Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Percentage Accurate: 96.8% → 96.8%

Time: 12.3s

Alternatives: 17

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{t}{\frac{z - y}{x - y}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

   \[\frac{x - y}{z - y} \cdot t \]
2. Step-by-step derivation

   1. associate-*l/ 83.2%

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

   2. associate-/l* 82.2%

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

3. Simplified 82.2%

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

   1. associate-*r/ 83.2%

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

   2. associate-*l/ 98.0%

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

   3. *-commutative 98.0%

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

   4. clear-num 97.9%

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

   5. un-div-inv 98.1%

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

6. Applied egg-rr 98.1%

   \[\leadsto \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]
7. Add Preprocessing

Alternative 2: 73.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ t_3 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;y \leq -8 \cdot 10^{-50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-120}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-236}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-242}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-277}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-288}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-142}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-68}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z)))
        (t_2 (* t (- 1.0 (/ x y))))
        (t_3 (* t (/ x (- z y)))))
   (if (<= y -8e-50)
     t_2
     (if (<= y -5e-98)
       t_1
       (if (<= y -1.3e-120)
         t_2
         (if (<= y -6e-236)
           t_3
           (if (<= y -5e-242)
             t_2
             (if (<= y -4.2e-277)
               (* x (/ t z))
               (if (<= y 3.4e-288)
                 t_3
                 (if (<= y 4.8e-142)
                   t_1
                   (if (<= y 5e-142)
                     t
                     (if (<= y 1.05e-68) t_3 (- t (* t (/ x y)))))))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t * (1.0 - (x / y));
	double t_3 = t * (x / (z - y));
	double tmp;
	if (y <= -8e-50) {
		tmp = t_2;
	} else if (y <= -5e-98) {
		tmp = t_1;
	} else if (y <= -1.3e-120) {
		tmp = t_2;
	} else if (y <= -6e-236) {
		tmp = t_3;
	} else if (y <= -5e-242) {
		tmp = t_2;
	} else if (y <= -4.2e-277) {
		tmp = x * (t / z);
	} else if (y <= 3.4e-288) {
		tmp = t_3;
	} else if (y <= 4.8e-142) {
		tmp = t_1;
	} else if (y <= 5e-142) {
		tmp = t;
	} else if (y <= 1.05e-68) {
		tmp = t_3;
	} else {
		tmp = t - (t * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * ((x - y) / z)
    t_2 = t * (1.0d0 - (x / y))
    t_3 = t * (x / (z - y))
    if (y <= (-8d-50)) then
        tmp = t_2
    else if (y <= (-5d-98)) then
        tmp = t_1
    else if (y <= (-1.3d-120)) then
        tmp = t_2
    else if (y <= (-6d-236)) then
        tmp = t_3
    else if (y <= (-5d-242)) then
        tmp = t_2
    else if (y <= (-4.2d-277)) then
        tmp = x * (t / z)
    else if (y <= 3.4d-288) then
        tmp = t_3
    else if (y <= 4.8d-142) then
        tmp = t_1
    else if (y <= 5d-142) then
        tmp = t
    else if (y <= 1.05d-68) then
        tmp = t_3
    else
        tmp = t - (t * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t * (1.0 - (x / y));
	double t_3 = t * (x / (z - y));
	double tmp;
	if (y <= -8e-50) {
		tmp = t_2;
	} else if (y <= -5e-98) {
		tmp = t_1;
	} else if (y <= -1.3e-120) {
		tmp = t_2;
	} else if (y <= -6e-236) {
		tmp = t_3;
	} else if (y <= -5e-242) {
		tmp = t_2;
	} else if (y <= -4.2e-277) {
		tmp = x * (t / z);
	} else if (y <= 3.4e-288) {
		tmp = t_3;
	} else if (y <= 4.8e-142) {
		tmp = t_1;
	} else if (y <= 5e-142) {
		tmp = t;
	} else if (y <= 1.05e-68) {
		tmp = t_3;
	} else {
		tmp = t - (t * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	t_2 = t * (1.0 - (x / y))
	t_3 = t * (x / (z - y))
	tmp = 0
	if y <= -8e-50:
		tmp = t_2
	elif y <= -5e-98:
		tmp = t_1
	elif y <= -1.3e-120:
		tmp = t_2
	elif y <= -6e-236:
		tmp = t_3
	elif y <= -5e-242:
		tmp = t_2
	elif y <= -4.2e-277:
		tmp = x * (t / z)
	elif y <= 3.4e-288:
		tmp = t_3
	elif y <= 4.8e-142:
		tmp = t_1
	elif y <= 5e-142:
		tmp = t
	elif y <= 1.05e-68:
		tmp = t_3
	else:
		tmp = t - (t * (x / y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / z))
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	t_3 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (y <= -8e-50)
		tmp = t_2;
	elseif (y <= -5e-98)
		tmp = t_1;
	elseif (y <= -1.3e-120)
		tmp = t_2;
	elseif (y <= -6e-236)
		tmp = t_3;
	elseif (y <= -5e-242)
		tmp = t_2;
	elseif (y <= -4.2e-277)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= 3.4e-288)
		tmp = t_3;
	elseif (y <= 4.8e-142)
		tmp = t_1;
	elseif (y <= 5e-142)
		tmp = t;
	elseif (y <= 1.05e-68)
		tmp = t_3;
	else
		tmp = Float64(t - Float64(t * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / z);
	t_2 = t * (1.0 - (x / y));
	t_3 = t * (x / (z - y));
	tmp = 0.0;
	if (y <= -8e-50)
		tmp = t_2;
	elseif (y <= -5e-98)
		tmp = t_1;
	elseif (y <= -1.3e-120)
		tmp = t_2;
	elseif (y <= -6e-236)
		tmp = t_3;
	elseif (y <= -5e-242)
		tmp = t_2;
	elseif (y <= -4.2e-277)
		tmp = x * (t / z);
	elseif (y <= 3.4e-288)
		tmp = t_3;
	elseif (y <= 4.8e-142)
		tmp = t_1;
	elseif (y <= 5e-142)
		tmp = t;
	elseif (y <= 1.05e-68)
		tmp = t_3;
	else
		tmp = t - (t * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e-50], t$95$2, If[LessEqual[y, -5e-98], t$95$1, If[LessEqual[y, -1.3e-120], t$95$2, If[LessEqual[y, -6e-236], t$95$3, If[LessEqual[y, -5e-242], t$95$2, If[LessEqual[y, -4.2e-277], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-288], t$95$3, If[LessEqual[y, 4.8e-142], t$95$1, If[LessEqual[y, 5e-142], t, If[LessEqual[y, 1.05e-68], t$95$3, N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -8.00000000000000006e-50 or -5.00000000000000018e-98 < y < -1.3000000000000001e-120 or -6.00000000000000027e-236 < y < -4.9999999999999998e-242

   1. Initial program 97.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 80.2%

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

      2. associate-/l* 79.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in y around inf 72.7%

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

      1. associate--l+ 72.7%

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

      2. distribute-lft-out-- 72.7%

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

      3. div-sub 72.7%

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

      4. mul-1-neg 72.7%

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

      5. unsub-neg 72.7%

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

      6. distribute-lft-out-- 72.7%

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

      7. associate-/l* 75.7%

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

   7. Simplified 75.7%

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

   8. Taylor expanded in x around inf 75.4%

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

   9. Taylor expanded in t around 0 75.4%

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

   if -8.00000000000000006e-50 < y < -5.00000000000000018e-98 or 3.39999999999999972e-288 < y < 4.79999999999999976e-142

