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

Percentage Accurate: 97.2% → 97.2%

Time: 10.8s

Alternatives: 14

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: 97.2% 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: 97.2% 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 96.4%

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

2. Final simplification 96.4%

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

Alternative 2: 66.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+137}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+68}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+17}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 19000000000000:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.12e+137)
   t
   (if (<= y -2.6e+68)
     (/ (- y) (/ z t))
     (if (<= y -1.5e+17)
       t
       (if (<= y 19000000000000.0) (* x (/ t (- z y))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.12e+137) {
		tmp = t;
	} else if (y <= -2.6e+68) {
		tmp = -y / (z / t);
	} else if (y <= -1.5e+17) {
		tmp = t;
	} else if (y <= 19000000000000.0) {
		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 <= (-1.12d+137)) then
        tmp = t
    else if (y <= (-2.6d+68)) then
        tmp = -y / (z / t)
    else if (y <= (-1.5d+17)) then
        tmp = t
    else if (y <= 19000000000000.0d0) 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 <= -1.12e+137) {
		tmp = t;
	} else if (y <= -2.6e+68) {
		tmp = -y / (z / t);
	} else if (y <= -1.5e+17) {
		tmp = t;
	} else if (y <= 19000000000000.0) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.12e+137:
		tmp = t
	elif y <= -2.6e+68:
		tmp = -y / (z / t)
	elif y <= -1.5e+17:
		tmp = t
	elif y <= 19000000000000.0:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.12e+137)
		tmp = t;
	elseif (y <= -2.6e+68)
		tmp = Float64(Float64(-y) / Float64(z / t));
	elseif (y <= -1.5e+17)
		tmp = t;
	elseif (y <= 19000000000000.0)
		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 <= -1.12e+137)
		tmp = t;
	elseif (y <= -2.6e+68)
		tmp = -y / (z / t);
	elseif (y <= -1.5e+17)
		tmp = t;
	elseif (y <= 19000000000000.0)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.12e+137], t, If[LessEqual[y, -2.6e+68], N[((-y) / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.5e+17], t, If[LessEqual[y, 19000000000000.0], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1200000000000001e137 or -2.5999999999999998e68 < y < -1.5e17 or 1.9e13 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 72.1%

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

      2. associate-*r/ 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. Taylor expanded in y around inf 62.3%

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

   if -1.1200000000000001e137 < y < -2.5999999999999998e68

   1. Initial program 99.9%

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

      1. associate-*l/ 93.3%

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

      2. associate-*r/ 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in x around 0 67.9%

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

      1. mul-1-neg 67.9%

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

      2. associate-*r/ 61.7%

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

      3. distribute-lft-neg-out 61.7%

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

      4. *-commutative 61.7%

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

   6. Simplified 61.7%

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

   7. Taylor expanded in z around inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. associate-/l* 54.9%

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

   9. Simplified 54.9%

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

   if -1.5e17 < y < 1.9e13

   1. Initial program 93.5%

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

      1. associate-*l/ 95.3%

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

      2. associate-*r/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in x around inf 77.2%

