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

Percentage Accurate: 96.7% → 96.7%

Time: 10.4s

Alternatives: 21

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: 96.7% 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: 96.7% 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 96.1%

   \[\frac{x - y}{z - y} \cdot t \]
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* 82.6%

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

3. Simplified 82.6%

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

   1. associate-*r/ 83.5%

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

   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 96.0%

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

   5. un-div-inv 96.6%

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

6. Applied egg-rr 96.6%

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

7. Final simplification 96.6%

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

Alternative 2: 69.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+154}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-270}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ t y))))
   (if (<= y -2.2e+154)
     t
     (if (<= y -8.5e+44)
       t_1
       (if (<= y 5.5e-270)
         (* (- x y) (/ t z))
         (if (<= y 1.6e+75)
           (* t (/ x (- z y)))
           (if (<= y 6e+142)
             t_1
             (if (<= y 4.8e+148) (* t (/ (- x y) z)) t))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (t / y);
	double tmp;
	if (y <= -2.2e+154) {
		tmp = t;
	} else if (y <= -8.5e+44) {
		tmp = t_1;
	} else if (y <= 5.5e-270) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.6e+75) {
		tmp = t * (x / (z - y));
	} else if (y <= 6e+142) {
		tmp = t_1;
	} else if (y <= 4.8e+148) {
		tmp = t * ((x - y) / 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) :: t_1
    real(8) :: tmp
    t_1 = (y - x) * (t / y)
    if (y <= (-2.2d+154)) then
        tmp = t
    else if (y <= (-8.5d+44)) then
        tmp = t_1
    else if (y <= 5.5d-270) then
        tmp = (x - y) * (t / z)
    else if (y <= 1.6d+75) then
        tmp = t * (x / (z - y))
    else if (y <= 6d+142) then
        tmp = t_1
    else if (y <= 4.8d+148) then
        tmp = t * ((x - y) / z)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (t / y);
	double tmp;
	if (y <= -2.2e+154) {
		tmp = t;
	} else if (y <= -8.5e+44) {
		tmp = t_1;
	} else if (y <= 5.5e-270) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.6e+75) {
		tmp = t * (x / (z - y));
	} else if (y <= 6e+142) {
		tmp = t_1;
	} else if (y <= 4.8e+148) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (t / y)
	tmp = 0
	if y <= -2.2e+154:
		tmp = t
	elif y <= -8.5e+44:
		tmp = t_1
	elif y <= 5.5e-270:
		tmp = (x - y) * (t / z)
	elif y <= 1.6e+75:
		tmp = t * (x / (z - y))
	elif y <= 6e+142:
		tmp = t_1
	elif y <= 4.8e+148:
		tmp = t * ((x - y) / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(t / y))
	tmp = 0.0
	if (y <= -2.2e+154)
		tmp = t;
	elseif (y <= -8.5e+44)
		tmp = t_1;
	elseif (y <= 5.5e-270)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 1.6e+75)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= 6e+142)
		tmp = t_1;
	elseif (y <= 4.8e+148)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (t / y);
	tmp = 0.0;
	if (y <= -2.2e+154)
		tmp = t;
	elseif (y <= -8.5e+44)
		tmp = t_1;
	elseif (y <= 5.5e-270)
		tmp = (x - y) * (t / z);
	elseif (y <= 1.6e+75)
		tmp = t * (x / (z - y));
	elseif (y <= 6e+142)
		tmp = t_1;
	elseif (y <= 4.8e+148)
		tmp = t * ((x - y) / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.2e+154], t, If[LessEqual[y, -8.5e+44], t$95$1, If[LessEqual[y, 5.5e-270], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+75], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+142], t$95$1, If[LessEqual[y, 4.8e+148], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.2000000000000001e154 or 4.79999999999999989e148 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 63.2%

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

      2. associate-/l* 63.1%

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

   3. Simplified 63.1%

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

   5. Taylor expanded in y around inf 77.1%

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

   if -2.2000000000000001e154 < y < -8.5e44 or 1.59999999999999992e75 < y < 5.99999999999999949e142

   1. Initial program 99.8%

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

      1. associate-*l/ 84.7%

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

      2. associate-/l* 91.9%

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

   3. Simplified 91.9%

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

      1. associate-*r/ 84.7%

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

      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 99.8%

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

      5. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around 0 81.4%

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

      1. neg-mul-1 81.4%

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

      2. distribute-neg-frac2 81.4%

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

      3. neg-sub0 81.4%

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

      4. associate--r- 81.4%

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

      5. neg-sub0 81.4%

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

   9. Simplified 81.4%

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

   10. Taylor expanded in t around 0 68.7%

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

       1. *-commutative 68.7%

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

       2. associate-/l* 76.2%

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

   12. Simplified 76.2%

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

   if -8.5e44 < y < 5.4999999999999996e-270

   1. Initial program 90.2%

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

      1. associate-*l/ 92.1%

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

      2. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in z around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-/l* 79.0%

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

   7. Simplified 79.0%

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

   if 5.4999999999999996e-270 < y < 1.59999999999999992e75

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf 73.8%

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

   if 5.99999999999999949e142 < y < 4.79999999999999989e148

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 88.5%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+154}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+44}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-270}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+142}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+148}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+49}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-61}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-296}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.2e+49)
   t
   (if (<= y -6.2e-61)
     (* t (/ y (- z)))
     (if (<= y 7.6e-296)
       (/ (* t x) z)
       (if (<= y 1.6e+75)
         (* t (/ x z))
         (if (<= y 1.85e+118) (* t (/ x (- y))) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.2e+49) {
		tmp = t;
	} else if (y <= -6.2e-61) {
		tmp = t * (y / -z);
	} else if (y <= 7.6e-296) {
		tmp = (t * x) / z;
	} else if (y <= 1.6e+75) {
		tmp = t * (x / z);
	} else if (y <= 1.85e+118) {
		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 <= (-7.2d+49)) then
        tmp = t
    else if (y <= (-6.2d-61)) then
        tmp = t * (y / -z)
    else if (y <= 7.6d-296) then
        tmp = (t * x) / z
    else if (y <= 1.6d+75) then
        tmp = t * (x / z)
    else if (y <= 1.85d+118) 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 <= -7.2e+49) {
		tmp = t;
	} else if (y <= -6.2e-61) {
		tmp = t * (y / -z);
	} else if (y <= 7.6e-296) {
		tmp = (t * x) / z;
	} else if (y <= 1.6e+75) {
		tmp = t * (x / z);
	} else if (y <= 1.85e+118) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.2e+49:
		tmp = t
	elif y <= -6.2e-61:
		tmp = t * (y / -z)
	elif y <= 7.6e-296:
		tmp = (t * x) / z
	elif y <= 1.6e+75:
		tmp = t * (x / z)
	elif y <= 1.85e+118:
		tmp = t * (x / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.2e+49)
		tmp = t;
	elseif (y <= -6.2e-61)
		tmp = Float64(t * Float64(y / Float64(-z)));
	elseif (y <= 7.6e-296)
		tmp = Float64(Float64(t * x) / z);
	elseif (y <= 1.6e+75)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= 1.85e+118)
		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 <= -7.2e+49)
		tmp = t;
	elseif (y <= -6.2e-61)
		tmp = t * (y / -z);
	elseif (y <= 7.6e-296)
		tmp = (t * x) / z;
	elseif (y <= 1.6e+75)
		tmp = t * (x / z);
	elseif (y <= 1.85e+118)
		tmp = t * (x / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.2e+49], t, If[LessEqual[y, -6.2e-61], N[(t * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.6e-296], N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.6e+75], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+118], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.19999999999999993e49 or 1.84999999999999993e118 < y

