Data.Colour.RGB:hslsv from colour-2.3.3, B

Percentage Accurate: 99.4% → 99.8%

Time: 13.3s

Alternatives: 17

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(a, 120, \frac{60}{z - t} \cdot \left(x - y\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (fma a 120.0 (* (/ 60.0 (- z t)) (- x y))))

C

double code(double x, double y, double z, double t, double a) {
	return fma(a, 120.0, ((60.0 / (z - t)) * (x - y)));
}

Julia

function code(x, y, z, t, a)
	return fma(a, 120.0, Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y)))
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0 + N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.1%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Step-by-step derivation

   1. +-commutative 99.1%

      \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

   2. fma-def 99.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z - t}\right)} \]

   3. associate-*l/ 99.8%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)}\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{z - t} \cdot \left(x - y\right)\right)} \]

4. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(a, 120, \frac{60}{z - t} \cdot \left(x - y\right)\right) \]

Alternative 2: 88.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t} + a \cdot 120\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+106}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-7} \lor \neg \left(y \leq 1.65 \cdot 10^{+78}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* -60.0 (/ y (- z t))) (* a 120.0))))
   (if (<= y -1.8e+152)
     t_1
     (if (<= y -3.8e+106)
       (* (/ 60.0 (- z t)) (- x y))
       (if (or (<= y -8.2e-7) (not (<= y 1.65e+78)))
         t_1
         (+ (* 60.0 (/ x (- z t))) (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 * (y / (z - t))) + (a * 120.0);
	double tmp;
	if (y <= -1.8e+152) {
		tmp = t_1;
	} else if (y <= -3.8e+106) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if ((y <= -8.2e-7) || !(y <= 1.65e+78)) {
		tmp = t_1;
	} else {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((-60.0d0) * (y / (z - t))) + (a * 120.0d0)
    if (y <= (-1.8d+152)) then
        tmp = t_1
    else if (y <= (-3.8d+106)) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    else if ((y <= (-8.2d-7)) .or. (.not. (y <= 1.65d+78))) then
        tmp = t_1
    else
        tmp = (60.0d0 * (x / (z - t))) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 * (y / (z - t))) + (a * 120.0);
	double tmp;
	if (y <= -1.8e+152) {
		tmp = t_1;
	} else if (y <= -3.8e+106) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if ((y <= -8.2e-7) || !(y <= 1.65e+78)) {
		tmp = t_1;
	} else {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-60.0 * (y / (z - t))) + (a * 120.0)
	tmp = 0
	if y <= -1.8e+152:
		tmp = t_1
	elif y <= -3.8e+106:
		tmp = (60.0 / (z - t)) * (x - y)
	elif (y <= -8.2e-7) or not (y <= 1.65e+78):
		tmp = t_1
	else:
		tmp = (60.0 * (x / (z - t))) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-60.0 * Float64(y / Float64(z - t))) + Float64(a * 120.0))
	tmp = 0.0
	if (y <= -1.8e+152)
		tmp = t_1;
	elseif (y <= -3.8e+106)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	elseif ((y <= -8.2e-7) || !(y <= 1.65e+78))
		tmp = t_1;
	else
		tmp = Float64(Float64(60.0 * Float64(x / Float64(z - t))) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-60.0 * (y / (z - t))) + (a * 120.0);
	tmp = 0.0;
	if (y <= -1.8e+152)
		tmp = t_1;
	elseif (y <= -3.8e+106)
		tmp = (60.0 / (z - t)) * (x - y);
	elseif ((y <= -8.2e-7) || ~((y <= 1.65e+78)))
		tmp = t_1;
	else
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+152], t$95$1, If[LessEqual[y, -3.8e+106], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -8.2e-7], N[Not[LessEqual[y, 1.65e+78]], $MachinePrecision]], t$95$1, N[(N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7999999999999999e152 or -3.7999999999999998e106 < y < -8.1999999999999998e-7 or 1.65e78 < y

   1. Initial program 98.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around 0 94.2%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} + a \cdot 120 \]

   if -1.7999999999999999e152 < y < -3.7999999999999998e106

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in a around 0 100.0%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 99.8%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      2. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} \]

      3. associate-*r/ 99.8%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]

