Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 74.0% → 82.4%

Time: 40.1s

Alternatives: 26

Speedup: 0.5×

• 57.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 74.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.4% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* 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))
     (* t (- (* c j) (* x a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = 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 = t * ((c * j) - (x * a));
	}
	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(t * Float64(Float64(c * j) - Float64(x * a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(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[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.5%

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

      1. +-commutative 90.5%

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

      2. fma-def 90.5%

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

      3. *-commutative 90.5%

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

      4. *-commutative 90.5%

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

      5. cancel-sign-sub-inv 90.5%

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

      6. cancel-sign-sub 90.5%

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

      7. fma-neg 90.5%

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

      8. distribute-rgt-neg-out 90.5%

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

      9. remove-double-neg 90.5%

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

      10. *-commutative 90.5%

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

      11. *-commutative 90.5%

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

   3. Simplified 90.5%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in i around -inf 16.1%

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

   3. Taylor expanded in t around inf 50.6%

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

      1. +-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

      4. *-commutative 50.6%

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

   5. Simplified 50.6%

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

4. Final simplification 80.9%

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

Alternative 2: 82.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.5%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in i around -inf 16.1%

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

   3. Taylor expanded in t around inf 50.6%

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

      1. +-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

      4. *-commutative 50.6%

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

   5. Simplified 50.6%

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

4. Final simplification 80.9%

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

Alternative 3: 50.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+191}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-239}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-104}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 3.55 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c))))
        (t_2 (+ (* j (- (* t c) (* y i))) (* i (* a b)))))
   (if (<= t -1.8e+191)
     (* a (- (* b i) (* x t)))
     (if (<= t -6.6e-24)
       t_2
       (if (<= t -3.7e-196)
         t_1
         (if (<= t -1.9e-239)
           (* y (- (* x z) (* i j)))
           (if (<= t 4.2e-190)
             t_1
             (if (<= t 3e-104)
               (* i (- (* a b) (* y j)))
               (if (<= t 3.55e-31)
                 (* x (- (* y z) (* t a)))
                 (if (<= t 4e+64) t_2 (* t (- (* c j) (* x a)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = (j * ((t * c) - (y * i))) + (i * (a * b));
	double tmp;
	if (t <= -1.8e+191) {
		tmp = a * ((b * i) - (x * t));
	} else if (t <= -6.6e-24) {
		tmp = t_2;
	} else if (t <= -3.7e-196) {
		tmp = t_1;
	} else if (t <= -1.9e-239) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 4.2e-190) {
		tmp = t_1;
	} else if (t <= 3e-104) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= 3.55e-31) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= 4e+64) {
		tmp = t_2;
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    t_2 = (j * ((t * c) - (y * i))) + (i * (a * b))
    if (t <= (-1.8d+191)) then
        tmp = a * ((b * i) - (x * t))
    else if (t <= (-6.6d-24)) then
        tmp = t_2
    else if (t <= (-3.7d-196)) then
        tmp = t_1
    else if (t <= (-1.9d-239)) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= 4.2d-190) then
        tmp = t_1
    else if (t <= 3d-104) then
        tmp = i * ((a * b) - (y * j))
    else if (t <= 3.55d-31) then
        tmp = x * ((y * z) - (t * a))
    else if (t <= 4d+64) then
        tmp = t_2
    else
        tmp = t * ((c * j) - (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * ((x * y) - (b * c));
	double t_2 = (j * ((t * c) - (y * i))) + (i * (a * b));
	double tmp;
	if (t <= -1.8e+191) {
		tmp = a * ((b * i) - (x * t));
	} else if (t <= -6.6e-24) {
		tmp = t_2;
	} else if (t <= -3.7e-196) {
		tmp = t_1;
	} else if (t <= -1.9e-239) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 4.2e-190) {
		tmp = t_1;
	} else if (t <= 3e-104) {
		tmp = i * ((a * b) - (y * j));
	} else if (t <= 3.55e-31) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= 4e+64) {
		tmp = t_2;
	} else {
		tmp = t * ((c * j) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = (j * ((t * c) - (y * i))) + (i * (a * b))
	tmp = 0
	if t <= -1.8e+191:
		tmp = a * ((b * i) - (x * t))
	elif t <= -6.6e-24:
		tmp = t_2
	elif t <= -3.7e-196:
		tmp = t_1
	elif t <= -1.9e-239:
		tmp = y * ((x * z) - (i * j))
	elif t <= 4.2e-190:
		tmp = t_1
	elif t <= 3e-104:
		tmp = i * ((a * b) - (y * j))
	elif t <= 3.55e-31:
		tmp = x * ((y * z) - (t * a))
	elif t <= 4e+64:
		tmp = t_2
	else:
		tmp = t * ((c * j) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(i * Float64(a * b)))
	tmp = 0.0
	if (t <= -1.8e+191)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (t <= -6.6e-24)
		tmp = t_2;
	elseif (t <= -3.7e-196)
		tmp = t_1;
	elseif (t <= -1.9e-239)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= 4.2e-190)
		tmp = t_1;
	elseif (t <= 3e-104)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (t <= 3.55e-31)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (t <= 4e+64)
		tmp = t_2;
	else
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * ((x * y) - (b * c));
	t_2 = (j * ((t * c) - (y * i))) + (i * (a * b));
	tmp = 0.0;
	if (t <= -1.8e+191)
		tmp = a * ((b * i) - (x * t));
	elseif (t <= -6.6e-24)
		tmp = t_2;
	elseif (t <= -3.7e-196)
		tmp = t_1;
	elseif (t <= -1.9e-239)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= 4.2e-190)
		tmp = t_1;
	elseif (t <= 3e-104)
		tmp = i * ((a * b) - (y * j));
	elseif (t <= 3.55e-31)
		tmp = x * ((y * z) - (t * a));
	elseif (t <= 4e+64)
		tmp = t_2;
	else
		tmp = t * ((c * j) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.8e+191], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.6e-24], t$95$2, If[LessEqual[t, -3.7e-196], t$95$1, If[LessEqual[t, -1.9e-239], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-190], t$95$1, If[LessEqual[t, 3e-104], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.55e-31], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+64], t$95$2, N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.8e191

   1. Initial program 59.1%

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

   2. Taylor expanded in i around -inf 62.1%

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

   3. Taylor expanded in a around inf 83.5%

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

      1. +-commutative 83.5%

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

      2. mul-1-neg 83.5%

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

      3. unsub-neg 83.5%

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

   5. Simplified 83.5%

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

   if -1.8e191 < t < -6.59999999999999968e-24 or 3.5499999999999999e-31 < t < 4.00000000000000009e64

   1. Initial program 72.6%

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

   2. Taylor expanded in i around inf 57.6%

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

      1. associate-*r* 65.8%

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

      2. *-commutative 65.8%

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

   4. Simplified 65.8%

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

   if -6.59999999999999968e-24 < t < -3.7000000000000001e-196 or -1.9000000000000001e-239 < t < 4.19999999999999983e-190

   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. Taylor expanded in z around inf 63.6%

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

      1. *-commutative 63.6%

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

      2. *-commutative 63.6%

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

   4. Simplified 63.6%

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

   if -3.7000000000000001e-196 < t < -1.9000000000000001e-239

   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. Taylor expanded in i around -inf 89.7%

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

   3. Taylor expanded in y around inf 99.8%

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

      1. +-commutative 99.8%

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

      2. mul-1-neg 99.8%

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

      3. unsub-neg 99.8%

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

      4. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   if 4.19999999999999983e-190 < t < 3.0000000000000002e-104

   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. Taylor expanded in i around -inf 77.8%

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

   3. Taylor expanded in i around inf 78.4%

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

      1. neg-mul-1 78.4%

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

      2. *-commutative 78.4%

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

      3. distribute-rgt-neg-in 78.4%

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

   5. Simplified 78.4%

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

   if 3.0000000000000002e-104 < t < 3.5499999999999999e-31

   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. Taylor expanded in i around -inf 92.4%

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

   3. Taylor expanded in x around inf 70.2%

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

      1. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   if 4.00000000000000009e64 < t

   1. Initial program 55.2%

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

   2. Taylor expanded in i around -inf 51.9%

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

   3. Taylor expanded in t around inf 72.7%

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

      1. +-commutative 72.7%

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

      2. mul-1-neg 72.7%

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

      3. unsub-neg 72.7%

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

      4. *-commutative 72.7%

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

   5. Simplified 72.7%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+191}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-24}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-196}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-239}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-190}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-104}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 3.55 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+64}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 4: 29.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := z \cdot \left(c \cdot \left(-b\right)\right)\\ t_3 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{+207}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-38}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-159}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.06 \cdot 10^{-193}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq -1.06 \cdot 10^{-196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-239}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-150}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;t \leq 2.9:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* z (* c (- b)))) (t_3 (* y (* i (- j)))))
   (if (<= t -1.2e+207)
     (* x (* t (- a)))
     (if (<= t -2.6e+109)
       t_1
       (if (<= t -6.5e+50)
         t_3
         (if (<= t -3.9e-38)
           (* i (* a b))
           (if (<= t -1e-159)
             t_2
             (if (<= t -2.06e-193)
               (* x (* y z))
               (if (<= t -1.06e-196)
                 t_2
                 (if (<= t -3.1e-239)
                   t_3
                   (if (<= t 2.4e-150)
                     (* (* z c) (- b))
                     (if (<= t 2.9)
                       (* j (* i (- y)))
                       (if (<= t 4.8e+94) t_1 (* (- 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 = c * (t * j);
	double t_2 = z * (c * -b);
	double t_3 = y * (i * -j);
	double tmp;
	if (t <= -1.2e+207) {
		tmp = x * (t * -a);
	} else if (t <= -2.6e+109) {
		tmp = t_1;
	} else if (t <= -6.5e+50) {
		tmp = t_3;
	} else if (t <= -3.9e-38) {
		tmp = i * (a * b);
	} else if (t <= -1e-159) {
		tmp = t_2;
	} else if (t <= -2.06e-193) {
		tmp = x * (y * z);
	} else if (t <= -1.06e-196) {
		tmp = t_2;
	} else if (t <= -3.1e-239) {
		tmp = t_3;
	} else if (t <= 2.4e-150) {
		tmp = (z * c) * -b;
	} else if (t <= 2.9) {
		tmp = j * (i * -y);
	} else if (t <= 4.8e+94) {
		tmp = t_1;
	} else {
		tmp = -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 = c * (t * j)
    t_2 = z * (c * -b)
    t_3 = y * (i * -j)
    if (t <= (-1.2d+207)) then
        tmp = x * (t * -a)
    else if (t <= (-2.6d+109)) then
        tmp = t_1
    else if (t <= (-6.5d+50)) then
        tmp = t_3
    else if (t <= (-3.9d-38)) then
        tmp = i * (a * b)
    else if (t <= (-1d-159)) then
        tmp = t_2
    else if (t <= (-2.06d-193)) then
        tmp = x * (y * z)
    else if (t <= (-1.06d-196)) then
        tmp = t_2
    else if (t <= (-3.1d-239)) then
        tmp = t_3
    else if (t <= 2.4d-150) then
        tmp = (z * c) * -b
    else if (t <= 2.9d0) then
        tmp = j * (i * -y)
    else if (t <= 4.8d+94) then
        tmp = t_1
    else
        tmp = -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 = c * (t * j);
	double t_2 = z * (c * -b);
	double t_3 = y * (i * -j);
	double tmp;
	if (t <= -1.2e+207) {
		tmp = x * (t * -a);
	} else if (t <= -2.6e+109) {
		tmp = t_1;
	} else if (t <= -6.5e+50) {
		tmp = t_3;
	} else if (t <= -3.9e-38) {
		tmp = i * (a * b);
	} else if (t <= -1e-159) {
		tmp = t_2;
	} else if (t <= -2.06e-193) {
		tmp = x * (y * z);
	} else if (t <= -1.06e-196) {
		tmp = t_2;
	} else if (t <= -3.1e-239) {
		tmp = t_3;
	} else if (t <= 2.4e-150) {
		tmp = (z * c) * -b;
	} else if (t <= 2.9) {
		tmp = j * (i * -y);
	} else if (t <= 4.8e+94) {
		tmp = t_1;
	} else {
		tmp = -a * (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = z * (c * -b)
	t_3 = y * (i * -j)
	tmp = 0
	if t <= -1.2e+207:
		tmp = x * (t * -a)
	elif t <= -2.6e+109:
		tmp = t_1
	elif t <= -6.5e+50:
		tmp = t_3
	elif t <= -3.9e-38:
		tmp = i * (a * b)
	elif t <= -1e-159:
		tmp = t_2
	elif t <= -2.06e-193:
		tmp = x * (y * z)
	elif t <= -1.06e-196:
		tmp = t_2
	elif t <= -3.1e-239:
		tmp = t_3
	elif t <= 2.4e-150:
		tmp = (z * c) * -b
	elif t <= 2.9:
		tmp = j * (i * -y)
	elif t <= 4.8e+94:
		tmp = t_1
	else:
		tmp = -a * (x * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(z * Float64(c * Float64(-b)))
	t_3 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (t <= -1.2e+207)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (t <= -2.6e+109)
		tmp = t_1;
	elseif (t <= -6.5e+50)
		tmp = t_3;
	elseif (t <= -3.9e-38)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= -1e-159)
		tmp = t_2;
	elseif (t <= -2.06e-193)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= -1.06e-196)
		tmp = t_2;
	elseif (t <= -3.1e-239)
		tmp = t_3;
	elseif (t <= 2.4e-150)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (t <= 2.9)
		tmp = Float64(j * Float64(i * Float64(-y)));
	elseif (t <= 4.8e+94)
		tmp = t_1;
	else
		tmp = Float64(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 = c * (t * j);
	t_2 = z * (c * -b);
	t_3 = y * (i * -j);
	tmp = 0.0;
	if (t <= -1.2e+207)
		tmp = x * (t * -a);
	elseif (t <= -2.6e+109)
		tmp = t_1;
	elseif (t <= -6.5e+50)
		tmp = t_3;
	elseif (t <= -3.9e-38)
		tmp = i * (a * b);
	elseif (t <= -1e-159)
		tmp = t_2;
	elseif (t <= -2.06e-193)
		tmp = x * (y * z);
	elseif (t <= -1.06e-196)
		tmp = t_2;
	elseif (t <= -3.1e-239)
		tmp = t_3;
	elseif (t <= 2.4e-150)
		tmp = (z * c) * -b;
	elseif (t <= 2.9)
		tmp = j * (i * -y);
	elseif (t <= 4.8e+94)
		tmp = t_1;
	else
		tmp = -a * (x * t);
	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]}, Block[{t$95$2 = N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e+207], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.6e+109], t$95$1, If[LessEqual[t, -6.5e+50], t$95$3, If[LessEqual[t, -3.9e-38], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1e-159], t$95$2, If[LessEqual[t, -2.06e-193], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.06e-196], t$95$2, If[LessEqual[t, -3.1e-239], t$95$3, If[LessEqual[t, 2.4e-150], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[t, 2.9], N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e+94], t$95$1, N[((-a) * N[(x * t), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 9 regimes

