Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.4% → 94.2%

Time: 19.5s

Alternatives: 22

Speedup: 0.3×

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: 80.4% 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: 94.2% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt[3]{a - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_3 := \frac{z}{t - x}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{-272}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{{t_1}^{2}}, \frac{t - x}{t_1}, x\right)\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\left(t - \frac{y}{t_3}\right) + \frac{a}{t_3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (cbrt (- a z)))
        (t_2 (+ x (* (- y z) (/ (- t x) (- a z)))))
        (t_3 (/ z (- t x))))
   (if (<= t_2 -2e-272)
     (fma (/ (- y z) (pow t_1 2.0)) (/ (- t x) t_1) x)
     (if (<= t_2 0.0)
       (+ (- t (/ y t_3)) (/ a t_3))
       (+ x (/ (- t x) (/ (- a z) (- y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = cbrt((a - z));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double t_3 = z / (t - x);
	double tmp;
	if (t_2 <= -2e-272) {
		tmp = fma(((y - z) / pow(t_1, 2.0)), ((t - x) / t_1), x);
	} else if (t_2 <= 0.0) {
		tmp = (t - (y / t_3)) + (a / t_3);
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = cbrt(Float64(a - z))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	t_3 = Float64(z / Float64(t - x))
	tmp = 0.0
	if (t_2 <= -2e-272)
		tmp = fma(Float64(Float64(y - z) / (t_1 ^ 2.0)), Float64(Float64(t - x) / t_1), x);
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(t - Float64(y / t_3)) + Float64(a / t_3));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	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[(x + N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-272], N[(N[(N[(y - z), $MachinePrecision] / N[Power[t$95$1, 2.0], $MachinePrecision]), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / t$95$1), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(N[(t - N[(y / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(a / t$95$3), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $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)))) < -1.99999999999999986e-272

   1. Initial program 93.2%

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

      1. +-commutative 93.2%

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

      2. associate-*r/ 79.8%

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

      3. add-cube-cbrt 78.9%

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

      4. times-frac 96.1%

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

      5. fma-def 96.1%

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

      6. pow2 96.1%

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

   3. Applied egg-rr 96.1%

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

   if -1.99999999999999986e-272 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

      1. *-commutative 3.4%

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

      2. associate-*l/ 3.0%

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

      3. associate-*r/ 3.4%

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

      4. clear-num 3.4%

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

      5. un-div-inv 3.4%

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

   3. Applied egg-rr 3.4%

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

   4. Taylor expanded in z around inf 85.3%

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

      1. sub-neg 85.3%

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

      2. +-commutative 85.3%

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

      3. mul-1-neg 85.3%

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

      4. unsub-neg 85.3%

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

      5. associate-/l* 97.0%

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

      6. mul-1-neg 97.0%

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

      7. remove-double-neg 97.0%

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

      8. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

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

   1. Initial program 88.4%

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

      1. *-commutative 88.4%

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

      2. associate-*l/ 76.7%

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

      3. associate-*r/ 91.8%

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

      4. clear-num 91.7%

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

      5. un-div-inv 92.7%

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

   3. Applied egg-rr 92.7%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-272}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{{\left(\sqrt[3]{a - z}\right)}^{2}}, \frac{t - x}{\sqrt[3]{a - z}}, x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;\left(t - \frac{y}{\frac{z}{t - x}}\right) + \frac{a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 2: 94.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := \frac{z}{t - x}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-272}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\left(t - \frac{y}{t_2}\right) + \frac{a}{t_2}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))) (t_2 (/ z (- t x))))
   (if (<= t_1 -2e-272)
     (fma (- t x) (/ (- y z) (- a z)) x)
     (if (<= t_1 0.0)
       (+ (- t (/ y t_2)) (/ a t_2))
       (+ x (/ (- t x) (/ (- a z) (- y 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 t_2 = z / (t - x);
	double tmp;
	if (t_1 <= -2e-272) {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	} else if (t_1 <= 0.0) {
		tmp = (t - (y / t_2)) + (a / t_2);
	} else {
		tmp = x + ((t - x) / ((a - z) / (y - 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))))
	t_2 = Float64(z / Float64(t - x))
	tmp = 0.0
	if (t_1 <= -2e-272)
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(t - Float64(y / t_2)) + Float64(a / t_2));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	end
	return 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]}, Block[{t$95$2 = N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-272], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(t - N[(y / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(a / t$95$2), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $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)))) < -1.99999999999999986e-272

   1. Initial program 93.2%

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

      1. +-commutative 93.2%

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

      2. associate-*r/ 79.8%

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

      3. *-commutative 79.8%

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

      4. associate-*r/ 95.6%

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

      5. fma-def 95.6%

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

   3. Simplified 95.6%

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

   if -1.99999999999999986e-272 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

      1. *-commutative 3.4%

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

      2. associate-*l/ 3.0%

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

      3. associate-*r/ 3.4%

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

      4. clear-num 3.4%

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

      5. un-div-inv 3.4%

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

   3. Applied egg-rr 3.4%

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

   4. Taylor expanded in z around inf 85.3%

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

      1. sub-neg 85.3%

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

      2. +-commutative 85.3%

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

      3. mul-1-neg 85.3%

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

      4. unsub-neg 85.3%

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

      5. associate-/l* 97.0%

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

      6. mul-1-neg 97.0%

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

      7. remove-double-neg 97.0%

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

      8. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

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

   1. Initial program 88.4%

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

      1. *-commutative 88.4%

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

      2. associate-*l/ 76.7%

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

      3. associate-*r/ 91.8%

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

      4. clear-num 91.7%

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

      5. un-div-inv 92.7%

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

   3. Applied egg-rr 92.7%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-272}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \mathbf{elif}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0:\\ \;\;\;\;\left(t - \frac{y}{\frac{z}{t - x}}\right) + \frac{a}{\frac{z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 3: 94.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := \frac{z}{t - x}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-272} \lor \neg \left(t_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(t - \frac{y}{t_2}\right) + \frac{a}{t_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))) (t_2 (/ z (- t x))))
   (if (or (<= t_1 -2e-272) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ (- t (/ y t_2)) (/ a t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = z / (t - x);
	double tmp;
	if ((t_1 <= -2e-272) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = (t - (y / t_2)) + (a / 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 = x + ((y - z) * ((t - x) / (a - z)))
    t_2 = z / (t - x)
    if ((t_1 <= (-2d-272)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = (t - (y / t_2)) + (a / 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 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = z / (t - x);
	double tmp;
	if ((t_1 <= -2e-272) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = (t - (y / t_2)) + (a / t_2);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	t_2 = z / (t - x)
	tmp = 0
	if (t_1 <= -2e-272) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = (t - (y / t_2)) + (a / t_2)
	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))))
	t_2 = Float64(z / Float64(t - x))
	tmp = 0.0
	if ((t_1 <= -2e-272) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(Float64(t - Float64(y / t_2)) + Float64(a / t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	t_2 = z / (t - x);
	tmp = 0.0;
	if ((t_1 <= -2e-272) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = (t - (y / t_2)) + (a / t_2);
	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]}, Block[{t$95$2 = N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-272], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - N[(y / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(a / t$95$2), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1.99999999999999986e-272 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 90.8%

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

      1. *-commutative 90.8%

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

      2. associate-*l/ 78.3%

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

      3. associate-*r/ 93.7%

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

      4. clear-num 93.7%

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

      5. un-div-inv 94.1%

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

   3. Applied egg-rr 94.1%

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

   if -1.99999999999999986e-272 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

      1. *-commutative 3.4%

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

      2. associate-*l/ 3.0%

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

      3. associate-*r/ 3.4%

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

      4. clear-num 3.4%

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

      5. un-div-inv 3.4%

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

   3. Applied egg-rr 3.4%

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

   4. Taylor expanded in z around inf 85.3%

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

      1. sub-neg 85.3%

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

      2. +-commutative 85.3%

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

      3. mul-1-neg 85.3%

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

      4. unsub-neg 85.3%

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

      5. associate-/l* 97.0%

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

      6. mul-1-neg 97.0%

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

      7. remove-double-neg 97.0%

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

      8. associate-/l* 99.9%

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

   6. Simplified 99.9%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -2 \cdot 10^{-272} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(t - \frac{y}{\frac{z}{t - x}}\right) + \frac{a}{\frac{z}{t - x}}\\ \end{array} \]

Alternative 4: 88.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-168} \lor \neg \left(t_1 \leq 2 \cdot 10^{-205}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -1e-168) (not (<= t_1 2e-205)))
     t_1
     (+ t (/ (* (- t x) (- a y)) 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 <= -1e-168) || !(t_1 <= 2e-205)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	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 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-1d-168)) .or. (.not. (t_1 <= 2d-205))) then
        tmp = t_1
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

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 <= -1e-168) || !(t_1 <= 2e-205)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) * (a - y)) / 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 <= -1e-168) or not (t_1 <= 2e-205):
		tmp = t_1
	else:
		tmp = t + (((t - x) * (a - y)) / 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 <= -1e-168) || !(t_1 <= 2e-205))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / 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 <= -1e-168) || ~((t_1 <= 2e-205)))
		tmp = t_1;
	else
		tmp = t + (((t - x) * (a - y)) / 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[Or[LessEqual[t$95$1, -1e-168], N[Not[LessEqual[t$95$1, 2e-205]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -1e-168 or 2e-205 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.7%

