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

Percentage Accurate: 96.9% → 97.0%

Time: 12.8s

Alternatives: 15

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: 96.9% 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

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

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 97.5%

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

   1. *-commutative 97.5%

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

   2. clear-num 97.5%

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

   3. un-div-inv 97.5%

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

4. Applied egg-rr 97.5%

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

5. Final simplification 97.5%

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

Alternative 2: 60.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -140000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-74}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-102}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -140000.0)
   t
   (if (<= y -1.9e-43)
     (* x (/ t z))
     (if (<= y -7e-74)
       t
       (if (<= y -3e-102)
         (* (/ t z) (- y))
         (if (<= y 2.55e-38)
           (* t (/ x z))
           (if (<= y 1.02e+43) (* t (/ (- y) z)) t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -140000.0) {
		tmp = t;
	} else if (y <= -1.9e-43) {
		tmp = x * (t / z);
	} else if (y <= -7e-74) {
		tmp = t;
	} else if (y <= -3e-102) {
		tmp = (t / z) * -y;
	} else if (y <= 2.55e-38) {
		tmp = t * (x / z);
	} else if (y <= 1.02e+43) {
		tmp = t * (-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) :: tmp
    if (y <= (-140000.0d0)) then
        tmp = t
    else if (y <= (-1.9d-43)) then
        tmp = x * (t / z)
    else if (y <= (-7d-74)) then
        tmp = t
    else if (y <= (-3d-102)) then
        tmp = (t / z) * -y
    else if (y <= 2.55d-38) then
        tmp = t * (x / z)
    else if (y <= 1.02d+43) then
        tmp = t * (-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 tmp;
	if (y <= -140000.0) {
		tmp = t;
	} else if (y <= -1.9e-43) {
		tmp = x * (t / z);
	} else if (y <= -7e-74) {
		tmp = t;
	} else if (y <= -3e-102) {
		tmp = (t / z) * -y;
	} else if (y <= 2.55e-38) {
		tmp = t * (x / z);
	} else if (y <= 1.02e+43) {
		tmp = t * (-y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -140000.0:
		tmp = t
	elif y <= -1.9e-43:
		tmp = x * (t / z)
	elif y <= -7e-74:
		tmp = t
	elif y <= -3e-102:
		tmp = (t / z) * -y
	elif y <= 2.55e-38:
		tmp = t * (x / z)
	elif y <= 1.02e+43:
		tmp = t * (-y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -140000.0)
		tmp = t;
	elseif (y <= -1.9e-43)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= -7e-74)
		tmp = t;
	elseif (y <= -3e-102)
		tmp = Float64(Float64(t / z) * Float64(-y));
	elseif (y <= 2.55e-38)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= 1.02e+43)
		tmp = Float64(t * Float64(Float64(-y) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -140000.0)
		tmp = t;
	elseif (y <= -1.9e-43)
		tmp = x * (t / z);
	elseif (y <= -7e-74)
		tmp = t;
	elseif (y <= -3e-102)
		tmp = (t / z) * -y;
	elseif (y <= 2.55e-38)
		tmp = t * (x / z);
	elseif (y <= 1.02e+43)
		tmp = t * (-y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -140000.0], t, If[LessEqual[y, -1.9e-43], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e-74], t, If[LessEqual[y, -3e-102], N[(N[(t / z), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[y, 2.55e-38], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e+43], N[(t * N[((-y) / z), $MachinePrecision]), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.4e5 or -1.89999999999999985e-43 < y < -7.00000000000000029e-74 or 1.02e43 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 68.8%

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

   if -1.4e5 < y < -1.89999999999999985e-43

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.8%

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

      1. associate-/l* 75.8%

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

      2. associate-/r/ 75.8%

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

   5. Simplified 75.8%

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

   if -7.00000000000000029e-74 < y < -3e-102

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 47.9%

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

      1. associate-/l* 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in x around 0 47.6%