   6. Simplified 99.8%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]

   if -8.1999999999999998e-7 < y < 1.65e78

   1. Initial program 99.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around inf 92.3%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} + a \cdot 120 \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+152}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t} + a \cdot 120\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+106}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-7} \lor \neg \left(y \leq 1.65 \cdot 10^{+78}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 3: 88.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+106}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-7}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t} + a \cdot 120\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+78}:\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (/ (* y -60.0) (- z t)) (* a 120.0))))
   (if (<= y -1.8e+152)
     t_1
     (if (<= y -5.8e+106)
       (* (/ 60.0 (- z t)) (- x y))
       (if (<= y -1.75e-7)
         (+ (* -60.0 (/ y (- z t))) (* a 120.0))
         (if (<= y 1.35e+78) (+ (* 60.0 (/ x (- z t))) (* a 120.0)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y * -60.0) / (z - t)) + (a * 120.0);
	double tmp;
	if (y <= -1.8e+152) {
		tmp = t_1;
	} else if (y <= -5.8e+106) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if (y <= -1.75e-7) {
		tmp = (-60.0 * (y / (z - t))) + (a * 120.0);
	} else if (y <= 1.35e+78) {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y * (-60.0d0)) / (z - t)) + (a * 120.0d0)
    if (y <= (-1.8d+152)) then
        tmp = t_1
    else if (y <= (-5.8d+106)) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    else if (y <= (-1.75d-7)) then
        tmp = ((-60.0d0) * (y / (z - t))) + (a * 120.0d0)
    else if (y <= 1.35d+78) then
        tmp = (60.0d0 * (x / (z - t))) + (a * 120.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y * -60.0) / (z - t)) + (a * 120.0);
	double tmp;
	if (y <= -1.8e+152) {
		tmp = t_1;
	} else if (y <= -5.8e+106) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else if (y <= -1.75e-7) {
		tmp = (-60.0 * (y / (z - t))) + (a * 120.0);
	} else if (y <= 1.35e+78) {
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y * -60.0) / (z - t)) + (a * 120.0)
	tmp = 0
	if y <= -1.8e+152:
		tmp = t_1
	elif y <= -5.8e+106:
		tmp = (60.0 / (z - t)) * (x - y)
	elif y <= -1.75e-7:
		tmp = (-60.0 * (y / (z - t))) + (a * 120.0)
	elif y <= 1.35e+78:
		tmp = (60.0 * (x / (z - t))) + (a * 120.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0))
	tmp = 0.0
	if (y <= -1.8e+152)
		tmp = t_1;
	elseif (y <= -5.8e+106)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	elseif (y <= -1.75e-7)
		tmp = Float64(Float64(-60.0 * Float64(y / Float64(z - t))) + Float64(a * 120.0));
	elseif (y <= 1.35e+78)
		tmp = Float64(Float64(60.0 * Float64(x / Float64(z - t))) + Float64(a * 120.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y * -60.0) / (z - t)) + (a * 120.0);
	tmp = 0.0;
	if (y <= -1.8e+152)
		tmp = t_1;
	elseif (y <= -5.8e+106)
		tmp = (60.0 / (z - t)) * (x - y);
	elseif (y <= -1.75e-7)
		tmp = (-60.0 * (y / (z - t))) + (a * 120.0);
	elseif (y <= 1.35e+78)
		tmp = (60.0 * (x / (z - t))) + (a * 120.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+152], t$95$1, If[LessEqual[y, -5.8e+106], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.75e-7], N[(N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+78], N[(N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.7999999999999999e152 or 1.35000000000000002e78 < y

   1. Initial program 98.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around 0 94.6%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} + a \cdot 120 \]
   3. Step-by-step derivation

      1. associate-*r/ 94.7%

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} + a \cdot 120 \]

   4. Simplified 94.7%

      \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} + a \cdot 120 \]

   if -1.7999999999999999e152 < y < -5.8000000000000004e106

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in a around 0 100.0%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 99.8%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      2. *-commutative 99.8%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} \]

      3. associate-*r/ 99.8%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]

   6. Simplified 99.8%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]

   if -5.8000000000000004e106 < y < -1.74999999999999992e-7

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around 0 93.0%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} + a \cdot 120 \]

   if -1.74999999999999992e-7 < y < 1.35000000000000002e78

   1. Initial program 99.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around inf 92.3%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} + a \cdot 120 \]
3. Recombined 4 regimes into one program.