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

   if -1e-168 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2e-205

   1. Initial program 8.4%

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

   2. Taylor expanded in z around inf 85.4%

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

      1. +-commutative 85.4%

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

      2. associate--l+ 85.4%

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

      3. associate-*r/ 85.4%

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

      4. associate-*r/ 85.4%

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

      5. div-sub 85.4%

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

      6. distribute-lft-out-- 85.4%

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

      7. mul-1-neg 85.4%

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

      8. distribute-neg-frac 85.4%

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

      9. unsub-neg 85.4%

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

      10. distribute-rgt-out-- 85.5%

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

   4. Simplified 85.5%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -1 \cdot 10^{-168} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{-205}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 5: 91.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-243} \lor \neg \left(t_1 \leq 2 \cdot 10^{-205}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z))))))
   (if (or (<= t_1 -5e-243) (not (<= t_1 2e-205)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ t (/ (* (- t x) (- a y)) 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 <= -5e-243) || !(t_1 <= 2e-205)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / z);
	}
	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 = x + ((y - z) * ((t - x) / (a - z)))
    if ((t_1 <= (-5d-243)) .or. (.not. (t_1 <= 2d-205))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + (((t - x) * (a - y)) / z)
    end if
    code = tmp
end function

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 <= -5e-243) || !(t_1 <= 2e-205)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) * (a - y)) / 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 <= -5e-243) or not (t_1 <= 2e-205):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + (((t - x) * (a - y)) / 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 <= -5e-243) || !(t_1 <= 2e-205))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / 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 <= -5e-243) || ~((t_1 <= 2e-205)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + (((t - x) * (a - y)) / 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[Or[LessEqual[t$95$1, -5e-243], N[Not[LessEqual[t$95$1, 2e-205]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -5e-243 or 2e-205 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 92.0%

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

      1. *-commutative 92.0%

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

      2. associate-*l/ 78.0%

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

      3. associate-*r/ 93.7%

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

      4. clear-num 93.6%

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

      5. un-div-inv 94.1%

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

   3. Applied egg-rr 94.1%

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

   if -5e-243 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 2e-205

   1. Initial program 3.5%

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

   2. Taylor expanded in z around inf 86.5%

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

      1. +-commutative 86.5%

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

      2. associate--l+ 86.5%

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

      3. associate-*r/ 86.5%

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

      4. associate-*r/ 86.5%

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

      5. div-sub 86.5%

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

      6. distribute-lft-out-- 86.5%

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

      7. mul-1-neg 86.5%

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

      8. distribute-neg-frac 86.5%

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

      9. unsub-neg 86.5%

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

      10. distribute-rgt-out-- 86.7%

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

   4. Simplified 86.7%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq -5 \cdot 10^{-243} \lor \neg \left(x + \left(y - z\right) \cdot \frac{t - x}{a - z} \leq 2 \cdot 10^{-205}\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \end{array} \]

Alternative 6: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(t - x\right) \cdot \frac{y}{a}\\ t_2 := t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.75:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.041:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-35}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (- t x) (/ y a)))) (t_2 (+ t (/ a (/ z (- t x))))))
   (if (<= z -6.5e+36)
     t_2
     (if (<= z -3.75)
       t_1
       (if (<= z -0.041)
         t_2
         (if (<= z -1.7e-35)
           (/ t (/ a (- y z)))
           (if (<= z 1.6e-24)
             t_1
             (if (<= z 2.7e+95)
               (* y (/ (- x t) z))
               (* t (- 1.0 (/ y z)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t + (a / (z / (t - x)));
	double tmp;
	if (z <= -6.5e+36) {
		tmp = t_2;
	} else if (z <= -3.75) {
		tmp = t_1;
	} else if (z <= -0.041) {
		tmp = t_2;
	} else if (z <= -1.7e-35) {
		tmp = t / (a / (y - z));
	} else if (z <= 1.6e-24) {
		tmp = t_1;
	} else if (z <= 2.7e+95) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t * (1.0 - (y / z));
	}
	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 = x + ((t - x) * (y / a))
    t_2 = t + (a / (z / (t - x)))
    if (z <= (-6.5d+36)) then
        tmp = t_2
    else if (z <= (-3.75d0)) then
        tmp = t_1
    else if (z <= (-0.041d0)) then
        tmp = t_2
    else if (z <= (-1.7d-35)) then
        tmp = t / (a / (y - z))
    else if (z <= 1.6d-24) then
        tmp = t_1
    else if (z <= 2.7d+95) then
        tmp = y * ((x - t) / z)
    else
        tmp = t * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t - x) * (y / a));
	double t_2 = t + (a / (z / (t - x)));
	double tmp;
	if (z <= -6.5e+36) {
		tmp = t_2;
	} else if (z <= -3.75) {
		tmp = t_1;
	} else if (z <= -0.041) {
		tmp = t_2;
	} else if (z <= -1.7e-35) {
		tmp = t / (a / (y - z));
	} else if (z <= 1.6e-24) {
		tmp = t_1;
	} else if (z <= 2.7e+95) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t - x) * (y / a))
	t_2 = t + (a / (z / (t - x)))
	tmp = 0
	if z <= -6.5e+36:
		tmp = t_2
	elif z <= -3.75:
		tmp = t_1
	elif z <= -0.041:
		tmp = t_2
	elif z <= -1.7e-35:
		tmp = t / (a / (y - z))
	elif z <= 1.6e-24:
		tmp = t_1
	elif z <= 2.7e+95:
		tmp = y * ((x - t) / z)
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t - x) * Float64(y / a)))
	t_2 = Float64(t + Float64(a / Float64(z / Float64(t - x))))
	tmp = 0.0
	if (z <= -6.5e+36)
		tmp = t_2;
	elseif (z <= -3.75)
		tmp = t_1;
	elseif (z <= -0.041)
		tmp = t_2;
	elseif (z <= -1.7e-35)
		tmp = Float64(t / Float64(a / Float64(y - z)));
	elseif (z <= 1.6e-24)
		tmp = t_1;
	elseif (z <= 2.7e+95)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t - x) * (y / a));
	t_2 = t + (a / (z / (t - x)));
	tmp = 0.0;
	if (z <= -6.5e+36)
		tmp = t_2;
	elseif (z <= -3.75)
		tmp = t_1;
	elseif (z <= -0.041)
		tmp = t_2;
	elseif (z <= -1.7e-35)
		tmp = t / (a / (y - z));
	elseif (z <= 1.6e-24)
		tmp = t_1;
	elseif (z <= 2.7e+95)
		tmp = y * ((x - t) / z);
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t - x), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+36], t$95$2, If[LessEqual[z, -3.75], t$95$1, If[LessEqual[z, -0.041], t$95$2, If[LessEqual[z, -1.7e-35], N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-24], t$95$1, If[LessEqual[z, 2.7e+95], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.4999999999999998e36 or -3.75 < z < -0.0410000000000000017

   1. Initial program 65.0%

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

   2. Taylor expanded in z around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. associate--l+ 67.1%

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

      3. associate-*r/ 67.1%

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

      4. associate-*r/ 67.1%

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

      5. div-sub 67.1%

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

      6. distribute-lft-out-- 67.1%

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

      7. mul-1-neg 67.1%

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

      8. distribute-neg-frac 67.1%

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

      9. unsub-neg 67.1%

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

      10. distribute-rgt-out-- 67.3%

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

   4. Simplified 67.3%

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

   5. Taylor expanded in y around 0 58.8%

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

      1. sub-neg 58.8%

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

      2. mul-1-neg 58.8%

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

      3. remove-double-neg 58.8%

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

      4. associate-/l* 63.7%

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

   7. Simplified 63.7%

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

   if -6.4999999999999998e36 < z < -3.75 or -1.7000000000000001e-35 < z < 1.60000000000000006e-24

   1. Initial program 94.3%

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

   2. Taylor expanded in z around 0 77.9%

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

      1. expm1-log1p-u 47.2%

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

      2. expm1-udef 35.4%

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

      3. +-commutative 35.4%

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

      4. associate-/l* 37.4%

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

   4. Applied egg-rr 37.4%

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

      1. expm1-def 49.2%

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

      2. expm1-log1p 81.0%

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

      3. associate-/r/ 80.7%

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

   6. Simplified 80.7%

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

   if -0.0410000000000000017 < z < -1.7000000000000001e-35

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0 75.7%

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

   3. Taylor expanded in a around inf 63.2%

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

      1. associate-/l* 63.6%

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

   5. Simplified 63.6%

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

   if 1.60000000000000006e-24 < z < 2.7e95

   1. Initial program 78.9%

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

   2. Taylor expanded in a around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. neg-mul-1 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in y around inf 55.1%