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

      1. mul-1-neg 47.6%

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

      2. associate-*l/ 55.1%

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

      3. *-commutative 55.1%

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

      4. distribute-rgt-neg-in 55.1%

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

   8. Simplified 55.1%

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

   if -3e-102 < y < 2.55000000000000014e-38

   1. Initial program 94.4%

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

   3. Taylor expanded in y around 0 69.6%

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

   if 2.55000000000000014e-38 < y < 1.02e43

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 59.6%

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

      1. neg-mul-1 59.6%

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

      2. distribute-neg-frac 59.6%

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

   5. Simplified 59.6%

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

   6. Taylor expanded in y around 0 60.2%

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

      1. associate-*r/ 60.2%

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

      2. neg-mul-1 60.2%

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

   8. Simplified 60.2%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -140000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-74}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-102}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+99}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-48}:\\ \;\;\;\;\frac{-t}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-78}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-102}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.2e+99)
   t
   (if (<= y -4.5e-48)
     (/ (- t) (/ y x))
     (if (<= y -1.45e-78)
       t
       (if (<= y -3e-102)
         (* (/ t z) (- y))
         (if (<= y 2.35e-39)
           (* t (/ x z))
           (if (<= y 2.9e+63) (* t (/ (- y) z)) t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.2e+99) {
		tmp = t;
	} else if (y <= -4.5e-48) {
		tmp = -t / (y / x);
	} else if (y <= -1.45e-78) {
		tmp = t;
	} else if (y <= -3e-102) {
		tmp = (t / z) * -y;
	} else if (y <= 2.35e-39) {
		tmp = t * (x / z);
	} else if (y <= 2.9e+63) {
		tmp = t * (-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) :: tmp
    if (y <= (-3.2d+99)) then
        tmp = t
    else if (y <= (-4.5d-48)) then
        tmp = -t / (y / x)
    else if (y <= (-1.45d-78)) then
        tmp = t
    else if (y <= (-3d-102)) then
        tmp = (t / z) * -y
    else if (y <= 2.35d-39) then
        tmp = t * (x / z)
    else if (y <= 2.9d+63) then
        tmp = t * (-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 tmp;
	if (y <= -3.2e+99) {
		tmp = t;
	} else if (y <= -4.5e-48) {
		tmp = -t / (y / x);
	} else if (y <= -1.45e-78) {
		tmp = t;
	} else if (y <= -3e-102) {
		tmp = (t / z) * -y;
	} else if (y <= 2.35e-39) {
		tmp = t * (x / z);
	} else if (y <= 2.9e+63) {
		tmp = t * (-y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.2e+99:
		tmp = t
	elif y <= -4.5e-48:
		tmp = -t / (y / x)
	elif y <= -1.45e-78:
		tmp = t
	elif y <= -3e-102:
		tmp = (t / z) * -y
	elif y <= 2.35e-39:
		tmp = t * (x / z)
	elif y <= 2.9e+63:
		tmp = t * (-y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.2e+99)
		tmp = t;
	elseif (y <= -4.5e-48)
		tmp = Float64(Float64(-t) / Float64(y / x));
	elseif (y <= -1.45e-78)
		tmp = t;
	elseif (y <= -3e-102)
		tmp = Float64(Float64(t / z) * Float64(-y));
	elseif (y <= 2.35e-39)
		tmp = Float64(t * Float64(x / z));
	elseif (y <= 2.9e+63)
		tmp = Float64(t * Float64(Float64(-y) / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.2e+99)
		tmp = t;
	elseif (y <= -4.5e-48)
		tmp = -t / (y / x);
	elseif (y <= -1.45e-78)
		tmp = t;
	elseif (y <= -3e-102)
		tmp = (t / z) * -y;
	elseif (y <= 2.35e-39)
		tmp = t * (x / z);
	elseif (y <= 2.9e+63)
		tmp = t * (-y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.2e+99], t, If[LessEqual[y, -4.5e-48], N[((-t) / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.45e-78], t, If[LessEqual[y, -3e-102], N[(N[(t / z), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[y, 2.35e-39], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+63], N[(t * N[((-y) / z), $MachinePrecision]), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.19999999999999999e99 or -4.49999999999999988e-48 < y < -1.45e-78 or 2.8999999999999999e63 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 74.6%

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

   if -3.19999999999999999e99 < y < -4.49999999999999988e-48

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 56.8%

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

      1. *-commutative 56.8%

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

      2. associate-*r/ 60.5%

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

   5. Simplified 60.5%

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

   6. Taylor expanded in z around 0 49.0%

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

      1. mul-1-neg 49.0%

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

      2. associate-/l* 49.9%

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

      3. distribute-neg-frac 49.9%

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

   8. Simplified 49.9%

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

   if -1.45e-78 < y < -3e-102

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 47.9%

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

      1. associate-/l* 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in x around 0 47.6%