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

      1. associate-*l/ 73.5%

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

      2. *-commutative 73.5%

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

   6. Simplified 73.5%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+137}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+68}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+17}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 19000000000000:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3: 68.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+109}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+68}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+18}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 20000000000000:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.3e+109)
   t
   (if (<= y -3.5e+68)
     (* (- x y) (/ t z))
     (if (<= y -2.6e+18)
       t
       (if (<= y 20000000000000.0) (* x (/ t (- z y))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.3e+109) {
		tmp = t;
	} else if (y <= -3.5e+68) {
		tmp = (x - y) * (t / z);
	} else if (y <= -2.6e+18) {
		tmp = t;
	} else if (y <= 20000000000000.0) {
		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 <= (-2.3d+109)) then
        tmp = t
    else if (y <= (-3.5d+68)) then
        tmp = (x - y) * (t / z)
    else if (y <= (-2.6d+18)) then
        tmp = t
    else if (y <= 20000000000000.0d0) 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 <= -2.3e+109) {
		tmp = t;
	} else if (y <= -3.5e+68) {
		tmp = (x - y) * (t / z);
	} else if (y <= -2.6e+18) {
		tmp = t;
	} else if (y <= 20000000000000.0) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.3e+109:
		tmp = t
	elif y <= -3.5e+68:
		tmp = (x - y) * (t / z)
	elif y <= -2.6e+18:
		tmp = t
	elif y <= 20000000000000.0:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.3e+109)
		tmp = t;
	elseif (y <= -3.5e+68)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= -2.6e+18)
		tmp = t;
	elseif (y <= 20000000000000.0)
		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 <= -2.3e+109)
		tmp = t;
	elseif (y <= -3.5e+68)
		tmp = (x - y) * (t / z);
	elseif (y <= -2.6e+18)
		tmp = t;
	elseif (y <= 20000000000000.0)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.3e+109], t, If[LessEqual[y, -3.5e+68], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.6e+18], t, If[LessEqual[y, 20000000000000.0], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3000000000000001e109 or -3.49999999999999977e68 < y < -2.6e18 or 2e13 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 73.4%

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

      2. associate-*r/ 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. Taylor expanded in y around inf 61.4%

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

   if -2.3000000000000001e109 < y < -3.49999999999999977e68

   1. Initial program 99.8%

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

      1. associate-*l/ 90.1%

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

      2. associate-*r/ 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in z around inf 74.3%

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

   if -2.6e18 < y < 2e13

   1. Initial program 93.5%

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

      1. associate-*l/ 95.3%

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

      2. associate-*r/ 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in x around inf 77.2%

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

      1. associate-*l/ 73.5%

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

      2. *-commutative 73.5%

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

   6. Simplified 73.5%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+109}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+68}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+18}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 20000000000000:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 69.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+109}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+68}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.75e+109)
   t
   (if (<= y -1.35e+68)
     (* (- x y) (/ t z))
     (if (<= y -1.6e+16) t (if (<= y 1.36e+88) (* t (/ x (- z y))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.75e+109) {
		tmp = t;
	} else if (y <= -1.35e+68) {
		tmp = (x - y) * (t / z);
	} else if (y <= -1.6e+16) {
		tmp = t;
	} else if (y <= 1.36e+88) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.75d+109)) then
        tmp = t
    else if (y <= (-1.35d+68)) then
        tmp = (x - y) * (t / z)
    else if (y <= (-1.6d+16)) then
        tmp = t
    else if (y <= 1.36d+88) then
        tmp = t * (x / (z - y))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.75e+109) {
		tmp = t;
	} else if (y <= -1.35e+68) {
		tmp = (x - y) * (t / z);
	} else if (y <= -1.6e+16) {
		tmp = t;
	} else if (y <= 1.36e+88) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.75e+109:
		tmp = t
	elif y <= -1.35e+68:
		tmp = (x - y) * (t / z)
	elif y <= -1.6e+16:
		tmp = t
	elif y <= 1.36e+88:
		tmp = t * (x / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.75e+109)
		tmp = t;
	elseif (y <= -1.35e+68)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= -1.6e+16)
		tmp = t;
	elseif (y <= 1.36e+88)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.75e+109)
		tmp = t;
	elseif (y <= -1.35e+68)
		tmp = (x - y) * (t / z);
	elseif (y <= -1.6e+16)
		tmp = t;
	elseif (y <= 1.36e+88)
		tmp = t * (x / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.75e+109], t, If[LessEqual[y, -1.35e+68], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.6e+16], t, If[LessEqual[y, 1.36e+88], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.74999999999999992e109 or -1.34999999999999995e68 < y < -1.6e16 or 1.3600000000000001e88 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 72.8%

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

      2. associate-*r/ 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in y around inf 65.0%

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

   if -1.74999999999999992e109 < y < -1.34999999999999995e68

   1. Initial program 99.8%

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

      1. associate-*l/ 90.1%

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

      2. associate-*r/ 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in z around inf 74.3%

