Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.2% → 93.4%

Time: 22.6s

Alternatives: 21

Speedup: 0.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 93.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt[3]{a - z}\\ t_2 := \frac{t - x}{a - z}\\ t_3 := x + \left(y - z\right) \cdot t_2\\ t_4 := x \cdot \left(\left(1 + \frac{z}{a - z}\right) - \frac{y}{a - z}\right)\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;x + \frac{\frac{\left(y - z\right) \cdot \left(t - x\right)}{{t_1}^{2}}}{t_1}\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{+58}:\\ \;\;\;\;t_4 + \frac{1}{\frac{\frac{a - z}{t}}{y - z}}\\ \mathbf{elif}\;t_3 \leq -1 \cdot 10^{-254}:\\ \;\;\;\;t_4 + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t_2, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (cbrt (- a z)))
        (t_2 (/ (- t x) (- a z)))
        (t_3 (+ x (* (- y z) t_2)))
        (t_4 (* x (- (+ 1.0 (/ z (- a z))) (/ y (- a z))))))
   (if (<= t_3 (- INFINITY))
     (+ x (/ (/ (* (- y z) (- t x)) (pow t_1 2.0)) t_1))
     (if (<= t_3 -5e+58)
       (+ t_4 (/ 1.0 (/ (/ (- a z) t) (- y z))))
       (if (<= t_3 -1e-254)
         (+ t_4 (/ (* (- y z) t) (- a z)))
         (if (<= t_3 0.0)
           (+ t (* (- y a) (/ (- x t) z)))
           (fma (- y z) t_2 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = cbrt((a - z));
	double t_2 = (t - x) / (a - z);
	double t_3 = x + ((y - z) * t_2);
	double t_4 = x * ((1.0 + (z / (a - z))) - (y / (a - z)));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = x + ((((y - z) * (t - x)) / pow(t_1, 2.0)) / t_1);
	} else if (t_3 <= -5e+58) {
		tmp = t_4 + (1.0 / (((a - z) / t) / (y - z)));
	} else if (t_3 <= -1e-254) {
		tmp = t_4 + (((y - z) * t) / (a - z));
	} else if (t_3 <= 0.0) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else {
		tmp = fma((y - z), t_2, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = cbrt(Float64(a - z))
	t_2 = Float64(Float64(t - x) / Float64(a - z))
	t_3 = Float64(x + Float64(Float64(y - z) * t_2))
	t_4 = Float64(x * Float64(Float64(1.0 + Float64(z / Float64(a - z))) - Float64(y / Float64(a - z))))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(Float64(Float64(y - z) * Float64(t - x)) / (t_1 ^ 2.0)) / t_1));
	elseif (t_3 <= -5e+58)
		tmp = Float64(t_4 + Float64(1.0 / Float64(Float64(Float64(a - z) / t) / Float64(y - z))));
	elseif (t_3 <= -1e-254)
		tmp = Float64(t_4 + Float64(Float64(Float64(y - z) * t) / Float64(a - z)));
	elseif (t_3 <= 0.0)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	else
		tmp = fma(Float64(y - z), t_2, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[Power[N[(a - z), $MachinePrecision], 1/3], $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(1.0 + N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(x + N[(N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[Power[t$95$1, 2.0], $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -5e+58], N[(t$95$4 + N[(1.0 / N[(N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -1e-254], N[(t$95$4 + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 0.0], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t$95$2 + x), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

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

   1. Initial program 70.1%

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

      1. associate-*r/ 99.9%

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

      2. add-cube-cbrt 99.4%

         \[\leadsto x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{\color{blue}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}} \]

      3. associate-/r* 99.3%

         \[\leadsto x + \color{blue}{\frac{\frac{\left(y - z\right) \cdot \left(t - x\right)}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}}{\sqrt[3]{a - z}}} \]

      4. pow2 99.3%

         \[\leadsto x + \frac{\frac{\left(y - z\right) \cdot \left(t - x\right)}{\color{blue}{{\left(\sqrt[3]{a - z}\right)}^{2}}}}{\sqrt[3]{a - z}} \]

   4. Applied egg-rr 99.3%

      \[\leadsto x + \color{blue}{\frac{\frac{\left(y - z\right) \cdot \left(t - x\right)}{{\left(\sqrt[3]{a - z}\right)}^{2}}}{\sqrt[3]{a - z}}} \]

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.99999999999999986e58

   1. Initial program 98.4%

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

   3. Taylor expanded in x around -inf 67.3%

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

      1. clear-num 67.3%

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

      2. inv-pow 67.3%

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

   5. Applied egg-rr 67.3%

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

      1. unpow-1 67.3%

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

      2. associate-/r* 98.6%

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

   7. Simplified 98.6%

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

   if -4.99999999999999986e58 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999991e-255

   1. Initial program 84.0%

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

   3. Taylor expanded in x around -inf 99.8%

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

   if -9.9999999999999991e-255 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.7%