   1. Initial program 99.7%

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

      1. associate-*l/ 68.6%

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

      2. associate-/l* 69.6%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in y around inf 67.1%

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

   if -7.19999999999999993e49 < y < -6.1999999999999999e-61

   1. Initial program 99.6%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in z around inf 70.8%

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

      1. *-commutative 70.8%

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

      2. associate-/l* 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in x around 0 50.3%

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

      1. mul-1-neg 50.3%

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

      2. associate-/l* 49.9%

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

      3. distribute-rgt-neg-in 49.9%

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

      4. distribute-frac-neg2 49.9%

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

   10. Simplified 49.9%

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

   if -6.1999999999999999e-61 < y < 7.6000000000000004e-296

   1. Initial program 89.7%

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

      1. associate-*l/ 93.7%

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

      2. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in y around 0 68.2%

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

   if 7.6000000000000004e-296 < y < 1.59999999999999992e75

   1. Initial program 94.9%

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

   3. Taylor expanded in y around 0 57.2%

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

   if 1.59999999999999992e75 < y < 1.84999999999999993e118

   1. Initial program 99.9%

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

      1. associate-*l/ 82.2%

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

      2. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in z around 0 75.1%

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

      1. associate-*r/ 75.1%

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

      2. mul-1-neg 75.1%

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

      3. distribute-lft-neg-out 75.1%

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

      4. *-commutative 75.1%

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

   7. Simplified 75.1%

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

   8. Taylor expanded in x around inf 57.8%

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

      1. associate-*r/ 57.8%

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

      2. mul-1-neg 57.8%

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

      3. distribute-rgt-neg-in 57.8%

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

   10. Simplified 57.8%

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

   11. Taylor expanded in t around 0 57.8%

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

       1. mul-1-neg 57.8%

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

       2. associate-*r/ 64.0%

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

       3. distribute-rgt-neg-in 64.0%

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

       4. distribute-neg-frac2 64.0%

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

   13. Simplified 64.0%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+49}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-61}:\\ \;\;\;\;t \cdot \frac{y}{-z}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-296}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+75}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+158}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+56}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y x) (/ t y))))
   (if (<= y -3.1e+158)
     t
     (if (<= y -7.6e+46)
       t_1
       (if (<= y 1.1e+56) (* (- x y) (/ t z)) (if (<= y 1.25e+127) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (t / y);
	double tmp;
	if (y <= -3.1e+158) {
		tmp = t;
	} else if (y <= -7.6e+46) {
		tmp = t_1;
	} else if (y <= 1.1e+56) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.25e+127) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (y - x) * (t / y)
    if (y <= (-3.1d+158)) then
        tmp = t
    else if (y <= (-7.6d+46)) then
        tmp = t_1
    else if (y <= 1.1d+56) then
        tmp = (x - y) * (t / z)
    else if (y <= 1.25d+127) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - x) * (t / y);
	double tmp;
	if (y <= -3.1e+158) {
		tmp = t;
	} else if (y <= -7.6e+46) {
		tmp = t_1;
	} else if (y <= 1.1e+56) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.25e+127) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - x) * (t / y)
	tmp = 0
	if y <= -3.1e+158:
		tmp = t
	elif y <= -7.6e+46:
		tmp = t_1
	elif y <= 1.1e+56:
		tmp = (x - y) * (t / z)
	elif y <= 1.25e+127:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - x) * Float64(t / y))
	tmp = 0.0
	if (y <= -3.1e+158)
		tmp = t;
	elseif (y <= -7.6e+46)
		tmp = t_1;
	elseif (y <= 1.1e+56)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 1.25e+127)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - x) * (t / y);
	tmp = 0.0;
	if (y <= -3.1e+158)
		tmp = t;
	elseif (y <= -7.6e+46)
		tmp = t_1;
	elseif (y <= 1.1e+56)
		tmp = (x - y) * (t / z);
	elseif (y <= 1.25e+127)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - x), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e+158], t, If[LessEqual[y, -7.6e+46], t$95$1, If[LessEqual[y, 1.1e+56], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+127], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1000000000000002e158 or 1.2500000000000001e127 < y

   1. Initial program 99.7%

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

      1. associate-*l/ 64.5%

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

      2. associate-/l* 63.1%

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

   3. Simplified 63.1%

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

   5. Taylor expanded in y around inf 74.8%

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

   if -3.1000000000000002e158 < y < -7.5999999999999998e46 or 1.10000000000000008e56 < y < 1.2500000000000001e127

   1. Initial program 99.8%

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

      1. associate-*l/ 86.1%

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

      2. associate-/l* 86.1%

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

   3. Simplified 86.1%

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

      1. associate-*r/ 86.1%

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

      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 99.8%

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

      5. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around 0 78.2%

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

      1. neg-mul-1 78.2%

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

      2. distribute-neg-frac2 78.2%

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

      3. neg-sub0 78.2%

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

      4. associate--r- 78.2%

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

      5. neg-sub0 78.2%

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

   9. Simplified 78.2%

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

   10. Taylor expanded in t around 0 66.7%

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

       1. *-commutative 66.7%

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

       2. associate-/l* 69.2%

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

   12. Simplified 69.2%

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

   if -7.5999999999999998e46 < y < 1.10000000000000008e56

   1. Initial program 93.3%

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

      1. associate-*l/ 91.8%

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

      2. associate-/l* 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in z around inf 73.2%