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

      1. mul-1-neg 47.6%

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

      2. associate-*l/ 55.1%

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

      3. *-commutative 55.1%

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

      4. distribute-rgt-neg-in 55.1%

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

   8. Simplified 55.1%

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

   if -3e-102 < y < 2.3500000000000001e-39

   1. Initial program 94.4%

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

   3. Taylor expanded in y around 0 69.6%

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

   if 2.3500000000000001e-39 < y < 2.8999999999999999e63

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 59.6%

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

      1. neg-mul-1 59.6%

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

      2. distribute-neg-frac 59.6%

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

   5. Simplified 59.6%

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

   6. Taylor expanded in y around 0 60.2%

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

      1. associate-*r/ 60.2%

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

      2. neg-mul-1 60.2%

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

   8. Simplified 60.2%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+99}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-48}:\\ \;\;\;\;\frac{-t}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-78}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-102}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+63}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -75000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-74}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-102}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -75000.0)
   t
   (if (<= y -1.8e-43)
     (* x (/ t z))
     (if (<= y -3.6e-74)
       t
       (if (<= y -1.05e-102)
         (* (/ t z) (- y))
         (if (<= y 4e+47) (* t (/ x z)) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -75000.0) {
		tmp = t;
	} else if (y <= -1.8e-43) {
		tmp = x * (t / z);
	} else if (y <= -3.6e-74) {
		tmp = t;
	} else if (y <= -1.05e-102) {
		tmp = (t / z) * -y;
	} else if (y <= 4e+47) {
		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 <= (-75000.0d0)) then
        tmp = t
    else if (y <= (-1.8d-43)) then
        tmp = x * (t / z)
    else if (y <= (-3.6d-74)) then
        tmp = t
    else if (y <= (-1.05d-102)) then
        tmp = (t / z) * -y
    else if (y <= 4d+47) 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 <= -75000.0) {
		tmp = t;
	} else if (y <= -1.8e-43) {
		tmp = x * (t / z);
	} else if (y <= -3.6e-74) {
		tmp = t;
	} else if (y <= -1.05e-102) {
		tmp = (t / z) * -y;
	} else if (y <= 4e+47) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -75000.0:
		tmp = t
	elif y <= -1.8e-43:
		tmp = x * (t / z)
	elif y <= -3.6e-74:
		tmp = t
	elif y <= -1.05e-102:
		tmp = (t / z) * -y
	elif y <= 4e+47:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -75000.0)
		tmp = t;
	elseif (y <= -1.8e-43)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= -3.6e-74)
		tmp = t;
	elseif (y <= -1.05e-102)
		tmp = Float64(Float64(t / z) * Float64(-y));
	elseif (y <= 4e+47)
		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 <= -75000.0)
		tmp = t;
	elseif (y <= -1.8e-43)
		tmp = x * (t / z);
	elseif (y <= -3.6e-74)
		tmp = t;
	elseif (y <= -1.05e-102)
		tmp = (t / z) * -y;
	elseif (y <= 4e+47)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -75000.0], t, If[LessEqual[y, -1.8e-43], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.6e-74], t, If[LessEqual[y, -1.05e-102], N[(N[(t / z), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[y, 4e+47], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -75000 or -1.7999999999999999e-43 < y < -3.6000000000000002e-74 or 4.0000000000000002e47 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 68.8%

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

   if -75000 < y < -1.7999999999999999e-43

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.8%

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

      1. associate-/l* 75.8%

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

      2. associate-/r/ 75.8%

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

   5. Simplified 75.8%

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

   if -3.6000000000000002e-74 < y < -1.05e-102

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 47.9%

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

      1. associate-/l* 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in x around 0 47.6%

