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

Percentage Accurate: 97.0% → 97.0%

Time: 11.7s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

3. Final simplification 97.2%

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

Alternative 2: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{z}{x - y}}\\ t_2 := \frac{t}{\frac{y}{y - x}}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-17}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ z (- x y)))) (t_2 (/ t (/ y (- y x)))))
   (if (<= y -2.5e-10)
     t_2
     (if (<= y -3.5e-225)
       t_1
       (if (<= y 3.8e-241)
         (* x (/ t (- z y)))
         (if (<= y 1.7e-39)
           t_1
           (if (<= y 2.25e-17)
             (* (- y x) (/ t y))
             (if (<= y 1.1e+100) 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 / (y / (y - x));
	double tmp;
	if (y <= -2.5e-10) {
		tmp = t_2;
	} else if (y <= -3.5e-225) {
		tmp = t_1;
	} else if (y <= 3.8e-241) {
		tmp = x * (t / (z - y));
	} else if (y <= 1.7e-39) {
		tmp = t_1;
	} else if (y <= 2.25e-17) {
		tmp = (y - x) * (t / y);
	} else if (y <= 1.1e+100) {
		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 / (y / (y - x))
    if (y <= (-2.5d-10)) then
        tmp = t_2
    else if (y <= (-3.5d-225)) then
        tmp = t_1
    else if (y <= 3.8d-241) then
        tmp = x * (t / (z - y))
    else if (y <= 1.7d-39) then
        tmp = t_1
    else if (y <= 2.25d-17) then
        tmp = (y - x) * (t / y)
    else if (y <= 1.1d+100) 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 / (y / (y - x));
	double tmp;
	if (y <= -2.5e-10) {
		tmp = t_2;
	} else if (y <= -3.5e-225) {
		tmp = t_1;
	} else if (y <= 3.8e-241) {
		tmp = x * (t / (z - y));
	} else if (y <= 1.7e-39) {
		tmp = t_1;
	} else if (y <= 2.25e-17) {
		tmp = (y - x) * (t / y);
	} else if (y <= 1.1e+100) {
		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 / (y / (y - x))
	tmp = 0
	if y <= -2.5e-10:
		tmp = t_2
	elif y <= -3.5e-225:
		tmp = t_1
	elif y <= 3.8e-241:
		tmp = x * (t / (z - y))
	elif y <= 1.7e-39:
		tmp = t_1
	elif y <= 2.25e-17:
		tmp = (y - x) * (t / y)
	elif y <= 1.1e+100:
		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(y / Float64(y - x)))
	tmp = 0.0
	if (y <= -2.5e-10)
		tmp = t_2;
	elseif (y <= -3.5e-225)
		tmp = t_1;
	elseif (y <= 3.8e-241)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 1.7e-39)
		tmp = t_1;
	elseif (y <= 2.25e-17)
		tmp = Float64(Float64(y - x) * Float64(t / y));
	elseif (y <= 1.1e+100)
		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 / (y / (y - x));
	tmp = 0.0;
	if (y <= -2.5e-10)
		tmp = t_2;
	elseif (y <= -3.5e-225)
		tmp = t_1;
	elseif (y <= 3.8e-241)
		tmp = x * (t / (z - y));
	elseif (y <= 1.7e-39)
		tmp = t_1;
	elseif (y <= 2.25e-17)
		tmp = (y - x) * (t / y);
	elseif (y <= 1.1e+100)
		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[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e-10], t$95$2, If[LessEqual[y, -3.5e-225], t$95$1, If[LessEqual[y, 3.8e-241], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-39], t$95$1, If[LessEqual[y, 2.25e-17], N[(N[(y - x), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+100], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.50000000000000016e-10 or 1.1e100 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 63.0%

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

      1. associate-*r/ 63.0%

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

      2. *-commutative 63.0%

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

      3. neg-mul-1 63.0%

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

      4. distribute-lft-neg-in 63.0%

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

      5. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in t around 0 63.0%

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

      1. associate-/l* 82.6%

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

   8. Simplified 82.6%

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

   if -2.50000000000000016e-10 < y < -3.4999999999999997e-225 or 3.7999999999999999e-241 < y < 1.7e-39 or 2.24999999999999989e-17 < y < 1.1e100