2. if t < -1.2e207

   1. Initial program 59.8%

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

   2. Taylor expanded in i around -inf 63.0%

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

   3. Taylor expanded in x around inf 77.5%

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

      1. *-commutative 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in y around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. associate-*r* 74.1%

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

      3. distribute-lft-neg-in 74.1%

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

      4. *-commutative 74.1%

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

      5. *-commutative 74.1%

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

      6. distribute-rgt-neg-in 74.1%

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

   8. Simplified 74.1%

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

   if -1.2e207 < t < -2.5999999999999998e109 or 2.89999999999999991 < t < 4.79999999999999965e94

   1. Initial program 67.2%

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

   2. Taylor expanded in b around 0 60.3%

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

   3. Taylor expanded in c around inf 56.7%

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

   if -2.5999999999999998e109 < t < -6.5000000000000003e50 or -1.05999999999999994e-196 < t < -3.09999999999999985e-239

   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. Taylor expanded in i around inf 59.9%

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

      1. distribute-lft-out-- 59.9%

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

   4. Simplified 59.9%

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

   5. Taylor expanded in j around inf 48.8%

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

      1. mul-1-neg 48.8%

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

      2. associate-*r* 62.2%

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

      3. *-commutative 62.2%

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

   7. Simplified 62.2%

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

   if -6.5000000000000003e50 < t < -3.8999999999999999e-38

   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. Taylor expanded in i around -inf 77.6%

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

   3. Taylor expanded in z around 0 68.9%

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

      1. +-commutative 68.9%

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

      2. associate-+l+ 68.9%

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

      3. neg-mul-1 68.9%

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

      4. *-commutative 68.9%

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

      5. distribute-rgt-neg-in 68.9%

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

      6. associate-*r* 68.9%

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

      7. *-commutative 68.9%

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

      8. associate-*r* 69.0%

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

      9. associate-*l* 69.0%

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

      10. distribute-rgt-in 69.0%

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

      11. mul-1-neg 69.0%

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

      12. unsub-neg 69.0%

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

      13. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in b around inf 40.4%

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

      1. associate-*r* 45.3%

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

   8. Simplified 45.3%

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

   if -3.8999999999999999e-38 < t < -9.99999999999999989e-160 or -2.0600000000000001e-193 < t < -1.05999999999999994e-196

   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. Taylor expanded in z around inf 66.6%

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

      1. *-commutative 66.6%

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

      2. *-commutative 66.6%

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

   4. Simplified 66.6%

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

   5. Taylor expanded in y around 0 53.1%

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

      1. neg-mul-1 53.1%

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

      2. *-commutative 53.1%

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

      3. distribute-rgt-neg-in 53.1%

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

   7. Simplified 53.1%

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

   if -9.99999999999999989e-160 < t < -2.0600000000000001e-193

   1. Initial program 68.2%

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

   2. Taylor expanded in i around -inf 77.4%

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

   3. Taylor expanded in x around inf 67.3%

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

      1. *-commutative 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in y around inf 67.3%

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

   if -3.09999999999999985e-239 < t < 2.4e-150

   1. Initial program 75.4%

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

   2. Taylor expanded in b around inf 51.5%

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

      1. *-commutative 51.5%

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

   4. Simplified 51.5%

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

   5. Taylor expanded in i around 0 41.4%

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

      1. mul-1-neg 41.4%

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

      2. distribute-lft-neg-out 41.4%

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

      3. *-commutative 41.4%

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

   7. Simplified 41.4%

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

   if 2.4e-150 < t < 2.89999999999999991

   1. Initial program 83.3%

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

   2. Taylor expanded in i around inf 53.4%

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

      1. distribute-lft-out-- 53.4%

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

   4. Simplified 53.4%

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

   5. Taylor expanded in j around inf 33.4%

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

      1. mul-1-neg 33.4%

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

      2. *-commutative 33.4%

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

      3. associate-*r* 40.8%

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

      4. *-commutative 40.8%

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

      5. distribute-rgt-neg-out 40.8%

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

      6. distribute-rgt-neg-in 40.8%

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

   7. Simplified 40.8%

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

   if 4.79999999999999965e94 < t

   1. Initial program 51.2%

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

   2. Taylor expanded in i around -inf 47.6%

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

   3. Taylor expanded in x around inf 50.0%

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

      1. *-commutative 50.0%

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

   5. Simplified 50.0%

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

   6. Taylor expanded in y around 0 53.8%

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

      1. mul-1-neg 53.8%

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

   8. Simplified 53.8%

      \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]
3. Recombined 9 regimes into one program.

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+207}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{+109}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+50}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-38}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-159}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq -2.06 \cdot 10^{-193}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq -1.06 \cdot 10^{-196}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-239}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-150}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;t \leq 2.9:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+94}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 5: 55.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ t_3 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -4.4 \cdot 10^{+60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -0.00065:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-30}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{-277}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 3:\\ \;\;\;\;t_1 - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ (* j (- (* t c) (* y i))) (* i (* a b))))
        (t_3 (* c (- (* t j) (* z b)))))
   (if (<= c -4.4e+60)
     t_3
     (if (<= c -0.00065)
       t_2
       (if (<= c -1.75e-30)
         t_3
         (if (<= c 3.9e-277)
           (* a (- (* b i) (* x t)))
           (if (<= c 3.0)
             (- t_1 (* j (* y i)))
             (if (<= c 5e+69) t_2 (if (<= c 1.15e+134) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (j * ((t * c) - (y * i))) + (i * (a * b));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4.4e+60) {
		tmp = t_3;
	} else if (c <= -0.00065) {
		tmp = t_2;
	} else if (c <= -1.75e-30) {
		tmp = t_3;
	} else if (c <= 3.9e-277) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 3.0) {
		tmp = t_1 - (j * (y * i));
	} else if (c <= 5e+69) {
		tmp = t_2;
	} else if (c <= 1.15e+134) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = (j * ((t * c) - (y * i))) + (i * (a * b))
    t_3 = c * ((t * j) - (z * b))
    if (c <= (-4.4d+60)) then
        tmp = t_3
    else if (c <= (-0.00065d0)) then
        tmp = t_2
    else if (c <= (-1.75d-30)) then
        tmp = t_3
    else if (c <= 3.9d-277) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 3.0d0) then
        tmp = t_1 - (j * (y * i))
    else if (c <= 5d+69) then
        tmp = t_2
    else if (c <= 1.15d+134) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (j * ((t * c) - (y * i))) + (i * (a * b));
	double t_3 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4.4e+60) {
		tmp = t_3;
	} else if (c <= -0.00065) {
		tmp = t_2;
	} else if (c <= -1.75e-30) {
		tmp = t_3;
	} else if (c <= 3.9e-277) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 3.0) {
		tmp = t_1 - (j * (y * i));
	} else if (c <= 5e+69) {
		tmp = t_2;
	} else if (c <= 1.15e+134) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = (j * ((t * c) - (y * i))) + (i * (a * b))
	t_3 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -4.4e+60:
		tmp = t_3
	elif c <= -0.00065:
		tmp = t_2
	elif c <= -1.75e-30:
		tmp = t_3
	elif c <= 3.9e-277:
		tmp = a * ((b * i) - (x * t))
	elif c <= 3.0:
		tmp = t_1 - (j * (y * i))
	elif c <= 5e+69:
		tmp = t_2
	elif c <= 1.15e+134:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(i * Float64(a * b)))
	t_3 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -4.4e+60)
		tmp = t_3;
	elseif (c <= -0.00065)
		tmp = t_2;
	elseif (c <= -1.75e-30)
		tmp = t_3;
	elseif (c <= 3.9e-277)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 3.0)
		tmp = Float64(t_1 - Float64(j * Float64(y * i)));
	elseif (c <= 5e+69)
		tmp = t_2;
	elseif (c <= 1.15e+134)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = (j * ((t * c) - (y * i))) + (i * (a * b));
	t_3 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -4.4e+60)
		tmp = t_3;
	elseif (c <= -0.00065)
		tmp = t_2;
	elseif (c <= -1.75e-30)
		tmp = t_3;
	elseif (c <= 3.9e-277)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 3.0)
		tmp = t_1 - (j * (y * i));
	elseif (c <= 5e+69)
		tmp = t_2;
	elseif (c <= 1.15e+134)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.4e+60], t$95$3, If[LessEqual[c, -0.00065], t$95$2, If[LessEqual[c, -1.75e-30], t$95$3, If[LessEqual[c, 3.9e-277], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.0], N[(t$95$1 - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5e+69], t$95$2, If[LessEqual[c, 1.15e+134], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -4.39999999999999992e60 or -6.4999999999999997e-4 < c < -1.7500000000000001e-30 or 1.1499999999999999e134 < c

   1. Initial program 57.5%

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

   2. Taylor expanded in c around inf 71.8%

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

      1. *-commutative 71.8%

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

   4. Simplified 71.8%

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

   if -4.39999999999999992e60 < c < -6.4999999999999997e-4 or 3 < c < 5.00000000000000036e69

   1. Initial program 72.7%

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

   2. Taylor expanded in i around inf 64.7%

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

      1. associate-*r* 71.1%

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

      2. *-commutative 71.1%

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

   4. Simplified 71.1%

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

   if -1.7500000000000001e-30 < c < 3.89999999999999987e-277

   1. Initial program 69.2%

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

   2. Taylor expanded in i around -inf 75.6%

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

   3. Taylor expanded in a around inf 66.7%

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

      1. +-commutative 66.7%

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

      2. mul-1-neg 66.7%

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

      3. unsub-neg 66.7%

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

   5. Simplified 66.7%

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

   if 3.89999999999999987e-277 < c < 3

   1. Initial program 82.8%

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

   2. Taylor expanded in b around 0 67.2%

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

   3. Taylor expanded in c around 0 65.8%

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

      1. +-commutative 65.8%

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

      2. mul-1-neg 65.8%

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

      3. unsub-neg 65.8%

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

      4. *-commutative 65.8%

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

      5. *-commutative 65.8%

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

      6. associate-*r* 67.3%

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

   5. Simplified 67.3%

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

   if 5.00000000000000036e69 < c < 1.1499999999999999e134

   1. Initial program 59.8%

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

   2. Taylor expanded in i around -inf 59.8%

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

   3. Taylor expanded in x around inf 80.0%

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

      1. *-commutative 80.0%

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

   5. Simplified 80.0%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.4 \cdot 10^{+60}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -0.00065:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq -1.75 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{-277}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 3:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;c \leq 5 \cdot 10^{+69}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 6: 59.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right) - z \cdot \left(b \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{+45}:\\ \;\;\;\;t_2 - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-250}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+64}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* i (- (* a b) (* y j))) (* z (* b c))))
        (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -2e+45)
     (- t_2 (* i (* y j)))
     (if (<= t -1.55e-273)
       t_1
       (if (<= t 4.8e-250)
         (* z (- (* x y) (* b c)))
         (if (<= t 1.32e-99)
           t_1
           (if (<= t 2.8e-22)
             (- (* x (- (* y z) (* t a))) (* j (* y i)))
             (if (<= t 1.5e+64)
               (+ (* j (- (* t c) (* y i))) (* i (* a b)))
               t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * ((a * b) - (y * j))) - (z * (b * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2e+45) {
		tmp = t_2 - (i * (y * j));
	} else if (t <= -1.55e-273) {
		tmp = t_1;
	} else if (t <= 4.8e-250) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1.32e-99) {
		tmp = t_1;
	} else if (t <= 2.8e-22) {
		tmp = (x * ((y * z) - (t * a))) - (j * (y * i));
	} else if (t <= 1.5e+64) {
		tmp = (j * ((t * c) - (y * i))) + (i * (a * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (i * ((a * b) - (y * j))) - (z * (b * c))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-2d+45)) then
        tmp = t_2 - (i * (y * j))
    else if (t <= (-1.55d-273)) then
        tmp = t_1
    else if (t <= 4.8d-250) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 1.32d-99) then
        tmp = t_1
    else if (t <= 2.8d-22) then
        tmp = (x * ((y * z) - (t * a))) - (j * (y * i))
    else if (t <= 1.5d+64) then
        tmp = (j * ((t * c) - (y * i))) + (i * (a * b))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * ((a * b) - (y * j))) - (z * (b * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2e+45) {
		tmp = t_2 - (i * (y * j));
	} else if (t <= -1.55e-273) {
		tmp = t_1;
	} else if (t <= 4.8e-250) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1.32e-99) {
		tmp = t_1;
	} else if (t <= 2.8e-22) {
		tmp = (x * ((y * z) - (t * a))) - (j * (y * i));
	} else if (t <= 1.5e+64) {
		tmp = (j * ((t * c) - (y * i))) + (i * (a * b));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * ((a * b) - (y * j))) - (z * (b * c))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -2e+45:
		tmp = t_2 - (i * (y * j))
	elif t <= -1.55e-273:
		tmp = t_1
	elif t <= 4.8e-250:
		tmp = z * ((x * y) - (b * c))
	elif t <= 1.32e-99:
		tmp = t_1
	elif t <= 2.8e-22:
		tmp = (x * ((y * z) - (t * a))) - (j * (y * i))
	elif t <= 1.5e+64:
		tmp = (j * ((t * c) - (y * i))) + (i * (a * b))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * Float64(Float64(a * b) - Float64(y * j))) - Float64(z * Float64(b * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2e+45)
		tmp = Float64(t_2 - Float64(i * Float64(y * j)));
	elseif (t <= -1.55e-273)
		tmp = t_1;
	elseif (t <= 4.8e-250)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 1.32e-99)
		tmp = t_1;
	elseif (t <= 2.8e-22)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(j * Float64(y * i)));
	elseif (t <= 1.5e+64)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(i * Float64(a * b)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (i * ((a * b) - (y * j))) - (z * (b * c));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -2e+45)
		tmp = t_2 - (i * (y * j));
	elseif (t <= -1.55e-273)
		tmp = t_1;
	elseif (t <= 4.8e-250)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 1.32e-99)
		tmp = t_1;
	elseif (t <= 2.8e-22)
		tmp = (x * ((y * z) - (t * a))) - (j * (y * i));
	elseif (t <= 1.5e+64)
		tmp = (j * ((t * c) - (y * i))) + (i * (a * b));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e+45], N[(t$95$2 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.55e-273], t$95$1, If[LessEqual[t, 4.8e-250], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.32e-99], t$95$1, If[LessEqual[t, 2.8e-22], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.5e+64], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.9999999999999999e45

