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

Percentage Accurate: 97.0% → 97.0%

Time: 10.5s

Alternatives: 13

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: 97.0% 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: 97.0% 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]

Derivation

1. Initial program 97.7%

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

3. Final simplification 97.7%

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

Alternative 2: 59.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2400000000000:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 14200000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.85e+112)
   t
   (if (<= y -2400000000000.0)
     (* t (/ x z))
     (if (<= y -2.1e-14)
       t
       (if (<= y 14200000.0)
         (* x (/ t z))
         (if (<= y 6.8e+85) (* t (/ x (- y))) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.85e+112) {
		tmp = t;
	} else if (y <= -2400000000000.0) {
		tmp = t * (x / z);
	} else if (y <= -2.1e-14) {
		tmp = t;
	} else if (y <= 14200000.0) {
		tmp = x * (t / z);
	} else if (y <= 6.8e+85) {
		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 <= (-1.85d+112)) then
        tmp = t
    else if (y <= (-2400000000000.0d0)) then
        tmp = t * (x / z)
    else if (y <= (-2.1d-14)) then
        tmp = t
    else if (y <= 14200000.0d0) then
        tmp = x * (t / z)
    else if (y <= 6.8d+85) 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 <= -1.85e+112) {
		tmp = t;
	} else if (y <= -2400000000000.0) {
		tmp = t * (x / z);
	} else if (y <= -2.1e-14) {
		tmp = t;
	} else if (y <= 14200000.0) {
		tmp = x * (t / z);
	} else if (y <= 6.8e+85) {
		tmp = t * (x / -y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.85e+112:
		tmp = t
	elif y <= -2400000000000.0:
		tmp = t * (x / z)
	elif y <= -2.1e-14:
		tmp = t
	elif y <= 14200000.0:
		tmp = x * (t / z)
	elif y <= 6.8e+85:
		tmp = t * (x / -y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.85e+112)
		tmp = t;
	elseif (y <= -2400000000000.0)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= -2.1e-14)
		tmp = t;
	elseif (y <= 14200000.0)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= 6.8e+85)
		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 <= -1.85e+112)
		tmp = t;
	elseif (y <= -2400000000000.0)
		tmp = t * (x / z);
	elseif (y <= -2.1e-14)
		tmp = t;
	elseif (y <= 14200000.0)
		tmp = x * (t / z);
	elseif (y <= 6.8e+85)
		tmp = t * (x / -y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.85e+112], t, If[LessEqual[y, -2400000000000.0], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.1e-14], t, If[LessEqual[y, 14200000.0], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e+85], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.85000000000000002e112 or -2.4e12 < y < -2.0999999999999999e-14 or 6.8000000000000007e85 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 73.2%

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

      2. associate-/l* 73.2%

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

   3. Simplified 73.2%

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

   5. Taylor expanded in y around inf 68.9%

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

   if -1.85000000000000002e112 < y < -2.4e12

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 49.2%

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

   if -2.0999999999999999e-14 < y < 1.42e7

   1. Initial program 95.7%

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

      1. associate-*l/ 90.5%

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

      2. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around 0 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-/l* 65.8%