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

   if -1.6e16 < y < 1.3600000000000001e88

   1. Initial program 94.2%

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

   2. Taylor expanded in x around inf 74.0%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+109}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{+68}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+16}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+88}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 76.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-34}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 18000000000000:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -2.8e+68)
     t_1
     (if (<= y -5.8e-34)
       (- t (* t (/ x y)))
       (if (<= y -2.5e-95)
         (* t (/ (- x y) z))
         (if (<= y 18000000000000.0) (* t (/ x (- z y))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -2.8e+68) {
		tmp = t_1;
	} else if (y <= -5.8e-34) {
		tmp = t - (t * (x / y));
	} else if (y <= -2.5e-95) {
		tmp = t * ((x - y) / z);
	} else if (y <= 18000000000000.0) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    if (y <= (-2.8d+68)) then
        tmp = t_1
    else if (y <= (-5.8d-34)) then
        tmp = t - (t * (x / y))
    else if (y <= (-2.5d-95)) then
        tmp = t * ((x - y) / z)
    else if (y <= 18000000000000.0d0) then
        tmp = t * (x / (z - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -2.8e+68) {
		tmp = t_1;
	} else if (y <= -5.8e-34) {
		tmp = t - (t * (x / y));
	} else if (y <= -2.5e-95) {
		tmp = t * ((x - y) / z);
	} else if (y <= 18000000000000.0) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -2.8e+68:
		tmp = t_1
	elif y <= -5.8e-34:
		tmp = t - (t * (x / y))
	elif y <= -2.5e-95:
		tmp = t * ((x - y) / z)
	elif y <= 18000000000000.0:
		tmp = t * (x / (z - y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -2.8e+68)
		tmp = t_1;
	elseif (y <= -5.8e-34)
		tmp = Float64(t - Float64(t * Float64(x / y)));
	elseif (y <= -2.5e-95)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (y <= 18000000000000.0)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -2.8e+68)
		tmp = t_1;
	elseif (y <= -5.8e-34)
		tmp = t - (t * (x / y));
	elseif (y <= -2.5e-95)
		tmp = t * ((x - y) / z);
	elseif (y <= 18000000000000.0)
		tmp = t * (x / (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e+68], t$95$1, If[LessEqual[y, -5.8e-34], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.5e-95], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 18000000000000.0], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.8e68 or 1.8e13 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 77.4%

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

      1. neg-mul-1 77.4%

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

      2. distribute-neg-frac 77.4%

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

   4. Simplified 77.4%

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

      1. frac-2neg 77.4%

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

      2. div-inv 77.3%

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

      3. remove-double-neg 77.3%

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

      4. sub-neg 77.3%

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

      5. distribute-neg-in 77.3%

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

      6. remove-double-neg 77.3%

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

   6. Applied egg-rr 77.3%

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

      1. associate-*r/ 77.4%

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

      2. *-rgt-identity 77.4%

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

      3. +-commutative 77.4%

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

      4. unsub-neg 77.4%

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

   8. Simplified 77.4%

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

   if -2.8e68 < y < -5.8000000000000004e-34

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 89.6%

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

      1. associate-*r/ 89.6%

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

      2. neg-mul-1 89.6%

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

      3. neg-sub0 89.6%

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

      4. associate--r- 89.6%

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

      5. neg-sub0 89.6%

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

   4. Simplified 89.6%

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

   5. Taylor expanded in x around 0 84.9%

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

      1. mul-1-neg 84.9%

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

      2. associate-/l* 89.6%

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

      3. unsub-neg 89.6%

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

      4. associate-/l* 84.9%

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

      5. associate-*r/ 89.7%

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

   7. Simplified 89.7%

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

   if -5.8000000000000004e-34 < y < -2.4999999999999999e-95

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf 75.0%

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

   if -2.4999999999999999e-95 < y < 1.8e13

   1. Initial program 92.5%

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

   2. Taylor expanded in x around inf 81.0%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-34}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 18000000000000:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]