   1. Initial program 65.8%

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

   2. Taylor expanded in i around -inf 67.2%

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

   3. Taylor expanded in z around 0 64.7%

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

      1. +-commutative 64.7%

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

      2. associate-+l+ 64.7%

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

      3. neg-mul-1 64.7%

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

      4. *-commutative 64.7%

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

      5. distribute-rgt-neg-in 64.7%

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

      6. associate-*r* 69.6%

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

      7. *-commutative 69.6%

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

      8. associate-*r* 68.8%

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

      9. associate-*l* 68.8%

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

      10. distribute-rgt-in 72.4%

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

      11. mul-1-neg 72.4%

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

      12. unsub-neg 72.4%

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

      13. *-commutative 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in j around inf 70.0%

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

      1. mul-1-neg 70.0%

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

      2. *-commutative 70.0%

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

      3. distribute-rgt-neg-in 70.0%

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

   8. Simplified 70.0%

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

   if -1.9999999999999999e45 < t < -1.54999999999999994e-273 or 4.7999999999999998e-250 < t < 1.31999999999999999e-99

   1. Initial program 76.9%

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

   2. Taylor expanded in i around -inf 81.1%

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

   3. Taylor expanded in t around 0 77.0%

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

      1. cancel-sign-sub-inv 77.0%

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

      2. associate-+l+ 77.0%

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

      3. neg-mul-1 77.0%

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

      4. *-commutative 77.0%

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

      5. distribute-rgt-neg-in 77.0%

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

      6. associate-*r* 78.9%

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

      7. *-commutative 78.9%

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

      8. associate-*r* 79.0%

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

      9. distribute-lft-neg-in 79.0%

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

      10. distribute-rgt-in 81.2%

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

      11. sub-neg 81.2%

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

      12. *-commutative 81.2%

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

      13. *-commutative 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in x around 0 68.7%

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

      1. mul-1-neg 68.7%

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

      2. associate-*r* 68.7%

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

      3. distribute-rgt-neg-in 68.7%

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

   8. Simplified 68.7%

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

   if -1.54999999999999994e-273 < t < 4.7999999999999998e-250

   1. Initial program 66.5%

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

   2. Taylor expanded in z around inf 80.3%

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

      1. *-commutative 80.3%

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

      2. *-commutative 80.3%

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

   4. Simplified 80.3%

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

   if 1.31999999999999999e-99 < t < 2.79999999999999995e-22

   1. Initial program 85.4%

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

   2. Taylor expanded in b around 0 85.8%

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

   3. Taylor expanded in c around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. mul-1-neg 79.9%

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

      3. unsub-neg 79.9%

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

      4. *-commutative 79.9%

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

      5. *-commutative 79.9%

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

      6. associate-*r* 85.8%

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

   5. Simplified 85.8%

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

   if 2.79999999999999995e-22 < t < 1.5000000000000001e64

   1. Initial program 70.1%

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

   2. Taylor expanded in i around inf 67.3%

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

      1. associate-*r* 72.3%

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

      2. *-commutative 72.3%

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

   4. Simplified 72.3%

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

   if 1.5000000000000001e64 < t

   1. Initial program 55.2%

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

   2. Taylor expanded in i around -inf 51.9%

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

   3. Taylor expanded in t around inf 72.7%

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

      1. +-commutative 72.7%

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

      2. mul-1-neg 72.7%

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

      3. unsub-neg 72.7%

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

      4. *-commutative 72.7%

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

   5. Simplified 72.7%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-273}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-250}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{-99}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+64}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 7: 62.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+174}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+32}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+171}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i)))))
        (t_2 (* z (- (* x y) (* b c)))))
   (if (<= z -2.7e+174)
     t_2
     (if (<= z -3.5e+113)
       t_1
       (if (<= z -3.6e+32)
         (* b (- (* a i) (* z c)))
         (if (<= z 1.15e+171) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.7e+174) {
		tmp = t_2;
	} else if (z <= -3.5e+113) {
		tmp = t_1;
	} else if (z <= -3.6e+32) {
		tmp = b * ((a * i) - (z * c));
	} else if (z <= 1.15e+171) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
    t_2 = z * ((x * y) - (b * c))
    if (z <= (-2.7d+174)) then
        tmp = t_2
    else if (z <= (-3.5d+113)) then
        tmp = t_1
    else if (z <= (-3.6d+32)) then
        tmp = b * ((a * i) - (z * c))
    else if (z <= 1.15d+171) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -2.7e+174) {
		tmp = t_2;
	} else if (z <= -3.5e+113) {
		tmp = t_1;
	} else if (z <= -3.6e+32) {
		tmp = b * ((a * i) - (z * c));
	} else if (z <= 1.15e+171) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -2.7e+174:
		tmp = t_2
	elif z <= -3.5e+113:
		tmp = t_1
	elif z <= -3.6e+32:
		tmp = b * ((a * i) - (z * c))
	elif z <= 1.15e+171:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -2.7e+174)
		tmp = t_2;
	elseif (z <= -3.5e+113)
		tmp = t_1;
	elseif (z <= -3.6e+32)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (z <= 1.15e+171)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -2.7e+174)
		tmp = t_2;
	elseif (z <= -3.5e+113)
		tmp = t_1;
	elseif (z <= -3.6e+32)
		tmp = b * ((a * i) - (z * c));
	elseif (z <= 1.15e+171)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+174], t$95$2, If[LessEqual[z, -3.5e+113], t$95$1, If[LessEqual[z, -3.6e+32], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+171], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6999999999999999e174 or 1.15000000000000009e171 < z

   1. Initial program 47.8%

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

   2. Taylor expanded in z around inf 78.3%

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

      1. *-commutative 78.3%

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

      2. *-commutative 78.3%

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

   4. Simplified 78.3%

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

   if -2.6999999999999999e174 < z < -3.5000000000000001e113 or -3.5999999999999997e32 < z < 1.15000000000000009e171

   1. Initial program 76.5%

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

   2. Taylor expanded in b around 0 66.4%

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

   if -3.5000000000000001e113 < z < -3.5999999999999997e32

   1. Initial program 66.7%

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

   2. Taylor expanded in b around inf 72.7%

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

      1. *-commutative 72.7%

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

   4. Simplified 72.7%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+174}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+113}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+32}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+171}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 8: 64.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.14 \cdot 10^{-69}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-128}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-80}:\\ \;\;\;\;t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -8e+17)
     t_2
     (if (<= x -1.14e-69)
       (* i (- (* a b) (* y j)))
       (if (<= x -1.15e-128)
         (* c (- (* t j) (* z b)))
         (if (<= x 1.15e-80)
           (+ t_1 (* b (- (* a i) (* z c))))
           (+ 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 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -8e+17) {
		tmp = t_2;
	} else if (x <= -1.14e-69) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= -1.15e-128) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 1.15e-80) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_2 + 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 = j * ((t * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-8d+17)) then
        tmp = t_2
    else if (x <= (-1.14d-69)) then
        tmp = i * ((a * b) - (y * j))
    else if (x <= (-1.15d-128)) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 1.15d-80) then
        tmp = t_1 + (b * ((a * i) - (z * c)))
    else
        tmp = t_2 + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -8e+17) {
		tmp = t_2;
	} else if (x <= -1.14e-69) {
		tmp = i * ((a * b) - (y * j));
	} else if (x <= -1.15e-128) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 1.15e-80) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -8e+17:
		tmp = t_2
	elif x <= -1.14e-69:
		tmp = i * ((a * b) - (y * j))
	elif x <= -1.15e-128:
		tmp = c * ((t * j) - (z * b))
	elif x <= 1.15e-80:
		tmp = t_1 + (b * ((a * i) - (z * c)))
	else:
		tmp = t_2 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -8e+17)
		tmp = t_2;
	elseif (x <= -1.14e-69)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (x <= -1.15e-128)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 1.15e-80)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(t_2 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -8e+17)
		tmp = t_2;
	elseif (x <= -1.14e-69)
		tmp = i * ((a * b) - (y * j));
	elseif (x <= -1.15e-128)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 1.15e-80)
		tmp = t_1 + (b * ((a * i) - (z * c)));
	else
		tmp = t_2 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8e+17], t$95$2, If[LessEqual[x, -1.14e-69], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.15e-128], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-80], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -8e17

