Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.9% → 93.5%

Time: 17.4s

Alternatives: 15

Speedup: 1.3×

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: 66.9% 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: 93.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{a - t}{y} - \frac{x}{z + -1}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t_3}{t_1}\\ t_5 := \frac{y}{{\left(b - y\right)}^{2}} \cdot \frac{a - t}{z}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_4 \leq -2 \cdot 10^{-295}:\\ \;\;\;\;\frac{t_3}{t_1} + \frac{x \cdot y}{t_1}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;\frac{\frac{x \cdot y}{z}}{b - y} + \left(\frac{t}{b - y} + \left(t_5 - \frac{a}{b - y}\right)\right)\\ \mathbf{elif}\;t_4 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, \frac{x}{b - y}, \frac{t - a}{b - y} + t_5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (- (/ (- a t) y) (/ x (+ z -1.0))))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) t_1))
        (t_5 (* (/ y (pow (- b y) 2.0)) (/ (- a t) z))))
   (if (<= t_4 (- INFINITY))
     t_2
     (if (<= t_4 -2e-295)
       (+ (/ t_3 t_1) (/ (* x y) t_1))
       (if (<= t_4 0.0)
         (+ (/ (/ (* x y) z) (- b y)) (+ (/ t (- b y)) (- t_5 (/ a (- b y)))))
         (if (<= t_4 5e+302)
           t_4
           (if (<= t_4 INFINITY)
             t_2
             (fma (/ y z) (/ x (- b y)) (+ (/ (- t a) (- b y)) t_5)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((a - t) / y) - (x / (z + -1.0));
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double t_5 = (y / pow((b - y), 2.0)) * ((a - t) / z);
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_4 <= -2e-295) {
		tmp = (t_3 / t_1) + ((x * y) / t_1);
	} else if (t_4 <= 0.0) {
		tmp = (((x * y) / z) / (b - y)) + ((t / (b - y)) + (t_5 - (a / (b - y))));
	} else if (t_4 <= 5e+302) {
		tmp = t_4;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = fma((y / z), (x / (b - y)), (((t - a) / (b - y)) + t_5));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(x * y) + t_3) / t_1)
	t_5 = Float64(Float64(y / (Float64(b - y) ^ 2.0)) * Float64(Float64(a - t) / z))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_4 <= -2e-295)
		tmp = Float64(Float64(t_3 / t_1) + Float64(Float64(x * y) / t_1));
	elseif (t_4 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(x * y) / z) / Float64(b - y)) + Float64(Float64(t / Float64(b - y)) + Float64(t_5 - Float64(a / Float64(b - y)))));
	elseif (t_4 <= 5e+302)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_2;
	else
		tmp = fma(Float64(y / z), Float64(x / Float64(b - y)), Float64(Float64(Float64(t - a) / Float64(b - y)) + t_5));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $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[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(y / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$2, If[LessEqual[t$95$4, -2e-295], N[(N[(t$95$3 / t$95$1), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 0.0], N[(N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(t$95$5 - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 5e+302], t$95$4, If[LessEqual[t$95$4, Infinity], t$95$2, N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 5e302 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 28.0%

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

   2. Taylor expanded in y around -inf 51.2%

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

      1. mul-1-neg 51.2%

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

      2. unsub-neg 51.2%

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

      3. mul-1-neg 51.2%

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

      4. distribute-neg-frac 51.2%

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

      5. cancel-sign-sub-inv 51.2%

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

      6. associate-/l* 65.9%

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

      7. metadata-eval 65.9%

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

      8. *-lft-identity 65.9%

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

      9. associate-/l* 67.7%

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

   4. Simplified 67.7%

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

   5. Taylor expanded in z around inf 81.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.00000000000000012e-295

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 99.6%

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

   if -2.00000000000000012e-295 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 26.7%

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

   2. Taylor expanded in z around inf 60.3%

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

      1. associate--l+ 60.3%

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

      2. associate-/r* 77.2%

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

      3. +-commutative 77.2%

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

      4. times-frac 99.9%

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

   4. Simplified 99.9%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5e302

   1. Initial program 99.6%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around inf 44.2%

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

      1. associate--l+ 44.2%

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

      2. times-frac 58.7%

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

      3. fma-def 58.7%

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

      4. +-commutative 58.7%

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

      5. *-commutative 58.7%

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

      6. associate--r+ 58.7%

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

      7. div-sub 58.7%

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

      8. *-commutative 58.7%

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

      9. times-frac 99.7%

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

   4. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{z}, \frac{x}{b - y}, \frac{t - a}{b - y} - \frac{t - a}{z} \cdot \frac{y}{{\left(b - y\right)}^{2}}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-295}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{\frac{x \cdot y}{z}}{b - y} + \left(\frac{t}{b - y} + \left(\frac{y}{{\left(b - y\right)}^{2}} \cdot \frac{a - t}{z} - \frac{a}{b - y}\right)\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{z}, \frac{x}{b - y}, \frac{t - a}{b - y} + \frac{y}{{\left(b - y\right)}^{2}} \cdot \frac{a - t}{z}\right)\\ \end{array} \]

