Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 65.7% → 92.8%

Time: 22.7s

Alternatives: 16

Speedup: 0.4×

Specification

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 65.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 92.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - \frac{y}{\frac{{\left(b - y\right)}^{2}}{\frac{t - a}{z}}}\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \frac{x \cdot y + t\_2}{y + z \cdot \left(b - y\right)}\\ t_4 := \frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq -1.5 \cdot 10^{-291}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t\_2\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+283}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (-
          (+ (* (/ y z) (/ x (- b y))) (/ (- t a) (- b y)))
          (/ y (/ (pow (- b y) 2.0) (/ (- t a) z)))))
        (t_2 (* z (- t a)))
        (t_3 (/ (+ (* x y) t_2) (+ y (* z (- b y)))))
        (t_4 (- (/ (- a t) y) (/ x (+ z -1.0)))))
   (if (<= t_3 (- INFINITY))
     t_4
     (if (<= t_3 -1.5e-291)
       (/ (fma x y t_2) (fma z (- b y) y))
       (if (<= t_3 0.0)
         t_1
         (if (<= t_3 2e+283) t_3 (if (<= t_3 INFINITY) t_4 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) - (y / (pow((b - y), 2.0) / ((t - a) / z)));
	double t_2 = z * (t - a);
	double t_3 = ((x * y) + t_2) / (y + (z * (b - y)));
	double t_4 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_3 <= -1.5e-291) {
		tmp = fma(x, y, t_2) / fma(z, (b - y), y);
	} else if (t_3 <= 0.0) {
		tmp = t_1;
	} else if (t_3 <= 2e+283) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y))) - Float64(y / Float64((Float64(b - y) ^ 2.0) / Float64(Float64(t - a) / z))))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(Float64(Float64(x * y) + t_2) / Float64(y + Float64(z * Float64(b - y))))
	t_4 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_3 <= -1.5e-291)
		tmp = Float64(fma(x, y, t_2) / fma(z, Float64(b - y), y));
	elseif (t_3 <= 0.0)
		tmp = t_1;
	elseif (t_3 <= 2e+283)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_4;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / N[(N[(t - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$4, If[LessEqual[t$95$3, -1.5e-291], N[(N[(x * y + t$95$2), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 0.0], t$95$1, If[LessEqual[t$95$3, 2e+283], t$95$3, If[LessEqual[t$95$3, Infinity], t$95$4, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 1.99999999999999991e283 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 27.2%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 47.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} + -1 \cdot \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 47.5%

         \[\leadsto -1 \cdot \frac{x}{z - 1} + \color{blue}{\left(-\frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y}\right)} \]

      2. unsub-neg 47.5%

         \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y}} \]

      3. associate-*r/ 47.5%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z - 1}} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      4. neg-mul-1 47.5%

         \[\leadsto \frac{\color{blue}{-x}}{z - 1} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      5. sub-neg 47.5%

         \[\leadsto \frac{-x}{\color{blue}{z + \left(-1\right)}} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      6. metadata-eval 47.5%

         \[\leadsto \frac{-x}{z + \color{blue}{-1}} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

   5. Simplified 63.6%

      \[\leadsto \color{blue}{\frac{-x}{z + -1} - \frac{\frac{z}{z + -1} \cdot \left(t - a\right) + \frac{b}{{\left(z + -1\right)}^{2}} \cdot \left(z \cdot x\right)}{y}} \]

   6. Taylor expanded in z around inf 77.0%

      \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{t - a}{y}} \]

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.5e-291

   1. Initial program 99.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Step-by-step derivation

      1. fma-def 99.5%

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

      2. +-commutative 99.5%

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

      3. fma-def 99.5%

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

   3. Simplified 99.5%

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

   if -1.5e-291 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 15.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 52.4%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + \frac{x \cdot y}{z \cdot \left(b - y\right)}\right) - \left(\frac{a}{b - y} + \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}\right)} \]
   4. Step-by-step derivation

      1. associate--r+ 52.4%

         \[\leadsto \color{blue}{\left(\left(\frac{t}{b - y} + \frac{x \cdot y}{z \cdot \left(b - y\right)}\right) - \frac{a}{b - y}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}} \]

      2. +-commutative 52.4%

         \[\leadsto \left(\color{blue}{\left(\frac{x \cdot y}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right)} - \frac{a}{b - y}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      3. associate--l+ 52.4%

         \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right)} - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      4. *-commutative 52.4%

         \[\leadsto \left(\frac{\color{blue}{y \cdot x}}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      5. times-frac 63.9%

         \[\leadsto \left(\color{blue}{\frac{y}{z} \cdot \frac{x}{b - y}} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      6. div-sub 64.0%

         \[\leadsto \left(\frac{y}{z} \cdot \frac{x}{b - y} + \color{blue}{\frac{t - a}{b - y}}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      7. associate-/l* 99.9%

         \[\leadsto \left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - \color{blue}{\frac{y}{\frac{z \cdot {\left(b - y\right)}^{2}}{t - a}}} \]

      8. *-commutative 99.9%

         \[\leadsto \left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - \frac{y}{\frac{\color{blue}{{\left(b - y\right)}^{2} \cdot z}}{t - a}} \]

      9. associate-/l* 99.9%

         \[\leadsto \left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - \frac{y}{\color{blue}{\frac{{\left(b - y\right)}^{2}}{\frac{t - a}{z}}}} \]

   5. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - \frac{y}{\frac{{\left(b - y\right)}^{2}}{\frac{t - a}{z}}}} \]

   if -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.99999999999999991e283

   1. Initial program 99.6%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing
3. Recombined 4 regimes into one program.

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1.5 \cdot 10^{-291}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - \frac{y}{\frac{{\left(b - y\right)}^{2}}{\frac{t - a}{z}}}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+283}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - \frac{y}{\frac{{\left(b - y\right)}^{2}}{\frac{t - a}{z}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - \frac{y}{\frac{{\left(b - y\right)}^{2}}{\frac{t - a}{z}}}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_3 := \frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -1.5 \cdot 10^{-291}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+283}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (-
          (+ (* (/ y z) (/ x (- b y))) (/ (- t a) (- b y)))
          (/ y (/ (pow (- b y) 2.0) (/ (- t a) z)))))
        (t_2 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
        (t_3 (- (/ (- a t) y) (/ x (+ z -1.0)))))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -1.5e-291)
       t_2
       (if (<= t_2 0.0)
         t_1
         (if (<= t_2 2e+283) t_2 (if (<= t_2 INFINITY) t_3 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) - (y / (pow((b - y), 2.0) / ((t - a) / z)));
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_3 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -1.5e-291) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 2e+283) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) - (y / (Math.pow((b - y), 2.0) / ((t - a) / z)));
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_3 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= -1.5e-291) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 2e+283) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) - (y / (math.pow((b - y), 2.0) / ((t - a) / z)))
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	t_3 = ((a - t) / y) - (x / (z + -1.0))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= -1.5e-291:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t_1
	elif t_2 <= 2e+283:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y))) - Float64(y / Float64((Float64(b - y) ^ 2.0) / Float64(Float64(t - a) / z))))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_3 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -1.5e-291)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 2e+283)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) - (y / (((b - y) ^ 2.0) / ((t - a) / z)));
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	t_3 = ((a - t) / y) - (x / (z + -1.0));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= -1.5e-291)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 2e+283)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / N[(N[(t - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -1.5e-291], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 2e+283], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$3, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 1.99999999999999991e283 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 27.2%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 47.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} + -1 \cdot \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 47.5%

         \[\leadsto -1 \cdot \frac{x}{z - 1} + \color{blue}{\left(-\frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y}\right)} \]

      2. unsub-neg 47.5%

         \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y}} \]

      3. associate-*r/ 47.5%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z - 1}} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      4. neg-mul-1 47.5%

         \[\leadsto \frac{\color{blue}{-x}}{z - 1} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      5. sub-neg 47.5%

         \[\leadsto \frac{-x}{\color{blue}{z + \left(-1\right)}} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      6. metadata-eval 47.5%

         \[\leadsto \frac{-x}{z + \color{blue}{-1}} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