   1. Initial program 67.1%

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

   2. Taylor expanded in i around -inf 69.0%

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

   3. Taylor expanded in x around inf 80.9%

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

      1. *-commutative 80.9%

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

   5. Simplified 80.9%

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

   if -8e17 < x < -1.14000000000000006e-69

   1. Initial program 60.3%

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

   2. Taylor expanded in i around -inf 66.7%

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

   3. Taylor expanded in i around inf 61.2%

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

      1. neg-mul-1 61.2%

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

      2. *-commutative 61.2%

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

      3. distribute-rgt-neg-in 61.2%

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

   5. Simplified 61.2%

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

   if -1.14000000000000006e-69 < x < -1.15e-128

   1. Initial program 54.1%

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

   2. Taylor expanded in c around inf 74.7%

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

      1. *-commutative 74.7%

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

   4. Simplified 74.7%

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

   if -1.15e-128 < x < 1.1499999999999999e-80

   1. Initial program 69.7%

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

   2. Taylor expanded in x around 0 73.0%

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

      1. *-commutative 73.0%

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

   4. Simplified 73.0%

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

   if 1.1499999999999999e-80 < x

   1. Initial program 73.2%

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

   2. Taylor expanded in b around 0 68.8%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -1.14 \cdot 10^{-69}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-128}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-80}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 9: 29.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := z \cdot \left(c \cdot \left(-b\right)\right)\\ t_3 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{+207}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+51}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-37}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-159}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-239}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-28}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* z (* c (- b)))) (t_3 (* y (* i (- j)))))
   (if (<= t -1.3e+207)
     (* x (* t (- a)))
     (if (<= t -1.35e+110)
       t_1
       (if (<= t -2.2e+51)
         t_3
         (if (<= t -4e-37)
           (* i (* a b))
           (if (<= t -8.5e-159)
             t_2
             (if (<= t -3.5e-192)
               (* x (* y z))
               (if (<= t -5.6e-197)
                 t_2
                 (if (<= t -1.15e-239)
                   t_3
                   (if (<= t 3.4e-28)
                     (* y (* x z))
                     (if (<= t 4.3e+103) t_1 (* (- 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 = c * (t * j);
	double t_2 = z * (c * -b);
	double t_3 = y * (i * -j);
	double tmp;
	if (t <= -1.3e+207) {
		tmp = x * (t * -a);
	} else if (t <= -1.35e+110) {
		tmp = t_1;
	} else if (t <= -2.2e+51) {
		tmp = t_3;
	} else if (t <= -4e-37) {
		tmp = i * (a * b);
	} else if (t <= -8.5e-159) {
		tmp = t_2;
	} else if (t <= -3.5e-192) {
		tmp = x * (y * z);
	} else if (t <= -5.6e-197) {
		tmp = t_2;
	} else if (t <= -1.15e-239) {
		tmp = t_3;
	} else if (t <= 3.4e-28) {
		tmp = y * (x * z);
	} else if (t <= 4.3e+103) {
		tmp = t_1;
	} else {
		tmp = -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 = c * (t * j)
    t_2 = z * (c * -b)
    t_3 = y * (i * -j)
    if (t <= (-1.3d+207)) then
        tmp = x * (t * -a)
    else if (t <= (-1.35d+110)) then
        tmp = t_1
    else if (t <= (-2.2d+51)) then
        tmp = t_3
    else if (t <= (-4d-37)) then
        tmp = i * (a * b)
    else if (t <= (-8.5d-159)) then
        tmp = t_2
    else if (t <= (-3.5d-192)) then
        tmp = x * (y * z)
    else if (t <= (-5.6d-197)) then
        tmp = t_2
    else if (t <= (-1.15d-239)) then
        tmp = t_3
    else if (t <= 3.4d-28) then
        tmp = y * (x * z)
    else if (t <= 4.3d+103) then
        tmp = t_1
    else
        tmp = -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 = c * (t * j);
	double t_2 = z * (c * -b);
	double t_3 = y * (i * -j);
	double tmp;
	if (t <= -1.3e+207) {
		tmp = x * (t * -a);
	} else if (t <= -1.35e+110) {
		tmp = t_1;
	} else if (t <= -2.2e+51) {
		tmp = t_3;
	} else if (t <= -4e-37) {
		tmp = i * (a * b);
	} else if (t <= -8.5e-159) {
		tmp = t_2;
	} else if (t <= -3.5e-192) {
		tmp = x * (y * z);
	} else if (t <= -5.6e-197) {
		tmp = t_2;
	} else if (t <= -1.15e-239) {
		tmp = t_3;
	} else if (t <= 3.4e-28) {
		tmp = y * (x * z);
	} else if (t <= 4.3e+103) {
		tmp = t_1;
	} else {
		tmp = -a * (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = z * (c * -b)
	t_3 = y * (i * -j)
	tmp = 0
	if t <= -1.3e+207:
		tmp = x * (t * -a)
	elif t <= -1.35e+110:
		tmp = t_1
	elif t <= -2.2e+51:
		tmp = t_3
	elif t <= -4e-37:
		tmp = i * (a * b)
	elif t <= -8.5e-159:
		tmp = t_2
	elif t <= -3.5e-192:
		tmp = x * (y * z)
	elif t <= -5.6e-197:
		tmp = t_2
	elif t <= -1.15e-239:
		tmp = t_3
	elif t <= 3.4e-28:
		tmp = y * (x * z)
	elif t <= 4.3e+103:
		tmp = t_1
	else:
		tmp = -a * (x * t)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(z * Float64(c * Float64(-b)))
	t_3 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (t <= -1.3e+207)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (t <= -1.35e+110)
		tmp = t_1;
	elseif (t <= -2.2e+51)
		tmp = t_3;
	elseif (t <= -4e-37)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= -8.5e-159)
		tmp = t_2;
	elseif (t <= -3.5e-192)
		tmp = Float64(x * Float64(y * z));
	elseif (t <= -5.6e-197)
		tmp = t_2;
	elseif (t <= -1.15e-239)
		tmp = t_3;
	elseif (t <= 3.4e-28)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 4.3e+103)
		tmp = t_1;
	else
		tmp = Float64(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 = c * (t * j);
	t_2 = z * (c * -b);
	t_3 = y * (i * -j);
	tmp = 0.0;
	if (t <= -1.3e+207)
		tmp = x * (t * -a);
	elseif (t <= -1.35e+110)
		tmp = t_1;
	elseif (t <= -2.2e+51)
		tmp = t_3;
	elseif (t <= -4e-37)
		tmp = i * (a * b);
	elseif (t <= -8.5e-159)
		tmp = t_2;
	elseif (t <= -3.5e-192)
		tmp = x * (y * z);
	elseif (t <= -5.6e-197)
		tmp = t_2;
	elseif (t <= -1.15e-239)
		tmp = t_3;
	elseif (t <= 3.4e-28)
		tmp = y * (x * z);
	elseif (t <= 4.3e+103)
		tmp = t_1;
	else
		tmp = -a * (x * t);
	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]}, Block[{t$95$2 = N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.3e+207], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.35e+110], t$95$1, If[LessEqual[t, -2.2e+51], t$95$3, If[LessEqual[t, -4e-37], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.5e-159], t$95$2, If[LessEqual[t, -3.5e-192], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.6e-197], t$95$2, If[LessEqual[t, -1.15e-239], t$95$3, If[LessEqual[t, 3.4e-28], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.3e+103], t$95$1, N[((-a) * N[(x * t), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -1.2999999999999999e207

   1. Initial program 59.8%

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

   2. Taylor expanded in i around -inf 63.0%

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

   3. Taylor expanded in x around inf 77.5%

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

      1. *-commutative 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in y around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. associate-*r* 74.1%

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

      3. distribute-lft-neg-in 74.1%

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

      4. *-commutative 74.1%

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

      5. *-commutative 74.1%

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

      6. distribute-rgt-neg-in 74.1%

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

   8. Simplified 74.1%

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

   if -1.2999999999999999e207 < t < -1.35000000000000005e110 or 3.4000000000000001e-28 < t < 4.29999999999999969e103

   1. Initial program 68.6%

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

   2. Taylor expanded in b around 0 57.9%

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

   3. Taylor expanded in c around inf 50.6%

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

   if -1.35000000000000005e110 < t < -2.19999999999999992e51 or -5.6000000000000004e-197 < t < -1.1499999999999999e-239

   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. Taylor expanded in i around inf 59.9%

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

      1. distribute-lft-out-- 59.9%

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

   4. Simplified 59.9%

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

   5. Taylor expanded in j around inf 48.8%

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

      1. mul-1-neg 48.8%

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

      2. associate-*r* 62.2%

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

      3. *-commutative 62.2%

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

   7. Simplified 62.2%

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

   if -2.19999999999999992e51 < t < -4.00000000000000027e-37

   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. Taylor expanded in i around -inf 77.6%

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

   3. Taylor expanded in z around 0 68.9%

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

      1. +-commutative 68.9%

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

      2. associate-+l+ 68.9%

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

      3. neg-mul-1 68.9%

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

      4. *-commutative 68.9%

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

      5. distribute-rgt-neg-in 68.9%

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

      6. associate-*r* 68.9%

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

      7. *-commutative 68.9%

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

      8. associate-*r* 69.0%

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

      9. associate-*l* 69.0%

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

      10. distribute-rgt-in 69.0%

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

      11. mul-1-neg 69.0%

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

      12. unsub-neg 69.0%

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

      13. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in b around inf 40.4%

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

      1. associate-*r* 45.3%

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

   8. Simplified 45.3%

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

   if -4.00000000000000027e-37 < t < -8.4999999999999998e-159 or -3.50000000000000014e-192 < t < -5.6000000000000004e-197

   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. Taylor expanded in z around inf 66.6%

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

      1. *-commutative 66.6%

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

      2. *-commutative 66.6%

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

   4. Simplified 66.6%

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

   5. Taylor expanded in y around 0 53.1%

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

      1. neg-mul-1 53.1%

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

      2. *-commutative 53.1%

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

      3. distribute-rgt-neg-in 53.1%

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

   7. Simplified 53.1%

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

   if -8.4999999999999998e-159 < t < -3.50000000000000014e-192

   1. Initial program 68.2%

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

   2. Taylor expanded in i around -inf 77.4%

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

   3. Taylor expanded in x around inf 67.3%

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

      1. *-commutative 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in y around inf 67.3%

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

   if -1.1499999999999999e-239 < t < 3.4000000000000001e-28

   1. Initial program 78.2%

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

   2. Taylor expanded in i around -inf 81.7%

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

   3. Taylor expanded in x around inf 41.6%

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

      1. *-commutative 41.6%

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

   5. Simplified 41.6%

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

   6. Taylor expanded in y around inf 35.1%

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

      1. associate-*r* 32.8%

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

      2. *-commutative 32.8%

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

      3. associate-*r* 37.3%

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

   8. Simplified 37.3%

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

   if 4.29999999999999969e103 < t

   1. Initial program 51.2%

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

   2. Taylor expanded in i around -inf 47.6%

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

   3. Taylor expanded in x around inf 50.0%

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

      1. *-commutative 50.0%

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

   5. Simplified 50.0%

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

   6. Taylor expanded in y around 0 53.8%

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

      1. mul-1-neg 53.8%

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

   8. Simplified 53.8%

      \[\leadsto \color{blue}{-a \cdot \left(t \cdot x\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+207}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+110}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-37}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-159}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-192}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-197}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-239}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-28}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{+103}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 10: 66.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-238}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-77}:\\ \;\;\;\;t_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -1.15e+25)
     t_2
     (if (<= x -2.3e-238)
       (+ (* t (- (* c j) (* x a))) (* i (- (* a b) (* y j))))
       (if (<= x 7.2e-77) (+ t_1 (* b (- (* a i) (* z c)))) (+ 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 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.15e+25) {
		tmp = t_2;
	} else if (x <= -2.3e-238) {
		tmp = (t * ((c * j) - (x * a))) + (i * ((a * b) - (y * j)));
	} else if (x <= 7.2e-77) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_2 + 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 = j * ((t * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-1.15d+25)) then
        tmp = t_2
    else if (x <= (-2.3d-238)) then
        tmp = (t * ((c * j) - (x * a))) + (i * ((a * b) - (y * j)))
    else if (x <= 7.2d-77) then
        tmp = t_1 + (b * ((a * i) - (z * c)))
    else
        tmp = t_2 + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.15e+25) {
		tmp = t_2;
	} else if (x <= -2.3e-238) {
		tmp = (t * ((c * j) - (x * a))) + (i * ((a * b) - (y * j)));
	} else if (x <= 7.2e-77) {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_2 + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -1.15e+25:
		tmp = t_2
	elif x <= -2.3e-238:
		tmp = (t * ((c * j) - (x * a))) + (i * ((a * b) - (y * j)))
	elif x <= 7.2e-77:
		tmp = t_1 + (b * ((a * i) - (z * c)))
	else:
		tmp = t_2 + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -1.15e+25)
		tmp = t_2;
	elseif (x <= -2.3e-238)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) + Float64(i * Float64(Float64(a * b) - Float64(y * j))));
	elseif (x <= 7.2e-77)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(t_2 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1.15e+25)
		tmp = t_2;
	elseif (x <= -2.3e-238)
		tmp = (t * ((c * j) - (x * a))) + (i * ((a * b) - (y * j)));
	elseif (x <= 7.2e-77)
		tmp = t_1 + (b * ((a * i) - (z * c)));
	else
		tmp = t_2 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.15e+25], t$95$2, If[LessEqual[x, -2.3e-238], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e-77], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + t$95$1), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.1499999999999999e25

   1. Initial program 65.8%

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

   2. Taylor expanded in i around -inf 67.8%

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

   3. Taylor expanded in x around inf 82.2%

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

      1. *-commutative 82.2%

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

   5. Simplified 82.2%

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

   if -1.1499999999999999e25 < x < -2.30000000000000005e-238

   1. Initial program 61.6%

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

   2. Taylor expanded in i around -inf 72.4%

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

   3. Taylor expanded in z around 0 68.8%

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

      1. +-commutative 68.8%

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

      2. associate-+l+ 68.8%

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

      3. neg-mul-1 68.8%

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

      4. *-commutative 68.8%

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

      5. distribute-rgt-neg-in 68.8%

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

      6. associate-*r* 70.3%

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

      7. *-commutative 70.3%

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

      8. associate-*r* 70.3%

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

      9. associate-*l* 70.3%

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

      10. distribute-rgt-in 70.3%

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

      11. mul-1-neg 70.3%

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

      12. unsub-neg 70.3%

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

      13. *-commutative 70.3%

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

   5. Simplified 70.3%

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

   if -2.30000000000000005e-238 < x < 7.2e-77

   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. Taylor expanded in x around 0 77.8%

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

      1. *-commutative 77.8%

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

   4. Simplified 77.8%

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

   if 7.2e-77 < x

   1. Initial program 73.2%

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

   2. Taylor expanded in b around 0 68.8%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-238}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-77}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 11: 67.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -5.7 \cdot 10^{+47}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+49}:\\ \;\;\;\;t_1 + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -5.7e+47)
     (+ t_2 t_1)
     (if (<= t 1.5e+49) (+ t_1 (* z (- (* x y) (* b c)))) 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 * ((a * b) - (y * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -5.7e+47) {
		tmp = t_2 + t_1;
	} else if (t <= 1.5e+49) {
		tmp = t_1 + (z * ((x * y) - (b * c)));
	} 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 * ((a * b) - (y * j))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-5.7d+47)) then
        tmp = t_2 + t_1
    else if (t <= 1.5d+49) then
        tmp = t_1 + (z * ((x * y) - (b * c)))
    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 * ((a * b) - (y * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -5.7e+47) {
		tmp = t_2 + t_1;
	} else if (t <= 1.5e+49) {
		tmp = t_1 + (z * ((x * y) - (b * c)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -5.7e+47:
		tmp = t_2 + t_1
	elif t <= 1.5e+49:
		tmp = t_1 + (z * ((x * y) - (b * c)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -5.7e+47)
		tmp = Float64(t_2 + t_1);
	elseif (t <= 1.5e+49)
		tmp = Float64(t_1 + Float64(z * Float64(Float64(x * y) - Float64(b * c))));
	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 * ((a * b) - (y * j));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -5.7e+47)
		tmp = t_2 + t_1;
	elseif (t <= 1.5e+49)
		tmp = t_1 + (z * ((x * y) - (b * c)));
	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[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.7e+47], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[t, 1.5e+49], N[(t$95$1 + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.6999999999999997e47

   1. Initial program 65.8%

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

   2. Taylor expanded in i around -inf 67.2%

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

   3. Taylor expanded in z around 0 64.7%

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

      1. +-commutative 64.7%

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

      2. associate-+l+ 64.7%

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

      3. neg-mul-1 64.7%

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

      4. *-commutative 64.7%

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

      5. distribute-rgt-neg-in 64.7%

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

      6. associate-*r* 69.6%

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

      7. *-commutative 69.6%

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

      8. associate-*r* 68.8%

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

      9. associate-*l* 68.8%

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

      10. distribute-rgt-in 72.4%

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

      11. mul-1-neg 72.4%

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

      12. unsub-neg 72.4%

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

      13. *-commutative 72.4%

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

   5. Simplified 72.4%

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

   if -5.6999999999999997e47 < t < 1.5000000000000001e49

   1. Initial program 76.1%

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

   2. Taylor expanded in i around -inf 79.0%

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

   3. Taylor expanded in t around 0 71.8%

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

      1. cancel-sign-sub-inv 71.8%

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

      2. associate-+l+ 71.8%

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

      3. neg-mul-1 71.8%

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

      4. *-commutative 71.8%

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

      5. distribute-rgt-neg-in 71.8%

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

      6. associate-*r* 73.9%

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

      7. *-commutative 73.9%

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

      8. associate-*r* 74.0%

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

      9. distribute-lft-neg-in 74.0%

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

      10. distribute-rgt-in 77.7%

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

      11. sub-neg 77.7%

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

      12. *-commutative 77.7%

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

      13. *-commutative 77.7%

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

   5. Simplified 77.7%

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

   if 1.5000000000000001e49 < t

   1. Initial program 56.2%

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

   2. Taylor expanded in i around -inf 54.6%

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

   3. Taylor expanded in t around inf 72.3%

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

      1. +-commutative 72.3%

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

      2. mul-1-neg 72.3%

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

      3. unsub-neg 72.3%

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

      4. *-commutative 72.3%

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

   5. Simplified 72.3%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) + i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+49}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right) + z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]

