a <= -2.7e+177)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (a <= -3.5e+14)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= -6e-64)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 1.02e-298)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 2.8e+47)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -7.2e+230)
		tmp = t * (x * -a);
	elseif (a <= -2.7e+177)
		tmp = i * (y * -j);
	elseif (a <= -3.5e+14)
		tmp = b * (t * i);
	elseif (a <= -6e-64)
		tmp = x * (y * z);
	elseif (a <= 1.02e-298)
		tmp = t * (b * i);
	elseif (a <= 2.8e+47)
		tmp = z * (x * y);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -7.2e+230], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.7e+177], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.5e+14], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -6e-64], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e-298], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e+47], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -7.20000000000000037e230

   1. Initial program 56.3%

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

   3. Taylor expanded in t around inf 69.5%

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

      1. distribute-lft-out-- 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in a around inf 75.8%

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

   if -7.20000000000000037e230 < a < -2.69999999999999991e177

   1. Initial program 61.4%

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

   3. Taylor expanded in y around inf 62.4%

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

      1. +-commutative 62.4%

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

      2. mul-1-neg 62.4%

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

      3. unsub-neg 62.4%

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

      4. *-commutative 62.4%

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

   5. Simplified 62.4%

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

   6. Taylor expanded in z around 0 70.2%

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

      1. associate-*r* 70.2%

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

      2. neg-mul-1 70.2%

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

   8. Simplified 70.2%

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

   if -2.69999999999999991e177 < a < -3.5e14

   1. Initial program 71.3%

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

   3. Taylor expanded in t around inf 43.6%

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

      1. distribute-lft-out-- 43.6%

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

   5. Simplified 43.6%

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

   6. Taylor expanded in a around 0 40.6%

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

      1. *-commutative 40.6%

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

   8. Simplified 40.6%

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

   if -3.5e14 < a < -6.0000000000000001e-64

   1. Initial program 72.6%

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

   3. Taylor expanded in y around inf 55.6%

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

      1. +-commutative 55.6%

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

      2. mul-1-neg 55.6%

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

      3. unsub-neg 55.6%

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

      4. *-commutative 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in z around inf 51.8%

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

      1. *-commutative 51.8%

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

   8. Simplified 51.8%

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

   if -6.0000000000000001e-64 < a < 1.02000000000000004e-298

   1. Initial program 81.0%

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

   3. Taylor expanded in t around inf 49.2%

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

      1. distribute-lft-out-- 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in a around 0 42.1%

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

      1. neg-mul-1 42.1%

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

      2. distribute-rgt-neg-in 42.1%

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

   8. Simplified 42.1%

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

   9. Taylor expanded in t around 0 38.9%

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

       1. *-commutative 38.9%

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

       2. *-commutative 38.9%

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

       3. associate-*r* 42.1%

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

   11. Simplified 42.1%

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

   if 1.02000000000000004e-298 < a < 2.79999999999999988e47

   1. Initial program 79.9%

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

   3. Taylor expanded in z around inf 50.7%

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

      1. *-commutative 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in y around inf 35.3%

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

   if 2.79999999999999988e47 < a

   1. Initial program 68.5%

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

   3. Taylor expanded in a around inf 59.1%

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

      1. +-commutative 59.1%

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

      2. mul-1-neg 59.1%

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

      3. unsub-neg 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in c around inf 45.5%