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

      1. clear-num 3.6%

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

      2. associate-/r/ 3.6%

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

   4. Applied egg-rr 3.6%

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

   5. Taylor expanded in z around inf 87.7%

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

      1. associate--l+ 87.7%

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

      2. associate-*r/ 87.7%

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

      3. associate-*r/ 87.7%

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

      4. div-sub 87.7%

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

      5. distribute-lft-out-- 87.7%

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

      6. associate-*r/ 87.7%

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

      7. mul-1-neg 87.7%

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

      8. unsub-neg 87.7%

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

      9. distribute-rgt-out-- 87.9%

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

   7. Simplified 87.9%

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

      1. *-commutative 87.9%

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

      2. *-un-lft-identity 87.9%

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

      3. times-frac 99.8%

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

   9. Applied egg-rr 99.8%

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

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

   1. Initial program 94.3%

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

      1. +-commutative 94.3%

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

      2. fma-def 94.3%

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

   3. Simplified 94.3%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -\infty:\\ \;\;\;\;x + \frac{\frac{\left(y - z\right) \cdot \left(t - x\right)}{{\left(\sqrt[3]{a - z}\right)}^{2}}}{\sqrt[3]{a - z}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{z}{a - z}\right) - \frac{y}{a - z}\right) + \frac{1}{\frac{\frac{a - z}{t}}{y - z}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-254}:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{z}{a - z}\right) - \frac{y}{a - z}\right) + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(1 + \frac{z}{a - z}\right) - \frac{y}{a - z}\right)\\ t_2 := t_1 + \frac{\left(y - z\right) \cdot t}{a - z}\\ t_3 := \frac{t - x}{a - z}\\ t_4 := x + \left(y - z\right) \cdot t_3\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_4 \leq -5 \cdot 10^{+58}:\\ \;\;\;\;t_1 + \frac{1}{\frac{\frac{a - z}{t}}{y - z}}\\ \mathbf{elif}\;t_4 \leq -1 \cdot 10^{-254}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_4 \leq 0:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t_3, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- (+ 1.0 (/ z (- a z))) (/ y (- a z)))))
        (t_2 (+ t_1 (/ (* (- y z) t) (- a z))))
        (t_3 (/ (- t x) (- a z)))
        (t_4 (+ x (* (- y z) t_3))))
   (if (<= t_4 (- INFINITY))
     t_2
     (if (<= t_4 -5e+58)
       (+ t_1 (/ 1.0 (/ (/ (- a z) t) (- y z))))
       (if (<= t_4 -1e-254)
         t_2
         (if (<= t_4 0.0)
           (+ t (* (- y a) (/ (- x t) z)))
           (fma (- y z) t_3 x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((1.0 + (z / (a - z))) - (y / (a - z)));
	double t_2 = t_1 + (((y - z) * t) / (a - z));
	double t_3 = (t - x) / (a - z);
	double t_4 = x + ((y - z) * t_3);
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_4 <= -5e+58) {
		tmp = t_1 + (1.0 / (((a - z) / t) / (y - z)));
	} else if (t_4 <= -1e-254) {
		tmp = t_2;
	} else if (t_4 <= 0.0) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else {
		tmp = fma((y - z), t_3, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(1.0 + Float64(z / Float64(a - z))) - Float64(y / Float64(a - z))))
	t_2 = Float64(t_1 + Float64(Float64(Float64(y - z) * t) / Float64(a - z)))
	t_3 = Float64(Float64(t - x) / Float64(a - z))
	t_4 = Float64(x + Float64(Float64(y - z) * t_3))
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_4 <= -5e+58)
		tmp = Float64(t_1 + Float64(1.0 / Float64(Float64(Float64(a - z) / t) / Float64(y - z))));
	elseif (t_4 <= -1e-254)
		tmp = t_2;
	elseif (t_4 <= 0.0)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	else
		tmp = fma(Float64(y - z), t_3, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(1.0 + N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x + N[(N[(y - z), $MachinePrecision] * t$95$3), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$2, If[LessEqual[t$95$4, -5e+58], N[(t$95$1 + N[(1.0 / N[(N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, -1e-254], t$95$2, If[LessEqual[t$95$4, 0.0], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t$95$3 + x), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0 or -4.99999999999999986e58 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999991e-255

   1. Initial program 78.4%

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

   3. Taylor expanded in x around -inf 96.6%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.99999999999999986e58

   1. Initial program 98.4%

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

   3. Taylor expanded in x around -inf 67.3%

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

      1. clear-num 67.3%

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

      2. inv-pow 67.3%

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

   5. Applied egg-rr 67.3%

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

      1. unpow-1 67.3%

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

      2. associate-/r* 98.6%

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

   7. Simplified 98.6%

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

   if -9.9999999999999991e-255 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.7%

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

      1. clear-num 3.6%

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

      2. associate-/r/ 3.6%

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

   4. Applied egg-rr 3.6%

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

   5. Taylor expanded in z around inf 87.7%

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

      1. associate--l+ 87.7%

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

      2. associate-*r/ 87.7%

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

      3. associate-*r/ 87.7%

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

      4. div-sub 87.7%

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

      5. distribute-lft-out-- 87.7%

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

      6. associate-*r/ 87.7%

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

      7. mul-1-neg 87.7%

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

      8. unsub-neg 87.7%

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

      9. distribute-rgt-out-- 87.9%

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

   7. Simplified 87.9%

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

      1. *-commutative 87.9%

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

      2. *-un-lft-identity 87.9%

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

      3. times-frac 99.8%

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

   9. Applied egg-rr 99.8%

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

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

   1. Initial program 94.3%

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

      1. +-commutative 94.3%

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

      2. fma-def 94.3%

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

   3. Simplified 94.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)} \]
   4. Add Preprocessing
3. Recombined 4 regimes into one program.

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -\infty:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{z}{a - z}\right) - \frac{y}{a - z}\right) + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{z}{a - z}\right) - \frac{y}{a - z}\right) + \frac{1}{\frac{\frac{a - z}{t}}{y - z}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-254}:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{z}{a - z}\right) - \frac{y}{a - z}\right) + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(1 + \frac{z}{a - z}\right) - \frac{y}{a - z}\right) + \frac{\left(y - z\right) \cdot t}{a - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1
         (+
          (* x (- (+ 1.0 (/ z (- a z))) (/ y (- a z))))
          (/ (* (- y z) t) (- a z))))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e+58)
       t_2
       (if (<= t_2 -1e-254)
         t_1
         (if (<= t_2 0.0) (+ t (* (- y a) (/ (- x t) z))) t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * ((1.0 + (z / (a - z))) - (y / (a - z)))) + (((y - z) * t) / (a - z));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e+58) {
		tmp = t_2;
	} else if (t_2 <= -1e-254) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * ((1.0 + (z / (a - z))) - (y / (a - z)))) + (((y - z) * t) / (a - z));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e+58) {
		tmp = t_2;
	} else if (t_2 <= -1e-254) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * ((1.0 + (z / (a - z))) - (y / (a - z)))) + (((y - z) * t) / (a - z))
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e+58:
		tmp = t_2
	elif t_2 <= -1e-254:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t + ((y - a) * ((x - t) / z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * Float64(Float64(1.0 + Float64(z / Float64(a - z))) - Float64(y / Float64(a - z)))) + Float64(Float64(Float64(y - z) * t) / Float64(a - z)))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e+58)
		tmp = t_2;
	elseif (t_2 <= -1e-254)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * ((1.0 + (z / (a - z))) - (y / (a - z)))) + (((y - z) * t) / (a - z));
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e+58)
		tmp = t_2;
	elseif (t_2 <= -1e-254)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t + ((y - a) * ((x - t) / z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * N[(N[(1.0 + N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e+58], t$95$2, If[LessEqual[t$95$2, -1e-254], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0 or -4.99999999999999986e58 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999991e-255

   1. Initial program 78.4%

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

   3. Taylor expanded in x around -inf 96.6%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.99999999999999986e58 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 95.7%

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

   if -9.9999999999999991e-255 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.7%