Alternative 12: 28.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ t_3 := \left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+207}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.7 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-60}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))) (t_2 (* y (* x z))) (t_3 (* (- a) (* x t))))
   (if (<= t -6.2e+207)
     t_3
     (if (<= t -6.5e+110)
       t_1
       (if (<= t -6.7e+105)
         t_2
         (if (<= t -5e+52)
           (* y (* i (- j)))
           (if (<= t -2.8e-60)
             (* i (* a b))
             (if (<= t 3.5e-28) t_2 (if (<= t 1.9e+105) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = y * (x * z);
	double t_3 = -a * (x * t);
	double tmp;
	if (t <= -6.2e+207) {
		tmp = t_3;
	} else if (t <= -6.5e+110) {
		tmp = t_1;
	} else if (t <= -6.7e+105) {
		tmp = t_2;
	} else if (t <= -5e+52) {
		tmp = y * (i * -j);
	} else if (t <= -2.8e-60) {
		tmp = i * (a * b);
	} else if (t <= 3.5e-28) {
		tmp = t_2;
	} else if (t <= 1.9e+105) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = c * (t * j)
    t_2 = y * (x * z)
    t_3 = -a * (x * t)
    if (t <= (-6.2d+207)) then
        tmp = t_3
    else if (t <= (-6.5d+110)) then
        tmp = t_1
    else if (t <= (-6.7d+105)) then
        tmp = t_2
    else if (t <= (-5d+52)) then
        tmp = y * (i * -j)
    else if (t <= (-2.8d-60)) then
        tmp = i * (a * b)
    else if (t <= 3.5d-28) then
        tmp = t_2
    else if (t <= 1.9d+105) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * (t * j);
	double t_2 = y * (x * z);
	double t_3 = -a * (x * t);
	double tmp;
	if (t <= -6.2e+207) {
		tmp = t_3;
	} else if (t <= -6.5e+110) {
		tmp = t_1;
	} else if (t <= -6.7e+105) {
		tmp = t_2;
	} else if (t <= -5e+52) {
		tmp = y * (i * -j);
	} else if (t <= -2.8e-60) {
		tmp = i * (a * b);
	} else if (t <= 3.5e-28) {
		tmp = t_2;
	} else if (t <= 1.9e+105) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	t_2 = y * (x * z)
	t_3 = -a * (x * t)
	tmp = 0
	if t <= -6.2e+207:
		tmp = t_3
	elif t <= -6.5e+110:
		tmp = t_1
	elif t <= -6.7e+105:
		tmp = t_2
	elif t <= -5e+52:
		tmp = y * (i * -j)
	elif t <= -2.8e-60:
		tmp = i * (a * b)
	elif t <= 3.5e-28:
		tmp = t_2
	elif t <= 1.9e+105:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(t * j))
	t_2 = Float64(y * Float64(x * z))
	t_3 = Float64(Float64(-a) * Float64(x * t))
	tmp = 0.0
	if (t <= -6.2e+207)
		tmp = t_3;
	elseif (t <= -6.5e+110)
		tmp = t_1;
	elseif (t <= -6.7e+105)
		tmp = t_2;
	elseif (t <= -5e+52)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (t <= -2.8e-60)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 3.5e-28)
		tmp = t_2;
	elseif (t <= 1.9e+105)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * (t * j);
	t_2 = y * (x * z);
	t_3 = -a * (x * t);
	tmp = 0.0;
	if (t <= -6.2e+207)
		tmp = t_3;
	elseif (t <= -6.5e+110)
		tmp = t_1;
	elseif (t <= -6.7e+105)
		tmp = t_2;
	elseif (t <= -5e+52)
		tmp = y * (i * -j);
	elseif (t <= -2.8e-60)
		tmp = i * (a * b);
	elseif (t <= 3.5e-28)
		tmp = t_2;
	elseif (t <= 1.9e+105)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[((-a) * N[(x * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e+207], t$95$3, If[LessEqual[t, -6.5e+110], t$95$1, If[LessEqual[t, -6.7e+105], t$95$2, If[LessEqual[t, -5e+52], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.8e-60], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-28], t$95$2, If[LessEqual[t, 1.9e+105], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.2000000000000005e207 or 1.9e105 < t

   1. Initial program 54.1%

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

   2. Taylor expanded in i around -inf 52.7%

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

   3. Taylor expanded in x around inf 59.1%

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

      1. *-commutative 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in y around 0 59.7%

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

      1. mul-1-neg 59.7%

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

   8. Simplified 59.7%

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

   if -6.2000000000000005e207 < t < -6.4999999999999997e110 or 3.5e-28 < t < 1.9e105

   1. Initial program 68.6%

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

   2. Taylor expanded in b around 0 57.9%

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

   3. Taylor expanded in c around inf 50.6%

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

   if -6.4999999999999997e110 < t < -6.7000000000000004e105 or -2.8000000000000002e-60 < t < 3.5e-28

   1. Initial program 77.4%

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

   2. Taylor expanded in i around -inf 83.2%

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

   3. Taylor expanded in x around inf 39.2%

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

      1. *-commutative 39.2%

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

   5. Simplified 39.2%

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

   6. Taylor expanded in y around inf 33.4%

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

      1. associate-*r* 31.1%

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

      2. *-commutative 31.1%

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

      3. associate-*r* 35.6%

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

   8. Simplified 35.6%

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

   if -6.7000000000000004e105 < t < -5e52

   1. Initial program 87.3%

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

   2. Taylor expanded in i around inf 61.4%

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

      1. distribute-lft-out-- 61.4%

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

   4. Simplified 61.4%

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

   5. Taylor expanded in j around inf 50.1%

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

      1. mul-1-neg 50.1%

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

      2. associate-*r* 61.9%

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

      3. *-commutative 61.9%

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

   7. Simplified 61.9%

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

   if -5e52 < t < -2.8000000000000002e-60

   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. Taylor expanded in i around -inf 76.0%

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

   3. Taylor expanded in z around 0 68.9%

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

      1. +-commutative 68.9%

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

      2. associate-+l+ 68.9%

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

      3. neg-mul-1 68.9%

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

      4. *-commutative 68.9%

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

      5. distribute-rgt-neg-in 68.9%

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

      6. associate-*r* 68.9%

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

      7. *-commutative 68.9%

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

      8. associate-*r* 69.0%

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

      9. associate-*l* 69.0%

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

      10. distribute-rgt-in 69.0%

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

      11. mul-1-neg 69.0%

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

      12. unsub-neg 69.0%

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

      13. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in b around inf 39.4%

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

      1. associate-*r* 43.7%

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

   8. Simplified 43.7%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+207}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+110}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -6.7 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-60}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-28}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 13: 51.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.9 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-278}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+70}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -1.9e-33)
     t_2
     (if (<= c 2.7e-278)
       (* a (- (* b i) (* x t)))
       (if (<= c 2.2e-20)
         t_1
         (if (<= c 3.4e+70)
           (* b (- (* a i) (* z c)))
           (if (<= c 6.5e+133) 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 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.9e-33) {
		tmp = t_2;
	} else if (c <= 2.7e-278) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 2.2e-20) {
		tmp = t_1;
	} else if (c <= 3.4e+70) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 6.5e+133) {
		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 = c * ((t * j) - (z * b))
    if (c <= (-1.9d-33)) then
        tmp = t_2
    else if (c <= 2.7d-278) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 2.2d-20) then
        tmp = t_1
    else if (c <= 3.4d+70) then
        tmp = b * ((a * i) - (z * c))
    else if (c <= 6.5d+133) 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 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.9e-33) {
		tmp = t_2;
	} else if (c <= 2.7e-278) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 2.2e-20) {
		tmp = t_1;
	} else if (c <= 3.4e+70) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 6.5e+133) {
		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 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -1.9e-33:
		tmp = t_2
	elif c <= 2.7e-278:
		tmp = a * ((b * i) - (x * t))
	elif c <= 2.2e-20:
		tmp = t_1
	elif c <= 3.4e+70:
		tmp = b * ((a * i) - (z * c))
	elif c <= 6.5e+133:
		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(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.9e-33)
		tmp = t_2;
	elseif (c <= 2.7e-278)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 2.2e-20)
		tmp = t_1;
	elseif (c <= 3.4e+70)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (c <= 6.5e+133)
		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 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.9e-33)
		tmp = t_2;
	elseif (c <= 2.7e-278)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 2.2e-20)
		tmp = t_1;
	elseif (c <= 3.4e+70)
		tmp = b * ((a * i) - (z * c));
	elseif (c <= 6.5e+133)
		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[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.9e-33], t$95$2, If[LessEqual[c, 2.7e-278], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.2e-20], t$95$1, If[LessEqual[c, 3.4e+70], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.5e+133], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.89999999999999997e-33 or 6.5000000000000004e133 < c

   1. Initial program 59.5%

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

   2. Taylor expanded in c around inf 67.8%

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

      1. *-commutative 67.8%

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

   4. Simplified 67.8%

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

   if -1.89999999999999997e-33 < c < 2.7000000000000001e-278

   1. Initial program 69.2%

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

   2. Taylor expanded in i around -inf 75.6%

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

   3. Taylor expanded in a around inf 66.7%

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

      1. +-commutative 66.7%

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

      2. mul-1-neg 66.7%

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

      3. unsub-neg 66.7%

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

   5. Simplified 66.7%

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

   if 2.7000000000000001e-278 < c < 2.19999999999999991e-20 or 3.4000000000000001e70 < c < 6.5000000000000004e133

   1. Initial program 77.4%

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

   2. Taylor expanded in i around -inf 73.6%

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

   3. Taylor expanded in x around inf 59.0%

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

      1. *-commutative 59.0%

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

   5. Simplified 59.0%

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

   if 2.19999999999999991e-20 < c < 3.4000000000000001e70

   1. Initial program 79.5%

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

   2. Taylor expanded in b around inf 49.6%

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

      1. *-commutative 49.6%

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

   4. Simplified 49.6%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{-33}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 2.7 \cdot 10^{-278}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{+70}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 14: 29.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+208}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-56}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-28}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= t -1.65e+208)
     (* x (* t (- a)))
     (if (<= t -2.3e+109)
       t_1
       (if (<= t -3.5e+51)
         (* y (* i (- j)))
         (if (<= t -2.7e-56)
           (* i (* a b))
           (if (<= t 3.4e-28)
             (* y (* x z))
             (if (<= t 9.5e+96) t_1 (* (- 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 = c * (t * j);
	double tmp;
	if (t <= -1.65e+208) {
		tmp = x * (t * -a);
	} else if (t <= -2.3e+109) {
		tmp = t_1;
	} else if (t <= -3.5e+51) {
		tmp = y * (i * -j);
	} else if (t <= -2.7e-56) {
		tmp = i * (a * b);
	} else if (t <= 3.4e-28) {
		tmp = y * (x * z);
	} else if (t <= 9.5e+96) {
		tmp = t_1;
	} else {
		tmp = -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) :: tmp
    t_1 = c * (t * j)
    if (t <= (-1.65d+208)) then
        tmp = x * (t * -a)
    else if (t <= (-2.3d+109)) then
        tmp = t_1
    else if (t <= (-3.5d+51)) then
        tmp = y * (i * -j)
    else if (t <= (-2.7d-56)) then
        tmp = i * (a * b)
    else if (t <= 3.4d-28) then
        tmp = y * (x * z)
    else if (t <= 9.5d+96) then
        tmp = t_1
    else
        tmp = -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 = c * (t * j);
	double tmp;
	if (t <= -1.65e+208) {
		tmp = x * (t * -a);
	} else if (t <= -2.3e+109) {
		tmp = t_1;
	} else if (t <= -3.5e+51) {
		tmp = y * (i * -j);
	} else if (t <= -2.7e-56) {
		tmp = i * (a * b);
	} else if (t <= 3.4e-28) {
		tmp = y * (x * z);
	} else if (t <= 9.5e+96) {
		tmp = t_1;
	} else {
		tmp = -a * (x * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * (t * j)
	tmp = 0
	if t <= -1.65e+208:
		tmp = x * (t * -a)
	elif t <= -2.3e+109:
		tmp = t_1
	elif t <= -3.5e+51:
		tmp = y * (i * -j)
	elif t <= -2.7e-56:
		tmp = i * (a * b)
	elif t <= 3.4e-28:
		tmp = y * (x * z)
	elif t <= 9.5e+96:
		tmp = t_1
	else:
		tmp = -a * (x * t)
	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 <= -1.65e+208)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (t <= -2.3e+109)
		tmp = t_1;
	elseif (t <= -3.5e+51)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (t <= -2.7e-56)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 3.4e-28)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 9.5e+96)
		tmp = t_1;
	else
		tmp = Float64(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 = c * (t * j);
	tmp = 0.0;
	if (t <= -1.65e+208)
		tmp = x * (t * -a);
	elseif (t <= -2.3e+109)
		tmp = t_1;
	elseif (t <= -3.5e+51)
		tmp = y * (i * -j);
	elseif (t <= -2.7e-56)
		tmp = i * (a * b);
	elseif (t <= 3.4e-28)
		tmp = y * (x * z);
	elseif (t <= 9.5e+96)
		tmp = t_1;
	else
		tmp = -a * (x * t);
	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, -1.65e+208], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.3e+109], t$95$1, If[LessEqual[t, -3.5e+51], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.7e-56], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e-28], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+96], t$95$1, N[((-a) * N[(x * t), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.65e208