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+152}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+106}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-7}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t} + a \cdot 120\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+78}:\\ \;\;\;\;60 \cdot \frac{x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 4: 82.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-87} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-136}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -2e-87) (not (<= (* a 120.0) 5e-136)))
   (+ (* -60.0 (/ y (- z t))) (* a 120.0))
   (* (/ 60.0 (- z t)) (- x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e-87) || !((a * 120.0) <= 5e-136)) {
		tmp = (-60.0 * (y / (z - t))) + (a * 120.0);
	} else {
		tmp = (60.0 / (z - t)) * (x - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-2d-87)) .or. (.not. ((a * 120.0d0) <= 5d-136))) then
        tmp = ((-60.0d0) * (y / (z - t))) + (a * 120.0d0)
    else
        tmp = (60.0d0 / (z - t)) * (x - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e-87) || !((a * 120.0) <= 5e-136)) {
		tmp = (-60.0 * (y / (z - t))) + (a * 120.0);
	} else {
		tmp = (60.0 / (z - t)) * (x - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -2e-87) or not ((a * 120.0) <= 5e-136):
		tmp = (-60.0 * (y / (z - t))) + (a * 120.0)
	else:
		tmp = (60.0 / (z - t)) * (x - y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -2e-87) || !(Float64(a * 120.0) <= 5e-136))
		tmp = Float64(Float64(-60.0 * Float64(y / Float64(z - t))) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -2e-87) || ~(((a * 120.0) <= 5e-136)))
		tmp = (-60.0 * (y / (z - t))) + (a * 120.0);
	else
		tmp = (60.0 / (z - t)) * (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-87], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-136]], $MachinePrecision]], N[(N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -2.00000000000000004e-87 or 5.0000000000000002e-136 < (*.f64 a 120)

   1. Initial program 98.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in x around 0 85.8%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} + a \cdot 120 \]

   if -2.00000000000000004e-87 < (*.f64 a 120) < 5.0000000000000002e-136

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in a around 0 87.4%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 87.6%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      2. *-commutative 87.6%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} \]

      3. associate-*r/ 87.5%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]

   6. Simplified 87.5%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-87} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-136}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]

Alternative 5: 74.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5000000 \lor \neg \left(a \cdot 120 \leq 4 \cdot 10^{-45}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -5000000.0) (not (<= (* a 120.0) 4e-45)))
   (* a 120.0)
   (* (/ 60.0 (- z t)) (- x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -5000000.0) || !((a * 120.0) <= 4e-45)) {
		tmp = a * 120.0;
	} else {
		tmp = (60.0 / (z - t)) * (x - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-5000000.0d0)) .or. (.not. ((a * 120.0d0) <= 4d-45))) then
        tmp = a * 120.0d0
    else
        tmp = (60.0d0 / (z - t)) * (x - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -5000000.0) || !((a * 120.0) <= 4e-45)) {
		tmp = a * 120.0;
	} else {
		tmp = (60.0 / (z - t)) * (x - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -5000000.0) or not ((a * 120.0) <= 4e-45):
		tmp = a * 120.0
	else:
		tmp = (60.0 / (z - t)) * (x - y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -5000000.0) || !(Float64(a * 120.0) <= 4e-45))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -5000000.0) || ~(((a * 120.0) <= 4e-45)))
		tmp = a * 120.0;
	else
		tmp = (60.0 / (z - t)) * (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -5000000.0], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 4e-45]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -5e6 or 3.99999999999999994e-45 < (*.f64 a 120)

   1. Initial program 98.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf 72.8%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -5e6 < (*.f64 a 120) < 3.99999999999999994e-45

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in a around 0 78.0%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 78.1%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      2. *-commutative 78.1%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} \]

      3. associate-*r/ 78.0%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]

   6. Simplified 78.0%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5000000 \lor \neg \left(a \cdot 120 \leq 4 \cdot 10^{-45}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]

Alternative 6: 72.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5000000 \lor \neg \left(a \cdot 120 \leq 4 \cdot 10^{-45}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -5000000.0) (not (<= (* a 120.0) 4e-45)))
   (+ (* -60.0 (/ y z)) (* a 120.0))
   (* (/ 60.0 (- z t)) (- x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -5000000.0) || !((a * 120.0) <= 4e-45)) {
		tmp = (-60.0 * (y / z)) + (a * 120.0);
	} else {
		tmp = (60.0 / (z - t)) * (x - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-5000000.0d0)) .or. (.not. ((a * 120.0d0) <= 4d-45))) then
        tmp = ((-60.0d0) * (y / z)) + (a * 120.0d0)
    else
        tmp = (60.0d0 / (z - t)) * (x - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -5000000.0) || !((a * 120.0) <= 4e-45)) {
		tmp = (-60.0 * (y / z)) + (a * 120.0);
	} else {
		tmp = (60.0 / (z - t)) * (x - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -5000000.0) or not ((a * 120.0) <= 4e-45):
		tmp = (-60.0 * (y / z)) + (a * 120.0)
	else:
		tmp = (60.0 / (z - t)) * (x - y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -5000000.0) || !(Float64(a * 120.0) <= 4e-45))
		tmp = Float64(Float64(-60.0 * Float64(y / z)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -5000000.0) || ~(((a * 120.0) <= 4e-45)))
		tmp = (-60.0 * (y / z)) + (a * 120.0);
	else
		tmp = (60.0 / (z - t)) * (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -5000000.0], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 4e-45]], $MachinePrecision]], N[(N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -5e6 or 3.99999999999999994e-45 < (*.f64 a 120)

