Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 80.0% → 95.2%

Time: 15.4s

Alternatives: 26

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 80.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t - x}{a - z} \cdot \left(z - y\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-282}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ (- t x) (- a z)) (- z y)))))
   (if (<= t_1 -2e-282)
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (if (<= t_1 0.0)
       (+ t (* (/ (- t x) z) (- a y)))
       (fma (- t x) (/ (- y z) (- a z)) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) / (a - z)) * (z - y));
	double tmp;
	if (t_1 <= -2e-282) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else if (t_1 <= 0.0) {
		tmp = t + (((t - x) / z) * (a - y));
	} else {
		tmp = fma((t - x), ((y - z) / (a - z)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(t - x) / Float64(a - z)) * Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -2e-282)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	elseif (t_1 <= 0.0)
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	else
		tmp = fma(Float64(t - x), Float64(Float64(y - z) / Float64(a - z)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-282], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-282

   1. Initial program 90.1%

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

      1. *-commutative 90.1%

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

      2. associate-*l/ 81.0%

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

      3. associate-*r/ 96.2%

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

      4. clear-num 96.2%

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

      5. un-div-inv 96.3%

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

   4. Applied egg-rr 96.3%

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

   if -2e-282 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

   3. Taylor expanded in z around inf 79.8%

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

      1. associate--l+ 79.8%

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

      2. distribute-lft-out-- 79.8%

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

      3. div-sub 79.8%

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

      4. mul-1-neg 79.8%

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

      5. unsub-neg 79.8%

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

      6. div-sub 79.8%

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

      7. associate-/l* 88.1%

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

      8. associate-/l* 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

   5. Simplified 99.9%

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

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

   1. Initial program 96.3%

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

      1. +-commutative 96.3%

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

      2. remove-double-neg 96.3%

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

      3. unsub-neg 96.3%

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

      4. *-commutative 96.3%

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

      5. associate-*l/ 80.3%

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

      6. associate-/l* 97.2%

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

      7. fma-neg 97.3%

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

      8. remove-double-neg 97.3%

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

   3. Simplified 97.3%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq -2 \cdot 10^{-282}:\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq 0:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, \frac{y - z}{a - z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t - x}{a - z} \cdot \left(z - y\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y}}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-265} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ (- t x) (- a z)) (- z y)))))
   (if (<= t_1 (- INFINITY))
     (- x (/ (- x t) (/ (- a z) y)))
     (if (or (<= t_1 -1e-265) (not (<= t_1 0.0)))
       t_1
       (+ t (* (/ (- t x) z) (- a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) / (a - z)) * (z - y));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x - ((x - t) / ((a - z) / y));
	} else if ((t_1 <= -1e-265) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) / (a - z)) * (z - y));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x - ((x - t) / ((a - z) / y));
	} else if ((t_1 <= -1e-265) || !(t_1 <= 0.0)) {
		tmp = t_1;
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((t - x) / (a - z)) * (z - y))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x - ((x - t) / ((a - z) / y))
	elif (t_1 <= -1e-265) or not (t_1 <= 0.0):
		tmp = t_1
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(t - x) / Float64(a - z)) * Float64(z - y)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x - Float64(Float64(x - t) / Float64(Float64(a - z) / y)));
	elseif ((t_1 <= -1e-265) || !(t_1 <= 0.0))
		tmp = t_1;
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((t - x) / (a - z)) * (z - y));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x - ((x - t) / ((a - z) / y));
	elseif ((t_1 <= -1e-265) || ~((t_1 <= 0.0)))
		tmp = t_1;
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x - N[(N[(x - t), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, -1e-265], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], t$95$1, N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 82.0%

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

      1. *-commutative 82.0%

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

      2. associate-*l/ 100.0%

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

      3. associate-*r/ 99.9%

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

      4. clear-num 99.8%

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

      5. un-div-inv 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around inf 99.4%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -9.99999999999999985e-266 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 94.9%

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

   if -9.99999999999999985e-266 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.5%

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

   3. Taylor expanded in z around inf 80.6%

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

      1. associate--l+ 80.6%

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

      2. distribute-lft-out-- 80.6%

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

      3. div-sub 80.6%

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

      4. mul-1-neg 80.6%

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

      5. unsub-neg 80.6%

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

      6. div-sub 80.6%

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

      7. associate-/l* 88.6%

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

      8. associate-/l* 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq -\infty:\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y}}\\ \mathbf{elif}\;x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq -1 \cdot 10^{-265} \lor \neg \left(x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq 0\right):\\ \;\;\;\;x - \frac{t - x}{a - z} \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{t - x}{a - z} \cdot \left(z - y\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-282} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ (- t x) (- a z)) (- z y)))))
   (if (or (<= t_1 -2e-282) (not (<= t_1 0.0)))
     (+ x (/ (- t x) (/ (- a z) (- y z))))
     (+ t (* (/ (- t x) z) (- a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) / (a - z)) * (z - y));
	double tmp;
	if ((t_1 <= -2e-282) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (((t - x) / (a - z)) * (z - y))
    if ((t_1 <= (-2d-282)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = x + ((t - x) / ((a - z) / (y - z)))
    else
        tmp = t + (((t - x) / z) * (a - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (((t - x) / (a - z)) * (z - y));
	double tmp;
	if ((t_1 <= -2e-282) || !(t_1 <= 0.0)) {
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	} else {
		tmp = t + (((t - x) / z) * (a - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (((t - x) / (a - z)) * (z - y))
	tmp = 0
	if (t_1 <= -2e-282) or not (t_1 <= 0.0):
		tmp = x + ((t - x) / ((a - z) / (y - z)))
	else:
		tmp = t + (((t - x) / z) * (a - y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(Float64(t - x) / Float64(a - z)) * Float64(z - y)))
	tmp = 0.0
	if ((t_1 <= -2e-282) || !(t_1 <= 0.0))
		tmp = Float64(x + Float64(Float64(t - x) / Float64(Float64(a - z) / Float64(y - z))));
	else
		tmp = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (((t - x) / (a - z)) * (z - y));
	tmp = 0.0;
	if ((t_1 <= -2e-282) || ~((t_1 <= 0.0)))
		tmp = x + ((t - x) / ((a - z) / (y - z)));
	else
		tmp = t + (((t - x) / z) * (a - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-282], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(x + N[(N[(t - x), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -2e-282 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 93.1%

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

      1. *-commutative 93.1%

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

      2. associate-*l/ 80.6%

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

      3. associate-*r/ 96.7%

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

      4. clear-num 96.7%

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

      5. un-div-inv 96.8%

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

   4. Applied egg-rr 96.8%

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

   if -2e-282 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 3.4%

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

   3. Taylor expanded in z around inf 79.8%

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

      1. associate--l+ 79.8%

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

      2. distribute-lft-out-- 79.8%

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

      3. div-sub 79.8%

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

      4. mul-1-neg 79.8%

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

      5. unsub-neg 79.8%

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

      6. div-sub 79.8%

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

      7. associate-/l* 88.1%

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

      8. associate-/l* 99.9%

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

      9. distribute-rgt-out-- 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq -2 \cdot 10^{-282} \lor \neg \left(x - \frac{t - x}{a - z} \cdot \left(z - y\right) \leq 0\right):\\ \;\;\;\;x + \frac{t - x}{\frac{a - z}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 47.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+191}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -5500000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-289}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))))
   (if (<= z -1.12e+191)
     t
     (if (<= z -5.8e+85)
       (* t (/ (- y z) a))
       (if (<= z -5500000000.0)
         t_1
         (if (<= z -8.2e-59)
           (* y (/ t (- a z)))
           (if (<= z -1.8e-231)
             t_1
             (if (<= z -5.4e-289)
               (* y (/ (- t x) a))
               (if (<= z 7.6e+119) t_1 t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.12e+191) {
		tmp = t;
	} else if (z <= -5.8e+85) {
		tmp = t * ((y - z) / a);
	} else if (z <= -5500000000.0) {
		tmp = t_1;
	} else if (z <= -8.2e-59) {
		tmp = y * (t / (a - z));
	} else if (z <= -1.8e-231) {
		tmp = t_1;
	} else if (z <= -5.4e-289) {
		tmp = y * ((t - x) / a);
	} else if (z <= 7.6e+119) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    if (z <= (-1.12d+191)) then
        tmp = t
    else if (z <= (-5.8d+85)) then
        tmp = t * ((y - z) / a)
    else if (z <= (-5500000000.0d0)) then
        tmp = t_1
    else if (z <= (-8.2d-59)) then
        tmp = y * (t / (a - z))
    else if (z <= (-1.8d-231)) then
        tmp = t_1
    else if (z <= (-5.4d-289)) then
        tmp = y * ((t - x) / a)
    else if (z <= 7.6d+119) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double tmp;
	if (z <= -1.12e+191) {
		tmp = t;
	} else if (z <= -5.8e+85) {
		tmp = t * ((y - z) / a);
	} else if (z <= -5500000000.0) {
		tmp = t_1;
	} else if (z <= -8.2e-59) {
		tmp = y * (t / (a - z));
	} else if (z <= -1.8e-231) {
		tmp = t_1;
	} else if (z <= -5.4e-289) {
		tmp = y * ((t - x) / a);
	} else if (z <= 7.6e+119) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	tmp = 0
	if z <= -1.12e+191:
		tmp = t
	elif z <= -5.8e+85:
		tmp = t * ((y - z) / a)
	elif z <= -5500000000.0:
		tmp = t_1
	elif z <= -8.2e-59:
		tmp = y * (t / (a - z))
	elif z <= -1.8e-231:
		tmp = t_1
	elif z <= -5.4e-289:
		tmp = y * ((t - x) / a)
	elif z <= 7.6e+119:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -1.12e+191)
		tmp = t;
	elseif (z <= -5.8e+85)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= -5500000000.0)
		tmp = t_1;
	elseif (z <= -8.2e-59)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (z <= -1.8e-231)
		tmp = t_1;
	elseif (z <= -5.4e-289)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 7.6e+119)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -1.12e+191)
		tmp = t;
	elseif (z <= -5.8e+85)
		tmp = t * ((y - z) / a);
	elseif (z <= -5500000000.0)
		tmp = t_1;
	elseif (z <= -8.2e-59)
		tmp = y * (t / (a - z));
	elseif (z <= -1.8e-231)
		tmp = t_1;
	elseif (z <= -5.4e-289)
		tmp = y * ((t - x) / a);
	elseif (z <= 7.6e+119)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.12e+191], t, If[LessEqual[z, -5.8e+85], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5500000000.0], t$95$1, If[LessEqual[z, -8.2e-59], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.8e-231], t$95$1, If[LessEqual[z, -5.4e-289], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.6e+119], t$95$1, t]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.11999999999999999e191 or 7.59999999999999979e119 < z