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

      1. div-sub 55.1%

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

   7. Simplified 55.1%

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

   if 2.7e95 < z

   1. Initial program 55.1%

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

   2. Taylor expanded in a around 0 41.5%

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

      1. associate-*r/ 41.5%

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

      2. neg-mul-1 41.5%

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

   4. Simplified 41.5%

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

   5. Taylor expanded in t around -inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. *-commutative 62.2%

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

      3. sub-neg 62.2%

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

      4. metadata-eval 62.2%

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

   7. Simplified 62.2%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+36}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -3.75:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -0.041:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-35}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-24}:\\ \;\;\;\;x + \left(t - x\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 7: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{t - x}}\\ t_2 := t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.5:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.023:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-35}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a (- t x))))) (t_2 (+ t (/ a (/ z (- t x))))))
   (if (<= z -1.6e+36)
     t_2
     (if (<= z -3.5)
       t_1
       (if (<= z -0.023)
         t_2
         (if (<= z -1.65e-35)
           (/ t (/ a (- y z)))
           (if (<= z 1.32e-21)
             t_1
             (if (<= z 2.5e+95)
               (* y (/ (- x t) z))
               (* t (- 1.0 (/ y z)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double t_2 = t + (a / (z / (t - x)));
	double tmp;
	if (z <= -1.6e+36) {
		tmp = t_2;
	} else if (z <= -3.5) {
		tmp = t_1;
	} else if (z <= -0.023) {
		tmp = t_2;
	} else if (z <= -1.65e-35) {
		tmp = t / (a / (y - z));
	} else if (z <= 1.32e-21) {
		tmp = t_1;
	} else if (z <= 2.5e+95) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t * (1.0 - (y / z));
	}
	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 = x + (y / (a / (t - x)))
    t_2 = t + (a / (z / (t - x)))
    if (z <= (-1.6d+36)) then
        tmp = t_2
    else if (z <= (-3.5d0)) then
        tmp = t_1
    else if (z <= (-0.023d0)) then
        tmp = t_2
    else if (z <= (-1.65d-35)) then
        tmp = t / (a / (y - z))
    else if (z <= 1.32d-21) then
        tmp = t_1
    else if (z <= 2.5d+95) then
        tmp = y * ((x - t) / z)
    else
        tmp = t * (1.0d0 - (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / (t - x)));
	double t_2 = t + (a / (z / (t - x)));
	double tmp;
	if (z <= -1.6e+36) {
		tmp = t_2;
	} else if (z <= -3.5) {
		tmp = t_1;
	} else if (z <= -0.023) {
		tmp = t_2;
	} else if (z <= -1.65e-35) {
		tmp = t / (a / (y - z));
	} else if (z <= 1.32e-21) {
		tmp = t_1;
	} else if (z <= 2.5e+95) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / (t - x)))
	t_2 = t + (a / (z / (t - x)))
	tmp = 0
	if z <= -1.6e+36:
		tmp = t_2
	elif z <= -3.5:
		tmp = t_1
	elif z <= -0.023:
		tmp = t_2
	elif z <= -1.65e-35:
		tmp = t / (a / (y - z))
	elif z <= 1.32e-21:
		tmp = t_1
	elif z <= 2.5e+95:
		tmp = y * ((x - t) / z)
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / Float64(t - x))))
	t_2 = Float64(t + Float64(a / Float64(z / Float64(t - x))))
	tmp = 0.0
	if (z <= -1.6e+36)
		tmp = t_2;
	elseif (z <= -3.5)
		tmp = t_1;
	elseif (z <= -0.023)
		tmp = t_2;
	elseif (z <= -1.65e-35)
		tmp = Float64(t / Float64(a / Float64(y - z)));
	elseif (z <= 1.32e-21)
		tmp = t_1;
	elseif (z <= 2.5e+95)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / (t - x)));
	t_2 = t + (a / (z / (t - x)));
	tmp = 0.0;
	if (z <= -1.6e+36)
		tmp = t_2;
	elseif (z <= -3.5)
		tmp = t_1;
	elseif (z <= -0.023)
		tmp = t_2;
	elseif (z <= -1.65e-35)
		tmp = t / (a / (y - z));
	elseif (z <= 1.32e-21)
		tmp = t_1;
	elseif (z <= 2.5e+95)
		tmp = y * ((x - t) / z);
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+36], t$95$2, If[LessEqual[z, -3.5], t$95$1, If[LessEqual[z, -0.023], t$95$2, If[LessEqual[z, -1.65e-35], N[(t / N[(a / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.32e-21], t$95$1, If[LessEqual[z, 2.5e+95], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.5999999999999999e36 or -3.5 < z < -0.023

   1. Initial program 65.0%

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

   2. Taylor expanded in z around inf 67.1%

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

      1. +-commutative 67.1%

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

      2. associate--l+ 67.1%

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

      3. associate-*r/ 67.1%

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

      4. associate-*r/ 67.1%

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

      5. div-sub 67.1%

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

      6. distribute-lft-out-- 67.1%

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

      7. mul-1-neg 67.1%

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

      8. distribute-neg-frac 67.1%

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

      9. unsub-neg 67.1%

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

      10. distribute-rgt-out-- 67.3%

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

   4. Simplified 67.3%

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

   5. Taylor expanded in y around 0 58.8%

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

      1. sub-neg 58.8%

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

      2. mul-1-neg 58.8%

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

      3. remove-double-neg 58.8%

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

      4. associate-/l* 63.7%

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

   7. Simplified 63.7%

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

   if -1.5999999999999999e36 < z < -3.5 or -1.65e-35 < z < 1.32e-21

   1. Initial program 94.3%

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

   2. Taylor expanded in z around 0 77.9%

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

      1. +-commutative 77.9%

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

      2. associate-/l* 81.0%

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

   4. Simplified 81.0%

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

   if -0.023 < z < -1.65e-35

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0 75.7%

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

   3. Taylor expanded in a around inf 63.2%

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

      1. associate-/l* 63.6%

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

   5. Simplified 63.6%

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

   if 1.32e-21 < z < 2.50000000000000012e95

   1. Initial program 78.9%

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

   2. Taylor expanded in a around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. neg-mul-1 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in y around inf 55.1%

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

      1. div-sub 55.1%

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

   7. Simplified 55.1%

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

   if 2.50000000000000012e95 < z

   1. Initial program 55.1%

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

   2. Taylor expanded in a around 0 41.5%

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

      1. associate-*r/ 41.5%

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

      2. neg-mul-1 41.5%

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

   4. Simplified 41.5%

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

   5. Taylor expanded in t around -inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. *-commutative 62.2%

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

      3. sub-neg 62.2%

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

      4. metadata-eval 62.2%

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

   7. Simplified 62.2%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+36}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -3.5:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq -0.023:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-35}:\\ \;\;\;\;\frac{t}{\frac{a}{y - z}}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-21}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 8: 65.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y \cdot \left(t - x\right)}{z}\\ t_2 := \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;z \leq -2.05 \cdot 10^{+207}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+231}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (* y (- t x)) z))) (t_2 (/ t (/ (- a z) (- y z)))))
   (if (<= z -2.05e+207)
     (+ t (/ a (/ z (- t x))))
     (if (<= z -2.35e+61)
       t_1
       (if (<= z -7e-58)
         t_2
         (if (<= z 1.4e-20)
           (+ x (/ y (/ a (- t x))))
           (if (<= z 8.5e+231) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y * (t - x)) / z);
	double t_2 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -2.05e+207) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -2.35e+61) {
		tmp = t_1;
	} else if (z <= -7e-58) {
		tmp = t_2;
	} else if (z <= 1.4e-20) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 8.5e+231) {
		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 * (t - x)) / z)
    t_2 = t / ((a - z) / (y - z))
    if (z <= (-2.05d+207)) then
        tmp = t + (a / (z / (t - x)))
    else if (z <= (-2.35d+61)) then
        tmp = t_1
    else if (z <= (-7d-58)) then
        tmp = t_2
    else if (z <= 1.4d-20) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 8.5d+231) 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 * (t - x)) / z);
	double t_2 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -2.05e+207) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -2.35e+61) {
		tmp = t_1;
	} else if (z <= -7e-58) {
		tmp = t_2;
	} else if (z <= 1.4e-20) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 8.5e+231) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y * (t - x)) / z)
	t_2 = t / ((a - z) / (y - z))
	tmp = 0
	if z <= -2.05e+207:
		tmp = t + (a / (z / (t - x)))
	elif z <= -2.35e+61:
		tmp = t_1
	elif z <= -7e-58:
		tmp = t_2
	elif z <= 1.4e-20:
		tmp = x + (y / (a / (t - x)))
	elif z <= 8.5e+231:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y * Float64(t - x)) / z))
	t_2 = Float64(t / Float64(Float64(a - z) / Float64(y - z)))
	tmp = 0.0
	if (z <= -2.05e+207)
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	elseif (z <= -2.35e+61)
		tmp = t_1;
	elseif (z <= -7e-58)
		tmp = t_2;
	elseif (z <= 1.4e-20)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 8.5e+231)
		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 * (t - x)) / z);
	t_2 = t / ((a - z) / (y - z));
	tmp = 0.0;
	if (z <= -2.05e+207)
		tmp = t + (a / (z / (t - x)));
	elseif (z <= -2.35e+61)
		tmp = t_1;
	elseif (z <= -7e-58)
		tmp = t_2;
	elseif (z <= 1.4e-20)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 8.5e+231)
		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 * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.05e+207], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.35e+61], t$95$1, If[LessEqual[z, -7e-58], t$95$2, If[LessEqual[z, 1.4e-20], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+231], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.05e207