Alternative 2: 93.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y} + \frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t_3}{t_1}\\ t_5 := \frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq -2 \cdot 10^{-295}:\\ \;\;\;\;\frac{t_3}{t_1} + \frac{x \cdot y}{t_1}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_4 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2
         (+
          (/ (- t a) (- b y))
          (/ (+ (/ y (/ (- b y) x)) (/ (- a t) (/ (pow (- b y) 2.0) y))) z)))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) t_1))
        (t_5 (- (/ (- a t) y) (/ x (+ z -1.0)))))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 -2e-295)
       (+ (/ t_3 t_1) (/ (* x y) t_1))
       (if (<= t_4 0.0)
         t_2
         (if (<= t_4 5e+302) t_4 (if (<= t_4 INFINITY) t_5 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = ((t - a) / (b - y)) + (((y / ((b - y) / x)) + ((a - t) / (pow((b - y), 2.0) / y))) / z);
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double t_5 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= -2e-295) {
		tmp = (t_3 / t_1) + ((x * y) / t_1);
	} else if (t_4 <= 0.0) {
		tmp = t_2;
	} else if (t_4 <= 5e+302) {
		tmp = t_4;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5;
	} 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 = y + (z * (b - y));
	double t_2 = ((t - a) / (b - y)) + (((y / ((b - y) / x)) + ((a - t) / (Math.pow((b - y), 2.0) / y))) / z);
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double t_5 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else if (t_4 <= -2e-295) {
		tmp = (t_3 / t_1) + ((x * y) / t_1);
	} else if (t_4 <= 0.0) {
		tmp = t_2;
	} else if (t_4 <= 5e+302) {
		tmp = t_4;
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = ((t - a) / (b - y)) + (((y / ((b - y) / x)) + ((a - t) / (math.pow((b - y), 2.0) / y))) / z)
	t_3 = z * (t - a)
	t_4 = ((x * y) + t_3) / t_1
	t_5 = ((a - t) / y) - (x / (z + -1.0))
	tmp = 0
	if t_4 <= -math.inf:
		tmp = t_5
	elif t_4 <= -2e-295:
		tmp = (t_3 / t_1) + ((x * y) / t_1)
	elif t_4 <= 0.0:
		tmp = t_2
	elif t_4 <= 5e+302:
		tmp = t_4
	elif t_4 <= math.inf:
		tmp = t_5
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(Float64(Float64(y / Float64(Float64(b - y) / x)) + Float64(Float64(a - t) / Float64((Float64(b - y) ^ 2.0) / y))) / z))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(x * y) + t_3) / t_1)
	t_5 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= -2e-295)
		tmp = Float64(Float64(t_3 / t_1) + Float64(Float64(x * y) / t_1));
	elseif (t_4 <= 0.0)
		tmp = t_2;
	elseif (t_4 <= 5e+302)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = ((t - a) / (b - y)) + (((y / ((b - y) / x)) + ((a - t) / (((b - y) ^ 2.0) / y))) / z);
	t_3 = z * (t - a);
	t_4 = ((x * y) + t_3) / t_1;
	t_5 = ((a - t) / y) - (x / (z + -1.0));
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = t_5;
	elseif (t_4 <= -2e-295)
		tmp = (t_3 / t_1) + ((x * y) / t_1);
	elseif (t_4 <= 0.0)
		tmp = t_2;
	elseif (t_4 <= 5e+302)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / N[(N[(b - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, -2e-295], N[(N[(t$95$3 / t$95$1), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 0.0], t$95$2, If[LessEqual[t$95$4, 5e+302], t$95$4, If[LessEqual[t$95$4, Infinity], t$95$5, t$95$2]]]]]]]]]]

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 5e302 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 28.0%

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

   2. Taylor expanded in y around -inf 51.2%

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

      1. mul-1-neg 51.2%

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

      2. unsub-neg 51.2%

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

      3. mul-1-neg 51.2%

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

      4. distribute-neg-frac 51.2%

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

      5. cancel-sign-sub-inv 51.2%

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

      6. associate-/l* 65.9%

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

      7. metadata-eval 65.9%

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

      8. *-lft-identity 65.9%

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

      9. associate-/l* 67.7%

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

   4. Simplified 67.7%

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

   5. Taylor expanded in z around inf 81.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.00000000000000012e-295

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 99.6%

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

   if -2.00000000000000012e-295 < (/.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 10.5%

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

   2. Taylor expanded in z around -inf 57.4%

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

      1. +-commutative 57.4%

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

      2. associate--l+ 57.4%

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

   4. Simplified 98.0%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5e302

   1. Initial program 99.6%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-295}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z}\\ \end{array} \]