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

      1. mul-1-neg 47.6%

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

      2. associate-*l/ 55.1%

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

      3. *-commutative 55.1%

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

      4. distribute-rgt-neg-in 55.1%

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

   8. Simplified 55.1%

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

   if -1.05e-102 < y < 4.0000000000000002e47

   1. Initial program 94.9%

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

   3. Taylor expanded in y around 0 64.8%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -75000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-74}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-102}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{z}{x - y}}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{-72}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-229}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+58}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ z (- x y)))) (t_2 (* t (- 1.0 (/ x y)))))
   (if (<= y -2e-72)
     t_2
     (if (<= y 1.25e-229)
       t_1
       (if (<= y 1.9e-40) (* x (/ t (- z y))) (if (<= y 3.7e+58) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (z / (x - y));
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -2e-72) {
		tmp = t_2;
	} else if (y <= 1.25e-229) {
		tmp = t_1;
	} else if (y <= 1.9e-40) {
		tmp = x * (t / (z - y));
	} else if (y <= 3.7e+58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t / (z / (x - y))
    t_2 = t * (1.0d0 - (x / y))
    if (y <= (-2d-72)) then
        tmp = t_2
    else if (y <= 1.25d-229) then
        tmp = t_1
    else if (y <= 1.9d-40) then
        tmp = x * (t / (z - y))
    else if (y <= 3.7d+58) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / (z / (x - y));
	double t_2 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -2e-72) {
		tmp = t_2;
	} else if (y <= 1.25e-229) {
		tmp = t_1;
	} else if (y <= 1.9e-40) {
		tmp = x * (t / (z - y));
	} else if (y <= 3.7e+58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (z / (x - y))
	t_2 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -2e-72:
		tmp = t_2
	elif y <= 1.25e-229:
		tmp = t_1
	elif y <= 1.9e-40:
		tmp = x * (t / (z - y))
	elif y <= 3.7e+58:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(z / Float64(x - y)))
	t_2 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -2e-72)
		tmp = t_2;
	elseif (y <= 1.25e-229)
		tmp = t_1;
	elseif (y <= 1.9e-40)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 3.7e+58)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (z / (x - y));
	t_2 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -2e-72)
		tmp = t_2;
	elseif (y <= 1.25e-229)
		tmp = t_1;
	elseif (y <= 1.9e-40)
		tmp = x * (t / (z - y));
	elseif (y <= 3.7e+58)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e-72], t$95$2, If[LessEqual[y, 1.25e-229], t$95$1, If[LessEqual[y, 1.9e-40], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e+58], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9999999999999999e-72 or 3.7000000000000002e58 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 80.9%

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

      1. associate-*r/ 80.9%

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

      2. neg-mul-1 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in x around 0 80.9%

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

      1. mul-1-neg 80.9%

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

      2. unsub-neg 80.9%

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

   8. Simplified 80.9%

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

   if -1.9999999999999999e-72 < y < 1.25000000000000004e-229 or 1.8999999999999999e-40 < y < 3.7000000000000002e58

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf 75.8%

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

      1. associate-/l* 80.7%

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

   5. Simplified 80.7%

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

   if 1.25000000000000004e-229 < y < 1.8999999999999999e-40

   1. Initial program 93.5%

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

   3. Taylor expanded in x around inf 75.7%

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

      1. *-commutative 75.7%

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

      2. associate-*r/ 84.4%

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

   5. Simplified 84.4%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-72}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-229}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+58}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.3 \cdot 10^{-69}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-230}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.3e-69)
   (* t (- 1.0 (/ x y)))
   (if (<= y 7.8e-230)
     (/ t (/ z (- x y)))
     (if (<= y 9e-42) (* x (/ t (- z y))) (/ t (/ (- y z) y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.3e-69) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 7.8e-230) {
		tmp = t / (z / (x - y));
	} else if (y <= 9e-42) {
		tmp = x * (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 <= (-8.3d-69)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= 7.8d-230) then
        tmp = t / (z / (x - y))
    else if (y <= 9d-42) then
        tmp = x * (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 <= -8.3e-69) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 7.8e-230) {
		tmp = t / (z / (x - y));
	} else if (y <= 9e-42) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t / ((y - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.3e-69:
		tmp = t * (1.0 - (x / y))
	elif y <= 7.8e-230:
		tmp = t / (z / (x - y))
	elif y <= 9e-42:
		tmp = x * (t / (z - y))
	else:
		tmp = t / ((y - z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.3e-69)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= 7.8e-230)
		tmp = Float64(t / Float64(z / Float64(x - y)));
	elseif (y <= 9e-42)
		tmp = Float64(x * 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 <= -8.3e-69)
		tmp = t * (1.0 - (x / y));
	elseif (y <= 7.8e-230)
		tmp = t / (z / (x - y));
	elseif (y <= 9e-42)
		tmp = x * (t / (z - y));
	else
		tmp = t / ((y - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.3e-69], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e-230], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-42], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.3000000000000004e-69