   1. Initial program 53.9%

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

   2. Taylor expanded in z around inf 71.1%

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

      1. +-commutative 71.1%

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

      2. associate--l+ 71.1%

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

      3. associate-*r/ 71.1%

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

      4. associate-*r/ 71.1%

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

      5. div-sub 71.1%

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

      6. distribute-lft-out-- 71.1%

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

      7. mul-1-neg 71.1%

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

      8. distribute-neg-frac 71.1%

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

      9. unsub-neg 71.1%

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

      10. distribute-rgt-out-- 71.6%

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

   4. Simplified 71.6%

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

   5. Taylor expanded in y around 0 75.1%

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

      1. sub-neg 75.1%

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

      2. mul-1-neg 75.1%

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

      3. remove-double-neg 75.1%

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

      4. associate-/l* 83.4%

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

   7. Simplified 83.4%

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

   if -2.05e207 < z < -2.3499999999999999e61 or 1.4000000000000001e-20 < z < 8.4999999999999994e231

   1. Initial program 69.2%

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

   2. Taylor expanded in z around inf 63.3%

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

      1. +-commutative 63.3%

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

      2. associate--l+ 63.3%

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

      3. associate-*r/ 63.3%

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

      4. associate-*r/ 63.3%

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

      5. div-sub 63.3%

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

      6. distribute-lft-out-- 63.3%

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

      7. mul-1-neg 63.3%

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

      8. distribute-neg-frac 63.3%

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

      9. unsub-neg 63.3%

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

      10. distribute-rgt-out-- 64.6%

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

   4. Simplified 64.6%

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

   5. Taylor expanded in y around inf 62.9%

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

   if -2.3499999999999999e61 < z < -6.9999999999999998e-58 or 8.4999999999999994e231 < z

   1. Initial program 72.7%

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

   2. Taylor expanded in x around 0 50.2%

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

      1. associate-/l* 68.7%

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

   4. Simplified 68.7%

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

   if -6.9999999999999998e-58 < z < 1.4000000000000001e-20

   1. Initial program 95.5%

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

   2. Taylor expanded in z around 0 80.1%

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

      1. +-commutative 80.1%

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

      2. associate-/l* 83.5%

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

   4. Simplified 83.5%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{+207}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{+61}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-58}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+231}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 9: 64.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+27}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-126}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+231}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ (- a z) (- y z)))))
   (if (<= z -3.3e+27)
     (- t (/ (* x (- a y)) z))
     (if (<= z -1.16e-57)
       t_1
       (if (<= z -3.2e-126)
         (* x (+ (/ (- z y) (- a z)) 1.0))
         (if (<= z 1.02e-18)
           (+ x (/ y (/ a (- t x))))
           (if (<= z 9.5e+231) (- t (/ (* y (- t x)) z)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -3.3e+27) {
		tmp = t - ((x * (a - y)) / z);
	} else if (z <= -1.16e-57) {
		tmp = t_1;
	} else if (z <= -3.2e-126) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else if (z <= 1.02e-18) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 9.5e+231) {
		tmp = t - ((y * (t - x)) / z);
	} else {
		tmp = 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) :: tmp
    t_1 = t / ((a - z) / (y - z))
    if (z <= (-3.3d+27)) then
        tmp = t - ((x * (a - y)) / z)
    else if (z <= (-1.16d-57)) then
        tmp = t_1
    else if (z <= (-3.2d-126)) then
        tmp = x * (((z - y) / (a - z)) + 1.0d0)
    else if (z <= 1.02d-18) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 9.5d+231) then
        tmp = t - ((y * (t - x)) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -3.3e+27) {
		tmp = t - ((x * (a - y)) / z);
	} else if (z <= -1.16e-57) {
		tmp = t_1;
	} else if (z <= -3.2e-126) {
		tmp = x * (((z - y) / (a - z)) + 1.0);
	} else if (z <= 1.02e-18) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 9.5e+231) {
		tmp = t - ((y * (t - x)) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / ((a - z) / (y - z))
	tmp = 0
	if z <= -3.3e+27:
		tmp = t - ((x * (a - y)) / z)
	elif z <= -1.16e-57:
		tmp = t_1
	elif z <= -3.2e-126:
		tmp = x * (((z - y) / (a - z)) + 1.0)
	elif z <= 1.02e-18:
		tmp = x + (y / (a / (t - x)))
	elif z <= 9.5e+231:
		tmp = t - ((y * (t - x)) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(Float64(a - z) / Float64(y - z)))
	tmp = 0.0
	if (z <= -3.3e+27)
		tmp = Float64(t - Float64(Float64(x * Float64(a - y)) / z));
	elseif (z <= -1.16e-57)
		tmp = t_1;
	elseif (z <= -3.2e-126)
		tmp = Float64(x * Float64(Float64(Float64(z - y) / Float64(a - z)) + 1.0));
	elseif (z <= 1.02e-18)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 9.5e+231)
		tmp = Float64(t - Float64(Float64(y * Float64(t - x)) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / ((a - z) / (y - z));
	tmp = 0.0;
	if (z <= -3.3e+27)
		tmp = t - ((x * (a - y)) / z);
	elseif (z <= -1.16e-57)
		tmp = t_1;
	elseif (z <= -3.2e-126)
		tmp = x * (((z - y) / (a - z)) + 1.0);
	elseif (z <= 1.02e-18)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 9.5e+231)
		tmp = t - ((y * (t - x)) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+27], N[(t - N[(N[(x * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.16e-57], t$95$1, If[LessEqual[z, -3.2e-126], N[(x * N[(N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-18], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e+231], N[(t - N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.2999999999999998e27

   1. Initial program 64.9%

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

   2. Taylor expanded in z around inf 65.4%

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

      1. +-commutative 65.4%

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

      2. associate--l+ 65.4%

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

      3. associate-*r/ 65.4%

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

      4. associate-*r/ 65.4%

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

      5. div-sub 65.4%

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

      6. distribute-lft-out-- 65.4%

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

      7. mul-1-neg 65.4%

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

      8. distribute-neg-frac 65.4%

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

      9. unsub-neg 65.4%

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

      10. distribute-rgt-out-- 65.6%

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

   4. Simplified 65.6%

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

   5. Taylor expanded in t around 0 72.6%

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

      1. associate-*r/ 72.6%

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

      2. mul-1-neg 72.6%

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

      3. *-commutative 72.6%

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

      4. distribute-rgt-neg-in 72.6%

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

   7. Simplified 72.6%

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

   if -3.2999999999999998e27 < z < -1.15999999999999996e-57 or 9.5000000000000002e231 < z