   5. Simplified 63.6%

      \[\leadsto \color{blue}{\frac{-x}{z + -1} - \frac{\frac{z}{z + -1} \cdot \left(t - a\right) + \frac{b}{{\left(z + -1\right)}^{2}} \cdot \left(z \cdot x\right)}{y}} \]

   6. Taylor expanded in z around inf 77.0%

      \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{t - a}{y}} \]

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.5e-291 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.99999999999999991e283

   1. Initial program 99.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   if -1.5e-291 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0 or +inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 15.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 52.4%

      \[\leadsto \color{blue}{\left(\frac{t}{b - y} + \frac{x \cdot y}{z \cdot \left(b - y\right)}\right) - \left(\frac{a}{b - y} + \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}\right)} \]
   4. Step-by-step derivation

      1. associate--r+ 52.4%

         \[\leadsto \color{blue}{\left(\left(\frac{t}{b - y} + \frac{x \cdot y}{z \cdot \left(b - y\right)}\right) - \frac{a}{b - y}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}}} \]

      2. +-commutative 52.4%

         \[\leadsto \left(\color{blue}{\left(\frac{x \cdot y}{z \cdot \left(b - y\right)} + \frac{t}{b - y}\right)} - \frac{a}{b - y}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      3. associate--l+ 52.4%

         \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right)} - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      4. *-commutative 52.4%

         \[\leadsto \left(\frac{\color{blue}{y \cdot x}}{z \cdot \left(b - y\right)} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      5. times-frac 63.9%

         \[\leadsto \left(\color{blue}{\frac{y}{z} \cdot \frac{x}{b - y}} + \left(\frac{t}{b - y} - \frac{a}{b - y}\right)\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      6. div-sub 64.0%

         \[\leadsto \left(\frac{y}{z} \cdot \frac{x}{b - y} + \color{blue}{\frac{t - a}{b - y}}\right) - \frac{y \cdot \left(t - a\right)}{z \cdot {\left(b - y\right)}^{2}} \]

      7. associate-/l* 99.9%

         \[\leadsto \left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - \color{blue}{\frac{y}{\frac{z \cdot {\left(b - y\right)}^{2}}{t - a}}} \]

      8. *-commutative 99.9%

         \[\leadsto \left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - \frac{y}{\frac{\color{blue}{{\left(b - y\right)}^{2} \cdot z}}{t - a}} \]

      9. associate-/l* 99.9%

         \[\leadsto \left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - \frac{y}{\color{blue}{\frac{{\left(b - y\right)}^{2}}{\frac{t - a}{z}}}} \]

   5. Simplified 99.9%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1.5 \cdot 10^{-291}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - \frac{y}{\frac{{\left(b - y\right)}^{2}}{\frac{t - a}{z}}}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+283}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) - \frac{y}{\frac{{\left(b - y\right)}^{2}}{\frac{t - a}{z}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq -1.5 \cdot 10^{-291}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+283}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
        (t_2 (- (/ (- a t) y) (/ x (+ z -1.0)))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -1.5e-291)
       t_1
       (if (<= t_1 0.0) (/ (- t a) (- b y)) (if (<= t_1 2e+283) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -1.5e-291) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (t - a) / (b - y);
	} else if (t_1 <= 2e+283) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_2 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= -1.5e-291) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (t - a) / (b - y);
	} else if (t_1 <= 2e+283) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	t_2 = ((a - t) / y) - (x / (z + -1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= -1.5e-291:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (t - a) / (b - y)
	elif t_1 <= 2e+283:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_2 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -1.5e-291)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(t - a) / Float64(b - y));
	elseif (t_1 <= 2e+283)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	t_2 = ((a - t) / y) - (x / (z + -1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= -1.5e-291)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (t - a) / (b - y);
	elseif (t_1 <= 2e+283)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -1.5e-291], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+283], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 1.99999999999999991e283 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 19.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 33.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} + -1 \cdot \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 33.6%

         \[\leadsto -1 \cdot \frac{x}{z - 1} + \color{blue}{\left(-\frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y}\right)} \]

      2. unsub-neg 33.6%

         \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y}} \]

      3. associate-*r/ 33.6%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z - 1}} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      4. neg-mul-1 33.6%

         \[\leadsto \frac{\color{blue}{-x}}{z - 1} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      5. sub-neg 33.6%

         \[\leadsto \frac{-x}{\color{blue}{z + \left(-1\right)}} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      6. metadata-eval 33.6%

         \[\leadsto \frac{-x}{z + \color{blue}{-1}} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

   5. Simplified 50.3%

      \[\leadsto \color{blue}{\frac{-x}{z + -1} - \frac{\frac{z}{z + -1} \cdot \left(t - a\right) + \frac{b}{{\left(z + -1\right)}^{2}} \cdot \left(z \cdot x\right)}{y}} \]

   6. Taylor expanded in z around inf 70.5%

      \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{t - a}{y}} \]

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -1.5e-291 or -0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 1.99999999999999991e283

   1. Initial program 99.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   if -1.5e-291 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -0.0

   1. Initial program 44.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 77.8%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -1.5 \cdot 10^{-291}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+283}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{if}\;z \leq -3.55 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1020000000000:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-123}:\\ \;\;\;\;x + z \cdot \left(\frac{t - a}{y} - \frac{b}{\frac{y}{x}}\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-306}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-236}:\\ \;\;\;\;x + \left(\left(t - a\right) \cdot \frac{z}{y} - \frac{b}{\frac{y}{x \cdot z}}\right)\\ \mathbf{elif}\;z \leq 135:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (/ (+ (* x y) (* z (- t a))) (+ y (* z b)))))
   (if (<= z -3.55e+59)
     t_1
     (if (<= z -1020000000000.0)
       (* (/ x z) (/ y (- b y)))
       (if (<= z -4.2e-65)
         t_2
         (if (<= z -4.2e-123)
           (+ x (* z (- (/ (- t a) y) (/ b (/ y x)))))
           (if (<= z -7.2e-306)
             t_2
             (if (<= z 6e-236)
               (+ x (- (* (- t a) (/ z y)) (/ b (/ y (* x z)))))
               (if (<= z 135.0) t_2 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * b));
	double tmp;
	if (z <= -3.55e+59) {
		tmp = t_1;
	} else if (z <= -1020000000000.0) {
		tmp = (x / z) * (y / (b - y));
	} else if (z <= -4.2e-65) {
		tmp = t_2;
	} else if (z <= -4.2e-123) {
		tmp = x + (z * (((t - a) / y) - (b / (y / x))));
	} else if (z <= -7.2e-306) {
		tmp = t_2;
	} else if (z <= 6e-236) {
		tmp = x + (((t - a) * (z / y)) - (b / (y / (x * z))));
	} else if (z <= 135.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = ((x * y) + (z * (t - a))) / (y + (z * b))
    if (z <= (-3.55d+59)) then
        tmp = t_1
    else if (z <= (-1020000000000.0d0)) then
        tmp = (x / z) * (y / (b - y))
    else if (z <= (-4.2d-65)) then
        tmp = t_2
    else if (z <= (-4.2d-123)) then
        tmp = x + (z * (((t - a) / y) - (b / (y / x))))
    else if (z <= (-7.2d-306)) then
        tmp = t_2
    else if (z <= 6d-236) then
        tmp = x + (((t - a) * (z / y)) - (b / (y / (x * z))))
    else if (z <= 135.0d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * b));
	double tmp;
	if (z <= -3.55e+59) {
		tmp = t_1;
	} else if (z <= -1020000000000.0) {
		tmp = (x / z) * (y / (b - y));
	} else if (z <= -4.2e-65) {
		tmp = t_2;
	} else if (z <= -4.2e-123) {
		tmp = x + (z * (((t - a) / y) - (b / (y / x))));
	} else if (z <= -7.2e-306) {
		tmp = t_2;
	} else if (z <= 6e-236) {
		tmp = x + (((t - a) * (z / y)) - (b / (y / (x * z))));
	} else if (z <= 135.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * b))
	tmp = 0
	if z <= -3.55e+59:
		tmp = t_1
	elif z <= -1020000000000.0:
		tmp = (x / z) * (y / (b - y))
	elif z <= -4.2e-65:
		tmp = t_2
	elif z <= -4.2e-123:
		tmp = x + (z * (((t - a) / y) - (b / (y / x))))
	elif z <= -7.2e-306:
		tmp = t_2
	elif z <= 6e-236:
		tmp = x + (((t - a) * (z / y)) - (b / (y / (x * z))))
	elif z <= 135.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * b)))
	tmp = 0.0
	if (z <= -3.55e+59)
		tmp = t_1;
	elseif (z <= -1020000000000.0)
		tmp = Float64(Float64(x / z) * Float64(y / Float64(b - y)));
	elseif (z <= -4.2e-65)
		tmp = t_2;
	elseif (z <= -4.2e-123)
		tmp = Float64(x + Float64(z * Float64(Float64(Float64(t - a) / y) - Float64(b / Float64(y / x)))));
	elseif (z <= -7.2e-306)
		tmp = t_2;
	elseif (z <= 6e-236)
		tmp = Float64(x + Float64(Float64(Float64(t - a) * Float64(z / y)) - Float64(b / Float64(y / Float64(x * z)))));
	elseif (z <= 135.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * b));
	tmp = 0.0;
	if (z <= -3.55e+59)
		tmp = t_1;
	elseif (z <= -1020000000000.0)
		tmp = (x / z) * (y / (b - y));
	elseif (z <= -4.2e-65)
		tmp = t_2;
	elseif (z <= -4.2e-123)
		tmp = x + (z * (((t - a) / y) - (b / (y / x))));
	elseif (z <= -7.2e-306)
		tmp = t_2;
	elseif (z <= 6e-236)
		tmp = x + (((t - a) * (z / y)) - (b / (y / (x * z))));
	elseif (z <= 135.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.55e+59], t$95$1, If[LessEqual[z, -1020000000000.0], N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.2e-65], t$95$2, If[LessEqual[z, -4.2e-123], N[(x + N[(z * N[(N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision] - N[(b / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.2e-306], t$95$2, If[LessEqual[z, 6e-236], N[(x + N[(N[(N[(t - a), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(b / N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 135.0], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.55000000000000002e59 or 135 < z

