Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.5% → 81.8%

Time: 24.7s

Alternatives: 25

Speedup: 0.5×

• 58.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot c - y \cdot i\\ \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\right) + j \cdot t\_2 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(j, t\_2, x \cdot \mathsf{fma}\left(y, z, t \cdot \left(-a\right)\right) + t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.6%

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

      1. +-commutative 91.6%

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

      2. fma-define 91.6%

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

      3. *-commutative 91.6%

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

      4. *-commutative 91.6%

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

      5. cancel-sign-sub-inv 91.6%

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

      6. cancel-sign-sub 91.6%

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

      7. sub-neg 91.6%

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

      8. sub-neg 91.6%

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

      9. *-commutative 91.6%

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

      10. fma-neg 91.6%

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

      11. *-commutative 91.6%

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

      12. distribute-rgt-neg-out 91.6%

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

      13. remove-double-neg 91.6%

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

      14. *-commutative 91.6%

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

      15. *-commutative 91.6%

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

   3. Simplified 91.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around inf 61.8%

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

      1. *-commutative 61.8%

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

      2. *-commutative 61.8%

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

   5. Simplified 61.8%

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

4. Final simplification 87.0%

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

Alternative 2: 81.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.6%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around inf 61.8%

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

      1. *-commutative 61.8%

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

      2. *-commutative 61.8%

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

   5. Simplified 61.8%

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

4. Final simplification 87.0%

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

Alternative 3: 58.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - t \cdot a\\ t_2 := x \cdot \left(t\_1 + \frac{a \cdot \left(b \cdot i\right)}{x}\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -6.7 \cdot 10^{+16}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -53:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-20}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -7 \cdot 10^{-120}:\\ \;\;\;\;x \cdot t\_1 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.75 \cdot 10^{+63}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y z) (* t a)))
        (t_2 (* x (+ t_1 (/ (* a (* b i)) x))))
        (t_3 (* j (- (* t c) (* y i)))))
   (if (<= j -6.7e+16)
     t_3
     (if (<= j -53.0)
       t_2
       (if (<= j -9.5e-20)
         t_3
         (if (<= j -7e-120)
           (- (* x t_1) (* i (* y j)))
           (if (<= j 3e-278)
             (+ (* x (* y z)) (* b (- (* a i) (* z c))))
             (if (<= j 2.75e+63) t_2 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * z) - (t * a);
	double t_2 = x * (t_1 + ((a * (b * i)) / x));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -6.7e+16) {
		tmp = t_3;
	} else if (j <= -53.0) {
		tmp = t_2;
	} else if (j <= -9.5e-20) {
		tmp = t_3;
	} else if (j <= -7e-120) {
		tmp = (x * t_1) - (i * (y * j));
	} else if (j <= 3e-278) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (j <= 2.75e+63) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y * z) - (t * a)
    t_2 = x * (t_1 + ((a * (b * i)) / x))
    t_3 = j * ((t * c) - (y * i))
    if (j <= (-6.7d+16)) then
        tmp = t_3
    else if (j <= (-53.0d0)) then
        tmp = t_2
    else if (j <= (-9.5d-20)) then
        tmp = t_3
    else if (j <= (-7d-120)) then
        tmp = (x * t_1) - (i * (y * j))
    else if (j <= 3d-278) then
        tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
    else if (j <= 2.75d+63) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * z) - (t * a);
	double t_2 = x * (t_1 + ((a * (b * i)) / x));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -6.7e+16) {
		tmp = t_3;
	} else if (j <= -53.0) {
		tmp = t_2;
	} else if (j <= -9.5e-20) {
		tmp = t_3;
	} else if (j <= -7e-120) {
		tmp = (x * t_1) - (i * (y * j));
	} else if (j <= 3e-278) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (j <= 2.75e+63) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * z) - (t * a)
	t_2 = x * (t_1 + ((a * (b * i)) / x))
	t_3 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -6.7e+16:
		tmp = t_3
	elif j <= -53.0:
		tmp = t_2
	elif j <= -9.5e-20:
		tmp = t_3
	elif j <= -7e-120:
		tmp = (x * t_1) - (i * (y * j))
	elif j <= 3e-278:
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
	elif j <= 2.75e+63:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * z) - Float64(t * a))
	t_2 = Float64(x * Float64(t_1 + Float64(Float64(a * Float64(b * i)) / x)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -6.7e+16)
		tmp = t_3;
	elseif (j <= -53.0)
		tmp = t_2;
	elseif (j <= -9.5e-20)
		tmp = t_3;
	elseif (j <= -7e-120)
		tmp = Float64(Float64(x * t_1) - Float64(i * Float64(y * j)));
	elseif (j <= 3e-278)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (j <= 2.75e+63)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * z) - (t * a);
	t_2 = x * (t_1 + ((a * (b * i)) / x));
	t_3 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -6.7e+16)
		tmp = t_3;
	elseif (j <= -53.0)
		tmp = t_2;
	elseif (j <= -9.5e-20)
		tmp = t_3;
	elseif (j <= -7e-120)
		tmp = (x * t_1) - (i * (y * j));
	elseif (j <= 3e-278)
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	elseif (j <= 2.75e+63)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t$95$1 + N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.7e+16], t$95$3, If[LessEqual[j, -53.0], t$95$2, If[LessEqual[j, -9.5e-20], t$95$3, If[LessEqual[j, -7e-120], N[(N[(x * t$95$1), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3e-278], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.75e+63], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -6.7e16 or -53 < j < -9.5e-20 or 2.75000000000000002e63 < j

   1. Initial program 78.6%

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

   3. Taylor expanded in j around inf 67.0%

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

   if -6.7e16 < j < -53 or 3e-278 < j < 2.75000000000000002e63

   1. Initial program 73.9%

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

   3. Taylor expanded in x around inf 72.9%

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

      1. associate--r+ 72.9%

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

      2. sub-neg 72.9%

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

      3. mul-1-neg 72.9%

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

      4. +-commutative 72.9%

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

      5. associate-+r+ 72.9%

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

      6. associate-+r- 72.9%

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

      7. +-commutative 72.9%

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

      8. div-sub 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in a around inf 72.5%

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

   if -9.5e-20 < j < -7e-120

   1. Initial program 75.4%

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

   3. Taylor expanded in b around 0 73.5%

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

   4. Taylor expanded in c around 0 70.5%

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

      1. +-commutative 70.5%

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

      2. sub-neg 70.5%

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

      3. *-commutative 70.5%

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

      4. sub-neg 70.5%

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

      5. mul-1-neg 70.5%

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

      6. unsub-neg 70.5%

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

   6. Simplified 70.5%

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

   if -7e-120 < j < 3e-278

   1. Initial program 82.7%

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

   3. Taylor expanded in t around 0 82.7%

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

      1. *-commutative 82.7%

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

      2. associate-*r* 80.3%

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

      3. associate-*r* 80.3%

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

      4. associate-*r* 80.3%

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

      5. distribute-rgt-in 80.3%

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

      6. +-commutative 80.3%

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

      7. mul-1-neg 80.3%

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

      8. unsub-neg 80.3%

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

      9. *-commutative 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in x around inf 78.0%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.7 \cdot 10^{+16}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -53:\\ \;\;\;\;x \cdot \left(\left(y \cdot z - t \cdot a\right) + \frac{a \cdot \left(b \cdot i\right)}{x}\right)\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-20}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -7 \cdot 10^{-120}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq 3 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.75 \cdot 10^{+63}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z - t \cdot a\right) + \frac{a \cdot \left(b \cdot i\right)}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - t \cdot a\\ t_2 := x \cdot \left(t\_1 + \frac{a \cdot \left(b \cdot i\right)}{x}\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.16 \cdot 10^{+17}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -33:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-20}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{-125}:\\ \;\;\;\;x \cdot t\_1 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 10^{-37}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(c \cdot \left(t - i \cdot \frac{y}{c}\right)\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y z) (* t a)))
        (t_2 (* x (+ t_1 (/ (* a (* b i)) x))))
        (t_3 (* j (- (* t c) (* y i)))))
   (if (<= j -1.16e+17)
     t_3
     (if (<= j -33.0)
       t_2
       (if (<= j -8.5e-20)
         t_3
         (if (<= j -1.7e-125)
           (- (* x t_1) (* i (* y j)))
           (if (<= j 1.5e-278)
             (+ (* x (* y z)) (* b (- (* a i) (* z c))))
             (if (<= j 1e-37)
               t_2
               (- (* j (* c (- t (* i (/ y c))))) (* a (* x t)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * z) - (t * a);
	double t_2 = x * (t_1 + ((a * (b * i)) / x));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.16e+17) {
		tmp = t_3;
	} else if (j <= -33.0) {
		tmp = t_2;
	} else if (j <= -8.5e-20) {
		tmp = t_3;
	} else if (j <= -1.7e-125) {
		tmp = (x * t_1) - (i * (y * j));
	} else if (j <= 1.5e-278) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (j <= 1e-37) {
		tmp = t_2;
	} else {
		tmp = (j * (c * (t - (i * (y / c))))) - (a * (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (y * z) - (t * a)
    t_2 = x * (t_1 + ((a * (b * i)) / x))
    t_3 = j * ((t * c) - (y * i))
    if (j <= (-1.16d+17)) then
        tmp = t_3
    else if (j <= (-33.0d0)) then
        tmp = t_2
    else if (j <= (-8.5d-20)) then
        tmp = t_3
    else if (j <= (-1.7d-125)) then
        tmp = (x * t_1) - (i * (y * j))
    else if (j <= 1.5d-278) then
        tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
    else if (j <= 1d-37) then
        tmp = t_2
    else
        tmp = (j * (c * (t - (i * (y / c))))) - (a * (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * z) - (t * a);
	double t_2 = x * (t_1 + ((a * (b * i)) / x));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.16e+17) {
		tmp = t_3;
	} else if (j <= -33.0) {
		tmp = t_2;
	} else if (j <= -8.5e-20) {
		tmp = t_3;
	} else if (j <= -1.7e-125) {
		tmp = (x * t_1) - (i * (y * j));
	} else if (j <= 1.5e-278) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (j <= 1e-37) {
		tmp = t_2;
	} else {
		tmp = (j * (c * (t - (i * (y / c))))) - (a * (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * z) - (t * a)
	t_2 = x * (t_1 + ((a * (b * i)) / x))
	t_3 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1.16e+17:
		tmp = t_3
	elif j <= -33.0:
		tmp = t_2
	elif j <= -8.5e-20:
		tmp = t_3
	elif j <= -1.7e-125:
		tmp = (x * t_1) - (i * (y * j))
	elif j <= 1.5e-278:
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
	elif j <= 1e-37:
		tmp = t_2
	else:
		tmp = (j * (c * (t - (i * (y / c))))) - (a * (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * z) - Float64(t * a))
	t_2 = Float64(x * Float64(t_1 + Float64(Float64(a * Float64(b * i)) / x)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.16e+17)
		tmp = t_3;
	elseif (j <= -33.0)
		tmp = t_2;
	elseif (j <= -8.5e-20)
		tmp = t_3;
	elseif (j <= -1.7e-125)
		tmp = Float64(Float64(x * t_1) - Float64(i * Float64(y * j)));
	elseif (j <= 1.5e-278)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (j <= 1e-37)
		tmp = t_2;
	else
		tmp = Float64(Float64(j * Float64(c * Float64(t - Float64(i * Float64(y / c))))) - Float64(a * Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * z) - (t * a);
	t_2 = x * (t_1 + ((a * (b * i)) / x));
	t_3 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.16e+17)
		tmp = t_3;
	elseif (j <= -33.0)
		tmp = t_2;
	elseif (j <= -8.5e-20)
		tmp = t_3;
	elseif (j <= -1.7e-125)
		tmp = (x * t_1) - (i * (y * j));
	elseif (j <= 1.5e-278)
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	elseif (j <= 1e-37)
		tmp = t_2;
	else
		tmp = (j * (c * (t - (i * (y / c))))) - (a * (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t$95$1 + N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.16e+17], t$95$3, If[LessEqual[j, -33.0], t$95$2, If[LessEqual[j, -8.5e-20], t$95$3, If[LessEqual[j, -1.7e-125], N[(N[(x * t$95$1), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.5e-278], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1e-37], t$95$2, N[(N[(j * N[(c * N[(t - N[(i * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.16e17 or -33 < j < -8.5000000000000005e-20

   1. Initial program 84.9%

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

   3. Taylor expanded in j around inf 71.9%

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

   if -1.16e17 < j < -33 or 1.5e-278 < j < 1.00000000000000007e-37

   1. Initial program 65.5%

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

   3. Taylor expanded in x around inf 67.7%

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

      1. associate--r+ 67.7%

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

      2. sub-neg 67.7%

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

      3. mul-1-neg 67.7%

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

      4. +-commutative 67.7%

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

      5. associate-+r+ 67.7%

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

      6. associate-+r- 67.7%

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

      7. +-commutative 67.7%

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

      8. div-sub 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in a around inf 74.5%

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

   if -8.5000000000000005e-20 < j < -1.69999999999999988e-125

   1. Initial program 75.4%

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

   3. Taylor expanded in b around 0 73.5%

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

   4. Taylor expanded in c around 0 70.5%

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

      1. +-commutative 70.5%

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

      2. sub-neg 70.5%

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

      3. *-commutative 70.5%

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

      4. sub-neg 70.5%

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

      5. mul-1-neg 70.5%

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

      6. unsub-neg 70.5%

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

   6. Simplified 70.5%

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

   if -1.69999999999999988e-125 < j < 1.5e-278

   1. Initial program 82.7%

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

   3. Taylor expanded in t around 0 82.7%

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

      1. *-commutative 82.7%

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

      2. associate-*r* 80.3%

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

      3. associate-*r* 80.3%

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

      4. associate-*r* 80.3%

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

      5. distribute-rgt-in 80.3%

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

      6. +-commutative 80.3%

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

      7. mul-1-neg 80.3%

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

      8. unsub-neg 80.3%

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

      9. *-commutative 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in x around inf 78.0%