   1. Initial program 72.4%

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

   2. Taylor expanded in x around 0 51.4%

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

      1. associate-/l* 71.8%

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

   4. Simplified 71.8%

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

   if -1.15999999999999996e-57 < z < -3.2000000000000001e-126

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 86.3%

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

      1. mul-1-neg 86.3%

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

      2. unsub-neg 86.3%

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

   4. Simplified 86.3%

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

   if -3.2000000000000001e-126 < z < 1.02e-18

   1. Initial program 95.2%

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

   2. Taylor expanded in z around 0 80.6%

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

      1. +-commutative 80.6%

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

      2. associate-/l* 84.2%

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

   4. Simplified 84.2%

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

   if 1.02e-18 < z < 9.5000000000000002e231

   1. Initial program 67.5%

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

   2. Taylor expanded in z around inf 63.8%

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

      1. +-commutative 63.8%

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

      2. associate--l+ 63.8%

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

      3. associate-*r/ 63.8%

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

      4. associate-*r/ 63.8%

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

      5. div-sub 63.7%

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

      6. distribute-lft-out-- 63.7%

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

      7. mul-1-neg 63.7%

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

      8. distribute-neg-frac 63.7%

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

      9. unsub-neg 63.7%

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

      10. distribute-rgt-out-- 65.8%

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

   4. Simplified 65.8%

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

   5. Taylor expanded in y around inf 61.0%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+27}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-57}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-126}:\\ \;\;\;\;x \cdot \left(\frac{z - y}{a - z} + 1\right)\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-18}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+231}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 10: 47.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+35}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-126}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-59}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e+35)
   t
   (if (<= z 1.05e-126)
     (* x (- 1.0 (/ y a)))
     (if (<= z 8e-59)
       (/ y (/ a t))
       (if (<= z 3.8e-20) x (if (<= z 3.1e+95) (* y (/ (- x t) z)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+35) {
		tmp = t;
	} else if (z <= 1.05e-126) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 8e-59) {
		tmp = y / (a / t);
	} else if (z <= 3.8e-20) {
		tmp = x;
	} else if (z <= 3.1e+95) {
		tmp = y * ((x - t) / z);
	} 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 <= (-1.2d+35)) then
        tmp = t
    else if (z <= 1.05d-126) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 8d-59) then
        tmp = y / (a / t)
    else if (z <= 3.8d-20) then
        tmp = x
    else if (z <= 3.1d+95) then
        tmp = y * ((x - t) / z)
    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 <= -1.2e+35) {
		tmp = t;
	} else if (z <= 1.05e-126) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 8e-59) {
		tmp = y / (a / t);
	} else if (z <= 3.8e-20) {
		tmp = x;
	} else if (z <= 3.1e+95) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e+35:
		tmp = t
	elif z <= 1.05e-126:
		tmp = x * (1.0 - (y / a))
	elif z <= 8e-59:
		tmp = y / (a / t)
	elif z <= 3.8e-20:
		tmp = x
	elif z <= 3.1e+95:
		tmp = y * ((x - t) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e+35)
		tmp = t;
	elseif (z <= 1.05e-126)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 8e-59)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 3.8e-20)
		tmp = x;
	elseif (z <= 3.1e+95)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2e+35)
		tmp = t;
	elseif (z <= 1.05e-126)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 8e-59)
		tmp = y / (a / t);
	elseif (z <= 3.8e-20)
		tmp = x;
	elseif (z <= 3.1e+95)
		tmp = y * ((x - t) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e+35], t, If[LessEqual[z, 1.05e-126], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e-59], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-20], x, If[LessEqual[z, 3.1e+95], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.20000000000000007e35 or 3.1000000000000003e95 < z

   1. Initial program 60.2%

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

   2. Taylor expanded in z around inf 53.3%

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

   if -1.20000000000000007e35 < z < 1.0499999999999999e-126

   1. Initial program 93.1%

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

   2. Taylor expanded in z around 0 73.1%

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

   3. Taylor expanded in x around inf 50.5%

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

      1. *-commutative 50.5%

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

      2. mul-1-neg 50.5%

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

      3. unsub-neg 50.5%

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

   5. Simplified 50.5%

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

   if 1.0499999999999999e-126 < z < 8.0000000000000002e-59

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 70.5%

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

   3. Taylor expanded in z around 0 62.5%

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

      1. associate-/l* 62.7%

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

   5. Simplified 62.7%

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

   if 8.0000000000000002e-59 < z < 3.7999999999999998e-20

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 58.2%

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

   if 3.7999999999999998e-20 < z < 3.1000000000000003e95

   1. Initial program 78.9%

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

   2. Taylor expanded in a around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. neg-mul-1 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in y around inf 55.1%

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

      1. div-sub 55.1%

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

   7. Simplified 55.1%

      \[\leadsto \color{blue}{y \cdot \frac{x - t}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+35}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-126}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-59}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 64.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+210}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 10^{+232}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ (* y (- t x)) z))))
   (if (<= z -1.45e+210)
     (+ t (/ a (/ z (- t x))))
     (if (<= z -5.2e+35)
       t_1
       (if (<= z 1.28e-24)
         (+ x (/ y (/ a (- t x))))
         (if (<= z 1e+232) t_1 (* t (- 1.0 (/ y z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y * (t - x)) / z);
	double tmp;
	if (z <= -1.45e+210) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -5.2e+35) {
		tmp = t_1;
	} else if (z <= 1.28e-24) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 1e+232) {
		tmp = t_1;
	} else {
		tmp = t * (1.0 - (y / z));
	}
	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 - ((y * (t - x)) / z)
    if (z <= (-1.45d+210)) then
        tmp = t + (a / (z / (t - x)))
    else if (z <= (-5.2d+35)) then
        tmp = t_1
    else if (z <= 1.28d-24) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 1d+232) then
        tmp = t_1
    else
        tmp = t * (1.0d0 - (y / z))
    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 * (t - x)) / z);
	double tmp;
	if (z <= -1.45e+210) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= -5.2e+35) {
		tmp = t_1;
	} else if (z <= 1.28e-24) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 1e+232) {
		tmp = t_1;
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y * (t - x)) / z)
	tmp = 0
	if z <= -1.45e+210:
		tmp = t + (a / (z / (t - x)))
	elif z <= -5.2e+35:
		tmp = t_1
	elif z <= 1.28e-24:
		tmp = x + (y / (a / (t - x)))
	elif z <= 1e+232:
		tmp = t_1
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y * Float64(t - x)) / z))
	tmp = 0.0
	if (z <= -1.45e+210)
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	elseif (z <= -5.2e+35)
		tmp = t_1;
	elseif (z <= 1.28e-24)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 1e+232)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y * (t - x)) / z);
	tmp = 0.0;
	if (z <= -1.45e+210)
		tmp = t + (a / (z / (t - x)));
	elseif (z <= -5.2e+35)
		tmp = t_1;
	elseif (z <= 1.28e-24)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 1e+232)
		tmp = t_1;
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+210], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.2e+35], t$95$1, If[LessEqual[z, 1.28e-24], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+232], t$95$1, N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.44999999999999996e210

   1. Initial program 53.9%

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

   2. Taylor expanded in z around inf 71.1%

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

      1. +-commutative 71.1%

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

      2. associate--l+ 71.1%

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

      3. associate-*r/ 71.1%

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

      4. associate-*r/ 71.1%

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

      5. div-sub 71.1%

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

      6. distribute-lft-out-- 71.1%

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

      7. mul-1-neg 71.1%

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

      8. distribute-neg-frac 71.1%

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

      9. unsub-neg 71.1%

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

      10. distribute-rgt-out-- 71.6%

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

   4. Simplified 71.6%

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

   5. Taylor expanded in y around 0 75.1%

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

      1. sub-neg 75.1%

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

      2. mul-1-neg 75.1%

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

      3. remove-double-neg 75.1%

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

      4. associate-/l* 83.4%

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

   7. Simplified 83.4%

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

   if -1.44999999999999996e210 < z < -5.20000000000000013e35 or 1.28e-24 < z < 1.00000000000000006e232

   1. Initial program 69.2%

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

   2. Taylor expanded in z around inf 63.5%

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

      1. +-commutative 63.5%

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

      2. associate--l+ 63.5%

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

      3. associate-*r/ 63.5%

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

      4. associate-*r/ 63.5%

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

      5. div-sub 63.5%

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

      6. distribute-lft-out-- 63.5%

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

      7. mul-1-neg 63.5%

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

      8. distribute-neg-frac 63.5%

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

      9. unsub-neg 63.5%

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

      10. distribute-rgt-out-- 64.8%

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

   4. Simplified 64.8%

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

   5. Taylor expanded in y around inf 62.3%

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

   if -5.20000000000000013e35 < z < 1.28e-24

   1. Initial program 94.0%

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

   2. Taylor expanded in z around 0 74.1%

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

      1. +-commutative 74.1%

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

      2. associate-/l* 76.9%

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

   4. Simplified 76.9%

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

   if 1.00000000000000006e232 < z

   1. Initial program 56.8%

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

   2. Taylor expanded in a around 0 51.9%

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

      1. associate-*r/ 51.9%

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

      2. neg-mul-1 51.9%

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

   4. Simplified 51.9%

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

   5. Taylor expanded in t around -inf 80.6%

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

      1. mul-1-neg 80.6%

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

      2. *-commutative 80.6%

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

      3. sub-neg 80.6%

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

      4. metadata-eval 80.6%

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

   7. Simplified 80.6%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+210}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+35}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-24}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 10^{+232}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 12: 45.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-127}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-53}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+37)
   t
   (if (<= z 2.7e-127)
     (* x (- 1.0 (/ y a)))
     (if (<= z 2.1e-53)
       (/ y (/ a t))
       (if (<= z 5.1e-26) x (if (<= z 2.5e+95) (* x (/ y z)) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+37) {
		tmp = t;
	} else if (z <= 2.7e-127) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.1e-53) {
		tmp = y / (a / t);
	} else if (z <= 5.1e-26) {
		tmp = x;
	} else if (z <= 2.5e+95) {
		tmp = x * (y / z);
	} 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 <= (-2.4d+37)) then
        tmp = t
    else if (z <= 2.7d-127) then
        tmp = x * (1.0d0 - (y / a))
    else if (z <= 2.1d-53) then
        tmp = y / (a / t)
    else if (z <= 5.1d-26) then
        tmp = x
    else if (z <= 2.5d+95) then
        tmp = x * (y / z)
    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 <= -2.4e+37) {
		tmp = t;
	} else if (z <= 2.7e-127) {
		tmp = x * (1.0 - (y / a));
	} else if (z <= 2.1e-53) {
		tmp = y / (a / t);
	} else if (z <= 5.1e-26) {
		tmp = x;
	} else if (z <= 2.5e+95) {
		tmp = x * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+37:
		tmp = t
	elif z <= 2.7e-127:
		tmp = x * (1.0 - (y / a))
	elif z <= 2.1e-53:
		tmp = y / (a / t)
	elif z <= 5.1e-26:
		tmp = x
	elif z <= 2.5e+95:
		tmp = x * (y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+37)
		tmp = t;
	elseif (z <= 2.7e-127)
		tmp = Float64(x * Float64(1.0 - Float64(y / a)));
	elseif (z <= 2.1e-53)
		tmp = Float64(y / Float64(a / t));
	elseif (z <= 5.1e-26)
		tmp = x;
	elseif (z <= 2.5e+95)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e+37)
		tmp = t;
	elseif (z <= 2.7e-127)
		tmp = x * (1.0 - (y / a));
	elseif (z <= 2.1e-53)
		tmp = y / (a / t);
	elseif (z <= 5.1e-26)
		tmp = x;
	elseif (z <= 2.5e+95)
		tmp = x * (y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+37], t, If[LessEqual[z, 2.7e-127], N[(x * N[(1.0 - N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-53], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.1e-26], x, If[LessEqual[z, 2.5e+95], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.4e37 or 2.50000000000000012e95 < z