   1. Initial program 98.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf 73.4%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z}} + a \cdot 120 \]

   3. Taylor expanded in x around 0 77.9%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z}} + a \cdot 120 \]

   if -5e6 < (*.f64 a 120) < 3.99999999999999994e-45

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in a around 0 78.0%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 78.1%

         \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]

      2. *-commutative 78.1%

         \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot 60}}{z - t} \]

      3. associate-*r/ 78.0%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]

   6. Simplified 78.0%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{60}{z - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5000000 \lor \neg \left(a \cdot 120 \leq 4 \cdot 10^{-45}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]

Alternative 7: 55.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-151}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-159}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+225}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= y -1.12e+46)
     t_1
     (if (<= y -2.35e-151)
       (* a 120.0)
       (if (<= y -3.1e-159)
         (* -60.0 (/ (- x y) t))
         (if (<= y 2.6e+225) (* a 120.0) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -1.12e+46) {
		tmp = t_1;
	} else if (y <= -2.35e-151) {
		tmp = a * 120.0;
	} else if (y <= -3.1e-159) {
		tmp = -60.0 * ((x - y) / t);
	} else if (y <= 2.6e+225) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * (y / (z - t))
    if (y <= (-1.12d+46)) then
        tmp = t_1
    else if (y <= (-2.35d-151)) then
        tmp = a * 120.0d0
    else if (y <= (-3.1d-159)) then
        tmp = (-60.0d0) * ((x - y) / t)
    else if (y <= 2.6d+225) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -1.12e+46) {
		tmp = t_1;
	} else if (y <= -2.35e-151) {
		tmp = a * 120.0;
	} else if (y <= -3.1e-159) {
		tmp = -60.0 * ((x - y) / t);
	} else if (y <= 2.6e+225) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	tmp = 0
	if y <= -1.12e+46:
		tmp = t_1
	elif y <= -2.35e-151:
		tmp = a * 120.0
	elif y <= -3.1e-159:
		tmp = -60.0 * ((x - y) / t)
	elif y <= 2.6e+225:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (y <= -1.12e+46)
		tmp = t_1;
	elseif (y <= -2.35e-151)
		tmp = Float64(a * 120.0);
	elseif (y <= -3.1e-159)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	elseif (y <= 2.6e+225)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (y <= -1.12e+46)
		tmp = t_1;
	elseif (y <= -2.35e-151)
		tmp = a * 120.0;
	elseif (y <= -3.1e-159)
		tmp = -60.0 * ((x - y) / t);
	elseif (y <= 2.6e+225)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.12e+46], t$95$1, If[LessEqual[y, -2.35e-151], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -3.1e-159], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+225], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.12e46 or 2.60000000000000004e225 < y

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in y around inf 73.4%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]

   if -1.12e46 < y < -2.35000000000000014e-151 or -3.1e-159 < y < 2.60000000000000004e225

   1. Initial program 98.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf 63.7%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -2.35000000000000014e-151 < y < -3.1e-159

   1. Initial program 100.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around 0 89.5%

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t}} + a \cdot 120 \]

   3. Taylor expanded in t around 0 89.5%

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+46}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-151}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-159}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+225}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]

Alternative 8: 52.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-141}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-256}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+225}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= y -7.2e+46)
     t_1
     (if (<= y -8.2e-141)
       (* a 120.0)
       (if (<= y -4.2e-256)
         (* (/ 60.0 (- z t)) x)
         (if (<= y 2.6e+225) (* a 120.0) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -7.2e+46) {
		tmp = t_1;
	} else if (y <= -8.2e-141) {
		tmp = a * 120.0;
	} else if (y <= -4.2e-256) {
		tmp = (60.0 / (z - t)) * x;
	} else if (y <= 2.6e+225) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * (y / (z - t))
    if (y <= (-7.2d+46)) then
        tmp = t_1
    else if (y <= (-8.2d-141)) then
        tmp = a * 120.0d0
    else if (y <= (-4.2d-256)) then
        tmp = (60.0d0 / (z - t)) * x
    else if (y <= 2.6d+225) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -7.2e+46) {
		tmp = t_1;
	} else if (y <= -8.2e-141) {
		tmp = a * 120.0;
	} else if (y <= -4.2e-256) {
		tmp = (60.0 / (z - t)) * x;
	} else if (y <= 2.6e+225) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	tmp = 0
	if y <= -7.2e+46:
		tmp = t_1
	elif y <= -8.2e-141:
		tmp = a * 120.0
	elif y <= -4.2e-256:
		tmp = (60.0 / (z - t)) * x
	elif y <= 2.6e+225:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (y <= -7.2e+46)
		tmp = t_1;
	elseif (y <= -8.2e-141)
		tmp = Float64(a * 120.0);
	elseif (y <= -4.2e-256)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	elseif (y <= 2.6e+225)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (y <= -7.2e+46)
		tmp = t_1;
	elseif (y <= -8.2e-141)
		tmp = a * 120.0;
	elseif (y <= -4.2e-256)
		tmp = (60.0 / (z - t)) * x;
	elseif (y <= 2.6e+225)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.2e+46], t$95$1, If[LessEqual[y, -8.2e-141], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -4.2e-256], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 2.6e+225], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.1999999999999997e46 or 2.60000000000000004e225 < y