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

      1. *-commutative 73.2%

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

      2. associate-/l* 72.5%

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

   7. Simplified 72.5%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+158}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{+46}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+56}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+127}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.32 \cdot 10^{+157}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+45}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-270}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.32e+157)
   t
   (if (<= y -2.65e+45)
     (* (- y x) (/ t y))
     (if (<= y 7e-270)
       (* (- x y) (/ t z))
       (if (<= y 1.4e+121) (* t (/ x (- z y))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.32e+157) {
		tmp = t;
	} else if (y <= -2.65e+45) {
		tmp = (y - x) * (t / y);
	} else if (y <= 7e-270) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.4e+121) {
		tmp = t * (x / (z - 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 <= (-2.32d+157)) then
        tmp = t
    else if (y <= (-2.65d+45)) then
        tmp = (y - x) * (t / y)
    else if (y <= 7d-270) then
        tmp = (x - y) * (t / z)
    else if (y <= 1.4d+121) then
        tmp = t * (x / (z - 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 <= -2.32e+157) {
		tmp = t;
	} else if (y <= -2.65e+45) {
		tmp = (y - x) * (t / y);
	} else if (y <= 7e-270) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.4e+121) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.32e+157:
		tmp = t
	elif y <= -2.65e+45:
		tmp = (y - x) * (t / y)
	elif y <= 7e-270:
		tmp = (x - y) * (t / z)
	elif y <= 1.4e+121:
		tmp = t * (x / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.32e+157)
		tmp = t;
	elseif (y <= -2.65e+45)
		tmp = Float64(Float64(y - x) * Float64(t / y));
	elseif (y <= 7e-270)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 1.4e+121)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.32e+157)
		tmp = t;
	elseif (y <= -2.65e+45)
		tmp = (y - x) * (t / y);
	elseif (y <= 7e-270)
		tmp = (x - y) * (t / z);
	elseif (y <= 1.4e+121)
		tmp = t * (x / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.32e+157], t, If[LessEqual[y, -2.65e+45], N[(N[(y - x), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-270], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+121], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.32000000000000008e157 or 1.40000000000000003e121 < y

   1. Initial program 99.7%

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

      1. associate-*l/ 65.0%

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

      2. associate-/l* 63.6%

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

   3. Simplified 63.6%

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

   5. Taylor expanded in y around inf 74.4%

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

   if -2.32000000000000008e157 < y < -2.64999999999999996e45

   1. Initial program 99.8%

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

      1. associate-*l/ 84.3%

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

      2. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

      1. associate-*r/ 84.3%

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

      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 99.8%

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

      5. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around 0 73.3%

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

      1. neg-mul-1 73.3%

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

      2. distribute-neg-frac2 73.3%

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

      3. neg-sub0 73.3%

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

      4. associate--r- 73.3%

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

      5. neg-sub0 73.3%

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

   9. Simplified 73.3%

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

   10. Taylor expanded in t around 0 57.8%

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

       1. *-commutative 57.8%

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

       2. associate-/l* 68.2%

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

   12. Simplified 68.2%

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

   if -2.64999999999999996e45 < y < 6.99999999999999987e-270

   1. Initial program 90.2%

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

      1. associate-*l/ 92.1%

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

      2. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in z around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-/l* 79.0%

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

   7. Simplified 79.0%

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

   if 6.99999999999999987e-270 < y < 1.40000000000000003e121

   1. Initial program 97.7%

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

   3. Taylor expanded in x around inf 73.0%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.32 \cdot 10^{+157}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{+45}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-270}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{+152}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+44}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-271}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -1.75e+152)
     t_1
     (if (<= y -9.5e+44)
       (* (- y x) (/ t y))
       (if (<= y 1.4e-271)
         (* (- x y) (/ t z))
         (if (<= y 1.4e+98) (* t (/ x (- z y))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -1.75e+152) {
		tmp = t_1;
	} else if (y <= -9.5e+44) {
		tmp = (y - x) * (t / y);
	} else if (y <= 1.4e-271) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.4e+98) {
		tmp = t * (x / (z - 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 * (y / (y - z))
    if (y <= (-1.75d+152)) then
        tmp = t_1
    else if (y <= (-9.5d+44)) then
        tmp = (y - x) * (t / y)
    else if (y <= 1.4d-271) then
        tmp = (x - y) * (t / z)
    else if (y <= 1.4d+98) then
        tmp = t * (x / (z - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -1.75e+152) {
		tmp = t_1;
	} else if (y <= -9.5e+44) {
		tmp = (y - x) * (t / y);
	} else if (y <= 1.4e-271) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.4e+98) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -1.75e+152:
		tmp = t_1
	elif y <= -9.5e+44:
		tmp = (y - x) * (t / y)
	elif y <= 1.4e-271:
		tmp = (x - y) * (t / z)
	elif y <= 1.4e+98:
		tmp = t * (x / (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -1.75e+152)
		tmp = t_1;
	elseif (y <= -9.5e+44)
		tmp = Float64(Float64(y - x) * Float64(t / y));
	elseif (y <= 1.4e-271)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 1.4e+98)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -1.75e+152)
		tmp = t_1;
	elseif (y <= -9.5e+44)
		tmp = (y - x) * (t / y);
	elseif (y <= 1.4e-271)
		tmp = (x - y) * (t / z);
	elseif (y <= 1.4e+98)
		tmp = t * (x / (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.75e+152], t$95$1, If[LessEqual[y, -9.5e+44], N[(N[(y - x), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-271], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+98], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.74999999999999991e152 or 1.4e98 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 86.3%

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

      1. neg-mul-1 86.3%

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

      2. distribute-neg-frac2 86.3%

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

   5. Simplified 86.3%

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

   if -1.74999999999999991e152 < y < -9.5000000000000004e44

   1. Initial program 99.8%

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

      1. associate-*l/ 83.4%

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

      2. associate-/l* 88.7%

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

   3. Simplified 88.7%

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

      1. associate-*r/ 83.4%

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

      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 99.8%

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

      5. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around 0 77.5%

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

      1. neg-mul-1 77.5%

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

      2. distribute-neg-frac2 77.5%

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

      3. neg-sub0 77.5%

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

      4. associate--r- 77.5%

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

      5. neg-sub0 77.5%

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

   9. Simplified 77.5%

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

   10. Taylor expanded in t around 0 61.1%

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

       1. *-commutative 61.1%

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

       2. associate-/l* 72.1%

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

   12. Simplified 72.1%

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

   if -9.5000000000000004e44 < y < 1.3999999999999999e-271

   1. Initial program 90.2%

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

      1. associate-*l/ 92.1%

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

      2. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in z around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-/l* 79.0%

