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

Percentage Accurate: 96.9% → 97.0%

Time: 9.2s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. associate-*l/ 83.0%

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

   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. Step-by-step derivation

   1. associate-*r/ 83.0%

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

   2. associate-*l/ 97.6%

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

   3. *-commutative 97.6%

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

   4. clear-num 97.6%

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

   5. un-div-inv 97.6%

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

5. Applied egg-rr 97.6%

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

6. Final simplification 97.6%

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

Alternative 2: 75.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -48:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-29}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -48.0)
     t_1
     (if (<= y -1.16e-29)
       (* (- x y) (/ t z))
       (if (<= y -3.2e-37)
         t_1
         (if (<= y 5.5e+16)
           (* t (/ x (- z y)))
           (if (<= y 6.2e+77) (* t (/ (- x y) z)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -48.0) {
		tmp = t_1;
	} else if (y <= -1.16e-29) {
		tmp = (x - y) * (t / z);
	} else if (y <= -3.2e-37) {
		tmp = t_1;
	} else if (y <= 5.5e+16) {
		tmp = t * (x / (z - y));
	} else if (y <= 6.2e+77) {
		tmp = t * ((x - y) / z);
	} 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 * (1.0d0 - (x / y))
    if (y <= (-48.0d0)) then
        tmp = t_1
    else if (y <= (-1.16d-29)) then
        tmp = (x - y) * (t / z)
    else if (y <= (-3.2d-37)) then
        tmp = t_1
    else if (y <= 5.5d+16) then
        tmp = t * (x / (z - y))
    else if (y <= 6.2d+77) then
        tmp = t * ((x - y) / z)
    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 * (1.0 - (x / y));
	double tmp;
	if (y <= -48.0) {
		tmp = t_1;
	} else if (y <= -1.16e-29) {
		tmp = (x - y) * (t / z);
	} else if (y <= -3.2e-37) {
		tmp = t_1;
	} else if (y <= 5.5e+16) {
		tmp = t * (x / (z - y));
	} else if (y <= 6.2e+77) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -48.0:
		tmp = t_1
	elif y <= -1.16e-29:
		tmp = (x - y) * (t / z)
	elif y <= -3.2e-37:
		tmp = t_1
	elif y <= 5.5e+16:
		tmp = t * (x / (z - y))
	elif y <= 6.2e+77:
		tmp = t * ((x - y) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -48.0)
		tmp = t_1;
	elseif (y <= -1.16e-29)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= -3.2e-37)
		tmp = t_1;
	elseif (y <= 5.5e+16)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	elseif (y <= 6.2e+77)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -48.0)
		tmp = t_1;
	elseif (y <= -1.16e-29)
		tmp = (x - y) * (t / z);
	elseif (y <= -3.2e-37)
		tmp = t_1;
	elseif (y <= 5.5e+16)
		tmp = t * (x / (z - y));
	elseif (y <= 6.2e+77)
		tmp = t * ((x - y) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -48.0], t$95$1, If[LessEqual[y, -1.16e-29], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.2e-37], t$95$1, If[LessEqual[y, 5.5e+16], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+77], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -48 or -1.15999999999999996e-29 < y < -3.1999999999999999e-37 or 6.19999999999999997e77 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 72.4%

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

      2. associate-*r/ 69.5%

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

   3. Simplified 69.5%

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

   4. Taylor expanded in z around 0 59.4%

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

      1. associate-*r/ 59.4%

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

      2. *-commutative 59.4%

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

      3. neg-mul-1 59.4%

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

      4. distribute-rgt-neg-in 59.4%

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

   6. Simplified 59.4%

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

   7. Taylor expanded in x around 0 76.4%

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

      1. mul-1-neg 76.4%

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

      2. unsub-neg 76.4%

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

      3. associate-/l* 85.3%

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

      4. associate-/r/ 80.5%

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

   9. Simplified 80.5%

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

   10. Taylor expanded in t around 0 85.3%

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

   if -48 < y < -1.15999999999999996e-29

   1. Initial program 99.3%

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

      1. associate-*l/ 86.0%

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

      2. associate-*r/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around inf 85.3%

