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

Percentage Accurate: 99.4% → 99.8%

Time: 13.1s

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 99.4%

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

   1. +-commutative 99.4%

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

   2. fma-def 99.5%

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

   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: 82.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-192} \lor \neg \left(a \cdot 120 \leq 10^{-77}\right):\\ \;\;\;\;t_1 \cdot x + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 60.0 (- z t))))
   (if (or (<= (* a 120.0) -5e-192) (not (<= (* a 120.0) 1e-77)))
     (+ (* t_1 x) (* a 120.0))
     (* t_1 (- x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / (z - t);
	double tmp;
	if (((a * 120.0) <= -5e-192) || !((a * 120.0) <= 1e-77)) {
		tmp = (t_1 * x) + (a * 120.0);
	} else {
		tmp = t_1 * (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) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 / (z - t)
    if (((a * 120.0d0) <= (-5d-192)) .or. (.not. ((a * 120.0d0) <= 1d-77))) then
        tmp = (t_1 * x) + (a * 120.0d0)
    else
        tmp = t_1 * (x - y)
    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 / (z - t);
	double tmp;
	if (((a * 120.0) <= -5e-192) || !((a * 120.0) <= 1e-77)) {
		tmp = (t_1 * x) + (a * 120.0);
	} else {
		tmp = t_1 * (x - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 / (z - t)
	tmp = 0
	if ((a * 120.0) <= -5e-192) or not ((a * 120.0) <= 1e-77):
		tmp = (t_1 * x) + (a * 120.0)
	else:
		tmp = t_1 * (x - y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 / Float64(z - t))
	tmp = 0.0
	if ((Float64(a * 120.0) <= -5e-192) || !(Float64(a * 120.0) <= 1e-77))
		tmp = Float64(Float64(t_1 * x) + Float64(a * 120.0));
	else
		tmp = Float64(t_1 * Float64(x - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 / (z - t);
	tmp = 0.0;
	if (((a * 120.0) <= -5e-192) || ~(((a * 120.0) <= 1e-77)))
		tmp = (t_1 * x) + (a * 120.0);
	else
		tmp = t_1 * (x - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-192], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-77]], $MachinePrecision]], N[(N[(t$95$1 * x), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(x - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -5.0000000000000001e-192 or 9.9999999999999993e-78 < (*.f64 a 120)

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 84.5%

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

      1. associate-*r/ 84.5%

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

      2. associate-*l/ 84.5%

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

      3. *-commutative 84.5%

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

   6. Simplified 84.5%

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

   if -5.0000000000000001e-192 < (*.f64 a 120) < 9.9999999999999993e-78

   1. Initial program 98.4%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 89.2%

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

      1. associate-*r/ 87.9%

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

      2. *-commutative 87.9%

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

      3. associate-*r/ 89.3%

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

   8. Simplified 89.3%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-192} \lor \neg \left(a \cdot 120 \leq 10^{-77}\right):\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]

Alternative 3: 82.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-192}:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-77}:\\ \;\;\;\;t_1 \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot x + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 60.0 (- z t))))
   (if (<= (* a 120.0) -5e-192)
     (+ (/ x (/ (- z t) 60.0)) (* a 120.0))
     (if (<= (* a 120.0) 1e-77) (* t_1 (- x y)) (+ (* t_1 x) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / (z - t);
	double tmp;
	if ((a * 120.0) <= -5e-192) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else if ((a * 120.0) <= 1e-77) {
		tmp = t_1 * (x - y);
	} else {
		tmp = (t_1 * x) + (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 / (z - t)
    if ((a * 120.0d0) <= (-5d-192)) then
        tmp = (x / ((z - t) / 60.0d0)) + (a * 120.0d0)
    else if ((a * 120.0d0) <= 1d-77) then
        tmp = t_1 * (x - y)
    else
        tmp = (t_1 * x) + (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 / (z - t);
	double tmp;
	if ((a * 120.0) <= -5e-192) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else if ((a * 120.0) <= 1e-77) {
		tmp = t_1 * (x - y);
	} else {
		tmp = (t_1 * x) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 / (z - t)
	tmp = 0
	if (a * 120.0) <= -5e-192:
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0)
	elif (a * 120.0) <= 1e-77:
		tmp = t_1 * (x - y)
	else:
		tmp = (t_1 * x) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 / Float64(z - t))
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e-192)
		tmp = Float64(Float64(x / Float64(Float64(z - t) / 60.0)) + Float64(a * 120.0));
	elseif (Float64(a * 120.0) <= 1e-77)
		tmp = Float64(t_1 * Float64(x - y));
	else
		tmp = Float64(Float64(t_1 * x) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 / (z - t);
	tmp = 0.0;
	if ((a * 120.0) <= -5e-192)
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	elseif ((a * 120.0) <= 1e-77)
		tmp = t_1 * (x - y);
	else
		tmp = (t_1 * x) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-192], N[(N[(x / N[(N[(z - t), $MachinePrecision] / 60.0), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-77], N[(t$95$1 * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * x), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -5.0000000000000001e-192