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

   7. Simplified 79.0%

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

   if 1.3999999999999999e-271 < y < 1.4e98

   1. Initial program 97.5%

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

   3. Taylor expanded in x around inf 74.9%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+152}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+44}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-271}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+152}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+46}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-269}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.75e+152)
   (* t (/ y (- y z)))
   (if (<= y -1.5e+46)
     (* (- y x) (/ t y))
     (if (<= y 1.02e-269)
       (* (- x y) (/ t z))
       (if (<= y 6.3e+98) (* t (/ x (- z y))) (/ t (/ (- y z) y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.75e+152) {
		tmp = t * (y / (y - z));
	} else if (y <= -1.5e+46) {
		tmp = (y - x) * (t / y);
	} else if (y <= 1.02e-269) {
		tmp = (x - y) * (t / z);
	} else if (y <= 6.3e+98) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t / ((y - 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) :: tmp
    if (y <= (-1.75d+152)) then
        tmp = t * (y / (y - z))
    else if (y <= (-1.5d+46)) then
        tmp = (y - x) * (t / y)
    else if (y <= 1.02d-269) then
        tmp = (x - y) * (t / z)
    else if (y <= 6.3d+98) then
        tmp = t * (x / (z - y))
    else
        tmp = t / ((y - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.75e+152) {
		tmp = t * (y / (y - z));
	} else if (y <= -1.5e+46) {
		tmp = (y - x) * (t / y);
	} else if (y <= 1.02e-269) {
		tmp = (x - y) * (t / z);
	} else if (y <= 6.3e+98) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t / ((y - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.75e+152:
		tmp = t * (y / (y - z))
	elif y <= -1.5e+46:
		tmp = (y - x) * (t / y)
	elif y <= 1.02e-269:
		tmp = (x - y) * (t / z)
	elif y <= 6.3e+98:
		tmp = t * (x / (z - y))
	else:
		tmp = t / ((y - z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.75e+152)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (y <= -1.5e+46)
		tmp = Float64(Float64(y - x) * Float64(t / y));
	elseif (y <= 1.02e-269)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 6.3e+98)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = Float64(t / Float64(Float64(y - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.75e+152)
		tmp = t * (y / (y - z));
	elseif (y <= -1.5e+46)
		tmp = (y - x) * (t / y);
	elseif (y <= 1.02e-269)
		tmp = (x - y) * (t / z);
	elseif (y <= 6.3e+98)
		tmp = t * (x / (z - y));
	else
		tmp = t / ((y - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.75e+152], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.5e+46], N[(N[(y - x), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e-269], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.3e+98], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.74999999999999991e152

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 89.7%

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

      1. neg-mul-1 89.7%

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

      2. distribute-neg-frac2 89.7%

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

   5. Simplified 89.7%

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

   if -1.74999999999999991e152 < y < -1.50000000000000012e46

   1. Initial program 99.8%

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

      1. associate-*l/ 83.4%

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

      2. associate-/l* 88.7%

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

   3. Simplified 88.7%

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

      1. associate-*r/ 83.4%

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

      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 99.8%

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

      5. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around 0 77.5%

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

      1. neg-mul-1 77.5%

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

      2. distribute-neg-frac2 77.5%

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

      3. neg-sub0 77.5%

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

      4. associate--r- 77.5%

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

      5. neg-sub0 77.5%

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

   9. Simplified 77.5%

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

   10. Taylor expanded in t around 0 61.1%

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

       1. *-commutative 61.1%

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

       2. associate-/l* 72.1%

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

   12. Simplified 72.1%

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

   if -1.50000000000000012e46 < y < 1.02000000000000002e-269

   1. Initial program 90.2%

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

      1. associate-*l/ 92.1%

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

      2. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in z around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-/l* 79.0%

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

   7. Simplified 79.0%

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

   if 1.02000000000000002e-269 < y < 6.29999999999999982e98

   1. Initial program 97.5%

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

   3. Taylor expanded in x around inf 74.9%

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

   if 6.29999999999999982e98 < y

   1. Initial program 99.6%

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

      1. associate-*l/ 75.8%

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

      2. associate-/l* 61.4%

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

   3. Simplified 61.4%

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

      1. associate-*r/ 75.8%

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

      2. associate-*l/ 99.6%

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

      3. *-commutative 99.6%

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

      4. clear-num 99.7%

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

      5. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 82.4%

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

      1. mul-1-neg 82.4%

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

   9. Simplified 82.4%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+152}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+46}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-269}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{+98}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+48}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+75}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.8e+48)
   t
   (if (<= y -1.02e-113)
     (* y (/ t (- z)))
     (if (<= y 1.6e+75)
       (/ t (/ z x))
       (if (<= y 5.5e+121) (* t (/ x (- y))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.8e+48) {
		tmp = t;
	} else if (y <= -1.02e-113) {
		tmp = y * (t / -z);
	} else if (y <= 1.6e+75) {
		tmp = t / (z / x);
	} else if (y <= 5.5e+121) {
		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 <= (-7.8d+48)) then
        tmp = t
    else if (y <= (-1.02d-113)) then
        tmp = y * (t / -z)
    else if (y <= 1.6d+75) then
        tmp = t / (z / x)
    else if (y <= 5.5d+121) 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 <= -7.8e+48) {
		tmp = t;
	} else if (y <= -1.02e-113) {
		tmp = y * (t / -z);
	} else if (y <= 1.6e+75) {
		tmp = t / (z / x);
	} else if (y <= 5.5e+121) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.8e+48:
		tmp = t
	elif y <= -1.02e-113:
		tmp = y * (t / -z)
	elif y <= 1.6e+75:
		tmp = t / (z / x)
	elif y <= 5.5e+121:
		tmp = t * (x / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.8e+48)
		tmp = t;
	elseif (y <= -1.02e-113)
		tmp = Float64(y * Float64(t / Float64(-z)));
	elseif (y <= 1.6e+75)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 5.5e+121)
		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 <= -7.8e+48)
		tmp = t;
	elseif (y <= -1.02e-113)
		tmp = y * (t / -z);
	elseif (y <= 1.6e+75)
		tmp = t / (z / x);
	elseif (y <= 5.5e+121)
		tmp = t * (x / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.8e+48], t, If[LessEqual[y, -1.02e-113], N[(y * N[(t / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+75], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+121], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.8000000000000002e48 or 5.4999999999999998e121 < y