   1. Initial program 60.2%

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

   2. Taylor expanded in z around inf 53.3%

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

   if -2.4e37 < z < 2.7e-127

   1. Initial program 93.1%

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

   2. Taylor expanded in z around 0 73.1%

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

   3. Taylor expanded in x around inf 50.5%

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

      1. *-commutative 50.5%

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

      2. mul-1-neg 50.5%

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

      3. unsub-neg 50.5%

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

   5. Simplified 50.5%

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

   if 2.7e-127 < z < 2.09999999999999977e-53

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 70.5%

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

   3. Taylor expanded in z around 0 62.5%

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

      1. associate-/l* 62.7%

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

   5. Simplified 62.7%

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

   if 2.09999999999999977e-53 < z < 5.09999999999999991e-26

   1. Initial program 99.8%

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

   2. Taylor expanded in a around inf 58.2%

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

   if 5.09999999999999991e-26 < z < 2.50000000000000012e95

   1. Initial program 78.9%

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

   2. Taylor expanded in a around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. neg-mul-1 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in x around inf 32.4%

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

      1. expm1-log1p-u 12.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot x}{z}\right)\right)} \]

      2. expm1-udef 5.6%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot x}{z}\right)} - 1} \]

      3. associate-/l* 14.3%

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

   7. Applied egg-rr 14.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{z}{x}}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 20.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{z}{x}}\right)\right)} \]

      2. expm1-log1p 41.9%

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

      3. associate-/r/ 42.1%

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

   9. Simplified 42.1%

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-127}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{a}\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-53}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-26}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 65.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+29}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+231}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5e+29)
   (- t (/ (* x (- a y)) z))
   (if (<= z 2.1e-19)
     (+ x (/ y (/ a (- t x))))
     (if (<= z 8.5e+231)
       (- t (/ (* y (- t x)) z))
       (/ t (/ (- a z) (- y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e+29) {
		tmp = t - ((x * (a - y)) / z);
	} else if (z <= 2.1e-19) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 8.5e+231) {
		tmp = t - ((y * (t - x)) / z);
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	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 <= (-5d+29)) then
        tmp = t - ((x * (a - y)) / z)
    else if (z <= 2.1d-19) then
        tmp = x + (y / (a / (t - x)))
    else if (z <= 8.5d+231) then
        tmp = t - ((y * (t - x)) / z)
    else
        tmp = t / ((a - z) / (y - z))
    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 <= -5e+29) {
		tmp = t - ((x * (a - y)) / z);
	} else if (z <= 2.1e-19) {
		tmp = x + (y / (a / (t - x)));
	} else if (z <= 8.5e+231) {
		tmp = t - ((y * (t - x)) / z);
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5e+29:
		tmp = t - ((x * (a - y)) / z)
	elif z <= 2.1e-19:
		tmp = x + (y / (a / (t - x)))
	elif z <= 8.5e+231:
		tmp = t - ((y * (t - x)) / z)
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5e+29)
		tmp = Float64(t - Float64(Float64(x * Float64(a - y)) / z));
	elseif (z <= 2.1e-19)
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - x))));
	elseif (z <= 8.5e+231)
		tmp = Float64(t - Float64(Float64(y * Float64(t - x)) / z));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5e+29)
		tmp = t - ((x * (a - y)) / z);
	elseif (z <= 2.1e-19)
		tmp = x + (y / (a / (t - x)));
	elseif (z <= 8.5e+231)
		tmp = t - ((y * (t - x)) / z);
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5e+29], N[(t - N[(N[(x * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-19], N[(x + N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+231], N[(t - N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.0000000000000001e29

   1. Initial program 64.2%

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

   2. Taylor expanded in z around inf 66.5%

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

      1. +-commutative 66.5%

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

      2. associate--l+ 66.5%

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

      3. associate-*r/ 66.5%

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

      4. associate-*r/ 66.5%

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

      5. div-sub 66.5%

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

      6. distribute-lft-out-- 66.5%

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

      7. mul-1-neg 66.5%

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

      8. distribute-neg-frac 66.5%

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

      9. unsub-neg 66.5%

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

      10. distribute-rgt-out-- 66.7%

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

   4. Simplified 66.7%

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

   5. Taylor expanded in t around 0 73.9%

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

      1. associate-*r/ 73.9%

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

      2. mul-1-neg 73.9%

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

      3. *-commutative 73.9%

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

      4. distribute-rgt-neg-in 73.9%

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

   7. Simplified 73.9%

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

   if -5.0000000000000001e29 < z < 2.0999999999999999e-19

   1. Initial program 94.0%

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

   2. Taylor expanded in z around 0 74.1%

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

      1. +-commutative 74.1%

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

      2. associate-/l* 76.9%

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

   4. Simplified 76.9%

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

   if 2.0999999999999999e-19 < z < 8.4999999999999994e231

   1. Initial program 67.5%

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

   2. Taylor expanded in z around inf 63.8%

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

      1. +-commutative 63.8%

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

      2. associate--l+ 63.8%

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

      3. associate-*r/ 63.8%

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

      4. associate-*r/ 63.8%

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

      5. div-sub 63.7%

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

      6. distribute-lft-out-- 63.7%

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

      7. mul-1-neg 63.7%

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

      8. distribute-neg-frac 63.7%

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

      9. unsub-neg 63.7%

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

      10. distribute-rgt-out-- 65.8%

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

   4. Simplified 65.8%

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

   5. Taylor expanded in y around inf 61.0%

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

   if 8.4999999999999994e231 < z

   1. Initial program 56.8%

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

   2. Taylor expanded in x around 0 38.1%

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

      1. associate-/l* 80.7%

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

   4. Simplified 80.7%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+29}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+231}:\\ \;\;\;\;t - \frac{y \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 14: 73.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+37}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+95}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+37)
   (- t (/ (* x (- a y)) z))
   (if (<= z 2e+95)
     (+ x (/ (- t x) (/ (- a z) y)))
     (/ t (/ (- a z) (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+37) {
		tmp = t - ((x * (a - y)) / z);
	} else if (z <= 2e+95) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	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+37)) then
        tmp = t - ((x * (a - y)) / z)
    else if (z <= 2d+95) then
        tmp = x + ((t - x) / ((a - z) / y))
    else
        tmp = t / ((a - z) / (y - z))
    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+37) {
		tmp = t - ((x * (a - y)) / z);
	} else if (z <= 2e+95) {
		tmp = x + ((t - x) / ((a - z) / y));
	} else {
		tmp = t / ((a - z) / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e+37:
		tmp = t - ((x * (a - y)) / z)
	elif z <= 2e+95:
		tmp = x + ((t - x) / ((a - z) / y))
	else:
		tmp = t / ((a - z) / (y - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+37)
		tmp = Float64(t - Float64(Float64(x * Float64(a - y)) / z));
	elseif (z <= 2e+95)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / y)));
	else
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.9e+37)
		tmp = t - ((x * (a - y)) / z);
	elseif (z <= 2e+95)
		tmp = x + ((t - x) / ((a - z) / y));
	else
		tmp = t / ((a - z) / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+37], N[(t - N[(N[(x * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+95], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.89999999999999995e37

   1. Initial program 64.2%

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

   2. Taylor expanded in z around inf 66.5%

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

      1. +-commutative 66.5%

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

      2. associate--l+ 66.5%

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

      3. associate-*r/ 66.5%

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

      4. associate-*r/ 66.5%

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

      5. div-sub 66.5%

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

      6. distribute-lft-out-- 66.5%

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

      7. mul-1-neg 66.5%

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

      8. distribute-neg-frac 66.5%

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

      9. unsub-neg 66.5%

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

      10. distribute-rgt-out-- 66.7%

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

   4. Simplified 66.7%

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

   5. Taylor expanded in t around 0 73.9%

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

      1. associate-*r/ 73.9%

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

      2. mul-1-neg 73.9%

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

      3. *-commutative 73.9%

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

      4. distribute-rgt-neg-in 73.9%

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

   7. Simplified 73.9%

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

   if -1.89999999999999995e37 < z < 2.00000000000000004e95

   1. Initial program 91.4%

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

      1. *-commutative 91.4%

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

      2. associate-*l/ 88.4%

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

      3. associate-*r/ 93.0%

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

      4. clear-num 92.9%

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

      5. un-div-inv 93.6%

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

   3. Applied egg-rr 93.6%

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

   4. Taylor expanded in y around inf 83.6%

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

   if 2.00000000000000004e95 < z

   1. Initial program 55.1%

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

   2. Taylor expanded in x around 0 42.8%

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

      1. associate-/l* 66.7%

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

   4. Simplified 66.7%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+37}:\\ \;\;\;\;t - \frac{x \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+95}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]