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

   if 1.00000000000000007e-37 < j

   1. Initial program 77.6%

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

   3. Taylor expanded in b around 0 72.8%

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

   4. Taylor expanded in c around inf 71.6%

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

      1. mul-1-neg 71.6%

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

      2. unsub-neg 71.6%

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

      3. associate-/l* 71.6%

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

   6. Simplified 71.6%

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

   7. Taylor expanded in y around 0 66.6%

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

      1. associate-*r* 66.6%

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

      2. mul-1-neg 66.6%

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

   9. Simplified 66.6%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.16 \cdot 10^{+17}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -33:\\ \;\;\;\;x \cdot \left(\left(y \cdot z - t \cdot a\right) + \frac{a \cdot \left(b \cdot i\right)}{x}\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-20}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 10^{-37}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z - t \cdot a\right) + \frac{a \cdot \left(b \cdot i\right)}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(c \cdot \left(t - i \cdot \frac{y}{c}\right)\right) - a \cdot \left(x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-77}:\\ \;\;\;\;i \cdot \left(y \cdot \left(a \cdot \frac{b}{y} - j\right)\right)\\ \mathbf{elif}\;t \leq 2.12 \cdot 10^{-20} \lor \neg \left(t \leq 6.6 \cdot 10^{+89}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* z (- x (* i (/ j z)))))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -1.4e+54)
     t_2
     (if (<= t -8.8e-94)
       t_1
       (if (<= t 1.18e-178)
         (+ (* x (* y z)) (* b (- (* a i) (* z c))))
         (if (<= t 1.8e-77)
           (* i (* y (- (* a (/ b y)) j)))
           (if (or (<= t 2.12e-20) (not (<= t 6.6e+89))) t_2 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 = y * (z * (x - (i * (j / z))));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.4e+54) {
		tmp = t_2;
	} else if (t <= -8.8e-94) {
		tmp = t_1;
	} else if (t <= 1.18e-178) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (t <= 1.8e-77) {
		tmp = i * (y * ((a * (b / y)) - j));
	} else if ((t <= 2.12e-20) || !(t <= 6.6e+89)) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = y * (z * (x - (i * (j / z))))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-1.4d+54)) then
        tmp = t_2
    else if (t <= (-8.8d-94)) then
        tmp = t_1
    else if (t <= 1.18d-178) then
        tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
    else if (t <= 1.8d-77) then
        tmp = i * (y * ((a * (b / y)) - j))
    else if ((t <= 2.12d-20) .or. (.not. (t <= 6.6d+89))) then
        tmp = t_2
    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 = y * (z * (x - (i * (j / z))));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.4e+54) {
		tmp = t_2;
	} else if (t <= -8.8e-94) {
		tmp = t_1;
	} else if (t <= 1.18e-178) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (t <= 1.8e-77) {
		tmp = i * (y * ((a * (b / y)) - j));
	} else if ((t <= 2.12e-20) || !(t <= 6.6e+89)) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (z * (x - (i * (j / z))))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -1.4e+54:
		tmp = t_2
	elif t <= -8.8e-94:
		tmp = t_1
	elif t <= 1.18e-178:
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
	elif t <= 1.8e-77:
		tmp = i * (y * ((a * (b / y)) - j))
	elif (t <= 2.12e-20) or not (t <= 6.6e+89):
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(z * Float64(x - Float64(i * Float64(j / z)))))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.4e+54)
		tmp = t_2;
	elseif (t <= -8.8e-94)
		tmp = t_1;
	elseif (t <= 1.18e-178)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (t <= 1.8e-77)
		tmp = Float64(i * Float64(y * Float64(Float64(a * Float64(b / y)) - j)));
	elseif ((t <= 2.12e-20) || !(t <= 6.6e+89))
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (z * (x - (i * (j / z))));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -1.4e+54)
		tmp = t_2;
	elseif (t <= -8.8e-94)
		tmp = t_1;
	elseif (t <= 1.18e-178)
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	elseif (t <= 1.8e-77)
		tmp = i * (y * ((a * (b / y)) - j));
	elseif ((t <= 2.12e-20) || ~((t <= 6.6e+89)))
		tmp = t_2;
	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[(y * N[(z * N[(x - N[(i * N[(j / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e+54], t$95$2, If[LessEqual[t, -8.8e-94], t$95$1, If[LessEqual[t, 1.18e-178], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e-77], N[(i * N[(y * N[(N[(a * N[(b / y), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 2.12e-20], N[Not[LessEqual[t, 6.6e+89]], $MachinePrecision]], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.40000000000000008e54 or 1.8e-77 < t < 2.12e-20 or 6.59999999999999948e89 < t

   1. Initial program 72.8%

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

   3. Taylor expanded in t around inf 69.6%

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

      1. +-commutative 69.6%

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

      2. mul-1-neg 69.6%

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

      3. unsub-neg 69.6%

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

      4. *-commutative 69.6%

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

   5. Simplified 69.6%

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

   if -1.40000000000000008e54 < t < -8.80000000000000004e-94 or 2.12e-20 < t < 6.59999999999999948e89

   1. Initial program 80.7%

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

   3. Taylor expanded in y around inf 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in z around inf 55.2%

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

      1. mul-1-neg 55.2%

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

      2. unsub-neg 55.2%

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

      3. associate-/l* 57.2%

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

   8. Simplified 57.2%

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

   if -8.80000000000000004e-94 < t < 1.18000000000000006e-178

   1. Initial program 81.3%

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

   3. Taylor expanded in t around 0 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*r* 73.0%

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

      3. associate-*r* 70.7%

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

      4. associate-*r* 70.7%

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

      5. distribute-rgt-in 72.0%

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

      6. +-commutative 72.0%

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

      7. mul-1-neg 72.0%

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

      8. unsub-neg 72.0%

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

      9. *-commutative 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in x around inf 69.3%

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

   if 1.18000000000000006e-178 < t < 1.8e-77

   1. Initial program 82.1%

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

   3. Taylor expanded in i around inf 76.2%

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

      1. distribute-lft-out-- 76.2%

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

      2. *-commutative 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in y around inf 76.2%

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

      1. mul-1-neg 76.2%

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

      2. unsub-neg 76.2%

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

      3. associate-/l* 76.2%

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

   8. Simplified 76.2%

      \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(y \cdot \left(j - a \cdot \frac{b}{y}\right)\right)}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+54}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ \mathbf{elif}\;t \leq 1.18 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-77}:\\ \;\;\;\;i \cdot \left(y \cdot \left(a \cdot \frac{b}{y} - j\right)\right)\\ \mathbf{elif}\;t \leq 2.12 \cdot 10^{-20} \lor \neg \left(t \leq 6.6 \cdot 10^{+89}\right):\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(x - i \cdot \frac{j}{z}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right) + t\_1\\ \mathbf{if}\;b \leq -3.15 \cdot 10^{+94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -0.0042:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + t\_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \left(y \cdot z + \left(\frac{t\_1}{x} - t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (+ (* y (- (* x z) (* i j))) t_1)))
   (if (<= b -3.15e+94)
     t_2
     (if (<= b -0.0042)
       (+ (* t (- (* c j) (* x a))) t_1)
       (if (<= b 2e-14)
         (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i))))
         (if (<= b 1.15e+122) (* x (+ (* y z) (- (/ t_1 x) (* t a)))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = (y * ((x * z) - (i * j))) + t_1;
	double tmp;
	if (b <= -3.15e+94) {
		tmp = t_2;
	} else if (b <= -0.0042) {
		tmp = (t * ((c * j) - (x * a))) + t_1;
	} else if (b <= 2e-14) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else if (b <= 1.15e+122) {
		tmp = x * ((y * z) + ((t_1 / x) - (t * a)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = (y * ((x * z) - (i * j))) + t_1
    if (b <= (-3.15d+94)) then
        tmp = t_2
    else if (b <= (-0.0042d0)) then
        tmp = (t * ((c * j) - (x * a))) + t_1
    else if (b <= 2d-14) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
    else if (b <= 1.15d+122) then
        tmp = x * ((y * z) + ((t_1 / x) - (t * a)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = (y * ((x * z) - (i * j))) + t_1;
	double tmp;
	if (b <= -3.15e+94) {
		tmp = t_2;
	} else if (b <= -0.0042) {
		tmp = (t * ((c * j) - (x * a))) + t_1;
	} else if (b <= 2e-14) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else if (b <= 1.15e+122) {
		tmp = x * ((y * z) + ((t_1 / x) - (t * a)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = (y * ((x * z) - (i * j))) + t_1
	tmp = 0
	if b <= -3.15e+94:
		tmp = t_2
	elif b <= -0.0042:
		tmp = (t * ((c * j) - (x * a))) + t_1
	elif b <= 2e-14:
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	elif b <= 1.15e+122:
		tmp = x * ((y * z) + ((t_1 / x) - (t * a)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_1)
	tmp = 0.0
	if (b <= -3.15e+94)
		tmp = t_2;
	elseif (b <= -0.0042)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + t_1);
	elseif (b <= 2e-14)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	elseif (b <= 1.15e+122)
		tmp = Float64(x * Float64(Float64(y * z) + Float64(Float64(t_1 / x) - Float64(t * a))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = (y * ((x * z) - (i * j))) + t_1;
	tmp = 0.0;
	if (b <= -3.15e+94)
		tmp = t_2;
	elseif (b <= -0.0042)
		tmp = (t * ((c * j) - (x * a))) + t_1;
	elseif (b <= 2e-14)
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	elseif (b <= 1.15e+122)
		tmp = x * ((y * z) + ((t_1 / x) - (t * a)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[b, -3.15e+94], t$95$2, If[LessEqual[b, -0.0042], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 2e-14], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.15e+122], N[(x * N[(N[(y * z), $MachinePrecision] + N[(N[(t$95$1 / x), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.15e94 or 1.15e122 < b

   1. Initial program 79.5%

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

   3. Taylor expanded in t around 0 77.2%

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

      1. *-commutative 77.2%

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

      2. associate-*r* 78.2%

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

      3. associate-*r* 76.0%

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

      4. associate-*r* 76.0%

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

      5. distribute-rgt-in 77.2%

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

      6. +-commutative 77.2%

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

      7. mul-1-neg 77.2%

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

      8. unsub-neg 77.2%

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

      9. *-commutative 77.2%

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

   5. Simplified 77.2%

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

   if -3.15e94 < b < -0.00419999999999999974

   1. Initial program 77.0%

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

   3. Taylor expanded in y around 0 80.6%

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

      1. +-commutative 80.6%

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

      2. *-commutative 80.6%

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

      3. associate-*r* 80.6%

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

      4. *-commutative 80.6%

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

      5. associate-*l* 76.1%

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

      6. mul-1-neg 76.1%

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

      7. associate-*r* 76.2%

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

      8. *-commutative 76.2%

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

      9. associate-*l* 76.2%

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

      10. distribute-rgt-neg-in 76.2%

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

      11. mul-1-neg 76.2%

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

      12. distribute-lft-in 80.7%

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

      13. mul-1-neg 80.7%

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

      14. unsub-neg 80.7%

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

      15. *-commutative 80.7%

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

      16. *-commutative 80.7%

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

   5. Simplified 80.7%

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

   if -0.00419999999999999974 < b < 2e-14

   1. Initial program 75.3%

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

   3. Taylor expanded in b around 0 77.7%

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

   if 2e-14 < b < 1.15e122

   1. Initial program 80.5%

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

   3. Taylor expanded in x around inf 80.6%

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

      1. associate--r+ 80.6%

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

      2. sub-neg 80.6%

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

      3. mul-1-neg 80.6%

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

      4. +-commutative 80.6%

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

      5. associate-+r+ 80.6%

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

      6. associate-+r- 80.6%

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

      7. +-commutative 80.6%

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

      8. div-sub 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in j around 0 75.9%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.15 \cdot 10^{+94}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -0.0042:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-14}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \left(y \cdot z + \left(\frac{b \cdot \left(a \cdot i - z \cdot c\right)}{x} - t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-167}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-252}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -1.5e+23)
     t_2
     (if (<= x -3.3e-96)
       t_1
       (if (<= x -2.4e-167)
         (* b (- (* a i) (* z c)))
         (if (<= x 4e-252)
           (* j (- (* t c) (* y i)))
           (if (<= x 2.05e-73)
             t_1
             (if (<= x 1.2e+53) (* y (- (* x z) (* i j))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.5e+23) {
		tmp = t_2;
	} else if (x <= -3.3e-96) {
		tmp = t_1;
	} else if (x <= -2.4e-167) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 4e-252) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= 2.05e-73) {
		tmp = t_1;
	} else if (x <= 1.2e+53) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-1.5d+23)) then
        tmp = t_2
    else if (x <= (-3.3d-96)) then
        tmp = t_1
    else if (x <= (-2.4d-167)) then
        tmp = b * ((a * i) - (z * c))
    else if (x <= 4d-252) then
        tmp = j * ((t * c) - (y * i))
    else if (x <= 2.05d-73) then
        tmp = t_1
    else if (x <= 1.2d+53) then
        tmp = y * ((x * z) - (i * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.5e+23) {
		tmp = t_2;
	} else if (x <= -3.3e-96) {
		tmp = t_1;
	} else if (x <= -2.4e-167) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 4e-252) {
		tmp = j * ((t * c) - (y * i));
	} else if (x <= 2.05e-73) {
		tmp = t_1;
	} else if (x <= 1.2e+53) {
		tmp = y * ((x * z) - (i * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.5e+23:
		tmp = t_2
	elif x <= -3.3e-96:
		tmp = t_1
	elif x <= -2.4e-167:
		tmp = b * ((a * i) - (z * c))
	elif x <= 4e-252:
		tmp = j * ((t * c) - (y * i))
	elif x <= 2.05e-73:
		tmp = t_1
	elif x <= 1.2e+53:
		tmp = y * ((x * z) - (i * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.5e+23)
		tmp = t_2;
	elseif (x <= -3.3e-96)
		tmp = t_1;
	elseif (x <= -2.4e-167)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (x <= 4e-252)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (x <= 2.05e-73)
		tmp = t_1;
	elseif (x <= 1.2e+53)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.5e+23)
		tmp = t_2;
	elseif (x <= -3.3e-96)
		tmp = t_1;
	elseif (x <= -2.4e-167)
		tmp = b * ((a * i) - (z * c));
	elseif (x <= 4e-252)
		tmp = j * ((t * c) - (y * i));
	elseif (x <= 2.05e-73)
		tmp = t_1;
	elseif (x <= 1.2e+53)
		tmp = y * ((x * z) - (i * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.5e+23], t$95$2, If[LessEqual[x, -3.3e-96], t$95$1, If[LessEqual[x, -2.4e-167], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e-252], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.05e-73], t$95$1, If[LessEqual[x, 1.2e+53], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.5e23 or 1.2e53 < x