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

   7. Simplified 65.8%

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

   if 1.42e7 < y < 6.8000000000000007e85

   1. Initial program 99.5%

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

   3. Taylor expanded in z around 0 76.5%

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

      1. mul-1-neg 76.5%

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

      2. div-sub 76.5%

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

      3. sub-neg 76.5%

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

      4. *-inverses 76.5%

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

      5. metadata-eval 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in x around inf 55.0%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2400000000000:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 14200000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2100000000000:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-16}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1000000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+85}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.85e+112)
   t
   (if (<= y -2100000000000.0)
     (* t (/ x z))
     (if (<= y -8e-16)
       t
       (if (<= y 1000000.0)
         (* x (/ t z))
         (if (<= y 8.2e+85) (/ t (/ y (- x))) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.85e+112) {
		tmp = t;
	} else if (y <= -2100000000000.0) {
		tmp = t * (x / z);
	} else if (y <= -8e-16) {
		tmp = t;
	} else if (y <= 1000000.0) {
		tmp = x * (t / z);
	} else if (y <= 8.2e+85) {
		tmp = t / (y / -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 <= (-1.85d+112)) then
        tmp = t
    else if (y <= (-2100000000000.0d0)) then
        tmp = t * (x / z)
    else if (y <= (-8d-16)) then
        tmp = t
    else if (y <= 1000000.0d0) then
        tmp = x * (t / z)
    else if (y <= 8.2d+85) then
        tmp = t / (y / -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 <= -1.85e+112) {
		tmp = t;
	} else if (y <= -2100000000000.0) {
		tmp = t * (x / z);
	} else if (y <= -8e-16) {
		tmp = t;
	} else if (y <= 1000000.0) {
		tmp = x * (t / z);
	} else if (y <= 8.2e+85) {
		tmp = t / (y / -x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.85e+112:
		tmp = t
	elif y <= -2100000000000.0:
		tmp = t * (x / z)
	elif y <= -8e-16:
		tmp = t
	elif y <= 1000000.0:
		tmp = x * (t / z)
	elif y <= 8.2e+85:
		tmp = t / (y / -x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.85e+112)
		tmp = t;
	elseif (y <= -2100000000000.0)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= -8e-16)
		tmp = t;
	elseif (y <= 1000000.0)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= 8.2e+85)
		tmp = Float64(t / Float64(y / Float64(-x)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.85e+112)
		tmp = t;
	elseif (y <= -2100000000000.0)
		tmp = t * (x / z);
	elseif (y <= -8e-16)
		tmp = t;
	elseif (y <= 1000000.0)
		tmp = x * (t / z);
	elseif (y <= 8.2e+85)
		tmp = t / (y / -x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.85e+112], t, If[LessEqual[y, -2100000000000.0], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8e-16], t, If[LessEqual[y, 1000000.0], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e+85], N[(t / N[(y / (-x)), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.85000000000000002e112 or -2.1e12 < y < -7.9999999999999998e-16 or 8.19999999999999957e85 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 73.2%

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

      2. associate-/l* 73.2%

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

   3. Simplified 73.2%

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

   5. Taylor expanded in y around inf 68.9%

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

   if -1.85000000000000002e112 < y < -2.1e12

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 49.2%

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

   if -7.9999999999999998e-16 < y < 1e6

   1. Initial program 95.7%

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

      1. associate-*l/ 90.5%

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

      2. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around 0 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-/l* 65.8%