   1. Initial program 96.8%

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

   3. Taylor expanded in z around inf 74.6%

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

      1. associate-/l* 80.6%

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

   5. Simplified 80.6%

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

   if -3.4999999999999997e-225 < y < 3.7999999999999999e-241

   1. Initial program 86.2%

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

   3. Taylor expanded in x around inf 96.5%

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

      1. *-commutative 96.5%

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

      2. associate-*r/ 94.3%

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

   5. Simplified 94.3%

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

   if 1.7e-39 < y < 2.24999999999999989e-17

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. *-commutative 100.0%

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

      3. neg-mul-1 100.0%

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

      4. distribute-lft-neg-in 100.0%

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

      5. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around 0 100.0%

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

      1. associate-/l* 99.7%

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

      2. associate-/r/ 99.7%

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

   8. Simplified 99.7%

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

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-225}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-39}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-17}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+100}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{z}{x - y}}\\ t_2 := \frac{t}{\frac{y}{y - x}}\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{-245}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+85}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ z (- x y)))) (t_2 (/ t (/ y (- y x)))))
   (if (<= y -3.7e-10)
     t_2
     (if (<= y -3.8e-225)
       t_1
       (if (<= y 3.35e-245)
         (* x (/ t (- z y)))
         (if (<= y 2.25e-57)
           t_1
           (if (<= y 6.2e+85) (/ t (/ (- z y) x)) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (z / (x - y));
	double t_2 = t / (y / (y - x));
	double tmp;
	if (y <= -3.7e-10) {
		tmp = t_2;
	} else if (y <= -3.8e-225) {
		tmp = t_1;
	} else if (y <= 3.35e-245) {
		tmp = x * (t / (z - y));
	} else if (y <= 2.25e-57) {
		tmp = t_1;
	} else if (y <= 6.2e+85) {
		tmp = t / ((z - y) / x);
	} 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 / (y / (y - x))
    if (y <= (-3.7d-10)) then
        tmp = t_2
    else if (y <= (-3.8d-225)) then
        tmp = t_1
    else if (y <= 3.35d-245) then
        tmp = x * (t / (z - y))
    else if (y <= 2.25d-57) then
        tmp = t_1
    else if (y <= 6.2d+85) then
        tmp = t / ((z - y) / x)
    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 / (y / (y - x));
	double tmp;
	if (y <= -3.7e-10) {
		tmp = t_2;
	} else if (y <= -3.8e-225) {
		tmp = t_1;
	} else if (y <= 3.35e-245) {
		tmp = x * (t / (z - y));
	} else if (y <= 2.25e-57) {
		tmp = t_1;
	} else if (y <= 6.2e+85) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (z / (x - y))
	t_2 = t / (y / (y - x))
	tmp = 0
	if y <= -3.7e-10:
		tmp = t_2
	elif y <= -3.8e-225:
		tmp = t_1
	elif y <= 3.35e-245:
		tmp = x * (t / (z - y))
	elif y <= 2.25e-57:
		tmp = t_1
	elif y <= 6.2e+85:
		tmp = t / ((z - y) / x)
	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(y / Float64(y - x)))
	tmp = 0.0
	if (y <= -3.7e-10)
		tmp = t_2;
	elseif (y <= -3.8e-225)
		tmp = t_1;
	elseif (y <= 3.35e-245)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 2.25e-57)
		tmp = t_1;
	elseif (y <= 6.2e+85)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	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 / (y / (y - x));
	tmp = 0.0;
	if (y <= -3.7e-10)
		tmp = t_2;
	elseif (y <= -3.8e-225)
		tmp = t_1;
	elseif (y <= 3.35e-245)
		tmp = x * (t / (z - y));
	elseif (y <= 2.25e-57)
		tmp = t_1;
	elseif (y <= 6.2e+85)
		tmp = t / ((z - y) / x);
	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[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.7e-10], t$95$2, If[LessEqual[y, -3.8e-225], t$95$1, If[LessEqual[y, 3.35e-245], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e-57], t$95$1, If[LessEqual[y, 6.2e+85], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.70000000000000015e-10 or 6.20000000000000023e85 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 62.8%

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

      1. associate-*r/ 62.8%

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

      2. *-commutative 62.8%

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

      3. neg-mul-1 62.8%

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

      4. distribute-lft-neg-in 62.8%

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

      5. *-commutative 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in t around 0 62.8%

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

      1. associate-/l* 82.1%

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

   8. Simplified 82.1%

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

   if -3.70000000000000015e-10 < y < -3.8000000000000003e-225 or 3.35e-245 < y < 2.24999999999999986e-57