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

      1. clear-num 3.6%

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

      2. associate-/r/ 3.6%

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

   4. Applied egg-rr 3.6%

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

   5. Taylor expanded in z around inf 87.7%

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

      1. associate--l+ 87.7%

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

      2. associate-*r/ 87.7%

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

      3. associate-*r/ 87.7%

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

      4. div-sub 87.7%

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

      5. distribute-lft-out-- 87.7%

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

      6. associate-*r/ 87.7%

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

      7. mul-1-neg 87.7%

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

      8. unsub-neg 87.7%

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

      9. distribute-rgt-out-- 87.9%

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

   7. Simplified 87.9%

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

      1. *-commutative 87.9%

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

      2. *-un-lft-identity 87.9%

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

      3. times-frac 99.8%

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

   9. Applied egg-rr 99.8%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -\infty:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{z}{a - z}\right) - \frac{y}{a - z}\right) + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{+58}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-254}:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{z}{a - z}\right) - \frac{y}{a - z}\right) + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(\left(1 + \frac{z}{a - z}\right) - \frac{y}{a - z}\right)\\ t_2 := t_1 + \frac{\left(y - z\right) \cdot t}{a - z}\\ t_3 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq -5 \cdot 10^{+58}:\\ \;\;\;\;t_1 + \frac{1}{\frac{\frac{a - z}{t}}{y - z}}\\ \mathbf{elif}\;t_3 \leq -1 \cdot 10^{-254}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (- (+ 1.0 (/ z (- a z))) (/ y (- a z)))))
        (t_2 (+ t_1 (/ (* (- y z) t) (- a z))))
        (t_3 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_3 (- INFINITY))
     t_2
     (if (<= t_3 -5e+58)
       (+ t_1 (/ 1.0 (/ (/ (- a z) t) (- y z))))
       (if (<= t_3 -1e-254)
         t_2
         (if (<= t_3 0.0) (+ t (* (- y a) (/ (- x t) z))) t_3))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((1.0 + (z / (a - z))) - (y / (a - z)));
	double t_2 = t_1 + (((y - z) * t) / (a - z));
	double t_3 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_3 <= -5e+58) {
		tmp = t_1 + (1.0 / (((a - z) / t) / (y - z)));
	} else if (t_3 <= -1e-254) {
		tmp = t_2;
	} else if (t_3 <= 0.0) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((1.0 + (z / (a - z))) - (y / (a - z)));
	double t_2 = t_1 + (((y - z) * t) / (a - z));
	double t_3 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_3 <= -5e+58) {
		tmp = t_1 + (1.0 / (((a - z) / t) / (y - z)));
	} else if (t_3 <= -1e-254) {
		tmp = t_2;
	} else if (t_3 <= 0.0) {
		tmp = t + ((y - a) * ((x - t) / z));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((1.0 + (z / (a - z))) - (y / (a - z)))
	t_2 = t_1 + (((y - z) * t) / (a - z))
	t_3 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_2
	elif t_3 <= -5e+58:
		tmp = t_1 + (1.0 / (((a - z) / t) / (y - z)))
	elif t_3 <= -1e-254:
		tmp = t_2
	elif t_3 <= 0.0:
		tmp = t + ((y - a) * ((x - t) / z))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(1.0 + Float64(z / Float64(a - z))) - Float64(y / Float64(a - z))))
	t_2 = Float64(t_1 + Float64(Float64(Float64(y - z) * t) / Float64(a - z)))
	t_3 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_3 <= -5e+58)
		tmp = Float64(t_1 + Float64(1.0 / Float64(Float64(Float64(a - z) / t) / Float64(y - z))));
	elseif (t_3 <= -1e-254)
		tmp = t_2;
	elseif (t_3 <= 0.0)
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((1.0 + (z / (a - z))) - (y / (a - z)));
	t_2 = t_1 + (((y - z) * t) / (a - z));
	t_3 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_2;
	elseif (t_3 <= -5e+58)
		tmp = t_1 + (1.0 / (((a - z) / t) / (y - z)));
	elseif (t_3 <= -1e-254)
		tmp = t_2;
	elseif (t_3 <= 0.0)
		tmp = t + ((y - a) * ((x - t) / z));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(1.0 + N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$2, If[LessEqual[t$95$3, -5e+58], N[(t$95$1 + N[(1.0 / N[(N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -1e-254], t$95$2, If[LessEqual[t$95$3, 0.0], N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -inf.0 or -4.99999999999999986e58 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.9999999999999991e-255

   1. Initial program 78.4%

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

   3. Taylor expanded in x around -inf 96.6%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.99999999999999986e58

   1. Initial program 98.4%

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

   3. Taylor expanded in x around -inf 67.3%

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

      1. clear-num 67.3%

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

      2. inv-pow 67.3%

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

   5. Applied egg-rr 67.3%

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

      1. unpow-1 67.3%

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

      2. associate-/r* 98.6%

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

   7. Simplified 98.6%

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

   if -9.9999999999999991e-255 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.7%

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

      1. clear-num 3.6%

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

      2. associate-/r/ 3.6%

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

   4. Applied egg-rr 3.6%

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

   5. Taylor expanded in z around inf 87.7%

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

      1. associate--l+ 87.7%

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

      2. associate-*r/ 87.7%

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

      3. associate-*r/ 87.7%

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

      4. div-sub 87.7%

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

      5. distribute-lft-out-- 87.7%

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

      6. associate-*r/ 87.7%

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

      7. mul-1-neg 87.7%

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

      8. unsub-neg 87.7%

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

      9. distribute-rgt-out-- 87.9%

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

   7. Simplified 87.9%

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

      1. *-commutative 87.9%

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

      2. *-un-lft-identity 87.9%

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

      3. times-frac 99.8%

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

   9. Applied egg-rr 99.8%

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

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

   1. Initial program 94.3%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -\infty:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{z}{a - z}\right) - \frac{y}{a - z}\right) + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{z}{a - z}\right) - \frac{y}{a - z}\right) + \frac{1}{\frac{\frac{a - z}{t}}{y - z}}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-254}:\\ \;\;\;\;x \cdot \left(\left(1 + \frac{z}{a - z}\right) - \frac{y}{a - z}\right) + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-236} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 (- INFINITY))
     (* (- t x) (/ y (- a z)))
     (if (or (<= t_1 -5e-236) (not (<= t_1 0.0)))
       t_1
       (- t (* (- t x) (/ (- y a) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (t - x) * (y / (a - z));
	} else if ((t_1 <= -5e-236) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) * ((y - a) / z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (t - x) * (y / (a - z));
	} else if ((t_1 <= -5e-236) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) * ((y - a) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (t - x) * (y / (a - z))
	elif (t_1 <= -5e-236) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t - ((t - x) * ((y - a) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif ((t_1 <= -5e-236) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(Float64(t - x) * Float64(Float64(y - a) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (t - x) * (y / (a - z));
	elseif ((t_1 <= -5e-236) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t - ((t - x) * ((y - a) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -5e-236], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t - N[(N[(t - x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 70.1%

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

   3. Taylor expanded in y around inf 69.2%

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

      1. div-sub 69.6%

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

      2. associate-*r/ 87.3%

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

      3. associate-/l* 69.6%

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

      4. associate-/r/ 87.4%

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

   5. Simplified 87.4%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.9999999999999998e-236 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 94.4%

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

   if -4.9999999999999998e-236 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.9%

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

      1. clear-num 3.8%

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

      2. associate-/r/ 3.8%

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

   4. Applied egg-rr 3.8%

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

   5. Taylor expanded in z around inf 88.4%

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

      1. associate--l+ 88.4%

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

      2. associate-*r/ 88.4%

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

      3. associate-*r/ 88.4%

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

      4. div-sub 88.4%

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

      5. distribute-lft-out-- 88.4%

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

      6. associate-*r/ 88.4%

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

      7. mul-1-neg 88.4%

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

      8. unsub-neg 88.4%

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

      9. distribute-rgt-out-- 88.6%

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

   7. Simplified 88.6%

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

   8. Taylor expanded in t around inf 88.6%

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

      1. +-commutative 88.6%

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

      2. mul-1-neg 88.6%

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

      3. sub-neg 88.6%

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

      4. associate-/l* 88.6%

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

      5. associate-/l* 96.8%

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

      6. div-sub 96.8%

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

      7. associate-/r/ 97.0%

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

      8. *-commutative 97.0%

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

      9. associate-*r/ 88.6%

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

      10. *-commutative 88.6%

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

      11. associate-*r/ 96.9%

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

   10. Simplified 96.9%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -\infty:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-236} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-236} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{1}{\frac{z}{y - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 (- INFINITY))
     (* (- t x) (/ y (- a z)))
     (if (or (<= t_1 -5e-236) (not (<= t_1 0.0)))
       t_1
       (- t (* (- t x) (/ 1.0 (/ z (- y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (t - x) * (y / (a - z));
	} else if ((t_1 <= -5e-236) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) * (1.0 / (z / (y - a))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (t - x) * (y / (a - z));
	} else if ((t_1 <= -5e-236) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t - ((t - x) * (1.0 / (z / (y - a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (t - x) * (y / (a - z))
	elif (t_1 <= -5e-236) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t - ((t - x) * (1.0 / (z / (y - a))))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif ((t_1 <= -5e-236) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t - Float64(Float64(t - x) * Float64(1.0 / Float64(z / Float64(y - a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (t - x) * (y / (a - z));
	elseif ((t_1 <= -5e-236) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t - ((t - x) * (1.0 / (z / (y - a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -5e-236], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t - N[(N[(t - x), $MachinePrecision] * N[(1.0 / N[(z / N[(y - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 70.1%