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in y around inf 73.4%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]

   if -7.1999999999999997e46 < y < -8.20000000000000005e-141 or -4.20000000000000005e-256 < y < 2.60000000000000004e225

   1. Initial program 98.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf 65.3%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -8.20000000000000005e-141 < y < -4.20000000000000005e-256

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in x around inf 63.8%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 64.0%

         \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} \]

      2. associate-/l* 64.2%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x}}} \]

   6. Simplified 64.2%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 63.8%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot x} \]

   8. Applied egg-rr 63.8%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+46}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-141}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-256}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+225}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]

Alternative 9: 52.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+46}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-139}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-258}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+225}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -7.2e+46)
   (* -60.0 (/ y (- z t)))
   (if (<= y -1.75e-139)
     (* a 120.0)
     (if (<= y -2.1e-258)
       (* (/ 60.0 (- z t)) x)
       (if (<= y 2.6e+225) (* a 120.0) (/ -60.0 (/ (- z t) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7.2e+46) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= -1.75e-139) {
		tmp = a * 120.0;
	} else if (y <= -2.1e-258) {
		tmp = (60.0 / (z - t)) * x;
	} else if (y <= 2.6e+225) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / ((z - t) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-7.2d+46)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (y <= (-1.75d-139)) then
        tmp = a * 120.0d0
    else if (y <= (-2.1d-258)) then
        tmp = (60.0d0 / (z - t)) * x
    else if (y <= 2.6d+225) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) / ((z - t) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7.2e+46) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= -1.75e-139) {
		tmp = a * 120.0;
	} else if (y <= -2.1e-258) {
		tmp = (60.0 / (z - t)) * x;
	} else if (y <= 2.6e+225) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / ((z - t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -7.2e+46:
		tmp = -60.0 * (y / (z - t))
	elif y <= -1.75e-139:
		tmp = a * 120.0
	elif y <= -2.1e-258:
		tmp = (60.0 / (z - t)) * x
	elif y <= 2.6e+225:
		tmp = a * 120.0
	else:
		tmp = -60.0 / ((z - t) / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -7.2e+46)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (y <= -1.75e-139)
		tmp = Float64(a * 120.0);
	elseif (y <= -2.1e-258)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	elseif (y <= 2.6e+225)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 / Float64(Float64(z - t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -7.2e+46)
		tmp = -60.0 * (y / (z - t));
	elseif (y <= -1.75e-139)
		tmp = a * 120.0;
	elseif (y <= -2.1e-258)
		tmp = (60.0 / (z - t)) * x;
	elseif (y <= 2.6e+225)
		tmp = a * 120.0;
	else
		tmp = -60.0 / ((z - t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -7.2e+46], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.75e-139], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -2.1e-258], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 2.6e+225], N[(a * 120.0), $MachinePrecision], N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.1999999999999997e46

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in y around inf 68.2%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]

   if -7.1999999999999997e46 < y < -1.75000000000000001e-139 or -2.0999999999999999e-258 < y < 2.60000000000000004e225

   1. Initial program 98.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf 65.3%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -1.75000000000000001e-139 < y < -2.0999999999999999e-258

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in x around inf 63.8%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 64.0%

         \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} \]

      2. associate-/l* 64.2%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x}}} \]

   6. Simplified 64.2%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 63.8%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot x} \]

   8. Applied egg-rr 63.8%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot x} \]

   if 2.60000000000000004e225 < y

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in y around inf 89.1%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 89.2%

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} \]

      2. associate-/l* 89.2%

         \[\leadsto \color{blue}{\frac{-60}{\frac{z - t}{y}}} \]

   6. Simplified 89.2%

      \[\leadsto \color{blue}{\frac{-60}{\frac{z - t}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+46}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-139}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-258}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+225}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \end{array} \]