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

   if -3.1999999999999999e-37 < y < 5.5e16

   1. Initial program 95.0%

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

   2. Taylor expanded in x around inf 81.7%

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

   if 5.5e16 < y < 6.19999999999999997e77

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 70.0%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -48:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-29}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-37}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+16}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 3: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -50:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-30}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -50.0)
     t_1
     (if (<= y -1.4e-30)
       (* (- x y) (/ t z))
       (if (<= y -4.4e-37)
         t_1
         (if (<= y 1.85e+15)
           (/ t (/ (- z y) x))
           (if (<= y 6e+77) (* t (/ (- x y) z)) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -50.0) {
		tmp = t_1;
	} else if (y <= -1.4e-30) {
		tmp = (x - y) * (t / z);
	} else if (y <= -4.4e-37) {
		tmp = t_1;
	} else if (y <= 1.85e+15) {
		tmp = t / ((z - y) / x);
	} else if (y <= 6e+77) {
		tmp = t * ((x - y) / z);
	} 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 * (1.0d0 - (x / y))
    if (y <= (-50.0d0)) then
        tmp = t_1
    else if (y <= (-1.4d-30)) then
        tmp = (x - y) * (t / z)
    else if (y <= (-4.4d-37)) then
        tmp = t_1
    else if (y <= 1.85d+15) then
        tmp = t / ((z - y) / x)
    else if (y <= 6d+77) then
        tmp = t * ((x - y) / z)
    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 * (1.0 - (x / y));
	double tmp;
	if (y <= -50.0) {
		tmp = t_1;
	} else if (y <= -1.4e-30) {
		tmp = (x - y) * (t / z);
	} else if (y <= -4.4e-37) {
		tmp = t_1;
	} else if (y <= 1.85e+15) {
		tmp = t / ((z - y) / x);
	} else if (y <= 6e+77) {
		tmp = t * ((x - y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -50.0:
		tmp = t_1
	elif y <= -1.4e-30:
		tmp = (x - y) * (t / z)
	elif y <= -4.4e-37:
		tmp = t_1
	elif y <= 1.85e+15:
		tmp = t / ((z - y) / x)
	elif y <= 6e+77:
		tmp = t * ((x - y) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -50.0)
		tmp = t_1;
	elseif (y <= -1.4e-30)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= -4.4e-37)
		tmp = t_1;
	elseif (y <= 1.85e+15)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	elseif (y <= 6e+77)
		tmp = Float64(t * Float64(Float64(x - y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -50.0)
		tmp = t_1;
	elseif (y <= -1.4e-30)
		tmp = (x - y) * (t / z);
	elseif (y <= -4.4e-37)
		tmp = t_1;
	elseif (y <= 1.85e+15)
		tmp = t / ((z - y) / x);
	elseif (y <= 6e+77)
		tmp = t * ((x - y) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -50.0], t$95$1, If[LessEqual[y, -1.4e-30], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.4e-37], t$95$1, If[LessEqual[y, 1.85e+15], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+77], N[(t * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -50 or -1.39999999999999994e-30 < y < -4.40000000000000004e-37 or 5.9999999999999996e77 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 72.4%

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

      2. associate-*r/ 69.5%

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

   3. Simplified 69.5%

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

   4. Taylor expanded in z around 0 59.4%

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

      1. associate-*r/ 59.4%

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

      2. *-commutative 59.4%

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

      3. neg-mul-1 59.4%

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

      4. distribute-rgt-neg-in 59.4%

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

   6. Simplified 59.4%

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

   7. Taylor expanded in x around 0 76.4%

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

      1. mul-1-neg 76.4%

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

      2. unsub-neg 76.4%

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

      3. associate-/l* 85.3%

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

      4. associate-/r/ 80.5%

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

   9. Simplified 80.5%

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

   10. Taylor expanded in t around 0 85.3%

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

   if -50 < y < -1.39999999999999994e-30

   1. Initial program 99.3%

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

      1. associate-*l/ 86.0%

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

      2. associate-*r/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around inf 85.3%

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

   if -4.40000000000000004e-37 < y < 1.85e15

   1. Initial program 95.0%

      \[\frac{x - y}{z - y} \cdot t \]
   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/ 93.5%