Alternative 3: 93.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := {\left(b - y\right)}^{2}\\ t_4 := \frac{x \cdot y + t_2}{t_1}\\ t_5 := \frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq -2 \cdot 10^{-295}:\\ \;\;\;\;\frac{t_2}{t_1} + \frac{x \cdot y}{t_1}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;\frac{\frac{x \cdot y}{z}}{b - y} + \left(\frac{t}{b - y} + \left(\frac{y}{t_3} \cdot \frac{a - t}{z} - \frac{a}{b - y}\right)\right)\\ \mathbf{elif}\;t_4 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{t_3}{y}}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (pow (- b y) 2.0))
        (t_4 (/ (+ (* x y) t_2) t_1))
        (t_5 (- (/ (- a t) y) (/ x (+ z -1.0)))))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 -2e-295)
       (+ (/ t_2 t_1) (/ (* x y) t_1))
       (if (<= t_4 0.0)
         (+
          (/ (/ (* x y) z) (- b y))
          (+ (/ t (- b y)) (- (* (/ y t_3) (/ (- a t) z)) (/ a (- b y)))))
         (if (<= t_4 5e+302)
           t_4
           (if (<= t_4 INFINITY)
             t_5
             (+
              (/ (- t a) (- b y))
              (/ (+ (/ y (/ (- b y) x)) (/ (- a t) (/ t_3 y))) z)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = pow((b - y), 2.0);
	double t_4 = ((x * y) + t_2) / t_1;
	double t_5 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= -2e-295) {
		tmp = (t_2 / t_1) + ((x * y) / t_1);
	} else if (t_4 <= 0.0) {
		tmp = (((x * y) / z) / (b - y)) + ((t / (b - y)) + (((y / t_3) * ((a - t) / z)) - (a / (b - y))));
	} else if (t_4 <= 5e+302) {
		tmp = t_4;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5;
	} else {
		tmp = ((t - a) / (b - y)) + (((y / ((b - y) / x)) + ((a - t) / (t_3 / y))) / z);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = z * (t - a);
	double t_3 = Math.pow((b - y), 2.0);
	double t_4 = ((x * y) + t_2) / t_1;
	double t_5 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else if (t_4 <= -2e-295) {
		tmp = (t_2 / t_1) + ((x * y) / t_1);
	} else if (t_4 <= 0.0) {
		tmp = (((x * y) / z) / (b - y)) + ((t / (b - y)) + (((y / t_3) * ((a - t) / z)) - (a / (b - y))));
	} else if (t_4 <= 5e+302) {
		tmp = t_4;
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else {
		tmp = ((t - a) / (b - y)) + (((y / ((b - y) / x)) + ((a - t) / (t_3 / y))) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = z * (t - a)
	t_3 = math.pow((b - y), 2.0)
	t_4 = ((x * y) + t_2) / t_1
	t_5 = ((a - t) / y) - (x / (z + -1.0))
	tmp = 0
	if t_4 <= -math.inf:
		tmp = t_5
	elif t_4 <= -2e-295:
		tmp = (t_2 / t_1) + ((x * y) / t_1)
	elif t_4 <= 0.0:
		tmp = (((x * y) / z) / (b - y)) + ((t / (b - y)) + (((y / t_3) * ((a - t) / z)) - (a / (b - y))))
	elif t_4 <= 5e+302:
		tmp = t_4
	elif t_4 <= math.inf:
		tmp = t_5
	else:
		tmp = ((t - a) / (b - y)) + (((y / ((b - y) / x)) + ((a - t) / (t_3 / y))) / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(b - y) ^ 2.0
	t_4 = Float64(Float64(Float64(x * y) + t_2) / t_1)
	t_5 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= -2e-295)
		tmp = Float64(Float64(t_2 / t_1) + Float64(Float64(x * y) / t_1));
	elseif (t_4 <= 0.0)
		tmp = Float64(Float64(Float64(Float64(x * y) / z) / Float64(b - y)) + Float64(Float64(t / Float64(b - y)) + Float64(Float64(Float64(y / t_3) * Float64(Float64(a - t) / z)) - Float64(a / Float64(b - y)))));
	elseif (t_4 <= 5e+302)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(Float64(Float64(y / Float64(Float64(b - y) / x)) + Float64(Float64(a - t) / Float64(t_3 / y))) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = z * (t - a);
	t_3 = (b - y) ^ 2.0;
	t_4 = ((x * y) + t_2) / t_1;
	t_5 = ((a - t) / y) - (x / (z + -1.0));
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = t_5;
	elseif (t_4 <= -2e-295)
		tmp = (t_2 / t_1) + ((x * y) / t_1);
	elseif (t_4 <= 0.0)
		tmp = (((x * y) / z) / (b - y)) + ((t / (b - y)) + (((y / t_3) * ((a - t) / z)) - (a / (b - y))));
	elseif (t_4 <= 5e+302)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = ((t - a) / (b - y)) + (((y / ((b - y) / x)) + ((a - t) / (t_3 / y))) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$2), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, -2e-295], N[(N[(t$95$2 / t$95$1), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 0.0], N[(N[(N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / t$95$3), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 5e+302], t$95$4, If[LessEqual[t$95$4, Infinity], t$95$5, N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y / N[(N[(b - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(N[(a - t), $MachinePrecision] / N[(t$95$3 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 5e302 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 28.0%

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

   2. Taylor expanded in y around -inf 51.2%

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

      1. mul-1-neg 51.2%

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

      2. unsub-neg 51.2%

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

      3. mul-1-neg 51.2%

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

      4. distribute-neg-frac 51.2%

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

      5. cancel-sign-sub-inv 51.2%

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

      6. associate-/l* 65.9%

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

      7. metadata-eval 65.9%

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

      8. *-lft-identity 65.9%

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

      9. associate-/l* 67.7%

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

   4. Simplified 67.7%

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

   5. Taylor expanded in z around inf 81.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.00000000000000012e-295

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 99.6%

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

   if -2.00000000000000012e-295 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 26.7%

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

   2. Taylor expanded in z around inf 60.3%

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

      1. associate--l+ 60.3%

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

      2. associate-/r* 77.2%

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

      3. +-commutative 77.2%

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

      4. times-frac 99.9%

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

   4. Simplified 99.9%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5e302

   1. Initial program 99.6%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in z around -inf 44.7%

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

      1. +-commutative 44.7%

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

      2. associate--l+ 44.7%

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

   4. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{1 \cdot \left(\frac{y}{\frac{b - y}{x}} - \frac{t - a}{\frac{{\left(b - y\right)}^{2}}{y}}\right)}{z} + \frac{t - a}{b - y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-295}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{\frac{x \cdot y}{z}}{b - y} + \left(\frac{t}{b - y} + \left(\frac{y}{{\left(b - y\right)}^{2}} \cdot \frac{a - t}{z} - \frac{a}{b - y}\right)\right)\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{\frac{y}{\frac{b - y}{x}} + \frac{a - t}{\frac{{\left(b - y\right)}^{2}}{y}}}{z}\\ \end{array} \]

Alternative 4: 88.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_3 := \frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-295}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (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 -2e-295)
       t_2
       (if (<= t_2 0.0)
         t_1
         (if (<= t_2 5e+302) 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 = (t - a) / (b - y);
	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 <= -2e-295) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 5e+302) {
		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 = (t - a) / (b - y);
	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 <= -2e-295) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 5e+302) {
		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 = (t - a) / (b - y)
	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 <= -2e-295:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t_1
	elif t_2 <= 5e+302:
		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(t - a) / Float64(b - y))
	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 <= -2e-295)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 5e+302)
		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 = (t - a) / (b - y);
	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 <= -2e-295)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 5e+302)
		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[(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 * 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, -2e-295], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 5e+302], 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 5e302 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 28.0%

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

   2. Taylor expanded in y around -inf 51.2%

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

      1. mul-1-neg 51.2%

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

      2. unsub-neg 51.2%

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

      3. mul-1-neg 51.2%

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

      4. distribute-neg-frac 51.2%

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

      5. cancel-sign-sub-inv 51.2%

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

      6. associate-/l* 65.9%

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

      7. metadata-eval 65.9%

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

      8. *-lft-identity 65.9%

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

      9. associate-/l* 67.7%

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

   4. Simplified 67.7%

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

   5. Taylor expanded in z around inf 81.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.00000000000000012e-295 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5e302