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 94.1%

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

   if -1.3000000000000001e-120 < y < -6.00000000000000027e-236 or -4.1999999999999999e-277 < y < 3.39999999999999972e-288 or 5.0000000000000002e-142 < y < 1.05000000000000004e-68

   1. Initial program 96.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 77.0%

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

   if -4.9999999999999998e-242 < y < -4.1999999999999999e-277

   1. Initial program 81.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 81.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 81.0%

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

      1. *-commutative 81.0%

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

      2. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   if 4.79999999999999976e-142 < y < 5.0000000000000002e-142

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 100.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   if 1.05000000000000004e-68 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 80.3%

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

      2. associate-/l* 74.8%

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

   3. Simplified 74.8%

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

   5. Taylor expanded in y around inf 78.2%

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

      1. associate--l+ 78.2%

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

      2. distribute-lft-out-- 78.2%

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

      3. div-sub 78.2%

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

      4. mul-1-neg 78.2%

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

      5. unsub-neg 78.2%

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

      6. distribute-lft-out-- 79.8%

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

      7. associate-/l* 89.4%

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

   7. Simplified 89.4%

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

   8. Taylor expanded in x around inf 88.9%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-98}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-120}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-236}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-277}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-288}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-142}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-142}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-68}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ t_3 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{-50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-120}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-236}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-242}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-277}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-287}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-142}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-68}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z)))
        (t_2 (* t (- 1.0 (/ x y))))
        (t_3 (* t (/ x (- z y)))))
   (if (<= y -7.8e-50)
     t_2
     (if (<= y -2.15e-97)
       t_1
       (if (<= y -1.3e-120)
         t_2
         (if (<= y -6e-236)
           t_3
           (if (<= y -5e-242)
             t_2
             (if (<= y -4.2e-277)
               (* x (/ t z))
               (if (<= y 5.4e-287)
                 t_3
                 (if (<= y 4.8e-142)
                   t_1
                   (if (<= y 5e-142) t (if (<= y 4.5e-68) t_3 t_2))))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t * (1.0 - (x / y));
	double t_3 = t * (x / (z - y));
	double tmp;
	if (y <= -7.8e-50) {
		tmp = t_2;
	} else if (y <= -2.15e-97) {
		tmp = t_1;
	} else if (y <= -1.3e-120) {
		tmp = t_2;
	} else if (y <= -6e-236) {
		tmp = t_3;
	} else if (y <= -5e-242) {
		tmp = t_2;
	} else if (y <= -4.2e-277) {
		tmp = x * (t / z);
	} else if (y <= 5.4e-287) {
		tmp = t_3;
	} else if (y <= 4.8e-142) {
		tmp = t_1;
	} else if (y <= 5e-142) {
		tmp = t;
	} else if (y <= 4.5e-68) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * ((x - y) / z)
    t_2 = t * (1.0d0 - (x / y))
    t_3 = t * (x / (z - y))
    if (y <= (-7.8d-50)) then
        tmp = t_2
    else if (y <= (-2.15d-97)) then
        tmp = t_1
    else if (y <= (-1.3d-120)) then
        tmp = t_2
    else if (y <= (-6d-236)) then
        tmp = t_3
    else if (y <= (-5d-242)) then
        tmp = t_2
    else if (y <= (-4.2d-277)) then
        tmp = x * (t / z)
    else if (y <= 5.4d-287) then
        tmp = t_3
    else if (y <= 4.8d-142) then
        tmp = t_1
    else if (y <= 5d-142) then
        tmp = t
    else if (y <= 4.5d-68) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t * (1.0 - (x / y));
	double t_3 = t * (x / (z - y));
	double tmp;
	if (y <= -7.8e-50) {
		tmp = t_2;
	} else if (y <= -2.15e-97) {
		tmp = t_1;
	} else if (y <= -1.3e-120) {
		tmp = t_2;
	} else if (y <= -6e-236) {
		tmp = t_3;
	} else if (y <= -5e-242) {
		tmp = t_2;
	} else if (y <= -4.2e-277) {
		tmp = x * (t / z);
	} else if (y <= 5.4e-287) {
		tmp = t_3;
	} else if (y <= 4.8e-142) {
		tmp = t_1;
	} else if (y <= 5e-142) {
		tmp = t;
	} else if (y <= 4.5e-68) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	t_2 = t * (1.0 - (x / y))
	t_3 = t * (x / (z - y))
	tmp = 0
	if y <= -7.8e-50:
		tmp = t_2
	elif y <= -2.15e-97:
		tmp = t_1
	elif y <= -1.3e-120:
		tmp = t_2
	elif y <= -6e-236:
		tmp = t_3
	elif y <= -5e-242:
		tmp = t_2
	elif y <= -4.2e-277:
		tmp = x * (t / z)
	elif y <= 5.4e-287:
		tmp = t_3
	elif y <= 4.8e-142:
		tmp = t_1
	elif y <= 5e-142:
		tmp = t
	elif y <= 4.5e-68:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / z))
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	t_3 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (y <= -7.8e-50)
		tmp = t_2;
	elseif (y <= -2.15e-97)
		tmp = t_1;
	elseif (y <= -1.3e-120)
		tmp = t_2;
	elseif (y <= -6e-236)
		tmp = t_3;
	elseif (y <= -5e-242)
		tmp = t_2;
	elseif (y <= -4.2e-277)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= 5.4e-287)
		tmp = t_3;
	elseif (y <= 4.8e-142)
		tmp = t_1;
	elseif (y <= 5e-142)
		tmp = t;
	elseif (y <= 4.5e-68)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / z);
	t_2 = t * (1.0 - (x / y));
	t_3 = t * (x / (z - y));
	tmp = 0.0;
	if (y <= -7.8e-50)
		tmp = t_2;
	elseif (y <= -2.15e-97)
		tmp = t_1;
	elseif (y <= -1.3e-120)
		tmp = t_2;
	elseif (y <= -6e-236)
		tmp = t_3;
	elseif (y <= -5e-242)
		tmp = t_2;
	elseif (y <= -4.2e-277)
		tmp = x * (t / z);
	elseif (y <= 5.4e-287)
		tmp = t_3;
	elseif (y <= 4.8e-142)
		tmp = t_1;
	elseif (y <= 5e-142)
		tmp = t;
	elseif (y <= 4.5e-68)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.8e-50], t$95$2, If[LessEqual[y, -2.15e-97], t$95$1, If[LessEqual[y, -1.3e-120], t$95$2, If[LessEqual[y, -6e-236], t$95$3, If[LessEqual[y, -5e-242], t$95$2, If[LessEqual[y, -4.2e-277], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e-287], t$95$3, If[LessEqual[y, 4.8e-142], t$95$1, If[LessEqual[y, 5e-142], t, If[LessEqual[y, 4.5e-68], t$95$3, t$95$2]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.80000000000000042e-50 or -2.15e-97 < y < -1.3000000000000001e-120 or -6.00000000000000027e-236 < y < -4.9999999999999998e-242 or 4.49999999999999999e-68 < y

   1. Initial program 98.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 80.2%

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

      2. associate-/l* 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in y around inf 75.0%