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 79.7%

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

      1. associate-/l* 85.4%

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

   5. Simplified 85.4%

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

   if -3.8000000000000003e-225 < y < 3.35e-245

   1. Initial program 86.2%

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

   3. Taylor expanded in x around inf 96.5%

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

      1. *-commutative 96.5%

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

      2. associate-*r/ 94.3%

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

   5. Simplified 94.3%

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

   if 2.24999999999999986e-57 < y < 6.20000000000000023e85

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 64.6%

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

      1. associate-/l* 70.8%

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

   5. Simplified 70.8%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-10}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-225}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 3.35 \cdot 10^{-245}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-57}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+85}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{z}{x - y}}\\ t_2 := \frac{t}{\frac{y}{y - x}}\\ \mathbf{if}\;y \leq -3 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-237}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+85}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ z (- x y)))) (t_2 (/ t (/ y (- y x)))))
   (if (<= y -3e-11)
     t_2
     (if (<= y -1.65e-245)
       t_1
       (if (<= y 2.15e-237)
         (/ (* x t) (- z y))
         (if (<= y 2.9e-57)
           t_1
           (if (<= y 4.2e+85) (/ t (/ (- z y) x)) t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (z / (x - y));
	double t_2 = t / (y / (y - x));
	double tmp;
	if (y <= -3e-11) {
		tmp = t_2;
	} else if (y <= -1.65e-245) {
		tmp = t_1;
	} else if (y <= 2.15e-237) {
		tmp = (x * t) / (z - y);
	} else if (y <= 2.9e-57) {
		tmp = t_1;
	} else if (y <= 4.2e+85) {
		tmp = t / ((z - y) / x);
	} 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 / (y / (y - x))
    if (y <= (-3d-11)) then
        tmp = t_2
    else if (y <= (-1.65d-245)) then
        tmp = t_1
    else if (y <= 2.15d-237) then
        tmp = (x * t) / (z - y)
    else if (y <= 2.9d-57) then
        tmp = t_1
    else if (y <= 4.2d+85) then
        tmp = t / ((z - y) / x)
    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 / (y / (y - x));
	double tmp;
	if (y <= -3e-11) {
		tmp = t_2;
	} else if (y <= -1.65e-245) {
		tmp = t_1;
	} else if (y <= 2.15e-237) {
		tmp = (x * t) / (z - y);
	} else if (y <= 2.9e-57) {
		tmp = t_1;
	} else if (y <= 4.2e+85) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (z / (x - y))
	t_2 = t / (y / (y - x))
	tmp = 0
	if y <= -3e-11:
		tmp = t_2
	elif y <= -1.65e-245:
		tmp = t_1
	elif y <= 2.15e-237:
		tmp = (x * t) / (z - y)
	elif y <= 2.9e-57:
		tmp = t_1
	elif y <= 4.2e+85:
		tmp = t / ((z - y) / x)
	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(y / Float64(y - x)))
	tmp = 0.0
	if (y <= -3e-11)
		tmp = t_2;
	elseif (y <= -1.65e-245)
		tmp = t_1;
	elseif (y <= 2.15e-237)
		tmp = Float64(Float64(x * t) / Float64(z - y));
	elseif (y <= 2.9e-57)
		tmp = t_1;
	elseif (y <= 4.2e+85)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	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 / (y / (y - x));
	tmp = 0.0;
	if (y <= -3e-11)
		tmp = t_2;
	elseif (y <= -1.65e-245)
		tmp = t_1;
	elseif (y <= 2.15e-237)
		tmp = (x * t) / (z - y);
	elseif (y <= 2.9e-57)
		tmp = t_1;
	elseif (y <= 4.2e+85)
		tmp = t / ((z - y) / x);
	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[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3e-11], t$95$2, If[LessEqual[y, -1.65e-245], t$95$1, If[LessEqual[y, 2.15e-237], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-57], t$95$1, If[LessEqual[y, 4.2e+85], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3e-11 or 4.2000000000000002e85 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 62.8%

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

      1. associate-*r/ 62.8%

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

      2. *-commutative 62.8%

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

      3. neg-mul-1 62.8%

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

      4. distribute-lft-neg-in 62.8%

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

      5. *-commutative 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in t around 0 62.8%

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

      1. associate-/l* 82.1%

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

   8. Simplified 82.1%

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

   if -3e-11 < y < -1.65e-245 or 2.14999999999999991e-237 < y < 2.90000000000000025e-57