   1. Initial program 56.8%

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

   3. Taylor expanded in z around inf 68.0%

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

   if -1.11999999999999999e191 < z < -5.79999999999999995e85

   1. Initial program 80.8%

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

   3. Taylor expanded in x around 0 43.7%

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

      1. associate-/l* 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in a around inf 33.1%

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

      1. associate-/l* 47.3%

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

   8. Simplified 47.3%

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

   if -5.79999999999999995e85 < z < -5.5e9 or -8.1999999999999991e-59 < z < -1.79999999999999987e-231 or -5.4e-289 < z < 7.59999999999999979e119

   1. Initial program 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-*l/ 89.7%

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

      3. associate-*r/ 95.5%

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

      4. clear-num 95.4%

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

      5. un-div-inv 95.5%

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

   4. Applied egg-rr 95.5%

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

   5. Taylor expanded in z around 0 73.4%

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

   6. Taylor expanded in t around inf 62.7%

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

   if -5.5e9 < z < -8.1999999999999991e-59

   1. Initial program 87.7%

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

   3. Taylor expanded in y around inf 51.8%

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

      1. div-sub 51.8%

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

   5. Simplified 51.8%

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

   6. Taylor expanded in t around inf 45.9%

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

   if -1.79999999999999987e-231 < z < -5.4e-289

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 74.5%

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

      1. div-sub 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in a around inf 75.5%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+191}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -5500000000:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-231}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-289}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+119}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 35.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+177}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-179}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-279}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-234}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e+177)
   t
   (if (<= z -1.26e+85)
     (* t (/ z (- a)))
     (if (<= z -6.2e+45)
       t
       (if (<= z -4.1e-179)
         x
         (if (<= z -1.85e-231)
           (* t (/ y a))
           (if (<= z -3.3e-279)
             (* (/ y a) (- x))
             (if (<= z 7.2e-234) (* y (/ t a)) (if (<= z 2.6e+118) x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+177) {
		tmp = t;
	} else if (z <= -1.26e+85) {
		tmp = t * (z / -a);
	} else if (z <= -6.2e+45) {
		tmp = t;
	} else if (z <= -4.1e-179) {
		tmp = x;
	} else if (z <= -1.85e-231) {
		tmp = t * (y / a);
	} else if (z <= -3.3e-279) {
		tmp = (y / a) * -x;
	} else if (z <= 7.2e-234) {
		tmp = y * (t / a);
	} else if (z <= 2.6e+118) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.5d+177)) then
        tmp = t
    else if (z <= (-1.26d+85)) then
        tmp = t * (z / -a)
    else if (z <= (-6.2d+45)) then
        tmp = t
    else if (z <= (-4.1d-179)) then
        tmp = x
    else if (z <= (-1.85d-231)) then
        tmp = t * (y / a)
    else if (z <= (-3.3d-279)) then
        tmp = (y / a) * -x
    else if (z <= 7.2d-234) then
        tmp = y * (t / a)
    else if (z <= 2.6d+118) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+177) {
		tmp = t;
	} else if (z <= -1.26e+85) {
		tmp = t * (z / -a);
	} else if (z <= -6.2e+45) {
		tmp = t;
	} else if (z <= -4.1e-179) {
		tmp = x;
	} else if (z <= -1.85e-231) {
		tmp = t * (y / a);
	} else if (z <= -3.3e-279) {
		tmp = (y / a) * -x;
	} else if (z <= 7.2e-234) {
		tmp = y * (t / a);
	} else if (z <= 2.6e+118) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e+177:
		tmp = t
	elif z <= -1.26e+85:
		tmp = t * (z / -a)
	elif z <= -6.2e+45:
		tmp = t
	elif z <= -4.1e-179:
		tmp = x
	elif z <= -1.85e-231:
		tmp = t * (y / a)
	elif z <= -3.3e-279:
		tmp = (y / a) * -x
	elif z <= 7.2e-234:
		tmp = y * (t / a)
	elif z <= 2.6e+118:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e+177)
		tmp = t;
	elseif (z <= -1.26e+85)
		tmp = Float64(t * Float64(z / Float64(-a)));
	elseif (z <= -6.2e+45)
		tmp = t;
	elseif (z <= -4.1e-179)
		tmp = x;
	elseif (z <= -1.85e-231)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= -3.3e-279)
		tmp = Float64(Float64(y / a) * Float64(-x));
	elseif (z <= 7.2e-234)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 2.6e+118)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e+177)
		tmp = t;
	elseif (z <= -1.26e+85)
		tmp = t * (z / -a);
	elseif (z <= -6.2e+45)
		tmp = t;
	elseif (z <= -4.1e-179)
		tmp = x;
	elseif (z <= -1.85e-231)
		tmp = t * (y / a);
	elseif (z <= -3.3e-279)
		tmp = (y / a) * -x;
	elseif (z <= 7.2e-234)
		tmp = y * (t / a);
	elseif (z <= 2.6e+118)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e+177], t, If[LessEqual[z, -1.26e+85], N[(t * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e+45], t, If[LessEqual[z, -4.1e-179], x, If[LessEqual[z, -1.85e-231], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.3e-279], N[(N[(y / a), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[z, 7.2e-234], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+118], x, t]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -5.49999999999999993e177 or -1.26000000000000003e85 < z < -6.19999999999999975e45 or 2.60000000000000016e118 < z

   1. Initial program 62.6%

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

   3. Taylor expanded in z around inf 63.0%

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

   if -5.49999999999999993e177 < z < -1.26000000000000003e85

   1. Initial program 79.9%

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

   3. Taylor expanded in x around 0 45.3%

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

      1. associate-/l* 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in y around 0 55.4%

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

      1. neg-mul-1 55.4%

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

      2. distribute-neg-frac2 55.4%

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

      3. neg-sub0 55.4%

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

      4. associate--r- 55.4%

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

      5. neg-sub0 55.4%

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

   8. Simplified 55.4%

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

   9. Taylor expanded in z around 0 33.8%

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

       1. mul-1-neg 33.8%

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

       2. associate-/l* 44.1%

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

       3. distribute-rgt-neg-in 44.1%

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

       4. distribute-frac-neg 44.1%

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

   11. Simplified 44.1%

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

   if -6.19999999999999975e45 < z < -4.1e-179 or 7.1999999999999997e-234 < z < 2.60000000000000016e118

   1. Initial program 91.2%

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

   3. Taylor expanded in a around inf 43.9%

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

   if -4.1e-179 < z < -1.84999999999999997e-231

   1. Initial program 93.9%

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

   3. Taylor expanded in y around inf 57.3%

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

      1. div-sub 63.5%

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

   5. Simplified 63.5%

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

   6. Taylor expanded in a around inf 51.0%

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

   7. Taylor expanded in t around inf 51.0%

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

      1. associate-/l* 57.0%

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

   9. Simplified 57.0%

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

   if -1.84999999999999997e-231 < z < -3.3e-279

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 65.4%

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

      1. div-sub 74.5%

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

   5. Simplified 74.5%

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

   6. Taylor expanded in a around inf 74.5%

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

   7. Taylor expanded in t around 0 65.9%

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

      1. mul-1-neg 65.9%

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

      2. associate-/l* 74.4%

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

      3. distribute-rgt-neg-in 74.4%

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

      4. distribute-frac-neg2 74.4%

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

   9. Simplified 74.4%

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

   if -3.3e-279 < z < 7.1999999999999997e-234

   1. Initial program 93.6%

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

   3. Taylor expanded in y around inf 75.7%

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

      1. div-sub 75.7%

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

   5. Simplified 75.7%

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

   6. Taylor expanded in a around inf 72.9%

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

   7. Taylor expanded in t around inf 59.5%

      \[\leadsto y \cdot \color{blue}{\frac{t}{a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+177}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-179}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-279}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-234}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 48.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - x \cdot \frac{y}{a}\\ t_2 := x + \frac{y \cdot t}{a}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+190}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-178}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-231}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-279}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+119}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* x (/ y a)))) (t_2 (+ x (/ (* y t) a))))
   (if (<= z -3.8e+190)
     t
     (if (<= z -2.65e+45)
       (* t (/ (- y z) a))
       (if (<= z -1.25e-178)
         t_1
         (if (<= z -3.8e-231)
           t_2
           (if (<= z -6.5e-279) t_1 (if (<= z 6.4e+119) t_2 t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (x * (y / a));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (z <= -3.8e+190) {
		tmp = t;
	} else if (z <= -2.65e+45) {
		tmp = t * ((y - z) / a);
	} else if (z <= -1.25e-178) {
		tmp = t_1;
	} else if (z <= -3.8e-231) {
		tmp = t_2;
	} else if (z <= -6.5e-279) {
		tmp = t_1;
	} else if (z <= 6.4e+119) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x - (x * (y / a))
    t_2 = x + ((y * t) / a)
    if (z <= (-3.8d+190)) then
        tmp = t
    else if (z <= (-2.65d+45)) then
        tmp = t * ((y - z) / a)
    else if (z <= (-1.25d-178)) then
        tmp = t_1
    else if (z <= (-3.8d-231)) then
        tmp = t_2
    else if (z <= (-6.5d-279)) then
        tmp = t_1
    else if (z <= 6.4d+119) then
        tmp = t_2
    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 = x - (x * (y / a));
	double t_2 = x + ((y * t) / a);
	double tmp;
	if (z <= -3.8e+190) {
		tmp = t;
	} else if (z <= -2.65e+45) {
		tmp = t * ((y - z) / a);
	} else if (z <= -1.25e-178) {
		tmp = t_1;
	} else if (z <= -3.8e-231) {
		tmp = t_2;
	} else if (z <= -6.5e-279) {
		tmp = t_1;
	} else if (z <= 6.4e+119) {
		tmp = t_2;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (x * (y / a))
	t_2 = x + ((y * t) / a)
	tmp = 0
	if z <= -3.8e+190:
		tmp = t
	elif z <= -2.65e+45:
		tmp = t * ((y - z) / a)
	elif z <= -1.25e-178:
		tmp = t_1
	elif z <= -3.8e-231:
		tmp = t_2
	elif z <= -6.5e-279:
		tmp = t_1
	elif z <= 6.4e+119:
		tmp = t_2
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(x * Float64(y / a)))
	t_2 = Float64(x + Float64(Float64(y * t) / a))
	tmp = 0.0
	if (z <= -3.8e+190)
		tmp = t;
	elseif (z <= -2.65e+45)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= -1.25e-178)
		tmp = t_1;
	elseif (z <= -3.8e-231)
		tmp = t_2;
	elseif (z <= -6.5e-279)
		tmp = t_1;
	elseif (z <= 6.4e+119)
		tmp = t_2;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (x * (y / a));
	t_2 = x + ((y * t) / a);
	tmp = 0.0;
	if (z <= -3.8e+190)
		tmp = t;
	elseif (z <= -2.65e+45)
		tmp = t * ((y - z) / a);
	elseif (z <= -1.25e-178)
		tmp = t_1;
	elseif (z <= -3.8e-231)
		tmp = t_2;
	elseif (z <= -6.5e-279)
		tmp = t_1;
	elseif (z <= 6.4e+119)
		tmp = t_2;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+190], t, If[LessEqual[z, -2.65e+45], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.25e-178], t$95$1, If[LessEqual[z, -3.8e-231], t$95$2, If[LessEqual[z, -6.5e-279], t$95$1, If[LessEqual[z, 6.4e+119], t$95$2, t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.79999999999999964e190 or 6.39999999999999979e119 < z