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

      1. associate--l+ 75.0%

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

      2. distribute-lft-out-- 75.0%

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

      3. div-sub 75.0%

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

      4. mul-1-neg 75.0%

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

      5. unsub-neg 75.0%

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

      6. distribute-lft-out-- 75.7%

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

      7. associate-/l* 81.3%

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

   7. Simplified 81.3%

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

   8. Taylor expanded in x around inf 81.0%

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

   9. Taylor expanded in t around 0 81.0%

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

   if -7.80000000000000042e-50 < y < -2.15e-97 or 5.4000000000000002e-287 < y < 4.79999999999999976e-142

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 94.1%

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

   if -1.3000000000000001e-120 < y < -6.00000000000000027e-236 or -4.1999999999999999e-277 < y < 5.4000000000000002e-287 or 5.0000000000000002e-142 < y < 4.49999999999999999e-68

   1. Initial program 96.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 77.0%

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

   if -4.9999999999999998e-242 < y < -4.1999999999999999e-277

   1. Initial program 81.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 81.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 81.0%

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

      1. *-commutative 81.0%

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

      2. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   if 4.79999999999999976e-142 < y < 5.0000000000000002e-142

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 100.0%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{t} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-97}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-120}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-236}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-242}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-277}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-287}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-142}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-142}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-68}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x - y}{z}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;y \leq -1.62 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-120}:\\ \;\;\;\;t - \frac{x}{\frac{y}{t}}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-142}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-289}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-73}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ (- x y) z))) (t_2 (* t (/ x (- z y)))))
   (if (<= y -1.62e-50)
     (* t (- 1.0 (/ x y)))
     (if (<= y -2.15e-98)
       t_1
       (if (<= y -1.3e-120)
         (- t (/ x (/ y t)))
         (if (<= y -9.5e-141)
           t_2
           (if (<= y -1.55e-142)
             t
             (if (<= y 9.5e-289)
               t_2
               (if (<= y 9e-232)
                 t_1
                 (if (<= y 4.8e-73) t_2 (- t (* t (/ x y)))))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t * (x / (z - y));
	double tmp;
	if (y <= -1.62e-50) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= -2.15e-98) {
		tmp = t_1;
	} else if (y <= -1.3e-120) {
		tmp = t - (x / (y / t));
	} else if (y <= -9.5e-141) {
		tmp = t_2;
	} else if (y <= -1.55e-142) {
		tmp = t;
	} else if (y <= 9.5e-289) {
		tmp = t_2;
	} else if (y <= 9e-232) {
		tmp = t_1;
	} else if (y <= 4.8e-73) {
		tmp = t_2;
	} else {
		tmp = t - (t * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * ((x - y) / z)
    t_2 = t * (x / (z - y))
    if (y <= (-1.62d-50)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= (-2.15d-98)) then
        tmp = t_1
    else if (y <= (-1.3d-120)) then
        tmp = t - (x / (y / t))
    else if (y <= (-9.5d-141)) then
        tmp = t_2
    else if (y <= (-1.55d-142)) then
        tmp = t
    else if (y <= 9.5d-289) then
        tmp = t_2
    else if (y <= 9d-232) then
        tmp = t_1
    else if (y <= 4.8d-73) then
        tmp = t_2
    else
        tmp = t - (t * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * ((x - y) / z);
	double t_2 = t * (x / (z - y));
	double tmp;
	if (y <= -1.62e-50) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= -2.15e-98) {
		tmp = t_1;
	} else if (y <= -1.3e-120) {
		tmp = t - (x / (y / t));
	} else if (y <= -9.5e-141) {
		tmp = t_2;
	} else if (y <= -1.55e-142) {
		tmp = t;
	} else if (y <= 9.5e-289) {
		tmp = t_2;
	} else if (y <= 9e-232) {
		tmp = t_1;
	} else if (y <= 4.8e-73) {
		tmp = t_2;
	} else {
		tmp = t - (t * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * ((x - y) / z)
	t_2 = t * (x / (z - y))
	tmp = 0
	if y <= -1.62e-50:
		tmp = t * (1.0 - (x / y))
	elif y <= -2.15e-98:
		tmp = t_1
	elif y <= -1.3e-120:
		tmp = t - (x / (y / t))
	elif y <= -9.5e-141:
		tmp = t_2
	elif y <= -1.55e-142:
		tmp = t
	elif y <= 9.5e-289:
		tmp = t_2
	elif y <= 9e-232:
		tmp = t_1
	elif y <= 4.8e-73:
		tmp = t_2
	else:
		tmp = t - (t * (x / y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(Float64(x - y) / z))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (y <= -1.62e-50)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= -2.15e-98)
		tmp = t_1;
	elseif (y <= -1.3e-120)
		tmp = Float64(t - Float64(x / Float64(y / t)));
	elseif (y <= -9.5e-141)
		tmp = t_2;
	elseif (y <= -1.55e-142)
		tmp = t;
	elseif (y <= 9.5e-289)
		tmp = t_2;
	elseif (y <= 9e-232)
		tmp = t_1;
	elseif (y <= 4.8e-73)
		tmp = t_2;
	else
		tmp = Float64(t - Float64(t * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * ((x - y) / z);
	t_2 = t * (x / (z - y));
	tmp = 0.0;
	if (y <= -1.62e-50)
		tmp = t * (1.0 - (x / y));
	elseif (y <= -2.15e-98)
		tmp = t_1;
	elseif (y <= -1.3e-120)
		tmp = t - (x / (y / t));
	elseif (y <= -9.5e-141)
		tmp = t_2;
	elseif (y <= -1.55e-142)
		tmp = t;
	elseif (y <= 9.5e-289)
		tmp = t_2;
	elseif (y <= 9e-232)
		tmp = t_1;
	elseif (y <= 4.8e-73)
		tmp = t_2;
	else
		tmp = t - (t * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.62e-50], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.15e-98], t$95$1, If[LessEqual[y, -1.3e-120], N[(t - N[(x / N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.5e-141], t$95$2, If[LessEqual[y, -1.55e-142], t, If[LessEqual[y, 9.5e-289], t$95$2, If[LessEqual[y, 9e-232], t$95$1, If[LessEqual[y, 4.8e-73], t$95$2, N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.6200000000000001e-50

   1. Initial program 98.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 78.6%

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

      2. associate-/l* 79.2%

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

   3. Simplified 79.2%

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

   5. Taylor expanded in y around inf 71.6%

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

      1. associate--l+ 71.6%

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

      2. distribute-lft-out-- 71.6%

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

      3. div-sub 71.6%

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

      4. mul-1-neg 71.6%

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

      5. unsub-neg 71.6%

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

      6. distribute-lft-out-- 71.7%

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

      7. associate-/l* 75.9%

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

   7. Simplified 75.9%

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

   8. Taylor expanded in x around inf 75.7%

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

   9. Taylor expanded in t around 0 75.7%

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

   if -1.6200000000000001e-50 < y < -2.14999999999999994e-98 or 9.4999999999999995e-289 < y < 8.99999999999999933e-232

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.9%

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

   if -2.14999999999999994e-98 < y < -1.3000000000000001e-120

   1. Initial program 68.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 99.5%

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

      2. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. distribute-lft-out-- 100.0%