   1. Initial program 95.7%

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

   3. Taylor expanded in z around inf 78.7%

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

      1. associate-/l* 85.5%

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

   5. Simplified 85.5%

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

   if -1.65e-245 < y < 2.14999999999999991e-237

   1. Initial program 85.8%

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

   3. Taylor expanded in x around inf 99.8%

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

   if 2.90000000000000025e-57 < y < 4.2000000000000002e85

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 64.6%

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

      1. associate-/l* 70.8%

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

   5. Simplified 70.8%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-11}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-245}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-237}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-57}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+85}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{y}{y - x}}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-245}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-228}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-57}:\\ \;\;\;\;\frac{x - y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+85}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ y (- y x)))))
   (if (<= y -1.05e-10)
     t_1
     (if (<= y -5.4e-245)
       (/ t (/ z (- x y)))
       (if (<= y 4.9e-228)
         (/ (* x t) (- z y))
         (if (<= y 3.3e-57)
           (/ (- x y) (/ z t))
           (if (<= y 2.4e+85) (/ t (/ (- z y) x)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (y / (y - x));
	double tmp;
	if (y <= -1.05e-10) {
		tmp = t_1;
	} else if (y <= -5.4e-245) {
		tmp = t / (z / (x - y));
	} else if (y <= 4.9e-228) {
		tmp = (x * t) / (z - y);
	} else if (y <= 3.3e-57) {
		tmp = (x - y) / (z / t);
	} else if (y <= 2.4e+85) {
		tmp = t / ((z - y) / x);
	} 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 - x))
    if (y <= (-1.05d-10)) then
        tmp = t_1
    else if (y <= (-5.4d-245)) then
        tmp = t / (z / (x - y))
    else if (y <= 4.9d-228) then
        tmp = (x * t) / (z - y)
    else if (y <= 3.3d-57) then
        tmp = (x - y) / (z / t)
    else if (y <= 2.4d+85) then
        tmp = t / ((z - y) / x)
    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 - x));
	double tmp;
	if (y <= -1.05e-10) {
		tmp = t_1;
	} else if (y <= -5.4e-245) {
		tmp = t / (z / (x - y));
	} else if (y <= 4.9e-228) {
		tmp = (x * t) / (z - y);
	} else if (y <= 3.3e-57) {
		tmp = (x - y) / (z / t);
	} else if (y <= 2.4e+85) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / (y / (y - x))
	tmp = 0
	if y <= -1.05e-10:
		tmp = t_1
	elif y <= -5.4e-245:
		tmp = t / (z / (x - y))
	elif y <= 4.9e-228:
		tmp = (x * t) / (z - y)
	elif y <= 3.3e-57:
		tmp = (x - y) / (z / t)
	elif y <= 2.4e+85:
		tmp = t / ((z - y) / x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(y / Float64(y - x)))
	tmp = 0.0
	if (y <= -1.05e-10)
		tmp = t_1;
	elseif (y <= -5.4e-245)
		tmp = Float64(t / Float64(z / Float64(x - y)));
	elseif (y <= 4.9e-228)
		tmp = Float64(Float64(x * t) / Float64(z - y));
	elseif (y <= 3.3e-57)
		tmp = Float64(Float64(x - y) / Float64(z / t));
	elseif (y <= 2.4e+85)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / (y / (y - x));
	tmp = 0.0;
	if (y <= -1.05e-10)
		tmp = t_1;
	elseif (y <= -5.4e-245)
		tmp = t / (z / (x - y));
	elseif (y <= 4.9e-228)
		tmp = (x * t) / (z - y);
	elseif (y <= 3.3e-57)
		tmp = (x - y) / (z / t);
	elseif (y <= 2.4e+85)
		tmp = t / ((z - y) / x);
	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 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e-10], t$95$1, If[LessEqual[y, -5.4e-245], N[(t / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.9e-228], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e-57], N[(N[(x - y), $MachinePrecision] / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+85], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.05e-10 or 2.39999999999999997e85 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 62.8%

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

      1. associate-*r/ 62.8%

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

      2. *-commutative 62.8%

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

      3. neg-mul-1 62.8%

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

      4. distribute-lft-neg-in 62.8%

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

      5. *-commutative 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in t around 0 62.8%

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

      1. associate-/l* 82.1%

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

   8. Simplified 82.1%

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

   if -1.05e-10 < y < -5.39999999999999979e-245

   1. Initial program 95.0%

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

   3. Taylor expanded in z around inf 76.8%

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

      1. associate-/l* 83.4%

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

   5. Simplified 83.4%

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

   if -5.39999999999999979e-245 < y < 4.89999999999999988e-228

   1. Initial program 85.8%

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

   3. Taylor expanded in x around inf 99.8%

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

   if 4.89999999999999988e-228 < y < 3.2999999999999998e-57

   1. Initial program 96.6%

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

      1. associate-/r/ 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around inf 90.3%

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

   if 3.2999999999999998e-57 < y < 2.39999999999999997e85

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 64.6%

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

      1. associate-/l* 70.8%

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

   5. Simplified 70.8%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-10}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-245}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-228}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-57}:\\ \;\;\;\;\frac{x - y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+85}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+118}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-10}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-57}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+132}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.55e+118)
   t
   (if (<= y -1.08e-10)
     (* (- y x) (/ t y))
     (if (<= y 4.5e-57)
       (* (- x y) (/ t z))
       (if (<= y 1.7e+91)
         (* x (/ t (- z y)))
         (if (<= y 4.4e+132) (* t (/ (- y) z)) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.55e+118) {
		tmp = t;
	} else if (y <= -1.08e-10) {
		tmp = (y - x) * (t / y);
	} else if (y <= 4.5e-57) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.7e+91) {
		tmp = x * (t / (z - y));
	} else if (y <= 4.4e+132) {
		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 <= (-1.55d+118)) then
        tmp = t
    else if (y <= (-1.08d-10)) then
        tmp = (y - x) * (t / y)
    else if (y <= 4.5d-57) then
        tmp = (x - y) * (t / z)
    else if (y <= 1.7d+91) then
        tmp = x * (t / (z - y))
    else if (y <= 4.4d+132) 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 <= -1.55e+118) {
		tmp = t;
	} else if (y <= -1.08e-10) {
		tmp = (y - x) * (t / y);
	} else if (y <= 4.5e-57) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.7e+91) {
		tmp = x * (t / (z - y));
	} else if (y <= 4.4e+132) {
		tmp = t * (-y / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.55e+118:
		tmp = t
	elif y <= -1.08e-10:
		tmp = (y - x) * (t / y)
	elif y <= 4.5e-57:
		tmp = (x - y) * (t / z)
	elif y <= 1.7e+91:
		tmp = x * (t / (z - y))
	elif y <= 4.4e+132:
		tmp = t * (-y / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.55e+118)
		tmp = t;
	elseif (y <= -1.08e-10)
		tmp = Float64(Float64(y - x) * Float64(t / y));
	elseif (y <= 4.5e-57)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 1.7e+91)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 4.4e+132)
		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 <= -1.55e+118)
		tmp = t;
	elseif (y <= -1.08e-10)
		tmp = (y - x) * (t / y);
	elseif (y <= 4.5e-57)
		tmp = (x - y) * (t / z);
	elseif (y <= 1.7e+91)
		tmp = x * (t / (z - y));
	elseif (y <= 4.4e+132)
		tmp = t * (-y / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.55e+118], t, If[LessEqual[y, -1.08e-10], N[(N[(y - x), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-57], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+91], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.4e+132], N[(t * N[((-y) / z), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.54999999999999993e118 or 4.39999999999999977e132 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 77.7%