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

   7. Simplified 65.8%

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

   if 1e6 < y < 8.19999999999999957e85

   1. Initial program 99.5%

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

      1. associate-*l/ 89.8%

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

      2. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

      1. associate-*r/ 89.8%

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

      2. associate-*l/ 99.5%

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

      3. *-commutative 99.5%

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

      4. clear-num 99.5%

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

      5. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 65.5%

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

   8. Taylor expanded in z around 0 55.1%

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

      1. neg-mul-1 55.1%

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

      2. distribute-neg-frac2 55.1%

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

   10. Simplified 55.1%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2100000000000:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-16}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1000000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+85}:\\ \;\;\;\;\frac{t}{\frac{y}{-x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2200000000000:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-12} \lor \neg \left(y \leq 1250000\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -1.85e+112)
     t_1
     (if (<= y -2200000000000.0)
       (* t (/ x (- z y)))
       (if (or (<= y -3.6e-12) (not (<= y 1250000.0)))
         t_1
         (* (- x y) (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.85e+112) {
		tmp = t_1;
	} else if (y <= -2200000000000.0) {
		tmp = t * (x / (z - y));
	} else if ((y <= -3.6e-12) || !(y <= 1250000.0)) {
		tmp = t_1;
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-1.85d+112)) then
        tmp = t_1
    else if (y <= (-2200000000000.0d0)) then
        tmp = t * (x / (z - y))
    else if ((y <= (-3.6d-12)) .or. (.not. (y <= 1250000.0d0))) then
        tmp = t_1
    else
        tmp = (x - y) * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.85e+112) {
		tmp = t_1;
	} else if (y <= -2200000000000.0) {
		tmp = t * (x / (z - y));
	} else if ((y <= -3.6e-12) || !(y <= 1250000.0)) {
		tmp = t_1;
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -1.85e+112:
		tmp = t_1
	elif y <= -2200000000000.0:
		tmp = t * (x / (z - y))
	elif (y <= -3.6e-12) or not (y <= 1250000.0):
		tmp = t_1
	else:
		tmp = (x - y) * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -1.85e+112)
		tmp = t_1;
	elseif (y <= -2200000000000.0)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif ((y <= -3.6e-12) || !(y <= 1250000.0))
		tmp = t_1;
	else
		tmp = Float64(Float64(x - y) * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -1.85e+112)
		tmp = t_1;
	elseif (y <= -2200000000000.0)
		tmp = t * (x / (z - y));
	elseif ((y <= -3.6e-12) || ~((y <= 1250000.0)))
		tmp = t_1;
	else
		tmp = (x - y) * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e+112], t$95$1, If[LessEqual[y, -2200000000000.0], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3.6e-12], N[Not[LessEqual[y, 1250000.0]], $MachinePrecision]], t$95$1, N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.85000000000000002e112 or -2.2e12 < y < -3.6e-12 or 1.25e6 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 75.6%

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

      2. associate-/l* 76.9%

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

   3. Simplified 76.9%

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

      1. associate-*r/ 75.6%

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

      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 68.1%

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

      1. mul-1-neg 68.1%

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

      2. associate-/l* 88.9%

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

      3. div-sub 88.9%

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

      4. *-inverses 88.9%

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

      5. sub-neg 88.9%

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

      6. metadata-eval 88.9%

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

      7. distribute-rgt-neg-in 88.9%

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

      8. +-commutative 88.9%

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

      9. distribute-neg-in 88.9%

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

      10. metadata-eval 88.9%

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

      11. sub-neg 88.9%

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

   9. Simplified 88.9%

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

   if -1.85000000000000002e112 < y < -2.2e12

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 67.4%

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

   if -3.6e-12 < y < 1.25e6

   1. Initial program 95.8%

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

      1. associate-*l/ 90.7%

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

      2. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around inf 74.6%

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

      1. *-commutative 74.6%

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

      2. associate-/l* 77.6%

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

   7. Simplified 77.6%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2200000000000:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-12} \lor \neg \left(y \leq 1250000\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-11} \lor \neg \left(y \leq 1560000\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -1.85e+112)
     t_1
     (if (<= y -2.9e+70)
       (* t (/ (- x y) z))
       (if (or (<= y -1.45e-11) (not (<= y 1560000.0)))
         t_1
         (* (- x y) (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.85e+112) {
		tmp = t_1;
	} else if (y <= -2.9e+70) {
		tmp = t * ((x - y) / z);
	} else if ((y <= -1.45e-11) || !(y <= 1560000.0)) {
		tmp = t_1;
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-1.85d+112)) then
        tmp = t_1
    else if (y <= (-2.9d+70)) then
        tmp = t * ((x - y) / z)
    else if ((y <= (-1.45d-11)) .or. (.not. (y <= 1560000.0d0))) then
        tmp = t_1
    else
        tmp = (x - y) * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -1.85e+112) {
		tmp = t_1;
	} else if (y <= -2.9e+70) {
		tmp = t * ((x - y) / z);
	} else if ((y <= -1.45e-11) || !(y <= 1560000.0)) {
		tmp = t_1;
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -1.85e+112:
		tmp = t_1
	elif y <= -2.9e+70:
		tmp = t * ((x - y) / z)
	elif (y <= -1.45e-11) or not (y <= 1560000.0):
		tmp = t_1
	else:
		tmp = (x - y) * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -1.85e+112)
		tmp = t_1;
	elseif (y <= -2.9e+70)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif ((y <= -1.45e-11) || !(y <= 1560000.0))
		tmp = t_1;
	else
		tmp = Float64(Float64(x - y) * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -1.85e+112)
		tmp = t_1;
	elseif (y <= -2.9e+70)
		tmp = t * ((x - y) / z);
	elseif ((y <= -1.45e-11) || ~((y <= 1560000.0)))
		tmp = t_1;
	else
		tmp = (x - y) * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e+112], t$95$1, If[LessEqual[y, -2.9e+70], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.45e-11], N[Not[LessEqual[y, 1560000.0]], $MachinePrecision]], t$95$1, N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.85000000000000002e112 or -2.8999999999999998e70 < y < -1.45e-11 or 1.56e6 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 77.8%

