Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3

Percentage Accurate: 69.3% → 88.4%

Time: 12.0s

Alternatives: 18

Speedup: 0.7×

Specification

Math

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

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(Float64(y - z) * 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 69.3% accurate, 1.0× speedup

Math

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

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(Float64(y - z) * 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[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 88.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-282}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (- y z) (/ (- t x) (- a z)) x))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -5e-163)
     t_1
     (if (<= t_2 1e-282)
       (+ t (/ (* (- t x) (- a y)) z))
       (if (<= t_2 5e+304) t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y - z), ((t - x) / (a - z)), x);
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e-163) {
		tmp = t_1;
	} else if (t_2 <= 1e-282) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 5e+304) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y - z), Float64(Float64(t - x) / Float64(a - z)), x)
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -5e-163)
		tmp = t_1;
	elseif (t_2 <= 1e-282)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (t_2 <= 5e+304)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-163], t$95$1, If[LessEqual[t$95$2, 1e-282], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+304], t$95$2, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999977e-163 or 4.9999999999999997e304 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 61.4%

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

      1. +-commutative 61.4%

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

      2. associate-/l* 86.2%

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

      3. fma-define 86.2%

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

   3. Simplified 86.2%

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

   if -4.99999999999999977e-163 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1e-282

   1. Initial program 19.5%

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

   3. Taylor expanded in z around inf 95.6%

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

      1. associate--l+ 95.6%

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

      2. distribute-lft-out-- 95.6%

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

      3. div-sub 95.5%

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

      4. mul-1-neg 95.5%

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

      5. unsub-neg 95.5%

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

      6. distribute-rgt-out-- 95.6%

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

   5. Simplified 95.6%

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

   if 1e-282 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 4.9999999999999997e304

   1. Initial program 97.0%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -5 \cdot 10^{-163}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 10^{-282}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t - x}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot \frac{x - t}{z}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{-274}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 10^{-282}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* y (/ (- x t) z))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-274)
       t_2
       (if (<= t_2 1e-282)
         (+ t (/ (* (- t x) (- a y)) z))
         (if (<= t_2 5e+304) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * ((x - t) / z));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-274) {
		tmp = t_2;
	} else if (t_2 <= 1e-282) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 5e+304) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (y * ((x - t) / z));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -1e-274) {
		tmp = t_2;
	} else if (t_2 <= 1e-282) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 5e+304) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (y * ((x - t) / z))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-274:
		tmp = t_2
	elif t_2 <= 1e-282:
		tmp = t + (((t - x) * (a - y)) / z)
	elif t_2 <= 5e+304:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(y * Float64(Float64(x - t) / z)))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e-274)
		tmp = t_2;
	elseif (t_2 <= 1e-282)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (t_2 <= 5e+304)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (y * ((x - t) / z));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-274)
		tmp = t_2;
	elseif (t_2 <= 1e-282)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (t_2 <= 5e+304)
		tmp = t_2;
	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[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e-274], t$95$2, If[LessEqual[t$95$2, 1e-282], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+304], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -inf.0 or 4.9999999999999997e304 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 41.1%

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

   3. Taylor expanded in z around inf 53.4%

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

      1. associate--l+ 53.4%

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

      2. distribute-lft-out-- 53.4%

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

      3. div-sub 54.4%

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

      4. mul-1-neg 54.4%

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

      5. unsub-neg 54.4%

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

      6. distribute-rgt-out-- 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in y around inf 55.7%

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

      1. associate-/l* 71.3%

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

   8. Simplified 71.3%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -9.99999999999999966e-275 or 1e-282 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 4.9999999999999997e304

   1. Initial program 98.1%

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

   if -9.99999999999999966e-275 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1e-282

   1. Initial program 5.7%

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

   3. Taylor expanded in z around inf 99.4%

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

      1. associate--l+ 99.4%

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

      2. distribute-lft-out-- 99.4%

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

      3. div-sub 99.3%

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

      4. mul-1-neg 99.3%

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

      5. unsub-neg 99.3%

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

      6. distribute-rgt-out-- 99.4%

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

   5. Simplified 99.4%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -\infty:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -1 \cdot 10^{-274}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 10^{-282}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - z}{\frac{a - z}{t - x}}\\ t_2 := x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{-163}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-282}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+304}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (- y z) (/ (- a z) (- t x)))))
        (t_2 (+ x (/ (* (- y z) (- t x)) (- a z)))))
   (if (<= t_2 -5e-163)
     t_1
     (if (<= t_2 1e-282)
       (+ t (/ (* (- t x) (- a y)) z))
       (if (<= t_2 5e+304) t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e-163) {
		tmp = t_1;
	} else if (t_2 <= 1e-282) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 5e+304) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x + ((y - z) / ((a - z) / (t - x)))
    t_2 = x + (((y - z) * (t - x)) / (a - z))
    if (t_2 <= (-5d-163)) then
        tmp = t_1
    else if (t_2 <= 1d-282) then
        tmp = t + (((t - x) * (a - y)) / z)
    else if (t_2 <= 5d+304) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) / ((a - z) / (t - x)));
	double t_2 = x + (((y - z) * (t - x)) / (a - z));
	double tmp;
	if (t_2 <= -5e-163) {
		tmp = t_1;
	} else if (t_2 <= 1e-282) {
		tmp = t + (((t - x) * (a - y)) / z);
	} else if (t_2 <= 5e+304) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) / ((a - z) / (t - x)))
	t_2 = x + (((y - z) * (t - x)) / (a - z))
	tmp = 0
	if t_2 <= -5e-163:
		tmp = t_1
	elif t_2 <= 1e-282:
		tmp = t + (((t - x) * (a - y)) / z)
	elif t_2 <= 5e+304:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))))
	t_2 = Float64(x + Float64(Float64(Float64(y - z) * Float64(t - x)) / Float64(a - z)))
	tmp = 0.0
	if (t_2 <= -5e-163)
		tmp = t_1;
	elseif (t_2 <= 1e-282)
		tmp = Float64(t + Float64(Float64(Float64(t - x) * Float64(a - y)) / z));
	elseif (t_2 <= 5e+304)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) / ((a - z) / (t - x)));
	t_2 = x + (((y - z) * (t - x)) / (a - z));
	tmp = 0.0;
	if (t_2 <= -5e-163)
		tmp = t_1;
	elseif (t_2 <= 1e-282)
		tmp = t + (((t - x) * (a - y)) / z);
	elseif (t_2 <= 5e+304)
		tmp = t_2;
	else
		tmp = t_1;
	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[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y - z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-163], t$95$1, If[LessEqual[t$95$2, 1e-282], N[(t + N[(N[(N[(t - x), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+304], t$95$2, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < -4.99999999999999977e-163 or 4.9999999999999997e304 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