Alternative 6: 75.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{-33}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -1.85e+68)
     t_1
     (if (<= y -1.26e-33)
       (- t (* t (/ x y)))
       (if (<= y -2.5e-95)
         (* t (/ (- x y) z))
         (if (<= y 4.4e-11) (/ (* x t) (- z y)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -1.85e+68) {
		tmp = t_1;
	} else if (y <= -1.26e-33) {
		tmp = t - (t * (x / y));
	} else if (y <= -2.5e-95) {
		tmp = t * ((x - y) / z);
	} else if (y <= 4.4e-11) {
		tmp = (x * t) / (z - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    if (y <= (-1.85d+68)) then
        tmp = t_1
    else if (y <= (-1.26d-33)) then
        tmp = t - (t * (x / y))
    else if (y <= (-2.5d-95)) then
        tmp = t * ((x - y) / z)
    else if (y <= 4.4d-11) then
        tmp = (x * t) / (z - y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -1.85e+68) {
		tmp = t_1;
	} else if (y <= -1.26e-33) {
		tmp = t - (t * (x / y));
	} else if (y <= -2.5e-95) {
		tmp = t * ((x - y) / z);
	} else if (y <= 4.4e-11) {
		tmp = (x * t) / (z - y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -1.85e+68:
		tmp = t_1
	elif y <= -1.26e-33:
		tmp = t - (t * (x / y))
	elif y <= -2.5e-95:
		tmp = t * ((x - y) / z)
	elif y <= 4.4e-11:
		tmp = (x * t) / (z - y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -1.85e+68)
		tmp = t_1;
	elseif (y <= -1.26e-33)
		tmp = Float64(t - Float64(t * Float64(x / y)));
	elseif (y <= -2.5e-95)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	elseif (y <= 4.4e-11)
		tmp = Float64(Float64(x * t) / Float64(z - y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -1.85e+68)
		tmp = t_1;
	elseif (y <= -1.26e-33)
		tmp = t - (t * (x / y));
	elseif (y <= -2.5e-95)
		tmp = t * ((x - y) / z);
	elseif (y <= 4.4e-11)
		tmp = (x * t) / (z - y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e+68], t$95$1, If[LessEqual[y, -1.26e-33], N[(t - N[(t * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.5e-95], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e-11], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.84999999999999999e68 or 4.4000000000000003e-11 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 74.9%

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

      1. neg-mul-1 74.9%

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

      2. distribute-neg-frac 74.9%

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

   4. Simplified 74.9%

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

      1. frac-2neg 74.9%

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

      2. div-inv 74.9%

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

      3. remove-double-neg 74.9%

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

      4. sub-neg 74.9%

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

      5. distribute-neg-in 74.9%

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

      6. remove-double-neg 74.9%

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

   6. Applied egg-rr 74.9%

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

      1. associate-*r/ 74.9%

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

      2. *-rgt-identity 74.9%

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

      3. +-commutative 74.9%

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

      4. unsub-neg 74.9%

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

   8. Simplified 74.9%

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

   if -1.84999999999999999e68 < y < -1.26000000000000005e-33

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 89.6%

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

      1. associate-*r/ 89.6%

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

      2. neg-mul-1 89.6%

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

      3. neg-sub0 89.6%

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

      4. associate--r- 89.6%

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

      5. neg-sub0 89.6%

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

   4. Simplified 89.6%

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

   5. Taylor expanded in x around 0 84.9%

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

      1. mul-1-neg 84.9%

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

      2. associate-/l* 89.6%

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

      3. unsub-neg 89.6%

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

      4. associate-/l* 84.9%

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

      5. associate-*r/ 89.7%

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

   7. Simplified 89.7%

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

   if -1.26000000000000005e-33 < y < -2.4999999999999999e-95

   1. Initial program 99.6%

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

   2. Taylor expanded in z around inf 75.0%

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

   if -2.4999999999999999e-95 < y < 4.4000000000000003e-11

   1. Initial program 92.0%

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

      1. associate-*l/ 95.9%

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

      2. associate-*r/ 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in x around inf 84.3%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{-33}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-95}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-11}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]