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

      2. associate-/l* 78.5%

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

   3. Simplified 78.5%

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

      1. associate-*r/ 77.8%

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

      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 67.4%

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

      1. mul-1-neg 67.4%

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

      2. associate-/l* 85.6%

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

      3. div-sub 85.6%

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

      4. *-inverses 85.6%

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

      5. sub-neg 85.6%

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

      6. metadata-eval 85.6%

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

      7. distribute-rgt-neg-in 85.6%

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

      8. +-commutative 85.6%

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

      9. distribute-neg-in 85.6%

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

      10. metadata-eval 85.6%

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

      11. sub-neg 85.6%

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

   9. Simplified 85.6%

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

   if -1.85000000000000002e112 < y < -2.8999999999999998e70

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 83.5%

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

   if -1.45e-11 < y < 1.56e6

   1. Initial program 95.8%

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

      1. associate-*l/ 90.7%

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

      2. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around inf 74.6%

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

      1. *-commutative 74.6%

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

      2. associate-/l* 77.6%

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

   7. Simplified 77.6%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-11} \lor \neg \left(y \leq 1560000\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-9} \lor \neg \left(y \leq 1100000\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -2e+112)
     t_1
     (if (<= y -2.9e+70)
       (* t (/ (- x y) z))
       (if (or (<= y -4.6e-9) (not (<= y 1100000.0)))
         t_1
         (/ (- x y) (/ z t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -2e+112) {
		tmp = t_1;
	} else if (y <= -2.9e+70) {
		tmp = t * ((x - y) / z);
	} else if ((y <= -4.6e-9) || !(y <= 1100000.0)) {
		tmp = t_1;
	} else {
		tmp = (x - y) / (z / 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 = t * (1.0d0 - (x / y))
    if (y <= (-2d+112)) then
        tmp = t_1
    else if (y <= (-2.9d+70)) then
        tmp = t * ((x - y) / z)
    else if ((y <= (-4.6d-9)) .or. (.not. (y <= 1100000.0d0))) then
        tmp = t_1
    else
        tmp = (x - y) / (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -2e+112) {
		tmp = t_1;
	} else if (y <= -2.9e+70) {
		tmp = t * ((x - y) / z);
	} else if ((y <= -4.6e-9) || !(y <= 1100000.0)) {
		tmp = t_1;
	} else {
		tmp = (x - y) / (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -2e+112:
		tmp = t_1
	elif y <= -2.9e+70:
		tmp = t * ((x - y) / z)
	elif (y <= -4.6e-9) or not (y <= 1100000.0):
		tmp = t_1
	else:
		tmp = (x - y) / (z / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -2e+112)
		tmp = t_1;
	elseif (y <= -2.9e+70)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif ((y <= -4.6e-9) || !(y <= 1100000.0))
		tmp = t_1;
	else
		tmp = Float64(Float64(x - y) / Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -2e+112)
		tmp = t_1;
	elseif (y <= -2.9e+70)
		tmp = t * ((x - y) / z);
	elseif ((y <= -4.6e-9) || ~((y <= 1100000.0)))
		tmp = t_1;
	else
		tmp = (x - y) / (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+112], t$95$1, If[LessEqual[y, -2.9e+70], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -4.6e-9], N[Not[LessEqual[y, 1100000.0]], $MachinePrecision]], t$95$1, N[(N[(x - y), $MachinePrecision] / N[(z / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9999999999999999e112 or -2.8999999999999998e70 < y < -4.5999999999999998e-9 or 1.1e6 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 77.8%