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

      1. *-commutative 45.5%

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

   8. Simplified 45.5%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+230}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+177}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-298}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+47}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -3.4 \cdot 10^{+110}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{-299}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.86 \cdot 10^{-90}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 7 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* j (- (* a c) (* y i))) (* x (* t a))))
        (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -3.4e+110)
     t_2
     (if (<= i -4.2e-299)
       t_1
       (if (<= i 1.86e-90)
         (* z (- (* x y) (* b c)))
         (if (<= i 7e+32) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) - (x * (t * a));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.4e+110) {
		tmp = t_2;
	} else if (i <= -4.2e-299) {
		tmp = t_1;
	} else if (i <= 1.86e-90) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 7e+32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (j * ((a * c) - (y * i))) - (x * (t * a))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-3.4d+110)) then
        tmp = t_2
    else if (i <= (-4.2d-299)) then
        tmp = t_1
    else if (i <= 1.86d-90) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= 7d+32) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((a * c) - (y * i))) - (x * (t * a));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.4e+110) {
		tmp = t_2;
	} else if (i <= -4.2e-299) {
		tmp = t_1;
	} else if (i <= 1.86e-90) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= 7e+32) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((a * c) - (y * i))) - (x * (t * a))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -3.4e+110:
		tmp = t_2
	elif i <= -4.2e-299:
		tmp = t_1
	elif i <= 1.86e-90:
		tmp = z * ((x * y) - (b * c))
	elif i <= 7e+32:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(x * Float64(t * a)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -3.4e+110)
		tmp = t_2;
	elseif (i <= -4.2e-299)
		tmp = t_1;
	elseif (i <= 1.86e-90)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= 7e+32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((a * c) - (y * i))) - (x * (t * a));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -3.4e+110)
		tmp = t_2;
	elseif (i <= -4.2e-299)
		tmp = t_1;
	elseif (i <= 1.86e-90)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= 7e+32)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.4e+110], t$95$2, If[LessEqual[i, -4.2e-299], t$95$1, If[LessEqual[i, 1.86e-90], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7e+32], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.4000000000000001e110 or 7.0000000000000002e32 < i

   1. Initial program 64.4%

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

   3. Taylor expanded in i around inf 73.0%

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

      1. distribute-lft-out-- 73.0%

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

   5. Simplified 73.0%

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

   if -3.4000000000000001e110 < i < -4.2000000000000002e-299 or 1.86e-90 < i < 7.0000000000000002e32

   1. Initial program 79.3%

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

   3. Taylor expanded in b around 0 68.9%

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

   4. Taylor expanded in z around 0 59.8%

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

      1. +-commutative 59.8%

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

      2. mul-1-neg 59.8%

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

      3. unsub-neg 59.8%

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

      4. associate-*r* 59.8%

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

      5. *-commutative 59.8%

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

   6. Simplified 59.8%

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

   if -4.2000000000000002e-299 < i < 1.86e-90

   1. Initial program 80.1%

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

   3. Taylor expanded in z around inf 68.7%

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

      1. *-commutative 68.7%

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

   5. Simplified 68.7%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.4 \cdot 10^{+110}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{-299}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;i \leq 1.86 \cdot 10^{-90}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq 7 \cdot 10^{+32}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 40.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;i \leq -4 \cdot 10^{+118}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-209}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{-91}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{+100}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+189}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (* t i))))
   (if (<= i -4e+118)
     t_2
     (if (<= i 1.2e-209)
       t_1
       (if (<= i 1.4e-91)
         (* z (* x y))
         (if (<= i 3.4e+100)
           t_1
           (if (<= i 6.2e+189) t_2 (* y (* i (- j))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * (t * i);
	double tmp;
	if (i <= -4e+118) {
		tmp = t_2;
	} else if (i <= 1.2e-209) {
		tmp = t_1;
	} else if (i <= 1.4e-91) {
		tmp = z * (x * y);
	} else if (i <= 3.4e+100) {
		tmp = t_1;
	} else if (i <= 6.2e+189) {
		tmp = t_2;
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = b * (t * i)
    if (i <= (-4d+118)) then
        tmp = t_2
    else if (i <= 1.2d-209) then
        tmp = t_1
    else if (i <= 1.4d-91) then
        tmp = z * (x * y)
    else if (i <= 3.4d+100) then
        tmp = t_1
    else if (i <= 6.2d+189) then
        tmp = t_2
    else
        tmp = y * (i * -j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = b * (t * i);
	double tmp;
	if (i <= -4e+118) {
		tmp = t_2;
	} else if (i <= 1.2e-209) {
		tmp = t_1;
	} else if (i <= 1.4e-91) {
		tmp = z * (x * y);
	} else if (i <= 3.4e+100) {
		tmp = t_1;
	} else if (i <= 6.2e+189) {
		tmp = t_2;
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * (t * i)
	tmp = 0
	if i <= -4e+118:
		tmp = t_2
	elif i <= 1.2e-209:
		tmp = t_1
	elif i <= 1.4e-91:
		tmp = z * (x * y)
	elif i <= 3.4e+100:
		tmp = t_1
	elif i <= 6.2e+189:
		tmp = t_2
	else:
		tmp = y * (i * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (i <= -4e+118)
		tmp = t_2;
	elseif (i <= 1.2e-209)
		tmp = t_1;
	elseif (i <= 1.4e-91)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 3.4e+100)
		tmp = t_1;
	elseif (i <= 6.2e+189)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(i * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * (t * i);
	tmp = 0.0;
	if (i <= -4e+118)
		tmp = t_2;
	elseif (i <= 1.2e-209)
		tmp = t_1;
	elseif (i <= 1.4e-91)
		tmp = z * (x * y);
	elseif (i <= 3.4e+100)
		tmp = t_1;
	elseif (i <= 6.2e+189)
		tmp = t_2;
	else
		tmp = y * (i * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4e+118], t$95$2, If[LessEqual[i, 1.2e-209], t$95$1, If[LessEqual[i, 1.4e-91], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.4e+100], t$95$1, If[LessEqual[i, 6.2e+189], t$95$2, N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -3.99999999999999987e118 or 3.39999999999999994e100 < i < 6.1999999999999999e189