   1. Initial program 79.6%

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

   3. Taylor expanded in b around 0 71.2%

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

   4. Taylor expanded in j around 0 64.6%

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

      1. sub-neg 64.6%

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

      2. *-commutative 64.6%

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

      3. sub-neg 64.6%

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

   6. Simplified 64.6%

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

   if -1.5e23 < x < -3.2999999999999999e-96 or 3.99999999999999977e-252 < x < 2.05000000000000008e-73

   1. Initial program 71.6%

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

   3. Taylor expanded in c around inf 57.4%

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

      1. *-commutative 57.4%

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

      2. *-commutative 57.4%

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

   5. Simplified 57.4%

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

   if -3.2999999999999999e-96 < x < -2.39999999999999993e-167

   1. Initial program 83.3%

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

   3. Taylor expanded in b around inf 76.0%

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

      1. *-commutative 76.0%

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

   5. Simplified 76.0%

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

   if -2.39999999999999993e-167 < x < 3.99999999999999977e-252

   1. Initial program 76.0%

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

   3. Taylor expanded in j around inf 69.0%

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

   if 2.05000000000000008e-73 < x < 1.2e53

   1. Initial program 82.9%

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

   3. Taylor expanded in y around inf 52.0%

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

      1. +-commutative 52.0%

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

      2. mul-1-neg 52.0%

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

      3. unsub-neg 52.0%

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

   5. Simplified 52.0%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+23}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-96}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-167}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-252}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-73}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.05 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -9.6 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-82}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -1.02 \cdot 10^{-143}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-216}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1650000000000:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -1.05e+109)
     t_1
     (if (<= c -9.6e-57)
       (* a (- (* b i) (* x t)))
       (if (<= c -3.6e-82)
         (* z (- (* x y) (* b c)))
         (if (<= c -1.02e-143)
           (* x (- (* y z) (* t a)))
           (if (<= c 6e-216)
             (* y (- (* x z) (* i j)))
             (if (<= c 1650000000000.0) (* i (- (* a b) (* y j))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.05e+109) {
		tmp = t_1;
	} else if (c <= -9.6e-57) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= -3.6e-82) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -1.02e-143) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 6e-216) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 1650000000000.0) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (c <= (-1.05d+109)) then
        tmp = t_1
    else if (c <= (-9.6d-57)) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= (-3.6d-82)) then
        tmp = z * ((x * y) - (b * c))
    else if (c <= (-1.02d-143)) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= 6d-216) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 1650000000000.0d0) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.05e+109) {
		tmp = t_1;
	} else if (c <= -9.6e-57) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= -3.6e-82) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -1.02e-143) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 6e-216) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 1650000000000.0) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -1.05e+109:
		tmp = t_1
	elif c <= -9.6e-57:
		tmp = a * ((b * i) - (x * t))
	elif c <= -3.6e-82:
		tmp = z * ((x * y) - (b * c))
	elif c <= -1.02e-143:
		tmp = x * ((y * z) - (t * a))
	elif c <= 6e-216:
		tmp = y * ((x * z) - (i * j))
	elif c <= 1650000000000.0:
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.05e+109)
		tmp = t_1;
	elseif (c <= -9.6e-57)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= -3.6e-82)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (c <= -1.02e-143)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= 6e-216)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 1650000000000.0)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.05e+109)
		tmp = t_1;
	elseif (c <= -9.6e-57)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= -3.6e-82)
		tmp = z * ((x * y) - (b * c));
	elseif (c <= -1.02e-143)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= 6e-216)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 1650000000000.0)
		tmp = i * ((a * b) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.05e+109], t$95$1, If[LessEqual[c, -9.6e-57], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.6e-82], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.02e-143], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6e-216], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1650000000000.0], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.0500000000000001e109 or 1.65e12 < c

   1. Initial program 68.1%

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

   3. Taylor expanded in c around inf 69.4%

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

      1. *-commutative 69.4%

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

      2. *-commutative 69.4%

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

   5. Simplified 69.4%

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

   if -1.0500000000000001e109 < c < -9.60000000000000025e-57

   1. Initial program 77.8%

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

   3. Taylor expanded in a around inf 62.4%

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

      1. distribute-lft-out-- 62.4%

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

      2. *-commutative 62.4%

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

   5. Simplified 62.4%

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

   if -9.60000000000000025e-57 < c < -3.59999999999999998e-82

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 74.9%

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

   if -3.59999999999999998e-82 < c < -1.02e-143

   1. Initial program 92.4%

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

   3. Taylor expanded in b around 0 68.2%

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

   4. Taylor expanded in j around 0 60.0%

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

      1. sub-neg 60.0%

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

      2. *-commutative 60.0%

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

      3. sub-neg 60.0%

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

   6. Simplified 60.0%

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

   if -1.02e-143 < c < 6.00000000000000025e-216

   1. Initial program 89.0%

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

   3. Taylor expanded in y around inf 60.8%

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

      1. +-commutative 60.8%

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

      2. mul-1-neg 60.8%

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

      3. unsub-neg 60.8%

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

   5. Simplified 60.8%

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

   if 6.00000000000000025e-216 < c < 1.65e12

   1. Initial program 79.2%

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

   3. Taylor expanded in i around inf 58.1%

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

      1. distribute-lft-out-- 58.1%

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

      2. *-commutative 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in i around 0 58.1%

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

      1. associate-*r* 58.1%

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

      2. mul-1-neg 58.1%

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

      3. *-commutative 58.1%

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

   8. Simplified 58.1%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.05 \cdot 10^{+109}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -9.6 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-82}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -1.02 \cdot 10^{-143}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 6 \cdot 10^{-216}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 1650000000000:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -7 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.92 \cdot 10^{+64}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* x (- (* y z) (* t a))) (* i (* y j))))
        (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -7e-20)
     t_2
     (if (<= j -3.7e-125)
       t_1
       (if (<= j 5.2e-122)
         (+ (* x (* y z)) (* b (- (* a i) (* z c))))
         (if (<= j 1.92e+64) 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))) - (i * (y * j));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -7e-20) {
		tmp = t_2;
	} else if (j <= -3.7e-125) {
		tmp = t_1;
	} else if (j <= 5.2e-122) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (j <= 1.92e+64) {
		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))) - (i * (y * j))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-7d-20)) then
        tmp = t_2
    else if (j <= (-3.7d-125)) then
        tmp = t_1
    else if (j <= 5.2d-122) then
        tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
    else if (j <= 1.92d+64) 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))) - (i * (y * j));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -7e-20) {
		tmp = t_2;
	} else if (j <= -3.7e-125) {
		tmp = t_1;
	} else if (j <= 5.2e-122) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (j <= 1.92e+64) {
		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))) - (i * (y * j))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -7e-20:
		tmp = t_2
	elif j <= -3.7e-125:
		tmp = t_1
	elif j <= 5.2e-122:
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
	elif j <= 1.92e+64:
		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(i * Float64(y * j)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -7e-20)
		tmp = t_2;
	elseif (j <= -3.7e-125)
		tmp = t_1;
	elseif (j <= 5.2e-122)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (j <= 1.92e+64)
		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))) - (i * (y * j));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -7e-20)
		tmp = t_2;
	elseif (j <= -3.7e-125)
		tmp = t_1;
	elseif (j <= 5.2e-122)
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	elseif (j <= 1.92e+64)
		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[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7e-20], t$95$2, If[LessEqual[j, -3.7e-125], t$95$1, If[LessEqual[j, 5.2e-122], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.92e+64], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -7.00000000000000007e-20 or 1.92e64 < j

   1. Initial program 77.8%

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

   3. Taylor expanded in j around inf 64.4%

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

   if -7.00000000000000007e-20 < j < -3.6999999999999999e-125 or 5.1999999999999995e-122 < j < 1.92e64

   1. Initial program 85.6%

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

   3. Taylor expanded in b around 0 72.6%

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

   4. Taylor expanded in c around 0 66.3%

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

      1. +-commutative 66.3%

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

      2. sub-neg 66.3%

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

      3. *-commutative 66.3%

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

      4. sub-neg 66.3%

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

      5. mul-1-neg 66.3%

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

      6. unsub-neg 66.3%

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

   6. Simplified 66.3%

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

   if -3.6999999999999999e-125 < j < 5.1999999999999995e-122

   1. Initial program 71.3%

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

   3. Taylor expanded in t around 0 72.5%

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

      1. *-commutative 72.5%

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

      2. associate-*r* 71.1%

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

      3. associate-*r* 71.1%

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

      4. associate-*r* 71.1%

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

      5. distribute-rgt-in 71.1%

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

      6. +-commutative 71.1%

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

      7. mul-1-neg 71.1%

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

      8. unsub-neg 71.1%

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

      9. *-commutative 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in x around inf 69.9%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7 \cdot 10^{-20}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -3.7 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.92 \cdot 10^{+64}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.7 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-190}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-306}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-210}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -2.7e-20)
     t_2
     (if (<= i -1.6e-190)
       t_1
       (if (<= i 6e-306)
         (* t (- (* c j) (* x a)))
         (if (<= i 2.3e-210)
           (* c (- (* t j) (* z b)))
           (if (<= i 1.8e+74) 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));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.7e-20) {
		tmp = t_2;
	} else if (i <= -1.6e-190) {
		tmp = t_1;
	} else if (i <= 6e-306) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 2.3e-210) {
		tmp = c * ((t * j) - (z * b));
	} else if (i <= 1.8e+74) {
		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))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-2.7d-20)) then
        tmp = t_2
    else if (i <= (-1.6d-190)) then
        tmp = t_1
    else if (i <= 6d-306) then
        tmp = t * ((c * j) - (x * a))
    else if (i <= 2.3d-210) then
        tmp = c * ((t * j) - (z * b))
    else if (i <= 1.8d+74) 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));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.7e-20) {
		tmp = t_2;
	} else if (i <= -1.6e-190) {
		tmp = t_1;
	} else if (i <= 6e-306) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 2.3e-210) {
		tmp = c * ((t * j) - (z * b));
	} else if (i <= 1.8e+74) {
		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))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -2.7e-20:
		tmp = t_2
	elif i <= -1.6e-190:
		tmp = t_1
	elif i <= 6e-306:
		tmp = t * ((c * j) - (x * a))
	elif i <= 2.3e-210:
		tmp = c * ((t * j) - (z * b))
	elif i <= 1.8e+74:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.7e-20)
		tmp = t_2;
	elseif (i <= -1.6e-190)
		tmp = t_1;
	elseif (i <= 6e-306)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (i <= 2.3e-210)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (i <= 1.8e+74)
		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));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.7e-20)
		tmp = t_2;
	elseif (i <= -1.6e-190)
		tmp = t_1;
	elseif (i <= 6e-306)
		tmp = t * ((c * j) - (x * a));
	elseif (i <= 2.3e-210)
		tmp = c * ((t * j) - (z * b));
	elseif (i <= 1.8e+74)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.7e-20], t$95$2, If[LessEqual[i, -1.6e-190], t$95$1, If[LessEqual[i, 6e-306], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.3e-210], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.8e+74], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.7e-20 or 1.79999999999999994e74 < i

   1. Initial program 72.1%

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

   3. Taylor expanded in i around inf 66.8%

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

      1. distribute-lft-out-- 66.8%

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

      2. *-commutative 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in i around 0 66.8%