   1. Initial program 56.8%

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

   3. Taylor expanded in z around inf 68.0%

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

   if -3.79999999999999964e190 < z < -2.64999999999999996e45

   1. Initial program 82.2%

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

   3. Taylor expanded in x around 0 51.1%

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

      1. associate-/l* 71.6%

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

   5. Simplified 71.6%

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

   6. Taylor expanded in a around inf 32.9%

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

      1. associate-/l* 43.5%

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

   8. Simplified 43.5%

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

   if -2.64999999999999996e45 < z < -1.24999999999999994e-178 or -3.80000000000000013e-231 < z < -6.4999999999999997e-279

   1. Initial program 92.0%

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

   3. Taylor expanded in t around 0 50.7%

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

      1. mul-1-neg 50.7%

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

      2. associate-/l* 57.0%

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

      3. distribute-rgt-neg-in 57.0%

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

      4. distribute-frac-neg2 57.0%

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

      5. neg-sub0 57.0%

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

      6. associate--r- 57.0%

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

      7. neg-sub0 57.0%

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

   5. Simplified 57.0%

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

   6. Taylor expanded in z around 0 51.8%

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

      1. mul-1-neg 51.8%

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

      2. unsub-neg 51.8%

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

      3. associate-/l* 61.0%

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

   8. Simplified 61.0%

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

   if -1.24999999999999994e-178 < z < -3.80000000000000013e-231 or -6.4999999999999997e-279 < z < 6.39999999999999979e119

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

      2. associate-*l/ 92.0%

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

      3. associate-*r/ 96.6%

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

      4. clear-num 96.5%

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

      5. un-div-inv 96.5%

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

   4. Applied egg-rr 96.5%

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

   5. Taylor expanded in z around 0 77.8%

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

   6. Taylor expanded in t around inf 66.4%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+190}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.65 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-178}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-231}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-279}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{+119}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+190}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -5.9 \cdot 10^{+26}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -1020000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-61}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-179}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-233}:\\ \;\;\;\;y \cdot \frac{t - x}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e+190)
   t
   (if (<= z -5.9e+26)
     (* t (/ (- y z) a))
     (if (<= z -1020000000.0)
       x
       (if (<= z -1.15e-61)
         (* y (/ t (- a z)))
         (if (<= z -9e-179)
           x
           (if (<= z 6.2e-233)
             (* y (/ (- t x) a))
             (if (<= z 2.6e+118) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+190) {
		tmp = t;
	} else if (z <= -5.9e+26) {
		tmp = t * ((y - z) / a);
	} else if (z <= -1020000000.0) {
		tmp = x;
	} else if (z <= -1.15e-61) {
		tmp = y * (t / (a - z));
	} else if (z <= -9e-179) {
		tmp = x;
	} else if (z <= 6.2e-233) {
		tmp = y * ((t - x) / a);
	} else if (z <= 2.6e+118) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.8d+190)) then
        tmp = t
    else if (z <= (-5.9d+26)) then
        tmp = t * ((y - z) / a)
    else if (z <= (-1020000000.0d0)) then
        tmp = x
    else if (z <= (-1.15d-61)) then
        tmp = y * (t / (a - z))
    else if (z <= (-9d-179)) then
        tmp = x
    else if (z <= 6.2d-233) then
        tmp = y * ((t - x) / a)
    else if (z <= 2.6d+118) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+190) {
		tmp = t;
	} else if (z <= -5.9e+26) {
		tmp = t * ((y - z) / a);
	} else if (z <= -1020000000.0) {
		tmp = x;
	} else if (z <= -1.15e-61) {
		tmp = y * (t / (a - z));
	} else if (z <= -9e-179) {
		tmp = x;
	} else if (z <= 6.2e-233) {
		tmp = y * ((t - x) / a);
	} else if (z <= 2.6e+118) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e+190:
		tmp = t
	elif z <= -5.9e+26:
		tmp = t * ((y - z) / a)
	elif z <= -1020000000.0:
		tmp = x
	elif z <= -1.15e-61:
		tmp = y * (t / (a - z))
	elif z <= -9e-179:
		tmp = x
	elif z <= 6.2e-233:
		tmp = y * ((t - x) / a)
	elif z <= 2.6e+118:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e+190)
		tmp = t;
	elseif (z <= -5.9e+26)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= -1020000000.0)
		tmp = x;
	elseif (z <= -1.15e-61)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (z <= -9e-179)
		tmp = x;
	elseif (z <= 6.2e-233)
		tmp = Float64(y * Float64(Float64(t - x) / a));
	elseif (z <= 2.6e+118)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.8e+190)
		tmp = t;
	elseif (z <= -5.9e+26)
		tmp = t * ((y - z) / a);
	elseif (z <= -1020000000.0)
		tmp = x;
	elseif (z <= -1.15e-61)
		tmp = y * (t / (a - z));
	elseif (z <= -9e-179)
		tmp = x;
	elseif (z <= 6.2e-233)
		tmp = y * ((t - x) / a);
	elseif (z <= 2.6e+118)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e+190], t, If[LessEqual[z, -5.9e+26], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1020000000.0], x, If[LessEqual[z, -1.15e-61], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e-179], x, If[LessEqual[z, 6.2e-233], N[(y * N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+118], x, t]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.79999999999999964e190 or 2.60000000000000016e118 < z

   1. Initial program 58.6%

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

   3. Taylor expanded in z around inf 67.3%

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

   if -3.79999999999999964e190 < z < -5.9000000000000003e26

   1. Initial program 83.5%

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

   3. Taylor expanded in x around 0 51.3%

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

      1. associate-/l* 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in a around inf 34.3%

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

      1. associate-/l* 44.1%

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

   8. Simplified 44.1%

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

   if -5.9000000000000003e26 < z < -1.02e9 or -1.14999999999999996e-61 < z < -8.99999999999999984e-179 or 6.2000000000000003e-233 < z < 2.60000000000000016e118

   1. Initial program 91.6%

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

   3. Taylor expanded in a around inf 47.9%

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

   if -1.02e9 < z < -1.14999999999999996e-61

   1. Initial program 86.9%

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

   3. Taylor expanded in y around inf 55.2%

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

      1. div-sub 55.2%

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

   5. Simplified 55.2%

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

   6. Taylor expanded in t around inf 48.9%

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

   if -8.99999999999999984e-179 < z < 6.2000000000000003e-233

   1. Initial program 94.9%

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

   3. Taylor expanded in y around inf 68.7%

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

      1. div-sub 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in a around inf 67.2%

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

Alternative 8: 36.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+190}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+29}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -6000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-178}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-233}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e+190)
   t
   (if (<= z -3.5e+29)
     (* t (/ (- y z) a))
     (if (<= z -6000000.0)
       x
       (if (<= z -6e-60)
         (* y (/ t (- a z)))
         (if (<= z -3.2e-178)
           x
           (if (<= z 4e-233)
             (* t (/ y (- a z)))
             (if (<= z 2.6e+118) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+190) {
		tmp = t;
	} else if (z <= -3.5e+29) {
		tmp = t * ((y - z) / a);
	} else if (z <= -6000000.0) {
		tmp = x;
	} else if (z <= -6e-60) {
		tmp = y * (t / (a - z));
	} else if (z <= -3.2e-178) {
		tmp = x;
	} else if (z <= 4e-233) {
		tmp = t * (y / (a - z));
	} else if (z <= 2.6e+118) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.8d+190)) then
        tmp = t
    else if (z <= (-3.5d+29)) then
        tmp = t * ((y - z) / a)
    else if (z <= (-6000000.0d0)) then
        tmp = x
    else if (z <= (-6d-60)) then
        tmp = y * (t / (a - z))
    else if (z <= (-3.2d-178)) then
        tmp = x
    else if (z <= 4d-233) then
        tmp = t * (y / (a - z))
    else if (z <= 2.6d+118) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+190) {
		tmp = t;
	} else if (z <= -3.5e+29) {
		tmp = t * ((y - z) / a);
	} else if (z <= -6000000.0) {
		tmp = x;
	} else if (z <= -6e-60) {
		tmp = y * (t / (a - z));
	} else if (z <= -3.2e-178) {
		tmp = x;
	} else if (z <= 4e-233) {
		tmp = t * (y / (a - z));
	} else if (z <= 2.6e+118) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e+190:
		tmp = t
	elif z <= -3.5e+29:
		tmp = t * ((y - z) / a)
	elif z <= -6000000.0:
		tmp = x
	elif z <= -6e-60:
		tmp = y * (t / (a - z))
	elif z <= -3.2e-178:
		tmp = x
	elif z <= 4e-233:
		tmp = t * (y / (a - z))
	elif z <= 2.6e+118:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e+190)
		tmp = t;
	elseif (z <= -3.5e+29)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= -6000000.0)
		tmp = x;
	elseif (z <= -6e-60)
		tmp = Float64(y * Float64(t / Float64(a - z)));
	elseif (z <= -3.2e-178)
		tmp = x;
	elseif (z <= 4e-233)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= 2.6e+118)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.8e+190)
		tmp = t;
	elseif (z <= -3.5e+29)
		tmp = t * ((y - z) / a);
	elseif (z <= -6000000.0)
		tmp = x;
	elseif (z <= -6e-60)
		tmp = y * (t / (a - z));
	elseif (z <= -3.2e-178)
		tmp = x;
	elseif (z <= 4e-233)
		tmp = t * (y / (a - z));
	elseif (z <= 2.6e+118)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e+190], t, If[LessEqual[z, -3.5e+29], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6000000.0], x, If[LessEqual[z, -6e-60], N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.2e-178], x, If[LessEqual[z, 4e-233], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+118], x, t]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.79999999999999964e190 or 2.60000000000000016e118 < z

   1. Initial program 58.6%

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

   3. Taylor expanded in z around inf 67.3%

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

   if -3.79999999999999964e190 < z < -3.49999999999999979e29

   1. Initial program 83.5%

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

   3. Taylor expanded in x around 0 51.3%

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

      1. associate-/l* 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in a around inf 34.3%

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

      1. associate-/l* 44.1%

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

   8. Simplified 44.1%

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

   if -3.49999999999999979e29 < z < -6e6 or -6.00000000000000038e-60 < z < -3.2000000000000001e-178 or 3.99999999999999983e-233 < z < 2.60000000000000016e118