Alternative 7: 59.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+137}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+68}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-25}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.12e+137)
   t
   (if (<= y -3.8e+68)
     (/ (- y) (/ z t))
     (if (<= y -1.2e-25) t (if (<= y 3.2e-12) (/ (* x t) z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.12e+137) {
		tmp = t;
	} else if (y <= -3.8e+68) {
		tmp = -y / (z / t);
	} else if (y <= -1.2e-25) {
		tmp = t;
	} else if (y <= 3.2e-12) {
		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 <= (-1.12d+137)) then
        tmp = t
    else if (y <= (-3.8d+68)) then
        tmp = -y / (z / t)
    else if (y <= (-1.2d-25)) then
        tmp = t
    else if (y <= 3.2d-12) 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 <= -1.12e+137) {
		tmp = t;
	} else if (y <= -3.8e+68) {
		tmp = -y / (z / t);
	} else if (y <= -1.2e-25) {
		tmp = t;
	} else if (y <= 3.2e-12) {
		tmp = (x * t) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.12e+137:
		tmp = t
	elif y <= -3.8e+68:
		tmp = -y / (z / t)
	elif y <= -1.2e-25:
		tmp = t
	elif y <= 3.2e-12:
		tmp = (x * t) / z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.12e+137)
		tmp = t;
	elseif (y <= -3.8e+68)
		tmp = Float64(Float64(-y) / Float64(z / t));
	elseif (y <= -1.2e-25)
		tmp = t;
	elseif (y <= 3.2e-12)
		tmp = Float64(Float64(x * t) / z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.12e+137)
		tmp = t;
	elseif (y <= -3.8e+68)
		tmp = -y / (z / t);
	elseif (y <= -1.2e-25)
		tmp = t;
	elseif (y <= 3.2e-12)
		tmp = (x * t) / z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.12e+137], t, If[LessEqual[y, -3.8e+68], N[((-y) / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.2e-25], t, If[LessEqual[y, 3.2e-12], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1200000000000001e137 or -3.8000000000000001e68 < y < -1.20000000000000005e-25 or 3.2000000000000001e-12 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 74.2%

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

      2. associate-*r/ 81.5%

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

   3. Simplified 81.5%

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

   4. Taylor expanded in y around inf 59.1%

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

   if -1.1200000000000001e137 < y < -3.8000000000000001e68

   1. Initial program 99.9%

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

      1. associate-*l/ 93.3%

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

      2. associate-*r/ 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in x around 0 67.9%

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

      1. mul-1-neg 67.9%

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

      2. associate-*r/ 61.7%

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

      3. distribute-lft-neg-out 61.7%

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

      4. *-commutative 61.7%

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

   6. Simplified 61.7%

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

   7. Taylor expanded in z around inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. associate-/l* 54.9%

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

   9. Simplified 54.9%

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

   if -1.20000000000000005e-25 < y < 3.2000000000000001e-12

   1. Initial program 92.7%

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

      1. associate-*l/ 96.3%

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

      2. associate-*r/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in y around 0 68.2%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+137}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+68}:\\ \;\;\;\;\frac{-y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-25}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 90.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{+206} \lor \neg \left(y \leq 1.7 \cdot 10^{+124}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.1e+206) (not (<= y 1.7e+124)))
   (* t (/ y (- y z)))
   (* (- x y) (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.1e+206) || !(y <= 1.7e+124)) {
		tmp = t * (y / (y - z));
	} 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 <= (-6.1d+206)) .or. (.not. (y <= 1.7d+124))) then
        tmp = t * (y / (y - z))
    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 <= -6.1e+206) || !(y <= 1.7e+124)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.1e+206) or not (y <= 1.7e+124):
		tmp = t * (y / (y - z))
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.1e+206) || !(y <= 1.7e+124))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	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 <= -6.1e+206) || ~((y <= 1.7e+124)))
		tmp = t * (y / (y - z));
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.1e+206], N[Not[LessEqual[y, 1.7e+124]], $MachinePrecision]], N[(t * N[(y / N[(y - z), $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 < -6.09999999999999967e206 or 1.7e124 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 87.7%