   1. Initial program 59.8%

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

   2. Taylor expanded in i around -inf 63.0%

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

   3. Taylor expanded in x around inf 77.5%

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

      1. *-commutative 77.5%

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

   5. Simplified 77.5%

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

   6. Taylor expanded in y around 0 71.8%

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

      1. mul-1-neg 71.8%

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

      2. associate-*r* 74.1%

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

      3. distribute-lft-neg-in 74.1%

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

      4. *-commutative 74.1%

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

      5. *-commutative 74.1%

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

      6. distribute-rgt-neg-in 74.1%

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

   8. Simplified 74.1%

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

   if -1.65e208 < t < -2.3000000000000001e109 or 3.4000000000000001e-28 < t < 9.50000000000000089e96

   1. Initial program 68.6%

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

   2. Taylor expanded in b around 0 57.9%

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

   3. Taylor expanded in c around inf 50.6%

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

   if -2.3000000000000001e109 < t < -3.5e51

   1. Initial program 90.5%

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

   2. Taylor expanded in i around inf 59.2%

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

      1. distribute-lft-out-- 59.2%

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

   4. Simplified 59.2%

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

   5. Taylor expanded in j around inf 37.2%

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

      1. mul-1-neg 37.2%

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

      2. associate-*r* 45.8%

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

      3. *-commutative 45.8%

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

   7. Simplified 45.8%

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

   if -3.5e51 < t < -2.69999999999999995e-56

   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. Taylor expanded in i around -inf 76.0%

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

   3. Taylor expanded in z around 0 68.9%

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

      1. +-commutative 68.9%

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

      2. associate-+l+ 68.9%

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

      3. neg-mul-1 68.9%

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

      4. *-commutative 68.9%

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

      5. distribute-rgt-neg-in 68.9%

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

      6. associate-*r* 68.9%

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

      7. *-commutative 68.9%

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

      8. associate-*r* 69.0%

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

      9. associate-*l* 69.0%

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

      10. distribute-rgt-in 69.0%

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

      11. mul-1-neg 69.0%

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

      12. unsub-neg 69.0%

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

      13. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in b around inf 39.4%

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

      1. associate-*r* 43.7%

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

   8. Simplified 43.7%

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

   if -2.69999999999999995e-56 < t < 3.4000000000000001e-28

   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. Taylor expanded in i around -inf 82.7%

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

   3. Taylor expanded in x around inf 38.4%

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

      1. *-commutative 38.4%

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

   5. Simplified 38.4%

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

   6. Taylor expanded in y around inf 33.3%

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

      1. associate-*r* 31.9%

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

      2. *-commutative 31.9%

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

      3. associate-*r* 34.7%

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

   8. Simplified 34.7%

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

   if 9.50000000000000089e96 < t

   1. Initial program 51.2%

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

   2. Taylor expanded in i around -inf 47.6%

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

   3. Taylor expanded in x around inf 50.0%

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

      1. *-commutative 50.0%

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

   5. Simplified 50.0%

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

   6. Taylor expanded in y around 0 53.8%

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

      1. mul-1-neg 53.8%

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

   8. Simplified 53.8%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.65 \cdot 10^{+208}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+109}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-56}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-28}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+96}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 15: 41.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;c \leq -2.5 \cdot 10^{+109}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= c -2.5e+109)
     (* z (* c (- b)))
     (if (<= c 7.5e-35)
       t_1
       (if (<= c 5.5e+35)
         (* y (* i (- j)))
         (if (<= c 6.4e+142) t_1 (* (* z c) (- b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (c <= -2.5e+109) {
		tmp = z * (c * -b);
	} else if (c <= 7.5e-35) {
		tmp = t_1;
	} else if (c <= 5.5e+35) {
		tmp = y * (i * -j);
	} else if (c <= 6.4e+142) {
		tmp = t_1;
	} else {
		tmp = (z * c) * -b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (c <= (-2.5d+109)) then
        tmp = z * (c * -b)
    else if (c <= 7.5d-35) then
        tmp = t_1
    else if (c <= 5.5d+35) then
        tmp = y * (i * -j)
    else if (c <= 6.4d+142) then
        tmp = t_1
    else
        tmp = (z * c) * -b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (c <= -2.5e+109) {
		tmp = z * (c * -b);
	} else if (c <= 7.5e-35) {
		tmp = t_1;
	} else if (c <= 5.5e+35) {
		tmp = y * (i * -j);
	} else if (c <= 6.4e+142) {
		tmp = t_1;
	} else {
		tmp = (z * c) * -b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if c <= -2.5e+109:
		tmp = z * (c * -b)
	elif c <= 7.5e-35:
		tmp = t_1
	elif c <= 5.5e+35:
		tmp = y * (i * -j)
	elif c <= 6.4e+142:
		tmp = t_1
	else:
		tmp = (z * c) * -b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (c <= -2.5e+109)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (c <= 7.5e-35)
		tmp = t_1;
	elseif (c <= 5.5e+35)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (c <= 6.4e+142)
		tmp = t_1;
	else
		tmp = Float64(Float64(z * c) * Float64(-b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (c <= -2.5e+109)
		tmp = z * (c * -b);
	elseif (c <= 7.5e-35)
		tmp = t_1;
	elseif (c <= 5.5e+35)
		tmp = y * (i * -j);
	elseif (c <= 6.4e+142)
		tmp = t_1;
	else
		tmp = (z * c) * -b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.5e+109], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.5e-35], t$95$1, If[LessEqual[c, 5.5e+35], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.4e+142], t$95$1, N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.5000000000000001e109

   1. Initial program 61.4%

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

   2. Taylor expanded in z around inf 64.3%

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

      1. *-commutative 64.3%

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

      2. *-commutative 64.3%

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

   4. Simplified 64.3%

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

   5. Taylor expanded in y around 0 51.0%

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

      1. neg-mul-1 51.0%

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

      2. *-commutative 51.0%

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

      3. distribute-rgt-neg-in 51.0%

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

   7. Simplified 51.0%

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

   if -2.5000000000000001e109 < c < 7.5e-35 or 5.50000000000000001e35 < c < 6.40000000000000011e142

   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. Taylor expanded in i around -inf 73.1%

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

   3. Taylor expanded in a around inf 52.4%

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

      1. +-commutative 52.4%

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

      2. mul-1-neg 52.4%

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

      3. unsub-neg 52.4%

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

   5. Simplified 52.4%

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

   if 7.5e-35 < c < 5.50000000000000001e35

   1. Initial program 71.2%

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

   2. Taylor expanded in i around inf 43.8%

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

      1. distribute-lft-out-- 43.8%

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

   4. Simplified 43.8%

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

   5. Taylor expanded in j around inf 38.0%

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

      1. mul-1-neg 38.0%

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

      2. associate-*r* 38.1%

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

      3. *-commutative 38.1%

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

   7. Simplified 38.1%

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

   if 6.40000000000000011e142 < c

   1. Initial program 46.5%

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

   2. Taylor expanded in b around inf 48.5%

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

      1. *-commutative 48.5%

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

   4. Simplified 48.5%

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

   5. Taylor expanded in i around 0 47.3%

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

      1. mul-1-neg 47.3%

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

      2. distribute-lft-neg-out 47.3%

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

      3. *-commutative 47.3%

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

   7. Simplified 47.3%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.5 \cdot 10^{+109}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{-35}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 5.5 \cdot 10^{+35}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;c \leq 6.4 \cdot 10^{+142}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \end{array} \]

Alternative 16: 45.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3.5 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-180}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= b -3.5e+55)
     t_2
     (if (<= b -2.7e-154)
       t_1
       (if (<= b 9.5e-180) (* i (* y (- j))) (if (<= b 1.06e+96) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.5e+55) {
		tmp = t_2;
	} else if (b <= -2.7e-154) {
		tmp = t_1;
	} else if (b <= 9.5e-180) {
		tmp = i * (y * -j);
	} else if (b <= 1.06e+96) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = b * ((a * i) - (z * c))
    if (b <= (-3.5d+55)) then
        tmp = t_2
    else if (b <= (-2.7d-154)) then
        tmp = t_1
    else if (b <= 9.5d-180) then
        tmp = i * (y * -j)
    else if (b <= 1.06d+96) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -3.5e+55) {
		tmp = t_2;
	} else if (b <= -2.7e-154) {
		tmp = t_1;
	} else if (b <= 9.5e-180) {
		tmp = i * (y * -j);
	} else if (b <= 1.06e+96) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -3.5e+55:
		tmp = t_2
	elif b <= -2.7e-154:
		tmp = t_1
	elif b <= 9.5e-180:
		tmp = i * (y * -j)
	elif b <= 1.06e+96:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3.5e+55)
		tmp = t_2;
	elseif (b <= -2.7e-154)
		tmp = t_1;
	elseif (b <= 9.5e-180)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (b <= 1.06e+96)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -3.5e+55)
		tmp = t_2;
	elseif (b <= -2.7e-154)
		tmp = t_1;
	elseif (b <= 9.5e-180)
		tmp = i * (y * -j);
	elseif (b <= 1.06e+96)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.5e+55], t$95$2, If[LessEqual[b, -2.7e-154], t$95$1, If[LessEqual[b, 9.5e-180], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.06e+96], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.5000000000000001e55 or 1.06e96 < b

   1. Initial program 59.4%

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

   2. Taylor expanded in b around inf 63.9%

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

      1. *-commutative 63.9%

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

   4. Simplified 63.9%

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

   if -3.5000000000000001e55 < b < -2.69999999999999989e-154 or 9.49999999999999934e-180 < b < 1.06e96

   1. Initial program 79.3%

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

   2. Taylor expanded in i around -inf 80.2%

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

   3. Taylor expanded in a around inf 45.0%

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

      1. +-commutative 45.0%

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

      2. mul-1-neg 45.0%

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

      3. unsub-neg 45.0%

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

   5. Simplified 45.0%

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

   if -2.69999999999999989e-154 < b < 9.49999999999999934e-180

   1. Initial program 66.0%

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

   2. Taylor expanded in i around inf 43.6%

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

      1. distribute-lft-out-- 43.6%

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

   4. Simplified 43.6%

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

   5. Taylor expanded in j around inf 43.6%

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

      1. mul-1-neg 43.6%

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

      2. associate-*r* 40.4%

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

      3. *-commutative 40.4%

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

   7. Simplified 40.4%

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

   8. Taylor expanded in j around 0 43.6%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+55}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-154}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-180}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;b \leq 1.06 \cdot 10^{+96}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 17: 51.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -4 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+69}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -4e-30)
     t_2
     (if (<= c 6.6e-54)
       t_1
       (if (<= c 8e+69)
         (* b (- (* a i) (* z c)))
         (if (<= c 1.55e+134) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4e-30) {
		tmp = t_2;
	} else if (c <= 6.6e-54) {
		tmp = t_1;
	} else if (c <= 8e+69) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 1.55e+134) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-4d-30)) then
        tmp = t_2
    else if (c <= 6.6d-54) then
        tmp = t_1
    else if (c <= 8d+69) then
        tmp = b * ((a * i) - (z * c))
    else if (c <= 1.55d+134) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -4e-30) {
		tmp = t_2;
	} else if (c <= 6.6e-54) {
		tmp = t_1;
	} else if (c <= 8e+69) {
		tmp = b * ((a * i) - (z * c));
	} else if (c <= 1.55e+134) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -4e-30:
		tmp = t_2
	elif c <= 6.6e-54:
		tmp = t_1
	elif c <= 8e+69:
		tmp = b * ((a * i) - (z * c))
	elif c <= 1.55e+134:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -4e-30)
		tmp = t_2;
	elseif (c <= 6.6e-54)
		tmp = t_1;
	elseif (c <= 8e+69)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (c <= 1.55e+134)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -4e-30)
		tmp = t_2;
	elseif (c <= 6.6e-54)
		tmp = t_1;
	elseif (c <= 8e+69)
		tmp = b * ((a * i) - (z * c));
	elseif (c <= 1.55e+134)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4e-30], t$95$2, If[LessEqual[c, 6.6e-54], t$95$1, If[LessEqual[c, 8e+69], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.55e+134], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4e-30 or 1.54999999999999991e134 < c

   1. Initial program 59.5%

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

   2. Taylor expanded in c around inf 67.8%

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

      1. *-commutative 67.8%

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

   4. Simplified 67.8%

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

   if -4e-30 < c < 6.59999999999999986e-54 or 8.0000000000000006e69 < c < 1.54999999999999991e134