   1. Initial program 91.5%

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

   3. Taylor expanded in a around inf 48.3%

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

   if -6e6 < z < -6.00000000000000038e-60

   1. Initial program 86.9%

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

   3. Taylor expanded in y around inf 55.2%

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

      1. div-sub 55.2%

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

   5. Simplified 55.2%

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

   6. Taylor expanded in t around inf 48.9%

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

   if -3.2000000000000001e-178 < z < 3.99999999999999983e-233

   1. Initial program 95.0%

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

   3. Taylor expanded in y around inf 69.2%

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

      1. div-sub 72.6%

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

   5. Simplified 72.6%

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

   6. Taylor expanded in t around inf 47.6%

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

      1. associate-/l* 52.5%

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

   8. Simplified 52.5%

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

Alternative 9: 36.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a - z}\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+190}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -390000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-177}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-233}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a z)))))
   (if (<= z -3.8e+190)
     t
     (if (<= z -2.7e+30)
       (* t (/ (- y z) a))
       (if (<= z -390000.0)
         x
         (if (<= z -8.8e-60)
           t_1
           (if (<= z -1.3e-177)
             x
             (if (<= z 1.9e-233) t_1 (if (<= z 2.6e+118) x t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / (a - z));
	double tmp;
	if (z <= -3.8e+190) {
		tmp = t;
	} else if (z <= -2.7e+30) {
		tmp = t * ((y - z) / a);
	} else if (z <= -390000.0) {
		tmp = x;
	} else if (z <= -8.8e-60) {
		tmp = t_1;
	} else if (z <= -1.3e-177) {
		tmp = x;
	} else if (z <= 1.9e-233) {
		tmp = t_1;
	} else if (z <= 2.6e+118) {
		tmp = x;
	} 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 - z))
    if (z <= (-3.8d+190)) then
        tmp = t
    else if (z <= (-2.7d+30)) then
        tmp = t * ((y - z) / a)
    else if (z <= (-390000.0d0)) then
        tmp = x
    else if (z <= (-8.8d-60)) then
        tmp = t_1
    else if (z <= (-1.3d-177)) then
        tmp = x
    else if (z <= 1.9d-233) then
        tmp = t_1
    else if (z <= 2.6d+118) then
        tmp = x
    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 - z));
	double tmp;
	if (z <= -3.8e+190) {
		tmp = t;
	} else if (z <= -2.7e+30) {
		tmp = t * ((y - z) / a);
	} else if (z <= -390000.0) {
		tmp = x;
	} else if (z <= -8.8e-60) {
		tmp = t_1;
	} else if (z <= -1.3e-177) {
		tmp = x;
	} else if (z <= 1.9e-233) {
		tmp = t_1;
	} else if (z <= 2.6e+118) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / (a - z))
	tmp = 0
	if z <= -3.8e+190:
		tmp = t
	elif z <= -2.7e+30:
		tmp = t * ((y - z) / a)
	elif z <= -390000.0:
		tmp = x
	elif z <= -8.8e-60:
		tmp = t_1
	elif z <= -1.3e-177:
		tmp = x
	elif z <= 1.9e-233:
		tmp = t_1
	elif z <= 2.6e+118:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (z <= -3.8e+190)
		tmp = t;
	elseif (z <= -2.7e+30)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif (z <= -390000.0)
		tmp = x;
	elseif (z <= -8.8e-60)
		tmp = t_1;
	elseif (z <= -1.3e-177)
		tmp = x;
	elseif (z <= 1.9e-233)
		tmp = t_1;
	elseif (z <= 2.6e+118)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / (a - z));
	tmp = 0.0;
	if (z <= -3.8e+190)
		tmp = t;
	elseif (z <= -2.7e+30)
		tmp = t * ((y - z) / a);
	elseif (z <= -390000.0)
		tmp = x;
	elseif (z <= -8.8e-60)
		tmp = t_1;
	elseif (z <= -1.3e-177)
		tmp = x;
	elseif (z <= 1.9e-233)
		tmp = t_1;
	elseif (z <= 2.6e+118)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e+190], t, If[LessEqual[z, -2.7e+30], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -390000.0], x, If[LessEqual[z, -8.8e-60], t$95$1, If[LessEqual[z, -1.3e-177], x, If[LessEqual[z, 1.9e-233], t$95$1, If[LessEqual[z, 2.6e+118], x, t]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.79999999999999964e190 or 2.60000000000000016e118 < z

   1. Initial program 58.6%

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

   3. Taylor expanded in z around inf 67.3%

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

   if -3.79999999999999964e190 < z < -2.6999999999999999e30

   1. Initial program 83.5%

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

   3. Taylor expanded in x around 0 51.3%

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

      1. associate-/l* 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in a around inf 34.3%

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

      1. associate-/l* 44.1%

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

   8. Simplified 44.1%

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

   if -2.6999999999999999e30 < z < -3.9e5 or -8.7999999999999995e-60 < z < -1.3e-177 or 1.9e-233 < z < 2.60000000000000016e118

   1. Initial program 91.5%

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

   3. Taylor expanded in a around inf 48.3%

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

   if -3.9e5 < z < -8.7999999999999995e-60 or -1.3e-177 < z < 1.9e-233

   1. Initial program 93.3%

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

   3. Taylor expanded in y around inf 66.3%

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

      1. div-sub 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in t around inf 47.9%

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

      1. associate-/l* 51.7%

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

   8. Simplified 51.7%

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

Alternative 10: 35.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+177}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -23000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-279}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.78 \cdot 10^{-233}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e+177)
   t
   (if (<= z -1.65e+86)
     (* t (/ z (- a)))
     (if (<= z -23000000000.0)
       t
       (if (<= z -1.8e-231)
         (* t (/ y (- a z)))
         (if (<= z -5.5e-279)
           (* (/ y a) (- x))
           (if (<= z 1.78e-233) (* y (/ t a)) (if (<= z 2.6e+118) x t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+177) {
		tmp = t;
	} else if (z <= -1.65e+86) {
		tmp = t * (z / -a);
	} else if (z <= -23000000000.0) {
		tmp = t;
	} else if (z <= -1.8e-231) {
		tmp = t * (y / (a - z));
	} else if (z <= -5.5e-279) {
		tmp = (y / a) * -x;
	} else if (z <= 1.78e-233) {
		tmp = y * (t / a);
	} else if (z <= 2.6e+118) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.5d+177)) then
        tmp = t
    else if (z <= (-1.65d+86)) then
        tmp = t * (z / -a)
    else if (z <= (-23000000000.0d0)) then
        tmp = t
    else if (z <= (-1.8d-231)) then
        tmp = t * (y / (a - z))
    else if (z <= (-5.5d-279)) then
        tmp = (y / a) * -x
    else if (z <= 1.78d-233) then
        tmp = y * (t / a)
    else if (z <= 2.6d+118) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+177) {
		tmp = t;
	} else if (z <= -1.65e+86) {
		tmp = t * (z / -a);
	} else if (z <= -23000000000.0) {
		tmp = t;
	} else if (z <= -1.8e-231) {
		tmp = t * (y / (a - z));
	} else if (z <= -5.5e-279) {
		tmp = (y / a) * -x;
	} else if (z <= 1.78e-233) {
		tmp = y * (t / a);
	} else if (z <= 2.6e+118) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e+177:
		tmp = t
	elif z <= -1.65e+86:
		tmp = t * (z / -a)
	elif z <= -23000000000.0:
		tmp = t
	elif z <= -1.8e-231:
		tmp = t * (y / (a - z))
	elif z <= -5.5e-279:
		tmp = (y / a) * -x
	elif z <= 1.78e-233:
		tmp = y * (t / a)
	elif z <= 2.6e+118:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e+177)
		tmp = t;
	elseif (z <= -1.65e+86)
		tmp = Float64(t * Float64(z / Float64(-a)));
	elseif (z <= -23000000000.0)
		tmp = t;
	elseif (z <= -1.8e-231)
		tmp = Float64(t * Float64(y / Float64(a - z)));
	elseif (z <= -5.5e-279)
		tmp = Float64(Float64(y / a) * Float64(-x));
	elseif (z <= 1.78e-233)
		tmp = Float64(y * Float64(t / a));
	elseif (z <= 2.6e+118)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e+177)
		tmp = t;
	elseif (z <= -1.65e+86)
		tmp = t * (z / -a);
	elseif (z <= -23000000000.0)
		tmp = t;
	elseif (z <= -1.8e-231)
		tmp = t * (y / (a - z));
	elseif (z <= -5.5e-279)
		tmp = (y / a) * -x;
	elseif (z <= 1.78e-233)
		tmp = y * (t / a);
	elseif (z <= 2.6e+118)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e+177], t, If[LessEqual[z, -1.65e+86], N[(t * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -23000000000.0], t, If[LessEqual[z, -1.8e-231], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e-279], N[(N[(y / a), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[z, 1.78e-233], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+118], x, t]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -5.49999999999999993e177 or -1.65e86 < z < -2.3e10 or 2.60000000000000016e118 < z

   1. Initial program 66.2%

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

   3. Taylor expanded in z around inf 59.4%

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

   if -5.49999999999999993e177 < z < -1.65e86

   1. Initial program 79.9%

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

   3. Taylor expanded in x around 0 45.3%

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

      1. associate-/l* 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in y around 0 55.4%

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

      1. neg-mul-1 55.4%

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

      2. distribute-neg-frac2 55.4%

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

      3. neg-sub0 55.4%

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

      4. associate--r- 55.4%

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

      5. neg-sub0 55.4%

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

   8. Simplified 55.4%

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

   9. Taylor expanded in z around 0 33.8%

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

       1. mul-1-neg 33.8%

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

       2. associate-/l* 44.1%

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

       3. distribute-rgt-neg-in 44.1%

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

       4. distribute-frac-neg 44.1%

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

   11. Simplified 44.1%

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

   if -2.3e10 < z < -1.79999999999999987e-231

   1. Initial program 91.4%

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

   3. Taylor expanded in y around inf 48.1%

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

      1. div-sub 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in t around inf 39.1%

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

      1. associate-/l* 40.6%

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

   8. Simplified 40.6%

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

   if -1.79999999999999987e-231 < z < -5.5000000000000002e-279

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 65.4%

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

      1. div-sub 74.5%

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

   5. Simplified 74.5%

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

   6. Taylor expanded in a around inf 74.5%

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

   7. Taylor expanded in t around 0 65.9%

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

      1. mul-1-neg 65.9%

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

      2. associate-/l* 74.4%

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

      3. distribute-rgt-neg-in 74.4%

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

      4. distribute-frac-neg2 74.4%

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

   9. Simplified 74.4%

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

   if -5.5000000000000002e-279 < z < 1.78000000000000009e-233

   1. Initial program 93.6%

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

   3. Taylor expanded in y around inf 75.7%

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

      1. div-sub 75.7%

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

   5. Simplified 75.7%

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

   6. Taylor expanded in a around inf 72.9%

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

   7. Taylor expanded in t around inf 59.5%

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

   if 1.78000000000000009e-233 < z < 2.60000000000000016e118

   1. Initial program 91.8%

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

   3. Taylor expanded in a around inf 48.2%

      \[\leadsto \color{blue}{x} \]
3. Recombined 6 regimes into one program.