   1. Initial program 63.8%

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

   3. Taylor expanded in t around inf 52.0%

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

      1. distribute-lft-out-- 52.0%

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

   5. Simplified 52.0%

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

   6. Taylor expanded in a around 0 55.5%

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

      1. *-commutative 55.5%

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

   8. Simplified 55.5%

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

   if -3.99999999999999987e118 < i < 1.2000000000000001e-209 or 1.4e-91 < i < 3.39999999999999994e100

   1. Initial program 78.8%

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

   3. Taylor expanded in a around inf 47.0%

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

      1. +-commutative 47.0%

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

      2. mul-1-neg 47.0%

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

      3. unsub-neg 47.0%

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

   5. Simplified 47.0%

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

   if 1.2000000000000001e-209 < i < 1.4e-91

   1. Initial program 84.7%

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

   3. Taylor expanded in z around inf 70.9%

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

      1. *-commutative 70.9%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in y around inf 51.6%

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

   if 6.1999999999999999e189 < i

   1. Initial program 54.7%

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

   3. Taylor expanded in y around inf 64.5%

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

      1. +-commutative 64.5%

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

      2. mul-1-neg 64.5%

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

      3. unsub-neg 64.5%

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

      4. *-commutative 64.5%

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

   5. Simplified 64.5%

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

   6. Taylor expanded in z around 0 56.3%

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

      1. associate-*r* 56.3%

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

      2. neg-mul-1 56.3%

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

   8. Simplified 56.3%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4 \cdot 10^{+118}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-209}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{-91}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 3.4 \cdot 10^{+100}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+189}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 27.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -2.95 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-135}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-112}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+29} \lor \neg \left(x \leq 5.4 \cdot 10^{+180}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= x -2.95e+47)
     t_1
     (if (<= x -1.2e-135)
       (* a (* c j))
       (if (<= x 2.05e-112)
         (* b (* t i))
         (if (or (<= x 8.5e+29) (not (<= x 5.4e+180))) t_1 (* i (* t 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 = x * (y * z);
	double tmp;
	if (x <= -2.95e+47) {
		tmp = t_1;
	} else if (x <= -1.2e-135) {
		tmp = a * (c * j);
	} else if (x <= 2.05e-112) {
		tmp = b * (t * i);
	} else if ((x <= 8.5e+29) || !(x <= 5.4e+180)) {
		tmp = t_1;
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (x <= (-2.95d+47)) then
        tmp = t_1
    else if (x <= (-1.2d-135)) then
        tmp = a * (c * j)
    else if (x <= 2.05d-112) then
        tmp = b * (t * i)
    else if ((x <= 8.5d+29) .or. (.not. (x <= 5.4d+180))) then
        tmp = t_1
    else
        tmp = i * (t * 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 = x * (y * z);
	double tmp;
	if (x <= -2.95e+47) {
		tmp = t_1;
	} else if (x <= -1.2e-135) {
		tmp = a * (c * j);
	} else if (x <= 2.05e-112) {
		tmp = b * (t * i);
	} else if ((x <= 8.5e+29) || !(x <= 5.4e+180)) {
		tmp = t_1;
	} else {
		tmp = i * (t * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if x <= -2.95e+47:
		tmp = t_1
	elif x <= -1.2e-135:
		tmp = a * (c * j)
	elif x <= 2.05e-112:
		tmp = b * (t * i)
	elif (x <= 8.5e+29) or not (x <= 5.4e+180):
		tmp = t_1
	else:
		tmp = i * (t * b)
	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 (x <= -2.95e+47)
		tmp = t_1;
	elseif (x <= -1.2e-135)
		tmp = Float64(a * Float64(c * j));
	elseif (x <= 2.05e-112)
		tmp = Float64(b * Float64(t * i));
	elseif ((x <= 8.5e+29) || !(x <= 5.4e+180))
		tmp = t_1;
	else
		tmp = Float64(i * Float64(t * b));
	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 (x <= -2.95e+47)
		tmp = t_1;
	elseif (x <= -1.2e-135)
		tmp = a * (c * j);
	elseif (x <= 2.05e-112)
		tmp = b * (t * i);
	elseif ((x <= 8.5e+29) || ~((x <= 5.4e+180)))
		tmp = t_1;
	else
		tmp = i * (t * b);
	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[x, -2.95e+47], t$95$1, If[LessEqual[x, -1.2e-135], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.05e-112], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 8.5e+29], N[Not[LessEqual[x, 5.4e+180]], $MachinePrecision]], t$95$1, N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.95000000000000017e47 or 2.04999999999999998e-112 < x < 8.5000000000000006e29 or 5.40000000000000033e180 < x