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

      2. associate-/l* 78.5%

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

   3. Simplified 78.5%

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

      1. associate-*r/ 77.8%

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

      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 67.4%

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

      1. mul-1-neg 67.4%

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

      2. associate-/l* 85.6%

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

      3. div-sub 85.6%

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

      4. *-inverses 85.6%

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

      5. sub-neg 85.6%

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

      6. metadata-eval 85.6%

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

      7. distribute-rgt-neg-in 85.6%

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

      8. +-commutative 85.6%

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

      9. distribute-neg-in 85.6%

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

      10. metadata-eval 85.6%

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

      11. sub-neg 85.6%

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

   9. Simplified 85.6%

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

   if -1.9999999999999999e112 < y < -2.8999999999999998e70

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 83.5%

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

   if -4.5999999999999998e-9 < y < 1.1e6

   1. Initial program 95.8%

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

      1. associate-*l/ 90.7%

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

      2. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

      1. clear-num 95.9%

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

      2. un-div-inv 96.1%

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

   6. Applied egg-rr 96.1%

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

   7. Taylor expanded in z around inf 77.6%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+112}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-9} \lor \neg \left(y \leq 1100000\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{\frac{z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+129}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-30} \lor \neg \left(x \leq 4.7 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.3e+129)
   (* t (/ x (- z y)))
   (if (<= x -3.9e+90)
     (* t (- 1.0 (/ x y)))
     (if (or (<= x -1.3e-30) (not (<= x 4.7e+30)))
       (/ t (/ (- z y) x))
       (* t (/ y (- y z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.3e+129) {
		tmp = t * (x / (z - y));
	} else if (x <= -3.9e+90) {
		tmp = t * (1.0 - (x / y));
	} else if ((x <= -1.3e-30) || !(x <= 4.7e+30)) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t * (y / (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 (x <= (-1.3d+129)) then
        tmp = t * (x / (z - y))
    else if (x <= (-3.9d+90)) then
        tmp = t * (1.0d0 - (x / y))
    else if ((x <= (-1.3d-30)) .or. (.not. (x <= 4.7d+30))) then
        tmp = t / ((z - y) / x)
    else
        tmp = t * (y / (y - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.3e+129) {
		tmp = t * (x / (z - y));
	} else if (x <= -3.9e+90) {
		tmp = t * (1.0 - (x / y));
	} else if ((x <= -1.3e-30) || !(x <= 4.7e+30)) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.3e+129:
		tmp = t * (x / (z - y))
	elif x <= -3.9e+90:
		tmp = t * (1.0 - (x / y))
	elif (x <= -1.3e-30) or not (x <= 4.7e+30):
		tmp = t / ((z - y) / x)
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.3e+129)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (x <= -3.9e+90)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif ((x <= -1.3e-30) || !(x <= 4.7e+30))
		tmp = Float64(t / Float64(Float64(z - y) / x));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.3e+129)
		tmp = t * (x / (z - y));
	elseif (x <= -3.9e+90)
		tmp = t * (1.0 - (x / y));
	elseif ((x <= -1.3e-30) || ~((x <= 4.7e+30)))
		tmp = t / ((z - y) / x);
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.3e+129], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.9e+90], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.3e-30], N[Not[LessEqual[x, 4.7e+30]], $MachinePrecision]], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.30000000000000006e129