   1. Initial program 61.4%

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

      1. associate-/l* 86.2%

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

      2. clear-num 86.1%

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

      3. un-div-inv 86.0%

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

   4. Applied egg-rr 86.0%

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

   if -4.99999999999999977e-163 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 1e-282

   1. Initial program 19.5%

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

   3. Taylor expanded in z around inf 95.6%

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

      1. associate--l+ 95.6%

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

      2. distribute-lft-out-- 95.6%

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

      3. div-sub 95.5%

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

      4. mul-1-neg 95.5%

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

      5. unsub-neg 95.5%

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

      6. distribute-rgt-out-- 95.6%

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

   5. Simplified 95.6%

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

   if 1e-282 < (+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z))) < 4.9999999999999997e304

   1. Initial program 97.0%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq -5 \cdot 10^{-163}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 10^{-282}:\\ \;\;\;\;t + \frac{\left(t - x\right) \cdot \left(a - y\right)}{z}\\ \mathbf{elif}\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z} \leq 5 \cdot 10^{+304}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + t \cdot \frac{y - z}{a}\\ \mathbf{if}\;a \leq -4.7 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-295}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* t (/ (- y z) a)))))
   (if (<= a -4.7e+38)
     t_2
     (if (<= a -9.5e-217)
       t_1
       (if (<= a -1.7e-295)
         (/ (* y (- x t)) z)
         (if (<= a 6.4e-32)
           t_1
           (if (<= a 7e+88) (* y (/ (- t x) (- a z))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (t * ((y - z) / a));
	double tmp;
	if (a <= -4.7e+38) {
		tmp = t_2;
	} else if (a <= -9.5e-217) {
		tmp = t_1;
	} else if (a <= -1.7e-295) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 6.4e-32) {
		tmp = t_1;
	} else if (a <= 7e+88) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (t * ((y - z) / a))
    if (a <= (-4.7d+38)) then
        tmp = t_2
    else if (a <= (-9.5d-217)) then
        tmp = t_1
    else if (a <= (-1.7d-295)) then
        tmp = (y * (x - t)) / z
    else if (a <= 6.4d-32) then
        tmp = t_1
    else if (a <= 7d+88) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (t * ((y - z) / a));
	double tmp;
	if (a <= -4.7e+38) {
		tmp = t_2;
	} else if (a <= -9.5e-217) {
		tmp = t_1;
	} else if (a <= -1.7e-295) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 6.4e-32) {
		tmp = t_1;
	} else if (a <= 7e+88) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (t * ((y - z) / a))
	tmp = 0
	if a <= -4.7e+38:
		tmp = t_2
	elif a <= -9.5e-217:
		tmp = t_1
	elif a <= -1.7e-295:
		tmp = (y * (x - t)) / z
	elif a <= 6.4e-32:
		tmp = t_1
	elif a <= 7e+88:
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(t * Float64(Float64(y - z) / a)))
	tmp = 0.0
	if (a <= -4.7e+38)
		tmp = t_2;
	elseif (a <= -9.5e-217)
		tmp = t_1;
	elseif (a <= -1.7e-295)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (a <= 6.4e-32)
		tmp = t_1;
	elseif (a <= 7e+88)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (t * ((y - z) / a));
	tmp = 0.0;
	if (a <= -4.7e+38)
		tmp = t_2;
	elseif (a <= -9.5e-217)
		tmp = t_1;
	elseif (a <= -1.7e-295)
		tmp = (y * (x - t)) / z;
	elseif (a <= 6.4e-32)
		tmp = t_1;
	elseif (a <= 7e+88)
		tmp = y * ((t - x) / (a - z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.7e+38], t$95$2, If[LessEqual[a, -9.5e-217], t$95$1, If[LessEqual[a, -1.7e-295], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 6.4e-32], t$95$1, If[LessEqual[a, 7e+88], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.6999999999999999e38 or 6.9999999999999995e88 < a

   1. Initial program 66.2%

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

   3. Taylor expanded in t around inf 63.8%

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

      1. associate-/l* 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in a around inf 61.3%

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

      1. associate-/l* 72.7%

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

   8. Simplified 72.7%

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

   if -4.6999999999999999e38 < a < -9.5000000000000001e-217 or -1.70000000000000004e-295 < a < 6.4000000000000004e-32

   1. Initial program 68.3%

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

      1. associate-/l* 75.0%

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

      2. clear-num 74.9%

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

      3. un-div-inv 74.9%

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

   4. Applied egg-rr 74.9%

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

   5. Taylor expanded in x around 0 60.9%

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

      1. associate-*r/ 74.8%

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

   7. Simplified 74.8%

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

   if -9.5000000000000001e-217 < a < -1.70000000000000004e-295

   1. Initial program 74.7%

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

   3. Taylor expanded in a around 0 70.5%

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

      1. mul-1-neg 70.5%

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

      2. unsub-neg 70.5%

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

      3. associate-/l* 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in y around -inf 70.2%