   1. Initial program 99.6%

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

   if -2.00000000000000012e-295 < (/.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 10.5%

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

   2. Taylor expanded in z around inf 79.5%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-295}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 5: 88.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t_3}{t_1}\\ t_5 := \frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t_4 \leq -2 \cdot 10^{-295}:\\ \;\;\;\;\frac{t_3}{t_1} + \frac{x \cdot y}{t_1}\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_4 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ (* x y) t_3) t_1))
        (t_5 (- (/ (- a t) y) (/ x (+ z -1.0)))))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 -2e-295)
       (+ (/ t_3 t_1) (/ (* x y) t_1))
       (if (<= t_4 0.0)
         t_2
         (if (<= t_4 5e+302) t_4 (if (<= t_4 INFINITY) t_5 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double t_5 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= -2e-295) {
		tmp = (t_3 / t_1) + ((x * y) / t_1);
	} else if (t_4 <= 0.0) {
		tmp = t_2;
	} else if (t_4 <= 5e+302) {
		tmp = t_4;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_5;
	} 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 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = ((x * y) + t_3) / t_1;
	double t_5 = ((a - t) / y) - (x / (z + -1.0));
	double tmp;
	if (t_4 <= -Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else if (t_4 <= -2e-295) {
		tmp = (t_3 / t_1) + ((x * y) / t_1);
	} else if (t_4 <= 0.0) {
		tmp = t_2;
	} else if (t_4 <= 5e+302) {
		tmp = t_4;
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_5;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	t_2 = (t - a) / (b - y)
	t_3 = z * (t - a)
	t_4 = ((x * y) + t_3) / t_1
	t_5 = ((a - t) / y) - (x / (z + -1.0))
	tmp = 0
	if t_4 <= -math.inf:
		tmp = t_5
	elif t_4 <= -2e-295:
		tmp = (t_3 / t_1) + ((x * y) / t_1)
	elif t_4 <= 0.0:
		tmp = t_2
	elif t_4 <= 5e+302:
		tmp = t_4
	elif t_4 <= math.inf:
		tmp = t_5
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(Float64(x * y) + t_3) / t_1)
	t_5 = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= -2e-295)
		tmp = Float64(Float64(t_3 / t_1) + Float64(Float64(x * y) / t_1));
	elseif (t_4 <= 0.0)
		tmp = t_2;
	elseif (t_4 <= 5e+302)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	t_2 = (t - a) / (b - y);
	t_3 = z * (t - a);
	t_4 = ((x * y) + t_3) / t_1;
	t_5 = ((a - t) / y) - (x / (z + -1.0));
	tmp = 0.0;
	if (t_4 <= -Inf)
		tmp = t_5;
	elseif (t_4 <= -2e-295)
		tmp = (t_3 / t_1) + ((x * y) / t_1);
	elseif (t_4 <= 0.0)
		tmp = t_2;
	elseif (t_4 <= 5e+302)
		tmp = t_4;
	elseif (t_4 <= Inf)
		tmp = t_5;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, -2e-295], N[(N[(t$95$3 / t$95$1), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 0.0], t$95$2, If[LessEqual[t$95$4, 5e+302], t$95$4, If[LessEqual[t$95$4, Infinity], t$95$5, t$95$2]]]]]]]]]]

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 5e302 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 28.0%

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

   2. Taylor expanded in y around -inf 51.2%

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

      1. mul-1-neg 51.2%

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

      2. unsub-neg 51.2%

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

      3. mul-1-neg 51.2%

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

      4. distribute-neg-frac 51.2%

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

      5. cancel-sign-sub-inv 51.2%

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

      6. associate-/l* 65.9%

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

      7. metadata-eval 65.9%

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

      8. *-lft-identity 65.9%

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

      9. associate-/l* 67.7%

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

   4. Simplified 67.7%

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

   5. Taylor expanded in z around inf 81.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -2.00000000000000012e-295

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 99.6%

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

   if -2.00000000000000012e-295 < (/.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 10.5%

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

   2. Taylor expanded in z around inf 79.5%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5e302

   1. Initial program 99.6%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -2 \cdot 10^{-295}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 6: 75.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+18}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- (+ b (/ y z)) y))))
   (if (<= z -3.9e-23)
     t_1
     (if (<= z 4.2e-91)
       (+ x (/ (* z (- t a)) y))
       (if (<= z 2.65e-8)
         t_1
         (if (<= z 9e+18)
           (- (/ (- a t) y) (/ x (+ z -1.0)))
           (/ (- t a) (- b y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / ((b + (y / z)) - y);
	double tmp;
	if (z <= -3.9e-23) {
		tmp = t_1;
	} else if (z <= 4.2e-91) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 2.65e-8) {
		tmp = t_1;
	} else if (z <= 9e+18) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / ((b + (y / z)) - y)
    if (z <= (-3.9d-23)) then
        tmp = t_1
    else if (z <= 4.2d-91) then
        tmp = x + ((z * (t - a)) / y)
    else if (z <= 2.65d-8) then
        tmp = t_1
    else if (z <= 9d+18) then
        tmp = ((a - t) / y) - (x / (z + (-1.0d0)))
    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 t_1 = (t - a) / ((b + (y / z)) - y);
	double tmp;
	if (z <= -3.9e-23) {
		tmp = t_1;
	} else if (z <= 4.2e-91) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 2.65e-8) {
		tmp = t_1;
	} else if (z <= 9e+18) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / ((b + (y / z)) - y)
	tmp = 0
	if z <= -3.9e-23:
		tmp = t_1
	elif z <= 4.2e-91:
		tmp = x + ((z * (t - a)) / y)
	elif z <= 2.65e-8:
		tmp = t_1
	elif z <= 9e+18:
		tmp = ((a - t) / y) - (x / (z + -1.0))
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(Float64(b + Float64(y / z)) - y))
	tmp = 0.0
	if (z <= -3.9e-23)
		tmp = t_1;
	elseif (z <= 4.2e-91)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	elseif (z <= 2.65e-8)
		tmp = t_1;
	elseif (z <= 9e+18)
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / ((b + (y / z)) - y);
	tmp = 0.0;
	if (z <= -3.9e-23)
		tmp = t_1;
	elseif (z <= 4.2e-91)
		tmp = x + ((z * (t - a)) / y);
	elseif (z <= 2.65e-8)
		tmp = t_1;
	elseif (z <= 9e+18)
		tmp = ((a - t) / y) - (x / (z + -1.0));
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(N[(b + N[(y / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.9e-23], t$95$1, If[LessEqual[z, 4.2e-91], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.65e-8], t$95$1, If[LessEqual[z, 9e+18], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.9e-23 or 4.1999999999999998e-91 < z < 2.6499999999999999e-8