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 88.3%

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

   if -1.30000000000000006e129 < x < -3.9000000000000002e90

   1. Initial program 99.8%

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

      1. associate-*l/ 86.3%

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

      2. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

      1. associate-*r/ 86.3%

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

      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 99.6%

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

      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 86.3%

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

      1. mul-1-neg 86.3%

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

      2. associate-/l* 99.8%

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

      3. div-sub 100.0%

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

      4. *-inverses 100.0%

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

      5. sub-neg 100.0%

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

      6. metadata-eval 100.0%

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

      7. distribute-rgt-neg-in 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-neg-in 100.0%

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

      10. metadata-eval 100.0%

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

      11. sub-neg 100.0%

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

   9. Simplified 100.0%

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

   if -3.9000000000000002e90 < x < -1.29999999999999993e-30 or 4.6999999999999999e30 < x

   1. Initial program 97.7%

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

      1. associate-*l/ 88.2%

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

      2. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

      1. associate-*r/ 88.2%

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

      2. associate-*l/ 97.7%

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

      3. *-commutative 97.7%

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

      4. clear-num 97.6%

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

      5. un-div-inv 97.8%

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

   6. Applied egg-rr 97.8%

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

   7. Taylor expanded in x around inf 84.0%

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

   if -1.29999999999999993e-30 < x < 4.6999999999999999e30

   1. Initial program 97.1%

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

   3. Taylor expanded in x around 0 81.0%

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

      1. neg-mul-1 81.0%

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

      2. distribute-neg-frac2 81.0%

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

   5. Simplified 81.0%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+129}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{+90}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-30} \lor \neg \left(x \leq 4.7 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+102}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1900000000000 \lor \neg \left(y \leq -1.35 \cdot 10^{-14}\right) \land y \leq 1020000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.4e+102)
   t
   (if (or (<= y -1900000000000.0)
           (and (not (<= y -1.35e-14)) (<= y 1020000.0)))
     (* x (/ t z))
     t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e+102) {
		tmp = t;
	} else if ((y <= -1900000000000.0) || (!(y <= -1.35e-14) && (y <= 1020000.0))) {
		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 <= (-1.4d+102)) then
        tmp = t
    else if ((y <= (-1900000000000.0d0)) .or. (.not. (y <= (-1.35d-14))) .and. (y <= 1020000.0d0)) 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 <= -1.4e+102) {
		tmp = t;
	} else if ((y <= -1900000000000.0) || (!(y <= -1.35e-14) && (y <= 1020000.0))) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.4e+102:
		tmp = t
	elif (y <= -1900000000000.0) or (not (y <= -1.35e-14) and (y <= 1020000.0)):
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.4e+102)
		tmp = t;
	elseif ((y <= -1900000000000.0) || (!(y <= -1.35e-14) && (y <= 1020000.0)))
		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 <= -1.4e+102)
		tmp = t;
	elseif ((y <= -1900000000000.0) || (~((y <= -1.35e-14)) && (y <= 1020000.0)))
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.4e+102], t, If[Or[LessEqual[y, -1900000000000.0], And[N[Not[LessEqual[y, -1.35e-14]], $MachinePrecision], LessEqual[y, 1020000.0]]], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.40000000000000009e102 or -1.9e12 < y < -1.3499999999999999e-14 or 1.02e6 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 76.5%

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

      2. associate-/l* 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in y around inf 58.5%

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

   if -1.40000000000000009e102 < y < -1.9e12 or -1.3499999999999999e-14 < y < 1.02e6