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

   3. Simplified 93.5%

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

      1. associate-*r/ 95.3%

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

      2. clear-num 95.1%

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

   5. Applied egg-rr 95.1%

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

   6. Taylor expanded in x around inf 80.5%

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

      1. associate-/l* 81.7%

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

   8. Simplified 81.7%

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

   if 1.85e15 < y < 5.9999999999999996e77

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 70.0%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -50:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-30}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-37}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+15}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 4: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -95:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-30}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-37} \lor \neg \left(y \leq 1.4 \cdot 10^{+53}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -95.0)
     t_1
     (if (<= y -2.05e-30)
       (* (- x y) (/ t z))
       (if (or (<= y -1.25e-37) (not (<= y 1.4e+53)))
         t_1
         (* x (/ t (- z y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -95.0) {
		tmp = t_1;
	} else if (y <= -2.05e-30) {
		tmp = (x - y) * (t / z);
	} else if ((y <= -1.25e-37) || !(y <= 1.4e+53)) {
		tmp = t_1;
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-95.0d0)) then
        tmp = t_1
    else if (y <= (-2.05d-30)) then
        tmp = (x - y) * (t / z)
    else if ((y <= (-1.25d-37)) .or. (.not. (y <= 1.4d+53))) then
        tmp = t_1
    else
        tmp = x * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -95.0) {
		tmp = t_1;
	} else if (y <= -2.05e-30) {
		tmp = (x - y) * (t / z);
	} else if ((y <= -1.25e-37) || !(y <= 1.4e+53)) {
		tmp = t_1;
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -95.0:
		tmp = t_1
	elif y <= -2.05e-30:
		tmp = (x - y) * (t / z)
	elif (y <= -1.25e-37) or not (y <= 1.4e+53):
		tmp = t_1
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -95.0)
		tmp = t_1;
	elseif (y <= -2.05e-30)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif ((y <= -1.25e-37) || !(y <= 1.4e+53))
		tmp = t_1;
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -95.0)
		tmp = t_1;
	elseif (y <= -2.05e-30)
		tmp = (x - y) * (t / z);
	elseif ((y <= -1.25e-37) || ~((y <= 1.4e+53)))
		tmp = t_1;
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -95.0], t$95$1, If[LessEqual[y, -2.05e-30], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.25e-37], N[Not[LessEqual[y, 1.4e+53]], $MachinePrecision]], t$95$1, N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -95 or -2.0500000000000002e-30 < y < -1.2499999999999999e-37 or 1.4e53 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 72.4%

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

      2. associate-*r/ 69.9%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in z around 0 56.6%

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

      1. associate-*r/ 56.6%

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

      2. *-commutative 56.6%

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

      3. neg-mul-1 56.6%

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

      4. distribute-rgt-neg-in 56.6%

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

   6. Simplified 56.6%

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

   7. Taylor expanded in x around 0 73.6%

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

      1. mul-1-neg 73.6%

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

      2. unsub-neg 73.6%

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

      3. associate-/l* 81.9%

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

      4. associate-/r/ 77.5%

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

   9. Simplified 77.5%

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

   10. Taylor expanded in t around 0 81.9%

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

   if -95 < y < -2.0500000000000002e-30

   1. Initial program 99.3%

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

      1. associate-*l/ 86.0%

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

      2. associate-*r/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around inf 85.3%

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

   if -1.2499999999999999e-37 < y < 1.4e53

   1. Initial program 95.2%

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

      1. associate-*l/ 94.0%

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

      2. associate-*r/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in x around inf 78.4%