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+177}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -23000000000:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-231}:\\ \;\;\;\;t \cdot \frac{y}{a - z}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-279}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.78 \cdot 10^{-233}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+177}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+84}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-179}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.96 \cdot 10^{-233}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e+177)
   t
   (if (<= z -3.6e+84)
     (* t (/ z (- a)))
     (if (<= z -7e+42)
       t
       (if (<= z -7.2e-179)
         x
         (if (<= z 1.96e-233) (* t (/ y a)) (if (<= z 2.6e+118) x t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+177) {
		tmp = t;
	} else if (z <= -3.6e+84) {
		tmp = t * (z / -a);
	} else if (z <= -7e+42) {
		tmp = t;
	} else if (z <= -7.2e-179) {
		tmp = x;
	} else if (z <= 1.96e-233) {
		tmp = t * (y / a);
	} else if (z <= 2.6e+118) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.5d+177)) then
        tmp = t
    else if (z <= (-3.6d+84)) then
        tmp = t * (z / -a)
    else if (z <= (-7d+42)) then
        tmp = t
    else if (z <= (-7.2d-179)) then
        tmp = x
    else if (z <= 1.96d-233) then
        tmp = t * (y / a)
    else if (z <= 2.6d+118) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+177) {
		tmp = t;
	} else if (z <= -3.6e+84) {
		tmp = t * (z / -a);
	} else if (z <= -7e+42) {
		tmp = t;
	} else if (z <= -7.2e-179) {
		tmp = x;
	} else if (z <= 1.96e-233) {
		tmp = t * (y / a);
	} else if (z <= 2.6e+118) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e+177:
		tmp = t
	elif z <= -3.6e+84:
		tmp = t * (z / -a)
	elif z <= -7e+42:
		tmp = t
	elif z <= -7.2e-179:
		tmp = x
	elif z <= 1.96e-233:
		tmp = t * (y / a)
	elif z <= 2.6e+118:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e+177)
		tmp = t;
	elseif (z <= -3.6e+84)
		tmp = Float64(t * Float64(z / Float64(-a)));
	elseif (z <= -7e+42)
		tmp = t;
	elseif (z <= -7.2e-179)
		tmp = x;
	elseif (z <= 1.96e-233)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 2.6e+118)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e+177)
		tmp = t;
	elseif (z <= -3.6e+84)
		tmp = t * (z / -a);
	elseif (z <= -7e+42)
		tmp = t;
	elseif (z <= -7.2e-179)
		tmp = x;
	elseif (z <= 1.96e-233)
		tmp = t * (y / a);
	elseif (z <= 2.6e+118)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e+177], t, If[LessEqual[z, -3.6e+84], N[(t * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7e+42], t, If[LessEqual[z, -7.2e-179], x, If[LessEqual[z, 1.96e-233], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+118], x, t]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.49999999999999993e177 or -3.5999999999999999e84 < z < -7.00000000000000047e42 or 2.60000000000000016e118 < z

   1. Initial program 62.6%

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

   3. Taylor expanded in z around inf 63.0%

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

   if -5.49999999999999993e177 < z < -3.5999999999999999e84

   1. Initial program 79.9%

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

   3. Taylor expanded in x around 0 45.3%

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

      1. associate-/l* 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in y around 0 55.4%

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

      1. neg-mul-1 55.4%

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

      2. distribute-neg-frac2 55.4%

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

      3. neg-sub0 55.4%

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

      4. associate--r- 55.4%

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

      5. neg-sub0 55.4%

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

   8. Simplified 55.4%

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

   9. Taylor expanded in z around 0 33.8%

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

       1. mul-1-neg 33.8%

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

       2. associate-/l* 44.1%

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

       3. distribute-rgt-neg-in 44.1%

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

       4. distribute-frac-neg 44.1%

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

   11. Simplified 44.1%

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

   if -7.00000000000000047e42 < z < -7.20000000000000015e-179 or 1.96000000000000003e-233 < z < 2.60000000000000016e118

   1. Initial program 91.2%

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

   3. Taylor expanded in a around inf 43.9%

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

   if -7.20000000000000015e-179 < z < 1.96000000000000003e-233

   1. Initial program 94.9%

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

   3. Taylor expanded in y around inf 68.7%

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

      1. div-sub 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in a around inf 67.2%

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

   7. Taylor expanded in t around inf 46.7%

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

      1. associate-/l* 51.7%

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

   9. Simplified 51.7%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+177}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+84}:\\ \;\;\;\;t \cdot \frac{z}{-a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-179}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.96 \cdot 10^{-233}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + x \cdot \frac{y}{z - a}\\ t_2 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -1.18 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-89}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* x (/ y (- z a))))) (t_2 (* t (/ (- y z) (- a z)))))
   (if (<= t -1.18e+55)
     t_2
     (if (<= t -1.8e-32)
       t_1
       (if (<= t -2.95e-89)
         (* y (/ (- t x) (- a z)))
         (if (<= t 6.2e-74) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (x * (y / (z - a)));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.18e+55) {
		tmp = t_2;
	} else if (t <= -1.8e-32) {
		tmp = t_1;
	} else if (t <= -2.95e-89) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 6.2e-74) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (x * (y / (z - a)))
    t_2 = t * ((y - z) / (a - z))
    if (t <= (-1.18d+55)) then
        tmp = t_2
    else if (t <= (-1.8d-32)) then
        tmp = t_1
    else if (t <= (-2.95d-89)) then
        tmp = y * ((t - x) / (a - z))
    else if (t <= 6.2d-74) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (x * (y / (z - a)));
	double t_2 = t * ((y - z) / (a - z));
	double tmp;
	if (t <= -1.18e+55) {
		tmp = t_2;
	} else if (t <= -1.8e-32) {
		tmp = t_1;
	} else if (t <= -2.95e-89) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 6.2e-74) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (x * (y / (z - a)))
	t_2 = t * ((y - z) / (a - z))
	tmp = 0
	if t <= -1.18e+55:
		tmp = t_2
	elif t <= -1.8e-32:
		tmp = t_1
	elif t <= -2.95e-89:
		tmp = y * ((t - x) / (a - z))
	elif t <= 6.2e-74:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(x * Float64(y / Float64(z - a))))
	t_2 = Float64(t * Float64(Float64(y - z) / Float64(a - z)))
	tmp = 0.0
	if (t <= -1.18e+55)
		tmp = t_2;
	elseif (t <= -1.8e-32)
		tmp = t_1;
	elseif (t <= -2.95e-89)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (t <= 6.2e-74)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (x * (y / (z - a)));
	t_2 = t * ((y - z) / (a - z));
	tmp = 0.0;
	if (t <= -1.18e+55)
		tmp = t_2;
	elseif (t <= -1.8e-32)
		tmp = t_1;
	elseif (t <= -2.95e-89)
		tmp = y * ((t - x) / (a - z));
	elseif (t <= 6.2e-74)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(x * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.18e+55], t$95$2, If[LessEqual[t, -1.8e-32], t$95$1, If[LessEqual[t, -2.95e-89], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e-74], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.1799999999999999e55 or 6.2000000000000003e-74 < t

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0 53.2%

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

      1. associate-/l* 74.1%

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

   5. Simplified 74.1%

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

   if -1.1799999999999999e55 < t < -1.79999999999999996e-32 or -2.9500000000000001e-89 < t < 6.2000000000000003e-74

   1. Initial program 78.2%

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

   3. Taylor expanded in t around 0 65.1%

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

      1. mul-1-neg 65.1%

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

      2. associate-/l* 70.5%

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

      3. distribute-rgt-neg-in 70.5%

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

      4. distribute-frac-neg2 70.5%

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

      5. neg-sub0 70.5%

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

      6. associate--r- 70.5%

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

      7. neg-sub0 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in y around inf 68.1%

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

   if -1.79999999999999996e-32 < t < -2.9500000000000001e-89

   1. Initial program 94.0%

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

   3. Taylor expanded in y around inf 83.8%

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

      1. div-sub 83.8%

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

   5. Simplified 83.8%

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

Alternative 13: 58.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y - z}{a - z}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-21}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-104}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y z) (- a z)))))
   (if (<= t -8.5e+65)
     t_1
     (if (<= t -4.6e-21)
       (+ x (/ (* y t) a))
       (if (<= t -4.3e-90)
         (* y (/ (- t x) (- a z)))
         (if (<= t 1.45e-104) (- x (* x (/ y 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 (t <= -8.5e+65) {
		tmp = t_1;
	} else if (t <= -4.6e-21) {
		tmp = x + ((y * t) / a);
	} else if (t <= -4.3e-90) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 1.45e-104) {
		tmp = x - (x * (y / 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 (t <= (-8.5d+65)) then
        tmp = t_1
    else if (t <= (-4.6d-21)) then
        tmp = x + ((y * t) / a)
    else if (t <= (-4.3d-90)) then
        tmp = y * ((t - x) / (a - z))
    else if (t <= 1.45d-104) then
        tmp = x - (x * (y / 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 (t <= -8.5e+65) {
		tmp = t_1;
	} else if (t <= -4.6e-21) {
		tmp = x + ((y * t) / a);
	} else if (t <= -4.3e-90) {
		tmp = y * ((t - x) / (a - z));
	} else if (t <= 1.45e-104) {
		tmp = x - (x * (y / 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 t <= -8.5e+65:
		tmp = t_1
	elif t <= -4.6e-21:
		tmp = x + ((y * t) / a)
	elif t <= -4.3e-90:
		tmp = y * ((t - x) / (a - z))
	elif t <= 1.45e-104:
		tmp = x - (x * (y / 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 (t <= -8.5e+65)
		tmp = t_1;
	elseif (t <= -4.6e-21)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (t <= -4.3e-90)
		tmp = Float64(y * Float64(Float64(t - x) / Float64(a - z)));
	elseif (t <= 1.45e-104)
		tmp = Float64(x - Float64(x * Float64(y / 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 (t <= -8.5e+65)
		tmp = t_1;
	elseif (t <= -4.6e-21)
		tmp = x + ((y * t) / a);
	elseif (t <= -4.3e-90)
		tmp = y * ((t - x) / (a - z));
	elseif (t <= 1.45e-104)
		tmp = x - (x * (y / 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[t, -8.5e+65], t$95$1, If[LessEqual[t, -4.6e-21], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.3e-90], N[(y * N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e-104], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.50000000000000075e65 or 1.4500000000000001e-104 < t