   1. Initial program 99.7%

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

      1. associate-*l/ 68.6%

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

      2. associate-/l* 69.6%

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

   3. Simplified 69.6%

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

   5. Taylor expanded in y around inf 67.1%

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

   if -7.8000000000000002e48 < y < -1.02e-113

   1. Initial program 94.0%

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

      1. associate-*l/ 94.2%

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

      2. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in z around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. associate-/l* 73.2%

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

   7. Simplified 73.2%

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

      1. clear-num 71.5%

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

      2. un-div-inv 71.4%

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

   9. Applied egg-rr 71.4%

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

   10. Taylor expanded in x around 0 54.0%

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

       1. mul-1-neg 54.0%

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

       2. *-commutative 54.0%

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

       3. associate-*r/ 52.8%

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

       4. distribute-rgt-neg-in 52.8%

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

   12. Simplified 52.8%

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

   if -1.02e-113 < y < 1.59999999999999992e75

   1. Initial program 93.5%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 87.7%

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

   3. Simplified 87.7%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   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/ 93.5%

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

      3. *-commutative 93.5%

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

      4. clear-num 93.4%

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

      5. un-div-inv 94.6%

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

   6. Applied egg-rr 94.6%

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

   7. Taylor expanded in y around 0 62.1%

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

   if 1.59999999999999992e75 < y < 5.4999999999999998e121

   1. Initial program 99.9%

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

      1. associate-*l/ 82.2%

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

      2. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in z around 0 75.1%

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

      1. associate-*r/ 75.1%

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

      2. mul-1-neg 75.1%

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

      3. distribute-lft-neg-out 75.1%

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

      4. *-commutative 75.1%

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

   7. Simplified 75.1%

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

   8. Taylor expanded in x around inf 57.8%

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

      1. associate-*r/ 57.8%

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

      2. mul-1-neg 57.8%

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

      3. distribute-rgt-neg-in 57.8%

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

   10. Simplified 57.8%

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

   11. Taylor expanded in t around 0 57.8%

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

       1. mul-1-neg 57.8%

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

       2. associate-*r/ 64.0%

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

       3. distribute-rgt-neg-in 64.0%

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

       4. distribute-neg-frac2 64.0%

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

   13. Simplified 64.0%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+48}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \frac{t}{-z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+75}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+75}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.8e+45)
   t
   (if (<= y 1.6e+75) (/ t (/ z x)) (if (<= y 9.6e+117) (* t (/ x (- y))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.8e+45) {
		tmp = t;
	} else if (y <= 1.6e+75) {
		tmp = t / (z / x);
	} else if (y <= 9.6e+117) {
		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 <= (-1.8d+45)) then
        tmp = t
    else if (y <= 1.6d+75) then
        tmp = t / (z / x)
    else if (y <= 9.6d+117) 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 <= -1.8e+45) {
		tmp = t;
	} else if (y <= 1.6e+75) {
		tmp = t / (z / x);
	} else if (y <= 9.6e+117) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.8e+45:
		tmp = t
	elif y <= 1.6e+75:
		tmp = t / (z / x)
	elif y <= 9.6e+117:
		tmp = t * (x / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.8e+45)
		tmp = t;
	elseif (y <= 1.6e+75)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= 9.6e+117)
		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 <= -1.8e+45)
		tmp = t;
	elseif (y <= 1.6e+75)
		tmp = t / (z / x);
	elseif (y <= 9.6e+117)
		tmp = t * (x / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.8e+45], t, If[LessEqual[y, 1.6e+75], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.6e+117], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8e45 or 9.5999999999999996e117 < y

   1. Initial program 99.7%

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

      1. associate-*l/ 68.9%

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

      2. associate-/l* 68.9%

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

   3. Simplified 68.9%

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

   5. Taylor expanded in y around inf 66.4%

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

   if -1.8e45 < y < 1.59999999999999992e75

   1. Initial program 93.5%

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

      1. associate-*l/ 92.1%

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

      2. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

      1. associate-*r/ 92.1%

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

      2. associate-*l/ 93.5%

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

      3. *-commutative 93.5%

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

      4. clear-num 93.4%

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

      5. un-div-inv 94.4%

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

   6. Applied egg-rr 94.4%

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

   7. Taylor expanded in y around 0 57.8%

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

   if 1.59999999999999992e75 < y < 9.5999999999999996e117

   1. Initial program 99.9%

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

      1. associate-*l/ 82.2%

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

      2. associate-/l* 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in z around 0 75.1%

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

      1. associate-*r/ 75.1%

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

      2. mul-1-neg 75.1%

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

      3. distribute-lft-neg-out 75.1%

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

      4. *-commutative 75.1%

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

   7. Simplified 75.1%

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

   8. Taylor expanded in x around inf 57.8%

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

      1. associate-*r/ 57.8%

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

      2. mul-1-neg 57.8%

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

      3. distribute-rgt-neg-in 57.8%

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

   10. Simplified 57.8%

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

   11. Taylor expanded in t around 0 57.8%

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

       1. mul-1-neg 57.8%

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

       2. associate-*r/ 64.0%

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

       3. distribute-rgt-neg-in 64.0%

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

       4. distribute-neg-frac2 64.0%

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

   13. Simplified 64.0%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+75}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+117}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+46}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+73}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4e+46)
   t
   (if (<= y 5.5e+73)
     (* (- x y) (/ t z))
     (if (<= y 2e+118) (* t (/ x (- y))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e+46) {
		tmp = t;
	} else if (y <= 5.5e+73) {
		tmp = (x - y) * (t / z);
	} else if (y <= 2e+118) {
		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 <= (-4d+46)) then
        tmp = t
    else if (y <= 5.5d+73) then
        tmp = (x - y) * (t / z)
    else if (y <= 2d+118) 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 <= -4e+46) {
		tmp = t;
	} else if (y <= 5.5e+73) {
		tmp = (x - y) * (t / z);
	} else if (y <= 2e+118) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4e+46:
		tmp = t
	elif y <= 5.5e+73:
		tmp = (x - y) * (t / z)
	elif y <= 2e+118:
		tmp = t * (x / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4e+46)
		tmp = t;
	elseif (y <= 5.5e+73)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 2e+118)
		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 <= -4e+46)
		tmp = t;
	elseif (y <= 5.5e+73)
		tmp = (x - y) * (t / z);
	elseif (y <= 2e+118)
		tmp = t * (x / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4e+46], t, If[LessEqual[y, 5.5e+73], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e+118], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -4e46 or 1.99999999999999993e118 < y