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

      1. associate-*l/ 77.9%

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

      2. *-commutative 77.9%

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

   6. Simplified 77.9%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -95:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-30}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-37} \lor \neg \left(y \leq 1.4 \cdot 10^{+53}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 5: 75.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -85:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-30}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-37} \lor \neg \left(y \leq 1.25 \cdot 10^{+53}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (- 1.0 (/ x y)))))
   (if (<= y -85.0)
     t_1
     (if (<= y -3.9e-30)
       (* (- x y) (/ t z))
       (if (or (<= y -4.4e-37) (not (<= y 1.25e+53)))
         t_1
         (* t (/ x (- z y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -85.0) {
		tmp = t_1;
	} else if (y <= -3.9e-30) {
		tmp = (x - y) * (t / z);
	} else if ((y <= -4.4e-37) || !(y <= 1.25e+53)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * (1.0d0 - (x / y))
    if (y <= (-85.0d0)) then
        tmp = t_1
    else if (y <= (-3.9d-30)) then
        tmp = (x - y) * (t / z)
    else if ((y <= (-4.4d-37)) .or. (.not. (y <= 1.25d+53))) then
        tmp = t_1
    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 t_1 = t * (1.0 - (x / y));
	double tmp;
	if (y <= -85.0) {
		tmp = t_1;
	} else if (y <= -3.9e-30) {
		tmp = (x - y) * (t / z);
	} else if ((y <= -4.4e-37) || !(y <= 1.25e+53)) {
		tmp = t_1;
	} else {
		tmp = t * (x / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (1.0 - (x / y))
	tmp = 0
	if y <= -85.0:
		tmp = t_1
	elif y <= -3.9e-30:
		tmp = (x - y) * (t / z)
	elif (y <= -4.4e-37) or not (y <= 1.25e+53):
		tmp = t_1
	else:
		tmp = t * (x / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(1.0 - Float64(x / y)))
	tmp = 0.0
	if (y <= -85.0)
		tmp = t_1;
	elseif (y <= -3.9e-30)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif ((y <= -4.4e-37) || !(y <= 1.25e+53))
		tmp = t_1;
	else
		tmp = Float64(t * Float64(x / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (1.0 - (x / y));
	tmp = 0.0;
	if (y <= -85.0)
		tmp = t_1;
	elseif (y <= -3.9e-30)
		tmp = (x - y) * (t / z);
	elseif ((y <= -4.4e-37) || ~((y <= 1.25e+53)))
		tmp = t_1;
	else
		tmp = t * (x / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -85.0], t$95$1, If[LessEqual[y, -3.9e-30], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -4.4e-37], N[Not[LessEqual[y, 1.25e+53]], $MachinePrecision]], t$95$1, N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -85 or -3.9000000000000003e-30 < y < -4.40000000000000004e-37 or 1.2500000000000001e53 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 72.4%

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

      2. associate-*r/ 69.9%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in z around 0 56.6%

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

      1. associate-*r/ 56.6%

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

      2. *-commutative 56.6%

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

      3. neg-mul-1 56.6%

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

      4. distribute-rgt-neg-in 56.6%

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

   6. Simplified 56.6%

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

   7. Taylor expanded in x around 0 73.6%

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

      1. mul-1-neg 73.6%

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

      2. unsub-neg 73.6%

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

      3. associate-/l* 81.9%

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

      4. associate-/r/ 77.5%

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

   9. Simplified 77.5%

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

   10. Taylor expanded in t around 0 81.9%

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

   if -85 < y < -3.9000000000000003e-30

   1. Initial program 99.3%

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

      1. associate-*l/ 86.0%

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

      2. associate-*r/ 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in z around inf 85.3%

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

   if -4.40000000000000004e-37 < y < 1.2500000000000001e53

   1. Initial program 95.2%

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

   2. Taylor expanded in x around inf 80.2%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -85:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-30}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-37} \lor \neg \left(y \leq 1.25 \cdot 10^{+53}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]

Alternative 6: 75.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{z - y}{x}}\\ \mathbf{if}\;x \leq -0.0071:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \frac{-y}{z - y}\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ (- z y) x))))
   (if (<= x -0.0071)
     t_1
     (if (<= x 5.4e-74)
       (* t (/ (- y) (- z y)))
       (if (<= x 2.35e+73) (* t (- 1.0 (/ x y))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / ((z - y) / x);
	double tmp;
	if (x <= -0.0071) {
		tmp = t_1;
	} else if (x <= 5.4e-74) {
		tmp = t * (-y / (z - y));
	} else if (x <= 2.35e+73) {
		tmp = t * (1.0 - (x / 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 / ((z - y) / x)
    if (x <= (-0.0071d0)) then
        tmp = t_1
    else if (x <= 5.4d-74) then
        tmp = t * (-y / (z - y))
    else if (x <= 2.35d+73) then
        tmp = t * (1.0d0 - (x / 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 / ((z - y) / x);
	double tmp;
	if (x <= -0.0071) {
		tmp = t_1;
	} else if (x <= 5.4e-74) {
		tmp = t * (-y / (z - y));
	} else if (x <= 2.35e+73) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / ((z - y) / x)
	tmp = 0
	if x <= -0.0071:
		tmp = t_1
	elif x <= 5.4e-74:
		tmp = t * (-y / (z - y))
	elif x <= 2.35e+73:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(Float64(z - y) / x))
	tmp = 0.0
	if (x <= -0.0071)
		tmp = t_1;
	elseif (x <= 5.4e-74)
		tmp = Float64(t * Float64(Float64(-y) / Float64(z - y)));
	elseif (x <= 2.35e+73)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / ((z - y) / x);
	tmp = 0.0;
	if (x <= -0.0071)
		tmp = t_1;
	elseif (x <= 5.4e-74)
		tmp = t * (-y / (z - y));
	elseif (x <= 2.35e+73)
		tmp = t * (1.0 - (x / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.0071], t$95$1, If[LessEqual[x, 5.4e-74], N[(t * N[((-y) / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.35e+73], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.0071000000000000004 or 2.3500000000000001e73 < x