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

      3. div-sub 100.0%

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

      4. mul-1-neg 100.0%

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

      5. unsub-neg 100.0%

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

      6. distribute-lft-out-- 100.0%

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

      7. associate-/l* 68.0%

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

   7. Simplified 68.0%

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

   8. Taylor expanded in x around inf 100.0%

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

      1. associate-/l* 68.0%

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

   10. Applied egg-rr 68.0%

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

       1. *-commutative 68.0%

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

       2. associate-/r/ 100.0%

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

   12. Simplified 100.0%

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

   if -1.3000000000000001e-120 < y < -9.49999999999999996e-141 or -1.55e-142 < y < 9.4999999999999995e-289 or 8.99999999999999933e-232 < y < 4.80000000000000011e-73

   1. Initial program 96.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 77.9%

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

   if -9.49999999999999996e-141 < y < -1.55e-142

   1. Initial program 100.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 53.8%

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

      2. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   if 4.80000000000000011e-73 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 80.3%

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

      2. associate-/l* 74.8%

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

   3. Simplified 74.8%

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

   5. Taylor expanded in y around inf 78.2%

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

      1. associate--l+ 78.2%

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

      2. distribute-lft-out-- 78.2%

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

      3. div-sub 78.2%

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

      4. mul-1-neg 78.2%

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

      5. unsub-neg 78.2%

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

      6. distribute-lft-out-- 79.8%

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

      7. associate-/l* 89.4%

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

   7. Simplified 89.4%

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

   8. Taylor expanded in x around inf 88.9%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-98}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-120}:\\ \;\;\;\;t - \frac{x}{\frac{y}{t}}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-141}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-142}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-289}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-232}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-73}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{z}{x}}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{-50}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-168}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-215}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-68}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-5} \lor \neg \left(y \leq 370000000000\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ z x))) (t_2 (* t (- 1.0 (/ x y)))))
   (if (<= y -4.1e-50)
     t_2
     (if (<= y -9.5e-141)
       t_1
       (if (<= y -8e-168)
         t_2
         (if (<= y -9.2e-215)
           (/ (* t x) z)
           (if (<= y 2.4e-68)
             t_1
             (if (or (<= y 2.65e-5) (not (<= y 370000000000.0)))
               t_2
               (* t (/ x z))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (z / x);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -4.1e-50) {
		tmp = t_2;
	} else if (y <= -9.5e-141) {
		tmp = t_1;
	} else if (y <= -8e-168) {
		tmp = t_2;
	} else if (y <= -9.2e-215) {
		tmp = (t * x) / z;
	} else if (y <= 2.4e-68) {
		tmp = t_1;
	} else if ((y <= 2.65e-5) || !(y <= 370000000000.0)) {
		tmp = t_2;
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (z / x)
    t_2 = t * (1.0d0 - (x / y))
    if (y <= (-4.1d-50)) then
        tmp = t_2
    else if (y <= (-9.5d-141)) then
        tmp = t_1
    else if (y <= (-8d-168)) then
        tmp = t_2
    else if (y <= (-9.2d-215)) then
        tmp = (t * x) / z
    else if (y <= 2.4d-68) then
        tmp = t_1
    else if ((y <= 2.65d-5) .or. (.not. (y <= 370000000000.0d0))) then
        tmp = t_2
    else
        tmp = t * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (z / x);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -4.1e-50) {
		tmp = t_2;
	} else if (y <= -9.5e-141) {
		tmp = t_1;
	} else if (y <= -8e-168) {
		tmp = t_2;
	} else if (y <= -9.2e-215) {
		tmp = (t * x) / z;
	} else if (y <= 2.4e-68) {
		tmp = t_1;
	} else if ((y <= 2.65e-5) || !(y <= 370000000000.0)) {
		tmp = t_2;
	} else {
		tmp = t * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (z / x)
	t_2 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -4.1e-50:
		tmp = t_2
	elif y <= -9.5e-141:
		tmp = t_1
	elif y <= -8e-168:
		tmp = t_2
	elif y <= -9.2e-215:
		tmp = (t * x) / z
	elif y <= 2.4e-68:
		tmp = t_1
	elif (y <= 2.65e-5) or not (y <= 370000000000.0):
		tmp = t_2
	else:
		tmp = t * (x / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(z / x))
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -4.1e-50)
		tmp = t_2;
	elseif (y <= -9.5e-141)
		tmp = t_1;
	elseif (y <= -8e-168)
		tmp = t_2;
	elseif (y <= -9.2e-215)
		tmp = Float64(Float64(t * x) / z);
	elseif (y <= 2.4e-68)
		tmp = t_1;
	elseif ((y <= 2.65e-5) || !(y <= 370000000000.0))
		tmp = t_2;
	else
		tmp = Float64(t * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (z / x);
	t_2 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -4.1e-50)
		tmp = t_2;
	elseif (y <= -9.5e-141)
		tmp = t_1;
	elseif (y <= -8e-168)
		tmp = t_2;
	elseif (y <= -9.2e-215)
		tmp = (t * x) / z;
	elseif (y <= 2.4e-68)
		tmp = t_1;
	elseif ((y <= 2.65e-5) || ~((y <= 370000000000.0)))
		tmp = t_2;
	else
		tmp = t * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e-50], t$95$2, If[LessEqual[y, -9.5e-141], t$95$1, If[LessEqual[y, -8e-168], t$95$2, If[LessEqual[y, -9.2e-215], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 2.4e-68], t$95$1, If[Or[LessEqual[y, 2.65e-5], N[Not[LessEqual[y, 370000000000.0]], $MachinePrecision]], t$95$2, N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.09999999999999985e-50 or -9.49999999999999996e-141 < y < -8.0000000000000004e-168 or 2.39999999999999991e-68 < y < 2.65e-5 or 3.7e11 < y

   1. Initial program 99.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 79.2%

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

      2. associate-/l* 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in y around inf 76.2%

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

      1. associate--l+ 76.2%

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

      2. distribute-lft-out-- 76.2%

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

      3. div-sub 76.2%

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

      4. mul-1-neg 76.2%

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

      5. unsub-neg 76.2%

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

      6. distribute-lft-out-- 76.2%

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

      7. associate-/l* 82.8%

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

   7. Simplified 82.8%

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

   8. Taylor expanded in x around inf 82.5%

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

   9. Taylor expanded in t around 0 82.5%

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

   if -4.09999999999999985e-50 < y < -9.49999999999999996e-141 or -9.1999999999999996e-215 < y < 2.39999999999999991e-68