   1. Initial program 99.7%

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

      1. associate-*l/ 68.9%

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

      2. associate-/l* 68.9%

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

   3. Simplified 68.9%

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

   5. Taylor expanded in y around inf 66.4%

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

   if -4e46 < y < 5.5000000000000003e73

   1. Initial program 93.4%

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

      1. associate-*l/ 92.0%

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

      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. Taylor expanded in z around inf 72.0%

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

      1. *-commutative 72.0%

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

      2. associate-/l* 71.3%

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

   7. Simplified 71.3%

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

   if 5.5000000000000003e73 < y < 1.99999999999999993e118

   1. Initial program 99.9%

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

      1. associate-*l/ 84.1%

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

      2. associate-/l* 84.0%

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

   3. Simplified 84.0%

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

   5. Taylor expanded in z around 0 72.4%

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

      1. associate-*r/ 72.4%

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

      2. mul-1-neg 72.4%

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

      3. distribute-lft-neg-out 72.4%

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

      4. *-commutative 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in x around inf 52.1%

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

      1. associate-*r/ 52.1%

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

      2. mul-1-neg 52.1%

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

      3. distribute-rgt-neg-in 52.1%

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

   10. Simplified 52.1%

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

   11. Taylor expanded in t around 0 52.1%

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

       1. mul-1-neg 52.1%

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

       2. associate-*r/ 57.6%

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

       3. distribute-rgt-neg-in 57.6%

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

       4. distribute-neg-frac2 57.6%

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

   13. Simplified 57.6%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+46}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+73}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+118}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-113}:\\ \;\;\;\;\frac{t \cdot y}{-z}\\ \mathbf{elif}\;y \leq 10^{+42}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.42e+50)
   t
   (if (<= y -1.02e-113) (/ (* t y) (- z)) (if (<= y 1e+42) (/ t (/ z x)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.42e+50) {
		tmp = t;
	} else if (y <= -1.02e-113) {
		tmp = (t * y) / -z;
	} else if (y <= 1e+42) {
		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 <= (-1.42d+50)) then
        tmp = t
    else if (y <= (-1.02d-113)) then
        tmp = (t * y) / -z
    else if (y <= 1d+42) 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 <= -1.42e+50) {
		tmp = t;
	} else if (y <= -1.02e-113) {
		tmp = (t * y) / -z;
	} else if (y <= 1e+42) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.42e+50:
		tmp = t
	elif y <= -1.02e-113:
		tmp = (t * y) / -z
	elif y <= 1e+42:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.42e+50)
		tmp = t;
	elseif (y <= -1.02e-113)
		tmp = Float64(Float64(t * y) / Float64(-z));
	elseif (y <= 1e+42)
		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 <= -1.42e+50)
		tmp = t;
	elseif (y <= -1.02e-113)
		tmp = (t * y) / -z;
	elseif (y <= 1e+42)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.42e+50], t, If[LessEqual[y, -1.02e-113], N[(N[(t * y), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[y, 1e+42], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.41999999999999994e50 or 1.00000000000000004e42 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 73.3%

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

      2. associate-/l* 71.5%

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

   3. Simplified 71.5%

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

   5. Taylor expanded in y around inf 59.2%

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

   if -1.41999999999999994e50 < y < -1.02e-113

   1. Initial program 94.0%

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

      1. associate-*l/ 94.2%

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

      2. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in z around inf 71.6%

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

      1. *-commutative 71.6%

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

      2. associate-/l* 73.2%

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

   7. Simplified 73.2%

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

      1. clear-num 71.5%

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

      2. un-div-inv 71.4%

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

   9. Applied egg-rr 71.4%

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

   10. Taylor expanded in x around 0 54.0%

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

       1. mul-1-neg 54.0%

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

       2. distribute-neg-frac2 54.0%

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

   12. Simplified 54.0%

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

   if -1.02e-113 < y < 1.00000000000000004e42

   1. Initial program 92.9%

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

      1. associate-*l/ 90.8%

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

      2. associate-/l* 90.8%

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

   3. Simplified 90.8%

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

      1. associate-*r/ 90.8%

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

      2. associate-*l/ 92.9%

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

      3. *-commutative 92.9%

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

      4. clear-num 92.8%

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

      5. un-div-inv 94.1%

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

   6. Applied egg-rr 94.1%

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

   7. Taylor expanded in y around 0 65.7%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+50}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-113}:\\ \;\;\;\;\frac{t \cdot y}{-z}\\ \mathbf{elif}\;y \leq 10^{+42}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 90.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+182}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+127}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.36e+182)
   (* t (/ y (- y z)))
   (if (<= y 1.5e+127) (* (- x y) (/ t (- z y))) (/ t (/ (- y z) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.36e+182) {
		tmp = t * (y / (y - z));
	} else if (y <= 1.5e+127) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t / ((y - 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) :: tmp
    if (y <= (-1.36d+182)) then
        tmp = t * (y / (y - z))
    else if (y <= 1.5d+127) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t / ((y - z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.36e+182) {
		tmp = t * (y / (y - z));
	} else if (y <= 1.5e+127) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t / ((y - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.36e+182:
		tmp = t * (y / (y - z))
	elif y <= 1.5e+127:
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t / ((y - z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.36e+182)
		tmp = Float64(t * Float64(y / Float64(y - z)));
	elseif (y <= 1.5e+127)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t / Float64(Float64(y - z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.36e+182)
		tmp = t * (y / (y - z));
	elseif (y <= 1.5e+127)
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t / ((y - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.36e+182], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+127], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.36000000000000012e182