   1. Initial program 61.0%

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

      1. flip-- 50.2%

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

      2. associate-*r/ 44.1%

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

      3. +-commutative 44.1%

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

   3. Applied egg-rr 44.1%

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

      1. *-commutative 44.1%

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

      2. associate-/l* 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in x around 0 40.4%

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

      1. associate-/l* 50.0%

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

      2. associate-/l* 53.4%

         \[\leadsto \frac{t - a}{\frac{y + \color{blue}{\frac{{b}^{2} - {y}^{2}}{\frac{y + b}{z}}}}{z}} \]

      3. unpow2 53.4%

         \[\leadsto \frac{t - a}{\frac{y + \frac{\color{blue}{b \cdot b} - {y}^{2}}{\frac{y + b}{z}}}{z}} \]

      4. unpow2 53.4%

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

      5. +-commutative 53.4%

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

   8. Simplified 53.4%

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

   9. Taylor expanded in b around inf 83.8%

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

   if -3.9e-23 < z < 4.1999999999999998e-91

   1. Initial program 78.2%

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

   2. Taylor expanded in z around 0 57.2%

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

   3. Taylor expanded in x around 0 78.8%

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

   if 2.6499999999999999e-8 < z < 9e18

   1. Initial program 58.7%

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

   2. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. distribute-neg-frac 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-/l* 100.0%

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

      7. metadata-eval 100.0%

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

      8. *-lft-identity 100.0%

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

      9. associate-/l* 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

   if 9e18 < z

   1. Initial program 33.9%

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

   2. Taylor expanded in z around inf 87.3%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{-23}:\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-8}:\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+18}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 7: 75.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \mathbf{if}\;z \leq -1.26 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- (+ b (/ y z)) y))))
   (if (<= z -1.26e-23)
     t_1
     (if (<= z 2.6e-91)
       (+ x (/ (* z (- t a)) y))
       (if (<= z 3e-6)
         t_1
         (if (<= z 9.5e+17) (/ x (- 1.0 z)) (/ (- t a) (- b y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / ((b + (y / z)) - y);
	double tmp;
	if (z <= -1.26e-23) {
		tmp = t_1;
	} else if (z <= 2.6e-91) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 3e-6) {
		tmp = t_1;
	} else if (z <= 9.5e+17) {
		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) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / ((b + (y / z)) - y)
    if (z <= (-1.26d-23)) then
        tmp = t_1
    else if (z <= 2.6d-91) then
        tmp = x + ((z * (t - a)) / y)
    else if (z <= 3d-6) then
        tmp = t_1
    else if (z <= 9.5d+17) 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 t_1 = (t - a) / ((b + (y / z)) - y);
	double tmp;
	if (z <= -1.26e-23) {
		tmp = t_1;
	} else if (z <= 2.6e-91) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 3e-6) {
		tmp = t_1;
	} else if (z <= 9.5e+17) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / ((b + (y / z)) - y)
	tmp = 0
	if z <= -1.26e-23:
		tmp = t_1
	elif z <= 2.6e-91:
		tmp = x + ((z * (t - a)) / y)
	elif z <= 3e-6:
		tmp = t_1
	elif z <= 9.5e+17:
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(Float64(b + Float64(y / z)) - y))
	tmp = 0.0
	if (z <= -1.26e-23)
		tmp = t_1;
	elseif (z <= 2.6e-91)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	elseif (z <= 3e-6)
		tmp = t_1;
	elseif (z <= 9.5e+17)
		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)
	t_1 = (t - a) / ((b + (y / z)) - y);
	tmp = 0.0;
	if (z <= -1.26e-23)
		tmp = t_1;
	elseif (z <= 2.6e-91)
		tmp = x + ((z * (t - a)) / y);
	elseif (z <= 3e-6)
		tmp = t_1;
	elseif (z <= 9.5e+17)
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(N[(b + N[(y / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.26e-23], t$95$1, If[LessEqual[z, 2.6e-91], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-6], t$95$1, If[LessEqual[z, 9.5e+17], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.25999999999999996e-23 or 2.60000000000000014e-91 < z < 3.0000000000000001e-6

   1. Initial program 61.0%

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

      1. flip-- 50.2%

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

      2. associate-*r/ 44.1%

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

      3. +-commutative 44.1%

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

   3. Applied egg-rr 44.1%

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

      1. *-commutative 44.1%

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

      2. associate-/l* 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in x around 0 40.4%

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

      1. associate-/l* 50.0%

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

      2. associate-/l* 53.4%

         \[\leadsto \frac{t - a}{\frac{y + \color{blue}{\frac{{b}^{2} - {y}^{2}}{\frac{y + b}{z}}}}{z}} \]

      3. unpow2 53.4%

         \[\leadsto \frac{t - a}{\frac{y + \frac{\color{blue}{b \cdot b} - {y}^{2}}{\frac{y + b}{z}}}{z}} \]