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

      1. neg-mul-1 87.7%

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

      2. distribute-neg-frac 87.7%

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

   4. Simplified 87.7%

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

      1. frac-2neg 87.7%

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

      2. div-inv 87.6%

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

      3. remove-double-neg 87.6%

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

      4. sub-neg 87.6%

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

      5. distribute-neg-in 87.6%

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

      6. remove-double-neg 87.6%

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

   6. Applied egg-rr 87.6%

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

      1. associate-*r/ 87.7%

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

      2. *-rgt-identity 87.7%

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

      3. +-commutative 87.7%

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

      4. unsub-neg 87.7%

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

   8. Simplified 87.7%

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

   if -6.09999999999999967e206 < y < 1.7e124

   1. Initial program 95.5%

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

      1. associate-*l/ 90.7%

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

      2. associate-*r/ 91.1%

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

   3. Simplified 91.1%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{+206} \lor \neg \left(y \leq 1.7 \cdot 10^{+124}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 9: 76.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+14} \lor \neg \left(y \leq 20000000000000\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.8e+14) (not (<= y 20000000000000.0)))
   (* t (/ y (- y z)))
   (* t (/ x (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e+14) || !(y <= 20000000000000.0)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.8d+14)) .or. (.not. (y <= 20000000000000.0d0))) then
        tmp = t * (y / (y - z))
    else
        tmp = t * (x / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e+14) || !(y <= 20000000000000.0)) {
		tmp = t * (y / (y - z));
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.8e+14) or not (y <= 20000000000000.0):
		tmp = t * (y / (y - z))
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.8e+14) || !(y <= 20000000000000.0))
		tmp = Float64(t * Float64(y / Float64(y - z)));
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.8e+14) || ~((y <= 20000000000000.0)))
		tmp = t * (y / (y - z));
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.8e+14], N[Not[LessEqual[y, 20000000000000.0]], $MachinePrecision]], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8e14 or 2e13 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 77.8%

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

      1. neg-mul-1 77.8%

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

      2. distribute-neg-frac 77.8%

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

   4. Simplified 77.8%

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

      1. frac-2neg 77.8%

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

      2. div-inv 77.7%

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

      3. remove-double-neg 77.7%

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

      4. sub-neg 77.7%

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

      5. distribute-neg-in 77.7%

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

      6. remove-double-neg 77.7%

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

   6. Applied egg-rr 77.7%

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

      1. associate-*r/ 77.8%

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

      2. *-rgt-identity 77.8%

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

      3. +-commutative 77.8%

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

      4. unsub-neg 77.8%

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

   8. Simplified 77.8%

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

   if -3.8e14 < y < 2e13

   1. Initial program 93.5%

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

   2. Taylor expanded in x around inf 77.7%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+14} \lor \neg \left(y \leq 20000000000000\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]

Alternative 10: 40.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-34}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-56}:\\ \;\;\;\;y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4e-34) t (if (<= y 1.05e-56) (* y (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4e-34) {
		tmp = t;
	} else if (y <= 1.05e-56) {
		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 <= (-4d-34)) then
        tmp = t
    else if (y <= 1.05d-56) 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 <= -4e-34) {
		tmp = t;
	} else if (y <= 1.05e-56) {
		tmp = y * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4e-34:
		tmp = t
	elif y <= 1.05e-56:
		tmp = y * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4e-34)
		tmp = t;
	elseif (y <= 1.05e-56)
		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 <= -4e-34)
		tmp = t;
	elseif (y <= 1.05e-56)
		tmp = y * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4e-34], t, If[LessEqual[y, 1.05e-56], N[(y * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999971e-34 or 1.05000000000000003e-56 < 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-*r/ 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in y around inf 51.1%

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

   if -3.99999999999999971e-34 < y < 1.05000000000000003e-56

   1. Initial program 92.2%

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

      1. associate-*l/ 96.0%

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

      2. associate-*r/ 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in x around 0 32.3%