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

   3. Taylor expanded in y around inf 69.2%

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

      1. div-sub 69.6%

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

      2. associate-*r/ 87.3%

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

      3. associate-/l* 69.6%

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

      4. associate-/r/ 87.4%

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

   5. Simplified 87.4%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.9999999999999998e-236 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 94.4%

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

   if -4.9999999999999998e-236 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.9%

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

      1. clear-num 3.8%

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

      2. associate-/r/ 3.8%

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

   4. Applied egg-rr 3.8%

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

   5. Taylor expanded in z around inf 88.4%

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

      1. associate--l+ 88.4%

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

      2. associate-*r/ 88.4%

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

      3. associate-*r/ 88.4%

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

      4. div-sub 88.4%

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

      5. distribute-lft-out-- 88.4%

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

      6. associate-*r/ 88.4%

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

      7. mul-1-neg 88.4%

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

      8. unsub-neg 88.4%

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

      9. distribute-rgt-out-- 88.6%

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

   7. Simplified 88.6%

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

      1. associate-/l* 96.8%

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

      2. div-inv 96.9%

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

   9. Applied egg-rr 96.9%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -\infty:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-236} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{1}{\frac{z}{y - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-236} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (<= t_1 (- INFINITY))
     (* (- t x) (/ y (- a z)))
     (if (or (<= t_1 -5e-236) (not (<= t_1 0.0)))
       t_1
       (+ t (* (- y a) (/ (- x t) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (t - x) * (y / (a - z));
	} else if ((t_1 <= -5e-236) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((y - a) * ((x - t) / z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (t - x) * (y / (a - z));
	} else if ((t_1 <= -5e-236) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + ((y - a) * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (t - x) * (y / (a - z))
	elif (t_1 <= -5e-236) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + ((y - a) * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif ((t_1 <= -5e-236) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(y - a) * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (t - x) * (y / (a - z));
	elseif ((t_1 <= -5e-236) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + ((y - a) * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -5e-236], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(y - a), $MachinePrecision] * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 70.1%

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

   3. Taylor expanded in y around inf 69.2%

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

      1. div-sub 69.6%

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

      2. associate-*r/ 87.3%

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

      3. associate-/l* 69.6%

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

      4. associate-/r/ 87.4%

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

   5. Simplified 87.4%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -4.9999999999999998e-236 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 94.4%

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

   if -4.9999999999999998e-236 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.9%

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

      1. clear-num 3.8%

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

      2. associate-/r/ 3.8%

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

   4. Applied egg-rr 3.8%

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

   5. Taylor expanded in z around inf 88.4%

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

      1. associate--l+ 88.4%

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

      2. associate-*r/ 88.4%

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

      3. associate-*r/ 88.4%

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

      4. div-sub 88.4%

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

      5. distribute-lft-out-- 88.4%

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

      6. associate-*r/ 88.4%

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

      7. mul-1-neg 88.4%

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

      8. unsub-neg 88.4%

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

      9. distribute-rgt-out-- 88.6%

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

   7. Simplified 88.6%

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

      1. *-commutative 88.6%

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

      2. *-un-lft-identity 88.6%

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

      3. times-frac 97.0%

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

   9. Applied egg-rr 97.0%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -\infty:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-236} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \left(y - a\right) \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 40.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+107}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-151}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-113}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- t x) (/ y a))))
   (if (<= z -1.8e+107)
     t
     (if (<= z -3.4e-151)
       x
       (if (<= z 1.26e-169)
         t_1
         (if (<= z 7e-113) (+ x t) (if (<= z 1.06e-37) t_1 t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / a);
	double tmp;
	if (z <= -1.8e+107) {
		tmp = t;
	} else if (z <= -3.4e-151) {
		tmp = x;
	} else if (z <= 1.26e-169) {
		tmp = t_1;
	} else if (z <= 7e-113) {
		tmp = x + t;
	} else if (z <= 1.06e-37) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = (t - x) * (y / a)
    if (z <= (-1.8d+107)) then
        tmp = t
    else if (z <= (-3.4d-151)) then
        tmp = x
    else if (z <= 1.26d-169) then
        tmp = t_1
    else if (z <= 7d-113) then
        tmp = x + t
    else if (z <= 1.06d-37) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / a);
	double tmp;
	if (z <= -1.8e+107) {
		tmp = t;
	} else if (z <= -3.4e-151) {
		tmp = x;
	} else if (z <= 1.26e-169) {
		tmp = t_1;
	} else if (z <= 7e-113) {
		tmp = x + t;
	} else if (z <= 1.06e-37) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / a)
	tmp = 0
	if z <= -1.8e+107:
		tmp = t
	elif z <= -3.4e-151:
		tmp = x
	elif z <= 1.26e-169:
		tmp = t_1
	elif z <= 7e-113:
		tmp = x + t
	elif z <= 1.06e-37:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / a))
	tmp = 0.0
	if (z <= -1.8e+107)
		tmp = t;
	elseif (z <= -3.4e-151)
		tmp = x;
	elseif (z <= 1.26e-169)
		tmp = t_1;
	elseif (z <= 7e-113)
		tmp = Float64(x + t);
	elseif (z <= 1.06e-37)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / a);
	tmp = 0.0;
	if (z <= -1.8e+107)
		tmp = t;
	elseif (z <= -3.4e-151)
		tmp = x;
	elseif (z <= 1.26e-169)
		tmp = t_1;
	elseif (z <= 7e-113)
		tmp = x + t;
	elseif (z <= 1.06e-37)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e+107], t, If[LessEqual[z, -3.4e-151], x, If[LessEqual[z, 1.26e-169], t$95$1, If[LessEqual[z, 7e-113], N[(x + t), $MachinePrecision], If[LessEqual[z, 1.06e-37], t$95$1, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.7999999999999999e107 or 1.06000000000000003e-37 < z

   1. Initial program 67.2%

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

   3. Taylor expanded in z around inf 54.6%

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

   if -1.7999999999999999e107 < z < -3.4000000000000003e-151

   1. Initial program 92.4%

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

   3. Taylor expanded in a around inf 42.9%

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

   if -3.4000000000000003e-151 < z < 1.26e-169 or 7.00000000000000057e-113 < z < 1.06000000000000003e-37