   1. Initial program 73.5%

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

   2. Taylor expanded in i around -inf 74.3%

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

   3. Taylor expanded in a around inf 57.0%

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

      1. +-commutative 57.0%

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

      2. mul-1-neg 57.0%

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

      3. unsub-neg 57.0%

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

   5. Simplified 57.0%

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

   if 6.59999999999999986e-54 < c < 8.0000000000000006e69

   1. Initial program 78.9%

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

   2. Taylor expanded in b around inf 44.7%

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

      1. *-commutative 44.7%

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

   4. Simplified 44.7%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{-54}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 8 \cdot 10^{+69}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;c \leq 1.55 \cdot 10^{+134}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 18: 51.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.4 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{+61}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))) (t_2 (* c (- (* t j) (* z b)))))
   (if (<= c -1.4e-33)
     t_2
     (if (<= c 1.35e-36)
       t_1
       (if (<= c 7.2e+61)
         (* j (- (* t c) (* y i)))
         (if (<= c 6.5e+133) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.4e-33) {
		tmp = t_2;
	} else if (c <= 1.35e-36) {
		tmp = t_1;
	} else if (c <= 7.2e+61) {
		tmp = j * ((t * c) - (y * i));
	} else if (c <= 6.5e+133) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    t_2 = c * ((t * j) - (z * b))
    if (c <= (-1.4d-33)) then
        tmp = t_2
    else if (c <= 1.35d-36) then
        tmp = t_1
    else if (c <= 7.2d+61) then
        tmp = j * ((t * c) - (y * i))
    else if (c <= 6.5d+133) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double t_2 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.4e-33) {
		tmp = t_2;
	} else if (c <= 1.35e-36) {
		tmp = t_1;
	} else if (c <= 7.2e+61) {
		tmp = j * ((t * c) - (y * i));
	} else if (c <= 6.5e+133) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	t_2 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -1.4e-33:
		tmp = t_2
	elif c <= 1.35e-36:
		tmp = t_1
	elif c <= 7.2e+61:
		tmp = j * ((t * c) - (y * i))
	elif c <= 6.5e+133:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.4e-33)
		tmp = t_2;
	elseif (c <= 1.35e-36)
		tmp = t_1;
	elseif (c <= 7.2e+61)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (c <= 6.5e+133)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	t_2 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.4e-33)
		tmp = t_2;
	elseif (c <= 1.35e-36)
		tmp = t_1;
	elseif (c <= 7.2e+61)
		tmp = j * ((t * c) - (y * i));
	elseif (c <= 6.5e+133)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.4e-33], t$95$2, If[LessEqual[c, 1.35e-36], t$95$1, If[LessEqual[c, 7.2e+61], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.5e+133], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.4e-33 or 6.5000000000000004e133 < c

   1. Initial program 59.5%

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

   2. Taylor expanded in c around inf 67.8%

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

      1. *-commutative 67.8%

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

   4. Simplified 67.8%

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

   if -1.4e-33 < c < 1.35000000000000004e-36 or 7.20000000000000021e61 < c < 6.5000000000000004e133

   1. Initial program 74.5%

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

   2. Taylor expanded in i around -inf 75.2%

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

   3. Taylor expanded in a around inf 56.5%

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

      1. +-commutative 56.5%

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

      2. mul-1-neg 56.5%

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

      3. unsub-neg 56.5%

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

   5. Simplified 56.5%

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

   if 1.35000000000000004e-36 < c < 7.20000000000000021e61

   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. Taylor expanded in j around inf 45.3%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.4 \cdot 10^{-33}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-36}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 7.2 \cdot 10^{+61}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{+133}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 19: 51.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.8 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-282}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))))
   (if (<= c -1.8e-31)
     t_1
     (if (<= c 8.5e-282)
       (* a (- (* b i) (* x t)))
       (if (<= c 9e+36)
         (* y (- (* x z) (* i j)))
         (if (<= c 6.5e+133) (* x (- (* y z) (* t a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1.8e-31) {
		tmp = t_1;
	} else if (c <= 8.5e-282) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 9e+36) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 6.5e+133) {
		tmp = x * ((y * z) - (t * a));
	} 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 <= (-1.8d-31)) then
        tmp = t_1
    else if (c <= 8.5d-282) then
        tmp = a * ((b * i) - (x * t))
    else if (c <= 9d+36) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= 6.5d+133) then
        tmp = x * ((y * z) - (t * a))
    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 <= -1.8e-31) {
		tmp = t_1;
	} else if (c <= 8.5e-282) {
		tmp = a * ((b * i) - (x * t));
	} else if (c <= 9e+36) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= 6.5e+133) {
		tmp = x * ((y * z) - (t * a));
	} 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 <= -1.8e-31:
		tmp = t_1
	elif c <= 8.5e-282:
		tmp = a * ((b * i) - (x * t))
	elif c <= 9e+36:
		tmp = y * ((x * z) - (i * j))
	elif c <= 6.5e+133:
		tmp = x * ((y * z) - (t * a))
	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 <= -1.8e-31)
		tmp = t_1;
	elseif (c <= 8.5e-282)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (c <= 9e+36)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= 6.5e+133)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	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 <= -1.8e-31)
		tmp = t_1;
	elseif (c <= 8.5e-282)
		tmp = a * ((b * i) - (x * t));
	elseif (c <= 9e+36)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= 6.5e+133)
		tmp = x * ((y * z) - (t * a));
	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, -1.8e-31], t$95$1, If[LessEqual[c, 8.5e-282], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9e+36], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.5e+133], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.80000000000000002e-31 or 6.5000000000000004e133 < c

   1. Initial program 59.5%

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

   2. Taylor expanded in c around inf 67.8%

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

      1. *-commutative 67.8%

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

   4. Simplified 67.8%

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

   if -1.80000000000000002e-31 < c < 8.499999999999999e-282

   1. Initial program 69.2%

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

   2. Taylor expanded in i around -inf 75.6%

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

   3. Taylor expanded in a around inf 66.7%

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

      1. +-commutative 66.7%

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

      2. mul-1-neg 66.7%

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

      3. unsub-neg 66.7%

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

   5. Simplified 66.7%

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

   if 8.499999999999999e-282 < c < 8.99999999999999994e36

   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. Taylor expanded in i around -inf 77.7%

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

   3. Taylor expanded in y around inf 54.4%

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

      1. +-commutative 54.4%

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

      2. mul-1-neg 54.4%

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

      3. unsub-neg 54.4%

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

      4. *-commutative 54.4%

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

   5. Simplified 54.4%

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

   if 8.99999999999999994e36 < c < 6.5000000000000004e133

   1. Initial program 69.4%

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

   2. Taylor expanded in i around -inf 64.9%

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

   3. Taylor expanded in x around inf 65.7%

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

      1. *-commutative 65.7%

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

   5. Simplified 65.7%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.8 \cdot 10^{-31}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-282}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;c \leq 9 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq 6.5 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 20: 28.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;t \leq -6 \cdot 10^{+262}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+208}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-57}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-28}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (* t j))))
   (if (<= t -6e+262)
     t_1
     (if (<= t -2.4e+208)
       (* a (* b i))
       (if (<= t -1.15e+111)
         t_1
         (if (<= t -3.8e-57)
           (* i (* a b))
           (if (<= t 2.7e-28) (* y (* x z)) 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 <= -6e+262) {
		tmp = t_1;
	} else if (t <= -2.4e+208) {
		tmp = a * (b * i);
	} else if (t <= -1.15e+111) {
		tmp = t_1;
	} else if (t <= -3.8e-57) {
		tmp = i * (a * b);
	} else if (t <= 2.7e-28) {
		tmp = y * (x * z);
	} 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 <= (-6d+262)) then
        tmp = t_1
    else if (t <= (-2.4d+208)) then
        tmp = a * (b * i)
    else if (t <= (-1.15d+111)) then
        tmp = t_1
    else if (t <= (-3.8d-57)) then
        tmp = i * (a * b)
    else if (t <= 2.7d-28) then
        tmp = y * (x * z)
    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 <= -6e+262) {
		tmp = t_1;
	} else if (t <= -2.4e+208) {
		tmp = a * (b * i);
	} else if (t <= -1.15e+111) {
		tmp = t_1;
	} else if (t <= -3.8e-57) {
		tmp = i * (a * b);
	} else if (t <= 2.7e-28) {
		tmp = y * (x * z);
	} 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 <= -6e+262:
		tmp = t_1
	elif t <= -2.4e+208:
		tmp = a * (b * i)
	elif t <= -1.15e+111:
		tmp = t_1
	elif t <= -3.8e-57:
		tmp = i * (a * b)
	elif t <= 2.7e-28:
		tmp = y * (x * z)
	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 <= -6e+262)
		tmp = t_1;
	elseif (t <= -2.4e+208)
		tmp = Float64(a * Float64(b * i));
	elseif (t <= -1.15e+111)
		tmp = t_1;
	elseif (t <= -3.8e-57)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 2.7e-28)
		tmp = Float64(y * Float64(x * z));
	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 <= -6e+262)
		tmp = t_1;
	elseif (t <= -2.4e+208)
		tmp = a * (b * i);
	elseif (t <= -1.15e+111)
		tmp = t_1;
	elseif (t <= -3.8e-57)
		tmp = i * (a * b);
	elseif (t <= 2.7e-28)
		tmp = y * (x * z);
	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, -6e+262], t$95$1, If[LessEqual[t, -2.4e+208], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.15e+111], t$95$1, If[LessEqual[t, -3.8e-57], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.7e-28], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.0000000000000001e262 or -2.39999999999999987e208 < t < -1.15000000000000001e111 or 2.6999999999999999e-28 < t

   1. Initial program 59.8%

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

   2. Taylor expanded in b around 0 57.6%

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

   3. Taylor expanded in c around inf 42.7%

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

   if -6.0000000000000001e262 < t < -2.39999999999999987e208

   1. Initial program 53.9%

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

   2. Taylor expanded in b around inf 21.2%

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

      1. *-commutative 21.2%

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

   4. Simplified 21.2%

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

   5. Taylor expanded in i around inf 34.6%

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

   if -1.15000000000000001e111 < t < -3.7999999999999997e-57

   1. Initial program 81.0%

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

   2. Taylor expanded in i around -inf 77.9%

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

   3. Taylor expanded in z around 0 68.7%

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

      1. +-commutative 68.7%

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

      2. associate-+l+ 68.7%

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

      3. neg-mul-1 68.7%

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

      4. *-commutative 68.7%

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

      5. distribute-rgt-neg-in 68.7%

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

      6. associate-*r* 71.8%

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

      7. *-commutative 71.8%

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

      8. associate-*r* 71.9%

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

      9. associate-*l* 71.9%

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

      10. distribute-rgt-in 71.9%

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

      11. mul-1-neg 71.9%

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

      12. unsub-neg 71.9%

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

      13. *-commutative 71.9%

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

   5. Simplified 71.9%

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

   6. Taylor expanded in b around inf 32.9%

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

      1. associate-*r* 40.2%

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

   8. Simplified 40.2%

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

   if -3.7999999999999997e-57 < t < 2.6999999999999999e-28

   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. Taylor expanded in i around -inf 82.7%

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

   3. Taylor expanded in x around inf 38.4%

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

      1. *-commutative 38.4%

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

   5. Simplified 38.4%

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

   6. Taylor expanded in y around inf 33.3%

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

      1. associate-*r* 31.9%

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

      2. *-commutative 31.9%

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

      3. associate-*r* 34.7%

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

   8. Simplified 34.7%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{+262}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+208}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+111}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-57}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-28}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 21: 27.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{if}\;t \leq -5.4 \cdot 10^{+218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-59}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-28}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+97}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- a) (* x t))))
   (if (<= t -5.4e+218)
     t_1
     (if (<= t -1.02e-59)
       (* i (* a b))
       (if (<= t 3.6e-28)
         (* y (* x z))
         (if (<= t 2.05e+97) (* c (* t j)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -a * (x * t);
	double tmp;
	if (t <= -5.4e+218) {
		tmp = t_1;
	} else if (t <= -1.02e-59) {
		tmp = i * (a * b);
	} else if (t <= 3.6e-28) {
		tmp = y * (x * z);
	} else if (t <= 2.05e+97) {
		tmp = c * (t * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a * (x * t)
    if (t <= (-5.4d+218)) then
        tmp = t_1
    else if (t <= (-1.02d-59)) then
        tmp = i * (a * b)
    else if (t <= 3.6d-28) then
        tmp = y * (x * z)
    else if (t <= 2.05d+97) then
        tmp = c * (t * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -a * (x * t);
	double tmp;
	if (t <= -5.4e+218) {
		tmp = t_1;
	} else if (t <= -1.02e-59) {
		tmp = i * (a * b);
	} else if (t <= 3.6e-28) {
		tmp = y * (x * z);
	} else if (t <= 2.05e+97) {
		tmp = c * (t * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -a * (x * t)
	tmp = 0
	if t <= -5.4e+218:
		tmp = t_1
	elif t <= -1.02e-59:
		tmp = i * (a * b)
	elif t <= 3.6e-28:
		tmp = y * (x * z)
	elif t <= 2.05e+97:
		tmp = c * (t * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-a) * Float64(x * t))
	tmp = 0.0
	if (t <= -5.4e+218)
		tmp = t_1;
	elseif (t <= -1.02e-59)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 3.6e-28)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 2.05e+97)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = -a * (x * t);
	tmp = 0.0;
	if (t <= -5.4e+218)
		tmp = t_1;
	elseif (t <= -1.02e-59)
		tmp = i * (a * b);
	elseif (t <= 3.6e-28)
		tmp = y * (x * z);
	elseif (t <= 2.05e+97)
		tmp = c * (t * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-a) * N[(x * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.4e+218], t$95$1, If[LessEqual[t, -1.02e-59], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-28], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e+97], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.40000000000000025e218 or 2.04999999999999994e97 < t

   1. Initial program 53.6%

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

   2. Taylor expanded in i around -inf 52.1%

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

   3. Taylor expanded in x around inf 60.0%

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

      1. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   6. Taylor expanded in y around 0 61.7%

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

      1. mul-1-neg 61.7%

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

   8. Simplified 61.7%

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

   if -5.40000000000000025e218 < t < -1.01999999999999996e-59

   1. Initial program 72.5%

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

   2. Taylor expanded in i around -inf 72.4%

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

   3. Taylor expanded in z around 0 66.7%

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

      1. +-commutative 66.7%

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

      2. associate-+l+ 66.7%

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

      3. neg-mul-1 66.7%

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

      4. *-commutative 66.7%

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

      5. distribute-rgt-neg-in 66.7%

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

      6. associate-*r* 68.6%

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

      7. *-commutative 68.6%

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

      8. associate-*r* 68.7%

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

      9. associate-*l* 68.7%

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

      10. distribute-rgt-in 68.7%

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

      11. mul-1-neg 68.7%

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

      12. unsub-neg 68.7%

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

      13. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in b around inf 32.9%

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

      1. associate-*r* 39.4%

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

   8. Simplified 39.4%

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

   if -1.01999999999999996e-59 < t < 3.5999999999999999e-28

   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. Taylor expanded in i around -inf 82.7%