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

      1. associate-*r/ 70.2%

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

      2. associate-*r* 70.2%

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

      3. mul-1-neg 70.2%

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

   8. Simplified 70.2%

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

   if 6.4000000000000004e-32 < a < 6.9999999999999995e88

   1. Initial program 56.5%

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

      1. associate-/l* 77.3%

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

      2. clear-num 77.1%

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

      3. un-div-inv 77.0%

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

   4. Applied egg-rr 77.0%

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

   5. Taylor expanded in y around inf 57.4%

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

      1. div-sub 57.4%

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

   7. Simplified 57.4%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+38}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-217}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-295}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-32}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ t_2 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{+38}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-215}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.38 \cdot 10^{-297}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))) (t_2 (+ x (* t (/ y a)))))
   (if (<= a -2.8e+38)
     t_2
     (if (<= a -1.8e-215)
       t_1
       (if (<= a -1.38e-297)
         (/ (* y (- x t)) z)
         (if (<= a 3.8e-31)
           t_1
           (if (<= a 2.9e+87) (* y (/ (- t x) (- a z))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -2.8e+38) {
		tmp = t_2;
	} else if (a <= -1.8e-215) {
		tmp = t_1;
	} else if (a <= -1.38e-297) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 3.8e-31) {
		tmp = t_1;
	} else if (a <= 2.9e+87) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((y - z) / (a - z))
    t_2 = x + (t * (y / a))
    if (a <= (-2.8d+38)) then
        tmp = t_2
    else if (a <= (-1.8d-215)) then
        tmp = t_1
    else if (a <= (-1.38d-297)) then
        tmp = (y * (x - t)) / z
    else if (a <= 3.8d-31) then
        tmp = t_1
    else if (a <= 2.9d+87) then
        tmp = y * ((t - x) / (a - z))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double t_2 = x + (t * (y / a));
	double tmp;
	if (a <= -2.8e+38) {
		tmp = t_2;
	} else if (a <= -1.8e-215) {
		tmp = t_1;
	} else if (a <= -1.38e-297) {
		tmp = (y * (x - t)) / z;
	} else if (a <= 3.8e-31) {
		tmp = t_1;
	} else if (a <= 2.9e+87) {
		tmp = y * ((t - x) / (a - z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	t_2 = x + (t * (y / a))
	tmp = 0
	if a <= -2.8e+38:
		tmp = t_2
	elif a <= -1.8e-215:
		tmp = t_1
	elif a <= -1.38e-297:
		tmp = (y * (x - t)) / z
	elif a <= 3.8e-31:
		tmp = t_1
	elif a <= 2.9e+87:
		tmp = y * ((t - x) / (a - z))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	t_2 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (a <= -2.8e+38)
		tmp = t_2;
	elseif (a <= -1.8e-215)
		tmp = t_1;
	elseif (a <= -1.38e-297)
		tmp = Float64(Float64(y * Float64(x - t)) / z);
	elseif (a <= 3.8e-31)
		tmp = t_1;
	elseif (a <= 2.9e+87)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	t_2 = x + (t * (y / a));
	tmp = 0.0;
	if (a <= -2.8e+38)
		tmp = t_2;
	elseif (a <= -1.8e-215)
		tmp = t_1;
	elseif (a <= -1.38e-297)
		tmp = (y * (x - t)) / z;
	elseif (a <= 3.8e-31)
		tmp = t_1;
	elseif (a <= 2.9e+87)
		tmp = y * ((t - x) / (a - z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.8e+38], t$95$2, If[LessEqual[a, -1.8e-215], t$95$1, If[LessEqual[a, -1.38e-297], N[(N[(y * N[(x - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 3.8e-31], t$95$1, If[LessEqual[a, 2.9e+87], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.8e38 or 2.8999999999999998e87 < a

   1. Initial program 66.2%

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

   3. Taylor expanded in t around inf 63.8%

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

      1. associate-/l* 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in z around 0 65.3%

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

   if -2.8e38 < a < -1.7999999999999999e-215 or -1.38000000000000004e-297 < a < 3.8e-31

   1. Initial program 68.3%

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

      1. associate-/l* 75.0%

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

      2. clear-num 74.9%

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

      3. un-div-inv 74.9%

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

   4. Applied egg-rr 74.9%

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

   5. Taylor expanded in x around 0 60.9%

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

      1. associate-*r/ 74.8%

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

   7. Simplified 74.8%

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

   if -1.7999999999999999e-215 < a < -1.38000000000000004e-297

   1. Initial program 74.7%

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

   3. Taylor expanded in a around 0 70.5%

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

      1. mul-1-neg 70.5%

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

      2. unsub-neg 70.5%

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

      3. associate-/l* 66.5%

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

   5. Simplified 66.5%

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

   6. Taylor expanded in y around -inf 70.2%

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

      1. associate-*r/ 70.2%

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

      2. associate-*r* 70.2%

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

      3. mul-1-neg 70.2%

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

   8. Simplified 70.2%

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

   if 3.8e-31 < a < 2.8999999999999998e87

   1. Initial program 56.5%

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

      1. associate-/l* 77.3%

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

      2. clear-num 77.1%

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

      3. un-div-inv 77.0%

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

   4. Applied egg-rr 77.0%

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

   5. Taylor expanded in y around inf 57.4%

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

      1. div-sub 57.4%

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

   7. Simplified 57.4%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{+38}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-215}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq -1.38 \cdot 10^{-297}:\\ \;\;\;\;\frac{y \cdot \left(x - t\right)}{z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-31}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+79}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= z -2.9e+72)
     t
     (if (<= z -1.75e-56)
       x
       (if (<= z -1.25e-237)
         t_1
         (if (<= z 4.2e-113)
           x
           (if (<= z 1e-28) t_1 (if (<= z 2.55e+79) (+ x t) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -2.9e+72) {
		tmp = t;
	} else if (z <= -1.75e-56) {
		tmp = x;
	} else if (z <= -1.25e-237) {
		tmp = t_1;
	} else if (z <= 4.2e-113) {
		tmp = x;
	} else if (z <= 1e-28) {
		tmp = t_1;
	} else if (z <= 2.55e+79) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (z <= (-2.9d+72)) then
        tmp = t
    else if (z <= (-1.75d-56)) then
        tmp = x
    else if (z <= (-1.25d-237)) then
        tmp = t_1
    else if (z <= 4.2d-113) then
        tmp = x
    else if (z <= 1d-28) then
        tmp = t_1
    else if (z <= 2.55d+79) then
        tmp = x + t
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (z <= -2.9e+72) {
		tmp = t;
	} else if (z <= -1.75e-56) {
		tmp = x;
	} else if (z <= -1.25e-237) {
		tmp = t_1;
	} else if (z <= 4.2e-113) {
		tmp = x;
	} else if (z <= 1e-28) {
		tmp = t_1;
	} else if (z <= 2.55e+79) {
		tmp = x + t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if z <= -2.9e+72:
		tmp = t
	elif z <= -1.75e-56:
		tmp = x
	elif z <= -1.25e-237:
		tmp = t_1
	elif z <= 4.2e-113:
		tmp = x
	elif z <= 1e-28:
		tmp = t_1
	elif z <= 2.55e+79:
		tmp = x + t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (z <= -2.9e+72)
		tmp = t;
	elseif (z <= -1.75e-56)
		tmp = x;
	elseif (z <= -1.25e-237)
		tmp = t_1;
	elseif (z <= 4.2e-113)
		tmp = x;
	elseif (z <= 1e-28)
		tmp = t_1;
	elseif (z <= 2.55e+79)
		tmp = Float64(x + t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (z <= -2.9e+72)
		tmp = t;
	elseif (z <= -1.75e-56)
		tmp = x;
	elseif (z <= -1.25e-237)
		tmp = t_1;
	elseif (z <= 4.2e-113)
		tmp = x;
	elseif (z <= 1e-28)
		tmp = t_1;
	elseif (z <= 2.55e+79)
		tmp = x + t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+72], t, If[LessEqual[z, -1.75e-56], x, If[LessEqual[z, -1.25e-237], t$95$1, If[LessEqual[z, 4.2e-113], x, If[LessEqual[z, 1e-28], t$95$1, If[LessEqual[z, 2.55e+79], N[(x + t), $MachinePrecision], t]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.90000000000000017e72 or 2.5500000000000001e79 < z