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 84.5%

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

      1. associate-*r/ 84.5%

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

      2. neg-mul-1 84.5%

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

   5. Simplified 84.5%

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

   6. Taylor expanded in x around 0 84.5%

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

      1. mul-1-neg 84.5%

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

      2. unsub-neg 84.5%

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

   8. Simplified 84.5%

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

   if -8.3000000000000004e-69 < y < 7.8000000000000004e-230

   1. Initial program 95.5%

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

   3. Taylor expanded in z around inf 75.5%

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

      1. associate-/l* 81.3%

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

   5. Simplified 81.3%

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

   if 7.8000000000000004e-230 < y < 9e-42

   1. Initial program 93.3%

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

   3. Taylor expanded in x around inf 77.4%

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

      1. *-commutative 77.4%

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

      2. associate-*r/ 86.2%

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

   5. Simplified 86.2%

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

   if 9e-42 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 88.2%

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

      1. neg-mul-1 88.2%

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

      2. distribute-neg-frac 88.2%

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

   5. Simplified 88.2%

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

      1. *-commutative 88.2%

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

      2. frac-2neg 88.2%

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

      3. remove-double-neg 88.2%

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

      4. associate-*r/ 70.9%

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

      5. sub-neg 70.9%

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

      6. distribute-neg-in 70.9%

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

      7. remove-double-neg 70.9%

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

   7. Applied egg-rr 70.9%

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

      1. associate-/l* 88.2%

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

      2. +-commutative 88.2%

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

      3. unsub-neg 88.2%

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

   9. Simplified 88.2%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.3 \cdot 10^{-69}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-230}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-69} \lor \neg \left(y \leq 3.55 \cdot 10^{-43}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.4e-69) (not (<= y 3.55e-43)))
   (* t (- 1.0 (/ x y)))
   (* x (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.4e-69) || !(y <= 3.55e-43)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (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 <= (-4.4d-69)) .or. (.not. (y <= 3.55d-43))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = x * (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 <= -4.4e-69) || !(y <= 3.55e-43)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.4e-69) or not (y <= 3.55e-43):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.4e-69) || !(y <= 3.55e-43))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.4e-69) || ~((y <= 3.55e-43)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.4e-69], N[Not[LessEqual[y, 3.55e-43]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4e-69 or 3.55000000000000013e-43 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 76.2%

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

      1. associate-*r/ 76.2%

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

      2. neg-mul-1 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in x around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. unsub-neg 76.2%

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

   8. Simplified 76.2%

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

   if -4.4e-69 < y < 3.55000000000000013e-43

   1. Initial program 94.6%

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

   3. Taylor expanded in x around inf 77.3%

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

      1. *-commutative 77.3%

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

      2. associate-*r/ 79.0%

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

   5. Simplified 79.0%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-69} \lor \neg \left(y \leq 3.55 \cdot 10^{-43}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+99}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.2e+99) t (if (<= y 2e+49) (* x (/ t (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.2e+99) {
		tmp = t;
	} else if (y <= 2e+49) {
		tmp = x * (t / (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 <= (-3.2d+99)) then
        tmp = t
    else if (y <= 2d+49) then
        tmp = x * (t / (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 <= -3.2e+99) {
		tmp = t;
	} else if (y <= 2e+49) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.2e+99:
		tmp = t
	elif y <= 2e+49:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.2e+99)
		tmp = t;
	elseif (y <= 2e+49)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.2e+99)
		tmp = t;
	elseif (y <= 2e+49)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.2e+99], t, If[LessEqual[y, 2e+49], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.19999999999999999e99 or 1.99999999999999989e49 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 75.9%