   1. Initial program 37.6%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 79.7%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -3.55000000000000002e59 < z < -1.02e12

   1. Initial program 75.6%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 59.8%

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

      1. *-commutative 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in z around inf 57.5%

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

      1. times-frac 81.5%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{y}{b - y}} \]

   8. Simplified 81.5%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{y}{b - y}} \]

   if -1.02e12 < z < -4.20000000000000006e-65 or -4.1999999999999998e-123 < z < -7.19999999999999982e-306 or 6.00000000000000027e-236 < z < 135

   1. Initial program 87.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 84.6%

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

      1. *-commutative 84.6%

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

   5. Simplified 84.6%

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

   if -4.20000000000000006e-65 < z < -4.1999999999999998e-123

   1. Initial program 57.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 57.0%

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

      1. *-commutative 57.0%

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

   5. Simplified 57.0%

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

   6. Taylor expanded in y around inf 81.9%

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

      1. associate--l+ 81.9%

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

      2. associate-/l* 81.9%

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

      3. associate-/l* 91.0%

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

      4. *-commutative 91.0%

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

   8. Simplified 91.0%

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

   9. Taylor expanded in z around 0 73.4%

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

       1. associate--r+ 73.4%

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

       2. div-sub 73.4%

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

       3. associate-/l* 91.0%

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

   11. Simplified 91.0%

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

   if -7.19999999999999982e-306 < z < 6.00000000000000027e-236

   1. Initial program 65.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 65.5%

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

      1. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in y around inf 89.5%

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

      1. associate--l+ 89.5%

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

      2. associate-/l* 89.5%

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

      3. associate-/l* 89.5%

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

      4. *-commutative 89.5%

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

   8. Simplified 89.5%

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

      1. associate-/r/ 89.6%

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

   10. Applied egg-rr 89.6%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{+59}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1020000000000:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-65}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-123}:\\ \;\;\;\;x + z \cdot \left(\frac{t - a}{y} - \frac{b}{\frac{y}{x}}\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-306}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-236}:\\ \;\;\;\;x + \left(\left(t - a\right) \cdot \frac{z}{y} - \frac{b}{\frac{y}{x \cdot z}}\right)\\ \mathbf{elif}\;z \leq 135:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{a}{\frac{y}{z}}}{z + -1} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-122}:\\ \;\;\;\;x + z \cdot \left(\frac{t - a}{y} - \frac{b}{\frac{y}{x}}\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-304}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-237}:\\ \;\;\;\;x + \left(\left(t - a\right) \cdot \frac{z}{y} - \frac{b}{\frac{y}{x \cdot z}}\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (/ (+ (* x y) (* z (- t a))) (+ y (* z b)))))
   (if (<= z -2.1e+19)
     t_1
     (if (<= z -3.9e-15)
       (- (/ (/ a (/ y z)) (+ z -1.0)) (/ x (+ z -1.0)))
       (if (<= z -5.8e-56)
         t_1
         (if (<= z -2.6e-122)
           (+ x (* z (- (/ (- t a) y) (/ b (/ y x)))))
           (if (<= z -3.9e-304)
             t_2
             (if (<= z 1.8e-237)
               (+ x (- (* (- t a) (/ z y)) (/ b (/ y (* x z)))))
               (if (<= z 1.0) t_2 t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * b));
	double tmp;
	if (z <= -2.1e+19) {
		tmp = t_1;
	} else if (z <= -3.9e-15) {
		tmp = ((a / (y / z)) / (z + -1.0)) - (x / (z + -1.0));
	} else if (z <= -5.8e-56) {
		tmp = t_1;
	} else if (z <= -2.6e-122) {
		tmp = x + (z * (((t - a) / y) - (b / (y / x))));
	} else if (z <= -3.9e-304) {
		tmp = t_2;
	} else if (z <= 1.8e-237) {
		tmp = x + (((t - a) * (z / y)) - (b / (y / (x * z))));
	} else if (z <= 1.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = ((x * y) + (z * (t - a))) / (y + (z * b))
    if (z <= (-2.1d+19)) then
        tmp = t_1
    else if (z <= (-3.9d-15)) then
        tmp = ((a / (y / z)) / (z + (-1.0d0))) - (x / (z + (-1.0d0)))
    else if (z <= (-5.8d-56)) then
        tmp = t_1
    else if (z <= (-2.6d-122)) then
        tmp = x + (z * (((t - a) / y) - (b / (y / x))))
    else if (z <= (-3.9d-304)) then
        tmp = t_2
    else if (z <= 1.8d-237) then
        tmp = x + (((t - a) * (z / y)) - (b / (y / (x * z))))
    else if (z <= 1.0d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * b));
	double tmp;
	if (z <= -2.1e+19) {
		tmp = t_1;
	} else if (z <= -3.9e-15) {
		tmp = ((a / (y / z)) / (z + -1.0)) - (x / (z + -1.0));
	} else if (z <= -5.8e-56) {
		tmp = t_1;
	} else if (z <= -2.6e-122) {
		tmp = x + (z * (((t - a) / y) - (b / (y / x))));
	} else if (z <= -3.9e-304) {
		tmp = t_2;
	} else if (z <= 1.8e-237) {
		tmp = x + (((t - a) * (z / y)) - (b / (y / (x * z))));
	} else if (z <= 1.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * b))
	tmp = 0
	if z <= -2.1e+19:
		tmp = t_1
	elif z <= -3.9e-15:
		tmp = ((a / (y / z)) / (z + -1.0)) - (x / (z + -1.0))
	elif z <= -5.8e-56:
		tmp = t_1
	elif z <= -2.6e-122:
		tmp = x + (z * (((t - a) / y) - (b / (y / x))))
	elif z <= -3.9e-304:
		tmp = t_2
	elif z <= 1.8e-237:
		tmp = x + (((t - a) * (z / y)) - (b / (y / (x * z))))
	elif z <= 1.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * b)))
	tmp = 0.0
	if (z <= -2.1e+19)
		tmp = t_1;
	elseif (z <= -3.9e-15)
		tmp = Float64(Float64(Float64(a / Float64(y / z)) / Float64(z + -1.0)) - Float64(x / Float64(z + -1.0)));
	elseif (z <= -5.8e-56)
		tmp = t_1;
	elseif (z <= -2.6e-122)
		tmp = Float64(x + Float64(z * Float64(Float64(Float64(t - a) / y) - Float64(b / Float64(y / x)))));
	elseif (z <= -3.9e-304)
		tmp = t_2;
	elseif (z <= 1.8e-237)
		tmp = Float64(x + Float64(Float64(Float64(t - a) * Float64(z / y)) - Float64(b / Float64(y / Float64(x * z)))));
	elseif (z <= 1.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * b));
	tmp = 0.0;
	if (z <= -2.1e+19)
		tmp = t_1;
	elseif (z <= -3.9e-15)
		tmp = ((a / (y / z)) / (z + -1.0)) - (x / (z + -1.0));
	elseif (z <= -5.8e-56)
		tmp = t_1;
	elseif (z <= -2.6e-122)
		tmp = x + (z * (((t - a) / y) - (b / (y / x))));
	elseif (z <= -3.9e-304)
		tmp = t_2;
	elseif (z <= 1.8e-237)
		tmp = x + (((t - a) * (z / y)) - (b / (y / (x * z))));
	elseif (z <= 1.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+19], t$95$1, If[LessEqual[z, -3.9e-15], N[(N[(N[(a / N[(y / z), $MachinePrecision]), $MachinePrecision] / N[(z + -1.0), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.8e-56], t$95$1, If[LessEqual[z, -2.6e-122], N[(x + N[(z * N[(N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision] - N[(b / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.9e-304], t$95$2, If[LessEqual[z, 1.8e-237], N[(x + N[(N[(N[(t - a), $MachinePrecision] * N[(z / y), $MachinePrecision]), $MachinePrecision] - N[(b / N[(y / N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.1e19 or -3.90000000000000026e-15 < z < -5.79999999999999982e-56 or 1 < z