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 93.6%

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

      1. neg-mul-1 93.6%

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

      2. distribute-neg-frac2 93.6%

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

   5. Simplified 93.6%

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

   if -1.36000000000000012e182 < y < 1.5000000000000001e127

   1. Initial program 94.8%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 89.1%

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

   3. Simplified 89.1%

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

   if 1.5000000000000001e127 < y

   1. Initial program 99.6%

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

      1. associate-*l/ 74.0%

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

      2. associate-/l* 53.5%

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

   3. Simplified 53.5%

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

      1. associate-*r/ 74.0%

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

      2. associate-*l/ 99.6%

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

      3. *-commutative 99.6%

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

      4. clear-num 99.7%

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

      5. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 87.3%

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

      1. mul-1-neg 87.3%

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

   9. Simplified 87.3%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+182}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+127}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 71.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-93} \lor \neg \left(z \leq 3.5 \cdot 10^{-21}\right):\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.6e-93) (not (<= z 3.5e-21)))
   (* t (/ (- x y) z))
   (- t (/ (* t x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-93) || !(z <= 3.5e-21)) {
		tmp = t * ((x - y) / z);
	} 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) :: tmp
    if ((z <= (-1.6d-93)) .or. (.not. (z <= 3.5d-21))) then
        tmp = t * ((x - y) / z)
    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 tmp;
	if ((z <= -1.6e-93) || !(z <= 3.5e-21)) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t - ((t * x) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.6e-93) or not (z <= 3.5e-21):
		tmp = t * ((x - y) / z)
	else:
		tmp = t - ((t * x) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.6e-93) || !(z <= 3.5e-21))
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = Float64(t - Float64(Float64(t * x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.6e-93) || ~((z <= 3.5e-21)))
		tmp = t * ((x - y) / z);
	else
		tmp = t - ((t * x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.6e-93], N[Not[LessEqual[z, 3.5e-21]], $MachinePrecision]], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(t - N[(N[(t * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.5999999999999999e-93 or 3.5000000000000003e-21 < z

   1. Initial program 97.1%

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

   3. Taylor expanded in z around inf 72.4%

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

   if -1.5999999999999999e-93 < z < 3.5000000000000003e-21

   1. Initial program 94.6%

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

      1. associate-*l/ 83.3%

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

      2. associate-/l* 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in z around 0 67.7%

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

      1. associate-*r/ 67.7%

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

      2. mul-1-neg 67.7%

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

      3. distribute-lft-neg-out 67.7%

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

      4. *-commutative 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in x around 0 76.5%

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

      1. mul-1-neg 76.5%

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

      2. unsub-neg 76.5%

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

   10. Simplified 76.5%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-93} \lor \neg \left(z \leq 3.5 \cdot 10^{-21}\right):\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 71.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-93}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-21}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e-93)
   (/ t (/ z (- x y)))
   (if (<= z 6.4e-21) (- t (/ (* t x) y)) (* t (/ (- x y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-93) {
		tmp = t / (z / (x - y));
	} else if (z <= 6.4e-21) {
		tmp = t - ((t * x) / y);
	} else {
		tmp = t * ((x - y) / 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) :: tmp
    if (z <= (-1.6d-93)) then
        tmp = t / (z / (x - y))
    else if (z <= 6.4d-21) then
        tmp = t - ((t * x) / y)
    else
        tmp = t * ((x - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-93) {
		tmp = t / (z / (x - y));
	} else if (z <= 6.4e-21) {
		tmp = t - ((t * x) / y);
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e-93:
		tmp = t / (z / (x - y))
	elif z <= 6.4e-21:
		tmp = t - ((t * x) / y)
	else:
		tmp = t * ((x - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e-93)
		tmp = Float64(t / Float64(z / Float64(x - y)));
	elseif (z <= 6.4e-21)
		tmp = Float64(t - Float64(Float64(t * x) / y));
	else
		tmp = Float64(t * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.6e-93)
		tmp = t / (z / (x - y));
	elseif (z <= 6.4e-21)
		tmp = t - ((t * x) / y);
	else
		tmp = t * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e-93], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.4e-21], N[(t - N[(N[(t * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5999999999999999e-93

   1. Initial program 97.3%

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

      1. associate-*l/ 84.5%

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

      2. associate-/l* 84.6%

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

   3. Simplified 84.6%

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

      1. associate-*r/ 84.5%

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

      2. associate-*l/ 97.3%

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

      3. *-commutative 97.3%

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

      4. clear-num 97.2%

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

      5. un-div-inv 97.3%

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

   6. Applied egg-rr 97.3%

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

   7. Taylor expanded in z around inf 71.4%

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

   if -1.5999999999999999e-93 < z < 6.4000000000000003e-21

   1. Initial program 94.6%

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

      1. associate-*l/ 83.3%

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

      2. associate-/l* 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in z around 0 67.7%

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

      1. associate-*r/ 67.7%

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

      2. mul-1-neg 67.7%

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

      3. distribute-lft-neg-out 67.7%

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

      4. *-commutative 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in x around 0 76.5%

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

      1. mul-1-neg 76.5%

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

      2. unsub-neg 76.5%

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

   10. Simplified 76.5%

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

   if 6.4000000000000003e-21 < z

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf 73.8%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-93}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-21}:\\ \;\;\;\;t - \frac{t \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-93}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-20}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e-93)
   (/ t (/ z (- x y)))
   (if (<= z 1.06e-20) (/ t (/ y (- y x))) (* t (/ (- x y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-93) {
		tmp = t / (z / (x - y));
	} else if (z <= 1.06e-20) {
		tmp = t / (y / (y - x));
	} else {
		tmp = t * ((x - y) / 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) :: tmp
    if (z <= (-1.6d-93)) then
        tmp = t / (z / (x - y))
    else if (z <= 1.06d-20) then
        tmp = t / (y / (y - x))
    else
        tmp = t * ((x - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e-93) {
		tmp = t / (z / (x - y));
	} else if (z <= 1.06e-20) {
		tmp = t / (y / (y - x));
	} else {
		tmp = t * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e-93:
		tmp = t / (z / (x - y))
	elif z <= 1.06e-20:
		tmp = t / (y / (y - x))
	else:
		tmp = t * ((x - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e-93)
		tmp = Float64(t / Float64(z / Float64(x - y)));
	elseif (z <= 1.06e-20)
		tmp = Float64(t / Float64(y / Float64(y - x)));
	else
		tmp = Float64(t * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.6e-93)
		tmp = t / (z / (x - y));
	elseif (z <= 1.06e-20)
		tmp = t / (y / (y - x));
	else
		tmp = t * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.6e-93], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.06e-20], N[(t / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5999999999999999e-93