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

      1. associate-*r* 66.8%

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

      2. mul-1-neg 66.8%

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

      3. *-commutative 66.8%

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

   8. Simplified 66.8%

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

   if -2.7e-20 < i < -1.6e-190 or 2.3e-210 < i < 1.79999999999999994e74

   1. Initial program 83.2%

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

   3. Taylor expanded in b around 0 71.7%

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

   4. Taylor expanded in j around 0 55.5%

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

      1. sub-neg 55.5%

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

      2. *-commutative 55.5%

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

      3. sub-neg 55.5%

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

   6. Simplified 55.5%

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

   if -1.6e-190 < i < 6.00000000000000048e-306

   1. Initial program 66.2%

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

   3. Taylor expanded in t around inf 77.2%

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

      1. +-commutative 77.2%

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

      2. mul-1-neg 77.2%

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

      3. unsub-neg 77.2%

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

      4. *-commutative 77.2%

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

   5. Simplified 77.2%

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

   if 6.00000000000000048e-306 < i < 2.3e-210

   1. Initial program 88.6%

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

   3. Taylor expanded in c around inf 63.0%

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

      1. *-commutative 63.0%

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

      2. *-commutative 63.0%

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

   5. Simplified 63.0%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.7 \cdot 10^{-20}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.6 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-306}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-210}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.35 \cdot 10^{-23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-307}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-210}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y - b \cdot \frac{c}{x}\right)\\ \mathbf{elif}\;i \leq 1.16 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* i (- (* a b) (* y j)))))
   (if (<= i -2.35e-23)
     t_2
     (if (<= i -3.8e-191)
       t_1
       (if (<= i 8.5e-307)
         (* t (- (* c j) (* x a)))
         (if (<= i 1.15e-210)
           (* (* x z) (- y (* b (/ c x))))
           (if (<= i 1.16e+78) 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));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.35e-23) {
		tmp = t_2;
	} else if (i <= -3.8e-191) {
		tmp = t_1;
	} else if (i <= 8.5e-307) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 1.15e-210) {
		tmp = (x * z) * (y - (b * (c / x)));
	} else if (i <= 1.16e+78) {
		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))
    t_2 = i * ((a * b) - (y * j))
    if (i <= (-2.35d-23)) then
        tmp = t_2
    else if (i <= (-3.8d-191)) then
        tmp = t_1
    else if (i <= 8.5d-307) then
        tmp = t * ((c * j) - (x * a))
    else if (i <= 1.15d-210) then
        tmp = (x * z) * (y - (b * (c / x)))
    else if (i <= 1.16d+78) 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));
	double t_2 = i * ((a * b) - (y * j));
	double tmp;
	if (i <= -2.35e-23) {
		tmp = t_2;
	} else if (i <= -3.8e-191) {
		tmp = t_1;
	} else if (i <= 8.5e-307) {
		tmp = t * ((c * j) - (x * a));
	} else if (i <= 1.15e-210) {
		tmp = (x * z) * (y - (b * (c / x)));
	} else if (i <= 1.16e+78) {
		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))
	t_2 = i * ((a * b) - (y * j))
	tmp = 0
	if i <= -2.35e-23:
		tmp = t_2
	elif i <= -3.8e-191:
		tmp = t_1
	elif i <= 8.5e-307:
		tmp = t * ((c * j) - (x * a))
	elif i <= 1.15e-210:
		tmp = (x * z) * (y - (b * (c / x)))
	elif i <= 1.16e+78:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.35e-23)
		tmp = t_2;
	elseif (i <= -3.8e-191)
		tmp = t_1;
	elseif (i <= 8.5e-307)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (i <= 1.15e-210)
		tmp = Float64(Float64(x * z) * Float64(y - Float64(b * Float64(c / x))));
	elseif (i <= 1.16e+78)
		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));
	t_2 = i * ((a * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.35e-23)
		tmp = t_2;
	elseif (i <= -3.8e-191)
		tmp = t_1;
	elseif (i <= 8.5e-307)
		tmp = t * ((c * j) - (x * a));
	elseif (i <= 1.15e-210)
		tmp = (x * z) * (y - (b * (c / x)));
	elseif (i <= 1.16e+78)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.35e-23], t$95$2, If[LessEqual[i, -3.8e-191], t$95$1, If[LessEqual[i, 8.5e-307], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.15e-210], N[(N[(x * z), $MachinePrecision] * N[(y - N[(b * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.16e+78], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.35e-23 or 1.1600000000000001e78 < i

   1. Initial program 72.1%

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

   3. Taylor expanded in i around inf 66.8%

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

      1. distribute-lft-out-- 66.8%

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

      2. *-commutative 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in i around 0 66.8%

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

      1. associate-*r* 66.8%

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

      2. mul-1-neg 66.8%

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

      3. *-commutative 66.8%

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

   8. Simplified 66.8%

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

   if -2.35e-23 < i < -3.7999999999999998e-191 or 1.15e-210 < i < 1.1600000000000001e78

   1. Initial program 83.2%

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

   3. Taylor expanded in b around 0 71.7%

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

   4. Taylor expanded in j around 0 55.5%

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

      1. sub-neg 55.5%

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

      2. *-commutative 55.5%

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

      3. sub-neg 55.5%

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

   6. Simplified 55.5%

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

   if -3.7999999999999998e-191 < i < 8.4999999999999995e-307

   1. Initial program 68.9%

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

   3. Taylor expanded in t around inf 80.4%

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

      1. +-commutative 80.4%

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

      2. mul-1-neg 80.4%

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

      3. unsub-neg 80.4%

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

      4. *-commutative 80.4%

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

   5. Simplified 80.4%

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

   if 8.4999999999999995e-307 < i < 1.15e-210

   1. Initial program 84.3%

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

   3. Taylor expanded in x around inf 69.3%

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

      1. associate--r+ 69.3%

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

      2. sub-neg 69.3%

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

      3. mul-1-neg 69.3%

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

      4. +-commutative 69.3%

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

      5. associate-+r+ 69.3%

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

      6. associate-+r- 69.3%

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

      7. +-commutative 69.3%

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

      8. div-sub 75.0%

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

   5. Simplified 75.0%

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

   6. Taylor expanded in z around inf 54.9%

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

      1. associate-*r* 59.2%

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

      2. *-commutative 59.2%

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

      3. associate-/l* 68.9%

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

   8. Simplified 68.9%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.35 \cdot 10^{-23}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-191}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-307}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{-210}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y - b \cdot \frac{c}{x}\right)\\ \mathbf{elif}\;i \leq 1.16 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - t \cdot a\\ t_2 := x \cdot t\_1 + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.05 \cdot 10^{-119}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(t\_1 + \frac{a \cdot \left(b \cdot i\right)}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y z) (* t a)))
        (t_2 (+ (* x t_1) (* j (- (* t c) (* y i))))))
   (if (<= j -1.05e-119)
     t_2
     (if (<= j 2.5e-278)
       (+ (* x (* y z)) (* b (- (* a i) (* z c))))
       (if (<= j 7.8e-33) (* x (+ t_1 (/ (* a (* b i)) x))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * z) - (t * a);
	double t_2 = (x * t_1) + (j * ((t * c) - (y * i)));
	double tmp;
	if (j <= -1.05e-119) {
		tmp = t_2;
	} else if (j <= 2.5e-278) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (j <= 7.8e-33) {
		tmp = x * (t_1 + ((a * (b * i)) / x));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * z) - (t * a)
    t_2 = (x * t_1) + (j * ((t * c) - (y * i)))
    if (j <= (-1.05d-119)) then
        tmp = t_2
    else if (j <= 2.5d-278) then
        tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
    else if (j <= 7.8d-33) then
        tmp = x * (t_1 + ((a * (b * i)) / x))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * z) - (t * a);
	double t_2 = (x * t_1) + (j * ((t * c) - (y * i)));
	double tmp;
	if (j <= -1.05e-119) {
		tmp = t_2;
	} else if (j <= 2.5e-278) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (j <= 7.8e-33) {
		tmp = x * (t_1 + ((a * (b * i)) / x));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * z) - (t * a)
	t_2 = (x * t_1) + (j * ((t * c) - (y * i)))
	tmp = 0
	if j <= -1.05e-119:
		tmp = t_2
	elif j <= 2.5e-278:
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
	elif j <= 7.8e-33:
		tmp = x * (t_1 + ((a * (b * i)) / x))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * z) - Float64(t * a))
	t_2 = Float64(Float64(x * t_1) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (j <= -1.05e-119)
		tmp = t_2;
	elseif (j <= 2.5e-278)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (j <= 7.8e-33)
		tmp = Float64(x * Float64(t_1 + Float64(Float64(a * Float64(b * i)) / x)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * z) - (t * a);
	t_2 = (x * t_1) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (j <= -1.05e-119)
		tmp = t_2;
	elseif (j <= 2.5e-278)
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	elseif (j <= 7.8e-33)
		tmp = x * (t_1 + ((a * (b * i)) / x));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * t$95$1), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.05e-119], t$95$2, If[LessEqual[j, 2.5e-278], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.8e-33], N[(x * N[(t$95$1 + N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.05e-119 or 7.79999999999999948e-33 < j

   1. Initial program 79.8%

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

   3. Taylor expanded in b around 0 73.1%

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

   if -1.05e-119 < j < 2.49999999999999992e-278

   1. Initial program 82.7%

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

   3. Taylor expanded in t around 0 82.7%

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

      1. *-commutative 82.7%

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

      2. associate-*r* 80.3%

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

      3. associate-*r* 80.3%

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

      4. associate-*r* 80.3%

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

      5. distribute-rgt-in 80.3%

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

      6. +-commutative 80.3%

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

      7. mul-1-neg 80.3%

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

      8. unsub-neg 80.3%

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

      9. *-commutative 80.3%

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

   5. Simplified 80.3%

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

   6. Taylor expanded in x around inf 78.0%

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

   if 2.49999999999999992e-278 < j < 7.79999999999999948e-33

   1. Initial program 66.8%

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

   3. Taylor expanded in x around inf 67.1%

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

      1. associate--r+ 67.1%

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

      2. sub-neg 67.1%

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

      3. mul-1-neg 67.1%

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

      4. +-commutative 67.1%

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

      5. associate-+r+ 67.1%

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

      6. associate-+r- 67.1%

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

      7. +-commutative 67.1%

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

      8. div-sub 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in a around inf 72.4%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.05 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z - t \cdot a\right) + \frac{a \cdot \left(b \cdot i\right)}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - t \cdot a\\ t_2 := x \cdot t\_1 + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -6 \cdot 10^{-109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(t\_1 + \frac{a \cdot \left(b \cdot i\right)}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y z) (* t a)))
        (t_2 (+ (* x t_1) (* j (- (* t c) (* y i))))))
   (if (<= j -6e-109)
     t_2
     (if (<= j 3.5e-274)
       (+ (* y (- (* x z) (* i j))) (* b (- (* a i) (* z c))))
       (if (<= j 3.8e-34) (* x (+ t_1 (/ (* a (* b i)) x))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * z) - (t * a);
	double t_2 = (x * t_1) + (j * ((t * c) - (y * i)));
	double tmp;
	if (j <= -6e-109) {
		tmp = t_2;
	} else if (j <= 3.5e-274) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)));
	} else if (j <= 3.8e-34) {
		tmp = x * (t_1 + ((a * (b * i)) / x));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * z) - (t * a)
    t_2 = (x * t_1) + (j * ((t * c) - (y * i)))
    if (j <= (-6d-109)) then
        tmp = t_2
    else if (j <= 3.5d-274) then
        tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)))
    else if (j <= 3.8d-34) then
        tmp = x * (t_1 + ((a * (b * i)) / x))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (y * z) - (t * a);
	double t_2 = (x * t_1) + (j * ((t * c) - (y * i)));
	double tmp;
	if (j <= -6e-109) {
		tmp = t_2;
	} else if (j <= 3.5e-274) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)));
	} else if (j <= 3.8e-34) {
		tmp = x * (t_1 + ((a * (b * i)) / x));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * z) - (t * a)
	t_2 = (x * t_1) + (j * ((t * c) - (y * i)))
	tmp = 0
	if j <= -6e-109:
		tmp = t_2
	elif j <= 3.5e-274:
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)))
	elif j <= 3.8e-34:
		tmp = x * (t_1 + ((a * (b * i)) / x))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * z) - Float64(t * a))
	t_2 = Float64(Float64(x * t_1) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (j <= -6e-109)
		tmp = t_2;
	elseif (j <= 3.5e-274)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (j <= 3.8e-34)
		tmp = Float64(x * Float64(t_1 + Float64(Float64(a * Float64(b * i)) / x)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (y * z) - (t * a);
	t_2 = (x * t_1) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (j <= -6e-109)
		tmp = t_2;
	elseif (j <= 3.5e-274)
		tmp = (y * ((x * z) - (i * j))) + (b * ((a * i) - (z * c)));
	elseif (j <= 3.8e-34)
		tmp = x * (t_1 + ((a * (b * i)) / x));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * t$95$1), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6e-109], t$95$2, If[LessEqual[j, 3.5e-274], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.8e-34], N[(x * N[(t$95$1 + N[(N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -6.00000000000000043e-109 or 3.8000000000000001e-34 < j