Alternative 10: 52.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+46}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-139}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-257}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+227}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6.4e+46)
   (* -60.0 (/ y (- z t)))
   (if (<= y -2.5e-139)
     (* a 120.0)
     (if (<= y -3e-257)
       (/ 60.0 (/ (- z t) x))
       (if (<= y 2.9e+227) (* a 120.0) (/ -60.0 (/ (- z t) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.4e+46) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= -2.5e-139) {
		tmp = a * 120.0;
	} else if (y <= -3e-257) {
		tmp = 60.0 / ((z - t) / x);
	} else if (y <= 2.9e+227) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / ((z - t) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-6.4d+46)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (y <= (-2.5d-139)) then
        tmp = a * 120.0d0
    else if (y <= (-3d-257)) then
        tmp = 60.0d0 / ((z - t) / x)
    else if (y <= 2.9d+227) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) / ((z - t) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.4e+46) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= -2.5e-139) {
		tmp = a * 120.0;
	} else if (y <= -3e-257) {
		tmp = 60.0 / ((z - t) / x);
	} else if (y <= 2.9e+227) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / ((z - t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -6.4e+46:
		tmp = -60.0 * (y / (z - t))
	elif y <= -2.5e-139:
		tmp = a * 120.0
	elif y <= -3e-257:
		tmp = 60.0 / ((z - t) / x)
	elif y <= 2.9e+227:
		tmp = a * 120.0
	else:
		tmp = -60.0 / ((z - t) / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6.4e+46)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (y <= -2.5e-139)
		tmp = Float64(a * 120.0);
	elseif (y <= -3e-257)
		tmp = Float64(60.0 / Float64(Float64(z - t) / x));
	elseif (y <= 2.9e+227)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 / Float64(Float64(z - t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -6.4e+46)
		tmp = -60.0 * (y / (z - t));
	elseif (y <= -2.5e-139)
		tmp = a * 120.0;
	elseif (y <= -3e-257)
		tmp = 60.0 / ((z - t) / x);
	elseif (y <= 2.9e+227)
		tmp = a * 120.0;
	else
		tmp = -60.0 / ((z - t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6.4e+46], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.5e-139], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -3e-257], N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+227], N[(a * 120.0), $MachinePrecision], N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.3999999999999996e46

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in y around inf 68.2%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]

   if -6.3999999999999996e46 < y < -2.50000000000000017e-139 or -2.9999999999999999e-257 < y < 2.8999999999999998e227

   1. Initial program 98.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf 65.3%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -2.50000000000000017e-139 < y < -2.9999999999999999e-257

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in x around inf 63.8%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 64.0%

         \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} \]

      2. associate-/l* 64.2%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x}}} \]

   6. Simplified 64.2%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x}}} \]

   if 2.8999999999999998e227 < y

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in y around inf 89.1%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 89.2%

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} \]

      2. associate-/l* 89.2%

         \[\leadsto \color{blue}{\frac{-60}{\frac{z - t}{y}}} \]

   6. Simplified 89.2%

      \[\leadsto \color{blue}{\frac{-60}{\frac{z - t}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+46}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-139}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-257}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+227}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \end{array} \]

Alternative 11: 52.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-141}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-256}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+225}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.2e+46)
   (/ (* y -60.0) (- z t))
   (if (<= y -8.2e-141)
     (* a 120.0)
     (if (<= y -4.2e-256)
       (/ 60.0 (/ (- z t) x))
       (if (<= y 2.7e+225) (* a 120.0) (/ -60.0 (/ (- z t) y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.2e+46) {
		tmp = (y * -60.0) / (z - t);
	} else if (y <= -8.2e-141) {
		tmp = a * 120.0;
	} else if (y <= -4.2e-256) {
		tmp = 60.0 / ((z - t) / x);
	} else if (y <= 2.7e+225) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / ((z - t) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.2d+46)) then
        tmp = (y * (-60.0d0)) / (z - t)
    else if (y <= (-8.2d-141)) then
        tmp = a * 120.0d0
    else if (y <= (-4.2d-256)) then
        tmp = 60.0d0 / ((z - t) / x)
    else if (y <= 2.7d+225) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) / ((z - t) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.2e+46) {
		tmp = (y * -60.0) / (z - t);
	} else if (y <= -8.2e-141) {
		tmp = a * 120.0;
	} else if (y <= -4.2e-256) {
		tmp = 60.0 / ((z - t) / x);
	} else if (y <= 2.7e+225) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / ((z - t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.2e+46:
		tmp = (y * -60.0) / (z - t)
	elif y <= -8.2e-141:
		tmp = a * 120.0
	elif y <= -4.2e-256:
		tmp = 60.0 / ((z - t) / x)
	elif y <= 2.7e+225:
		tmp = a * 120.0
	else:
		tmp = -60.0 / ((z - t) / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.2e+46)
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	elseif (y <= -8.2e-141)
		tmp = Float64(a * 120.0);
	elseif (y <= -4.2e-256)
		tmp = Float64(60.0 / Float64(Float64(z - t) / x));
	elseif (y <= 2.7e+225)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 / Float64(Float64(z - t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.2e+46)
		tmp = (y * -60.0) / (z - t);
	elseif (y <= -8.2e-141)
		tmp = a * 120.0;
	elseif (y <= -4.2e-256)
		tmp = 60.0 / ((z - t) / x);
	elseif (y <= 2.7e+225)
		tmp = a * 120.0;
	else
		tmp = -60.0 / ((z - t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.2e+46], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8.2e-141], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -4.2e-256], N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+225], N[(a * 120.0), $MachinePrecision], N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.20000000000000004e46