   1. Initial program 89.5%

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

   3. Taylor expanded in y around inf 57.5%

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

      1. div-sub 60.0%

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

      2. associate-*r/ 63.2%

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

      3. associate-/l* 60.1%

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

      4. associate-/r/ 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in a around inf 51.7%

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

   if 1.26e-169 < z < 7.00000000000000057e-113

   1. Initial program 85.2%

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

      1. +-commutative 85.2%

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

      2. fma-def 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in t around inf 71.0%

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

   6. Taylor expanded in z around inf 57.5%

      \[\leadsto \color{blue}{t + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+107}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-151}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-169}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-113}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-37}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{t - x}\\ t_2 := t - \left(t - x\right) \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+18}:\\ \;\;\;\;x - \frac{z}{t_1}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-12} \lor \neg \left(z \leq 3.65 \cdot 10^{-115}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- t x))) (t_2 (- t (* (- t x) (/ y z)))))
   (if (<= z -6.6e+104)
     t_2
     (if (<= z -2.4e+18)
       (- x (/ z t_1))
       (if (or (<= z -1.85e-12) (not (<= z 3.65e-115)))
         t_2
         (+ x (/ y t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (t - x);
	double t_2 = t - ((t - x) * (y / z));
	double tmp;
	if (z <= -6.6e+104) {
		tmp = t_2;
	} else if (z <= -2.4e+18) {
		tmp = x - (z / t_1);
	} else if ((z <= -1.85e-12) || !(z <= 3.65e-115)) {
		tmp = t_2;
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a / (t - x)
    t_2 = t - ((t - x) * (y / z))
    if (z <= (-6.6d+104)) then
        tmp = t_2
    else if (z <= (-2.4d+18)) then
        tmp = x - (z / t_1)
    else if ((z <= (-1.85d-12)) .or. (.not. (z <= 3.65d-115))) then
        tmp = t_2
    else
        tmp = x + (y / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (t - x);
	double t_2 = t - ((t - x) * (y / z));
	double tmp;
	if (z <= -6.6e+104) {
		tmp = t_2;
	} else if (z <= -2.4e+18) {
		tmp = x - (z / t_1);
	} else if ((z <= -1.85e-12) || !(z <= 3.65e-115)) {
		tmp = t_2;
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (t - x)
	t_2 = t - ((t - x) * (y / z))
	tmp = 0
	if z <= -6.6e+104:
		tmp = t_2
	elif z <= -2.4e+18:
		tmp = x - (z / t_1)
	elif (z <= -1.85e-12) or not (z <= 3.65e-115):
		tmp = t_2
	else:
		tmp = x + (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(t - x))
	t_2 = Float64(t - Float64(Float64(t - x) * Float64(y / z)))
	tmp = 0.0
	if (z <= -6.6e+104)
		tmp = t_2;
	elseif (z <= -2.4e+18)
		tmp = Float64(x - Float64(z / t_1));
	elseif ((z <= -1.85e-12) || !(z <= 3.65e-115))
		tmp = t_2;
	else
		tmp = Float64(x + Float64(y / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (t - x);
	t_2 = t - ((t - x) * (y / z));
	tmp = 0.0;
	if (z <= -6.6e+104)
		tmp = t_2;
	elseif (z <= -2.4e+18)
		tmp = x - (z / t_1);
	elseif ((z <= -1.85e-12) || ~((z <= 3.65e-115)))
		tmp = t_2;
	else
		tmp = x + (y / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(N[(t - x), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e+104], t$95$2, If[LessEqual[z, -2.4e+18], N[(x - N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -1.85e-12], N[Not[LessEqual[z, 3.65e-115]], $MachinePrecision]], t$95$2, N[(x + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.59999999999999969e104 or -2.4e18 < z < -1.84999999999999999e-12 or 3.64999999999999982e-115 < z

   1. Initial program 71.6%

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

      1. clear-num 70.7%

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

      2. associate-/r/ 71.4%

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

   4. Applied egg-rr 71.4%

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

   5. Taylor expanded in z around inf 69.7%

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

      1. associate--l+ 69.7%

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

      2. associate-*r/ 69.7%

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

      3. associate-*r/ 69.7%

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

      4. div-sub 69.7%

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

      5. distribute-lft-out-- 69.7%

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

      6. associate-*r/ 69.7%

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

      7. mul-1-neg 69.7%

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

      8. unsub-neg 69.7%

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

      9. distribute-rgt-out-- 70.6%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in t around inf 70.6%

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

      1. +-commutative 70.6%

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

      2. mul-1-neg 70.6%

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

      3. sub-neg 70.6%

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

      4. associate-/l* 75.6%

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

      5. associate-/l* 79.7%

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

      6. div-sub 80.5%

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

      7. associate-/r/ 79.7%

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

      8. *-commutative 79.7%

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

      9. associate-*r/ 70.6%

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

      10. *-commutative 70.6%

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

      11. associate-*r/ 80.5%

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

   10. Simplified 80.5%

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

   11. Taylor expanded in y around inf 73.3%

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

   if -6.59999999999999969e104 < z < -2.4e18

   1. Initial program 83.8%

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

   3. Taylor expanded in y around 0 54.2%

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

      1. mul-1-neg 54.2%

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

      2. unsub-neg 54.2%

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

      3. associate-/l* 65.4%

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

      4. associate-/r/ 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in a around inf 57.9%

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

      1. mul-1-neg 57.9%

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

      2. unsub-neg 57.9%

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

      3. associate-/l* 63.7%

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

   8. Simplified 63.7%

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

   if -1.84999999999999999e-12 < z < 3.64999999999999982e-115

   1. Initial program 90.6%

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

   3. Taylor expanded in z around 0 78.5%

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

      1. associate-/l* 78.6%

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

   5. Simplified 78.6%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+104}:\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+18}:\\ \;\;\;\;x - \frac{z}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-12} \lor \neg \left(z \leq 3.65 \cdot 10^{-115}\right):\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;a \leq -1.05 \cdot 10^{+140}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-224}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (/ t (/ a y)))))
   (if (<= a -1.05e+140)
     t_2
     (if (<= a -1.05e-124)
       t_1
       (if (<= a -8e-224)
         (* (- t x) (/ y (- a z)))
         (if (<= a 2.4e+74) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (t / (a / y));
	double tmp;
	if (a <= -1.05e+140) {
		tmp = t_2;
	} else if (a <= -1.05e-124) {
		tmp = t_1;
	} else if (a <= -8e-224) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 2.4e+74) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (t / (a / y))
    if (a <= (-1.05d+140)) then
        tmp = t_2
    else if (a <= (-1.05d-124)) then
        tmp = t_1
    else if (a <= (-8d-224)) then
        tmp = (t - x) * (y / (a - z))
    else if (a <= 2.4d+74) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (t / (a / y));
	double tmp;
	if (a <= -1.05e+140) {
		tmp = t_2;
	} else if (a <= -1.05e-124) {
		tmp = t_1;
	} else if (a <= -8e-224) {
		tmp = (t - x) * (y / (a - z));
	} else if (a <= 2.4e+74) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (t / (a / y))
	tmp = 0
	if a <= -1.05e+140:
		tmp = t_2
	elif a <= -1.05e-124:
		tmp = t_1
	elif a <= -8e-224:
		tmp = (t - x) * (y / (a - z))
	elif a <= 2.4e+74:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(t / Float64(a / y)))
	tmp = 0.0
	if (a <= -1.05e+140)
		tmp = t_2;
	elseif (a <= -1.05e-124)
		tmp = t_1;
	elseif (a <= -8e-224)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	elseif (a <= 2.4e+74)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (t / (a / y));
	tmp = 0.0;
	if (a <= -1.05e+140)
		tmp = t_2;
	elseif (a <= -1.05e-124)
		tmp = t_1;
	elseif (a <= -8e-224)
		tmp = (t - x) * (y / (a - z));
	elseif (a <= 2.4e+74)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.05e+140], t$95$2, If[LessEqual[a, -1.05e-124], t$95$1, If[LessEqual[a, -8e-224], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e+74], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.0500000000000001e140 or 2.40000000000000008e74 < a