      4. unpow2 53.4%

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

      5. +-commutative 53.4%

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

   8. Simplified 53.4%

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

   9. Taylor expanded in b around inf 83.8%

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

   if -1.25999999999999996e-23 < z < 2.60000000000000014e-91

   1. Initial program 78.2%

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

   2. Taylor expanded in z around 0 57.2%

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

   3. Taylor expanded in x around 0 78.8%

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

   if 3.0000000000000001e-6 < z < 9.5e17

   1. Initial program 58.7%

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

   2. Taylor expanded in y around inf 86.1%

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

      1. +-commutative 86.1%

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

      2. mul-1-neg 86.1%

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

      3. unsub-neg 86.1%

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

   4. Simplified 86.1%

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

   if 9.5e17 < z

   1. Initial program 33.9%

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

   2. Taylor expanded in z around inf 87.3%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-23}:\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-91}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-6}:\\ \;\;\;\;\frac{t - a}{\left(b + \frac{y}{z}\right) - y}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 8: 63.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-6}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.35e-23)
     t_1
     (if (<= z 8.8e-103)
       x
       (if (<= z 2.8e-6)
         (/ (- t a) b)
         (if (<= z 8.2e+17) (/ x (- 1.0 z)) 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 tmp;
	if (z <= -2.35e-23) {
		tmp = t_1;
	} else if (z <= 8.8e-103) {
		tmp = x;
	} else if (z <= 2.8e-6) {
		tmp = (t - a) / b;
	} else if (z <= 8.2e+17) {
		tmp = x / (1.0 - z);
	} 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 = (t - a) / (b - y)
    if (z <= (-2.35d-23)) then
        tmp = t_1
    else if (z <= 8.8d-103) then
        tmp = x
    else if (z <= 2.8d-6) then
        tmp = (t - a) / b
    else if (z <= 8.2d+17) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.35e-23) {
		tmp = t_1;
	} else if (z <= 8.8e-103) {
		tmp = x;
	} else if (z <= 2.8e-6) {
		tmp = (t - a) / b;
	} else if (z <= 8.2e+17) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.35e-23:
		tmp = t_1
	elif z <= 8.8e-103:
		tmp = x
	elif z <= 2.8e-6:
		tmp = (t - a) / b
	elif z <= 8.2e+17:
		tmp = x / (1.0 - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.35e-23)
		tmp = t_1;
	elseif (z <= 8.8e-103)
		tmp = x;
	elseif (z <= 2.8e-6)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= 8.2e+17)
		tmp = Float64(x / Float64(1.0 - z));
	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);
	tmp = 0.0;
	if (z <= -2.35e-23)
		tmp = t_1;
	elseif (z <= 8.8e-103)
		tmp = x;
	elseif (z <= 2.8e-6)
		tmp = (t - a) / b;
	elseif (z <= 8.2e+17)
		tmp = x / (1.0 - z);
	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]}, If[LessEqual[z, -2.35e-23], t$95$1, If[LessEqual[z, 8.8e-103], x, If[LessEqual[z, 2.8e-6], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 8.2e+17], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.35e-23 or 8.2e17 < z

   1. Initial program 43.2%

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

   2. Taylor expanded in z around inf 85.8%

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

   if -2.35e-23 < z < 8.7999999999999997e-103

   1. Initial program 78.5%

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

   2. Taylor expanded in z around 0 57.6%

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

   if 8.7999999999999997e-103 < z < 2.79999999999999987e-6

   1. Initial program 90.3%

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

   2. Taylor expanded in y around 0 46.5%

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

   if 2.79999999999999987e-6 < z < 8.2e17

   1. Initial program 58.7%

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

   2. Taylor expanded in y around inf 86.1%

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

      1. +-commutative 86.1%

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

      2. mul-1-neg 86.1%

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

      3. unsub-neg 86.1%

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

   4. Simplified 86.1%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-23}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-6}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 9: 44.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-9}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -3.4e-22)
     t_1
     (if (<= z 4.2e-91)
       x
       (if (<= z 3.8e-9)
         (/ (- a) b)
         (if (<= z 1.4e+22) (/ x (- 1.0 z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -3.4e-22) {
		tmp = t_1;
	} else if (z <= 4.2e-91) {
		tmp = x;
	} else if (z <= 3.8e-9) {
		tmp = -a / b;
	} else if (z <= 1.4e+22) {
		tmp = x / (1.0 - z);
	} 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 = t / (b - y)
    if (z <= (-3.4d-22)) then
        tmp = t_1
    else if (z <= 4.2d-91) then
        tmp = x
    else if (z <= 3.8d-9) then
        tmp = -a / b
    else if (z <= 1.4d+22) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -3.4e-22) {
		tmp = t_1;
	} else if (z <= 4.2e-91) {
		tmp = x;
	} else if (z <= 3.8e-9) {
		tmp = -a / b;
	} else if (z <= 1.4e+22) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -3.4e-22:
		tmp = t_1
	elif z <= 4.2e-91:
		tmp = x
	elif z <= 3.8e-9:
		tmp = -a / b
	elif z <= 1.4e+22:
		tmp = x / (1.0 - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -3.4e-22)
		tmp = t_1;
	elseif (z <= 4.2e-91)
		tmp = x;
	elseif (z <= 3.8e-9)
		tmp = Float64(Float64(-a) / b);
	elseif (z <= 1.4e+22)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -3.4e-22)
		tmp = t_1;
	elseif (z <= 4.2e-91)
		tmp = x;
	elseif (z <= 3.8e-9)
		tmp = -a / b;
	elseif (z <= 1.4e+22)
		tmp = x / (1.0 - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e-22], t$95$1, If[LessEqual[z, 4.2e-91], x, If[LessEqual[z, 3.8e-9], N[((-a) / b), $MachinePrecision], If[LessEqual[z, 1.4e+22], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3999999999999998e-22 or 1.4e22 < z

   1. Initial program 42.8%

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

   2. Taylor expanded in z around inf 85.7%

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

   3. Taylor expanded in t around inf 52.4%

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

   if -3.3999999999999998e-22 < z < 4.1999999999999998e-91

   1. Initial program 78.2%

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

   2. Taylor expanded in z around 0 57.0%

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

   if 4.1999999999999998e-91 < z < 3.80000000000000011e-9

   1. Initial program 94.0%

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

   2. Taylor expanded in a around inf 64.6%

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

      1. mul-1-neg 64.6%

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

      2. distribute-lft-neg-out 64.6%

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

      3. *-commutative 64.6%

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

   4. Simplified 64.6%

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

   5. Taylor expanded in y around 0 47.8%

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

      1. associate-*r/ 47.8%

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

      2. neg-mul-1 47.8%

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

   7. Simplified 47.8%

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

   if 3.80000000000000011e-9 < z < 1.4e22

   1. Initial program 63.7%

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

   2. Taylor expanded in y around inf 75.6%

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

      1. +-commutative 75.6%

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

      2. mul-1-neg 75.6%

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

      3. unsub-neg 75.6%

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

   4. Simplified 75.6%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-22}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-9}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+22}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]