   1. Initial program 41.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 78.3%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -2.1e19 < z < -3.90000000000000026e-15

   1. Initial program 52.2%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 75.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} + -1 \cdot \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 75.0%

         \[\leadsto -1 \cdot \frac{x}{z - 1} + \color{blue}{\left(-\frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y}\right)} \]

      2. unsub-neg 75.0%

         \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y}} \]

      3. associate-*r/ 75.0%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z - 1}} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      4. neg-mul-1 75.0%

         \[\leadsto \frac{\color{blue}{-x}}{z - 1} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      5. sub-neg 75.0%

         \[\leadsto \frac{-x}{\color{blue}{z + \left(-1\right)}} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      6. metadata-eval 75.0%

         \[\leadsto \frac{-x}{z + \color{blue}{-1}} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

   5. Simplified 75.0%

      \[\leadsto \color{blue}{\frac{-x}{z + -1} - \frac{\frac{z}{z + -1} \cdot \left(t - a\right) + \frac{b}{{\left(z + -1\right)}^{2}} \cdot \left(z \cdot x\right)}{y}} \]

   6. Taylor expanded in a around inf 76.7%

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

      1. mul-1-neg 76.7%

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

      2. sub-neg 76.7%

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

      3. metadata-eval 76.7%

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

      4. associate-/r* 76.7%

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

      5. distribute-neg-frac 76.7%

         \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{-\frac{a \cdot z}{y}}{z + -1}} \]

      6. associate-/l* 76.7%

         \[\leadsto \frac{-x}{z + -1} - \frac{-\color{blue}{\frac{a}{\frac{y}{z}}}}{z + -1} \]

      7. distribute-neg-frac 76.7%

         \[\leadsto \frac{-x}{z + -1} - \frac{\color{blue}{\frac{-a}{\frac{y}{z}}}}{z + -1} \]

   8. Simplified 76.7%

      \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{\frac{-a}{\frac{y}{z}}}{z + -1}} \]

   if -5.79999999999999982e-56 < z < -2.59999999999999975e-122

   1. Initial program 57.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 57.0%

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

      1. *-commutative 57.0%

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

   5. Simplified 57.0%

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

   6. Taylor expanded in y around inf 81.9%

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

      1. associate--l+ 81.9%

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

      2. associate-/l* 81.9%

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

      3. associate-/l* 91.0%

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

      4. *-commutative 91.0%

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

   8. Simplified 91.0%

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

   9. Taylor expanded in z around 0 73.4%

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

       1. associate--r+ 73.4%

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

       2. div-sub 73.4%

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

       3. associate-/l* 91.0%

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

   11. Simplified 91.0%

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

   if -2.59999999999999975e-122 < z < -3.89999999999999975e-304 or 1.79999999999999998e-237 < z < 1

   1. Initial program 88.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 87.5%

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

      1. *-commutative 87.5%

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

   5. Simplified 87.5%

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

   if -3.89999999999999975e-304 < z < 1.79999999999999998e-237

   1. Initial program 65.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 65.5%

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

      1. *-commutative 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in y around inf 89.5%

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

      1. associate--l+ 89.5%

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

      2. associate-/l* 89.5%

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

      3. associate-/l* 89.5%

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

      4. *-commutative 89.5%

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

   8. Simplified 89.5%

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

      1. associate-/r/ 89.6%

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

   10. Applied egg-rr 89.6%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+19}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-15}:\\ \;\;\;\;\frac{\frac{a}{\frac{y}{z}}}{z + -1} - \frac{x}{z + -1}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-56}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-122}:\\ \;\;\;\;x + z \cdot \left(\frac{t - a}{y} - \frac{b}{\frac{y}{x}}\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-304}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-237}:\\ \;\;\;\;x + \left(\left(t - a\right) \cdot \frac{z}{y} - \frac{b}{\frac{y}{x \cdot z}}\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{if}\;z \leq -3.55 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1020000000000:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-62}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-122}:\\ \;\;\;\;x + z \cdot \left(\frac{t - a}{y} - \frac{b}{\frac{y}{x}}\right)\\ \mathbf{elif}\;z \leq 20:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (/ (+ (* x y) (* z (- t a))) (+ y (* z b)))))
   (if (<= z -3.55e+59)
     t_1
     (if (<= z -1020000000000.0)
       (* (/ x z) (/ y (- b y)))
       (if (<= z -3.3e-62)
         t_2
         (if (<= z -2.9e-122)
           (+ x (* z (- (/ (- t a) y) (/ b (/ y x)))))
           (if (<= z 20.0) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * b));
	double tmp;
	if (z <= -3.55e+59) {
		tmp = t_1;
	} else if (z <= -1020000000000.0) {
		tmp = (x / z) * (y / (b - y));
	} else if (z <= -3.3e-62) {
		tmp = t_2;
	} else if (z <= -2.9e-122) {
		tmp = x + (z * (((t - a) / y) - (b / (y / x))));
	} else if (z <= 20.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = ((x * y) + (z * (t - a))) / (y + (z * b))
    if (z <= (-3.55d+59)) then
        tmp = t_1
    else if (z <= (-1020000000000.0d0)) then
        tmp = (x / z) * (y / (b - y))
    else if (z <= (-3.3d-62)) then
        tmp = t_2
    else if (z <= (-2.9d-122)) then
        tmp = x + (z * (((t - a) / y) - (b / (y / x))))
    else if (z <= 20.0d0) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * b));
	double tmp;
	if (z <= -3.55e+59) {
		tmp = t_1;
	} else if (z <= -1020000000000.0) {
		tmp = (x / z) * (y / (b - y));
	} else if (z <= -3.3e-62) {
		tmp = t_2;
	} else if (z <= -2.9e-122) {
		tmp = x + (z * (((t - a) / y) - (b / (y / x))));
	} else if (z <= 20.0) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * b))
	tmp = 0
	if z <= -3.55e+59:
		tmp = t_1
	elif z <= -1020000000000.0:
		tmp = (x / z) * (y / (b - y))
	elif z <= -3.3e-62:
		tmp = t_2
	elif z <= -2.9e-122:
		tmp = x + (z * (((t - a) / y) - (b / (y / x))))
	elif z <= 20.0:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * b)))
	tmp = 0.0
	if (z <= -3.55e+59)
		tmp = t_1;
	elseif (z <= -1020000000000.0)
		tmp = Float64(Float64(x / z) * Float64(y / Float64(b - y)));
	elseif (z <= -3.3e-62)
		tmp = t_2;
	elseif (z <= -2.9e-122)
		tmp = Float64(x + Float64(z * Float64(Float64(Float64(t - a) / y) - Float64(b / Float64(y / x)))));
	elseif (z <= 20.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * b));
	tmp = 0.0;
	if (z <= -3.55e+59)
		tmp = t_1;
	elseif (z <= -1020000000000.0)
		tmp = (x / z) * (y / (b - y));
	elseif (z <= -3.3e-62)
		tmp = t_2;
	elseif (z <= -2.9e-122)
		tmp = x + (z * (((t - a) / y) - (b / (y / x))));
	elseif (z <= 20.0)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.55e+59], t$95$1, If[LessEqual[z, -1020000000000.0], N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3e-62], t$95$2, If[LessEqual[z, -2.9e-122], N[(x + N[(z * N[(N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision] - N[(b / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 20.0], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.55000000000000002e59 or 20 < z