   1. Initial program 97.3%

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

      1. associate-*l/ 84.5%

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

      2. associate-/l* 84.6%

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

   3. Simplified 84.6%

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

      1. associate-*r/ 84.5%

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

      2. associate-*l/ 97.3%

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

      3. *-commutative 97.3%

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

      4. clear-num 97.2%

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

      5. un-div-inv 97.3%

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

   6. Applied egg-rr 97.3%

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

   7. Taylor expanded in z around inf 71.4%

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

   if -1.5999999999999999e-93 < z < 1.06e-20

   1. Initial program 94.6%

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

      1. associate-*l/ 83.3%

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

      2. associate-/l* 81.9%

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

   3. Simplified 81.9%

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

      1. associate-*r/ 83.3%

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

      2. associate-*l/ 94.6%

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

      3. *-commutative 94.6%

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

      4. clear-num 94.7%

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

      5. un-div-inv 95.9%

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

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in z around 0 80.0%

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

      1. neg-mul-1 80.0%

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

      2. distribute-neg-frac2 80.0%

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

      3. neg-sub0 80.0%

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

      4. associate--r- 80.0%

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

      5. neg-sub0 80.0%

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

   9. Simplified 80.0%

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

   if 1.06e-20 < z

   1. Initial program 96.9%

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

   3. Taylor expanded in z around inf 73.8%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-93}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-20}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 60.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.24 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.24e+45) t (if (<= y 1.35e+42) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.24e+45) {
		tmp = t;
	} else if (y <= 1.35e+42) {
		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 (y <= (-1.24d+45)) then
        tmp = t
    else if (y <= 1.35d+42) 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 (y <= -1.24e+45) {
		tmp = t;
	} else if (y <= 1.35e+42) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.24e+45:
		tmp = t
	elif y <= 1.35e+42:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.24e+45)
		tmp = t;
	elseif (y <= 1.35e+42)
		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 (y <= -1.24e+45)
		tmp = t;
	elseif (y <= 1.35e+42)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.24e+45], t, If[LessEqual[y, 1.35e+42], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.23999999999999998e45 or 1.35e42 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 73.5%

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

      2. associate-/l* 71.0%

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

   3. Simplified 71.0%

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

   5. Taylor expanded in y around inf 58.7%

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

   if -1.23999999999999998e45 < y < 1.35e42

   1. Initial program 93.1%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in y around 0 57.4%

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

      1. *-commutative 57.4%

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

      2. associate-/l* 57.8%

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

   7. Simplified 57.8%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.24 \cdot 10^{+45}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+42}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 62.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+46}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.3e+46) t (if (<= y 8e+41) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e+46) {
		tmp = t;
	} else if (y <= 8e+41) {
		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 (y <= (-3.3d+46)) then
        tmp = t
    else if (y <= 8d+41) 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 (y <= -3.3e+46) {
		tmp = t;
	} else if (y <= 8e+41) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.3e+46:
		tmp = t
	elif y <= 8e+41:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.3e+46)
		tmp = t;
	elseif (y <= 8e+41)
		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 (y <= -3.3e+46)
		tmp = t;
	elseif (y <= 8e+41)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.3e+46], t, If[LessEqual[y, 8e+41], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2999999999999998e46 or 8.00000000000000005e41 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 73.5%

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

      2. associate-/l* 71.0%

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

   3. Simplified 71.0%

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

   5. Taylor expanded in y around inf 58.7%

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

   if -3.2999999999999998e46 < y < 8.00000000000000005e41

   1. Initial program 93.1%

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

   3. Taylor expanded in y around 0 59.3%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+46}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+41}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 62.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+46}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+41}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.8e+46) t (if (<= y 2.1e+41) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.8e+46) {
		tmp = t;
	} else if (y <= 2.1e+41) {
		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 <= (-3.8d+46)) then
        tmp = t
    else if (y <= 2.1d+41) 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 <= -3.8e+46) {
		tmp = t;
	} else if (y <= 2.1e+41) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.8e+46:
		tmp = t
	elif y <= 2.1e+41:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.8e+46)
		tmp = t;
	elseif (y <= 2.1e+41)
		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 <= -3.8e+46)
		tmp = t;
	elseif (y <= 2.1e+41)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.8e+46], t, If[LessEqual[y, 2.1e+41], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7999999999999999e46 or 2.1e41 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 73.5%

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

      2. associate-/l* 71.0%

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

   3. Simplified 71.0%

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

   5. Taylor expanded in y around inf 58.7%

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

   if -3.7999999999999999e46 < y < 2.1e41

   1. Initial program 93.1%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 92.0%

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

   3. Simplified 92.0%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
   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/ 93.1%

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

      3. *-commutative 93.1%

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

      4. clear-num 93.0%

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

      5. un-div-inv 94.0%

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

   6. Applied egg-rr 94.0%

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

   7. Taylor expanded in y around 0 60.3%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+46}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+41}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 35.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+210}:\\ \;\;\;\;x \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= x -3e+210) (* x (/ t y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3e+210) {
		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 (x <= (-3d+210)) 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 (x <= -3e+210) {
		tmp = x * (t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3e+210:
		tmp = x * (t / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3e+210)
		tmp = Float64(x * Float64(t / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3e+210)
		tmp = x * (t / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3e+210], N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if x < -3.00000000000000022e210

   1. Initial program 99.7%

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

      1. associate-*l/ 83.3%

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

      2. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in z around 0 40.3%

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

      1. associate-*r/ 40.3%

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

      2. mul-1-neg 40.3%

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

      3. distribute-lft-neg-out 40.3%

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

      4. *-commutative 40.3%

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

   7. Simplified 40.3%

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

   8. Taylor expanded in x around inf 40.3%

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

      1. associate-*r/ 40.3%

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

      2. mul-1-neg 40.3%

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

      3. distribute-rgt-neg-in 40.3%

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

   10. Simplified 40.3%

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

       1. *-commutative 40.3%

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

       2. associate-/l* 40.6%

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

       3. add-sqr-sqrt 40.3%

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

       4. sqrt-unprod 10.7%

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

       5. sqr-neg 10.7%

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

       6. sqrt-unprod 0.0%

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

       7. add-sqr-sqrt 23.3%

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

   12. Applied egg-rr 23.3%

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

   if -3.00000000000000022e210 < x

   1. Initial program 95.7%

      \[\frac{x - y}{z - y} \cdot t \]
   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* 81.8%

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

   3. Simplified 81.8%

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

   5. Taylor expanded in y around inf 35.1%

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

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+210}:\\ \;\;\;\;x \cdot \frac{t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 96.7% 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 96.1%

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

3. Final simplification 96.1%

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

Alternative 21: 35.2% 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 96.1%

   \[\frac{x - y}{z - y} \cdot t \]
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* 82.6%

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

3. Simplified 82.6%

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

5. Taylor expanded in y around inf 32.3%

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

6. Final simplification 32.3%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 96.7% 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 2024077 
(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))