   1. Initial program 73.2%

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

   3. Taylor expanded in y around inf 52.6%

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

      1. +-commutative 52.6%

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

      2. mul-1-neg 52.6%

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

      3. unsub-neg 52.6%

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

      4. *-commutative 52.6%

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

   5. Simplified 52.6%

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

   6. Taylor expanded in z around inf 39.5%

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

      1. *-commutative 39.5%

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

   8. Simplified 39.5%

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

   if -2.95000000000000017e47 < x < -1.1999999999999999e-135

   1. Initial program 66.8%

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

   3. Taylor expanded in a around inf 56.3%

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

      1. +-commutative 56.3%

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

      2. mul-1-neg 56.3%

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

      3. unsub-neg 56.3%

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

   5. Simplified 56.3%

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

   6. Taylor expanded in c around inf 45.2%

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

      1. *-commutative 45.2%

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

   8. Simplified 45.2%

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

   if -1.1999999999999999e-135 < x < 2.04999999999999998e-112

   1. Initial program 74.1%

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

   3. Taylor expanded in t around inf 35.7%

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

      1. distribute-lft-out-- 35.7%

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

   5. Simplified 35.7%

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

   6. Taylor expanded in a around 0 36.5%

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

      1. *-commutative 36.5%

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

   8. Simplified 36.5%

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

   if 8.5000000000000006e29 < x < 5.40000000000000033e180

   1. Initial program 87.9%

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

   3. Taylor expanded in t around inf 56.9%

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

      1. distribute-lft-out-- 56.9%

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

   5. Simplified 56.9%

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

   6. Taylor expanded in a around 0 37.9%

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

      1. neg-mul-1 37.9%

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

      2. distribute-rgt-neg-in 37.9%

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

   8. Simplified 37.9%

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

   9. Taylor expanded in t around 0 41.6%

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

       1. *-commutative 41.6%

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

       2. associate-*l* 41.8%

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

   11. Simplified 41.8%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.95 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-135}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-112}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+29} \lor \neg \left(x \leq 5.4 \cdot 10^{+180}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 46.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{+184}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-251}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-53}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+66}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -2.6e+184)
     t_2
     (if (<= a 6.3e-251)
       t_1
       (if (<= a 4.2e-53) (* z (* x y)) (if (<= a 1.7e+66) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.6e+184) {
		tmp = t_2;
	} else if (a <= 6.3e-251) {
		tmp = t_1;
	} else if (a <= 4.2e-53) {
		tmp = z * (x * y);
	} else if (a <= 1.7e+66) {
		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 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-2.6d+184)) then
        tmp = t_2
    else if (a <= 6.3d-251) then
        tmp = t_1
    else if (a <= 4.2d-53) then
        tmp = z * (x * y)
    else if (a <= 1.7d+66) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.6e+184) {
		tmp = t_2;
	} else if (a <= 6.3e-251) {
		tmp = t_1;
	} else if (a <= 4.2e-53) {
		tmp = z * (x * y);
	} else if (a <= 1.7e+66) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2.6e+184:
		tmp = t_2
	elif a <= 6.3e-251:
		tmp = t_1
	elif a <= 4.2e-53:
		tmp = z * (x * y)
	elif a <= 1.7e+66:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.6e+184)
		tmp = t_2;
	elseif (a <= 6.3e-251)
		tmp = t_1;
	elseif (a <= 4.2e-53)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 1.7e+66)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.6e+184)
		tmp = t_2;
	elseif (a <= 6.3e-251)
		tmp = t_1;
	elseif (a <= 4.2e-53)
		tmp = z * (x * y);
	elseif (a <= 1.7e+66)
		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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.6e+184], t$95$2, If[LessEqual[a, 6.3e-251], t$95$1, If[LessEqual[a, 4.2e-53], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e+66], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.59999999999999993e184 or 1.70000000000000015e66 < a