   1. Initial program 98.2%

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

      1. associate-*l/ 82.4%

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

      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. Step-by-step derivation

      1. associate-*r/ 82.4%

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

      2. clear-num 82.4%

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

   5. Applied egg-rr 82.4%

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

   6. Taylor expanded in x around inf 69.6%

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

      1. associate-/l* 77.2%

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

   8. Simplified 77.2%

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

   if -0.0071000000000000004 < x < 5.40000000000000036e-74

   1. Initial program 96.5%

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

   2. Taylor expanded in x around 0 85.5%

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

      1. neg-mul-1 85.5%

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

      2. distribute-neg-frac 85.5%

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

   4. Simplified 85.5%

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

   if 5.40000000000000036e-74 < x < 2.3500000000000001e73

   1. Initial program 99.9%

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

      1. associate-*l/ 78.8%

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

      2. associate-*r/ 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in z around 0 57.5%

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

      1. associate-*r/ 57.5%

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

      2. *-commutative 57.5%

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

      3. neg-mul-1 57.5%

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

      4. distribute-rgt-neg-in 57.5%

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

   6. Simplified 57.5%

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

   7. Taylor expanded in x around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. unsub-neg 78.5%

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

      3. associate-/l* 78.5%

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

      4. associate-/r/ 78.5%

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

   9. Simplified 78.5%

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

   10. Taylor expanded in t around 0 78.5%

       \[\leadsto \color{blue}{t \cdot \left(1 - \frac{x}{y}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.0071:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{-74}:\\ \;\;\;\;t \cdot \frac{-y}{z - y}\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \]

Alternative 7: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+172} \lor \neg \left(y \leq 3 \cdot 10^{+131}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.8e+172) (not (<= y 3e+131)))
   (* t (- 1.0 (/ x y)))
   (* (- x y) (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.8e+172) || !(y <= 3e+131)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6.8d+172)) .or. (.not. (y <= 3d+131))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = (x - y) * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.8e+172) || !(y <= 3e+131)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x - y) * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.8e+172) or not (y <= 3e+131):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = (x - y) * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.8e+172) || !(y <= 3e+131))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.8e+172) || ~((y <= 3e+131)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = (x - y) * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.8e+172], N[Not[LessEqual[y, 3e+131]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.7999999999999996e172 or 3.0000000000000001e131 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 65.5%

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

      2. associate-*r/ 57.7%

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

   3. Simplified 57.7%

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

   4. Taylor expanded in z around 0 63.5%

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

      1. associate-*r/ 63.5%

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

      2. *-commutative 63.5%

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

      3. neg-mul-1 63.5%

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

      4. distribute-rgt-neg-in 63.5%

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

   6. Simplified 63.5%

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

   7. Taylor expanded in x around 0 89.7%

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

      1. mul-1-neg 89.7%

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

      2. unsub-neg 89.7%

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

      3. associate-/l* 98.0%

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

      4. associate-/r/ 93.7%

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

   9. Simplified 93.7%

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

   10. Taylor expanded in t around 0 98.0%

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

   if -6.7999999999999996e172 < y < 3.0000000000000001e131

   1. Initial program 96.8%

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

      1. associate-*l/ 89.5%

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

      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 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+172} \lor \neg \left(y \leq 3 \cdot 10^{+131}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 8: 70.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-67} \lor \neg \left(y \leq 6.2 \cdot 10^{-9}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.1e-67) (not (<= y 6.2e-9)))
   (* t (- 1.0 (/ x y)))
   (/ t (/ z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.1e-67) || !(y <= 6.2e-9)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t / (z / x);
	}
	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 <= (-2.1d-67)) .or. (.not. (y <= 6.2d-9))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.1e-67) || !(y <= 6.2e-9)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.1e-67) or not (y <= 6.2e-9):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t / (z / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.1e-67) || !(y <= 6.2e-9))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.1e-67) || ~((y <= 6.2e-9)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.1e-67], N[Not[LessEqual[y, 6.2e-9]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1000000000000002e-67 or 6.2000000000000001e-9 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 75.8%