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

   if -1.54999999999999993e118 < y < -1.08000000000000002e-10

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 66.8%

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

      1. associate-*r/ 66.8%

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

      2. *-commutative 66.8%

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

      3. neg-mul-1 66.8%

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

      4. distribute-lft-neg-in 66.8%

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

      5. *-commutative 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in t around 0 66.8%

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

      1. associate-/l* 69.8%

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

      2. associate-/r/ 69.4%

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

   8. Simplified 69.4%

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

   if -1.08000000000000002e-10 < y < 4.49999999999999973e-57

   1. Initial program 93.1%

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

   3. Taylor expanded in z around inf 80.4%

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

      1. associate-/l* 82.7%

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

      2. associate-/r/ 82.1%

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

   5. Simplified 82.1%

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

   if 4.49999999999999973e-57 < y < 1.7e91

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 65.7%

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

      1. *-commutative 65.7%

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

      2. associate-*r/ 67.9%

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

   5. Simplified 67.9%

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

   if 1.7e91 < y < 4.39999999999999977e132

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.0%

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

      1. neg-mul-1 79.0%

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

      2. distribute-neg-frac 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in y around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. distribute-neg-frac 56.4%

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

   8. Simplified 56.4%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+118}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-10}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-57}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+132}:\\ \;\;\;\;t \cdot \frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-11} \lor \neg \left(y \leq 3.9 \cdot 10^{-57}\right) \land \left(y \leq 1.3 \cdot 10^{-15} \lor \neg \left(y \leq 3.2 \cdot 10^{+91}\right)\right):\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.2e-11)
         (and (not (<= y 3.9e-57)) (or (<= y 1.3e-15) (not (<= y 3.2e+91)))))
   (/ t (/ y (- y x)))
   (* (- x y) (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.2e-11) || (!(y <= 3.9e-57) && ((y <= 1.3e-15) || !(y <= 3.2e+91)))) {
		tmp = t / (y / (y - x));
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-5.2d-11)) .or. (.not. (y <= 3.9d-57)) .and. (y <= 1.3d-15) .or. (.not. (y <= 3.2d+91))) then
        tmp = t / (y / (y - x))
    else
        tmp = (x - y) * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.2e-11) || (!(y <= 3.9e-57) && ((y <= 1.3e-15) || !(y <= 3.2e+91)))) {
		tmp = t / (y / (y - x));
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5.2e-11) or (not (y <= 3.9e-57) and ((y <= 1.3e-15) or not (y <= 3.2e+91))):
		tmp = t / (y / (y - x))
	else:
		tmp = (x - y) * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5.2e-11) || (!(y <= 3.9e-57) && ((y <= 1.3e-15) || !(y <= 3.2e+91))))
		tmp = Float64(t / Float64(y / Float64(y - x)));
	else
		tmp = Float64(Float64(x - y) * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5.2e-11) || (~((y <= 3.9e-57)) && ((y <= 1.3e-15) || ~((y <= 3.2e+91)))))
		tmp = t / (y / (y - x));
	else
		tmp = (x - y) * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5.2e-11], And[N[Not[LessEqual[y, 3.9e-57]], $MachinePrecision], Or[LessEqual[y, 1.3e-15], N[Not[LessEqual[y, 3.2e+91]], $MachinePrecision]]]], N[(t / N[(y / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2000000000000001e-11 or 3.90000000000000006e-57 < y < 1.30000000000000002e-15 or 3.19999999999999989e91 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 64.3%

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

      1. associate-*r/ 64.3%

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

      2. *-commutative 64.3%

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

      3. neg-mul-1 64.3%

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

      4. distribute-lft-neg-in 64.3%

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

      5. *-commutative 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in t around 0 64.3%

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

      1. associate-/l* 82.7%

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

   8. Simplified 82.7%

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

   if -5.2000000000000001e-11 < y < 3.90000000000000006e-57 or 1.30000000000000002e-15 < y < 3.19999999999999989e91