   1. Initial program 36.5%

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

   3. Taylor expanded in z around inf 47.0%

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

   if -2.90000000000000017e72 < z < -1.7499999999999999e-56 or -1.2500000000000001e-237 < z < 4.2e-113

   1. Initial program 88.1%

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

   3. Taylor expanded in a around inf 45.2%

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

   if -1.7499999999999999e-56 < z < -1.2500000000000001e-237 or 4.2e-113 < z < 9.99999999999999971e-29

   1. Initial program 93.8%

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

      1. associate-/l* 93.6%

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

      2. clear-num 92.2%

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

      3. un-div-inv 92.1%

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

   4. Applied egg-rr 92.1%

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

   5. Taylor expanded in y around inf 68.3%

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

      1. div-sub 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in t around inf 43.9%

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

   9. Taylor expanded in a around inf 34.2%

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

       1. associate-/l* 45.4%

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

   11. Simplified 45.4%

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

   if 9.99999999999999971e-29 < z < 2.5500000000000001e79

   1. Initial program 74.3%

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

   3. Taylor expanded in t around inf 71.6%

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

      1. associate-/l* 77.0%

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

   5. Simplified 77.0%

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

   6. Taylor expanded in z around inf 39.8%

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

4. Final simplification 45.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-237}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{-28}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+79}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -7000000:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -140:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 58000000000000:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.6e+70)
   (* t (/ (- z y) z))
   (if (<= z -7000000.0)
     (* y (/ (- x t) z))
     (if (<= z -140.0)
       t
       (if (<= z 58000000000000.0)
         (+ x (* t (/ y a)))
         (* t (- 1.0 (/ y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.6e+70) {
		tmp = t * ((z - y) / z);
	} else if (z <= -7000000.0) {
		tmp = y * ((x - t) / z);
	} else if (z <= -140.0) {
		tmp = t;
	} else if (z <= 58000000000000.0) {
		tmp = x + (t * (y / a));
	} 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 <= (-8.6d+70)) then
        tmp = t * ((z - y) / z)
    else if (z <= (-7000000.0d0)) then
        tmp = y * ((x - t) / z)
    else if (z <= (-140.0d0)) then
        tmp = t
    else if (z <= 58000000000000.0d0) then
        tmp = x + (t * (y / a))
    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 <= -8.6e+70) {
		tmp = t * ((z - y) / z);
	} else if (z <= -7000000.0) {
		tmp = y * ((x - t) / z);
	} else if (z <= -140.0) {
		tmp = t;
	} else if (z <= 58000000000000.0) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.6e+70:
		tmp = t * ((z - y) / z)
	elif z <= -7000000.0:
		tmp = y * ((x - t) / z)
	elif z <= -140.0:
		tmp = t
	elif z <= 58000000000000.0:
		tmp = x + (t * (y / a))
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.6e+70)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	elseif (z <= -7000000.0)
		tmp = Float64(y * Float64(Float64(x - t) / z));
	elseif (z <= -140.0)
		tmp = t;
	elseif (z <= 58000000000000.0)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	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 <= -8.6e+70)
		tmp = t * ((z - y) / z);
	elseif (z <= -7000000.0)
		tmp = y * ((x - t) / z);
	elseif (z <= -140.0)
		tmp = t;
	elseif (z <= 58000000000000.0)
		tmp = x + (t * (y / a));
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.6e+70], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7000000.0], N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -140.0], t, If[LessEqual[z, 58000000000000.0], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.6000000000000002e70