Alternative 10: 52.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-88}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+101}:\\ \;\;\;\;\frac{t + a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -2.7e+35)
     t_1
     (if (<= y 5.4e-88)
       (/ (- t a) b)
       (if (<= y 4.1e+101) (/ (+ t a) (- 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 <= -2.7e+35) {
		tmp = t_1;
	} else if (y <= 5.4e-88) {
		tmp = (t - a) / b;
	} else if (y <= 4.1e+101) {
		tmp = (t + a) / (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 <= (-2.7d+35)) then
        tmp = t_1
    else if (y <= 5.4d-88) then
        tmp = (t - a) / b
    else if (y <= 4.1d+101) then
        tmp = (t + a) / (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 <= -2.7e+35) {
		tmp = t_1;
	} else if (y <= 5.4e-88) {
		tmp = (t - a) / b;
	} else if (y <= 4.1e+101) {
		tmp = (t + a) / (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 <= -2.7e+35:
		tmp = t_1
	elif y <= 5.4e-88:
		tmp = (t - a) / b
	elif y <= 4.1e+101:
		tmp = (t + a) / (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 <= -2.7e+35)
		tmp = t_1;
	elseif (y <= 5.4e-88)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 4.1e+101)
		tmp = Float64(Float64(t + a) / 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 <= -2.7e+35)
		tmp = t_1;
	elseif (y <= 5.4e-88)
		tmp = (t - a) / b;
	elseif (y <= 4.1e+101)
		tmp = (t + a) / (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, -2.7e+35], t$95$1, If[LessEqual[y, 5.4e-88], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 4.1e+101], N[(N[(t + a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.70000000000000003e35 or 4.1e101 < y

   1. Initial program 42.9%

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

   2. Taylor expanded in y around inf 58.6%

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

      1. +-commutative 58.6%

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

      2. mul-1-neg 58.6%

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

      3. unsub-neg 58.6%

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

   4. Simplified 58.6%

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

   if -2.70000000000000003e35 < y < 5.39999999999999989e-88

   1. Initial program 82.2%

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

   2. Taylor expanded in y around 0 60.1%

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

   if 5.39999999999999989e-88 < y < 4.1e101

   1. Initial program 60.9%

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

   2. Taylor expanded in z around inf 61.7%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
   3. Step-by-step derivation

      1. expm1-log1p-u 42.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t - a}{b - y}\right)\right)} \]

      2. expm1-udef 24.5%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{t - a}{b - y}\right)} - 1} \]

      3. sub-neg 24.5%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{t + \left(-a\right)}}{b - y}\right)} - 1 \]

      4. add-sqr-sqrt 11.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{t + \color{blue}{\sqrt{-a} \cdot \sqrt{-a}}}{b - y}\right)} - 1 \]

      5. sqrt-unprod 18.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{t + \color{blue}{\sqrt{\left(-a\right) \cdot \left(-a\right)}}}{b - y}\right)} - 1 \]

      6. sqr-neg 18.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{t + \sqrt{\color{blue}{a \cdot a}}}{b - y}\right)} - 1 \]

      7. sqrt-unprod 9.0%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{t + \color{blue}{\sqrt{a} \cdot \sqrt{a}}}{b - y}\right)} - 1 \]

      8. add-sqr-sqrt 18.7%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{t + \color{blue}{a}}{b - y}\right)} - 1 \]

   4. Applied egg-rr 18.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{t + a}{b - y}\right)} - 1} \]
   5. Step-by-step derivation

      1. expm1-def 32.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t + a}{b - y}\right)\right)} \]

      2. expm1-log1p 49.4%

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

      3. +-commutative 49.4%

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

   6. Simplified 49.4%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-88}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+101}:\\ \;\;\;\;\frac{t + a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 11: 75.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-22} \lor \neg \left(z \leq 3.6 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2e-22) (not (<= z 3.6e-11)))
   (/ (- t a) (- b y))
   (+ x (/ (* z (- t a)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2e-22) || !(z <= 3.6e-11)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / 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 ((z <= (-2d-22)) .or. (.not. (z <= 3.6d-11))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * (t - a)) / 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 ((z <= -2e-22) || !(z <= 3.6e-11)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -2e-22) or not (z <= 3.6e-11):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * (t - a)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2e-22) || !(z <= 3.6e-11))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -2e-22) || ~((z <= 3.6e-11)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * (t - a)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2e-22], N[Not[LessEqual[z, 3.6e-11]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0000000000000001e-22 or 3.59999999999999985e-11 < z

   1. Initial program 44.5%

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

   2. Taylor expanded in z around inf 82.2%

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

   if -2.0000000000000001e-22 < z < 3.59999999999999985e-11

   1. Initial program 80.2%

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

   2. Taylor expanded in z around 0 56.1%

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

   3. Taylor expanded in x around 0 75.0%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-22} \lor \neg \left(z \leq 3.6 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \]