   1. Initial program 94.5%

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

   3. Taylor expanded in z around inf 76.6%

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

      1. associate-/l* 79.9%

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

      2. associate-/r/ 79.4%

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

   5. Simplified 79.4%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-11} \lor \neg \left(y \leq 3.9 \cdot 10^{-57}\right) \land \left(y \leq 1.3 \cdot 10^{-15} \lor \neg \left(y \leq 3.2 \cdot 10^{+91}\right)\right):\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+71}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8200000000 \lor \neg \left(y \leq -7.8 \cdot 10^{-26}\right) \land y \leq 1.05 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.2e+71)
   t
   (if (or (<= y -8200000000.0) (and (not (<= y -7.8e-26)) (<= y 1.05e+88)))
     (* x (/ t (- z y)))
     t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.2e+71) {
		tmp = t;
	} else if ((y <= -8200000000.0) || (!(y <= -7.8e-26) && (y <= 1.05e+88))) {
		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 <= (-2.2d+71)) then
        tmp = t
    else if ((y <= (-8200000000.0d0)) .or. (.not. (y <= (-7.8d-26))) .and. (y <= 1.05d+88)) 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 <= -2.2e+71) {
		tmp = t;
	} else if ((y <= -8200000000.0) || (!(y <= -7.8e-26) && (y <= 1.05e+88))) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.2e+71:
		tmp = t
	elif (y <= -8200000000.0) or (not (y <= -7.8e-26) and (y <= 1.05e+88)):
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.2e+71)
		tmp = t;
	elseif ((y <= -8200000000.0) || (!(y <= -7.8e-26) && (y <= 1.05e+88)))
		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 <= -2.2e+71)
		tmp = t;
	elseif ((y <= -8200000000.0) || (~((y <= -7.8e-26)) && (y <= 1.05e+88)))
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.2e+71], t, If[Or[LessEqual[y, -8200000000.0], And[N[Not[LessEqual[y, -7.8e-26]], $MachinePrecision], LessEqual[y, 1.05e+88]]], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.19999999999999995e71 or -8.2e9 < y < -7.79999999999999973e-26 or 1.05e88 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 70.8%

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

   if -2.19999999999999995e71 < y < -8.2e9 or -7.79999999999999973e-26 < y < 1.05e88

   1. Initial program 95.2%

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

   3. Taylor expanded in x around inf 71.5%

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

      1. *-commutative 71.5%

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

      2. associate-*r/ 74.6%

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

   5. Simplified 74.6%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+71}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8200000000 \lor \neg \left(y \leq -7.8 \cdot 10^{-26}\right) \land y \leq 1.05 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -23000000000:\\ \;\;\;\;x \cdot \left(-\frac{t}{y}\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-12}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.1e+72)
   t
   (if (<= y -23000000000.0)
     (* x (- (/ t y)))
     (if (<= y -2.3e-12) t (if (<= y 4e+87) (* t (/ x z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.1e+72) {
		tmp = t;
	} else if (y <= -23000000000.0) {
		tmp = x * -(t / y);
	} else if (y <= -2.3e-12) {
		tmp = t;
	} else if (y <= 4e+87) {
		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 <= (-1.1d+72)) then
        tmp = t
    else if (y <= (-23000000000.0d0)) then
        tmp = x * -(t / y)
    else if (y <= (-2.3d-12)) then
        tmp = t
    else if (y <= 4d+87) 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 <= -1.1e+72) {
		tmp = t;
	} else if (y <= -23000000000.0) {
		tmp = x * -(t / y);
	} else if (y <= -2.3e-12) {
		tmp = t;
	} else if (y <= 4e+87) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.1e+72:
		tmp = t
	elif y <= -23000000000.0:
		tmp = x * -(t / y)
	elif y <= -2.3e-12:
		tmp = t
	elif y <= 4e+87:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.1e+72)
		tmp = t;
	elseif (y <= -23000000000.0)
		tmp = Float64(x * Float64(-Float64(t / y)));
	elseif (y <= -2.3e-12)
		tmp = t;
	elseif (y <= 4e+87)
		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 <= -1.1e+72)
		tmp = t;
	elseif (y <= -23000000000.0)
		tmp = x * -(t / y);
	elseif (y <= -2.3e-12)
		tmp = t;
	elseif (y <= 4e+87)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.1e+72], t, If[LessEqual[y, -23000000000.0], N[(x * (-N[(t / y), $MachinePrecision])), $MachinePrecision], If[LessEqual[y, -2.3e-12], t, If[LessEqual[y, 4e+87], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e72 or -2.3e10 < y < -2.29999999999999989e-12 or 3.9999999999999998e87 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 71.4%