   1. Initial program 67.4%

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

   3. Taylor expanded in a around inf 70.8%

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

      1. +-commutative 70.8%

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

      2. mul-1-neg 70.8%

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

      3. unsub-neg 70.8%

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

   5. Simplified 70.8%

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

   if -2.59999999999999993e184 < a < 6.2999999999999998e-251 or 4.19999999999999955e-53 < a < 1.70000000000000015e66

   1. Initial program 75.8%

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

   3. Taylor expanded in b around inf 49.2%

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

   if 6.2999999999999998e-251 < a < 4.19999999999999955e-53

   1. Initial program 78.3%

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

   3. Taylor expanded in z around inf 51.3%

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

      1. *-commutative 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in y around inf 42.0%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+184}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-251}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-53}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+66}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.95 \cdot 10^{+176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -3 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq -4.4 \cdot 10^{-299}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+25}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -1.95e+176)
     t_1
     (if (<= i -3e-11)
       (* y (- (* x z) (* i j)))
       (if (<= i -4.4e-299)
         (* a (- (* c j) (* x t)))
         (if (<= i 2.5e+25) (* z (- (* x y) (* b 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 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.95e+176) {
		tmp = t_1;
	} else if (i <= -3e-11) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= -4.4e-299) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 2.5e+25) {
		tmp = z * ((x * y) - (b * 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 = i * ((t * b) - (y * j))
    if (i <= (-1.95d+176)) then
        tmp = t_1
    else if (i <= (-3d-11)) then
        tmp = y * ((x * z) - (i * j))
    else if (i <= (-4.4d-299)) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 2.5d+25) then
        tmp = z * ((x * y) - (b * 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 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.95e+176) {
		tmp = t_1;
	} else if (i <= -3e-11) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= -4.4e-299) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 2.5e+25) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -1.95e+176:
		tmp = t_1
	elif i <= -3e-11:
		tmp = y * ((x * z) - (i * j))
	elif i <= -4.4e-299:
		tmp = a * ((c * j) - (x * t))
	elif i <= 2.5e+25:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.95e+176)
		tmp = t_1;
	elseif (i <= -3e-11)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (i <= -4.4e-299)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 2.5e+25)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * 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 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.95e+176)
		tmp = t_1;
	elseif (i <= -3e-11)
		tmp = y * ((x * z) - (i * j));
	elseif (i <= -4.4e-299)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 2.5e+25)
		tmp = z * ((x * y) - (b * 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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.95e+176], t$95$1, If[LessEqual[i, -3e-11], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -4.4e-299], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.5e+25], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.9500000000000001e176 or 2.50000000000000012e25 < i