   1. Initial program 38.7%

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

   3. Taylor expanded in a around 0 28.1%

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

      1. mul-1-neg 28.1%

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

      2. unsub-neg 28.1%

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

      3. associate-/l* 46.2%

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

   5. Simplified 46.2%

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

   6. Taylor expanded in t around inf 53.2%

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

   7. Taylor expanded in z around 0 53.3%

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

   if -8.6000000000000002e70 < z < -7e6

   1. Initial program 70.6%

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

      1. associate-/l* 75.5%

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

      2. clear-num 75.5%

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

      3. un-div-inv 75.5%

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

   4. Applied egg-rr 75.5%

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

   5. Taylor expanded in y around inf 76.4%

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

      1. div-sub 76.4%

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

   7. Simplified 76.4%

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

   8. Taylor expanded in a around 0 69.0%

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

      1. mul-1-neg 69.0%

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

      2. distribute-neg-frac2 69.0%

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

   10. Simplified 69.0%

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

   if -7e6 < z < -140

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   if -140 < z < 5.8e13

   1. Initial program 93.7%

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

   3. Taylor expanded in t around inf 71.1%

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

      1. associate-/l* 76.6%

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

   5. Simplified 76.6%

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

   6. Taylor expanded in z around 0 67.0%

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

   if 5.8e13 < z

   1. Initial program 41.4%

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

   3. Taylor expanded in a around 0 34.3%

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

      1. mul-1-neg 34.3%

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

      2. unsub-neg 34.3%

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

      3. associate-/l* 54.9%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in t around inf 62.9%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq -7000000:\\ \;\;\;\;y \cdot \frac{x - t}{z}\\ \mathbf{elif}\;z \leq -140:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 58000000000000:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-178}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.7e+38)
   x
   (if (<= a -3.5e-178)
     (* t (- 1.0 (/ y z)))
     (if (<= a -3.7e-259)
       (* x (/ y z))
       (if (<= a 3.8e+82) (* t (/ (- z y) z)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.7e+38) {
		tmp = x;
	} else if (a <= -3.5e-178) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= -3.7e-259) {
		tmp = x * (y / z);
	} else if (a <= 3.8e+82) {
		tmp = t * ((z - y) / z);
	} 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 <= (-4.7d+38)) then
        tmp = x
    else if (a <= (-3.5d-178)) then
        tmp = t * (1.0d0 - (y / z))
    else if (a <= (-3.7d-259)) then
        tmp = x * (y / z)
    else if (a <= 3.8d+82) then
        tmp = t * ((z - y) / z)
    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 <= -4.7e+38) {
		tmp = x;
	} else if (a <= -3.5e-178) {
		tmp = t * (1.0 - (y / z));
	} else if (a <= -3.7e-259) {
		tmp = x * (y / z);
	} else if (a <= 3.8e+82) {
		tmp = t * ((z - y) / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.7e+38:
		tmp = x
	elif a <= -3.5e-178:
		tmp = t * (1.0 - (y / z))
	elif a <= -3.7e-259:
		tmp = x * (y / z)
	elif a <= 3.8e+82:
		tmp = t * ((z - y) / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.7e+38)
		tmp = x;
	elseif (a <= -3.5e-178)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (a <= -3.7e-259)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 3.8e+82)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.7e+38)
		tmp = x;
	elseif (a <= -3.5e-178)
		tmp = t * (1.0 - (y / z));
	elseif (a <= -3.7e-259)
		tmp = x * (y / z);
	elseif (a <= 3.8e+82)
		tmp = t * ((z - y) / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.7e+38], x, If[LessEqual[a, -3.5e-178], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -3.7e-259], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.8e+82], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.6999999999999999e38 or 3.80000000000000033e82 < a

   1. Initial program 66.3%

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

   3. Taylor expanded in a around inf 48.9%

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

   if -4.6999999999999999e38 < a < -3.49999999999999983e-178

   1. Initial program 71.3%

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

   3. Taylor expanded in a around 0 54.6%

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

      1. mul-1-neg 54.6%

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

      2. unsub-neg 54.6%

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

      3. associate-/l* 56.8%

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

   5. Simplified 56.8%

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

   6. Taylor expanded in t around inf 67.9%

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

   if -3.49999999999999983e-178 < a < -3.69999999999999991e-259

   1. Initial program 79.3%

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

   3. Taylor expanded in a around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. unsub-neg 65.2%

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

      3. associate-/l* 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in x around -inf 58.1%

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

      1. associate-/l* 64.9%

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

   8. Simplified 64.9%

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

   if -3.69999999999999991e-259 < a < 3.80000000000000033e82

   1. Initial program 63.9%

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

   3. Taylor expanded in a around 0 46.0%

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

      1. mul-1-neg 46.0%

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

      2. unsub-neg 46.0%

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

      3. associate-/l* 59.6%

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

   5. Simplified 59.6%

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

   6. Taylor expanded in t around inf 55.2%

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

   7. Taylor expanded in z around 0 55.2%

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

Alternative 9: 48.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -4.4 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ y z)))))
   (if (<= a -4.4e+38)
     x
     (if (<= a -5e-178)
       t_1
       (if (<= a -3.2e-259) (* x (/ y z)) (if (<= a 1.3e+81) t_1 x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -4.4e+38) {
		tmp = x;
	} else if (a <= -5e-178) {
		tmp = t_1;
	} else if (a <= -3.2e-259) {
		tmp = x * (y / z);
	} else if (a <= 1.3e+81) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (y / z))
    if (a <= (-4.4d+38)) then
        tmp = x
    else if (a <= (-5d-178)) then
        tmp = t_1
    else if (a <= (-3.2d-259)) then
        tmp = x * (y / z)
    else if (a <= 1.3d+81) then
        tmp = t_1
    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 t_1 = t * (1.0 - (y / z));
	double tmp;
	if (a <= -4.4e+38) {
		tmp = x;
	} else if (a <= -5e-178) {
		tmp = t_1;
	} else if (a <= -3.2e-259) {
		tmp = x * (y / z);
	} else if (a <= 1.3e+81) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if a <= -4.4e+38:
		tmp = x
	elif a <= -5e-178:
		tmp = t_1
	elif a <= -3.2e-259:
		tmp = x * (y / z)
	elif a <= 1.3e+81:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (a <= -4.4e+38)
		tmp = x;
	elseif (a <= -5e-178)
		tmp = t_1;
	elseif (a <= -3.2e-259)
		tmp = Float64(x * Float64(y / z));
	elseif (a <= 1.3e+81)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (a <= -4.4e+38)
		tmp = x;
	elseif (a <= -5e-178)
		tmp = t_1;
	elseif (a <= -3.2e-259)
		tmp = x * (y / z);
	elseif (a <= 1.3e+81)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.4e+38], x, If[LessEqual[a, -5e-178], t$95$1, If[LessEqual[a, -3.2e-259], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.3e+81], t$95$1, x]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.40000000000000013e38 or 1.29999999999999996e81 < a

   1. Initial program 66.3%

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

   3. Taylor expanded in a around inf 48.9%

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

   if -4.40000000000000013e38 < a < -4.99999999999999976e-178 or -3.19999999999999988e-259 < a < 1.29999999999999996e81

   1. Initial program 66.1%

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

   3. Taylor expanded in a around 0 48.6%

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

      1. mul-1-neg 48.6%

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

      2. unsub-neg 48.6%

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

      3. associate-/l* 58.7%

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

   5. Simplified 58.7%

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

   6. Taylor expanded in t around inf 59.0%

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

   if -4.99999999999999976e-178 < a < -3.19999999999999988e-259

   1. Initial program 79.3%

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

   3. Taylor expanded in a around 0 65.2%

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

      1. mul-1-neg 65.2%

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

      2. unsub-neg 65.2%

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

      3. associate-/l* 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in x around -inf 58.1%