   1. Initial program 96.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 88.8%

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

      2. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

      1. associate-*r/ 88.8%

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

      2. associate-*l/ 96.1%

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

      3. *-commutative 96.1%

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

      4. clear-num 96.1%

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

      5. un-div-inv 96.2%

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

   6. Applied egg-rr 96.2%

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

   7. Taylor expanded in y around 0 72.6%

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

   if -8.0000000000000004e-168 < y < -9.1999999999999996e-215

   1. Initial program 94.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 93.6%

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

      2. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in y around 0 76.0%

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

   if 2.65e-5 < y < 3.7e11

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 58.7%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-50}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-141}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-168}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-215}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-68}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-5} \lor \neg \left(y \leq 370000000000\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{t}{z}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{-53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-120}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-308}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-163}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ t z))) (t_2 (* t (- 1.0 (/ x y)))))
   (if (<= y -2e-53)
     t_2
     (if (<= y -2.4e-98)
       t_1
       (if (<= y -1.3e-120)
         t_2
         (if (<= y -2.4e-308)
           t_1
           (if (<= y 1.1e-163)
             (/ t (/ z x))
             (if (<= y 9.5e-123) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / z);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -2e-53) {
		tmp = t_2;
	} else if (y <= -2.4e-98) {
		tmp = t_1;
	} else if (y <= -1.3e-120) {
		tmp = t_2;
	} else if (y <= -2.4e-308) {
		tmp = t_1;
	} else if (y <= 1.1e-163) {
		tmp = t / (z / x);
	} else if (y <= 9.5e-123) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) * (t / z)
    t_2 = t * (1.0d0 - (x / y))
    if (y <= (-2d-53)) then
        tmp = t_2
    else if (y <= (-2.4d-98)) then
        tmp = t_1
    else if (y <= (-1.3d-120)) then
        tmp = t_2
    else if (y <= (-2.4d-308)) then
        tmp = t_1
    else if (y <= 1.1d-163) then
        tmp = t / (z / x)
    else if (y <= 9.5d-123) 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 t_1 = (x - y) * (t / z);
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -2e-53) {
		tmp = t_2;
	} else if (y <= -2.4e-98) {
		tmp = t_1;
	} else if (y <= -1.3e-120) {
		tmp = t_2;
	} else if (y <= -2.4e-308) {
		tmp = t_1;
	} else if (y <= 1.1e-163) {
		tmp = t / (z / x);
	} else if (y <= 9.5e-123) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) * (t / z)
	t_2 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -2e-53:
		tmp = t_2
	elif y <= -2.4e-98:
		tmp = t_1
	elif y <= -1.3e-120:
		tmp = t_2
	elif y <= -2.4e-308:
		tmp = t_1
	elif y <= 1.1e-163:
		tmp = t / (z / x)
	elif y <= 9.5e-123:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) * Float64(t / z))
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -2e-53)
		tmp = t_2;
	elseif (y <= -2.4e-98)
		tmp = t_1;
	elseif (y <= -1.3e-120)
		tmp = t_2;
	elseif (y <= -2.4e-308)
		tmp = t_1;
	elseif (y <= 1.1e-163)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 9.5e-123)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) * (t / z);
	t_2 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -2e-53)
		tmp = t_2;
	elseif (y <= -2.4e-98)
		tmp = t_1;
	elseif (y <= -1.3e-120)
		tmp = t_2;
	elseif (y <= -2.4e-308)
		tmp = t_1;
	elseif (y <= 1.1e-163)
		tmp = t / (z / x);
	elseif (y <= 9.5e-123)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e-53], t$95$2, If[LessEqual[y, -2.4e-98], t$95$1, If[LessEqual[y, -1.3e-120], t$95$2, If[LessEqual[y, -2.4e-308], t$95$1, If[LessEqual[y, 1.1e-163], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-123], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.00000000000000006e-53 or -2.40000000000000005e-98 < y < -1.3000000000000001e-120 or 9.5000000000000002e-123 < y

   1. Initial program 98.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 80.1%

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

      2. associate-/l* 78.2%

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

   3. Simplified 78.2%

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

   5. Taylor expanded in y around inf 72.9%

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

      1. associate--l+ 72.9%

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

      2. distribute-lft-out-- 72.9%

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

      3. div-sub 72.9%

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

      4. mul-1-neg 72.9%

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

      5. unsub-neg 72.9%

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

      6. distribute-lft-out-- 73.6%

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

      7. associate-/l* 79.2%

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

   7. Simplified 79.2%

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

   8. Taylor expanded in x around inf 78.8%

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

   9. Taylor expanded in t around 0 78.8%

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

   if -2.00000000000000006e-53 < y < -2.40000000000000005e-98 or -1.3000000000000001e-120 < y < -2.40000000000000008e-308 or 1.10000000000000005e-163 < y < 9.5000000000000002e-123

   1. Initial program 95.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 88.2%

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

      2. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in z around inf 69.5%

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

      1. *-commutative 69.5%

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

      2. associate-/l* 75.2%

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

   7. Simplified 75.2%

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

   if -2.40000000000000008e-308 < y < 1.10000000000000005e-163

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 91.5%

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

      2. associate-/l* 74.5%

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

   3. Simplified 74.5%

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

      1. associate-*r/ 91.5%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.7%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in y around 0 90.3%

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

Alternative 7: 87.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+184}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-307}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-234}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ t (- z y)))))
   (if (<= y -1.9e+184)
     (* t (- 1.0 (/ x y)))
     (if (<= y 9e-307)
       t_1
       (if (<= y 4.9e-234)
         (/ t (/ z (- x y)))
         (if (<= y 1.05e+17) t_1 (- t (* t (/ x y)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / (z - y));
	double tmp;
	if (y <= -1.9e+184) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 9e-307) {
		tmp = t_1;
	} else if (y <= 4.9e-234) {
		tmp = t / (z / (x - y));
	} else if (y <= 1.05e+17) {
		tmp = t_1;
	} else {
		tmp = t - (t * (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - y) * (t / (z - y))
    if (y <= (-1.9d+184)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= 9d-307) then
        tmp = t_1
    else if (y <= 4.9d-234) then
        tmp = t / (z / (x - y))
    else if (y <= 1.05d+17) then
        tmp = t_1
    else
        tmp = t - (t * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / (z - y));
	double tmp;
	if (y <= -1.9e+184) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 9e-307) {
		tmp = t_1;
	} else if (y <= 4.9e-234) {
		tmp = t / (z / (x - y));
	} else if (y <= 1.05e+17) {
		tmp = t_1;
	} else {
		tmp = t - (t * (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) * (t / (z - y))
	tmp = 0
	if y <= -1.9e+184:
		tmp = t * (1.0 - (x / y))
	elif y <= 9e-307:
		tmp = t_1
	elif y <= 4.9e-234:
		tmp = t / (z / (x - y))
	elif y <= 1.05e+17:
		tmp = t_1
	else:
		tmp = t - (t * (x / y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (y <= -1.9e+184)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= 9e-307)
		tmp = t_1;
	elseif (y <= 4.9e-234)
		tmp = Float64(t / Float64(z / Float64(x - y)));
	elseif (y <= 1.05e+17)
		tmp = t_1;
	else
		tmp = Float64(t - Float64(t * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) * (t / (z - y));
	tmp = 0.0;
	if (y <= -1.9e+184)
		tmp = t * (1.0 - (x / y));
	elseif (y <= 9e-307)
		tmp = t_1;
	elseif (y <= 4.9e-234)
		tmp = t / (z / (x - y));
	elseif (y <= 1.05e+17)
		tmp = t_1;
	else
		tmp = t - (t * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e+184], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-307], t$95$1, If[LessEqual[y, 4.9e-234], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+17], t$95$1, N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.9000000000000001e184

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 66.1%

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

      2. associate-/l* 61.0%

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

   3. Simplified 61.0%

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

   5. Taylor expanded in y around inf 81.1%

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

      1. associate--l+ 81.1%

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

      2. distribute-lft-out-- 81.1%

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

      3. div-sub 81.1%

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

      4. mul-1-neg 81.1%

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

      5. unsub-neg 81.1%

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

      6. distribute-lft-out-- 81.3%

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

      7. associate-/l* 90.4%

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

   7. Simplified 90.4%

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

   8. Taylor expanded in x around inf 90.9%

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

   9. Taylor expanded in t around 0 90.9%

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

   if -1.9000000000000001e184 < y < 8.99999999999999978e-307 or 4.90000000000000007e-234 < y < 1.05e17