   1. Initial program 37.6%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 79.7%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -3.55000000000000002e59 < z < -1.02e12

   1. Initial program 75.6%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 59.8%

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

      1. *-commutative 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in z around inf 57.5%

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

      1. times-frac 81.5%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{y}{b - y}} \]

   8. Simplified 81.5%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{y}{b - y}} \]

   if -1.02e12 < z < -3.30000000000000004e-62 or -2.9000000000000002e-122 < z < 20

   1. Initial program 83.6%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 81.6%

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

      1. *-commutative 81.6%

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

   5. Simplified 81.6%

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

   if -3.30000000000000004e-62 < z < -2.9000000000000002e-122

   1. Initial program 57.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 57.0%

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

      1. *-commutative 57.0%

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

   5. Simplified 57.0%

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

   6. Taylor expanded in y around inf 81.9%

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

      1. associate--l+ 81.9%

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

      2. associate-/l* 81.9%

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

      3. associate-/l* 91.0%

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

      4. *-commutative 91.0%

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

   8. Simplified 91.0%

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

   9. Taylor expanded in z around 0 73.4%

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

       1. associate--r+ 73.4%

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

       2. div-sub 73.4%

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

       3. associate-/l* 91.0%

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

   11. Simplified 91.0%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{+59}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -1020000000000:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{b - y}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-62}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-122}:\\ \;\;\;\;x + z \cdot \left(\frac{t - a}{y} - \frac{b}{\frac{y}{x}}\right)\\ \mathbf{elif}\;z \leq 20:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a - t}{y} - \frac{x}{z + -1}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -0.000135:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-110}:\\ \;\;\;\;\frac{1}{\frac{\left(b - y\right) + \frac{y}{z}}{t}}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+81}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (/ (- a t) y) (/ x (+ z -1.0)))) (t_2 (/ (- t a) (- b y))))
   (if (<= y -1.4e+37)
     t_1
     (if (<= y -0.000135)
       (/ (+ (* x y) (* z (- t a))) y)
       (if (<= y -1e-74)
         t_2
         (if (<= y -5e-110)
           (/ 1.0 (/ (+ (- b y) (/ y z)) t))
           (if (<= y 9.6e+81) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / y) - (x / (z + -1.0));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (y <= -1.4e+37) {
		tmp = t_1;
	} else if (y <= -0.000135) {
		tmp = ((x * y) + (z * (t - a))) / y;
	} else if (y <= -1e-74) {
		tmp = t_2;
	} else if (y <= -5e-110) {
		tmp = 1.0 / (((b - y) + (y / z)) / t);
	} else if (y <= 9.6e+81) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((a - t) / y) - (x / (z + (-1.0d0)))
    t_2 = (t - a) / (b - y)
    if (y <= (-1.4d+37)) then
        tmp = t_1
    else if (y <= (-0.000135d0)) then
        tmp = ((x * y) + (z * (t - a))) / y
    else if (y <= (-1d-74)) then
        tmp = t_2
    else if (y <= (-5d-110)) then
        tmp = 1.0d0 / (((b - y) + (y / z)) / t)
    else if (y <= 9.6d+81) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((a - t) / y) - (x / (z + -1.0));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (y <= -1.4e+37) {
		tmp = t_1;
	} else if (y <= -0.000135) {
		tmp = ((x * y) + (z * (t - a))) / y;
	} else if (y <= -1e-74) {
		tmp = t_2;
	} else if (y <= -5e-110) {
		tmp = 1.0 / (((b - y) + (y / z)) / t);
	} else if (y <= 9.6e+81) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((a - t) / y) - (x / (z + -1.0))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if y <= -1.4e+37:
		tmp = t_1
	elif y <= -0.000135:
		tmp = ((x * y) + (z * (t - a))) / y
	elif y <= -1e-74:
		tmp = t_2
	elif y <= -5e-110:
		tmp = 1.0 / (((b - y) + (y / z)) / t)
	elif y <= 9.6e+81:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (y <= -1.4e+37)
		tmp = t_1;
	elseif (y <= -0.000135)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / y);
	elseif (y <= -1e-74)
		tmp = t_2;
	elseif (y <= -5e-110)
		tmp = Float64(1.0 / Float64(Float64(Float64(b - y) + Float64(y / z)) / t));
	elseif (y <= 9.6e+81)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((a - t) / y) - (x / (z + -1.0));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (y <= -1.4e+37)
		tmp = t_1;
	elseif (y <= -0.000135)
		tmp = ((x * y) + (z * (t - a))) / y;
	elseif (y <= -1e-74)
		tmp = t_2;
	elseif (y <= -5e-110)
		tmp = 1.0 / (((b - y) + (y / z)) / t);
	elseif (y <= 9.6e+81)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e+37], t$95$1, If[LessEqual[y, -0.000135], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -1e-74], t$95$2, If[LessEqual[y, -5e-110], N[(1.0 / N[(N[(N[(b - y), $MachinePrecision] + N[(y / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.6e+81], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3999999999999999e37 or 9.59999999999999958e81 < y

   1. Initial program 42.6%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 62.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} + -1 \cdot \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 62.1%

         \[\leadsto -1 \cdot \frac{x}{z - 1} + \color{blue}{\left(-\frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y}\right)} \]

      2. unsub-neg 62.1%

         \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y}} \]

      3. associate-*r/ 62.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z - 1}} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      4. neg-mul-1 62.1%

         \[\leadsto \frac{\color{blue}{-x}}{z - 1} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      5. sub-neg 62.1%

         \[\leadsto \frac{-x}{\color{blue}{z + \left(-1\right)}} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      6. metadata-eval 62.1%

         \[\leadsto \frac{-x}{z + \color{blue}{-1}} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

   5. Simplified 73.2%

      \[\leadsto \color{blue}{\frac{-x}{z + -1} - \frac{\frac{z}{z + -1} \cdot \left(t - a\right) + \frac{b}{{\left(z + -1\right)}^{2}} \cdot \left(z \cdot x\right)}{y}} \]

   6. Taylor expanded in z around inf 69.5%

      \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{t - a}{y}} \]

   if -1.3999999999999999e37 < y < -1.35000000000000002e-4

   1. Initial program 85.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 71.4%

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

      1. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in b around 0 64.1%

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

   if -1.35000000000000002e-4 < y < -9.99999999999999958e-75 or -5e-110 < y < 9.59999999999999958e81

   1. Initial program 75.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 71.5%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -9.99999999999999958e-75 < y < -5e-110

   1. Initial program 82.2%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 47.0%

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

      1. associate-/l* 64.5%

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

      2. +-commutative 64.5%

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

      3. fma-udef 64.5%

         \[\leadsto \frac{t}{\frac{\color{blue}{\mathsf{fma}\left(z, b - y, y\right)}}{z}} \]