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

      1. mul-1-neg 32.3%

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

      2. associate-*r/ 37.0%

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

      3. distribute-lft-neg-out 37.0%

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

      4. *-commutative 37.0%

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

   6. Simplified 37.0%

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

   7. Taylor expanded in z around inf 30.7%

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

      1. expm1-log1p-u 28.7%

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

      2. expm1-udef 20.0%

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

      3. add-sqr-sqrt 8.7%

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

      4. sqrt-unprod 19.0%

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

      5. sqr-neg 19.0%

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

      6. sqrt-unprod 13.8%

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

      7. add-sqr-sqrt 21.7%

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

      8. *-commutative 21.7%

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

   9. Applied egg-rr 21.7%

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

       1. expm1-def 21.8%

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

       2. expm1-log1p 24.8%

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

   11. Simplified 24.8%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-34}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-56}:\\ \;\;\;\;y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 61.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{-25}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.52e-25) t (if (<= y 6.8e-12) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.52e-25) {
		tmp = t;
	} else if (y <= 6.8e-12) {
		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 <= (-1.52d-25)) then
        tmp = t
    else if (y <= 6.8d-12) 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 <= -1.52e-25) {
		tmp = t;
	} else if (y <= 6.8e-12) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.52e-25:
		tmp = t
	elif y <= 6.8e-12:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.52e-25)
		tmp = t;
	elseif (y <= 6.8e-12)
		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 <= -1.52e-25)
		tmp = t;
	elseif (y <= 6.8e-12)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.52e-25], t, If[LessEqual[y, 6.8e-12], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.52000000000000006e-25 or 6.8000000000000001e-12 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 76.4%

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

      2. associate-*r/ 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in y around inf 54.3%

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

   if -1.52000000000000006e-25 < y < 6.8000000000000001e-12

   1. Initial program 92.7%

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

      1. clear-num 90.4%

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

      2. associate-/r/ 92.7%

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

   3. Applied egg-rr 92.7%

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

   4. Taylor expanded in y around 0 68.2%

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

      1. associate-/l* 65.2%

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

      2. associate-/r/ 64.4%

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

   6. Simplified 64.4%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{-25}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12: 62.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{-25}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.52e-25) t (if (<= y 2.4e-21) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.52e-25) {
		tmp = t;
	} else if (y <= 2.4e-21) {
		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 <= (-1.52d-25)) then
        tmp = t
    else if (y <= 2.4d-21) 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 <= -1.52e-25) {
		tmp = t;
	} else if (y <= 2.4e-21) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.52e-25:
		tmp = t
	elif y <= 2.4e-21:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.52e-25)
		tmp = t;
	elseif (y <= 2.4e-21)
		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 <= -1.52e-25)
		tmp = t;
	elseif (y <= 2.4e-21)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.52e-25], t, If[LessEqual[y, 2.4e-21], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.52000000000000006e-25 or 2.3999999999999999e-21 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 76.4%

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

      2. associate-*r/ 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in y around inf 54.3%

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

   if -1.52000000000000006e-25 < y < 2.3999999999999999e-21

   1. Initial program 92.7%

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

   2. Taylor expanded in y around 0 67.1%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{-25}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-25}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-12}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.25e-25) t (if (<= y 1.05e-12) (/ (* x t) z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e-25) {
		tmp = t;
	} else if (y <= 1.05e-12) {
		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 <= (-1.25d-25)) then
        tmp = t
    else if (y <= 1.05d-12) 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 <= -1.25e-25) {
		tmp = t;
	} else if (y <= 1.05e-12) {
		tmp = (x * t) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.25e-25:
		tmp = t
	elif y <= 1.05e-12:
		tmp = (x * t) / z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.25e-25)
		tmp = t;
	elseif (y <= 1.05e-12)
		tmp = Float64(Float64(x * t) / z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.25e-25)
		tmp = t;
	elseif (y <= 1.05e-12)
		tmp = (x * t) / z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.25e-25], t, If[LessEqual[y, 1.05e-12], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2499999999999999e-25 or 1.04999999999999997e-12 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 76.4%

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

      2. associate-*r/ 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in y around inf 54.3%

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

   if -1.2499999999999999e-25 < y < 1.04999999999999997e-12

   1. Initial program 92.7%

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

      1. associate-*l/ 96.3%

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

      2. associate-*r/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in y around 0 68.2%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-25}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-12}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14: 35.0% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.4%

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

   1. associate-*l/ 85.9%

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

   2. associate-*r/ 86.3%

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

3. Simplified 86.3%

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

4. Taylor expanded in y around inf 31.9%

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

5. Final simplification 31.9%

   \[\leadsto t \]

Developer target: 97.1% 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 2023200 
(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))