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

   3. Taylor expanded in x around inf 38.4%

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

      1. *-commutative 38.4%

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

   5. Simplified 38.4%

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

   6. Taylor expanded in y around inf 33.3%

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

      1. associate-*r* 31.9%

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

      2. *-commutative 31.9%

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

      3. associate-*r* 34.7%

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

   8. Simplified 34.7%

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

   if 3.5999999999999999e-28 < t < 2.04999999999999994e97

   1. Initial program 75.2%

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

   2. Taylor expanded in b around 0 65.1%

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

   3. Taylor expanded in c around inf 46.6%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{+218}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-59}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-28}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+97}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-a\right) \cdot \left(x \cdot t\right)\\ \end{array} \]

Alternative 22: 29.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;j \leq -13500000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -5.1 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))) (t_2 (* c (* t j))))
   (if (<= j -13500000000.0)
     t_2
     (if (<= j -5.1e-275)
       t_1
       (if (<= j 2.6e-99) (* a (* b i)) (if (<= j 2.7e+75) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = c * (t * j);
	double tmp;
	if (j <= -13500000000.0) {
		tmp = t_2;
	} else if (j <= -5.1e-275) {
		tmp = t_1;
	} else if (j <= 2.6e-99) {
		tmp = a * (b * i);
	} else if (j <= 2.7e+75) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = c * (t * j)
    if (j <= (-13500000000.0d0)) then
        tmp = t_2
    else if (j <= (-5.1d-275)) then
        tmp = t_1
    else if (j <= 2.6d-99) then
        tmp = a * (b * i)
    else if (j <= 2.7d+75) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = c * (t * j);
	double tmp;
	if (j <= -13500000000.0) {
		tmp = t_2;
	} else if (j <= -5.1e-275) {
		tmp = t_1;
	} else if (j <= 2.6e-99) {
		tmp = a * (b * i);
	} else if (j <= 2.7e+75) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = c * (t * j)
	tmp = 0
	if j <= -13500000000.0:
		tmp = t_2
	elif j <= -5.1e-275:
		tmp = t_1
	elif j <= 2.6e-99:
		tmp = a * (b * i)
	elif j <= 2.7e+75:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (j <= -13500000000.0)
		tmp = t_2;
	elseif (j <= -5.1e-275)
		tmp = t_1;
	elseif (j <= 2.6e-99)
		tmp = Float64(a * Float64(b * i));
	elseif (j <= 2.7e+75)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = c * (t * j);
	tmp = 0.0;
	if (j <= -13500000000.0)
		tmp = t_2;
	elseif (j <= -5.1e-275)
		tmp = t_1;
	elseif (j <= 2.6e-99)
		tmp = a * (b * i);
	elseif (j <= 2.7e+75)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -13500000000.0], t$95$2, If[LessEqual[j, -5.1e-275], t$95$1, If[LessEqual[j, 2.6e-99], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.7e+75], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.35e10 or 2.69999999999999998e75 < j

   1. Initial program 63.7%

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

   2. Taylor expanded in b around 0 61.5%

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

   3. Taylor expanded in c around inf 44.9%

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

   if -1.35e10 < j < -5.09999999999999984e-275 or 2.60000000000000005e-99 < j < 2.69999999999999998e75

   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. Taylor expanded in i around -inf 78.7%

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

   3. Taylor expanded in x around inf 49.9%

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

      1. *-commutative 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in y around inf 29.8%

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

   if -5.09999999999999984e-275 < j < 2.60000000000000005e-99

   1. Initial program 68.5%

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

   2. Taylor expanded in b around inf 46.3%

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

      1. *-commutative 46.3%

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

   4. Simplified 46.3%

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

   5. Taylor expanded in i around inf 33.6%

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

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -13500000000:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -5.1 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-99}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 23: 29.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := c \cdot \left(t \cdot j\right)\\ \mathbf{if}\;j \leq -1500000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-248}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-211}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))) (t_2 (* c (* t j))))
   (if (<= j -1500000000.0)
     t_2
     (if (<= j -1.65e-248)
       t_1
       (if (<= j 1.8e-211) (* b (* a i)) (if (<= j 2.6e+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 = y * (x * z);
	double t_2 = c * (t * j);
	double tmp;
	if (j <= -1500000000.0) {
		tmp = t_2;
	} else if (j <= -1.65e-248) {
		tmp = t_1;
	} else if (j <= 1.8e-211) {
		tmp = b * (a * i);
	} else if (j <= 2.6e+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 = y * (x * z)
    t_2 = c * (t * j)
    if (j <= (-1500000000.0d0)) then
        tmp = t_2
    else if (j <= (-1.65d-248)) then
        tmp = t_1
    else if (j <= 1.8d-211) then
        tmp = b * (a * i)
    else if (j <= 2.6d+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 = y * (x * z);
	double t_2 = c * (t * j);
	double tmp;
	if (j <= -1500000000.0) {
		tmp = t_2;
	} else if (j <= -1.65e-248) {
		tmp = t_1;
	} else if (j <= 1.8e-211) {
		tmp = b * (a * i);
	} else if (j <= 2.6e+74) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	t_2 = c * (t * j)
	tmp = 0
	if j <= -1500000000.0:
		tmp = t_2
	elif j <= -1.65e-248:
		tmp = t_1
	elif j <= 1.8e-211:
		tmp = b * (a * i)
	elif j <= 2.6e+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(y * Float64(x * z))
	t_2 = Float64(c * Float64(t * j))
	tmp = 0.0
	if (j <= -1500000000.0)
		tmp = t_2;
	elseif (j <= -1.65e-248)
		tmp = t_1;
	elseif (j <= 1.8e-211)
		tmp = Float64(b * Float64(a * i));
	elseif (j <= 2.6e+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 = y * (x * z);
	t_2 = c * (t * j);
	tmp = 0.0;
	if (j <= -1500000000.0)
		tmp = t_2;
	elseif (j <= -1.65e-248)
		tmp = t_1;
	elseif (j <= 1.8e-211)
		tmp = b * (a * i);
	elseif (j <= 2.6e+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[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1500000000.0], t$95$2, If[LessEqual[j, -1.65e-248], t$95$1, If[LessEqual[j, 1.8e-211], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.6e+74], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.5e9 or 2.6000000000000001e74 < j

   1. Initial program 63.7%

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

   2. Taylor expanded in b around 0 61.5%

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

   3. Taylor expanded in c around inf 44.9%

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

   if -1.5e9 < j < -1.6500000000000001e-248 or 1.7999999999999999e-211 < j < 2.6000000000000001e74

   1. Initial program 70.8%

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

   2. Taylor expanded in i around -inf 77.8%

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

   3. Taylor expanded in x around inf 46.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   4. Step-by-step derivation

      1. *-commutative 46.8%

         \[\leadsto x \cdot \left(y \cdot z - \color{blue}{t \cdot a}\right) \]

   5. Simplified 46.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right)} \]

   6. Taylor expanded in y around inf 29.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 27.5%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

      2. *-commutative 27.5%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

      3. associate-*r* 31.4%

         \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   8. Simplified 31.4%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   if -1.6500000000000001e-248 < j < 1.7999999999999999e-211

   1. Initial program 74.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 47.5%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 47.5%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 47.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 30.2%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 34.1%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative 34.1%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i \]

      3. associate-*l* 34.1%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} \]

   7. Simplified 34.1%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1500000000:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-248}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-211}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]

Alternative 24: 29.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.9 \cdot 10^{+24}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.9e+24)
   (* a (* b i))
   (if (<= i 4e+105) (* 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 (i <= -1.9e+24) {
		tmp = a * (b * i);
	} else if (i <= 4e+105) {
		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 (i <= (-1.9d+24)) then
        tmp = a * (b * i)
    else if (i <= 4d+105) 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 (i <= -1.9e+24) {
		tmp = a * (b * i);
	} else if (i <= 4e+105) {
		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 i <= -1.9e+24:
		tmp = a * (b * i)
	elif i <= 4e+105:
		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 (i <= -1.9e+24)
		tmp = Float64(a * Float64(b * i));
	elseif (i <= 4e+105)
		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 (i <= -1.9e+24)
		tmp = a * (b * i);
	elseif (i <= 4e+105)
		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[LessEqual[i, -1.9e+24], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4e+105], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.90000000000000008e24

   1. Initial program 55.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 52.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 52.8%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 52.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 46.0%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

   if -1.90000000000000008e24 < i < 3.9999999999999998e105

   1. Initial program 75.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around 0 59.1%

      \[\leadsto \color{blue}{j \cdot \left(c \cdot t - i \cdot y\right) + x \cdot \left(y \cdot z - a \cdot t\right)} \]

   3. Taylor expanded in c around inf 23.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot t\right)} \]

   if 3.9999999999999998e105 < i

   1. Initial program 58.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 46.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 46.2%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 46.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 39.6%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 41.7%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative 41.7%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i \]

      3. associate-*l* 46.0%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} \]

   7. Simplified 46.0%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.9 \cdot 10^{+24}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{+105}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]

Alternative 25: 22.5% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.12 \cdot 10^{+216}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z 1.12e+216) (* b (* a i)) (* b (* z c))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= 1.12e+216) {
		tmp = b * (a * i);
	} else {
		tmp = b * (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 (z <= 1.12d+216) then
        tmp = b * (a * i)
    else
        tmp = b * (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 (z <= 1.12e+216) {
		tmp = b * (a * i);
	} else {
		tmp = b * (z * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= 1.12e+216:
		tmp = b * (a * i)
	else:
		tmp = b * (z * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= 1.12e+216)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(b * 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 (z <= 1.12e+216)
		tmp = b * (a * i);
	else
		tmp = b * (z * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, 1.12e+216], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.12e216

   1. Initial program 70.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 39.2%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 39.2%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 39.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around inf 21.7%

      \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 22.7%

         \[\leadsto \color{blue}{\left(a \cdot b\right) \cdot i} \]

      2. *-commutative 22.7%

         \[\leadsto \color{blue}{\left(b \cdot a\right)} \cdot i \]

      3. associate-*l* 21.8%

         \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} \]

   7. Simplified 21.8%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i\right)} \]

   if 1.12e216 < z

   1. Initial program 47.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

   2. Taylor expanded in b around inf 40.4%

      \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 40.4%

         \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

   4. Simplified 40.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

   5. Taylor expanded in i around 0 40.5%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 40.5%

         \[\leadsto \color{blue}{-b \cdot \left(c \cdot z\right)} \]

      2. distribute-lft-neg-out 40.5%

         \[\leadsto \color{blue}{\left(-b\right) \cdot \left(c \cdot z\right)} \]

      3. *-commutative 40.5%

         \[\leadsto \color{blue}{\left(c \cdot z\right) \cdot \left(-b\right)} \]

   7. Simplified 40.5%

      \[\leadsto \color{blue}{\left(c \cdot z\right) \cdot \left(-b\right)} \]
   8. Step-by-step derivation

      1. expm1-log1p-u 23.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(c \cdot z\right) \cdot \left(-b\right)\right)\right)} \]

      2. expm1-udef 24.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(c \cdot z\right) \cdot \left(-b\right)\right)} - 1} \]

      3. *-commutative 24.0%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(-b\right) \cdot \left(c \cdot z\right)}\right)} - 1 \]

      4. add-sqr-sqrt 12.2%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\sqrt{-b} \cdot \sqrt{-b}\right)} \cdot \left(c \cdot z\right)\right)} - 1 \]

      5. sqrt-unprod 20.6%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\sqrt{\left(-b\right) \cdot \left(-b\right)}} \cdot \left(c \cdot z\right)\right)} - 1 \]

      6. sqr-neg 20.6%

         \[\leadsto e^{\mathsf{log1p}\left(\sqrt{\color{blue}{b \cdot b}} \cdot \left(c \cdot z\right)\right)} - 1 \]

      7. sqrt-unprod 8.4%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\sqrt{b} \cdot \sqrt{b}\right)} \cdot \left(c \cdot z\right)\right)} - 1 \]

      8. add-sqr-sqrt 12.9%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{b} \cdot \left(c \cdot z\right)\right)} - 1 \]

      9. *-commutative 12.9%

         \[\leadsto e^{\mathsf{log1p}\left(b \cdot \color{blue}{\left(z \cdot c\right)}\right)} - 1 \]

   9. Applied egg-rr 12.9%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(b \cdot \left(z \cdot c\right)\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 13.0%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(b \cdot \left(z \cdot c\right)\right)\right)} \]

       2. expm1-log1p 33.3%

          \[\leadsto \color{blue}{b \cdot \left(z \cdot c\right)} \]

   11. Simplified 33.3%

       \[\leadsto \color{blue}{b \cdot \left(z \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 22.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.12 \cdot 10^{+216}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(z \cdot c\right)\\ \end{array} \]

Alternative 26: 22.7% 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 68.6%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right) \]

2. Taylor expanded in b around inf 39.3%

   \[\leadsto \color{blue}{b \cdot \left(a \cdot i - c \cdot z\right)} \]
3. Step-by-step derivation

   1. *-commutative 39.3%

      \[\leadsto b \cdot \left(\color{blue}{i \cdot a} - c \cdot z\right) \]

4. Simplified 39.3%

   \[\leadsto \color{blue}{b \cdot \left(i \cdot a - c \cdot z\right)} \]

5. Taylor expanded in i around inf 21.3%

   \[\leadsto \color{blue}{a \cdot \left(b \cdot i\right)} \]

6. Final simplification 21.3%

   \[\leadsto a \cdot \left(b \cdot i\right) \]

Developer target: 69.4% 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 2023321 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))