   1. Initial program 91.2%

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

      1. +-commutative 91.2%

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

      2. fma-def 91.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in t around inf 83.6%

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

   6. Taylor expanded in z around 0 65.6%

      \[\leadsto \color{blue}{x + \frac{t \cdot y}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 69.4%

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

   8. Simplified 69.4%

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

   if -1.0500000000000001e140 < a < -1.05e-124 or -8.0000000000000002e-224 < a < 2.40000000000000008e74

   1. Initial program 75.7%

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

   3. Taylor expanded in x around 0 48.7%

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

      1. associate-/l* 65.2%

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

   5. Simplified 65.2%

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

      1. div-inv 65.1%

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

      2. clear-num 65.2%

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

   7. Applied egg-rr 65.2%

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

   if -1.05e-124 < a < -8.0000000000000002e-224

   1. Initial program 73.3%

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

   3. Taylor expanded in y around inf 75.0%

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

      1. div-sub 75.0%

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

      2. associate-*r/ 74.9%

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

      3. associate-/l* 74.9%

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

      4. associate-/r/ 74.9%

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

   5. Simplified 74.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+140}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-124}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-224}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-13} \lor \neg \left(z \leq 3.65 \cdot 10^{-115}\right):\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3e-13) (not (<= z 3.65e-115)))
   (- t (* (- t x) (/ (- y a) z)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3e-13) || !(z <= 3.65e-115)) {
		tmp = t - ((t - x) * ((y - a) / z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((z <= (-3d-13)) .or. (.not. (z <= 3.65d-115))) then
        tmp = t - ((t - x) * ((y - a) / z))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3e-13) || !(z <= 3.65e-115)) {
		tmp = t - ((t - x) * ((y - a) / z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3e-13) or not (z <= 3.65e-115):
		tmp = t - ((t - x) * ((y - a) / z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3e-13) || !(z <= 3.65e-115))
		tmp = Float64(t - Float64(Float64(t - x) * Float64(Float64(y - a) / z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3e-13) || ~((z <= 3.65e-115)))
		tmp = t - ((t - x) * ((y - a) / z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3e-13], N[Not[LessEqual[z, 3.65e-115]], $MachinePrecision]], N[(t - N[(N[(t - x), $MachinePrecision] * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.99999999999999984e-13 or 3.64999999999999982e-115 < z

   1. Initial program 72.8%

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

      1. clear-num 72.0%

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

      2. associate-/r/ 72.7%

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

   4. Applied egg-rr 72.7%

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

   5. Taylor expanded in z around inf 67.0%

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

      1. associate--l+ 67.0%

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

      2. associate-*r/ 67.0%

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

      3. associate-*r/ 67.0%

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

      4. div-sub 67.0%

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

      5. distribute-lft-out-- 67.0%

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

      6. associate-*r/ 67.0%

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

      7. mul-1-neg 67.0%

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

      8. unsub-neg 67.0%

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

      9. distribute-rgt-out-- 67.9%

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

   7. Simplified 67.9%

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

   8. Taylor expanded in t around inf 67.2%

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

      1. +-commutative 67.2%

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

      2. mul-1-neg 67.2%

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

      3. sub-neg 67.2%

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

      4. associate-/l* 71.6%

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

      5. associate-/l* 75.3%

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

      6. div-sub 76.6%

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

      7. associate-/r/ 76.0%

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

      8. *-commutative 76.0%

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

      9. associate-*r/ 67.9%

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

      10. *-commutative 67.9%

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

      11. associate-*r/ 76.7%

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

   10. Simplified 76.7%

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

   if -2.99999999999999984e-13 < z < 3.64999999999999982e-115

   1. Initial program 90.6%

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

   3. Taylor expanded in z around 0 78.5%

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

      1. associate-/l* 78.6%

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

   5. Simplified 78.6%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-13} \lor \neg \left(z \leq 3.65 \cdot 10^{-115}\right):\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y - a}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-12} \lor \neg \left(z \leq 6.4 \cdot 10^{-114}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.9e-12) (not (<= z 6.4e-114)))
   (* t (/ (- y z) (- a z)))
   (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e-12) || !(z <= 6.4e-114)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((z <= (-1.9d-12)) .or. (.not. (z <= 6.4d-114))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (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 tmp;
	if ((z <= -1.9e-12) || !(z <= 6.4e-114)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.9e-12) or not (z <= 6.4e-114):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.9e-12) || !(z <= 6.4e-114))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.9e-12) || ~((z <= 6.4e-114)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.9e-12], N[Not[LessEqual[z, 6.4e-114]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.89999999999999998e-12 or 6.4000000000000003e-114 < z

   1. Initial program 72.7%

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

   3. Taylor expanded in x around 0 41.5%

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

      1. associate-/l* 61.9%

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

   5. Simplified 61.9%

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

      1. div-inv 61.9%

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

      2. clear-num 61.9%

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

   7. Applied egg-rr 61.9%

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

   if -1.89999999999999998e-12 < z < 6.4000000000000003e-114

   1. Initial program 90.7%

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

      1. +-commutative 90.7%

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

      2. fma-def 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in t around inf 66.9%

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

   6. Taylor expanded in z around 0 62.8%

      \[\leadsto \color{blue}{x + \frac{t \cdot y}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 65.5%

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

   8. Simplified 65.5%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-12} \lor \neg \left(z \leq 6.4 \cdot 10^{-114}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 64.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+39} \lor \neg \left(z \leq 1.8 \cdot 10^{-113}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.5e+39) (not (<= z 1.8e-113)))
   (* t (/ (- y z) (- a z)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e+39) || !(z <= 1.8e-113)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((z <= (-6.5d+39)) .or. (.not. (z <= 1.8d-113))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.5e+39) || !(z <= 1.8e-113)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.5e+39) or not (z <= 1.8e-113):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.5e+39) || !(z <= 1.8e-113))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.5e+39) || ~((z <= 1.8e-113)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.5e+39], N[Not[LessEqual[z, 1.8e-113]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5000000000000001e39 or 1.79999999999999987e-113 < z