   5. Simplified 64.5%

      \[\leadsto \color{blue}{\frac{t}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{z}}} \]

   6. Taylor expanded in z around 0 64.5%

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

      1. clear-num 64.5%

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

      2. inv-pow 64.5%

         \[\leadsto \color{blue}{{\left(\frac{\left(b + \frac{y}{z}\right) - y}{t}\right)}^{-1}} \]

      3. associate--l+ 64.5%

         \[\leadsto {\left(\frac{\color{blue}{b + \left(\frac{y}{z} - y\right)}}{t}\right)}^{-1} \]

   8. Applied egg-rr 64.5%

      \[\leadsto \color{blue}{{\left(\frac{b + \left(\frac{y}{z} - y\right)}{t}\right)}^{-1}} \]
   9. Step-by-step derivation

      1. unpow-1 64.5%

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

      2. associate-+r- 64.5%

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

      3. +-commutative 64.5%

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

      4. associate-+r- 64.5%

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

      5. +-commutative 64.5%

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

   10. Simplified 64.5%

       \[\leadsto \color{blue}{\frac{1}{\frac{\left(b - y\right) + \frac{y}{z}}{t}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;y \leq -0.000135:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-74}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-110}:\\ \;\;\;\;\frac{1}{\frac{\left(b - y\right) + \frac{y}{z}}{t}}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+81}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot y + z \cdot \left(t - a\right)\\ t_2 := \frac{a - t}{y} - \frac{x}{z + -1}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;y \leq -8.1 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{t\_1}{y}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-110}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-173}:\\ \;\;\;\;\frac{t\_1}{z \cdot b}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+88}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (* x y) (* z (- t a))))
        (t_2 (- (/ (- a t) y) (/ x (+ z -1.0))))
        (t_3 (/ (- t a) (- b y))))
   (if (<= y -8.1e+42)
     t_2
     (if (<= y -7.5e-7)
       (/ t_1 y)
       (if (<= y -5.6e-110)
         t_3
         (if (<= y -1.55e-173)
           (/ t_1 (* z b))
           (if (<= y 6.4e+88) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * (t - a));
	double t_2 = ((a - t) / y) - (x / (z + -1.0));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (y <= -8.1e+42) {
		tmp = t_2;
	} else if (y <= -7.5e-7) {
		tmp = t_1 / y;
	} else if (y <= -5.6e-110) {
		tmp = t_3;
	} else if (y <= -1.55e-173) {
		tmp = t_1 / (z * b);
	} else if (y <= 6.4e+88) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (x * y) + (z * (t - a))
    t_2 = ((a - t) / y) - (x / (z + (-1.0d0)))
    t_3 = (t - a) / (b - y)
    if (y <= (-8.1d+42)) then
        tmp = t_2
    else if (y <= (-7.5d-7)) then
        tmp = t_1 / y
    else if (y <= (-5.6d-110)) then
        tmp = t_3
    else if (y <= (-1.55d-173)) then
        tmp = t_1 / (z * b)
    else if (y <= 6.4d+88) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * y) + (z * (t - a));
	double t_2 = ((a - t) / y) - (x / (z + -1.0));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (y <= -8.1e+42) {
		tmp = t_2;
	} else if (y <= -7.5e-7) {
		tmp = t_1 / y;
	} else if (y <= -5.6e-110) {
		tmp = t_3;
	} else if (y <= -1.55e-173) {
		tmp = t_1 / (z * b);
	} else if (y <= 6.4e+88) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * y) + (z * (t - a))
	t_2 = ((a - t) / y) - (x / (z + -1.0))
	t_3 = (t - a) / (b - y)
	tmp = 0
	if y <= -8.1e+42:
		tmp = t_2
	elif y <= -7.5e-7:
		tmp = t_1 / y
	elif y <= -5.6e-110:
		tmp = t_3
	elif y <= -1.55e-173:
		tmp = t_1 / (z * b)
	elif y <= 6.4e+88:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * y) + Float64(z * Float64(t - a)))
	t_2 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (y <= -8.1e+42)
		tmp = t_2;
	elseif (y <= -7.5e-7)
		tmp = Float64(t_1 / y);
	elseif (y <= -5.6e-110)
		tmp = t_3;
	elseif (y <= -1.55e-173)
		tmp = Float64(t_1 / Float64(z * b));
	elseif (y <= 6.4e+88)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * y) + (z * (t - a));
	t_2 = ((a - t) / y) - (x / (z + -1.0));
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (y <= -8.1e+42)
		tmp = t_2;
	elseif (y <= -7.5e-7)
		tmp = t_1 / y;
	elseif (y <= -5.6e-110)
		tmp = t_3;
	elseif (y <= -1.55e-173)
		tmp = t_1 / (z * b);
	elseif (y <= 6.4e+88)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.1e+42], t$95$2, If[LessEqual[y, -7.5e-7], N[(t$95$1 / y), $MachinePrecision], If[LessEqual[y, -5.6e-110], t$95$3, If[LessEqual[y, -1.55e-173], N[(t$95$1 / N[(z * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e+88], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.0999999999999996e42 or 6.3999999999999997e88 < y

   1. Initial program 42.6%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 62.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} + -1 \cdot \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y}} \]
   4. Step-by-step derivation

      1. mul-1-neg 62.1%

         \[\leadsto -1 \cdot \frac{x}{z - 1} + \color{blue}{\left(-\frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y}\right)} \]

      2. unsub-neg 62.1%

         \[\leadsto \color{blue}{-1 \cdot \frac{x}{z - 1} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y}} \]

      3. associate-*r/ 62.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot x}{z - 1}} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      4. neg-mul-1 62.1%

         \[\leadsto \frac{\color{blue}{-x}}{z - 1} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      5. sub-neg 62.1%

         \[\leadsto \frac{-x}{\color{blue}{z + \left(-1\right)}} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

      6. metadata-eval 62.1%

         \[\leadsto \frac{-x}{z + \color{blue}{-1}} - \frac{\frac{z \cdot \left(t - a\right)}{z - 1} - -1 \cdot \frac{b \cdot \left(x \cdot z\right)}{{\left(z - 1\right)}^{2}}}{y} \]

   5. Simplified 73.2%

      \[\leadsto \color{blue}{\frac{-x}{z + -1} - \frac{\frac{z}{z + -1} \cdot \left(t - a\right) + \frac{b}{{\left(z + -1\right)}^{2}} \cdot \left(z \cdot x\right)}{y}} \]

   6. Taylor expanded in z around inf 69.5%

      \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{t - a}{y}} \]

   if -8.0999999999999996e42 < y < -7.5000000000000002e-7

   1. Initial program 85.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 71.4%

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

      1. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   6. Taylor expanded in b around 0 64.1%

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

   if -7.5000000000000002e-7 < y < -5.6000000000000001e-110 or -1.55000000000000003e-173 < y < 6.3999999999999997e88

   1. Initial program 73.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 69.3%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -5.6000000000000001e-110 < y < -1.55000000000000003e-173