Alternative 15: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.2e+37)
   t
   (if (<= z 6.2e-19)
     (+ x (/ (* y t) a))
     (if (<= z 2.8e+95) (* y (/ (- x t) z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.2e+37) {
		tmp = t;
	} else if (z <= 6.2e-19) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.8e+95) {
		tmp = y * ((x - t) / z);
	} 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 <= (-2.2d+37)) then
        tmp = t
    else if (z <= 6.2d-19) then
        tmp = x + ((y * t) / a)
    else if (z <= 2.8d+95) then
        tmp = y * ((x - t) / z)
    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 <= -2.2e+37) {
		tmp = t;
	} else if (z <= 6.2e-19) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.8e+95) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.2e+37:
		tmp = t
	elif z <= 6.2e-19:
		tmp = x + ((y * t) / a)
	elif z <= 2.8e+95:
		tmp = y * ((x - t) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.2e+37)
		tmp = t;
	elseif (z <= 6.2e-19)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 2.8e+95)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.2e+37)
		tmp = t;
	elseif (z <= 6.2e-19)
		tmp = x + ((y * t) / a);
	elseif (z <= 2.8e+95)
		tmp = y * ((x - t) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.2e+37], t, If[LessEqual[z, 6.2e-19], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+95], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2000000000000001e37 or 2.7999999999999998e95 < z

   1. Initial program 60.2%

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

   2. Taylor expanded in z around inf 53.3%

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

   if -2.2000000000000001e37 < z < 6.1999999999999998e-19

   1. Initial program 94.0%

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

   2. Taylor expanded in z around 0 74.1%

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

   3. Taylor expanded in t around inf 62.1%

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

   if 6.1999999999999998e-19 < z < 2.7999999999999998e95

   1. Initial program 78.9%

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

   2. Taylor expanded in a around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. neg-mul-1 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in y around inf 55.1%

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

      1. div-sub 55.1%

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

   7. Simplified 55.1%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+37}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16: 53.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{\frac{z}{t}}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (/ y (/ z t)))))
   (if (<= z -5.5e+30)
     t_1
     (if (<= z 5.8e-22)
       (+ x (/ (* y t) a))
       (if (<= z 3.2e+95) (* y (/ (- x t) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (y / (z / t));
	double tmp;
	if (z <= -5.5e+30) {
		tmp = t_1;
	} else if (z <= 5.8e-22) {
		tmp = x + ((y * t) / a);
	} else if (z <= 3.2e+95) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = 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) :: tmp
    t_1 = t - (y / (z / t))
    if (z <= (-5.5d+30)) then
        tmp = t_1
    else if (z <= 5.8d-22) then
        tmp = x + ((y * t) / a)
    else if (z <= 3.2d+95) then
        tmp = y * ((x - t) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (y / (z / t));
	double tmp;
	if (z <= -5.5e+30) {
		tmp = t_1;
	} else if (z <= 5.8e-22) {
		tmp = x + ((y * t) / a);
	} else if (z <= 3.2e+95) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (y / (z / t))
	tmp = 0
	if z <= -5.5e+30:
		tmp = t_1
	elif z <= 5.8e-22:
		tmp = x + ((y * t) / a)
	elif z <= 3.2e+95:
		tmp = y * ((x - t) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(y / Float64(z / t)))
	tmp = 0.0
	if (z <= -5.5e+30)
		tmp = t_1;
	elseif (z <= 5.8e-22)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 3.2e+95)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (y / (z / t));
	tmp = 0.0;
	if (z <= -5.5e+30)
		tmp = t_1;
	elseif (z <= 5.8e-22)
		tmp = x + ((y * t) / a);
	elseif (z <= 3.2e+95)
		tmp = y * ((x - t) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+30], t$95$1, If[LessEqual[z, 5.8e-22], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+95], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.50000000000000025e30 or 3.2000000000000001e95 < z

   1. Initial program 60.2%

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

   2. Taylor expanded in x around 0 39.5%

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

   3. Taylor expanded in a around 0 36.6%

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

      1. associate-*r/ 36.6%

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

      2. neg-mul-1 36.6%

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

      3. distribute-lft-neg-in 36.6%

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

   5. Simplified 36.6%

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

   6. Taylor expanded in y around 0 49.9%

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

      1. +-commutative 49.9%

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

      2. mul-1-neg 49.9%

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

      3. unsub-neg 49.9%

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

      4. associate-/l* 56.9%

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

   8. Simplified 56.9%

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

   if -5.50000000000000025e30 < z < 5.8000000000000003e-22

   1. Initial program 94.0%

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

   2. Taylor expanded in z around 0 74.1%

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

   3. Taylor expanded in t around inf 62.1%

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

   if 5.8000000000000003e-22 < z < 3.2000000000000001e95

   1. Initial program 78.9%

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

   2. Taylor expanded in a around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. neg-mul-1 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in y around inf 55.1%

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

      1. div-sub 55.1%

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

   7. Simplified 55.1%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+30}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \end{array} \]

Alternative 17: 53.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+32}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.6e+32)
   (- t (/ y (/ z t)))
   (if (<= z 4.2e-19)
     (+ x (/ (* y t) a))
     (if (<= z 2.5e+95) (* y (/ (- x t) z)) (* t (- 1.0 (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.6e+32) {
		tmp = t - (y / (z / t));
	} else if (z <= 4.2e-19) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.5e+95) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t * (1.0 - (y / z));
	}
	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 <= (-5.6d+32)) then
        tmp = t - (y / (z / t))
    else if (z <= 4.2d-19) then
        tmp = x + ((y * t) / a)
    else if (z <= 2.5d+95) then
        tmp = y * ((x - t) / z)
    else
        tmp = t * (1.0d0 - (y / z))
    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 <= -5.6e+32) {
		tmp = t - (y / (z / t));
	} else if (z <= 4.2e-19) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.5e+95) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.6e+32:
		tmp = t - (y / (z / t))
	elif z <= 4.2e-19:
		tmp = x + ((y * t) / a)
	elif z <= 2.5e+95:
		tmp = y * ((x - t) / z)
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.6e+32)
		tmp = Float64(t - Float64(y / Float64(z / t)));
	elseif (z <= 4.2e-19)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 2.5e+95)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.6e+32)
		tmp = t - (y / (z / t));
	elseif (z <= 4.2e-19)
		tmp = x + ((y * t) / a);
	elseif (z <= 2.5e+95)
		tmp = y * ((x - t) / z);
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.6e+32], N[(t - N[(y / N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-19], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+95], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.6e32

   1. Initial program 64.2%

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

   2. Taylor expanded in x around 0 37.0%

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

   3. Taylor expanded in a around 0 35.2%

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

      1. associate-*r/ 35.2%

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

      2. neg-mul-1 35.2%

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

      3. distribute-lft-neg-in 35.2%

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

   5. Simplified 35.2%

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

   6. Taylor expanded in y around 0 50.9%

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

      1. +-commutative 50.9%

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

      2. mul-1-neg 50.9%

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

      3. unsub-neg 50.9%

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

      4. associate-/l* 56.1%

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

   8. Simplified 56.1%

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

   if -5.6e32 < z < 4.1999999999999998e-19

   1. Initial program 94.0%

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

   2. Taylor expanded in z around 0 74.1%

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

   3. Taylor expanded in t around inf 62.1%

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

   if 4.1999999999999998e-19 < z < 2.50000000000000012e95

   1. Initial program 78.9%

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

   2. Taylor expanded in a around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. neg-mul-1 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in y around inf 55.1%

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

      1. div-sub 55.1%

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

   7. Simplified 55.1%

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

   if 2.50000000000000012e95 < z

   1. Initial program 55.1%

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

   2. Taylor expanded in a around 0 41.5%

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

      1. associate-*r/ 41.5%

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

      2. neg-mul-1 41.5%

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

   4. Simplified 41.5%

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

   5. Taylor expanded in t around -inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. *-commutative 62.2%

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

      3. sub-neg 62.2%

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

      4. metadata-eval 62.2%

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

   7. Simplified 62.2%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+32}:\\ \;\;\;\;t - \frac{y}{\frac{z}{t}}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 18: 53.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+32}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5e+32)
   (+ t (/ a (/ z (- t x))))
   (if (<= z 4.1e-19)
     (+ x (/ (* y t) a))
     (if (<= z 2.1e+95) (* y (/ (- x t) z)) (* t (- 1.0 (/ y z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e+32) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= 4.1e-19) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.1e+95) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t * (1.0 - (y / z));
	}
	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 <= (-5d+32)) then
        tmp = t + (a / (z / (t - x)))
    else if (z <= 4.1d-19) then
        tmp = x + ((y * t) / a)
    else if (z <= 2.1d+95) then
        tmp = y * ((x - t) / z)
    else
        tmp = t * (1.0d0 - (y / z))
    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 <= -5e+32) {
		tmp = t + (a / (z / (t - x)));
	} else if (z <= 4.1e-19) {
		tmp = x + ((y * t) / a);
	} else if (z <= 2.1e+95) {
		tmp = y * ((x - t) / z);
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5e+32:
		tmp = t + (a / (z / (t - x)))
	elif z <= 4.1e-19:
		tmp = x + ((y * t) / a)
	elif z <= 2.1e+95:
		tmp = y * ((x - t) / z)
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5e+32)
		tmp = Float64(t + Float64(a / Float64(z / Float64(t - x))));
	elseif (z <= 4.1e-19)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (z <= 2.1e+95)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5e+32)
		tmp = t + (a / (z / (t - x)));
	elseif (z <= 4.1e-19)
		tmp = x + ((y * t) / a);
	elseif (z <= 2.1e+95)
		tmp = y * ((x - t) / z);
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5e+32], N[(t + N[(a / N[(z / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e-19], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+95], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.9999999999999997e32