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

      1. associate-/l* 64.9%

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

   8. Simplified 64.9%

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

Alternative 10: 38.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+173}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+20}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+140} \lor \neg \left(y \leq 4.25 \cdot 10^{+273}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.2e+173)
   (* t (/ (- y) z))
   (if (<= y 9e+20)
     (+ x t)
     (if (or (<= y 3.8e+140) (not (<= y 4.25e+273)))
       (* x (/ y z))
       (* t (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.2e+173) {
		tmp = t * (-y / z);
	} else if (y <= 9e+20) {
		tmp = x + t;
	} else if ((y <= 3.8e+140) || !(y <= 4.25e+273)) {
		tmp = x * (y / z);
	} else {
		tmp = t * (y / a);
	}
	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 (y <= (-1.2d+173)) then
        tmp = t * (-y / z)
    else if (y <= 9d+20) then
        tmp = x + t
    else if ((y <= 3.8d+140) .or. (.not. (y <= 4.25d+273))) then
        tmp = x * (y / z)
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.2e+173) {
		tmp = t * (-y / z);
	} else if (y <= 9e+20) {
		tmp = x + t;
	} else if ((y <= 3.8e+140) || !(y <= 4.25e+273)) {
		tmp = x * (y / z);
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.2e+173:
		tmp = t * (-y / z)
	elif y <= 9e+20:
		tmp = x + t
	elif (y <= 3.8e+140) or not (y <= 4.25e+273):
		tmp = x * (y / z)
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.2e+173)
		tmp = Float64(t * Float64(Float64(-y) / z));
	elseif (y <= 9e+20)
		tmp = Float64(x + t);
	elseif ((y <= 3.8e+140) || !(y <= 4.25e+273))
		tmp = Float64(x * Float64(y / z));
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.2e+173)
		tmp = t * (-y / z);
	elseif (y <= 9e+20)
		tmp = x + t;
	elseif ((y <= 3.8e+140) || ~((y <= 4.25e+273)))
		tmp = x * (y / z);
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.2e+173], N[(t * N[((-y) / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+20], N[(x + t), $MachinePrecision], If[Or[LessEqual[y, 3.8e+140], N[Not[LessEqual[y, 4.25e+273]], $MachinePrecision]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.2e173

   1. Initial program 74.9%

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

   3. Taylor expanded in a around 0 64.6%

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

      1. mul-1-neg 64.6%

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

      2. unsub-neg 64.6%

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

      3. associate-/l* 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in t around inf 59.1%

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

   7. Taylor expanded in y around inf 40.2%

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

      1. mul-1-neg 40.2%

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

      2. associate-/l* 46.6%

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

      3. distribute-rgt-neg-in 46.6%

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

      4. distribute-frac-neg2 46.6%

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

   9. Simplified 46.6%

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

   if -1.2e173 < y < 9e20

   1. Initial program 65.2%

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

   3. Taylor expanded in t around inf 60.2%

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

      1. associate-/l* 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in z around inf 44.3%

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

   if 9e20 < y < 3.8000000000000001e140 or 4.2500000000000001e273 < y

   1. Initial program 66.5%

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

   3. Taylor expanded in a around 0 44.5%

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

      1. mul-1-neg 44.5%

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

      2. unsub-neg 44.5%

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

      3. associate-/l* 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in x around -inf 37.8%

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

      1. associate-/l* 46.1%

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

   8. Simplified 46.1%

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

   if 3.8000000000000001e140 < y < 4.2500000000000001e273

   1. Initial program 67.8%

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

      1. associate-/l* 86.3%

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

      2. clear-num 86.3%

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

      3. un-div-inv 86.3%

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

   4. Applied egg-rr 86.3%

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

   5. Taylor expanded in y around inf 83.6%

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

      1. div-sub 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in t around inf 53.9%

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

   9. Taylor expanded in a around inf 32.9%

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

       1. associate-/l* 46.9%

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

   11. Simplified 46.9%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+173}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+20}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+140} \lor \neg \left(y \leq 4.25 \cdot 10^{+273}\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{+71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+21}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= z -6.4e+71)
     t_1
     (if (<= z -1.12e+24)
       (* y (/ (- t x) (- a z)))
       (if (<= z 2.9e+21) (+ x (* y (/ (- t x) a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -6.4e+71) {
		tmp = t_1;
	} else if (z <= -1.12e+24) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 2.9e+21) {
		tmp = x + (y * ((t - x) / a));
	} 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) / (a - z))
    if (z <= (-6.4d+71)) then
        tmp = t_1
    else if (z <= (-1.12d+24)) then
        tmp = y * ((t - x) / (a - z))
    else if (z <= 2.9d+21) then
        tmp = x + (y * ((t - x) / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y - z) / (a - z));
	double tmp;
	if (z <= -6.4e+71) {
		tmp = t_1;
	} else if (z <= -1.12e+24) {
		tmp = y * ((t - x) / (a - z));
	} else if (z <= 2.9e+21) {
		tmp = x + (y * ((t - x) / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y - z) / (a - z))
	tmp = 0
	if z <= -6.4e+71:
		tmp = t_1
	elif z <= -1.12e+24:
		tmp = y * ((t - x) / (a - z))
	elif z <= 2.9e+21:
		tmp = x + (y * ((t - x) / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (z <= -6.4e+71)
		tmp = t_1;
	elseif (z <= -1.12e+24)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (z <= 2.9e+21)
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (z <= -6.4e+71)
		tmp = t_1;
	elseif (z <= -1.12e+24)
		tmp = y * ((t - x) / (a - z));
	elseif (z <= 2.9e+21)
		tmp = x + (y * ((t - x) / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.4e+71], t$95$1, If[LessEqual[z, -1.12e+24], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.9e+21], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.40000000000000046e71 or 2.9e21 < z

   1. Initial program 39.3%

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

      1. associate-/l* 63.4%

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

      2. clear-num 63.3%

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

      3. un-div-inv 63.3%

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

   4. Applied egg-rr 63.3%

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

   5. Taylor expanded in x around 0 43.3%

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

      1. associate-*r/ 67.2%

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

   7. Simplified 67.2%

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

   if -6.40000000000000046e71 < z < -1.12e24

   1. Initial program 68.6%

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

      1. associate-/l* 73.9%

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

      2. clear-num 74.0%

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

      3. un-div-inv 74.0%

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

   4. Applied egg-rr 74.0%

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

   5. Taylor expanded in y around inf 74.9%

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

      1. div-sub 74.9%

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

   7. Simplified 74.9%

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

   if -1.12e24 < z < 2.9e21

   1. Initial program 93.2%

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

   3. Taylor expanded in z around 0 70.9%

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

      1. associate-/l* 76.7%

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

   5. Simplified 76.7%

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

Alternative 12: 75.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -150 \lor \neg \left(z \leq 2.9 \cdot 10^{+21}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -150.0) (not (<= z 2.9e+21)))
   (+ t (* y (/ (- x t) z)))
   (+ x (* y (/ (- t x) (- a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -150.0) || !(z <= 2.9e+21)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (y * ((t - x) / (a - 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 <= (-150.0d0)) .or. (.not. (z <= 2.9d+21))) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + (y * ((t - x) / (a - 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 <= -150.0) || !(z <= 2.9e+21)) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (y * ((t - x) / (a - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -150.0) or not (z <= 2.9e+21):
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + (y * ((t - x) / (a - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -150.0) || !(z <= 2.9e+21))
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / Float64(a - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -150.0) || ~((z <= 2.9e+21)))
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + (y * ((t - x) / (a - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -150.0], N[Not[LessEqual[z, 2.9e+21]], $MachinePrecision]], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -150 or 2.9e21 < z