   1. Initial program 89.2%

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

   3. Taylor expanded in x around 0 52.5%

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

      1. associate-/l* 73.4%

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

   5. Simplified 73.4%

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

   if -8.50000000000000075e65 < t < -4.59999999999999999e-21

   1. Initial program 83.6%

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

      1. *-commutative 83.6%

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

      2. associate-*l/ 81.9%

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

      3. associate-*r/ 87.1%

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

      4. clear-num 87.0%

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

      5. un-div-inv 86.9%

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

   4. Applied egg-rr 86.9%

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

   5. Taylor expanded in z around 0 72.7%

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

   6. Taylor expanded in t around inf 61.1%

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

   if -4.59999999999999999e-21 < t < -4.3000000000000002e-90

   1. Initial program 83.5%

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

   3. Taylor expanded in y around inf 75.8%

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

      1. div-sub 75.8%

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

   5. Simplified 75.8%

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

   if -4.3000000000000002e-90 < t < 1.4500000000000001e-104

   1. Initial program 77.6%

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

   3. Taylor expanded in t around 0 66.8%

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

      1. mul-1-neg 66.8%

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

      2. associate-/l* 73.0%

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

      3. distribute-rgt-neg-in 73.0%

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

      4. distribute-frac-neg2 73.0%

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

      5. neg-sub0 73.0%

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

      6. associate--r- 73.0%

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

      7. neg-sub0 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in z around 0 60.2%

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

      1. mul-1-neg 60.2%

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

      2. unsub-neg 60.2%

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

      3. associate-/l* 64.9%

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

   8. Simplified 64.9%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-21}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq -4.3 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \frac{t - x}{a - z}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-104}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(\frac{y}{-z} - -1\right)\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-59} \lor \neg \left(z \leq 6 \cdot 10^{+119}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- (/ y (- z)) -1.0))))
   (if (<= z -5.5e+177)
     t_1
     (if (<= z -1.5e+86)
       (* t (/ (- y z) a))
       (if (or (<= z -6.6e-59) (not (<= z 6e+119)))
         t_1
         (+ x (/ (* y t) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * ((y / -z) - -1.0);
	double tmp;
	if (z <= -5.5e+177) {
		tmp = t_1;
	} else if (z <= -1.5e+86) {
		tmp = t * ((y - z) / a);
	} else if ((z <= -6.6e-59) || !(z <= 6e+119)) {
		tmp = t_1;
	} else {
		tmp = x + ((y * t) / 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) :: t_1
    real(8) :: tmp
    t_1 = t * ((y / -z) - (-1.0d0))
    if (z <= (-5.5d+177)) then
        tmp = t_1
    else if (z <= (-1.5d+86)) then
        tmp = t * ((y - z) / a)
    else if ((z <= (-6.6d-59)) .or. (.not. (z <= 6d+119))) then
        tmp = t_1
    else
        tmp = x + ((y * t) / a)
    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) - -1.0);
	double tmp;
	if (z <= -5.5e+177) {
		tmp = t_1;
	} else if (z <= -1.5e+86) {
		tmp = t * ((y - z) / a);
	} else if ((z <= -6.6e-59) || !(z <= 6e+119)) {
		tmp = t_1;
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * ((y / -z) - -1.0)
	tmp = 0
	if z <= -5.5e+177:
		tmp = t_1
	elif z <= -1.5e+86:
		tmp = t * ((y - z) / a)
	elif (z <= -6.6e-59) or not (z <= 6e+119):
		tmp = t_1
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(y / Float64(-z)) - -1.0))
	tmp = 0.0
	if (z <= -5.5e+177)
		tmp = t_1;
	elseif (z <= -1.5e+86)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	elseif ((z <= -6.6e-59) || !(z <= 6e+119))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * ((y / -z) - -1.0);
	tmp = 0.0;
	if (z <= -5.5e+177)
		tmp = t_1;
	elseif (z <= -1.5e+86)
		tmp = t * ((y - z) / a);
	elseif ((z <= -6.6e-59) || ~((z <= 6e+119)))
		tmp = t_1;
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y / (-z)), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+177], t$95$1, If[LessEqual[z, -1.5e+86], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -6.6e-59], N[Not[LessEqual[z, 6e+119]], $MachinePrecision]], t$95$1, N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.49999999999999993e177 or -1.49999999999999988e86 < z < -6.59999999999999964e-59 or 6.00000000000000002e119 < z

   1. Initial program 69.6%

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

   3. Taylor expanded in x around 0 46.5%

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

      1. associate-/l* 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in a around 0 63.8%

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

      1. mul-1-neg 63.8%

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

      2. div-sub 63.9%

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

      3. sub-neg 63.9%

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

      4. *-inverses 63.9%

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

      5. metadata-eval 63.9%

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

   8. Simplified 63.9%

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

   if -5.49999999999999993e177 < z < -1.49999999999999988e86

   1. Initial program 79.9%

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

   3. Taylor expanded in x around 0 45.3%

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

      1. associate-/l* 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in a around inf 34.2%

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

      1. associate-/l* 49.2%

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

   8. Simplified 49.2%

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

   if -6.59999999999999964e-59 < z < 6.00000000000000002e119

   1. Initial program 93.1%

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

      1. *-commutative 93.1%

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

      2. associate-*l/ 91.4%

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

      3. associate-*r/ 96.7%

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

      4. clear-num 96.6%

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

      5. un-div-inv 96.7%

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

   4. Applied egg-rr 96.7%

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

   5. Taylor expanded in z around 0 78.2%

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

   6. Taylor expanded in t around inf 62.9%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+177}:\\ \;\;\;\;t \cdot \left(\frac{y}{-z} - -1\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-59} \lor \neg \left(z \leq 6 \cdot 10^{+119}\right):\\ \;\;\;\;t \cdot \left(\frac{y}{-z} - -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot t}{a}\\ t_2 := t \cdot \frac{z}{z - a}\\ \mathbf{if}\;z \leq -8 \cdot 10^{+81}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-231}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-289}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y t) a))) (t_2 (* t (/ z (- z a)))))
   (if (<= z -8e+81)
     t_2
     (if (<= z -1.8e-231)
       t_1
       (if (<= z -5.5e-289) (/ y (/ a (- t x))) (if (<= z 1e+120) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -8e+81) {
		tmp = t_2;
	} else if (z <= -1.8e-231) {
		tmp = t_1;
	} else if (z <= -5.5e-289) {
		tmp = y / (a / (t - x));
	} else if (z <= 1e+120) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((y * t) / a)
    t_2 = t * (z / (z - a))
    if (z <= (-8d+81)) then
        tmp = t_2
    else if (z <= (-1.8d-231)) then
        tmp = t_1
    else if (z <= (-5.5d-289)) then
        tmp = y / (a / (t - x))
    else if (z <= 1d+120) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * t) / a);
	double t_2 = t * (z / (z - a));
	double tmp;
	if (z <= -8e+81) {
		tmp = t_2;
	} else if (z <= -1.8e-231) {
		tmp = t_1;
	} else if (z <= -5.5e-289) {
		tmp = y / (a / (t - x));
	} else if (z <= 1e+120) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * t) / a)
	t_2 = t * (z / (z - a))
	tmp = 0
	if z <= -8e+81:
		tmp = t_2
	elif z <= -1.8e-231:
		tmp = t_1
	elif z <= -5.5e-289:
		tmp = y / (a / (t - x))
	elif z <= 1e+120:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * t) / a))
	t_2 = Float64(t * Float64(z / Float64(z - a)))
	tmp = 0.0
	if (z <= -8e+81)
		tmp = t_2;
	elseif (z <= -1.8e-231)
		tmp = t_1;
	elseif (z <= -5.5e-289)
		tmp = Float64(y / Float64(a / Float64(t - x)));
	elseif (z <= 1e+120)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * t) / a);
	t_2 = t * (z / (z - a));
	tmp = 0.0;
	if (z <= -8e+81)
		tmp = t_2;
	elseif (z <= -1.8e-231)
		tmp = t_1;
	elseif (z <= -5.5e-289)
		tmp = y / (a / (t - x));
	elseif (z <= 1e+120)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e+81], t$95$2, If[LessEqual[z, -1.8e-231], t$95$1, If[LessEqual[z, -5.5e-289], N[(y / N[(a / N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e+120], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.99999999999999937e81 or 9.9999999999999998e119 < z

   1. Initial program 64.4%

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

   3. Taylor expanded in x around 0 38.8%

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

      1. associate-/l* 73.5%

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

   5. Simplified 73.5%

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

   6. Taylor expanded in y around 0 66.9%

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

      1. neg-mul-1 66.9%

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

      2. distribute-neg-frac2 66.9%

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

      3. neg-sub0 66.9%

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

      4. associate--r- 66.9%

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

      5. neg-sub0 66.9%

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

   8. Simplified 66.9%

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

   if -7.99999999999999937e81 < z < -1.79999999999999987e-231 or -5.5000000000000004e-289 < z < 9.9999999999999998e119

   1. Initial program 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-*l/ 88.9%

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

      3. associate-*r/ 94.8%

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

      4. clear-num 94.7%

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

      5. un-div-inv 94.8%

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

   4. Applied egg-rr 94.8%

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

   5. Taylor expanded in z around 0 70.6%

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

   6. Taylor expanded in t around inf 60.7%

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

   if -1.79999999999999987e-231 < z < -5.5000000000000004e-289

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 74.5%

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

      1. div-sub 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in a around inf 75.5%

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

      1. clear-num 75.5%

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

      2. un-div-inv 75.5%

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

   8. Applied egg-rr 75.5%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+81}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-231}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-289}:\\ \;\;\;\;\frac{y}{\frac{a}{t - x}}\\ \mathbf{elif}\;z \leq 10^{+120}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 69.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+115}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-146} \lor \neg \left(z \leq 25000\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.5e+115)
   (/ t (/ (- a z) (- y z)))
   (if (or (<= z -4.3e-146) (not (<= z 25000.0)))
     (+ x (* (- y z) (/ t (- a z))))
     (+ x (/ (- t x) (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+115) {
		tmp = t / ((a - z) / (y - z));
	} else if ((z <= -4.3e-146) || !(z <= 25000.0)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.5d+115)) then
        tmp = t / ((a - z) / (y - z))
    else if ((z <= (-4.3d-146)) .or. (.not. (z <= 25000.0d0))) then
        tmp = x + ((y - z) * (t / (a - z)))
    else
        tmp = x + ((t - x) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+115) {
		tmp = t / ((a - z) / (y - z));
	} else if ((z <= -4.3e-146) || !(z <= 25000.0)) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else {
		tmp = x + ((t - x) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.5e+115:
		tmp = t / ((a - z) / (y - z))
	elif (z <= -4.3e-146) or not (z <= 25000.0):
		tmp = x + ((y - z) * (t / (a - z)))
	else:
		tmp = x + ((t - x) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.5e+115)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif ((z <= -4.3e-146) || !(z <= 25000.0))
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	else
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.5e+115)
		tmp = t / ((a - z) / (y - z));
	elseif ((z <= -4.3e-146) || ~((z <= 25000.0)))
		tmp = x + ((y - z) * (t / (a - z)));
	else
		tmp = x + ((t - x) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.5e+115], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -4.3e-146], N[Not[LessEqual[z, 25000.0]], $MachinePrecision]], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.4999999999999997e115