   1. Initial program 64.2%

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

   2. Taylor expanded in z around inf 66.5%

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

      1. +-commutative 66.5%

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

      2. associate--l+ 66.5%

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

      3. associate-*r/ 66.5%

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

      4. associate-*r/ 66.5%

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

      5. div-sub 66.5%

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

      6. distribute-lft-out-- 66.5%

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

      7. mul-1-neg 66.5%

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

      8. distribute-neg-frac 66.5%

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

      9. unsub-neg 66.5%

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

      10. distribute-rgt-out-- 66.7%

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

   4. Simplified 66.7%

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

   5. Taylor expanded in y around 0 55.8%

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

      1. sub-neg 55.8%

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

      2. mul-1-neg 55.8%

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

      3. remove-double-neg 55.8%

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

      4. associate-/l* 61.0%

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

   7. Simplified 61.0%

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

   if -4.9999999999999997e32 < z < 4.09999999999999985e-19

   1. Initial program 94.0%

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

   2. Taylor expanded in z around 0 74.1%

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

   3. Taylor expanded in t around inf 62.1%

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

   if 4.09999999999999985e-19 < z < 2.1e95

   1. Initial program 78.9%

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

   2. Taylor expanded in a around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. neg-mul-1 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in y around inf 55.1%

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

      1. div-sub 55.1%

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

   7. Simplified 55.1%

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

   if 2.1e95 < z

   1. Initial program 55.1%

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

   2. Taylor expanded in a around 0 41.5%

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

      1. associate-*r/ 41.5%

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

      2. neg-mul-1 41.5%

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

   4. Simplified 41.5%

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

   5. Taylor expanded in t around -inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. *-commutative 62.2%

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

      3. sub-neg 62.2%

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

      4. metadata-eval 62.2%

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

   7. Simplified 62.2%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+32}:\\ \;\;\;\;t + \frac{a}{\frac{z}{t - x}}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+95}:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

Alternative 19: 37.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-58}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.4e-58)
   t
   (if (<= z 1.2e-19) x (if (<= z 1.9e+95) (* x (/ y z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e-58) {
		tmp = t;
	} else if (z <= 1.2e-19) {
		tmp = x;
	} else if (z <= 1.9e+95) {
		tmp = x * (y / z);
	} 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 <= (-4.4d-58)) then
        tmp = t
    else if (z <= 1.2d-19) then
        tmp = x
    else if (z <= 1.9d+95) then
        tmp = x * (y / z)
    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 <= -4.4e-58) {
		tmp = t;
	} else if (z <= 1.2e-19) {
		tmp = x;
	} else if (z <= 1.9e+95) {
		tmp = x * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.4e-58:
		tmp = t
	elif z <= 1.2e-19:
		tmp = x
	elif z <= 1.9e+95:
		tmp = x * (y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.4e-58)
		tmp = t;
	elseif (z <= 1.2e-19)
		tmp = x;
	elseif (z <= 1.9e+95)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.4e-58)
		tmp = t;
	elseif (z <= 1.2e-19)
		tmp = x;
	elseif (z <= 1.9e+95)
		tmp = x * (y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.4e-58], t, If[LessEqual[z, 1.2e-19], x, If[LessEqual[z, 1.9e+95], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.40000000000000011e-58 or 1.9e95 < z

   1. Initial program 65.4%

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

   2. Taylor expanded in z around inf 46.3%

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

   if -4.40000000000000011e-58 < z < 1.20000000000000011e-19

   1. Initial program 95.5%

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

   2. Taylor expanded in a around inf 35.9%

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

   if 1.20000000000000011e-19 < z < 1.9e95

   1. Initial program 78.9%

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

   2. Taylor expanded in a around 0 57.9%

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

      1. associate-*r/ 57.9%

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

      2. neg-mul-1 57.9%

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

   4. Simplified 57.9%

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

   5. Taylor expanded in x around inf 32.4%

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

      1. expm1-log1p-u 12.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot x}{z}\right)\right)} \]

      2. expm1-udef 5.6%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot x}{z}\right)} - 1} \]

      3. associate-/l* 14.3%

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

   7. Applied egg-rr 14.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{z}{x}}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 20.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{z}{x}}\right)\right)} \]

      2. expm1-log1p 41.9%

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

      3. associate-/r/ 42.1%

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

   9. Simplified 42.1%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-58}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 20: 34.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.42:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-31}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.42)
   t
   (if (<= z 5e-31) (/ t (/ a y)) (if (<= z 2.5e+95) (* x (/ y z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.42) {
		tmp = t;
	} else if (z <= 5e-31) {
		tmp = t / (a / y);
	} else if (z <= 2.5e+95) {
		tmp = x * (y / z);
	} 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 <= (-0.42d0)) then
        tmp = t
    else if (z <= 5d-31) then
        tmp = t / (a / y)
    else if (z <= 2.5d+95) then
        tmp = x * (y / z)
    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 <= -0.42) {
		tmp = t;
	} else if (z <= 5e-31) {
		tmp = t / (a / y);
	} else if (z <= 2.5e+95) {
		tmp = x * (y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.42:
		tmp = t
	elif z <= 5e-31:
		tmp = t / (a / y)
	elif z <= 2.5e+95:
		tmp = x * (y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -0.42)
		tmp = t;
	elseif (z <= 5e-31)
		tmp = Float64(t / Float64(a / y));
	elseif (z <= 2.5e+95)
		tmp = Float64(x * Float64(y / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -0.42)
		tmp = t;
	elseif (z <= 5e-31)
		tmp = t / (a / y);
	elseif (z <= 2.5e+95)
		tmp = x * (y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.42], t, If[LessEqual[z, 5e-31], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+95], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.419999999999999984 or 2.50000000000000012e95 < z

   1. Initial program 63.4%

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

   2. Taylor expanded in z around inf 50.1%

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

   if -0.419999999999999984 < z < 5e-31

   1. Initial program 94.2%

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

   2. Taylor expanded in x around 0 45.5%

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

   3. Taylor expanded in a around inf 39.4%

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

      1. associate-/l* 40.2%

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

   5. Simplified 40.2%

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

   6. Taylor expanded in y around inf 34.9%

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

   if 5e-31 < z < 2.50000000000000012e95

   1. Initial program 79.7%

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

   2. Taylor expanded in a around 0 56.0%

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

      1. associate-*r/ 56.0%

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

      2. neg-mul-1 56.0%

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

   4. Simplified 56.0%

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

   5. Taylor expanded in x around inf 31.5%

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

      1. expm1-log1p-u 12.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y \cdot x}{z}\right)\right)} \]

      2. expm1-udef 5.7%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y \cdot x}{z}\right)} - 1} \]

      3. associate-/l* 14.1%

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

   7. Applied egg-rr 14.1%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y}{\frac{z}{x}}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 20.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\frac{z}{x}}\right)\right)} \]

      2. expm1-log1p 40.8%

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

      3. associate-/r/ 40.9%

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

   9. Simplified 40.9%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.42:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-31}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 21: 38.2% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.5e+110) x (if (<= a 7.5e+106) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.5e+110) {
		tmp = x;
	} else if (a <= 7.5e+106) {
		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 <= (-7.5d+110)) then
        tmp = x
    else if (a <= 7.5d+106) 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 <= -7.5e+110) {
		tmp = x;
	} else if (a <= 7.5e+106) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.5e+110:
		tmp = x
	elif a <= 7.5e+106:
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.5e+110)
		tmp = x;
	elseif (a <= 7.5e+106)
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.5e+110)
		tmp = x;
	elseif (a <= 7.5e+106)
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.5e+110], x, If[LessEqual[a, 7.5e+106], t, x]]

Derivation

1. Split input into 2 regimes

2. if a < -7.5e110 or 7.50000000000000058e106 < a

   1. Initial program 94.0%

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

   2. Taylor expanded in a around inf 58.4%

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

   if -7.5e110 < a < 7.50000000000000058e106

   1. Initial program 73.1%

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

   2. Taylor expanded in z around inf 32.1%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+110}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+106}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22: 24.7% 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 79.5%

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

2. Taylor expanded in z around inf 25.3%

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

3. Final simplification 25.3%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023224 
(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)))))