Alternative 12: 43.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+84}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))))
   (if (<= z -1.15e-23)
     t_1
     (if (<= z 3.8e-91) x (if (<= z 9.5e+84) (/ (- a) b) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double tmp;
	if (z <= -1.15e-23) {
		tmp = t_1;
	} else if (z <= 3.8e-91) {
		tmp = x;
	} else if (z <= 9.5e+84) {
		tmp = -a / b;
	} 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 = t / (b - y)
    if (z <= (-1.15d-23)) then
        tmp = t_1
    else if (z <= 3.8d-91) then
        tmp = x
    else if (z <= 9.5d+84) then
        tmp = -a / b
    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 / (b - y);
	double tmp;
	if (z <= -1.15e-23) {
		tmp = t_1;
	} else if (z <= 3.8e-91) {
		tmp = x;
	} else if (z <= 9.5e+84) {
		tmp = -a / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	tmp = 0
	if z <= -1.15e-23:
		tmp = t_1
	elif z <= 3.8e-91:
		tmp = x
	elif z <= 9.5e+84:
		tmp = -a / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	tmp = 0.0
	if (z <= -1.15e-23)
		tmp = t_1;
	elseif (z <= 3.8e-91)
		tmp = x;
	elseif (z <= 9.5e+84)
		tmp = Float64(Float64(-a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t / (b - y);
	tmp = 0.0;
	if (z <= -1.15e-23)
		tmp = t_1;
	elseif (z <= 3.8e-91)
		tmp = x;
	elseif (z <= 9.5e+84)
		tmp = -a / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e-23], t$95$1, If[LessEqual[z, 3.8e-91], x, If[LessEqual[z, 9.5e+84], N[((-a) / b), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15000000000000005e-23 or 9.49999999999999979e84 < z

   1. Initial program 41.3%

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

   2. Taylor expanded in z around inf 86.4%

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

   3. Taylor expanded in t around inf 54.1%

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

   if -1.15000000000000005e-23 < z < 3.79999999999999978e-91

   1. Initial program 78.2%

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

   2. Taylor expanded in z around 0 57.0%

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

   if 3.79999999999999978e-91 < z < 9.49999999999999979e84

   1. Initial program 79.4%

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

   2. Taylor expanded in a around inf 46.6%

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

      1. mul-1-neg 46.6%

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

      2. distribute-lft-neg-out 46.6%

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

      3. *-commutative 46.6%

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

   4. Simplified 46.6%

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

   5. Taylor expanded in y around 0 32.3%

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

      1. associate-*r/ 32.3%

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

      2. neg-mul-1 32.3%

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

   7. Simplified 32.3%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-23}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+84}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]

Alternative 13: 52.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-87}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+101}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -2.9e+35)
     t_1
     (if (<= y 3.4e-87)
       (/ (- t a) b)
       (if (<= y 4.5e+101) (/ 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 <= -2.9e+35) {
		tmp = t_1;
	} else if (y <= 3.4e-87) {
		tmp = (t - a) / b;
	} else if (y <= 4.5e+101) {
		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 <= (-2.9d+35)) then
        tmp = t_1
    else if (y <= 3.4d-87) then
        tmp = (t - a) / b
    else if (y <= 4.5d+101) 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 <= -2.9e+35) {
		tmp = t_1;
	} else if (y <= 3.4e-87) {
		tmp = (t - a) / b;
	} else if (y <= 4.5e+101) {
		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 <= -2.9e+35:
		tmp = t_1
	elif y <= 3.4e-87:
		tmp = (t - a) / b
	elif y <= 4.5e+101:
		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 <= -2.9e+35)
		tmp = t_1;
	elseif (y <= 3.4e-87)
		tmp = Float64(Float64(t - a) / b);
	elseif (y <= 4.5e+101)
		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 <= -2.9e+35)
		tmp = t_1;
	elseif (y <= 3.4e-87)
		tmp = (t - a) / b;
	elseif (y <= 4.5e+101)
		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, -2.9e+35], t$95$1, If[LessEqual[y, 3.4e-87], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 4.5e+101], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.89999999999999995e35 or 4.5000000000000002e101 < y

   1. Initial program 42.9%

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

   2. Taylor expanded in y around inf 58.6%

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

      1. +-commutative 58.6%

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

      2. mul-1-neg 58.6%

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

      3. unsub-neg 58.6%

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

   4. Simplified 58.6%

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

   if -2.89999999999999995e35 < y < 3.3999999999999999e-87

   1. Initial program 82.2%

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

   2. Taylor expanded in y around 0 60.1%

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

   if 3.3999999999999999e-87 < y < 4.5000000000000002e101

   1. Initial program 60.9%

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

   2. Taylor expanded in z around inf 61.7%

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

   3. Taylor expanded in t around inf 49.3%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-87}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+101}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 14: 36.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-22} \lor \neg \left(z \leq 4.2 \cdot 10^{-91}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.6e-22) (not (<= z 4.2e-91))) (/ (- a) b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.6e-22) || !(z <= 4.2e-91)) {
		tmp = -a / 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 ((z <= (-6.6d-22)) .or. (.not. (z <= 4.2d-91))) then
        tmp = -a / 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 ((z <= -6.6e-22) || !(z <= 4.2e-91)) {
		tmp = -a / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.6e-22) or not (z <= 4.2e-91):
		tmp = -a / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.6e-22) || !(z <= 4.2e-91))
		tmp = Float64(Float64(-a) / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.6e-22) || ~((z <= 4.2e-91)))
		tmp = -a / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.6e-22], N[Not[LessEqual[z, 4.2e-91]], $MachinePrecision]], N[((-a) / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -6.6000000000000002e-22 or 4.1999999999999998e-91 < z

   1. Initial program 49.8%

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

   2. Taylor expanded in a around inf 25.5%

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

      1. mul-1-neg 25.5%

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

      2. distribute-lft-neg-out 25.5%

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

      3. *-commutative 25.5%

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

   4. Simplified 25.5%

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

   5. Taylor expanded in y around 0 24.5%

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

      1. associate-*r/ 24.5%

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

      2. neg-mul-1 24.5%

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

   7. Simplified 24.5%

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

   if -6.6000000000000002e-22 < z < 4.1999999999999998e-91

   1. Initial program 78.2%

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

   2. Taylor expanded in z around 0 57.0%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-22} \lor \neg \left(z \leq 4.2 \cdot 10^{-91}\right):\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 25.4% 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 61.9%

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

2. Taylor expanded in z around 0 26.8%

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

3. Final simplification 26.8%

   \[\leadsto x \]

Developer target: 73.8% 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 2023257 
(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)))))