   1. Initial program 92.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 85.3%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.1 \cdot 10^{+42}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-7}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-110}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-173}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{z \cdot b}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+88}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 42.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{-9}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-287}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))) (t_2 (/ x (- 1.0 z))))
   (if (<= y -2.1e-9)
     t_2
     (if (<= y -5.2e-271)
       t_1
       (if (<= y 9.4e-287) (/ (- a) b) (if (<= y 7.2e+120) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.1e-9) {
		tmp = t_2;
	} else if (y <= -5.2e-271) {
		tmp = t_1;
	} else if (y <= 9.4e-287) {
		tmp = -a / b;
	} else if (y <= 7.2e+120) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (b - y)
    t_2 = x / (1.0d0 - z)
    if (y <= (-2.1d-9)) then
        tmp = t_2
    else if (y <= (-5.2d-271)) then
        tmp = t_1
    else if (y <= 9.4d-287) then
        tmp = -a / b
    else if (y <= 7.2d+120) 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 t_1 = t / (b - y);
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -2.1e-9) {
		tmp = t_2;
	} else if (y <= -5.2e-271) {
		tmp = t_1;
	} else if (y <= 9.4e-287) {
		tmp = -a / b;
	} else if (y <= 7.2e+120) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -2.1e-9:
		tmp = t_2
	elif y <= -5.2e-271:
		tmp = t_1
	elif y <= 9.4e-287:
		tmp = -a / b
	elif y <= 7.2e+120:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -2.1e-9)
		tmp = t_2;
	elseif (y <= -5.2e-271)
		tmp = t_1;
	elseif (y <= 9.4e-287)
		tmp = Float64(Float64(-a) / b);
	elseif (y <= 7.2e+120)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -2.1e-9)
		tmp = t_2;
	elseif (y <= -5.2e-271)
		tmp = t_1;
	elseif (y <= 9.4e-287)
		tmp = -a / b;
	elseif (y <= 7.2e+120)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e-9], t$95$2, If[LessEqual[y, -5.2e-271], t$95$1, If[LessEqual[y, 9.4e-287], N[((-a) / b), $MachinePrecision], If[LessEqual[y, 7.2e+120], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.10000000000000019e-9 or 7.20000000000000031e120 < y

   1. Initial program 45.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 60.7%

      \[\leadsto \color{blue}{\frac{x}{1 + -1 \cdot z}} \]
   4. Step-by-step derivation

      1. mul-1-neg 60.7%

         \[\leadsto \frac{x}{1 + \color{blue}{\left(-z\right)}} \]

      2. unsub-neg 60.7%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   5. Simplified 60.7%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   if -2.10000000000000019e-9 < y < -5.2e-271 or 9.3999999999999997e-287 < y < 7.20000000000000031e120

   1. Initial program 77.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 36.2%

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

      1. associate-/l* 47.1%

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

      2. +-commutative 47.1%

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

      3. fma-udef 47.1%

         \[\leadsto \frac{t}{\frac{\color{blue}{\mathsf{fma}\left(z, b - y, y\right)}}{z}} \]

   5. Simplified 47.1%

      \[\leadsto \color{blue}{\frac{t}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{z}}} \]

   6. Taylor expanded in z around inf 45.3%

      \[\leadsto \frac{t}{\color{blue}{b - y}} \]

   if -5.2e-271 < y < 9.3999999999999997e-287

   1. Initial program 69.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 59.8%

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

   4. Taylor expanded in a around inf 77.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{a}{b}} \]
   5. Step-by-step derivation

      1. associate-*r/ 77.5%

         \[\leadsto \color{blue}{\frac{-1 \cdot a}{b}} \]

      2. neg-mul-1 77.5%

         \[\leadsto \frac{\color{blue}{-a}}{b} \]

   6. Simplified 77.5%

      \[\leadsto \color{blue}{\frac{-a}{b}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-271}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-287}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+120}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 34.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-279}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-285}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-96}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.15e-38)
   x
   (if (<= y -1.9e-279)
     (/ t b)
     (if (<= y 1.15e-285) (/ (- a) b) (if (<= y 4.2e-96) (/ t b) x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.15e-38) {
		tmp = x;
	} else if (y <= -1.9e-279) {
		tmp = t / b;
	} else if (y <= 1.15e-285) {
		tmp = -a / b;
	} else if (y <= 4.2e-96) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (y <= (-1.15d-38)) then
        tmp = x
    else if (y <= (-1.9d-279)) then
        tmp = t / b
    else if (y <= 1.15d-285) then
        tmp = -a / b
    else if (y <= 4.2d-96) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.15e-38) {
		tmp = x;
	} else if (y <= -1.9e-279) {
		tmp = t / b;
	} else if (y <= 1.15e-285) {
		tmp = -a / b;
	} else if (y <= 4.2e-96) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.15e-38:
		tmp = x
	elif y <= -1.9e-279:
		tmp = t / b
	elif y <= 1.15e-285:
		tmp = -a / b
	elif y <= 4.2e-96:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.15e-38)
		tmp = x;
	elseif (y <= -1.9e-279)
		tmp = Float64(t / b);
	elseif (y <= 1.15e-285)
		tmp = Float64(Float64(-a) / b);
	elseif (y <= 4.2e-96)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.15e-38)
		tmp = x;
	elseif (y <= -1.9e-279)
		tmp = t / b;
	elseif (y <= 1.15e-285)
		tmp = -a / b;
	elseif (y <= 4.2e-96)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.15e-38], x, If[LessEqual[y, -1.9e-279], N[(t / b), $MachinePrecision], If[LessEqual[y, 1.15e-285], N[((-a) / b), $MachinePrecision], If[LessEqual[y, 4.2e-96], N[(t / b), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15000000000000001e-38 or 4.20000000000000002e-96 < y

   1. Initial program 52.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 33.9%

      \[\leadsto \color{blue}{x} \]

   if -1.15000000000000001e-38 < y < -1.90000000000000016e-279 or 1.14999999999999998e-285 < y < 4.20000000000000002e-96

   1. Initial program 78.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 43.0%

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

      1. associate-/l* 54.8%

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

      2. +-commutative 54.8%

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

      3. fma-udef 54.8%

         \[\leadsto \frac{t}{\frac{\color{blue}{\mathsf{fma}\left(z, b - y, y\right)}}{z}} \]

   5. Simplified 54.8%

      \[\leadsto \color{blue}{\frac{t}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{z}}} \]

   6. Taylor expanded in b around inf 44.4%

      \[\leadsto \frac{t}{\color{blue}{b}} \]

   if -1.90000000000000016e-279 < y < 1.14999999999999998e-285

   1. Initial program 69.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 59.8%

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

   4. Taylor expanded in a around inf 77.5%

      \[\leadsto \color{blue}{-1 \cdot \frac{a}{b}} \]
   5. Step-by-step derivation

      1. associate-*r/ 77.5%

         \[\leadsto \color{blue}{\frac{-1 \cdot a}{b}} \]

      2. neg-mul-1 77.5%

         \[\leadsto \frac{\color{blue}{-a}}{b} \]

   6. Simplified 77.5%

      \[\leadsto \color{blue}{\frac{-a}{b}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-279}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-285}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-96}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+19}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+120}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -2.3e-5)
     t_1
     (if (<= y 3.7e+19)
       (/ (- t a) b)
       (if (<= y 1.28e+120) (/ t (- b y)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -2.3e-5) {
		tmp = t_1;
	} else if (y <= 3.7e+19) {
		tmp = (t - a) / b;
	} else if (y <= 1.28e+120) {
		tmp = t / (b - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-2.3d-5)) then
        tmp = t_1
    else if (y <= 3.7d+19) then
        tmp = (t - a) / b
    else if (y <= 1.28d+120) then
        tmp = t / (b - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -2.3e-5) {
		tmp = t_1;
	} else if (y <= 3.7e+19) {
		tmp = (t - a) / b;
	} else if (y <= 1.28e+120) {
		tmp = t / (b - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -2.3e-5:
		tmp = t_1
	elif y <= 3.7e+19:
		tmp = (t - a) / b
	elif y <= 1.28e+120:
		tmp = t / (b - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -2.3e-5)
		tmp = t_1;
	elseif (y <= 3.7e+19)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 1.28e+120)
		tmp = Float64(t / Float64(b - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -2.3e-5)
		tmp = t_1;
	elseif (y <= 3.7e+19)
		tmp = (t - a) / b;
	elseif (y <= 1.28e+120)
		tmp = t / (b - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e-5], t$95$1, If[LessEqual[y, 3.7e+19], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 1.28e+120], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3e-5 or 1.27999999999999996e120 < y

   1. Initial program 44.6%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 61.2%

      \[\leadsto \color{blue}{\frac{x}{1 + -1 \cdot z}} \]
   4. Step-by-step derivation

      1. mul-1-neg 61.2%

         \[\leadsto \frac{x}{1 + \color{blue}{\left(-z\right)}} \]

      2. unsub-neg 61.2%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   5. Simplified 61.2%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   if -2.3e-5 < y < 3.7e19