   1. Initial program 80.0%

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

   3. Taylor expanded in b around 0 73.4%

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

   if -6.00000000000000043e-109 < j < 3.49999999999999982e-274

   1. Initial program 82.1%

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

   3. Taylor expanded in t around 0 80.2%

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

      1. *-commutative 80.2%

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

      2. associate-*r* 80.1%

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

      3. associate-*r* 80.1%

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

      4. associate-*r* 80.1%

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

      5. distribute-rgt-in 80.1%

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

      6. +-commutative 80.1%

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

      7. mul-1-neg 80.1%

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

      8. unsub-neg 80.1%

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

      9. *-commutative 80.1%

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

   5. Simplified 80.1%

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

   if 3.49999999999999982e-274 < j < 3.8000000000000001e-34

   1. Initial program 66.2%

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

   3. Taylor expanded in x around inf 66.5%

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

      1. associate--r+ 66.5%

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

      2. sub-neg 66.5%

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

      3. mul-1-neg 66.5%

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

      4. +-commutative 66.5%

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

      5. associate-+r+ 66.5%

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

      6. associate-+r- 66.5%

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

      7. +-commutative 66.5%

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

      8. div-sub 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in a around inf 71.9%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6 \cdot 10^{-109}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-274}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-34}:\\ \;\;\;\;x \cdot \left(\left(y \cdot z - t \cdot a\right) + \frac{a \cdot \left(b \cdot i\right)}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-173}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-153}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))) (t_2 (* c (* t j))))
   (if (<= t -2.25e+51)
     t_2
     (if (<= t -8.2e-173)
       t_1
       (if (<= t 4.1e-218)
         (* x (* y z))
         (if (<= t 1.55e-153) (* i (* a b)) (if (<= t 8.5e+127) 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 = i * (y * -j);
	double t_2 = c * (t * j);
	double tmp;
	if (t <= -2.25e+51) {
		tmp = t_2;
	} else if (t <= -8.2e-173) {
		tmp = t_1;
	} else if (t <= 4.1e-218) {
		tmp = x * (y * z);
	} else if (t <= 1.55e-153) {
		tmp = i * (a * b);
	} else if (t <= 8.5e+127) {
		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 = i * (y * -j)
    t_2 = c * (t * j)
    if (t <= (-2.25d+51)) then
        tmp = t_2
    else if (t <= (-8.2d-173)) then
        tmp = t_1
    else if (t <= 4.1d-218) then
        tmp = x * (y * z)
    else if (t <= 1.55d-153) then
        tmp = i * (a * b)
    else if (t <= 8.5d+127) 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 = i * (y * -j);
	double t_2 = c * (t * j);
	double tmp;
	if (t <= -2.25e+51) {
		tmp = t_2;
	} else if (t <= -8.2e-173) {
		tmp = t_1;
	} else if (t <= 4.1e-218) {
		tmp = x * (y * z);
	} else if (t <= 1.55e-153) {
		tmp = i * (a * b);
	} else if (t <= 8.5e+127) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	t_2 = c * (t * j)
	tmp = 0
	if t <= -2.25e+51:
		tmp = t_2
	elif t <= -8.2e-173:
		tmp = t_1
	elif t <= 4.1e-218:
		tmp = x * (y * z)
	elif t <= 1.55e-153:
		tmp = i * (a * b)
	elif t <= 8.5e+127:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(y * Float64(-j)))
	t_2 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (t <= -2.25e+51)
		tmp = t_2;
	elseif (t <= -8.2e-173)
		tmp = t_1;
	elseif (t <= 4.1e-218)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= 1.55e-153)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 8.5e+127)
		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 = i * (y * -j);
	t_2 = c * (t * j);
	tmp = 0.0;
	if (t <= -2.25e+51)
		tmp = t_2;
	elseif (t <= -8.2e-173)
		tmp = t_1;
	elseif (t <= 4.1e-218)
		tmp = x * (y * z);
	elseif (t <= 1.55e-153)
		tmp = i * (a * b);
	elseif (t <= 8.5e+127)
		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[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.25e+51], t$95$2, If[LessEqual[t, -8.2e-173], t$95$1, If[LessEqual[t, 4.1e-218], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e-153], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e+127], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.25e51 or 8.4999999999999997e127 < t

   1. Initial program 72.2%

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

   3. Taylor expanded in x around inf 68.1%

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

      1. associate--r+ 68.1%

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

      2. sub-neg 68.1%

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

      3. mul-1-neg 68.1%

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

      4. +-commutative 68.1%

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

      5. associate-+r+ 68.1%

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

      6. associate-+r- 68.1%

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

      7. +-commutative 68.1%

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

      8. div-sub 68.1%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in c around inf 54.9%

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

      1. associate-*r* 54.7%

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

      2. associate-/l* 52.3%

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

      3. associate-/l* 47.7%

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

   8. Simplified 47.7%

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

   9. Taylor expanded in z around inf 57.1%

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

       1. +-commutative 57.1%

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

       2. mul-1-neg 57.1%

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

       3. unsub-neg 57.1%

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

       4. associate-*r* 53.8%

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

       5. *-commutative 53.8%

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

       6. *-commutative 53.8%

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

   11. Simplified 53.8%

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

   12. Taylor expanded in z around 0 53.6%

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

   if -2.25e51 < t < -8.1999999999999995e-173 or 1.54999999999999997e-153 < t < 8.4999999999999997e127

   1. Initial program 79.7%

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

   3. Taylor expanded in t around 0 62.9%

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

      1. *-commutative 62.9%

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

      2. associate-*r* 64.7%

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

      3. associate-*r* 63.0%

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

      4. associate-*r* 63.0%

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

      5. distribute-rgt-in 63.0%

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

      6. +-commutative 63.0%

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

      7. mul-1-neg 63.0%

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

      8. unsub-neg 63.0%

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

      9. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in j around inf 32.0%

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

      1. mul-1-neg 32.0%

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

      2. *-commutative 32.0%

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

      3. distribute-rgt-neg-out 32.0%

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

      4. distribute-rgt-neg-in 32.0%

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

   8. Simplified 32.0%

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

   if -8.1999999999999995e-173 < t < 4.0999999999999998e-218

   1. Initial program 81.8%

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

   3. Taylor expanded in y around inf 46.2%

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

      1. +-commutative 46.2%

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

      2. mul-1-neg 46.2%

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

      3. unsub-neg 46.2%

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

   5. Simplified 46.2%

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

   6. Taylor expanded in x around inf 39.6%

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

   if 4.0999999999999998e-218 < t < 1.54999999999999997e-153

   1. Initial program 80.8%

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

   3. Taylor expanded in b around inf 61.3%

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

      1. *-commutative 61.3%

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

   5. Simplified 61.3%

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

   6. Taylor expanded in a around inf 46.4%

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

      1. associate-*r* 59.1%

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

      2. *-commutative 59.1%

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

   8. Simplified 59.1%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{+51}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-173}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-153}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+127}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;t \leq -1.02 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-219}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+44}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+107}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= t -1.02e+46)
     t_1
     (if (<= t 4e-219)
       (* x (* y z))
       (if (<= t 9.5e-59)
         (* b (* a i))
         (if (<= t 3.8e+44)
           (* j (* t c))
           (if (<= t 8e+107) (* a (* b i)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (t <= -1.02e+46) {
		tmp = t_1;
	} else if (t <= 4e-219) {
		tmp = x * (y * z);
	} else if (t <= 9.5e-59) {
		tmp = b * (a * i);
	} else if (t <= 3.8e+44) {
		tmp = j * (t * c);
	} else if (t <= 8e+107) {
		tmp = a * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (t <= (-1.02d+46)) then
        tmp = t_1
    else if (t <= 4d-219) then
        tmp = x * (y * z)
    else if (t <= 9.5d-59) then
        tmp = b * (a * i)
    else if (t <= 3.8d+44) then
        tmp = j * (t * c)
    else if (t <= 8d+107) then
        tmp = a * (b * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (t <= -1.02e+46) {
		tmp = t_1;
	} else if (t <= 4e-219) {
		tmp = x * (y * z);
	} else if (t <= 9.5e-59) {
		tmp = b * (a * i);
	} else if (t <= 3.8e+44) {
		tmp = j * (t * c);
	} else if (t <= 8e+107) {
		tmp = a * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if t <= -1.02e+46:
		tmp = t_1
	elif t <= 4e-219:
		tmp = x * (y * z)
	elif t <= 9.5e-59:
		tmp = b * (a * i)
	elif t <= 3.8e+44:
		tmp = j * (t * c)
	elif t <= 8e+107:
		tmp = a * (b * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (t <= -1.02e+46)
		tmp = t_1;
	elseif (t <= 4e-219)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= 9.5e-59)
		tmp = Float64(b * Float64(a * i));
	elseif (t <= 3.8e+44)
		tmp = Float64(j * Float64(t * c));
	elseif (t <= 8e+107)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (t <= -1.02e+46)
		tmp = t_1;
	elseif (t <= 4e-219)
		tmp = x * (y * z);
	elseif (t <= 9.5e-59)
		tmp = b * (a * i);
	elseif (t <= 3.8e+44)
		tmp = j * (t * c);
	elseif (t <= 8e+107)
		tmp = a * (b * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.02e+46], t$95$1, If[LessEqual[t, 4e-219], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-59], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e+44], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8e+107], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.0199999999999999e46 or 7.9999999999999998e107 < t

   1. Initial program 73.7%

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

   3. Taylor expanded in x around inf 67.7%

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

      1. associate--r+ 67.7%

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

      2. sub-neg 67.7%

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

      3. mul-1-neg 67.7%

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

      4. +-commutative 67.7%

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

      5. associate-+r+ 67.7%

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

      6. associate-+r- 67.7%

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

      7. +-commutative 67.7%

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

      8. div-sub 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in c around inf 53.0%

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

      1. associate-*r* 52.9%

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

      2. associate-/l* 50.6%

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

      3. associate-/l* 47.3%

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

   8. Simplified 47.3%

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

   9. Taylor expanded in z around inf 54.0%

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

       1. +-commutative 54.0%

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

       2. mul-1-neg 54.0%

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

       3. unsub-neg 54.0%

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

       4. associate-*r* 50.9%

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

       5. *-commutative 50.9%

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

       6. *-commutative 50.9%

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

   11. Simplified 50.9%

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

   12. Taylor expanded in z around 0 51.8%

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

   if -1.0199999999999999e46 < t < 4.0000000000000001e-219

   1. Initial program 80.9%

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

   3. Taylor expanded in y around inf 46.2%

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

      1. +-commutative 46.2%

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

      2. mul-1-neg 46.2%

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

      3. unsub-neg 46.2%

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

   5. Simplified 46.2%

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

   6. Taylor expanded in x around inf 31.9%

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

   if 4.0000000000000001e-219 < t < 9.4999999999999994e-59

   1. Initial program 80.5%

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

   3. Taylor expanded in b around inf 41.5%

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

      1. *-commutative 41.5%

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

   5. Simplified 41.5%

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

   6. Taylor expanded in a around inf 32.2%

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

      1. *-commutative 32.2%

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

   8. Simplified 32.2%

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

   if 9.4999999999999994e-59 < t < 3.8000000000000002e44

   1. Initial program 88.1%

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

   3. Taylor expanded in x around inf 71.4%

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

      1. associate--r+ 71.4%

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

      2. sub-neg 71.4%

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

      3. mul-1-neg 71.4%

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

      4. +-commutative 71.4%

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

      5. associate-+r+ 71.4%

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

      6. associate-+r- 71.4%

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

      7. +-commutative 71.4%

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

      8. div-sub 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in c around inf 53.4%

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

      1. associate-*r* 47.2%

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

      2. associate-/l* 47.2%

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

      3. associate-/l* 47.3%

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

   8. Simplified 47.3%

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

   9. Taylor expanded in z around inf 42.8%

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

       1. +-commutative 42.8%

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

       2. mul-1-neg 42.8%

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

       3. unsub-neg 42.8%

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

       4. associate-*r* 42.9%

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

       5. *-commutative 42.9%

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

       6. *-commutative 42.9%

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

   11. Simplified 42.9%

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

   12. Taylor expanded in z around 0 37.1%

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

       1. *-commutative 37.1%

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

       2. associate-*r* 37.2%

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

       3. *-commutative 37.2%

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

   14. Simplified 37.2%

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

   if 3.8000000000000002e44 < t < 7.9999999999999998e107

   1. Initial program 60.0%

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

   3. Taylor expanded in b around inf 36.1%

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

      1. *-commutative 36.1%

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

   5. Simplified 36.1%

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

   6. Taylor expanded in a around inf 30.5%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{+46}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-219}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-59}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+44}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+107}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-153}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 0.0029:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+108}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= t -3.4e+46)
     t_1
     (if (<= t 2e-218)
       (* x (* y z))
       (if (<= t 2.5e-153)
         (* i (* a b))
         (if (<= t 0.0029)
           (* y (* x z))
           (if (<= t 1.3e+108) (* a (* b i)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (t <= -3.4e+46) {
		tmp = t_1;
	} else if (t <= 2e-218) {
		tmp = x * (y * z);
	} else if (t <= 2.5e-153) {
		tmp = i * (a * b);
	} else if (t <= 0.0029) {
		tmp = y * (x * z);
	} else if (t <= 1.3e+108) {
		tmp = a * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (t <= (-3.4d+46)) then
        tmp = t_1
    else if (t <= 2d-218) then
        tmp = x * (y * z)
    else if (t <= 2.5d-153) then
        tmp = i * (a * b)
    else if (t <= 0.0029d0) then
        tmp = y * (x * z)
    else if (t <= 1.3d+108) then
        tmp = a * (b * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (t <= -3.4e+46) {
		tmp = t_1;
	} else if (t <= 2e-218) {
		tmp = x * (y * z);
	} else if (t <= 2.5e-153) {
		tmp = i * (a * b);
	} else if (t <= 0.0029) {
		tmp = y * (x * z);
	} else if (t <= 1.3e+108) {
		tmp = a * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if t <= -3.4e+46:
		tmp = t_1
	elif t <= 2e-218:
		tmp = x * (y * z)
	elif t <= 2.5e-153:
		tmp = i * (a * b)
	elif t <= 0.0029:
		tmp = y * (x * z)
	elif t <= 1.3e+108:
		tmp = a * (b * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (t <= -3.4e+46)
		tmp = t_1;
	elseif (t <= 2e-218)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= 2.5e-153)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 0.0029)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 1.3e+108)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (t <= -3.4e+46)
		tmp = t_1;
	elseif (t <= 2e-218)
		tmp = x * (y * z);
	elseif (t <= 2.5e-153)
		tmp = i * (a * b);
	elseif (t <= 0.0029)
		tmp = y * (x * z);
	elseif (t <= 1.3e+108)
		tmp = a * (b * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e+46], t$95$1, If[LessEqual[t, 2e-218], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e-153], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.0029], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e+108], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.3999999999999998e46 or 1.3000000000000001e108 < t

   1. Initial program 73.7%

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

   3. Taylor expanded in x around inf 67.7%

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

      1. associate--r+ 67.7%

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

      2. sub-neg 67.7%

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

      3. mul-1-neg 67.7%

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

      4. +-commutative 67.7%

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

      5. associate-+r+ 67.7%

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

      6. associate-+r- 67.7%

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

      7. +-commutative 67.7%

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

      8. div-sub 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in c around inf 53.0%