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

   if -3.19999999999999999e99 < y < 1.99999999999999989e49

   1. Initial program 96.1%

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

   3. Taylor expanded in x around inf 69.6%

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

      1. *-commutative 69.6%

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

      2. associate-*r/ 70.3%

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

   5. Simplified 70.3%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+99}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.04 \cdot 10^{-70}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 8.6:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.04e-70)
   (* t (- 1.0 (/ x y)))
   (if (<= y 8.6) (/ t (/ (- z y) x)) (/ t (/ (- y z) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.04e-70) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 8.6) {
		tmp = t / ((z - y) / x);
	} 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 <= (-1.04d-70)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= 8.6d0) then
        tmp = t / ((z - y) / x)
    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 <= -1.04e-70) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= 8.6) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t / ((y - z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.04e-70:
		tmp = t * (1.0 - (x / y))
	elif y <= 8.6:
		tmp = t / ((z - y) / x)
	else:
		tmp = t / ((y - z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.04e-70)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= 8.6)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	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 <= -1.04e-70)
		tmp = t * (1.0 - (x / y));
	elseif (y <= 8.6)
		tmp = t / ((z - y) / x);
	else
		tmp = t / ((y - z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.04e-70], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.6], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(y - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0399999999999999e-70

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 84.5%

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

      1. associate-*r/ 84.5%

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

      2. neg-mul-1 84.5%

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

   5. Simplified 84.5%

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

   6. Taylor expanded in x around 0 84.5%

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

      1. mul-1-neg 84.5%

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

      2. unsub-neg 84.5%

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

   8. Simplified 84.5%

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

   if -1.0399999999999999e-70 < y < 8.59999999999999964

   1. Initial program 95.0%

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

      1. *-commutative 95.0%

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

      2. clear-num 94.9%

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

      3. un-div-inv 95.0%

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

   4. Applied egg-rr 95.0%

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

   5. Taylor expanded in x around inf 75.9%

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

      1. associate-/l* 79.8%

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

   7. Simplified 79.8%

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

   if 8.59999999999999964 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 93.2%

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

      1. neg-mul-1 93.2%

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

      2. distribute-neg-frac 93.2%

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

   5. Simplified 93.2%

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

      1. *-commutative 93.2%

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

      2. frac-2neg 93.2%

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

      3. remove-double-neg 93.2%

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

      4. associate-*r/ 73.8%

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

      5. sub-neg 73.8%

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

      6. distribute-neg-in 73.8%

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

      7. remove-double-neg 73.8%

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

   7. Applied egg-rr 73.8%

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

      1. associate-/l* 93.2%

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

      2. +-commutative 93.2%

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

      3. unsub-neg 93.2%

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

   9. Simplified 93.2%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.04 \cdot 10^{-70}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 8.6:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 39.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-122}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.2e-122) t (if (<= y 2.15e-72) (* y (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.2e-122) {
		tmp = t;
	} else if (y <= 2.15e-72) {
		tmp = y * (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 <= (-8.2d-122)) then
        tmp = t
    else if (y <= 2.15d-72) then
        tmp = y * (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 <= -8.2e-122) {
		tmp = t;
	} else if (y <= 2.15e-72) {
		tmp = y * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.2e-122:
		tmp = t
	elif y <= 2.15e-72:
		tmp = y * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.2e-122)
		tmp = t;
	elseif (y <= 2.15e-72)
		tmp = Float64(y * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.2e-122)
		tmp = t;
	elseif (y <= 2.15e-72)
		tmp = y * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.2e-122], t, If[LessEqual[y, 2.15e-72], N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2000000000000001e-122 or 2.1499999999999999e-72 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 55.2%

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

   if -8.2000000000000001e-122 < y < 2.1499999999999999e-72

   1. Initial program 93.4%

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

   3. Taylor expanded in z around inf 75.3%

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

      1. associate-/l* 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in x around 0 26.1%

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

      1. mul-1-neg 26.1%

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

      2. associate-*l/ 27.0%

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

      3. *-commutative 27.0%

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

      4. distribute-rgt-neg-in 27.0%

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

   8. Simplified 27.0%

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

      1. expm1-log1p-u 23.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \left(-\frac{t}{z}\right)\right)\right)} \]

      2. expm1-udef 21.6%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(y \cdot \left(-\frac{t}{z}\right)\right)} - 1} \]

      3. add-sqr-sqrt 18.8%

         \[\leadsto e^{\mathsf{log1p}\left(y \cdot \color{blue}{\left(\sqrt{-\frac{t}{z}} \cdot \sqrt{-\frac{t}{z}}\right)}\right)} - 1 \]

      4. sqrt-unprod 22.8%

         \[\leadsto e^{\mathsf{log1p}\left(y \cdot \color{blue}{\sqrt{\left(-\frac{t}{z}\right) \cdot \left(-\frac{t}{z}\right)}}\right)} - 1 \]