   1. Initial program 76.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 57.7%

      \[\leadsto \color{blue}{\frac{t - a}{b}} \]

   if 3.7e19 < y < 1.27999999999999996e120

   1. Initial program 78.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 41.1%

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

      1. associate-/l* 51.5%

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

      2. +-commutative 51.5%

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

      3. fma-udef 51.5%

         \[\leadsto \frac{t}{\frac{\color{blue}{\mathsf{fma}\left(z, b - y, y\right)}}{z}} \]

   5. Simplified 51.5%

      \[\leadsto \color{blue}{\frac{t}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{z}}} \]

   6. Taylor expanded in z around inf 46.3%

      \[\leadsto \frac{t}{\color{blue}{b - y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+19}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+120}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-85}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+121}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -5.8e-5)
     t_1
     (if (<= y 4.2e-85)
       (/ (- t a) b)
       (if (<= y 4.1e+121) (/ (- a t) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -5.8e-5) {
		tmp = t_1;
	} else if (y <= 4.2e-85) {
		tmp = (t - a) / b;
	} else if (y <= 4.1e+121) {
		tmp = (a - t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-5.8d-5)) then
        tmp = t_1
    else if (y <= 4.2d-85) then
        tmp = (t - a) / b
    else if (y <= 4.1d+121) then
        tmp = (a - t) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -5.8e-5) {
		tmp = t_1;
	} else if (y <= 4.2e-85) {
		tmp = (t - a) / b;
	} else if (y <= 4.1e+121) {
		tmp = (a - t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -5.8e-5:
		tmp = t_1
	elif y <= 4.2e-85:
		tmp = (t - a) / b
	elif y <= 4.1e+121:
		tmp = (a - t) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -5.8e-5)
		tmp = t_1;
	elseif (y <= 4.2e-85)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 4.1e+121)
		tmp = Float64(Float64(a - t) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -5.8e-5)
		tmp = t_1;
	elseif (y <= 4.2e-85)
		tmp = (t - a) / b;
	elseif (y <= 4.1e+121)
		tmp = (a - t) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e-5], t$95$1, If[LessEqual[y, 4.2e-85], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 4.1e+121], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8e-5 or 4.1e121 < y

   1. Initial program 44.2%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 61.7%

      \[\leadsto \color{blue}{\frac{x}{1 + -1 \cdot z}} \]
   4. Step-by-step derivation

      1. mul-1-neg 61.7%

         \[\leadsto \frac{x}{1 + \color{blue}{\left(-z\right)}} \]

      2. unsub-neg 61.7%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   5. Simplified 61.7%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   if -5.8e-5 < y < 4.2e-85

   1. Initial program 76.6%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 62.6%

      \[\leadsto \color{blue}{\frac{t - a}{b}} \]

   if 4.2e-85 < y < 4.1e121

   1. Initial program 76.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 58.6%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   4. Taylor expanded in b around 0 37.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{t - a}{y}} \]
   5. Step-by-step derivation

      1. associate-*r/ 37.4%

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

      2. neg-mul-1 37.4%

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

      3. neg-sub0 37.4%

         \[\leadsto \frac{\color{blue}{0 - \left(t - a\right)}}{y} \]

      4. associate--r- 37.4%

         \[\leadsto \frac{\color{blue}{\left(0 - t\right) + a}}{y} \]

      5. neg-sub0 37.4%

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

   6. Simplified 37.4%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-85}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+121}:\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.000215 \lor \neg \left(y \leq 2.9 \cdot 10^{+122}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -0.000215) (not (<= y 2.9e+122)))
   (/ x (- 1.0 z))
   (/ (- t a) (- b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -0.000215) || !(y <= 2.9e+122)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((y <= (-0.000215d0)) .or. (.not. (y <= 2.9d+122))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / (b - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -0.000215) || !(y <= 2.9e+122)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -0.000215) or not (y <= 2.9e+122):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -0.000215) || !(y <= 2.9e+122))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -0.000215) || ~((y <= 2.9e+122)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -0.000215], N[Not[LessEqual[y, 2.9e+122]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.14999999999999995e-4 or 2.9000000000000001e122 < y

   1. Initial program 44.2%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 61.7%

      \[\leadsto \color{blue}{\frac{x}{1 + -1 \cdot z}} \]
   4. Step-by-step derivation

      1. mul-1-neg 61.7%

         \[\leadsto \frac{x}{1 + \color{blue}{\left(-z\right)}} \]

      2. unsub-neg 61.7%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   5. Simplified 61.7%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   if -2.14999999999999995e-4 < y < 2.9000000000000001e122

   1. Initial program 76.6%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 68.4%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.000215 \lor \neg \left(y \leq 2.9 \cdot 10^{+122}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 44.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-65} \lor \neg \left(z \leq 1.25 \cdot 10^{-47}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.15e-65) (not (<= z 1.25e-47))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.15e-65) || !(z <= 1.25e-47)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((z <= (-1.15d-65)) .or. (.not. (z <= 1.25d-47))) then
        tmp = t / (b - y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.15e-65) || !(z <= 1.25e-47)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.15e-65) or not (z <= 1.25e-47):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.15e-65) || !(z <= 1.25e-47))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.15e-65) || ~((z <= 1.25e-47)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.15e-65], N[Not[LessEqual[z, 1.25e-47]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e-65 or 1.25000000000000003e-47 < z

   1. Initial program 46.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 23.3%

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

      1. associate-/l* 34.7%

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

      2. +-commutative 34.7%

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

      3. fma-udef 34.7%

         \[\leadsto \frac{t}{\frac{\color{blue}{\mathsf{fma}\left(z, b - y, y\right)}}{z}} \]

   5. Simplified 34.7%

      \[\leadsto \color{blue}{\frac{t}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{z}}} \]

   6. Taylor expanded in z around inf 41.0%

      \[\leadsto \frac{t}{\color{blue}{b - y}} \]

   if -1.15e-65 < z < 1.25000000000000003e-47

   1. Initial program 80.6%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 49.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-65} \lor \neg \left(z \leq 1.25 \cdot 10^{-47}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 34.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-95}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2e-37) x (if (<= y 1.15e-95) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2e-37) {
		tmp = x;
	} else if (y <= 1.15e-95) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (y <= (-2d-37)) then
        tmp = x
    else if (y <= 1.15d-95) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2e-37) {
		tmp = x;
	} else if (y <= 1.15e-95) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2e-37:
		tmp = x
	elif y <= 1.15e-95:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2e-37)
		tmp = x;
	elseif (y <= 1.15e-95)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2e-37)
		tmp = x;
	elseif (y <= 1.15e-95)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2e-37], x, If[LessEqual[y, 1.15e-95], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.00000000000000013e-37 or 1.15e-95 < y

   1. Initial program 52.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 33.9%

      \[\leadsto \color{blue}{x} \]

   if -2.00000000000000013e-37 < y < 1.15e-95

   1. Initial program 77.2%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 40.2%

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

      1. associate-/l* 50.4%

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

      2. +-commutative 50.4%

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

      3. fma-udef 50.4%

         \[\leadsto \frac{t}{\frac{\color{blue}{\mathsf{fma}\left(z, b - y, y\right)}}{z}} \]

   5. Simplified 50.4%

      \[\leadsto \color{blue}{\frac{t}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{z}}} \]

   6. Taylor expanded in b around inf 41.2%

      \[\leadsto \frac{t}{\color{blue}{b}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-95}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 25.5% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 61.6%

   \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]
2. Add Preprocessing

3. Taylor expanded in z around 0 24.3%

   \[\leadsto \color{blue}{x} \]

4. Final simplification 24.3%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 73.6% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (/ (+ (* z t) (* y x)) (+ y (* z (- b y)))) (/ a (+ (- b y) (/ y z)))))

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = (((z * t) + (y * x)) / (y + (z * (b - y)))) - (a / ((b - y) + (y / z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(N[(z * t), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(N[(b - y), $MachinePrecision] + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024029 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

  :herbie-target
  (- (/ (+ (* z t) (* y x)) (+ y (* z (- b y)))) (/ a (+ (- b y) (/ y z))))

  (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))