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

      1. associate-*r* 52.9%

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

      2. associate-/l* 50.6%

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

      3. associate-/l* 47.3%

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

   8. Simplified 47.3%

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

   9. Taylor expanded in z around inf 54.0%

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

       1. +-commutative 54.0%

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

       2. mul-1-neg 54.0%

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

       3. unsub-neg 54.0%

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

       4. associate-*r* 50.9%

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

       5. *-commutative 50.9%

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

       6. *-commutative 50.9%

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

   11. Simplified 50.9%

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

   12. Taylor expanded in z around 0 51.8%

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

   if -3.3999999999999998e46 < t < 2.0000000000000001e-218

   1. Initial program 80.9%

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

   3. Taylor expanded in y around inf 46.2%

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

      1. +-commutative 46.2%

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

      2. mul-1-neg 46.2%

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

      3. unsub-neg 46.2%

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

   5. Simplified 46.2%

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

   6. Taylor expanded in x around inf 31.9%

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

   if 2.0000000000000001e-218 < t < 2.50000000000000016e-153

   1. Initial program 80.8%

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

   3. Taylor expanded in b around inf 61.3%

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

      1. *-commutative 61.3%

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

   5. Simplified 61.3%

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

   6. Taylor expanded in a around inf 46.4%

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

      1. associate-*r* 59.1%

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

      2. *-commutative 59.1%

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

   8. Simplified 59.1%

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

   if 2.50000000000000016e-153 < t < 0.0029

   1. Initial program 80.2%

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

   3. Taylor expanded in y around inf 42.1%

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

      1. +-commutative 42.1%

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

      2. mul-1-neg 42.1%

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

      3. unsub-neg 42.1%

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

   5. Simplified 42.1%

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

   6. Taylor expanded in x around inf 25.2%

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

      1. *-commutative 25.2%

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

   8. Simplified 25.2%

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

   if 0.0029 < t < 1.3000000000000001e108

   1. Initial program 73.3%

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

   3. Taylor expanded in b around inf 34.0%

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

      1. *-commutative 34.0%

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

   5. Simplified 34.0%

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

   6. Taylor expanded in a around inf 30.3%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+46}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-153}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 0.0029:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+108}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-219}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-154}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 0.0038:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= t -3.6e+45)
     t_1
     (if (<= t 3.7e-219)
       (* x (* y z))
       (if (<= t 4.5e-154)
         (* i (* a b))
         (if (<= t 0.0038)
           (* z (* x y))
           (if (<= t 2.1e+113) (* a (* b i)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (t <= -3.6e+45) {
		tmp = t_1;
	} else if (t <= 3.7e-219) {
		tmp = x * (y * z);
	} else if (t <= 4.5e-154) {
		tmp = i * (a * b);
	} else if (t <= 0.0038) {
		tmp = z * (x * y);
	} else if (t <= 2.1e+113) {
		tmp = a * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (t <= (-3.6d+45)) then
        tmp = t_1
    else if (t <= 3.7d-219) then
        tmp = x * (y * z)
    else if (t <= 4.5d-154) then
        tmp = i * (a * b)
    else if (t <= 0.0038d0) then
        tmp = z * (x * y)
    else if (t <= 2.1d+113) then
        tmp = a * (b * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (t <= -3.6e+45) {
		tmp = t_1;
	} else if (t <= 3.7e-219) {
		tmp = x * (y * z);
	} else if (t <= 4.5e-154) {
		tmp = i * (a * b);
	} else if (t <= 0.0038) {
		tmp = z * (x * y);
	} else if (t <= 2.1e+113) {
		tmp = a * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if t <= -3.6e+45:
		tmp = t_1
	elif t <= 3.7e-219:
		tmp = x * (y * z)
	elif t <= 4.5e-154:
		tmp = i * (a * b)
	elif t <= 0.0038:
		tmp = z * (x * y)
	elif t <= 2.1e+113:
		tmp = a * (b * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (t <= -3.6e+45)
		tmp = t_1;
	elseif (t <= 3.7e-219)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= 4.5e-154)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 0.0038)
		tmp = Float64(z * Float64(x * y));
	elseif (t <= 2.1e+113)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (t <= -3.6e+45)
		tmp = t_1;
	elseif (t <= 3.7e-219)
		tmp = x * (y * z);
	elseif (t <= 4.5e-154)
		tmp = i * (a * b);
	elseif (t <= 0.0038)
		tmp = z * (x * y);
	elseif (t <= 2.1e+113)
		tmp = a * (b * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e+45], t$95$1, If[LessEqual[t, 3.7e-219], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-154], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.0038], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e+113], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.6e45 or 2.0999999999999999e113 < t

   1. Initial program 73.7%

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

   3. Taylor expanded in x around inf 67.7%

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

      1. associate--r+ 67.7%

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

      2. sub-neg 67.7%

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

      3. mul-1-neg 67.7%

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

      4. +-commutative 67.7%

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

      5. associate-+r+ 67.7%

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

      6. associate-+r- 67.7%

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

      7. +-commutative 67.7%

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

      8. div-sub 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in c around inf 53.0%

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

      1. associate-*r* 52.9%

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

      2. associate-/l* 50.6%

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

      3. associate-/l* 47.3%

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

   8. Simplified 47.3%

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

   9. Taylor expanded in z around inf 54.0%

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

       1. +-commutative 54.0%

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

       2. mul-1-neg 54.0%

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

       3. unsub-neg 54.0%

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

       4. associate-*r* 50.9%

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

       5. *-commutative 50.9%

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

       6. *-commutative 50.9%

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

   11. Simplified 50.9%

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

   12. Taylor expanded in z around 0 51.8%

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

   if -3.6e45 < t < 3.7e-219

   1. Initial program 80.9%

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

   3. Taylor expanded in y around inf 46.2%

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

      1. +-commutative 46.2%

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

      2. mul-1-neg 46.2%

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

      3. unsub-neg 46.2%

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

   5. Simplified 46.2%

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

   6. Taylor expanded in x around inf 31.9%

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

   if 3.7e-219 < t < 4.4999999999999997e-154

   1. Initial program 80.8%

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

   3. Taylor expanded in b around inf 61.3%

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

      1. *-commutative 61.3%

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

   5. Simplified 61.3%

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

   6. Taylor expanded in a around inf 46.4%

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

      1. associate-*r* 59.1%

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

      2. *-commutative 59.1%

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

   8. Simplified 59.1%

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

   if 4.4999999999999997e-154 < t < 0.00379999999999999999

   1. Initial program 80.2%

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

   3. Taylor expanded in t around 0 58.0%

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

      1. *-commutative 58.0%

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

      2. associate-*r* 61.0%

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

      3. associate-*r* 57.8%

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

      4. associate-*r* 57.8%

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

      5. distribute-rgt-in 57.8%

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

      6. +-commutative 57.8%

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

      7. mul-1-neg 57.8%

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

      8. unsub-neg 57.8%

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

      9. *-commutative 57.8%

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

   5. Simplified 57.8%

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

   6. Taylor expanded in x around inf 22.2%

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

      1. associate-*r* 25.3%

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

      2. *-commutative 25.3%

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

   8. Simplified 25.3%

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

   if 0.00379999999999999999 < t < 2.0999999999999999e113

   1. Initial program 73.3%

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

   3. Taylor expanded in b around inf 34.0%

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

      1. *-commutative 34.0%

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

   5. Simplified 34.0%

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

   6. Taylor expanded in a around inf 30.3%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+45}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-219}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-154}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 0.0038:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;t \leq -4 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-128}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{-5}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+108}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= t -4e+45)
     t_1
     (if (<= t 5e-218)
       (* x (* y z))
       (if (<= t 1.2e-128)
         (* i (* a b))
         (if (<= t 6.1e-5)
           (* c (* z (- b)))
           (if (<= t 1.15e+108) (* a (* b i)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (t <= -4e+45) {
		tmp = t_1;
	} else if (t <= 5e-218) {
		tmp = x * (y * z);
	} else if (t <= 1.2e-128) {
		tmp = i * (a * b);
	} else if (t <= 6.1e-5) {
		tmp = c * (z * -b);
	} else if (t <= 1.15e+108) {
		tmp = a * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * (t * j)
    if (t <= (-4d+45)) then
        tmp = t_1
    else if (t <= 5d-218) then
        tmp = x * (y * z)
    else if (t <= 1.2d-128) then
        tmp = i * (a * b)
    else if (t <= 6.1d-5) then
        tmp = c * (z * -b)
    else if (t <= 1.15d+108) then
        tmp = a * (b * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double tmp;
	if (t <= -4e+45) {
		tmp = t_1;
	} else if (t <= 5e-218) {
		tmp = x * (y * z);
	} else if (t <= 1.2e-128) {
		tmp = i * (a * b);
	} else if (t <= 6.1e-5) {
		tmp = c * (z * -b);
	} else if (t <= 1.15e+108) {
		tmp = a * (b * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if t <= -4e+45:
		tmp = t_1
	elif t <= 5e-218:
		tmp = x * (y * z)
	elif t <= 1.2e-128:
		tmp = i * (a * b)
	elif t <= 6.1e-5:
		tmp = c * (z * -b)
	elif t <= 1.15e+108:
		tmp = a * (b * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (t <= -4e+45)
		tmp = t_1;
	elseif (t <= 5e-218)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= 1.2e-128)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 6.1e-5)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (t <= 1.15e+108)
		tmp = Float64(a * Float64(b * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	tmp = 0.0;
	if (t <= -4e+45)
		tmp = t_1;
	elseif (t <= 5e-218)
		tmp = x * (y * z);
	elseif (t <= 1.2e-128)
		tmp = i * (a * b);
	elseif (t <= 6.1e-5)
		tmp = c * (z * -b);
	elseif (t <= 1.15e+108)
		tmp = a * (b * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4e+45], t$95$1, If[LessEqual[t, 5e-218], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-128], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.1e-5], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+108], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -3.9999999999999997e45 or 1.1499999999999999e108 < t

   1. Initial program 73.7%

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

   3. Taylor expanded in x around inf 67.7%

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

      1. associate--r+ 67.7%

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

      2. sub-neg 67.7%

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

      3. mul-1-neg 67.7%

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

      4. +-commutative 67.7%

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

      5. associate-+r+ 67.7%

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

      6. associate-+r- 67.7%

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

      7. +-commutative 67.7%

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

      8. div-sub 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in c around inf 53.0%

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

      1. associate-*r* 52.9%

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

      2. associate-/l* 50.6%

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

      3. associate-/l* 47.3%

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

   8. Simplified 47.3%

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

   9. Taylor expanded in z around inf 54.0%

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

       1. +-commutative 54.0%

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

       2. mul-1-neg 54.0%

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

       3. unsub-neg 54.0%

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

       4. associate-*r* 50.9%

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

       5. *-commutative 50.9%

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

       6. *-commutative 50.9%

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

   11. Simplified 50.9%

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

   12. Taylor expanded in z around 0 51.8%

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

   if -3.9999999999999997e45 < t < 5.00000000000000041e-218

   1. Initial program 80.9%

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

   3. Taylor expanded in y around inf 46.2%

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

      1. +-commutative 46.2%

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

      2. mul-1-neg 46.2%

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

      3. unsub-neg 46.2%

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

   5. Simplified 46.2%

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

   6. Taylor expanded in x around inf 31.9%

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

   if 5.00000000000000041e-218 < t < 1.1999999999999999e-128

   1. Initial program 77.7%

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

   3. Taylor expanded in b around inf 51.1%

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

      1. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in a around inf 41.0%

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

      1. associate-*r* 49.2%

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

      2. *-commutative 49.2%

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

   8. Simplified 49.2%

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

   if 1.1999999999999999e-128 < t < 6.09999999999999987e-5

   1. Initial program 82.2%

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

   3. Taylor expanded in t around 0 56.3%

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

      1. *-commutative 56.3%

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

      2. associate-*r* 60.4%

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

      3. associate-*r* 56.0%

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

      4. associate-*r* 56.0%

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

      5. distribute-rgt-in 56.0%

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

      6. +-commutative 56.0%

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

      7. mul-1-neg 56.0%

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

      8. unsub-neg 56.0%

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

      9. *-commutative 56.0%

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

   5. Simplified 56.0%

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

   6. Taylor expanded in c around inf 24.8%

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

      1. mul-1-neg 24.8%

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

      2. associate-*r* 20.8%

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

      3. *-commutative 20.8%

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

      4. associate-*r* 29.0%

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

      5. distribute-rgt-neg-out 29.0%

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

      6. *-commutative 29.0%

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

      7. distribute-rgt-neg-in 29.0%

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

   8. Simplified 29.0%

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

   if 6.09999999999999987e-5 < t < 1.1499999999999999e108

   1. Initial program 74.5%

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

   3. Taylor expanded in b around inf 32.5%

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

      1. *-commutative 32.5%

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

   5. Simplified 32.5%

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

   6. Taylor expanded in a around inf 29.0%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+45}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-128}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 6.1 \cdot 10^{-5}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+108}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 41.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+167} \lor \neg \left(y \leq -4.8 \cdot 10^{+70}\right) \land \left(y \leq -4 \cdot 10^{-24} \lor \neg \left(y \leq 1.6 \cdot 10^{+103}\right)\right):\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -1.16e+167)
         (and (not (<= y -4.8e+70)) (or (<= y -4e-24) (not (<= y 1.6e+103)))))
   (* i (* y (- j)))
   (* b (- (* a i) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -1.16e+167) || (!(y <= -4.8e+70) && ((y <= -4e-24) || !(y <= 1.6e+103)))) {
		tmp = i * (y * -j);
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((y <= (-1.16d+167)) .or. (.not. (y <= (-4.8d+70))) .and. (y <= (-4d-24)) .or. (.not. (y <= 1.6d+103))) then
        tmp = i * (y * -j)
    else
        tmp = b * ((a * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -1.16e+167) || (!(y <= -4.8e+70) && ((y <= -4e-24) || !(y <= 1.6e+103)))) {
		tmp = i * (y * -j);
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -1.16e+167) or (not (y <= -4.8e+70) and ((y <= -4e-24) or not (y <= 1.6e+103))):
		tmp = i * (y * -j)
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -1.16e+167) || (!(y <= -4.8e+70) && ((y <= -4e-24) || !(y <= 1.6e+103))))
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -1.16e+167) || (~((y <= -4.8e+70)) && ((y <= -4e-24) || ~((y <= 1.6e+103)))))
		tmp = i * (y * -j);
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -1.16e+167], And[N[Not[LessEqual[y, -4.8e+70]], $MachinePrecision], Or[LessEqual[y, -4e-24], N[Not[LessEqual[y, 1.6e+103]], $MachinePrecision]]]], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1600000000000001e167 or -4.79999999999999974e70 < y < -3.99999999999999969e-24 or 1.59999999999999996e103 < y