   1. Initial program 70.9%

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

   3. Taylor expanded in x around 0 41.2%

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

      1. associate-/l* 62.9%

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

   5. Simplified 62.9%

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

      1. div-inv 62.9%

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

      2. clear-num 62.9%

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

   7. Applied egg-rr 62.9%

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

   if -6.5000000000000001e39 < z < 1.79999999999999987e-113

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 76.1%

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

      1. associate-/l* 76.2%

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

   5. Simplified 76.2%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+39} \lor \neg \left(z \leq 1.8 \cdot 10^{-113}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 67.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-14} \lor \neg \left(z \leq 3.65 \cdot 10^{-115}\right):\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.6e-14) (not (<= z 3.65e-115)))
   (- t (* (- t x) (/ y z)))
   (+ x (/ y (/ a (- t x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.6e-14) || !(z <= 3.65e-115)) {
		tmp = t - ((t - x) * (y / z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((z <= (-9.6d-14)) .or. (.not. (z <= 3.65d-115))) then
        tmp = t - ((t - x) * (y / z))
    else
        tmp = x + (y / (a / (t - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.6e-14) || !(z <= 3.65e-115)) {
		tmp = t - ((t - x) * (y / z));
	} else {
		tmp = x + (y / (a / (t - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.6e-14) or not (z <= 3.65e-115):
		tmp = t - ((t - x) * (y / z))
	else:
		tmp = x + (y / (a / (t - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.6e-14) || !(z <= 3.65e-115))
		tmp = Float64(t - Float64(Float64(t - x) * Float64(y / z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.6e-14) || ~((z <= 3.65e-115)))
		tmp = t - ((t - x) * (y / z));
	else
		tmp = x + (y / (a / (t - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.6e-14], N[Not[LessEqual[z, 3.65e-115]], $MachinePrecision]], N[(t - N[(N[(t - x), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.599999999999999e-14 or 3.64999999999999982e-115 < z

   1. Initial program 72.8%

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

      1. clear-num 72.0%

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

      2. associate-/r/ 72.7%

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

   4. Applied egg-rr 72.7%

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

   5. Taylor expanded in z around inf 67.0%

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

      1. associate--l+ 67.0%

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

      2. associate-*r/ 67.0%

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

      3. associate-*r/ 67.0%

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

      4. div-sub 67.0%

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

      5. distribute-lft-out-- 67.0%

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

      6. associate-*r/ 67.0%

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

      7. mul-1-neg 67.0%

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

      8. unsub-neg 67.0%

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

      9. distribute-rgt-out-- 67.9%

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

   7. Simplified 67.9%

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

   8. Taylor expanded in t around inf 67.2%

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

      1. +-commutative 67.2%

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

      2. mul-1-neg 67.2%

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

      3. sub-neg 67.2%

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

      4. associate-/l* 71.6%

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

      5. associate-/l* 75.3%

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

      6. div-sub 76.6%

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

      7. associate-/r/ 76.0%

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

      8. *-commutative 76.0%

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

      9. associate-*r/ 67.9%

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

      10. *-commutative 67.9%

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

      11. associate-*r/ 76.7%

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

   10. Simplified 76.7%

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

   11. Taylor expanded in y around inf 69.4%

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

   if -9.599999999999999e-14 < z < 3.64999999999999982e-115

   1. Initial program 90.6%

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

   3. Taylor expanded in z around 0 78.5%

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

      1. associate-/l* 78.6%

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

   5. Simplified 78.6%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-14} \lor \neg \left(z \leq 3.65 \cdot 10^{-115}\right):\\ \;\;\;\;t - \left(t - x\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 54.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+106} \lor \neg \left(z \leq 3.7 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{z}{a - z} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1e+106) (not (<= z 3.7e-36)))
   (* (/ z (- a z)) (- t))
   (+ x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1e+106) || !(z <= 3.7e-36)) {
		tmp = (z / (a - z)) * -t;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if ((z <= (-1d+106)) .or. (.not. (z <= 3.7d-36))) then
        tmp = (z / (a - z)) * -t
    else
        tmp = x + (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 tmp;
	if ((z <= -1e+106) || !(z <= 3.7e-36)) {
		tmp = (z / (a - z)) * -t;
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1e+106) or not (z <= 3.7e-36):
		tmp = (z / (a - z)) * -t
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1e+106) || !(z <= 3.7e-36))
		tmp = Float64(Float64(z / Float64(a - z)) * Float64(-t));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1e+106) || ~((z <= 3.7e-36)))
		tmp = (z / (a - z)) * -t;
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1e+106], N[Not[LessEqual[z, 3.7e-36]], $MachinePrecision]], N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] * (-t)), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000009e106 or 3.70000000000000002e-36 < z

   1. Initial program 67.5%

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

   3. Taylor expanded in x around 0 40.4%

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

      1. associate-/l* 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in y around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. associate-*r/ 59.7%

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

   8. Simplified 59.7%

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

   if -1.00000000000000009e106 < z < 3.70000000000000002e-36

   1. Initial program 89.6%

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

      1. +-commutative 89.6%

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

      2. fma-def 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in t around inf 65.8%

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

   6. Taylor expanded in z around 0 56.1%

      \[\leadsto \color{blue}{x + \frac{t \cdot y}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 57.9%

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

   8. Simplified 57.9%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+106} \lor \neg \left(z \leq 3.7 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{z}{a - z} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 54.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+105}:\\ \;\;\;\;\frac{-t}{-1 + \frac{a}{z}}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a - z} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.25e+105)
   (/ (- t) (+ -1.0 (/ a z)))
   (if (<= z 5.7e-36) (+ x (/ t (/ a y))) (* (/ z (- a z)) (- t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.25e+105) {
		tmp = -t / (-1.0 + (a / z));
	} else if (z <= 5.7e-36) {
		tmp = x + (t / (a / y));
	} else {
		tmp = (z / (a - z)) * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (z <= (-2.25d+105)) then
        tmp = -t / ((-1.0d0) + (a / z))
    else if (z <= 5.7d-36) then
        tmp = x + (t / (a / y))
    else
        tmp = (z / (a - z)) * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.25e+105) {
		tmp = -t / (-1.0 + (a / z));
	} else if (z <= 5.7e-36) {
		tmp = x + (t / (a / y));
	} else {
		tmp = (z / (a - z)) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.25e+105:
		tmp = -t / (-1.0 + (a / z))
	elif z <= 5.7e-36:
		tmp = x + (t / (a / y))
	else:
		tmp = (z / (a - z)) * -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.25e+105)
		tmp = Float64(Float64(-t) / Float64(-1.0 + Float64(a / z)));
	elseif (z <= 5.7e-36)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(Float64(z / Float64(a - z)) * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.25e+105)
		tmp = -t / (-1.0 + (a / z));
	elseif (z <= 5.7e-36)
		tmp = x + (t / (a / y));
	else
		tmp = (z / (a - z)) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.25e+105], N[((-t) / N[(-1.0 + N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.7e-36], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] * (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2500000000000001e105

   1. Initial program 61.7%

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

   3. Taylor expanded in x around 0 43.6%

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

      1. associate-/l* 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in y around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. associate-/l* 55.1%

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

      3. distribute-neg-frac 55.1%

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

      4. div-sub 55.1%

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

      5. sub-neg 55.1%

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

      6. *-inverses 55.1%

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

      7. metadata-eval 55.1%

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

   8. Simplified 55.1%

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

   if -2.2500000000000001e105 < z < 5.6999999999999999e-36

   1. Initial program 89.6%

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

      1. +-commutative 89.6%

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

      2. fma-def 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in t around inf 65.8%