   1. Initial program 96.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 88.5%

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

      2. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

   if 8.99999999999999978e-307 < y < 4.90000000000000007e-234

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 86.9%

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

      2. associate-/l* 73.2%

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

   3. Simplified 73.2%

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

      1. associate-*r/ 86.9%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.7%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around inf 99.9%

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

   if 1.05e17 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 76.5%

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

      2. associate-/l* 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in y around inf 83.1%

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

      1. associate--l+ 83.1%

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

      2. distribute-lft-out-- 83.1%

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

      3. div-sub 83.1%

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

      4. mul-1-neg 83.1%

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

      5. unsub-neg 83.1%

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

      6. distribute-lft-out-- 83.1%

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

      7. associate-/l* 95.4%

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

   7. Simplified 95.4%

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

   8. Taylor expanded in x around inf 94.7%

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

Alternative 8: 73.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-98}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-120} \lor \neg \left(y \leq 2.8 \cdot 10^{-101}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -2.5e-52)
     t_1
     (if (<= y -2e-98)
       (* (- x y) (/ t z))
       (if (or (<= y -1.3e-120) (not (<= y 2.8e-101)))
         t_1
         (* t (/ x (- z y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -2.5e-52) {
		tmp = t_1;
	} else if (y <= -2e-98) {
		tmp = (x - y) * (t / z);
	} else if ((y <= -1.3e-120) || !(y <= 2.8e-101)) {
		tmp = t_1;
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-2.5d-52)) then
        tmp = t_1
    else if (y <= (-2d-98)) then
        tmp = (x - y) * (t / z)
    else if ((y <= (-1.3d-120)) .or. (.not. (y <= 2.8d-101))) then
        tmp = t_1
    else
        tmp = t * (x / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -2.5e-52) {
		tmp = t_1;
	} else if (y <= -2e-98) {
		tmp = (x - y) * (t / z);
	} else if ((y <= -1.3e-120) || !(y <= 2.8e-101)) {
		tmp = t_1;
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -2.5e-52:
		tmp = t_1
	elif y <= -2e-98:
		tmp = (x - y) * (t / z)
	elif (y <= -1.3e-120) or not (y <= 2.8e-101):
		tmp = t_1
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -2.5e-52)
		tmp = t_1;
	elseif (y <= -2e-98)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif ((y <= -1.3e-120) || !(y <= 2.8e-101))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -2.5e-52)
		tmp = t_1;
	elseif (y <= -2e-98)
		tmp = (x - y) * (t / z);
	elseif ((y <= -1.3e-120) || ~((y <= 2.8e-101)))
		tmp = t_1;
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e-52], t$95$1, If[LessEqual[y, -2e-98], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.3e-120], N[Not[LessEqual[y, 2.8e-101]], $MachinePrecision]], t$95$1, N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5e-52 or -1.99999999999999988e-98 < y < -1.3000000000000001e-120 or 2.79999999999999989e-101 < y

   1. Initial program 98.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 79.5%

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

      2. associate-/l* 78.1%

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

   3. Simplified 78.1%

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

   5. Taylor expanded in y around inf 74.2%

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

      1. associate--l+ 74.2%

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

      2. distribute-lft-out-- 74.2%

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

      3. div-sub 74.2%

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

      4. mul-1-neg 74.2%

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

      5. unsub-neg 74.2%

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

      6. distribute-lft-out-- 74.9%

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

      7. associate-/l* 80.7%

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

   7. Simplified 80.7%

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

   8. Taylor expanded in x around inf 80.3%

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

   9. Taylor expanded in t around 0 80.3%

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

   if -2.5e-52 < y < -1.99999999999999988e-98

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 78.6%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 78.6%

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

      1. *-commutative 78.6%

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

      2. associate-/l* 99.7%

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

   7. Simplified 99.7%

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

   if -1.3000000000000001e-120 < y < 2.79999999999999989e-101

   1. Initial program 96.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 77.9%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-98}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-120} \lor \neg \left(y \leq 2.8 \cdot 10^{-101}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{z - y}{x}}\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 0.19:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+95}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ (- z y) x))))
   (if (<= x -1.6e+106)
     t_1
     (if (<= x 0.19)
       (/ t (- 1.0 (/ z y)))
       (if (<= x 5e+95) (- t (/ (* t x) y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / ((z - y) / x);
	double tmp;
	if (x <= -1.6e+106) {
		tmp = t_1;
	} else if (x <= 0.19) {
		tmp = t / (1.0 - (z / y));
	} else if (x <= 5e+95) {
		tmp = t - ((t * x) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / ((z - y) / x)
    if (x <= (-1.6d+106)) then
        tmp = t_1
    else if (x <= 0.19d0) then
        tmp = t / (1.0d0 - (z / y))
    else if (x <= 5d+95) then
        tmp = t - ((t * x) / 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 t_1 = t / ((z - y) / x);
	double tmp;
	if (x <= -1.6e+106) {
		tmp = t_1;
	} else if (x <= 0.19) {
		tmp = t / (1.0 - (z / y));
	} else if (x <= 5e+95) {
		tmp = t - ((t * x) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / ((z - y) / x)
	tmp = 0
	if x <= -1.6e+106:
		tmp = t_1
	elif x <= 0.19:
		tmp = t / (1.0 - (z / y))
	elif x <= 5e+95:
		tmp = t - ((t * x) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(Float64(z - y) / x))
	tmp = 0.0
	if (x <= -1.6e+106)
		tmp = t_1;
	elseif (x <= 0.19)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	elseif (x <= 5e+95)
		tmp = Float64(t - Float64(Float64(t * x) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / ((z - y) / x);
	tmp = 0.0;
	if (x <= -1.6e+106)
		tmp = t_1;
	elseif (x <= 0.19)
		tmp = t / (1.0 - (z / y));
	elseif (x <= 5e+95)
		tmp = t - ((t * x) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.6e+106], t$95$1, If[LessEqual[x, 0.19], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+95], N[(t - N[(N[(t * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.5999999999999999e106 or 5.00000000000000025e95 < x

   1. Initial program 97.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 76.6%

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

      2. associate-/l* 80.1%

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

   3. Simplified 80.1%

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

      1. associate-*r/ 76.6%

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

      2. associate-*l/ 97.6%

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

      3. *-commutative 97.6%

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

      4. clear-num 97.5%

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

      5. un-div-inv 97.9%

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

   6. Applied egg-rr 97.9%

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

   7. Taylor expanded in x around inf 83.1%

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

   if -1.5999999999999999e106 < x < 0.19

   1. Initial program 98.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 87.3%

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

      2. associate-/l* 84.2%

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

   3. Simplified 84.2%

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

      1. associate-*r/ 87.3%

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

      2. associate-*l/ 98.0%

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

      3. *-commutative 98.0%

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

      4. clear-num 98.0%

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

      5. un-div-inv 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in x around 0 81.1%

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

      1. mul-1-neg 81.1%

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

      2. neg-sub0 81.1%

         \[\leadsto \frac{t}{\color{blue}{0 - \frac{z - y}{y}}} \]

      3. div-sub 81.1%

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

      4. *-inverses 81.1%

         \[\leadsto \frac{t}{0 - \left(\frac{z}{y} - \color{blue}{1}\right)} \]

      5. associate-+l- 81.1%

         \[\leadsto \frac{t}{\color{blue}{\left(0 - \frac{z}{y}\right) + 1}} \]