   1. Initial program 96.3%

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

      1. associate-*l/ 91.1%

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

      2. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in y around 0 61.4%

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

      1. *-commutative 61.4%

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

      2. associate-/l* 63.6%

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

   7. Simplified 63.6%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+102}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1900000000000 \lor \neg \left(y \leq -1.35 \cdot 10^{-14}\right) \land y \leq 1020000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2000000000000:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 11600000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.85e+112)
   t
   (if (<= y -2000000000000.0)
     (* t (/ x z))
     (if (<= y -1.85e-14) t (if (<= y 11600000.0) (* x (/ t z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.85e+112) {
		tmp = t;
	} else if (y <= -2000000000000.0) {
		tmp = t * (x / z);
	} else if (y <= -1.85e-14) {
		tmp = t;
	} else if (y <= 11600000.0) {
		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 <= (-1.85d+112)) then
        tmp = t
    else if (y <= (-2000000000000.0d0)) then
        tmp = t * (x / z)
    else if (y <= (-1.85d-14)) then
        tmp = t
    else if (y <= 11600000.0d0) 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 <= -1.85e+112) {
		tmp = t;
	} else if (y <= -2000000000000.0) {
		tmp = t * (x / z);
	} else if (y <= -1.85e-14) {
		tmp = t;
	} else if (y <= 11600000.0) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.85e+112:
		tmp = t
	elif y <= -2000000000000.0:
		tmp = t * (x / z)
	elif y <= -1.85e-14:
		tmp = t
	elif y <= 11600000.0:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.85e+112)
		tmp = t;
	elseif (y <= -2000000000000.0)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= -1.85e-14)
		tmp = t;
	elseif (y <= 11600000.0)
		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 <= -1.85e+112)
		tmp = t;
	elseif (y <= -2000000000000.0)
		tmp = t * (x / z);
	elseif (y <= -1.85e-14)
		tmp = t;
	elseif (y <= 11600000.0)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.85e+112], t, If[LessEqual[y, -2000000000000.0], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.85e-14], t, If[LessEqual[y, 11600000.0], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.85000000000000002e112 or -2e12 < y < -1.85000000000000001e-14 or 1.16e7 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 76.3%

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

      2. associate-/l* 77.6%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in y around inf 60.2%

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

   if -1.85000000000000002e112 < y < -2e12

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 49.2%

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

   if -1.85000000000000001e-14 < y < 1.16e7

   1. Initial program 95.7%

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

      1. associate-*l/ 90.5%

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

      2. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around 0 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-/l* 65.8%

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

   7. Simplified 65.8%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+112}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2000000000000:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-14}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 11600000:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 90.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+115} \lor \neg \left(y \leq 1.55 \cdot 10^{+182}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9.5e+115) (not (<= y 1.55e+182)))
   (* t (- 1.0 (/ x y)))
   (* (- x y) (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.5e+115) || !(y <= 1.55e+182)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (t / (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 <= (-9.5d+115)) .or. (.not. (y <= 1.55d+182))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = (x - y) * (t / (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 <= -9.5e+115) || !(y <= 1.55e+182)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9.5e+115) or not (y <= 1.55e+182):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9.5e+115) || !(y <= 1.55e+182))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9.5e+115) || ~((y <= 1.55e+182)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9.5e+115], N[Not[LessEqual[y, 1.55e+182]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.4999999999999997e115 or 1.54999999999999998e182 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 69.5%

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

      2. associate-/l* 62.5%

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

   3. Simplified 62.5%

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

      1. associate-*r/ 69.5%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.9%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 66.7%