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in y around inf 68.2%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]
   5. Step-by-step derivation

      1. *-commutative 68.2%

         \[\leadsto \color{blue}{\frac{y}{z - t} \cdot -60} \]

      2. associate-*l/ 68.3%

         \[\leadsto \color{blue}{\frac{y \cdot -60}{z - t}} \]

   6. Applied egg-rr 68.3%

      \[\leadsto \color{blue}{\frac{y \cdot -60}{z - t}} \]

   if -1.20000000000000004e46 < y < -8.20000000000000005e-141 or -4.20000000000000005e-256 < y < 2.6999999999999999e225

   1. Initial program 98.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf 65.3%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -8.20000000000000005e-141 < y < -4.20000000000000005e-256

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in x around inf 63.8%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 64.0%

         \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} \]

      2. associate-/l* 64.2%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x}}} \]

   6. Simplified 64.2%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x}}} \]

   if 2.6999999999999999e225 < y

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in y around inf 89.1%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 89.2%

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} \]

      2. associate-/l* 89.2%

         \[\leadsto \color{blue}{\frac{-60}{\frac{z - t}{y}}} \]

   6. Simplified 89.2%

      \[\leadsto \color{blue}{\frac{-60}{\frac{z - t}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-141}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-256}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+225}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \end{array} \]

Alternative 12: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{60}{z - t} \cdot \left(x - y\right) + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (* (/ 60.0 (- z t)) (- x y)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 / (z - t)) * (x - y)) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((60.0d0 / (z - t)) * (x - y)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 / (z - t)) * (x - y)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 / (z - t)) * (x - y)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 / (z - t)) * (x - y)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.1%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Step-by-step derivation

   1. associate-*l/ 99.8%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

3. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

4. Final simplification 99.8%

   \[\leadsto \frac{60}{z - t} \cdot \left(x - y\right) + a \cdot 120 \]

Alternative 13: 55.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+46} \lor \neg \left(y \leq 2.9 \cdot 10^{+225}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -7.2e+46) (not (<= y 2.9e+225)))
   (* -60.0 (/ y (- z t)))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -7.2e+46) || !(y <= 2.9e+225)) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-7.2d+46)) .or. (.not. (y <= 2.9d+225))) then
        tmp = (-60.0d0) * (y / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -7.2e+46) || !(y <= 2.9e+225)) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -7.2e+46) or not (y <= 2.9e+225):
		tmp = -60.0 * (y / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -7.2e+46) || !(y <= 2.9e+225))
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -7.2e+46) || ~((y <= 2.9e+225)))
		tmp = -60.0 * (y / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -7.2e+46], N[Not[LessEqual[y, 2.9e+225]], $MachinePrecision]], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.1999999999999997e46 or 2.9000000000000001e225 < y

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in y around inf 73.4%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]

   if -7.1999999999999997e46 < y < 2.9000000000000001e225

   1. Initial program 98.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf 62.1%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+46} \lor \neg \left(y \leq 2.9 \cdot 10^{+225}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14: 50.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+99} \lor \neg \left(y \leq 3.7 \cdot 10^{+233}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.5e+99) (not (<= y 3.7e+233))) (* -60.0 (/ y z)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.5e+99) || !(y <= 3.7e+233)) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.5d+99)) .or. (.not. (y <= 3.7d+233))) then
        tmp = (-60.0d0) * (y / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.5e+99) || !(y <= 3.7e+233)) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.5e+99) or not (y <= 3.7e+233):
		tmp = -60.0 * (y / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.5e+99) || !(y <= 3.7e+233))
		tmp = Float64(-60.0 * Float64(y / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.5e+99) || ~((y <= 3.7e+233)))
		tmp = -60.0 * (y / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.5e+99], N[Not[LessEqual[y, 3.7e+233]], $MachinePrecision]], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.50000000000000007e99 or 3.6999999999999998e233 < y