   1. Initial program 58.4%

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

   3. Taylor expanded in x around 0 44.8%

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

      1. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

      1. clear-num 80.7%

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

      2. un-div-inv 80.8%

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

   7. Applied egg-rr 80.8%

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

   if -7.4999999999999997e115 < z < -4.2999999999999999e-146 or 25000 < z

   1. Initial program 83.8%

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

   3. Taylor expanded in t around inf 72.8%

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

   if -4.2999999999999999e-146 < z < 25000

   1. Initial program 93.8%

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

      1. *-commutative 93.8%

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

      2. associate-*l/ 93.8%

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

      3. associate-*r/ 99.0%

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

      4. clear-num 98.9%

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

      5. un-div-inv 98.9%

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

   4. Applied egg-rr 98.9%

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

   5. Taylor expanded in z around 0 88.2%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+115}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-146} \lor \neg \left(z \leq 25000\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 79.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-67}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ t (* (/ (- t x) z) (- a y)))))
   (if (<= z -1.85e+161)
     t_1
     (if (<= z -3.3e-67)
       (+ x (* (- y z) (/ t (- a z))))
       (if (<= z 2.6e+118) (- x (/ (- x t) (/ (- a z) y))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) / z) * (a - y));
	double tmp;
	if (z <= -1.85e+161) {
		tmp = t_1;
	} else if (z <= -3.3e-67) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (z <= 2.6e+118) {
		tmp = x - ((x - t) / ((a - z) / y));
	} 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 + (((t - x) / z) * (a - y))
    if (z <= (-1.85d+161)) then
        tmp = t_1
    else if (z <= (-3.3d-67)) then
        tmp = x + ((y - z) * (t / (a - z)))
    else if (z <= 2.6d+118) then
        tmp = x - ((x - t) / ((a - z) / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t + (((t - x) / z) * (a - y));
	double tmp;
	if (z <= -1.85e+161) {
		tmp = t_1;
	} else if (z <= -3.3e-67) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (z <= 2.6e+118) {
		tmp = x - ((x - t) / ((a - z) / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t + (((t - x) / z) * (a - y))
	tmp = 0
	if z <= -1.85e+161:
		tmp = t_1
	elif z <= -3.3e-67:
		tmp = x + ((y - z) * (t / (a - z)))
	elif z <= 2.6e+118:
		tmp = x - ((x - t) / ((a - z) / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t + Float64(Float64(Float64(t - x) / z) * Float64(a - y)))
	tmp = 0.0
	if (z <= -1.85e+161)
		tmp = t_1;
	elseif (z <= -3.3e-67)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	elseif (z <= 2.6e+118)
		tmp = Float64(x - Float64(Float64(x - t) / Float64(Float64(a - z) / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t + (((t - x) / z) * (a - y));
	tmp = 0.0;
	if (z <= -1.85e+161)
		tmp = t_1;
	elseif (z <= -3.3e-67)
		tmp = x + ((y - z) * (t / (a - z)));
	elseif (z <= 2.6e+118)
		tmp = x - ((x - t) / ((a - z) / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t + N[(N[(N[(t - x), $MachinePrecision] / z), $MachinePrecision] * N[(a - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.85e+161], t$95$1, If[LessEqual[z, -3.3e-67], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+118], N[(x - N[(N[(x - t), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8499999999999999e161 or 2.60000000000000016e118 < z

   1. Initial program 58.6%

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

   3. Taylor expanded in z around inf 59.1%

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

      1. associate--l+ 59.1%

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

      2. distribute-lft-out-- 59.1%

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

      3. div-sub 59.1%

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

      4. mul-1-neg 59.1%

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

      5. unsub-neg 59.1%

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

      6. div-sub 59.1%

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

      7. associate-/l* 76.7%

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

      8. associate-/l* 90.9%

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

      9. distribute-rgt-out-- 90.9%

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

   5. Simplified 90.9%

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

   if -1.8499999999999999e161 < z < -3.3000000000000002e-67

   1. Initial program 88.1%

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

   3. Taylor expanded in t around inf 78.6%

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

   if -3.3000000000000002e-67 < z < 2.60000000000000016e118

   1. Initial program 92.9%

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

      1. *-commutative 92.9%

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

      2. associate-*l/ 92.3%

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

      3. associate-*r/ 96.6%

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

      4. clear-num 96.5%

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

      5. un-div-inv 96.6%

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

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in y around inf 90.4%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+161}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-67}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{t - x}{z} \cdot \left(a - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a - z}{y - z}}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-69}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+124}:\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ (- a z) (- y z)))))
   (if (<= z -3.2e+116)
     t_1
     (if (<= z -7e-69)
       (+ x (* (- y z) (/ t (- a z))))
       (if (<= z 3.9e+124) (- x (/ (- x t) (/ (- a z) y))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -3.2e+116) {
		tmp = t_1;
	} else if (z <= -7e-69) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (z <= 3.9e+124) {
		tmp = x - ((x - t) / ((a - z) / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / ((a - z) / (y - z))
    if (z <= (-3.2d+116)) then
        tmp = t_1
    else if (z <= (-7d-69)) then
        tmp = x + ((y - z) * (t / (a - z)))
    else if (z <= 3.9d+124) then
        tmp = x - ((x - t) / ((a - z) / y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / ((a - z) / (y - z));
	double tmp;
	if (z <= -3.2e+116) {
		tmp = t_1;
	} else if (z <= -7e-69) {
		tmp = x + ((y - z) * (t / (a - z)));
	} else if (z <= 3.9e+124) {
		tmp = x - ((x - t) / ((a - z) / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / ((a - z) / (y - z))
	tmp = 0
	if z <= -3.2e+116:
		tmp = t_1
	elif z <= -7e-69:
		tmp = x + ((y - z) * (t / (a - z)))
	elif z <= 3.9e+124:
		tmp = x - ((x - t) / ((a - z) / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(Float64(a - z) / Float64(y - z)))
	tmp = 0.0
	if (z <= -3.2e+116)
		tmp = t_1;
	elseif (z <= -7e-69)
		tmp = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))));
	elseif (z <= 3.9e+124)
		tmp = Float64(x - Float64(Float64(x - t) / Float64(Float64(a - z) / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / ((a - z) / (y - z));
	tmp = 0.0;
	if (z <= -3.2e+116)
		tmp = t_1;
	elseif (z <= -7e-69)
		tmp = x + ((y - z) * (t / (a - z)));
	elseif (z <= 3.9e+124)
		tmp = x - ((x - t) / ((a - z) / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+116], t$95$1, If[LessEqual[z, -7e-69], N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e+124], N[(x - N[(N[(x - t), $MachinePrecision] / N[(N[(a - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2e116 or 3.9e124 < z

   1. Initial program 60.1%

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

   3. Taylor expanded in x around 0 38.3%

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

      1. associate-/l* 75.7%

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

   5. Simplified 75.7%

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

      1. clear-num 75.8%

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

      2. un-div-inv 75.8%

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

   7. Applied egg-rr 75.8%

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

   if -3.2e116 < z < -7.0000000000000003e-69

   1. Initial program 91.0%

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

   3. Taylor expanded in t around inf 81.4%

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

   if -7.0000000000000003e-69 < z < 3.9e124

   1. Initial program 92.4%

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

      1. *-commutative 92.4%

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

      2. associate-*l/ 91.3%

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

      3. associate-*r/ 96.0%

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

      4. clear-num 96.0%

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

      5. un-div-inv 96.0%

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

   4. Applied egg-rr 96.0%

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

   5. Taylor expanded in y around inf 89.4%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+116}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-69}:\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+124}:\\ \;\;\;\;x - \frac{x - t}{\frac{a - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 38.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+41}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-179}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-233}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e+41)
   t
   (if (<= z -6.8e-179)
     x
     (if (<= z 2.6e-233) (* t (/ y a)) (if (<= z 2.6e+118) x t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+41) {
		tmp = t;
	} else if (z <= -6.8e-179) {
		tmp = x;
	} else if (z <= 2.6e-233) {
		tmp = t * (y / a);
	} else if (z <= 2.6e+118) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.5d+41)) then
        tmp = t
    else if (z <= (-6.8d-179)) then
        tmp = x
    else if (z <= 2.6d-233) then
        tmp = t * (y / a)
    else if (z <= 2.6d+118) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e+41) {
		tmp = t;
	} else if (z <= -6.8e-179) {
		tmp = x;
	} else if (z <= 2.6e-233) {
		tmp = t * (y / a);
	} else if (z <= 2.6e+118) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e+41:
		tmp = t
	elif z <= -6.8e-179:
		tmp = x
	elif z <= 2.6e-233:
		tmp = t * (y / a)
	elif z <= 2.6e+118:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e+41)
		tmp = t;
	elseif (z <= -6.8e-179)
		tmp = x;
	elseif (z <= 2.6e-233)
		tmp = Float64(t * Float64(y / a));
	elseif (z <= 2.6e+118)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e+41)
		tmp = t;
	elseif (z <= -6.8e-179)
		tmp = x;
	elseif (z <= 2.6e-233)
		tmp = t * (y / a);
	elseif (z <= 2.6e+118)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e+41], t, If[LessEqual[z, -6.8e-179], x, If[LessEqual[z, 2.6e-233], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+118], x, t]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5000000000000003e41 or 2.60000000000000016e118 < z

   1. Initial program 66.9%

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

   3. Taylor expanded in z around inf 52.2%

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

   if -5.5000000000000003e41 < z < -6.7999999999999995e-179 or 2.5999999999999998e-233 < z < 2.60000000000000016e118

   1. Initial program 91.2%

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

   3. Taylor expanded in a around inf 43.9%

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

   if -6.7999999999999995e-179 < z < 2.5999999999999998e-233

   1. Initial program 94.9%

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

   3. Taylor expanded in y around inf 68.7%

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

      1. div-sub 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in a around inf 67.2%