      6. neg-sub0 81.1%

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

      7. neg-mul-1 81.1%

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

      8. +-commutative 81.1%

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

      9. neg-mul-1 81.1%

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

      10. unsub-neg 81.1%

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

   9. Simplified 81.1%

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

   if 0.19 < x < 5.00000000000000025e95

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 80.6%

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

      2. associate-/l* 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in y around inf 77.8%

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

      1. associate--l+ 77.8%

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

      2. distribute-lft-out-- 77.8%

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

      3. div-sub 78.0%

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

      4. mul-1-neg 78.0%

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

      5. unsub-neg 78.0%

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

      6. distribute-lft-out-- 78.0%

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

      7. associate-/l* 77.9%

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

   7. Simplified 77.9%

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

   8. Taylor expanded in x around inf 77.0%

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

Alternative 10: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.2:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+97}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x (- z y)))))
   (if (<= x -1.45e+106)
     t_1
     (if (<= x 2.2)
       (/ t (- 1.0 (/ z y)))
       (if (<= x 4.2e+97) (- t (/ (* t x) y)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / (z - y));
	double tmp;
	if (x <= -1.45e+106) {
		tmp = t_1;
	} else if (x <= 2.2) {
		tmp = t / (1.0 - (z / y));
	} else if (x <= 4.2e+97) {
		tmp = t - ((t * x) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (x / (z - y))
    if (x <= (-1.45d+106)) then
        tmp = t_1
    else if (x <= 2.2d0) then
        tmp = t / (1.0d0 - (z / y))
    else if (x <= 4.2d+97) then
        tmp = t - ((t * x) / 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 t_1 = t * (x / (z - y));
	double tmp;
	if (x <= -1.45e+106) {
		tmp = t_1;
	} else if (x <= 2.2) {
		tmp = t / (1.0 - (z / y));
	} else if (x <= 4.2e+97) {
		tmp = t - ((t * x) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / (z - y))
	tmp = 0
	if x <= -1.45e+106:
		tmp = t_1
	elif x <= 2.2:
		tmp = t / (1.0 - (z / y))
	elif x <= 4.2e+97:
		tmp = t - ((t * x) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (x <= -1.45e+106)
		tmp = t_1;
	elseif (x <= 2.2)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	elseif (x <= 4.2e+97)
		tmp = Float64(t - Float64(Float64(t * x) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / (z - y));
	tmp = 0.0;
	if (x <= -1.45e+106)
		tmp = t_1;
	elseif (x <= 2.2)
		tmp = t / (1.0 - (z / y));
	elseif (x <= 4.2e+97)
		tmp = t - ((t * x) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.45e+106], t$95$1, If[LessEqual[x, 2.2], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e+97], N[(t - N[(N[(t * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4500000000000001e106 or 4.20000000000000023e97 < x

   1. Initial program 97.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 82.7%

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

   if -1.4500000000000001e106 < x < 2.2000000000000002

   1. Initial program 98.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 87.3%

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

      2. associate-/l* 84.2%

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

   3. Simplified 84.2%

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

      1. associate-*r/ 87.3%

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

      2. associate-*l/ 98.0%

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

      3. *-commutative 98.0%

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

      4. clear-num 98.0%

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

      5. un-div-inv 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in x around 0 81.1%

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

      1. mul-1-neg 81.1%

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

      2. neg-sub0 81.1%

         \[\leadsto \frac{t}{\color{blue}{0 - \frac{z - y}{y}}} \]

      3. div-sub 81.1%

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

      4. *-inverses 81.1%

         \[\leadsto \frac{t}{0 - \left(\frac{z}{y} - \color{blue}{1}\right)} \]

      5. associate-+l- 81.1%

         \[\leadsto \frac{t}{\color{blue}{\left(0 - \frac{z}{y}\right) + 1}} \]

      6. neg-sub0 81.1%

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

      7. neg-mul-1 81.1%

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

      8. +-commutative 81.1%

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

      9. neg-mul-1 81.1%

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

      10. unsub-neg 81.1%

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

   9. Simplified 81.1%

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

   if 2.2000000000000002 < x < 4.20000000000000023e97

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 80.6%

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

      2. associate-/l* 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in y around inf 77.8%

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

      1. associate--l+ 77.8%

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

      2. distribute-lft-out-- 77.8%

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

      3. div-sub 78.0%

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

      4. mul-1-neg 78.0%

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

      5. unsub-neg 78.0%

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

      6. distribute-lft-out-- 78.0%

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

      7. associate-/l* 77.9%

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

   7. Simplified 77.9%

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

   8. Taylor expanded in x around inf 77.0%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+106}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq 2.2:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+97}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 61.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-49}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \frac{t}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.65e-49)
   t
   (if (<= y 1.55e+15) (/ t (/ z x)) (if (<= y 3.4e+58) (* x (/ t (- y))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e-49) {
		tmp = t;
	} else if (y <= 1.55e+15) {
		tmp = t / (z / x);
	} else if (y <= 3.4e+58) {
		tmp = x * (t / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.65d-49)) then
        tmp = t
    else if (y <= 1.55d+15) then
        tmp = t / (z / x)
    else if (y <= 3.4d+58) then
        tmp = x * (t / -y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e-49) {
		tmp = t;
	} else if (y <= 1.55e+15) {
		tmp = t / (z / x);
	} else if (y <= 3.4e+58) {
		tmp = x * (t / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.65e-49:
		tmp = t
	elif y <= 1.55e+15:
		tmp = t / (z / x)
	elif y <= 3.4e+58:
		tmp = x * (t / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.65e-49)
		tmp = t;
	elseif (y <= 1.55e+15)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 3.4e+58)
		tmp = Float64(x * Float64(t / Float64(-y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.65e-49)
		tmp = t;
	elseif (y <= 1.55e+15)
		tmp = t / (z / x);
	elseif (y <= 3.4e+58)
		tmp = x * (t / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.65e-49], t, If[LessEqual[y, 1.55e+15], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+58], N[(x * N[(t / (-y)), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.65e-49 or 3.4000000000000001e58 < y