   1. Initial program 43.9%

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

   3. Taylor expanded in z around inf 65.9%

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

      1. associate--l+ 65.9%

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

      2. distribute-lft-out-- 65.9%

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

      3. div-sub 65.9%

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

      4. mul-1-neg 65.9%

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

      5. unsub-neg 65.9%

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

      6. distribute-rgt-out-- 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in y around inf 63.7%

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

      1. associate-/l* 74.5%

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

   8. Simplified 74.5%

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

   if -150 < z < 2.9e21

   1. Initial program 93.0%

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

   3. Taylor expanded in y around inf 85.6%

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

      1. associate-/l* 90.1%

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

   5. Simplified 90.1%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -150 \lor \neg \left(z \leq 2.9 \cdot 10^{+21}\right):\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-95} \lor \neg \left(a \leq 8 \cdot 10^{-7}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.7e-95) (not (<= a 8e-7)))
   (+ x (* t (/ (- y z) (- a z))))
   (+ t (* y (/ (- x t) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.7e-95) || !(a <= 8e-7)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t + (y * ((x - t) / 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 ((a <= (-4.7d-95)) .or. (.not. (a <= 8d-7))) then
        tmp = x + (t * ((y - z) / (a - z)))
    else
        tmp = t + (y * ((x - t) / 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 ((a <= -4.7e-95) || !(a <= 8e-7)) {
		tmp = x + (t * ((y - z) / (a - z)));
	} else {
		tmp = t + (y * ((x - t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.7e-95) or not (a <= 8e-7):
		tmp = x + (t * ((y - z) / (a - z)))
	else:
		tmp = t + (y * ((x - t) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.7e-95) || !(a <= 8e-7))
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / Float64(a - z))));
	else
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.7e-95) || ~((a <= 8e-7)))
		tmp = x + (t * ((y - z) / (a - z)));
	else
		tmp = t + (y * ((x - t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.7e-95], N[Not[LessEqual[a, 8e-7]], $MachinePrecision]], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.6999999999999998e-95 or 7.9999999999999996e-7 < a

   1. Initial program 64.6%

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

   3. Taylor expanded in t around inf 59.5%

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

      1. associate-/l* 75.2%

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

   5. Simplified 75.2%

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

   if -4.6999999999999998e-95 < a < 7.9999999999999996e-7

   1. Initial program 69.6%

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

   3. Taylor expanded in z around inf 82.0%

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

      1. associate--l+ 82.0%

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

      2. distribute-lft-out-- 82.0%

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

      3. div-sub 82.8%

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

      4. mul-1-neg 82.8%

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

      5. unsub-neg 82.8%

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

      6. distribute-rgt-out-- 82.8%

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

   5. Simplified 82.8%

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

   6. Taylor expanded in y around inf 81.7%

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

      1. associate-/l* 86.4%

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

   8. Simplified 86.4%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-95} \lor \neg \left(a \leq 8 \cdot 10^{-7}\right):\\ \;\;\;\;x + t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+24} \lor \neg \left(z \leq 2.2 \cdot 10^{+14}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.8e+24) (not (<= z 2.2e+14)))
   (* t (/ (- y z) (- a z)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.8e+24) || !(z <= 2.2e+14)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (t * (y / a));
	}
	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 <= (-2.8d+24)) .or. (.not. (z <= 2.2d+14))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x + (t * (y / a))
    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 <= -2.8e+24) || !(z <= 2.2e+14)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.8e+24) or not (z <= 2.2e+14):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.8e+24) || !(z <= 2.2e+14))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.8e+24) || ~((z <= 2.2e+14)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.8e+24], N[Not[LessEqual[z, 2.2e+14]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8000000000000002e24 or 2.2e14 < z

   1. Initial program 42.8%

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

      1. associate-/l* 65.1%

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

      2. clear-num 65.0%

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

      3. un-div-inv 65.0%

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

   4. Applied egg-rr 65.0%

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

   5. Taylor expanded in x around 0 43.9%

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

      1. associate-*r/ 64.8%

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

   7. Simplified 64.8%

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

   if -2.8000000000000002e24 < z < 2.2e14

   1. Initial program 93.8%

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

   3. Taylor expanded in t around inf 71.1%

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

      1. associate-/l* 76.4%

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

   5. Simplified 76.4%

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

   6. Taylor expanded in z around 0 66.3%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+24} \lor \neg \left(z \leq 2.2 \cdot 10^{+14}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 70.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{+38}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-7}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.75e+38)
   (+ x (* t (/ (- y z) a)))
   (if (<= a 9e-7) (+ t (* y (/ (- x t) z))) (+ x (* y (/ (- t x) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.75e+38) {
		tmp = x + (t * ((y - z) / a));
	} else if (a <= 9e-7) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.75d+38)) then
        tmp = x + (t * ((y - z) / a))
    else if (a <= 9d-7) then
        tmp = t + (y * ((x - t) / z))
    else
        tmp = x + (y * ((t - x) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.75e+38) {
		tmp = x + (t * ((y - z) / a));
	} else if (a <= 9e-7) {
		tmp = t + (y * ((x - t) / z));
	} else {
		tmp = x + (y * ((t - x) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.75e+38:
		tmp = x + (t * ((y - z) / a))
	elif a <= 9e-7:
		tmp = t + (y * ((x - t) / z))
	else:
		tmp = x + (y * ((t - x) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.75e+38)
		tmp = Float64(x + Float64(t * Float64(Float64(y - z) / a)));
	elseif (a <= 9e-7)
		tmp = Float64(t + Float64(y * Float64(Float64(x - t) / z)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - x) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.75e+38)
		tmp = x + (t * ((y - z) / a));
	elseif (a <= 9e-7)
		tmp = t + (y * ((x - t) / z));
	else
		tmp = x + (y * ((t - x) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.75e+38], N[(x + N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e-7], N[(t + N[(y * N[(N[(x - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.7500000000000002e38