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

      2. associate-*r/ 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in z around 0 54.8%

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

      1. associate-*r/ 54.8%

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

      2. *-commutative 54.8%

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

      3. neg-mul-1 54.8%

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

      4. distribute-rgt-neg-in 54.8%

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

   6. Simplified 54.8%

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

   7. Taylor expanded in x around 0 68.6%

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

      1. mul-1-neg 68.6%

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

      2. unsub-neg 68.6%

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

      3. associate-/l* 75.3%

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

      4. associate-/r/ 71.7%

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

   9. Simplified 71.7%

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

   10. Taylor expanded in t around 0 75.2%

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

   if -2.1000000000000002e-67 < y < 6.2000000000000001e-9

   1. Initial program 94.2%

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

      1. associate-*l/ 94.5%

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

      2. associate-*r/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in y around 0 72.8%

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

      1. associate-/l* 75.2%

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

   6. Simplified 75.2%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-67} \lor \neg \left(y \leq 6.2 \cdot 10^{-9}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \end{array} \]

Alternative 9: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-37} \lor \neg \left(y \leq 1.4 \cdot 10^{+53}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.25e-37) (not (<= y 1.4e+53)))
   (* t (- 1.0 (/ x y)))
   (* x (/ t (- z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.25e-37) || !(y <= 1.4e+53)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.25d-37)) .or. (.not. (y <= 1.4d+53))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = x * (t / (z - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.25e-37) || !(y <= 1.4e+53)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * (t / (z - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.25e-37) or not (y <= 1.4e+53):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = x * (t / (z - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.25e-37) || !(y <= 1.4e+53))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(x * Float64(t / Float64(z - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.25e-37) || ~((y <= 1.4e+53)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = x * (t / (z - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.25e-37], N[Not[LessEqual[y, 1.4e+53]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2499999999999999e-37 or 1.4e53 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 73.1%

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

      2. associate-*r/ 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in z around 0 55.0%

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

      1. associate-*r/ 55.0%

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

      2. *-commutative 55.0%

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

      3. neg-mul-1 55.0%

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

      4. distribute-rgt-neg-in 55.0%

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

   6. Simplified 55.0%

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

   7. Taylor expanded in x around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. unsub-neg 71.2%

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

      3. associate-/l* 79.0%

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

      4. associate-/r/ 74.8%

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

   9. Simplified 74.8%

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

   10. Taylor expanded in t around 0 79.0%

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

   if -1.2499999999999999e-37 < y < 1.4e53

   1. Initial program 95.2%

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

      1. associate-*l/ 94.0%

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

      2. associate-*r/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in x around inf 78.4%

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

      1. associate-*l/ 77.9%

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

      2. *-commutative 77.9%

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

   6. Simplified 77.9%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-37} \lor \neg \left(y \leq 1.4 \cdot 10^{+53}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 10: 62.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+47}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.3e+47) t (if (<= y 1.36e+53) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e+47) {
		tmp = t;
	} else if (y <= 1.36e+53) {
		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 <= (-1.3d+47)) then
        tmp = t
    else if (y <= 1.36d+53) 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 <= -1.3e+47) {
		tmp = t;
	} else if (y <= 1.36e+53) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.3e+47:
		tmp = t
	elif y <= 1.36e+53:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.3e+47)
		tmp = t;
	elseif (y <= 1.36e+53)
		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 <= -1.3e+47)
		tmp = t;
	elseif (y <= 1.36e+53)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.3e+47], t, If[LessEqual[y, 1.36e+53], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.30000000000000002e47 or 1.36e53 < y

   1. Initial program 99.9%

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

      1. associate-*l/ 70.3%

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

      2. associate-*r/ 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in y around inf 68.5%

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

   if -1.30000000000000002e47 < y < 1.36e53

   1. Initial program 95.7%

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

   2. Taylor expanded in y around 0 64.8%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+47}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

2. Final simplification 97.6%

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

Alternative 12: 34.5% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

   1. associate-*l/ 83.0%

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

   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 38.1%

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

5. Final simplification 38.1%

   \[\leadsto t \]

Developer target: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023173 
(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))