      5. sqr-neg 22.8%

         \[\leadsto e^{\mathsf{log1p}\left(y \cdot \sqrt{\color{blue}{\frac{t}{z} \cdot \frac{t}{z}}}\right)} - 1 \]

      6. sqrt-unprod 11.8%

         \[\leadsto e^{\mathsf{log1p}\left(y \cdot \color{blue}{\left(\sqrt{\frac{t}{z}} \cdot \sqrt{\frac{t}{z}}\right)}\right)} - 1 \]

      7. add-sqr-sqrt 22.7%

         \[\leadsto e^{\mathsf{log1p}\left(y \cdot \color{blue}{\frac{t}{z}}\right)} - 1 \]

   10. Applied egg-rr 22.7%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(y \cdot \frac{t}{z}\right)} - 1} \]
   11. Step-by-step derivation

       1. expm1-def 22.8%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \frac{t}{z}\right)\right)} \]

       2. expm1-log1p 24.1%

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

   12. Simplified 24.1%

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

4. Final simplification 44.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-122}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -65000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -65000.0) t (if (<= y 7.8e-43) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -65000.0) {
		tmp = t;
	} else if (y <= 7.8e-43) {
		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 <= (-65000.0d0)) then
        tmp = t
    else if (y <= 7.8d-43) 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 <= -65000.0) {
		tmp = t;
	} else if (y <= 7.8e-43) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -65000.0:
		tmp = t
	elif y <= 7.8e-43:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -65000.0)
		tmp = t;
	elseif (y <= 7.8e-43)
		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 <= -65000.0)
		tmp = t;
	elseif (y <= 7.8e-43)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -65000.0], t, If[LessEqual[y, 7.8e-43], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -65000 or 7.80000000000000001e-43 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 64.2%

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

   if -65000 < y < 7.80000000000000001e-43

   1. Initial program 95.2%

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

   3. Taylor expanded in y around 0 60.4%

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

      1. associate-/l* 65.4%

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

      2. associate-/r/ 62.3%

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

   5. Simplified 62.3%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -65000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -140000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -140000.0) t (if (<= y 3.5e+58) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -140000.0) {
		tmp = t;
	} else if (y <= 3.5e+58) {
		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 <= (-140000.0d0)) then
        tmp = t
    else if (y <= 3.5d+58) 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 <= -140000.0) {
		tmp = t;
	} else if (y <= 3.5e+58) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -140000.0:
		tmp = t
	elif y <= 3.5e+58:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -140000.0)
		tmp = t;
	elseif (y <= 3.5e+58)
		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 <= -140000.0)
		tmp = t;
	elseif (y <= 3.5e+58)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -140000.0], t, If[LessEqual[y, 3.5e+58], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e5 or 3.4999999999999997e58 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 71.1%

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

   if -1.4e5 < y < 3.4999999999999997e58

   1. Initial program 95.7%

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

   3. Taylor expanded in y around 0 60.6%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -140000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+58}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -42000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+38}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -42000.0) t (if (<= y 8.6e+38) (/ t (/ z x)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -42000.0) {
		tmp = t;
	} else if (y <= 8.6e+38) {
		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 <= (-42000.0d0)) then
        tmp = t
    else if (y <= 8.6d+38) 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 <= -42000.0) {
		tmp = t;
	} else if (y <= 8.6e+38) {
		tmp = t / (z / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -42000.0:
		tmp = t
	elif y <= 8.6e+38:
		tmp = t / (z / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -42000.0)
		tmp = t;
	elseif (y <= 8.6e+38)
		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 <= -42000.0)
		tmp = t;
	elseif (y <= 8.6e+38)
		tmp = t / (z / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -42000.0], t, If[LessEqual[y, 8.6e+38], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -42000 or 8.5999999999999994e38 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 71.1%

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

   if -42000 < y < 8.5999999999999994e38

   1. Initial program 95.7%

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

   3. Taylor expanded in y around 0 56.2%

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

      1. associate-/l* 60.6%

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

   5. Simplified 60.6%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -42000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{+38}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 96.9% 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 97.5%

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

3. Final simplification 97.5%

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

Alternative 15: 35.5% 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 97.5%

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

3. Taylor expanded in y around inf 38.0%

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

4. Final simplification 38.0%

   \[\leadsto t \]
5. 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 2024040 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

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