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

   7. Taylor expanded in t around inf 46.7%

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

      1. associate-/l* 51.7%

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

   9. Simplified 51.7%

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

Alternative 20: 58.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+55} \lor \neg \left(t \leq 3.4 \cdot 10^{-93}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.3e+55) (not (<= t 3.4e-93)))
   (* t (/ (- y z) (- a z)))
   (- x (* x (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.3e+55) || !(t <= 3.4e-93)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x - (x * (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 ((t <= (-1.3d+55)) .or. (.not. (t <= 3.4d-93))) then
        tmp = t * ((y - z) / (a - z))
    else
        tmp = x - (x * (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 ((t <= -1.3e+55) || !(t <= 3.4e-93)) {
		tmp = t * ((y - z) / (a - z));
	} else {
		tmp = x - (x * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.3e+55) or not (t <= 3.4e-93):
		tmp = t * ((y - z) / (a - z))
	else:
		tmp = x - (x * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.3e+55) || !(t <= 3.4e-93))
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	else
		tmp = Float64(x - Float64(x * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.3e+55) || ~((t <= 3.4e-93)))
		tmp = t * ((y - z) / (a - z));
	else
		tmp = x - (x * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.3e+55], N[Not[LessEqual[t, 3.4e-93]], $MachinePrecision]], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3e55 or 3.40000000000000001e-93 < t

   1. Initial program 88.7%

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

   3. Taylor expanded in x around 0 52.8%

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

      1. associate-/l* 73.3%

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

   5. Simplified 73.3%

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

   if -1.3e55 < t < 3.40000000000000001e-93

   1. Initial program 80.0%

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

   3. Taylor expanded in t around 0 62.4%

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

      1. mul-1-neg 62.4%

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

      2. associate-/l* 68.2%

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

      3. distribute-rgt-neg-in 68.2%

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

      4. distribute-frac-neg2 68.2%

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

      5. neg-sub0 68.2%

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

      6. associate--r- 68.2%

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

      7. neg-sub0 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in z around 0 55.2%

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

      1. mul-1-neg 55.2%

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

      2. unsub-neg 55.2%

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

      3. associate-/l* 59.9%

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

   8. Simplified 59.9%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+55} \lor \neg \left(t \leq 3.4 \cdot 10^{-93}\right):\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 64.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-59}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.7e-59)
   (/ t (/ (- a z) (- y z)))
   (if (<= z 2.6e+118) (+ x (/ (- t x) (/ a y))) (* t (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e-59) {
		tmp = t / ((a - z) / (y - z));
	} else if (z <= 2.6e+118) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t * (z / (z - 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 <= (-1.7d-59)) then
        tmp = t / ((a - z) / (y - z))
    else if (z <= 2.6d+118) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t * (z / (z - 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 <= -1.7e-59) {
		tmp = t / ((a - z) / (y - z));
	} else if (z <= 2.6e+118) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t * (z / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.7e-59:
		tmp = t / ((a - z) / (y - z))
	elif z <= 2.6e+118:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t * (z / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.7e-59)
		tmp = Float64(t / Float64(Float64(a - z) / Float64(y - z)));
	elseif (z <= 2.6e+118)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = Float64(t * Float64(z / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.7e-59)
		tmp = t / ((a - z) / (y - z));
	elseif (z <= 2.6e+118)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t * (z / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.7e-59], N[(t / N[(N[(a - z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+118], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.70000000000000009e-59

   1. Initial program 75.6%

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

   3. Taylor expanded in x around 0 52.6%

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

      1. associate-/l* 72.7%

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

   5. Simplified 72.7%

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

      1. clear-num 72.8%

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

      2. un-div-inv 72.9%

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

   7. Applied egg-rr 72.9%

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

   if -1.70000000000000009e-59 < z < 2.60000000000000016e118

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

      2. associate-*l/ 91.8%

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

      3. associate-*r/ 96.7%

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

      4. clear-num 96.6%

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

      5. un-div-inv 96.6%

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

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in z around 0 79.1%

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

   if 2.60000000000000016e118 < z

   1. Initial program 62.9%

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

   3. Taylor expanded in x around 0 26.8%

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

      1. associate-/l* 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in y around 0 65.3%

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

      1. neg-mul-1 65.3%

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

      2. distribute-neg-frac2 65.3%

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

      3. neg-sub0 65.3%

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

      4. associate--r- 65.3%

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

      5. neg-sub0 65.3%

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

   8. Simplified 65.3%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-59}:\\ \;\;\;\;\frac{t}{\frac{a - z}{y - z}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 64.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.1e-59)
   (* t (/ (- y z) (- a z)))
   (if (<= z 2.6e+118) (+ x (/ (- t x) (/ a y))) (* t (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.1e-59) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 2.6e+118) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t * (z / (z - 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 <= (-3.1d-59)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 2.6d+118) then
        tmp = x + ((t - x) / (a / y))
    else
        tmp = t * (z / (z - 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 <= -3.1e-59) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 2.6e+118) {
		tmp = x + ((t - x) / (a / y));
	} else {
		tmp = t * (z / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.1e-59:
		tmp = t * ((y - z) / (a - z))
	elif z <= 2.6e+118:
		tmp = x + ((t - x) / (a / y))
	else:
		tmp = t * (z / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.1e-59)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 2.6e+118)
		tmp = Float64(x + Float64(Float64(t - x) / Float64(a / y)));
	else
		tmp = Float64(t * Float64(z / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.1e-59)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 2.6e+118)
		tmp = x + ((t - x) / (a / y));
	else
		tmp = t * (z / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.1e-59], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+118], N[(x + N[(N[(t - x), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.09999999999999999e-59

   1. Initial program 75.6%

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

   3. Taylor expanded in x around 0 52.6%

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

      1. associate-/l* 72.7%

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

   5. Simplified 72.7%

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

   if -3.09999999999999999e-59 < z < 2.60000000000000016e118

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

      2. associate-*l/ 91.8%

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

      3. associate-*r/ 96.7%

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

      4. clear-num 96.6%

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

      5. un-div-inv 96.6%

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

   4. Applied egg-rr 96.6%

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

   5. Taylor expanded in z around 0 79.1%

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

   if 2.60000000000000016e118 < z

   1. Initial program 62.9%

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

   3. Taylor expanded in x around 0 26.8%

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

      1. associate-/l* 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in y around 0 65.3%

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

      1. neg-mul-1 65.3%

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

      2. distribute-neg-frac2 65.3%

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

      3. neg-sub0 65.3%

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

      4. associate--r- 65.3%

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

      5. neg-sub0 65.3%

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

   8. Simplified 65.3%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;x + \frac{t - x}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 63.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.2e-59)
   (* t (/ (- y z) (- a z)))
   (if (<= z 2.6e+118) (- x (* y (/ (- x t) a))) (* t (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e-59) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 2.6e+118) {
		tmp = x - (y * ((x - t) / a));
	} else {
		tmp = t * (z / (z - 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 <= (-8.2d-59)) then
        tmp = t * ((y - z) / (a - z))
    else if (z <= 2.6d+118) then
        tmp = x - (y * ((x - t) / a))
    else
        tmp = t * (z / (z - 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 <= -8.2e-59) {
		tmp = t * ((y - z) / (a - z));
	} else if (z <= 2.6e+118) {
		tmp = x - (y * ((x - t) / a));
	} else {
		tmp = t * (z / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.2e-59:
		tmp = t * ((y - z) / (a - z))
	elif z <= 2.6e+118:
		tmp = x - (y * ((x - t) / a))
	else:
		tmp = t * (z / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.2e-59)
		tmp = Float64(t * Float64(Float64(y - z) / Float64(a - z)));
	elseif (z <= 2.6e+118)
		tmp = Float64(x - Float64(y * Float64(Float64(x - t) / a)));
	else
		tmp = Float64(t * Float64(z / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.2e-59)
		tmp = t * ((y - z) / (a - z));
	elseif (z <= 2.6e+118)
		tmp = x - (y * ((x - t) / a));
	else
		tmp = t * (z / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.2e-59], N[(t * N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+118], N[(x - N[(y * N[(N[(x - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.1999999999999991e-59

   1. Initial program 75.6%

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

   3. Taylor expanded in x around 0 52.6%

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

      1. associate-/l* 72.7%

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

   5. Simplified 72.7%

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

   if -8.1999999999999991e-59 < z < 2.60000000000000016e118

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0 74.2%

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

      1. associate-/l* 76.4%

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

   5. Simplified 76.4%

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

   if 2.60000000000000016e118 < z

   1. Initial program 62.9%

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

   3. Taylor expanded in x around 0 26.8%

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

      1. associate-/l* 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in y around 0 65.3%

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

      1. neg-mul-1 65.3%

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

      2. distribute-neg-frac2 65.3%

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

      3. neg-sub0 65.3%

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

      4. associate--r- 65.3%

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

      5. neg-sub0 65.3%

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

   8. Simplified 65.3%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{-59}:\\ \;\;\;\;t \cdot \frac{y - z}{a - z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;x - y \cdot \frac{x - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 38.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+41}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.4e+41) t (if (<= z 2.6e+118) x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+41) {
		tmp = t;
	} else if (z <= 2.6e+118) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.4d+41)) then
        tmp = t
    else if (z <= 2.6d+118) then
        tmp = x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.4e+41) {
		tmp = t;
	} else if (z <= 2.6e+118) {
		tmp = x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.4e+41:
		tmp = t
	elif z <= 2.6e+118:
		tmp = x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.4e+41)
		tmp = t;
	elseif (z <= 2.6e+118)
		tmp = x;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.4e+41)
		tmp = t;
	elseif (z <= 2.6e+118)
		tmp = x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.4e+41], t, If[LessEqual[z, 2.6e+118], x, t]]

Derivation

1. Split input into 2 regimes

2. if z < -5.39999999999999999e41 or 2.60000000000000016e118 < z

   1. Initial program 66.9%

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

   3. Taylor expanded in z around inf 52.2%

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

   if -5.39999999999999999e41 < z < 2.60000000000000016e118

   1. Initial program 92.4%

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

   3. Taylor expanded in a around inf 38.1%

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

Alternative 25: 25.4% 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 84.7%

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

3. Taylor expanded in z around inf 21.3%

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

Alternative 26: 2.8% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 0.0)

C

double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

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 = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return 0.0;
}

Python

def code(x, y, z, t, a):
	return 0.0

Julia

function code(x, y, z, t, a)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := 0.0

Derivation

1. Initial program 84.7%

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

3. Taylor expanded in t around 0 43.9%

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

   1. mul-1-neg 43.9%

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

   2. associate-/l* 48.5%

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

   3. distribute-rgt-neg-in 48.5%

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

   4. distribute-frac-neg2 48.5%

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

   5. neg-sub0 48.5%

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

   6. associate--r- 48.5%

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

   7. neg-sub0 48.5%

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

5. Simplified 48.5%

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

6. Taylor expanded in z around inf 2.8%

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

   1. distribute-rgt1-in 2.8%

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

   2. metadata-eval 2.8%

      \[\leadsto \color{blue}{0} \cdot x \]

   3. mul0-lft 2.8%

      \[\leadsto \color{blue}{0} \]

8. Simplified 2.8%

   \[\leadsto \color{blue}{0} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024103 
(FPCore (x y z t a)
  :name "Numeric.Signal:interpolate   from hsignal-0.2.7.1"
  :precision binary64
  (+ x (* (- y z) (/ (- t x) (- a z)))))