   1. Initial program 62.9%

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

   3. Taylor expanded in i around inf 72.5%

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

      1. distribute-lft-out-- 72.5%

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

   5. Simplified 72.5%

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

   if -1.9500000000000001e176 < i < -3e-11

   1. Initial program 79.4%

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

   3. Taylor expanded in y around inf 61.7%

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

      1. +-commutative 61.7%

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

      2. mul-1-neg 61.7%

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

      3. unsub-neg 61.7%

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

      4. *-commutative 61.7%

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

   5. Simplified 61.7%

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

   if -3e-11 < i < -4.3999999999999999e-299

   1. Initial program 75.9%

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

   3. Taylor expanded in a around inf 56.2%

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

      1. +-commutative 56.2%

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

      2. mul-1-neg 56.2%

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

      3. unsub-neg 56.2%

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

   5. Simplified 56.2%

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

   if -4.3999999999999999e-299 < i < 2.50000000000000012e25

   1. Initial program 83.3%

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

   3. Taylor expanded in z around inf 56.9%

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

      1. *-commutative 56.9%

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

   5. Simplified 56.9%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.95 \cdot 10^{+176}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -3 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq -4.4 \cdot 10^{-299}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+25}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 70.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;b \leq -1.9 \cdot 10^{+20} \lor \neg \left(b \leq 8.4 \cdot 10^{-8}\right):\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (or (<= b -1.9e+20) (not (<= b 8.4e-8)))
     (+ t_1 (* b (- (* t i) (* z c))))
     (+ (* x (- (* y z) (* t a))) 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 * ((a * c) - (y * i));
	double tmp;
	if ((b <= -1.9e+20) || !(b <= 8.4e-8)) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + 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 * ((a * c) - (y * i))
    if ((b <= (-1.9d+20)) .or. (.not. (b <= 8.4d-8))) then
        tmp = t_1 + (b * ((t * i) - (z * c)))
    else
        tmp = (x * ((y * z) - (t * a))) + 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 * ((a * c) - (y * i));
	double tmp;
	if ((b <= -1.9e+20) || !(b <= 8.4e-8)) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if (b <= -1.9e+20) or not (b <= 8.4e-8):
		tmp = t_1 + (b * ((t * i) - (z * c)))
	else:
		tmp = (x * ((y * z) - (t * a))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if ((b <= -1.9e+20) || !(b <= 8.4e-8))
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if ((b <= -1.9e+20) || ~((b <= 8.4e-8)))
		tmp = t_1 + (b * ((t * i) - (z * c)));
	else
		tmp = (x * ((y * z) - (t * a))) + 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[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -1.9e+20], N[Not[LessEqual[b, 8.4e-8]], $MachinePrecision]], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.9e20 or 8.39999999999999978e-8 < b

   1. Initial program 75.4%

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

   3. Taylor expanded in x around 0 69.9%

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

      1. *-commutative 69.9%

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

   5. Simplified 69.9%

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

   if -1.9e20 < b < 8.39999999999999978e-8

   1. Initial program 72.2%

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

   3. Taylor expanded in b around 0 73.9%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+20} \lor \neg \left(b \leq 8.4 \cdot 10^{-8}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-93} \lor \neg \left(t \leq 2.2 \cdot 10^{+27}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -3.4e-93) (not (<= t 2.2e+27))) (* b (* t i)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -3.4e-93) || !(t <= 2.2e+27)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-3.4d-93)) .or. (.not. (t <= 2.2d+27))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -3.4e-93) || !(t <= 2.2e+27)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -3.4e-93) or not (t <= 2.2e+27):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -3.4e-93) || !(t <= 2.2e+27))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -3.4e-93) || ~((t <= 2.2e+27)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -3.4e-93], N[Not[LessEqual[t, 2.2e+27]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.40000000000000001e-93 or 2.1999999999999999e27 < t

   1. Initial program 70.0%

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

   3. Taylor expanded in t around inf 58.3%

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

      1. distribute-lft-out-- 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in a around 0 39.3%

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

      1. *-commutative 39.3%

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

   8. Simplified 39.3%

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

   if -3.40000000000000001e-93 < t < 2.1999999999999999e27

   1. Initial program 78.5%

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

   3. Taylor expanded in a around inf 33.5%

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

      1. +-commutative 33.5%

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

      2. mul-1-neg 33.5%

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

      3. unsub-neg 33.5%

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

   5. Simplified 33.5%

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

   6. Taylor expanded in c around inf 27.5%

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

      1. *-commutative 27.5%

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

   8. Simplified 27.5%

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

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-93} \lor \neg \left(t \leq 2.2 \cdot 10^{+27}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-91} \lor \neg \left(t \leq 1.1 \cdot 10^{+23}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -3.6e-91) (not (<= t 1.1e+23))) (* b (* t i)) (* c (* a 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-91) || !(t <= 1.1e+23)) {
		tmp = b * (t * i);
	} else {
		tmp = c * (a * 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-91)) .or. (.not. (t <= 1.1d+23))) then
        tmp = b * (t * i)
    else
        tmp = c * (a * 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-91) || !(t <= 1.1e+23)) {
		tmp = b * (t * i);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -3.6e-91) or not (t <= 1.1e+23):
		tmp = b * (t * i)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -3.6e-91) || !(t <= 1.1e+23))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(c * Float64(a * 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-91) || ~((t <= 1.1e+23)))
		tmp = b * (t * i);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -3.6e-91], N[Not[LessEqual[t, 1.1e+23]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.6e-91 or 1.10000000000000004e23 < t