   1. Initial program 70.2%

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

   3. Taylor expanded in t around 0 63.9%

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

      1. *-commutative 63.9%

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

      2. associate-*r* 67.8%

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

      3. associate-*r* 69.0%

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

      4. associate-*r* 69.0%

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

      5. distribute-rgt-in 71.2%

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

      6. +-commutative 71.2%

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

      7. mul-1-neg 71.2%

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

      8. unsub-neg 71.2%

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

      9. *-commutative 71.2%

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

   5. Simplified 71.2%

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

   6. Taylor expanded in j around inf 42.8%

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

      1. mul-1-neg 42.8%

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

      2. *-commutative 42.8%

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

      3. distribute-rgt-neg-out 42.8%

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

      4. distribute-rgt-neg-in 42.8%

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

   8. Simplified 42.8%

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

   if -1.1600000000000001e167 < y < -4.79999999999999974e70 or -3.99999999999999969e-24 < y < 1.59999999999999996e103

   1. Initial program 82.0%

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

   3. Taylor expanded in b around inf 45.6%

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

      1. *-commutative 45.6%

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

   5. Simplified 45.6%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{+167} \lor \neg \left(y \leq -4.8 \cdot 10^{+70}\right) \land \left(y \leq -4 \cdot 10^{-24} \lor \neg \left(y \leq 1.6 \cdot 10^{+103}\right)\right):\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 43.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;i \leq -5.2 \cdot 10^{+24}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{-48}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= i -5.2e+24)
     (* i (* y (- j)))
     (if (<= i 3.2e-60)
       t_1
       (if (<= i 2.1e-48)
         (* z (* x y))
         (if (<= i 1.25e+71) t_1 (* b (- (* a i) (* z c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (i <= -5.2e+24) {
		tmp = i * (y * -j);
	} else if (i <= 3.2e-60) {
		tmp = t_1;
	} else if (i <= 2.1e-48) {
		tmp = z * (x * y);
	} else if (i <= 1.25e+71) {
		tmp = t_1;
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((t * j) - (z * b))
    if (i <= (-5.2d+24)) then
        tmp = i * (y * -j)
    else if (i <= 3.2d-60) then
        tmp = t_1
    else if (i <= 2.1d-48) then
        tmp = z * (x * y)
    else if (i <= 1.25d+71) then
        tmp = t_1
    else
        tmp = b * ((a * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (i <= -5.2e+24) {
		tmp = i * (y * -j);
	} else if (i <= 3.2e-60) {
		tmp = t_1;
	} else if (i <= 2.1e-48) {
		tmp = z * (x * y);
	} else if (i <= 1.25e+71) {
		tmp = t_1;
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	tmp = 0
	if i <= -5.2e+24:
		tmp = i * (y * -j)
	elif i <= 3.2e-60:
		tmp = t_1
	elif i <= 2.1e-48:
		tmp = z * (x * y)
	elif i <= 1.25e+71:
		tmp = t_1
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (i <= -5.2e+24)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (i <= 3.2e-60)
		tmp = t_1;
	elseif (i <= 2.1e-48)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 1.25e+71)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (i <= -5.2e+24)
		tmp = i * (y * -j);
	elseif (i <= 3.2e-60)
		tmp = t_1;
	elseif (i <= 2.1e-48)
		tmp = z * (x * y);
	elseif (i <= 1.25e+71)
		tmp = t_1;
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5.2e+24], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.2e-60], t$95$1, If[LessEqual[i, 2.1e-48], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.25e+71], t$95$1, N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -5.1999999999999997e24

   1. Initial program 67.5%

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

   3. Taylor expanded in t around 0 69.6%

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

      1. *-commutative 69.6%

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

      2. associate-*r* 67.8%

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

      3. associate-*r* 62.6%

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

      4. associate-*r* 62.6%

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

      5. distribute-rgt-in 64.5%

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

      6. +-commutative 64.5%

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

      7. mul-1-neg 64.5%

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

      8. unsub-neg 64.5%

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

      9. *-commutative 64.5%

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

   5. Simplified 64.5%

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

   6. Taylor expanded in j around inf 40.4%

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

      1. mul-1-neg 40.4%

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

      2. *-commutative 40.4%

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

      3. distribute-rgt-neg-out 40.4%

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

      4. distribute-rgt-neg-in 40.4%

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

   8. Simplified 40.4%

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

   if -5.1999999999999997e24 < i < 3.2000000000000001e-60 or 2.09999999999999989e-48 < i < 1.24999999999999993e71

   1. Initial program 82.6%

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

   3. Taylor expanded in c around inf 50.1%

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

      1. *-commutative 50.1%

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

      2. *-commutative 50.1%

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

   5. Simplified 50.1%

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

   if 3.2000000000000001e-60 < i < 2.09999999999999989e-48

   1. Initial program 82.6%

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

   3. Taylor expanded in t around 0 82.6%

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

      1. *-commutative 82.6%

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

      2. associate-*r* 67.1%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 67.1%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 67.1%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 67.1%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 67.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 67.1%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 67.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 67.1%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 67.1%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in x around inf 84.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 84.5%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

      2. *-commutative 84.5%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   8. Simplified 84.5%

      \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot z} \]

   if 1.24999999999999993e71 < i

   1. Initial program 71.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 49.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 49.8%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 49.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.2 \cdot 10^{+24}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-60}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{-48}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{+71}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 49.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -7.2 \cdot 10^{-128}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{-276}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{-214}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-35}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -7.2e-128)
     t_2
     (if (<= j 1.3e-276)
       t_1
       (if (<= j 6.8e-214) (* z (* x y)) (if (<= j 2e-35) 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 * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -7.2e-128) {
		tmp = t_2;
	} else if (j <= 1.3e-276) {
		tmp = t_1;
	} else if (j <= 6.8e-214) {
		tmp = z * (x * y);
	} else if (j <= 2e-35) {
		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 * ((a * i) - (z * c))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-7.2d-128)) then
        tmp = t_2
    else if (j <= 1.3d-276) then
        tmp = t_1
    else if (j <= 6.8d-214) then
        tmp = z * (x * y)
    else if (j <= 2d-35) 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 * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -7.2e-128) {
		tmp = t_2;
	} else if (j <= 1.3e-276) {
		tmp = t_1;
	} else if (j <= 6.8e-214) {
		tmp = z * (x * y);
	} else if (j <= 2e-35) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -7.2e-128:
		tmp = t_2
	elif j <= 1.3e-276:
		tmp = t_1
	elif j <= 6.8e-214:
		tmp = z * (x * y)
	elif j <= 2e-35:
		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(a * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -7.2e-128)
		tmp = t_2;
	elseif (j <= 1.3e-276)
		tmp = t_1;
	elseif (j <= 6.8e-214)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 2e-35)
		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 * ((a * i) - (z * c));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -7.2e-128)
		tmp = t_2;
	elseif (j <= 1.3e-276)
		tmp = t_1;
	elseif (j <= 6.8e-214)
		tmp = z * (x * y);
	elseif (j <= 2e-35)
		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[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.2e-128], t$95$2, If[LessEqual[j, 1.3e-276], t$95$1, If[LessEqual[j, 6.8e-214], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2e-35], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -7.20000000000000049e-128 or 2.00000000000000002e-35 < j

   1. Initial program 79.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 59.2%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]

   if -7.20000000000000049e-128 < j < 1.29999999999999992e-276 or 6.7999999999999998e-214 < j < 2.00000000000000002e-35

   1. Initial program 77.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 54.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 54.1%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 54.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   if 1.29999999999999992e-276 < j < 6.7999999999999998e-214

   1. Initial program 58.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 57.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z - a \cdot i\right)} \]
   4. Step-by-step derivation

      1. *-commutative 57.1%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + x \cdot \color{blue}{\left(z \cdot y\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      2. associate-*r* 51.7%

         \[\leadsto \left(-1 \cdot \left(i \cdot \left(j \cdot y\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot y}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      3. associate-*r* 51.7%

         \[\leadsto \left(-1 \cdot \color{blue}{\left(\left(i \cdot j\right) \cdot y\right)} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      4. associate-*r* 51.7%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right) \cdot y} + \left(x \cdot z\right) \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      5. distribute-rgt-in 51.7%

         \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      6. +-commutative 51.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      7. mul-1-neg 51.7%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) - b \cdot \left(c \cdot z - a \cdot i\right) \]

      8. unsub-neg 51.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} - b \cdot \left(c \cdot z - a \cdot i\right) \]

      9. *-commutative 51.7%

         \[\leadsto y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(\color{blue}{z \cdot c} - a \cdot i\right) \]

   5. Simplified 51.7%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c - a \cdot i\right)} \]

   6. Taylor expanded in x around inf 51.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 51.8%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

      2. *-commutative 51.8%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   8. Simplified 51.8%

      \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.2 \cdot 10^{-128}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{-276}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 6.8 \cdot 10^{-214}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-35}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 51.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.65 \cdot 10^{-95}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-167}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -4.2e+24)
     t_1
     (if (<= x -2.65e-95)
       (* c (- (* t j) (* z b)))
       (if (<= x -2.5e-167)
         (* b (- (* a i) (* z c)))
         (if (<= x 1.3e+48) (* j (- (* t c) (* y i))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4.2e+24) {
		tmp = t_1;
	} else if (x <= -2.65e-95) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= -2.5e-167) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 1.3e+48) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-4.2d+24)) then
        tmp = t_1
    else if (x <= (-2.65d-95)) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= (-2.5d-167)) then
        tmp = b * ((a * i) - (z * c))
    else if (x <= 1.3d+48) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -4.2e+24) {
		tmp = t_1;
	} else if (x <= -2.65e-95) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= -2.5e-167) {
		tmp = b * ((a * i) - (z * c));
	} else if (x <= 1.3e+48) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -4.2e+24:
		tmp = t_1
	elif x <= -2.65e-95:
		tmp = c * ((t * j) - (z * b))
	elif x <= -2.5e-167:
		tmp = b * ((a * i) - (z * c))
	elif x <= 1.3e+48:
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -4.2e+24)
		tmp = t_1;
	elseif (x <= -2.65e-95)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= -2.5e-167)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (x <= 1.3e+48)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -4.2e+24)
		tmp = t_1;
	elseif (x <= -2.65e-95)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= -2.5e-167)
		tmp = b * ((a * i) - (z * c));
	elseif (x <= 1.3e+48)
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.2e+24], t$95$1, If[LessEqual[x, -2.65e-95], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.5e-167], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+48], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.2000000000000003e24 or 1.29999999999999998e48 < x

   1. Initial program 79.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 71.4%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   4. Taylor expanded in j around 0 64.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   5. Step-by-step derivation

      1. sub-neg 64.8%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)} \]

      2. *-commutative 64.8%

         \[\leadsto x \cdot \left(y \cdot z + \left(-\color{blue}{t \cdot a}\right)\right) \]

      3. sub-neg 64.8%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} \]

   6. Simplified 64.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right)} \]

   if -4.2000000000000003e24 < x < -2.6499999999999999e-95

   1. Initial program 77.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf 52.6%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t - b \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 52.6%

         \[\leadsto c \cdot \left(\color{blue}{t \cdot j} - b \cdot z\right) \]

      2. *-commutative 52.6%

         \[\leadsto c \cdot \left(t \cdot j - \color{blue}{z \cdot b}\right) \]

   5. Simplified 52.6%

      \[\leadsto \color{blue}{c \cdot \left(t \cdot j - z \cdot b\right)} \]

   if -2.6499999999999999e-95 < x < -2.5000000000000001e-167

   1. Initial program 83.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 76.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 76.0%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 76.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   if -2.5000000000000001e-167 < x < 1.29999999999999998e48

   1. Initial program 74.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 55.2%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.65 \cdot 10^{-95}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-167}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+48}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 29.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -3 \cdot 10^{-109} \lor \neg \left(j \leq 2.5 \cdot 10^{-34}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -3e-109) (not (<= j 2.5e-34))) (* c (* t j)) (* b (* a i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -3e-109) || !(j <= 2.5e-34)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-3d-109)) .or. (.not. (j <= 2.5d-34))) then
        tmp = c * (t * j)
    else
        tmp = b * (a * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -3e-109) || !(j <= 2.5e-34)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -3e-109) or not (j <= 2.5e-34):
		tmp = c * (t * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -3e-109) || !(j <= 2.5e-34))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -3e-109) || ~((j <= 2.5e-34)))
		tmp = c * (t * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -3e-109], N[Not[LessEqual[j, 2.5e-34]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -3.00000000000000021e-109 or 2.5000000000000001e-34 < j

   1. Initial program 79.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 72.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right) - \left(a \cdot t + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ 72.5%

         \[\leadsto x \cdot \color{blue}{\left(\left(\left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right) - a \cdot t\right) - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right)} \]

      2. sub-neg 72.5%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right) + \left(-a \cdot t\right)\right)} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right) \]

      3. mul-1-neg 72.5%

         \[\leadsto x \cdot \left(\left(\left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right) + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right) - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right) \]

      4. +-commutative 72.5%

         \[\leadsto x \cdot \left(\color{blue}{\left(-1 \cdot \left(a \cdot t\right) + \left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right)\right)} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right) \]

      5. associate-+r+ 72.5%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right) + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right)} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right) \]

      6. associate-+r- 72.5%

         \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right) + \left(\frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right)\right)} \]