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

   if -1.1e72 < y < -2.3e10

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 63.9%

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

      1. *-commutative 63.9%

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

      2. associate-*r/ 69.9%

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

   5. Simplified 69.9%

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

   6. Taylor expanded in z around 0 53.6%

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

      1. associate-*r/ 53.6%

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

      2. neg-mul-1 53.6%

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

   8. Simplified 53.6%

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

   if -2.29999999999999989e-12 < y < 3.9999999999999998e87

   1. Initial program 94.6%

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

   3. Taylor expanded in y around 0 64.1%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -23000000000:\\ \;\;\;\;x \cdot \left(-\frac{t}{y}\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-12}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -10800000000:\\ \;\;\;\;\frac{x}{\frac{y}{-t}}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-13}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.8e+72)
   t
   (if (<= y -10800000000.0)
     (/ x (/ y (- t)))
     (if (<= y -8.5e-13) t (if (<= y 5.6e+87) (* t (/ x z)) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.8e+72) {
		tmp = t;
	} else if (y <= -10800000000.0) {
		tmp = x / (y / -t);
	} else if (y <= -8.5e-13) {
		tmp = t;
	} else if (y <= 5.6e+87) {
		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 <= (-2.8d+72)) then
        tmp = t
    else if (y <= (-10800000000.0d0)) then
        tmp = x / (y / -t)
    else if (y <= (-8.5d-13)) then
        tmp = t
    else if (y <= 5.6d+87) 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 <= -2.8e+72) {
		tmp = t;
	} else if (y <= -10800000000.0) {
		tmp = x / (y / -t);
	} else if (y <= -8.5e-13) {
		tmp = t;
	} else if (y <= 5.6e+87) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.8e+72:
		tmp = t
	elif y <= -10800000000.0:
		tmp = x / (y / -t)
	elif y <= -8.5e-13:
		tmp = t
	elif y <= 5.6e+87:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.8e+72)
		tmp = t;
	elseif (y <= -10800000000.0)
		tmp = Float64(x / Float64(y / Float64(-t)));
	elseif (y <= -8.5e-13)
		tmp = t;
	elseif (y <= 5.6e+87)
		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 <= -2.8e+72)
		tmp = t;
	elseif (y <= -10800000000.0)
		tmp = x / (y / -t);
	elseif (y <= -8.5e-13)
		tmp = t;
	elseif (y <= 5.6e+87)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.8e+72], t, If[LessEqual[y, -10800000000.0], N[(x / N[(y / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.5e-13], t, If[LessEqual[y, 5.6e+87], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7999999999999999e72 or -1.08e10 < y < -8.5000000000000001e-13 or 5.6000000000000003e87 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 71.4%

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

   if -2.7999999999999999e72 < y < -1.08e10

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 63.9%

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

      1. associate-/l* 75.7%

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

   5. Simplified 75.7%

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

   6. Taylor expanded in z around 0 47.8%

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

      1. associate-*r/ 47.8%

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

      2. neg-mul-1 47.8%

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

      3. distribute-lft-neg-in 47.8%

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

      4. *-commutative 47.8%

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

      5. associate-/l* 53.7%

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

   8. Simplified 53.7%

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

   if -8.5000000000000001e-13 < y < 5.6000000000000003e87

   1. Initial program 94.6%

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

   3. Taylor expanded in y around 0 64.1%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+72}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -10800000000:\\ \;\;\;\;\frac{x}{\frac{y}{-t}}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-13}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 69.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+117}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-13}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.3e+117)
   t
   (if (<= y -1.32e-13)
     (* (- y x) (/ t y))
     (if (<= y 4.2e+90) (* x (/ t (- z y))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.3e+117) {
		tmp = t;
	} else if (y <= -1.32e-13) {
		tmp = (y - x) * (t / y);
	} else if (y <= 4.2e+90) {
		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 <= (-4.3d+117)) then
        tmp = t
    else if (y <= (-1.32d-13)) then
        tmp = (y - x) * (t / y)
    else if (y <= 4.2d+90) 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 <= -4.3e+117) {
		tmp = t;
	} else if (y <= -1.32e-13) {
		tmp = (y - x) * (t / y);
	} else if (y <= 4.2e+90) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.3e+117:
		tmp = t
	elif y <= -1.32e-13:
		tmp = (y - x) * (t / y)
	elif y <= 4.2e+90:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.3e+117)
		tmp = t;
	elseif (y <= -1.32e-13)
		tmp = Float64(Float64(y - x) * Float64(t / y));
	elseif (y <= 4.2e+90)
		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 <= -4.3e+117)
		tmp = t;
	elseif (y <= -1.32e-13)
		tmp = (y - x) * (t / y);
	elseif (y <= 4.2e+90)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.3e+117], t, If[LessEqual[y, -1.32e-13], N[(N[(y - x), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+90], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.29999999999999998e117 or 4.19999999999999961e90 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 72.5%

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

   if -4.29999999999999998e117 < y < -1.3199999999999999e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 64.9%

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

      1. associate-*r/ 64.9%

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

      2. *-commutative 64.9%

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

      3. neg-mul-1 64.9%

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

      4. distribute-lft-neg-in 64.9%

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

      5. *-commutative 64.9%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in t around 0 64.9%

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

      1. associate-/l* 67.8%

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

      2. associate-/r/ 67.5%

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

   8. Simplified 67.5%

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

   if -1.3199999999999999e-13 < y < 4.19999999999999961e90

   1. Initial program 94.6%

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

   3. Taylor expanded in x around inf 72.6%

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

      1. *-commutative 72.6%

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

      2. associate-*r/ 74.7%

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

   5. Simplified 74.7%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+117}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-13}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+84} \lor \neg \left(x \leq 4 \cdot 10^{+66}\right):\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.2e+84) (not (<= x 4e+66)))
   (/ t (/ (- z y) x))
   (* t (/ (- y) (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.2e+84) || !(x <= 4e+66)) {
		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 ((x <= (-4.2d+84)) .or. (.not. (x <= 4d+66))) 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 ((x <= -4.2e+84) || !(x <= 4e+66)) {
		tmp = t / ((z - y) / x);
	} else {
		tmp = t * (-y / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.2e+84) or not (x <= 4e+66):
		tmp = t / ((z - y) / x)
	else:
		tmp = t * (-y / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.2e+84) || !(x <= 4e+66))
		tmp = Float64(t / Float64(Float64(z - y) / x));
	else
		tmp = Float64(t * Float64(Float64(-y) / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.2e+84) || ~((x <= 4e+66)))
		tmp = t / ((z - y) / x);
	else
		tmp = t * (-y / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.2e+84], N[Not[LessEqual[x, 4e+66]], $MachinePrecision]], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(t * N[((-y) / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.20000000000000037e84 or 3.99999999999999978e66 < x