   1. Initial program 70.0%

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

   3. Taylor expanded in t around inf 58.3%

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

      1. distribute-lft-out-- 58.3%

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

   5. Simplified 58.3%

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

   6. Taylor expanded in a around 0 39.3%

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

      1. *-commutative 39.3%

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

   8. Simplified 39.3%

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

   if -3.6e-91 < t < 1.10000000000000004e23

   1. Initial program 78.5%

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

   3. Taylor expanded in a around inf 33.5%

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

      1. +-commutative 33.5%

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

      2. mul-1-neg 33.5%

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

      3. unsub-neg 33.5%

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

   5. Simplified 33.5%

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

   6. Taylor expanded in c around inf 27.5%

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

      1. *-commutative 27.5%

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

      2. associate-*l* 27.5%

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

      3. *-commutative 27.5%

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

   8. Simplified 27.5%

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

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-91} \lor \neg \left(t \leq 1.1 \cdot 10^{+23}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-91}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+27}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4.2e-91)
   (* i (* t b))
   (if (<= t 1.15e+27) (* c (* a j)) (* b (* t 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 <= -4.2e-91) {
		tmp = i * (t * b);
	} else if (t <= 1.15e+27) {
		tmp = c * (a * j);
	} else {
		tmp = b * (t * 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 <= (-4.2d-91)) then
        tmp = i * (t * b)
    else if (t <= 1.15d+27) then
        tmp = c * (a * j)
    else
        tmp = b * (t * 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 <= -4.2e-91) {
		tmp = i * (t * b);
	} else if (t <= 1.15e+27) {
		tmp = c * (a * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -4.2e-91:
		tmp = i * (t * b)
	elif t <= 1.15e+27:
		tmp = c * (a * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4.2e-91)
		tmp = Float64(i * Float64(t * b));
	elseif (t <= 1.15e+27)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -4.2e-91)
		tmp = i * (t * b);
	elseif (t <= 1.15e+27)
		tmp = c * (a * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4.2e-91], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+27], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.1999999999999998e-91

   1. Initial program 65.3%

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

   3. Taylor expanded in t around inf 53.3%

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

      1. distribute-lft-out-- 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in a around 0 30.6%

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

      1. neg-mul-1 30.6%

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

      2. distribute-rgt-neg-in 30.6%

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

   8. Simplified 30.6%

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

   9. Taylor expanded in t around 0 32.4%

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

       1. *-commutative 32.4%

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

       2. associate-*l* 33.6%

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

   11. Simplified 33.6%

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

   if -4.1999999999999998e-91 < t < 1.15e27

   1. Initial program 78.5%

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

   3. Taylor expanded in a around inf 33.5%

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

      1. +-commutative 33.5%

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

      2. mul-1-neg 33.5%

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

      3. unsub-neg 33.5%

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

   5. Simplified 33.5%

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

   6. Taylor expanded in c around inf 27.5%

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

      1. *-commutative 27.5%

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

      2. associate-*l* 27.5%

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

      3. *-commutative 27.5%

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

   8. Simplified 27.5%

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

   if 1.15e27 < t

   1. Initial program 76.7%

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

   3. Taylor expanded in t around inf 65.4%

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

      1. distribute-lft-out-- 65.4%

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

   5. Simplified 65.4%

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

   6. Taylor expanded in a around 0 49.0%

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

      1. *-commutative 49.0%

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

   8. Simplified 49.0%

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

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-91}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+27}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 22.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 73.8%

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

3. Taylor expanded in a around inf 37.2%

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

   1. +-commutative 37.2%

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

   2. mul-1-neg 37.2%

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

   3. unsub-neg 37.2%

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

5. Simplified 37.2%

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

6. Taylor expanded in c around inf 20.3%

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

   1. *-commutative 20.3%

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

8. Simplified 20.3%

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

9. Final simplification 20.3%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer target: 59.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024039 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

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