      7. +-commutative 72.5%

         \[\leadsto x \cdot \left(\color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} + \left(\frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right)\right) \]

      8. div-sub 75.2%

         \[\leadsto x \cdot \left(\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right) + \color{blue}{\frac{j \cdot \left(c \cdot t - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{x}}\right) \]

   5. Simplified 75.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot z - a \cdot t\right) + \frac{j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - a \cdot i\right)}{x}\right)} \]

   6. Taylor expanded in c around inf 46.7%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(\frac{j \cdot t}{x} - \frac{b \cdot z}{x}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 43.6%

         \[\leadsto \color{blue}{\left(c \cdot x\right) \cdot \left(\frac{j \cdot t}{x} - \frac{b \cdot z}{x}\right)} \]

      2. associate-/l* 41.2%

         \[\leadsto \left(c \cdot x\right) \cdot \left(\color{blue}{j \cdot \frac{t}{x}} - \frac{b \cdot z}{x}\right) \]

      3. associate-/l* 38.2%

         \[\leadsto \left(c \cdot x\right) \cdot \left(j \cdot \frac{t}{x} - \color{blue}{b \cdot \frac{z}{x}}\right) \]

   8. Simplified 38.2%

      \[\leadsto \color{blue}{\left(c \cdot x\right) \cdot \left(j \cdot \frac{t}{x} - b \cdot \frac{z}{x}\right)} \]

   9. Taylor expanded in z around inf 40.1%

      \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \left(b \cdot c\right) + \frac{c \cdot \left(j \cdot t\right)}{z}\right)} \]
   10. Step-by-step derivation

       1. +-commutative 40.1%

          \[\leadsto z \cdot \color{blue}{\left(\frac{c \cdot \left(j \cdot t\right)}{z} + -1 \cdot \left(b \cdot c\right)\right)} \]

       2. mul-1-neg 40.1%

          \[\leadsto z \cdot \left(\frac{c \cdot \left(j \cdot t\right)}{z} + \color{blue}{\left(-b \cdot c\right)}\right) \]

       3. unsub-neg 40.1%

          \[\leadsto z \cdot \color{blue}{\left(\frac{c \cdot \left(j \cdot t\right)}{z} - b \cdot c\right)} \]

       4. associate-*r* 37.1%

          \[\leadsto z \cdot \left(\frac{\color{blue}{\left(c \cdot j\right) \cdot t}}{z} - b \cdot c\right) \]

       5. *-commutative 37.1%

          \[\leadsto z \cdot \left(\frac{\color{blue}{t \cdot \left(c \cdot j\right)}}{z} - b \cdot c\right) \]

       6. *-commutative 37.1%

          \[\leadsto z \cdot \left(\frac{t \cdot \left(c \cdot j\right)}{z} - \color{blue}{c \cdot b}\right) \]

   11. Simplified 37.1%

       \[\leadsto \color{blue}{z \cdot \left(\frac{t \cdot \left(c \cdot j\right)}{z} - c \cdot b\right)} \]

   12. Taylor expanded in z around 0 34.5%

       \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if -3.00000000000000021e-109 < j < 2.5000000000000001e-34

   1. Initial program 74.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 47.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 47.1%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 47.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 30.8%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 30.8%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   8. Simplified 30.8%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3 \cdot 10^{-109} \lor \neg \left(j \leq 2.5 \cdot 10^{-34}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 29.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.46 \cdot 10^{-111}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-35}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.46e-111)
   (* j (* t c))
   (if (<= j 8.5e-35) (* b (* a i)) (* c (* t j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.46e-111) {
		tmp = j * (t * c);
	} else if (j <= 8.5e-35) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-1.46d-111)) then
        tmp = j * (t * c)
    else if (j <= 8.5d-35) then
        tmp = b * (a * i)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -1.46e-111) {
		tmp = j * (t * c);
	} else if (j <= 8.5e-35) {
		tmp = b * (a * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.46e-111:
		tmp = j * (t * c)
	elif j <= 8.5e-35:
		tmp = b * (a * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.46e-111)
		tmp = Float64(j * Float64(t * c));
	elseif (j <= 8.5e-35)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1.46e-111)
		tmp = j * (t * c);
	elseif (j <= 8.5e-35)
		tmp = b * (a * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.46e-111], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.5e-35], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.46e-111

   1. Initial program 81.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 74.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right) - \left(a \cdot t + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ 74.1%

         \[\leadsto x \cdot \color{blue}{\left(\left(\left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right) - a \cdot t\right) - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right)} \]

      2. sub-neg 74.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right) + \left(-a \cdot t\right)\right)} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right) \]

      3. mul-1-neg 74.1%

         \[\leadsto x \cdot \left(\left(\left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right) + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right) - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right) \]

      4. +-commutative 74.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(-1 \cdot \left(a \cdot t\right) + \left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right)\right)} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right) \]

      5. associate-+r+ 74.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right) + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right)} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right) \]

      6. associate-+r- 74.1%

         \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right) + \left(\frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right)\right)} \]

      7. +-commutative 74.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} + \left(\frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right)\right) \]

      8. div-sub 75.4%

         \[\leadsto x \cdot \left(\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right) + \color{blue}{\frac{j \cdot \left(c \cdot t - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{x}}\right) \]

   5. Simplified 75.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot z - a \cdot t\right) + \frac{j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - a \cdot i\right)}{x}\right)} \]

   6. Taylor expanded in c around inf 42.0%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(\frac{j \cdot t}{x} - \frac{b \cdot z}{x}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 38.6%

         \[\leadsto \color{blue}{\left(c \cdot x\right) \cdot \left(\frac{j \cdot t}{x} - \frac{b \cdot z}{x}\right)} \]

      2. associate-/l* 37.6%

         \[\leadsto \left(c \cdot x\right) \cdot \left(\color{blue}{j \cdot \frac{t}{x}} - \frac{b \cdot z}{x}\right) \]

      3. associate-/l* 33.3%

         \[\leadsto \left(c \cdot x\right) \cdot \left(j \cdot \frac{t}{x} - \color{blue}{b \cdot \frac{z}{x}}\right) \]

   8. Simplified 33.3%

      \[\leadsto \color{blue}{\left(c \cdot x\right) \cdot \left(j \cdot \frac{t}{x} - b \cdot \frac{z}{x}\right)} \]

   9. Taylor expanded in z around inf 32.3%

      \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \left(b \cdot c\right) + \frac{c \cdot \left(j \cdot t\right)}{z}\right)} \]
   10. Step-by-step derivation

       1. +-commutative 32.3%

          \[\leadsto z \cdot \color{blue}{\left(\frac{c \cdot \left(j \cdot t\right)}{z} + -1 \cdot \left(b \cdot c\right)\right)} \]

       2. mul-1-neg 32.3%

          \[\leadsto z \cdot \left(\frac{c \cdot \left(j \cdot t\right)}{z} + \color{blue}{\left(-b \cdot c\right)}\right) \]

       3. unsub-neg 32.3%

          \[\leadsto z \cdot \color{blue}{\left(\frac{c \cdot \left(j \cdot t\right)}{z} - b \cdot c\right)} \]

       4. associate-*r* 32.3%

          \[\leadsto z \cdot \left(\frac{\color{blue}{\left(c \cdot j\right) \cdot t}}{z} - b \cdot c\right) \]

       5. *-commutative 32.3%

          \[\leadsto z \cdot \left(\frac{\color{blue}{t \cdot \left(c \cdot j\right)}}{z} - b \cdot c\right) \]

       6. *-commutative 32.3%

          \[\leadsto z \cdot \left(\frac{t \cdot \left(c \cdot j\right)}{z} - \color{blue}{c \cdot b}\right) \]

   11. Simplified 32.3%

       \[\leadsto \color{blue}{z \cdot \left(\frac{t \cdot \left(c \cdot j\right)}{z} - c \cdot b\right)} \]

   12. Taylor expanded in z around 0 31.0%

       \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
   13. Step-by-step derivation

       1. *-commutative 31.0%

          \[\leadsto \color{blue}{\left(j \cdot t\right) \cdot c} \]

       2. associate-*r* 31.6%

          \[\leadsto \color{blue}{j \cdot \left(t \cdot c\right)} \]

       3. *-commutative 31.6%

          \[\leadsto j \cdot \color{blue}{\left(c \cdot t\right)} \]

   14. Simplified 31.6%

       \[\leadsto \color{blue}{j \cdot \left(c \cdot t\right)} \]

   if -1.46e-111 < j < 8.5000000000000001e-35

   1. Initial program 74.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 48.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 48.0%

         \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 48.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

   6. Taylor expanded in a around inf 31.4%

      \[\leadsto b \cdot \color{blue}{\left(a \cdot i\right)} \]
   7. Step-by-step derivation

      1. *-commutative 31.4%

         \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   8. Simplified 31.4%

      \[\leadsto b \cdot \color{blue}{\left(i \cdot a\right)} \]

   if 8.5000000000000001e-35 < j

   1. Initial program 76.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 70.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right) - \left(a \cdot t + \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right)\right)} \]
   4. Step-by-step derivation

      1. associate--r+ 70.1%

         \[\leadsto x \cdot \color{blue}{\left(\left(\left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right) - a \cdot t\right) - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right)} \]

      2. sub-neg 70.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right) + \left(-a \cdot t\right)\right)} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right) \]

      3. mul-1-neg 70.1%

         \[\leadsto x \cdot \left(\left(\left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right) + \color{blue}{-1 \cdot \left(a \cdot t\right)}\right) - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right) \]

      4. +-commutative 70.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(-1 \cdot \left(a \cdot t\right) + \left(y \cdot z + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right)\right)} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right) \]

      5. associate-+r+ 70.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right) + \frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x}\right)} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right) \]

      6. associate-+r- 70.1%

         \[\leadsto x \cdot \color{blue}{\left(\left(-1 \cdot \left(a \cdot t\right) + y \cdot z\right) + \left(\frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right)\right)} \]

      7. +-commutative 70.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right)} + \left(\frac{j \cdot \left(c \cdot t - i \cdot y\right)}{x} - \frac{b \cdot \left(c \cdot z - a \cdot i\right)}{x}\right)\right) \]

      8. div-sub 74.2%

         \[\leadsto x \cdot \left(\left(y \cdot z + -1 \cdot \left(a \cdot t\right)\right) + \color{blue}{\frac{j \cdot \left(c \cdot t - i \cdot y\right) - b \cdot \left(c \cdot z - a \cdot i\right)}{x}}\right) \]

   5. Simplified 74.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(y \cdot z - a \cdot t\right) + \frac{j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c - a \cdot i\right)}{x}\right)} \]

   6. Taylor expanded in c around inf 51.5%

      \[\leadsto \color{blue}{c \cdot \left(x \cdot \left(\frac{j \cdot t}{x} - \frac{b \cdot z}{x}\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 48.7%

         \[\leadsto \color{blue}{\left(c \cdot x\right) \cdot \left(\frac{j \cdot t}{x} - \frac{b \cdot z}{x}\right)} \]

      2. associate-/l* 44.6%

         \[\leadsto \left(c \cdot x\right) \cdot \left(\color{blue}{j \cdot \frac{t}{x}} - \frac{b \cdot z}{x}\right) \]

      3. associate-/l* 43.3%

         \[\leadsto \left(c \cdot x\right) \cdot \left(j \cdot \frac{t}{x} - \color{blue}{b \cdot \frac{z}{x}}\right) \]

   8. Simplified 43.3%

      \[\leadsto \color{blue}{\left(c \cdot x\right) \cdot \left(j \cdot \frac{t}{x} - b \cdot \frac{z}{x}\right)} \]

   9. Taylor expanded in z around inf 48.9%

      \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \left(b \cdot c\right) + \frac{c \cdot \left(j \cdot t\right)}{z}\right)} \]
   10. Step-by-step derivation

       1. +-commutative 48.9%

          \[\leadsto z \cdot \color{blue}{\left(\frac{c \cdot \left(j \cdot t\right)}{z} + -1 \cdot \left(b \cdot c\right)\right)} \]

       2. mul-1-neg 48.9%

          \[\leadsto z \cdot \left(\frac{c \cdot \left(j \cdot t\right)}{z} + \color{blue}{\left(-b \cdot c\right)}\right) \]

       3. unsub-neg 48.9%

          \[\leadsto z \cdot \color{blue}{\left(\frac{c \cdot \left(j \cdot t\right)}{z} - b \cdot c\right)} \]

       4. associate-*r* 43.7%

          \[\leadsto z \cdot \left(\frac{\color{blue}{\left(c \cdot j\right) \cdot t}}{z} - b \cdot c\right) \]

       5. *-commutative 43.7%

          \[\leadsto z \cdot \left(\frac{\color{blue}{t \cdot \left(c \cdot j\right)}}{z} - b \cdot c\right) \]

       6. *-commutative 43.7%

          \[\leadsto z \cdot \left(\frac{t \cdot \left(c \cdot j\right)}{z} - \color{blue}{c \cdot b}\right) \]

   11. Simplified 43.7%

       \[\leadsto \color{blue}{z \cdot \left(\frac{t \cdot \left(c \cdot j\right)}{z} - c \cdot b\right)} \]

   12. Taylor expanded in z around 0 38.0%

       \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.46 \cdot 10^{-111}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;j \leq 8.5 \cdot 10^{-35}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 22.3% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(b \cdot i\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* b i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (b * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (b * i);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (b * i)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(b * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (b * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.6%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]
2. Add Preprocessing

3. Taylor expanded in b around inf 34.8%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
4. Step-by-step derivation

   1. *-commutative 34.8%

      \[\leadsto b \cdot \left(a \cdot i - \color{blue}{z \cdot c}\right) \]

5. Simplified 34.8%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - z \cdot c\right)} \]

6. Taylor expanded in a around inf 19.1%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

7. Final simplification 19.1%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
8. Add Preprocessing

Developer target: 68.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024078 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))