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in y around inf 77.9%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]

   5. Taylor expanded in z around inf 54.5%

      \[\leadsto -60 \cdot \color{blue}{\frac{y}{z}} \]

   if -1.50000000000000007e99 < y < 3.6999999999999998e233

   1. Initial program 98.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf 60.9%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+99} \lor \neg \left(y \leq 3.7 \cdot 10^{+233}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 15: 50.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+99}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{+233}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.4e+99)
   (* -60.0 (/ y z))
   (if (<= y 6.9e+233) (* a 120.0) (/ (* y -60.0) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.4e+99) {
		tmp = -60.0 * (y / z);
	} else if (y <= 6.9e+233) {
		tmp = a * 120.0;
	} else {
		tmp = (y * -60.0) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.4d+99)) then
        tmp = (-60.0d0) * (y / z)
    else if (y <= 6.9d+233) then
        tmp = a * 120.0d0
    else
        tmp = (y * (-60.0d0)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.4e+99) {
		tmp = -60.0 * (y / z);
	} else if (y <= 6.9e+233) {
		tmp = a * 120.0;
	} else {
		tmp = (y * -60.0) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.4e+99:
		tmp = -60.0 * (y / z)
	elif y <= 6.9e+233:
		tmp = a * 120.0
	else:
		tmp = (y * -60.0) / z
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.4e+99)
		tmp = Float64(-60.0 * Float64(y / z));
	elseif (y <= 6.9e+233)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(y * -60.0) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.4e+99)
		tmp = -60.0 * (y / z);
	elseif (y <= 6.9e+233)
		tmp = a * 120.0;
	else
		tmp = (y * -60.0) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.4e+99], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.9e+233], N[(a * 120.0), $MachinePrecision], N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4e99

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in y around inf 73.6%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]

   5. Taylor expanded in z around inf 51.4%

      \[\leadsto -60 \cdot \color{blue}{\frac{y}{z}} \]

   if -1.4e99 < y < 6.8999999999999996e233

   1. Initial program 98.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf 60.9%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if 6.8999999999999996e233 < y

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf 73.0%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z}} + a \cdot 120 \]

   3. Taylor expanded in x around 0 73.0%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z}} + a \cdot 120 \]
   4. Step-by-step derivation

      1. +-commutative 73.0%

         \[\leadsto \color{blue}{a \cdot 120 + -60 \cdot \frac{y}{z}} \]

      2. fma-def 73.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, -60 \cdot \frac{y}{z}\right)} \]

   5. Applied egg-rr 73.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, -60 \cdot \frac{y}{z}\right)} \]

   6. Taylor expanded in a around 0 61.9%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 62.0%

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z}} \]

   8. Simplified 62.0%

      \[\leadsto \color{blue}{\frac{-60 \cdot y}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+99}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{+233}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \end{array} \]

Alternative 16: 51.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+167}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.3e+167) (* -60.0 (/ x t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.3e+167) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.3d+167)) then
        tmp = (-60.0d0) * (x / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.3e+167) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.3e+167:
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.3e+167)
		tmp = Float64(-60.0 * Float64(x / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.3e+167)
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.3e+167], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3000000000000001e167

   1. Initial program 97.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   4. Taylor expanded in x around inf 67.0%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   5. Step-by-step derivation

      1. associate-*r/ 64.3%

         \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} \]

      2. associate-/l* 67.1%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x}}} \]

   6. Simplified 67.1%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x}}} \]

   7. Taylor expanded in z around 0 44.2%

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t}} \]

   if -1.3000000000000001e167 < x

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

   2. Taylor expanded in z around inf 53.3%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+167}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 17: 50.5% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* a 120.0))

C

double code(double x, double y, double z, double t, double a) {
	return a * 120.0;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = a * 120.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return a * 120.0;
}

Python

def code(x, y, z, t, a):
	return a * 120.0

Julia

function code(x, y, z, t, a)
	return Float64(a * 120.0)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = a * 120.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0), $MachinePrecision]

Derivation

1. Initial program 99.1%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]

2. Taylor expanded in z around inf 49.7%

   \[\leadsto \color{blue}{120 \cdot a} \]

3. Final simplification 49.7%

   \[\leadsto a \cdot 120 \]

Developer target: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{60}{\frac{z - t}{x - y}} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ 60.0 (/ (- z t) (- x y))) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (60.0d0 / ((z - t) / (x - y))) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(60.0 / Float64(Float64(z - t) / Float64(x - y))) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (60.0 / ((z - t) / (x - y))) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023318 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (+ (/ 60.0 (/ (- z t) (- x y))) (* a 120.0))

  (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))