   1. Initial program 99.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 77.6%

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

      2. associate-/l* 74.5%

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

   3. Simplified 74.5%

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

   5. Taylor expanded in y around inf 62.8%

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

   if -1.65e-49 < y < 1.55e15

   1. Initial program 96.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 89.9%

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

      2. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

      1. associate-*r/ 89.9%

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

      2. associate-*l/ 96.5%

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

      3. *-commutative 96.5%

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

      4. clear-num 96.4%

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

      5. un-div-inv 96.5%

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

   6. Applied egg-rr 96.5%

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

   7. Taylor expanded in y around 0 64.7%

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

   if 1.55e15 < y < 3.4000000000000001e58

   1. Initial program 99.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 84.0%

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

      2. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around inf 68.0%

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

      1. associate--l+ 68.0%

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

      2. distribute-lft-out-- 68.0%

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

      3. div-sub 68.0%

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

      4. mul-1-neg 68.0%

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

      5. unsub-neg 68.0%

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

      6. distribute-lft-out-- 68.0%

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

      7. associate-/l* 82.6%

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

   7. Simplified 82.6%

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

   8. Taylor expanded in x around inf 83.3%

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

   9. Taylor expanded in t around 0 83.3%

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

   10. Taylor expanded in x around inf 59.8%

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

       1. associate-*l/ 74.8%

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

       2. associate-*l* 74.8%

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

       3. *-commutative 74.8%

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

       4. mul-1-neg 74.8%

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

       5. distribute-neg-frac2 74.8%

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

   12. Simplified 74.8%

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

Alternative 12: 61.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-50}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1450000000000:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.8e-50)
   t
   (if (<= y 1450000000000.0)
     (/ t (/ z x))
     (if (<= y 1.42e+59) (* t (/ x (- y))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e-50) {
		tmp = t;
	} else if (y <= 1450000000000.0) {
		tmp = t / (z / x);
	} else if (y <= 1.42e+59) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.8d-50)) then
        tmp = t
    else if (y <= 1450000000000.0d0) then
        tmp = t / (z / x)
    else if (y <= 1.42d+59) then
        tmp = t * (x / -y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e-50) {
		tmp = t;
	} else if (y <= 1450000000000.0) {
		tmp = t / (z / x);
	} else if (y <= 1.42e+59) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.8e-50:
		tmp = t
	elif y <= 1450000000000.0:
		tmp = t / (z / x)
	elif y <= 1.42e+59:
		tmp = t * (x / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.8e-50)
		tmp = t;
	elseif (y <= 1450000000000.0)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 1.42e+59)
		tmp = Float64(t * Float64(x / Float64(-y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.8e-50)
		tmp = t;
	elseif (y <= 1450000000000.0)
		tmp = t / (z / x);
	elseif (y <= 1.42e+59)
		tmp = t * (x / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.8e-50], t, If[LessEqual[y, 1450000000000.0], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.42e+59], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.80000000000000016e-50 or 1.42000000000000005e59 < y

   1. Initial program 99.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 77.6%

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

      2. associate-/l* 74.5%

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

   3. Simplified 74.5%

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

   5. Taylor expanded in y around inf 62.8%

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

   if -5.80000000000000016e-50 < y < 1.45e12

   1. Initial program 96.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 89.9%

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

      2. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

      1. associate-*r/ 89.9%

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

      2. associate-*l/ 96.5%

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

      3. *-commutative 96.5%

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

      4. clear-num 96.4%

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

      5. un-div-inv 96.5%

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

   6. Applied egg-rr 96.5%

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

   7. Taylor expanded in y around 0 64.7%

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

   if 1.45e12 < y < 1.42000000000000005e59

   1. Initial program 99.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 84.0%

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

      2. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around inf 68.0%

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

      1. associate--l+ 68.0%

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

      2. distribute-lft-out-- 68.0%

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

      3. div-sub 68.0%

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

      4. mul-1-neg 68.0%

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

      5. unsub-neg 68.0%

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

      6. distribute-lft-out-- 68.0%

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

      7. associate-/l* 82.6%

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

   7. Simplified 82.6%

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

   8. Taylor expanded in x around inf 83.3%

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

   9. Taylor expanded in x around inf 59.8%

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

       1. mul-1-neg 59.8%

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

       2. associate-*r/ 74.8%

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

       3. distribute-rgt-neg-in 74.8%

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

       4. distribute-neg-frac2 74.8%

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

   11. Simplified 74.8%

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

Alternative 13: 49.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+22} \lor \neg \left(z \leq 2.5 \cdot 10^{+31}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3e+22) (not (<= z 2.5e+31))) (* t (/ x z)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3e+22) || !(z <= 2.5e+31)) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3d+22)) .or. (.not. (z <= 2.5d+31))) then
        tmp = t * (x / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3e+22) || !(z <= 2.5e+31)) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3e+22) or not (z <= 2.5e+31):
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3e+22) || !(z <= 2.5e+31))
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3e+22) || ~((z <= 2.5e+31)))
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3e+22], N[Not[LessEqual[z, 2.5e+31]], $MachinePrecision]], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -3e22 or 2.50000000000000013e31 < z

   1. Initial program 97.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 61.3%

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

   if -3e22 < z < 2.50000000000000013e31

   1. Initial program 98.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 82.9%

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

      2. associate-/l* 81.7%

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

   3. Simplified 81.7%

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

   5. Taylor expanded in y around inf 61.4%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+22} \lor \neg \left(z \leq 2.5 \cdot 10^{+31}\right):\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 47.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+26} \lor \neg \left(z \leq 1.32 \cdot 10^{+73}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9e+26) (not (<= z 1.32e+73))) (* x (/ t z)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9e+26) || !(z <= 1.32e+73)) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-9d+26)) .or. (.not. (z <= 1.32d+73))) then
        tmp = x * (t / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9e+26) || !(z <= 1.32e+73)) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9e+26) or not (z <= 1.32e+73):
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9e+26) || !(z <= 1.32e+73))
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9e+26) || ~((z <= 1.32e+73)))
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9e+26], N[Not[LessEqual[z, 1.32e+73]], $MachinePrecision]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999957e26 or 1.32e73 < z

   1. Initial program 97.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 83.5%

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

      2. associate-/l* 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in y around 0 56.7%

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

      1. *-commutative 56.7%

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

      2. associate-/l* 59.8%

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

   7. Simplified 59.8%

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

   if -8.99999999999999957e26 < z < 1.32e73

   1. Initial program 98.5%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 82.9%

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

      2. associate-/l* 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in y around inf 59.8%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+26} \lor \neg \left(z \leq 1.32 \cdot 10^{+73}\right):\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 58.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-49}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-124}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.65e-49) t (if (<= y 5.1e-124) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e-49) {
		tmp = t;
	} else if (y <= 5.1e-124) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.65d-49)) then
        tmp = t
    else if (y <= 5.1d-124) then
        tmp = t / (z / x)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e-49) {
		tmp = t;
	} else if (y <= 5.1e-124) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.65e-49:
		tmp = t
	elif y <= 5.1e-124:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.65e-49)
		tmp = t;
	elseif (y <= 5.1e-124)
		tmp = Float64(t / Float64(z / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.65e-49)
		tmp = t;
	elseif (y <= 5.1e-124)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.65e-49], t, If[LessEqual[y, 5.1e-124], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e-49 or 5.1000000000000001e-124 < y

   1. Initial program 98.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 79.9%

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

      2. associate-/l* 78.0%

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

   3. Simplified 78.0%

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

   5. Taylor expanded in y around inf 56.1%

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

   if -1.65e-49 < y < 5.1000000000000001e-124

   1. Initial program 96.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 89.3%

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

      2. associate-/l* 90.1%

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

   3. Simplified 90.1%

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

      1. associate-*r/ 89.3%

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

      2. associate-*l/ 96.6%

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

      3. *-commutative 96.6%

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

      4. clear-num 96.6%

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

      5. un-div-inv 96.7%

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

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in y around 0 70.2%

      \[\leadsto \frac{t}{\color{blue}{\frac{z}{x}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 96.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ t \cdot \frac{x - y}{z - y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing

3. Final simplification 98.0%

   \[\leadsto t \cdot \frac{x - y}{z - y} \]
4. Add Preprocessing

Alternative 17: 35.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.0%

   \[\frac{x - y}{z - y} \cdot t \]
2. Step-by-step derivation

   1. associate-*l/ 83.2%

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

   2. associate-/l* 82.2%

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

3. Simplified 82.2%

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

5. Taylor expanded in y around inf 42.0%

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

Developer target: 96.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{t}{\frac{z - y}{x - y}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024107 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (/ t (/ (- z y) (- x y)))

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