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

   6. Taylor expanded in z around 0 56.1%

      \[\leadsto \color{blue}{x + \frac{t \cdot y}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 57.9%

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

   8. Simplified 57.9%

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

   if 5.6999999999999999e-36 < z

   1. Initial program 71.9%

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

   3. Taylor expanded in x around 0 37.9%

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

      1. associate-/l* 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in y around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. associate-*r/ 63.3%

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

   8. Simplified 63.3%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+105}:\\ \;\;\;\;\frac{-t}{-1 + \frac{a}{z}}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a - z} \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 53.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+104}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a - z} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.6e+104)
   (/ (- t) (/ z (- y z)))
   (if (<= z 5.7e-36) (+ x (/ t (/ a y))) (* (/ z (- a z)) (- t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.6e+104) {
		tmp = -t / (z / (y - z));
	} else if (z <= 5.7e-36) {
		tmp = x + (t / (a / y));
	} else {
		tmp = (z / (a - z)) * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (z <= (-6.6d+104)) then
        tmp = -t / (z / (y - z))
    else if (z <= 5.7d-36) then
        tmp = x + (t / (a / y))
    else
        tmp = (z / (a - z)) * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.6e+104) {
		tmp = -t / (z / (y - z));
	} else if (z <= 5.7e-36) {
		tmp = x + (t / (a / y));
	} else {
		tmp = (z / (a - z)) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.6e+104:
		tmp = -t / (z / (y - z))
	elif z <= 5.7e-36:
		tmp = x + (t / (a / y))
	else:
		tmp = (z / (a - z)) * -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.6e+104)
		tmp = Float64(Float64(-t) / Float64(z / Float64(y - z)));
	elseif (z <= 5.7e-36)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = Float64(Float64(z / Float64(a - z)) * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.6e+104)
		tmp = -t / (z / (y - z));
	elseif (z <= 5.7e-36)
		tmp = x + (t / (a / y));
	else
		tmp = (z / (a - z)) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.6e+104], N[((-t) / N[(z / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.7e-36], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision] * (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.59999999999999969e104

   1. Initial program 61.7%

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

   3. Taylor expanded in x around 0 43.6%

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

      1. associate-/l* 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in a around 0 39.7%

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

      1. mul-1-neg 39.7%

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

      2. associate-/l* 60.9%

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

      3. distribute-neg-frac 60.9%

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

   8. Simplified 60.9%

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

   if -6.59999999999999969e104 < z < 5.6999999999999999e-36

   1. Initial program 89.6%

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

      1. +-commutative 89.6%

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

      2. fma-def 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in t around inf 65.8%

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

   6. Taylor expanded in z around 0 56.1%

      \[\leadsto \color{blue}{x + \frac{t \cdot y}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 57.9%

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

   8. Simplified 57.9%

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

   if 5.6999999999999999e-36 < z

   1. Initial program 71.9%

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

   3. Taylor expanded in x around 0 37.9%

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

      1. associate-/l* 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in y around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. associate-*r/ 63.3%

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

   8. Simplified 63.3%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+104}:\\ \;\;\;\;\frac{-t}{\frac{z}{y - z}}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-36}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a - z} \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+105}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-29}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e+105) t (if (<= z 1.05e-29) (+ x (/ t (/ a y))) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+105) {
		tmp = t;
	} else if (z <= 1.05e-29) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (z <= (-7.2d+105)) then
        tmp = t
    else if (z <= 1.05d-29) then
        tmp = x + (t / (a / y))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e+105) {
		tmp = t;
	} else if (z <= 1.05e-29) {
		tmp = x + (t / (a / y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.2e+105:
		tmp = t
	elif z <= 1.05e-29:
		tmp = x + (t / (a / y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e+105)
		tmp = t;
	elseif (z <= 1.05e-29)
		tmp = Float64(x + Float64(t / Float64(a / y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.2e+105)
		tmp = t;
	elseif (z <= 1.05e-29)
		tmp = x + (t / (a / y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e+105], t, If[LessEqual[z, 1.05e-29], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if z < -7.1999999999999998e105 or 1.04999999999999995e-29 < z

   1. Initial program 66.9%

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

   3. Taylor expanded in z around inf 55.6%

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

   if -7.1999999999999998e105 < z < 1.04999999999999995e-29

   1. Initial program 89.7%

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

      1. +-commutative 89.7%

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

      2. fma-def 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in t around inf 66.3%

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

   6. Taylor expanded in z around 0 56.0%

      \[\leadsto \color{blue}{x + \frac{t \cdot y}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 57.9%

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

   8. Simplified 57.9%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+105}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-29}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 37.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.0036:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9e+132) x (if (<= a 0.0036) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+132) {
		tmp = x;
	} else if (a <= 0.0036) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (a <= (-9d+132)) then
        tmp = x
    else if (a <= 0.0036d0) then
        tmp = t
    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 tmp;
	if (a <= -9e+132) {
		tmp = x;
	} else if (a <= 0.0036) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9e+132:
		tmp = x
	elif a <= 0.0036:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9e+132)
		tmp = x;
	elseif (a <= 0.0036)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9e+132)
		tmp = x;
	elseif (a <= 0.0036)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9e+132], x, If[LessEqual[a, 0.0036], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -8.99999999999999944e132 or 0.0035999999999999999 < a

   1. Initial program 88.8%

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

   3. Taylor expanded in a around inf 55.9%

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

   if -8.99999999999999944e132 < a < 0.0035999999999999999

   1. Initial program 75.1%

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

   3. Taylor expanded in z around inf 37.3%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 0.0036:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 37.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+54}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 0.0033:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.2e+54) (+ x t) (if (<= a 0.0033) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.2e+54) {
		tmp = x + t;
	} else if (a <= 0.0033) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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) :: tmp
    if (a <= (-2.2d+54)) then
        tmp = x + t
    else if (a <= 0.0033d0) then
        tmp = t
    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 tmp;
	if (a <= -2.2e+54) {
		tmp = x + t;
	} else if (a <= 0.0033) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.2e+54:
		tmp = x + t
	elif a <= 0.0033:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.2e+54)
		tmp = Float64(x + t);
	elseif (a <= 0.0033)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.2e+54)
		tmp = x + t;
	elseif (a <= 0.0033)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.2e+54], N[(x + t), $MachinePrecision], If[LessEqual[a, 0.0033], t, x]]

Derivation

1. Split input into 3 regimes

2. if a < -2.1999999999999999e54

   1. Initial program 85.8%

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

      1. +-commutative 85.8%

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

      2. fma-def 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in t around inf 74.0%

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

   6. Taylor expanded in z around inf 49.8%

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

   if -2.1999999999999999e54 < a < 0.0033

   1. Initial program 74.6%

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

   3. Taylor expanded in z around inf 36.6%

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

   if 0.0033 < a

   1. Initial program 88.0%

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

   3. Taylor expanded in a around inf 57.2%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+54}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;a \leq 0.0033:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 24.9% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := t

Derivation

1. Initial program 80.0%

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

3. Taylor expanded in z around inf 28.4%

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

4. Final simplification 28.4%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024017 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))