   1. Initial program 98.0%

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

   3. Taylor expanded in x around inf 69.8%

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

      1. associate-/l* 79.8%

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

   5. Simplified 79.8%

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

   if -4.20000000000000037e84 < x < 3.99999999999999978e66

   1. Initial program 96.6%

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

   3. Taylor expanded in x around 0 81.2%

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

      1. neg-mul-1 81.2%

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

      2. distribute-neg-frac 81.2%

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

   5. Simplified 81.2%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+84} \lor \neg \left(x \leq 4 \cdot 10^{+66}\right):\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-32}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.5e-32) t (if (<= y 1.35e+88) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e-32) {
		tmp = t;
	} else if (y <= 1.35e+88) {
		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 <= (-1.5d-32)) then
        tmp = t
    else if (y <= 1.35d+88) 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 <= -1.5e-32) {
		tmp = t;
	} else if (y <= 1.35e+88) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.5e-32:
		tmp = t
	elif y <= 1.35e+88:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.5e-32)
		tmp = t;
	elseif (y <= 1.35e+88)
		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 <= -1.5e-32)
		tmp = t;
	elseif (y <= 1.35e+88)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.5e-32], t, If[LessEqual[y, 1.35e+88], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e-32 or 1.35000000000000008e88 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 62.6%

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

   if -1.5e-32 < y < 1.35000000000000008e88

   1. Initial program 94.5%

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

   3. Taylor expanded in y around 0 61.4%

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

      1. associate-/l* 64.8%

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

      2. associate-/r/ 63.6%

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

   5. Simplified 63.6%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-32}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+88}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 60.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-12}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.5e-12) t (if (<= y 1.45e+87) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e-12) {
		tmp = t;
	} else if (y <= 1.45e+87) {
		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 <= (-5.5d-12)) then
        tmp = t
    else if (y <= 1.45d+87) 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 <= -5.5e-12) {
		tmp = t;
	} else if (y <= 1.45e+87) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.5e-12:
		tmp = t
	elif y <= 1.45e+87:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.5e-12)
		tmp = t;
	elseif (y <= 1.45e+87)
		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 <= -5.5e-12)
		tmp = t;
	elseif (y <= 1.45e+87)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.5e-12], t, If[LessEqual[y, 1.45e+87], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5000000000000004e-12 or 1.4499999999999999e87 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 64.1%

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

   if -5.5000000000000004e-12 < y < 1.4499999999999999e87

   1. Initial program 94.6%

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

   3. Taylor expanded in y around 0 64.1%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-12}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+87}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 35.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.82 \cdot 10^{+127}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= z 1.82e+127) t (* t (/ y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.82e+127) {
		tmp = t;
	} else {
		tmp = t * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= 1.82d+127) then
        tmp = t
    else
        tmp = t * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.82e+127) {
		tmp = t;
	} else {
		tmp = t * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 1.82e+127:
		tmp = t
	else:
		tmp = t * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 1.82e+127)
		tmp = t;
	else
		tmp = Float64(t * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 1.82e+127)
		tmp = t;
	else
		tmp = t * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 1.82e+127], t, N[(t * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.82000000000000009e127

   1. Initial program 98.4%

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

   3. Taylor expanded in y around inf 41.8%

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

   if 1.82000000000000009e127 < z

   1. Initial program 91.4%

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

   3. Taylor expanded in x around 0 52.5%

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

      1. neg-mul-1 52.5%

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

      2. distribute-neg-frac 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in y around 0 48.3%

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

      1. mul-1-neg 48.3%

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

      2. distribute-neg-frac 48.3%

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

   8. Simplified 48.3%

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

      1. expm1-log1p-u 45.7%

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

      2. expm1-udef 36.4%

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

      3. *-commutative 36.4%

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

      4. div-inv 36.4%

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

      5. div-inv 36.4%

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

      6. add-sqr-sqrt 15.3%

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

      7. sqrt-unprod 34.3%

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

      8. sqr-neg 34.3%

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

      9. sqrt-unprod 21.2%

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

      10. add-sqr-sqrt 34.5%

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

   10. Applied egg-rr 34.5%

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

       1. expm1-def 34.7%

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

       2. expm1-log1p 34.8%

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

   12. Simplified 34.8%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.82 \cdot 10^{+127}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 34.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

3. Taylor expanded in y around inf 35.8%

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

4. Final simplification 35.8%

   \[\leadsto t \]
5. Add Preprocessing

Developer target: 96.9% 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 2024010 
(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))