   1. Initial program 70.7%

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

   3. Taylor expanded in t around inf 68.8%

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

      1. associate-/l* 85.4%

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

   5. Simplified 85.4%

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

   6. Taylor expanded in a around inf 64.1%

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

      1. associate-/l* 73.4%

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

   8. Simplified 73.4%

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

   if -2.7500000000000002e38 < a < 8.99999999999999959e-7

   1. Initial program 69.4%

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

   3. Taylor expanded in z around inf 79.3%

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

      1. associate--l+ 79.3%

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

      2. distribute-lft-out-- 79.3%

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

      3. div-sub 80.0%

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

      4. mul-1-neg 80.0%

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

      5. unsub-neg 80.0%

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

      6. distribute-rgt-out-- 80.0%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in y around inf 78.2%

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

      1. associate-/l* 82.7%

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

   8. Simplified 82.7%

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

   if 8.99999999999999959e-7 < a

   1. Initial program 57.7%

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

   3. Taylor expanded in z around 0 50.9%

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

      1. associate-/l* 63.2%

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

   5. Simplified 63.2%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{+38}:\\ \;\;\;\;x + t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-7}:\\ \;\;\;\;t + y \cdot \frac{x - t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 56.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+24}:\\ \;\;\;\;t \cdot \frac{z - y}{z}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+14}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8e+24)
   (* t (/ (- z y) z))
   (if (<= z 3.2e+14) (+ x (* t (/ y a))) (* t (- 1.0 (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e+24) {
		tmp = t * ((z - y) / z);
	} else if (z <= 3.2e+14) {
		tmp = x + (t * (y / a));
	} 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 <= (-2.8d+24)) then
        tmp = t * ((z - y) / z)
    else if (z <= 3.2d+14) then
        tmp = x + (t * (y / a))
    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 <= -2.8e+24) {
		tmp = t * ((z - y) / z);
	} else if (z <= 3.2e+14) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.8e+24:
		tmp = t * ((z - y) / z)
	elif z <= 3.2e+14:
		tmp = x + (t * (y / a))
	else:
		tmp = t * (1.0 - (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.8e+24)
		tmp = Float64(t * Float64(Float64(z - y) / z));
	elseif (z <= 3.2e+14)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	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 <= -2.8e+24)
		tmp = t * ((z - y) / z);
	elseif (z <= 3.2e+14)
		tmp = x + (t * (y / a));
	else
		tmp = t * (1.0 - (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.8e+24], N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+14], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8000000000000002e24

   1. Initial program 43.8%

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

   3. Taylor expanded in a around 0 32.4%

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

      1. mul-1-neg 32.4%

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

      2. unsub-neg 32.4%

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

      3. associate-/l* 48.1%

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

   5. Simplified 48.1%

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

   6. Taylor expanded in t around inf 51.3%

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

   7. Taylor expanded in z around 0 51.3%

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

   if -2.8000000000000002e24 < z < 3.2e14

   1. Initial program 93.8%

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

   3. Taylor expanded in t around inf 71.1%

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

      1. associate-/l* 76.4%

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

   5. Simplified 76.4%

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

   6. Taylor expanded in z around 0 66.3%

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

   if 3.2e14 < z

   1. Initial program 41.4%

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

   3. Taylor expanded in a around 0 34.3%

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

      1. mul-1-neg 34.3%

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

      2. unsub-neg 34.3%

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

      3. associate-/l* 54.9%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in t around inf 62.9%

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

Alternative 17: 38.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+71} \lor \neg \left(z \leq 85000000000000\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.5e+71) (not (<= z 85000000000000.0))) t x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.5e+71) || !(z <= 85000000000000.0)) {
		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 ((z <= (-4.5d+71)) .or. (.not. (z <= 85000000000000.0d0))) 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 ((z <= -4.5e+71) || !(z <= 85000000000000.0)) {
		tmp = t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.5e+71) or not (z <= 85000000000000.0):
		tmp = t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.5e+71) || !(z <= 85000000000000.0))
		tmp = t;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.5e+71) || ~((z <= 85000000000000.0)))
		tmp = t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.5e+71], N[Not[LessEqual[z, 85000000000000.0]], $MachinePrecision]], t, x]

Derivation

1. Split input into 2 regimes

2. if z < -4.50000000000000043e71 or 8.5e13 < z

   1. Initial program 39.5%

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

   3. Taylor expanded in z around inf 45.3%

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

   if -4.50000000000000043e71 < z < 8.5e13

   1. Initial program 91.0%

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

   3. Taylor expanded in a around inf 34.1%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+71} \lor \neg \left(z \leq 85000000000000\right):\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 24.8% 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 66.9%

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

3. Taylor expanded in z around inf 24.7%

   \[\leadsto \color{blue}{t} \]
4. Add Preprocessing

Developer target: 84.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - \frac{y}{z} \cdot \left(t - x\right)\\ \mathbf{if}\;z < -1.2536131056095036 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 4.446702369113811 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y - z}{\frac{a - z}{t - x}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* (/ y z) (- t x)))))
   (if (< z -1.2536131056095036e+188)
     t_1
     (if (< z 4.446702369113811e+64)
       (+ x (/ (- y z) (/ (- a z) (- t x))))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - ((y / z) * (t - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} 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 - x))
    if (z < (-1.2536131056095036d+188)) then
        tmp = t_1
    else if (z < 4.446702369113811d+64) then
        tmp = x + ((y - z) / ((a - z) / (t - x)))
    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 - x));
	double tmp;
	if (z < -1.2536131056095036e+188) {
		tmp = t_1;
	} else if (z < 4.446702369113811e+64) {
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - ((y / z) * (t - x))
	tmp = 0
	if z < -1.2536131056095036e+188:
		tmp = t_1
	elif z < 4.446702369113811e+64:
		tmp = x + ((y - z) / ((a - z) / (t - x)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(Float64(y / z) * Float64(t - x)))
	tmp = 0.0
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = Float64(x + Float64(Float64(y - z) / Float64(Float64(a - z) / Float64(t - x))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - ((y / z) * (t - x));
	tmp = 0.0;
	if (z < -1.2536131056095036e+188)
		tmp = t_1;
	elseif (z < 4.446702369113811e+64)
		tmp = x + ((y - z) / ((a - z) / (t - x)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(N[(y / z), $MachinePrecision] * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.2536131056095036e+188], t$95$1, If[Less[z, 4.446702369113811e+64], N[(x + N[(N[(y - z), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:invLinMap from Chart-1.5.3"
  :precision binary64

  :alt
  (if (< z -1.2536131056095036e+188) (- t (* (/ y z) (- t x))) (if (< z 4.446702369113811e+64) (+ x (/ (- y z) (/ (- a z) (- t x)))) (- t (* (/ y z) (- t x)))))

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