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

      1. mul-1-neg 66.7%

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

      2. associate-/l* 97.1%

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

      3. div-sub 97.1%

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

      4. *-inverses 97.1%

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

      5. sub-neg 97.1%

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

      6. metadata-eval 97.1%

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

      7. distribute-rgt-neg-in 97.1%

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

      8. +-commutative 97.1%

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

      9. distribute-neg-in 97.1%

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

      10. metadata-eval 97.1%

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

      11. sub-neg 97.1%

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

   9. Simplified 97.1%

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

   if -9.4999999999999997e115 < y < 1.54999999999999998e182

   1. Initial program 97.2%

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

      1. associate-*l/ 88.9%

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

      2. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+115} \lor \neg \left(y \leq 1.55 \cdot 10^{+182}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-16} \lor \neg \left(y \leq 2500000\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.3e-16) (not (<= y 2500000.0)))
   (* t (- 1.0 (/ x y)))
   (* x (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.3e-16) || !(y <= 2500000.0)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (t / 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 ((y <= (-4.3d-16)) .or. (.not. (y <= 2500000.0d0))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = x * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.3e-16) || !(y <= 2500000.0)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.3e-16) or not (y <= 2500000.0):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = x * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.3e-16) || !(y <= 2500000.0))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(x * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.3e-16) || ~((y <= 2500000.0)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = x * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.3e-16], N[Not[LessEqual[y, 2500000.0]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2999999999999999e-16 or 2.5e6 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 79.6%

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

      2. associate-/l* 79.5%

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

   3. Simplified 79.5%

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

      1. associate-*r/ 79.6%

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

      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 62.9%

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

      1. mul-1-neg 62.9%

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

      2. associate-/l* 79.6%

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

      3. div-sub 79.7%

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

      4. *-inverses 79.7%

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

      5. sub-neg 79.7%

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

      6. metadata-eval 79.7%

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

      7. distribute-rgt-neg-in 79.7%

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

      8. +-commutative 79.7%

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

      9. distribute-neg-in 79.7%

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

      10. metadata-eval 79.7%

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

      11. sub-neg 79.7%

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

   9. Simplified 79.7%

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

   if -4.2999999999999999e-16 < y < 2.5e6

   1. Initial program 95.7%

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

      1. associate-*l/ 90.5%

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

      2. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in y around 0 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-/l* 65.8%

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

   7. Simplified 65.8%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-16} \lor \neg \left(y \leq 2500000\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-9} \lor \neg \left(y \leq 8000000\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.85e-9) (not (<= y 8000000.0)))
   (* t (- 1.0 (/ x y)))
   (* (- x y) (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.85e-9) || !(y <= 8000000.0)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (t / 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 ((y <= (-2.85d-9)) .or. (.not. (y <= 8000000.0d0))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = (x - y) * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.85e-9) || !(y <= 8000000.0)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.85e-9) or not (y <= 8000000.0):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = (x - y) * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.85e-9) || !(y <= 8000000.0))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(Float64(x - y) * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.85e-9) || ~((y <= 8000000.0)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = (x - y) * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.85e-9], N[Not[LessEqual[y, 8000000.0]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8499999999999999e-9 or 8e6 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 79.2%

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

      2. associate-/l* 79.0%

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

   3. Simplified 79.0%

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

      1. associate-*r/ 79.2%

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

      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 63.5%

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

      1. mul-1-neg 63.5%

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

      2. associate-/l* 80.7%

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

      3. div-sub 80.7%

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

      4. *-inverses 80.7%

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

      5. sub-neg 80.7%

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

      6. metadata-eval 80.7%

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

      7. distribute-rgt-neg-in 80.7%

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

      8. +-commutative 80.7%

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

      9. distribute-neg-in 80.7%

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

      10. metadata-eval 80.7%

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

      11. sub-neg 80.7%

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

   9. Simplified 80.7%

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

   if -2.8499999999999999e-9 < y < 8e6

   1. Initial program 95.8%

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

      1. associate-*l/ 90.7%

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

      2. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in z around inf 74.6%

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

      1. *-commutative 74.6%

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

      2. associate-/l* 77.6%

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

   7. Simplified 77.6%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-9} \lor \neg \left(y \leq 8000000\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.7% 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 97.7%

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

   1. associate-*l/ 85.1%

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

   2. associate-/l* 87.8%

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

3. Simplified 87.8%

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

5. Taylor expanded in y around inf 31.4%

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

6. Final simplification 31.4%

   \[\leadsto t \]
7. Add Preprocessing

Developer target: 97.0% 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 2024055 
(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))