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 79.3%

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

      1. associate-*r/ 79.4%

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

      2. *-commutative 79.4%

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

      3. associate-/l* 79.4%

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

   6. Simplified 79.4%

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

   if -5.0000000000000001e-192 < (*.f64 a 120) < 9.9999999999999993e-78

   1. Initial program 98.4%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 89.2%

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

      1. associate-*r/ 87.9%

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

      2. *-commutative 87.9%

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

      3. associate-*r/ 89.3%

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

   8. Simplified 89.3%

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

   if 9.9999999999999993e-78 < (*.f64 a 120)

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 91.2%

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

      1. associate-*r/ 91.1%

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

      2. associate-*l/ 91.1%

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

      3. *-commutative 91.1%

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

   6. Simplified 91.1%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-192}:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-77}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \end{array} \]

Alternative 4: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-8}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 30000000000:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -1e-8)
   (+ (* a 120.0) (* -60.0 (/ y z)))
   (if (<= (* a 120.0) 30000000000.0)
     (* (/ 60.0 (- z t)) (- x y))
     (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -1e-8) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 30000000000.0) {
		tmp = (60.0 / (z - t)) * (x - y);
	} 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 ((a * 120.0d0) <= (-1d-8)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if ((a * 120.0d0) <= 30000000000.0d0) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    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 ((a * 120.0) <= -1e-8) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 30000000000.0) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -1e-8:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif (a * 120.0) <= 30000000000.0:
		tmp = (60.0 / (z - t)) * (x - y)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -1e-8)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (Float64(a * 120.0) <= 30000000000.0)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -1e-8)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif ((a * 120.0) <= 30000000000.0)
		tmp = (60.0 / (z - t)) * (x - y);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-8], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 30000000000.0], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -1e-8

   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* 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 92.4%

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

      1. fma-def 92.4%

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

      2. associate-*r/ 92.4%

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

   8. Simplified 92.4%

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

   9. Taylor expanded in t around 0 77.5%

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

   if -1e-8 < (*.f64 a 120) < 3e10

   1. Initial program 99.0%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 74.6%

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

      1. associate-*r/ 73.9%

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

      2. *-commutative 73.9%

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

      3. associate-*r/ 74.6%

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

   8. Simplified 74.6%

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

   if 3e10 < (*.f64 a 120)

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 82.6%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-8}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 30000000000:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 5: 57.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{-34}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 5 \cdot 10^{-6}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- z t) -5e-34)
   (* a 120.0)
   (if (<= (- z t) 5e-6) (* (- x y) (/ 60.0 z)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -5e-34) {
		tmp = a * 120.0;
	} else if ((z - t) <= 5e-6) {
		tmp = (x - y) * (60.0 / 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 ((z - t) <= (-5d-34)) then
        tmp = a * 120.0d0
    else if ((z - t) <= 5d-6) then
        tmp = (x - y) * (60.0d0 / 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 ((z - t) <= -5e-34) {
		tmp = a * 120.0;
	} else if ((z - t) <= 5e-6) {
		tmp = (x - y) * (60.0 / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z - t) <= -5e-34:
		tmp = a * 120.0
	elif (z - t) <= 5e-6:
		tmp = (x - y) * (60.0 / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z - t) <= -5e-34)
		tmp = Float64(a * 120.0);
	elseif (Float64(z - t) <= 5e-6)
		tmp = Float64(Float64(x - y) * Float64(60.0 / 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 ((z - t) <= -5e-34)
		tmp = a * 120.0;
	elseif ((z - t) <= 5e-6)
		tmp = (x - y) * (60.0 / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z - t), $MachinePrecision], -5e-34], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 5e-6], N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z t) < -5.0000000000000003e-34 or 5.00000000000000041e-6 < (-.f64 z t)

   1. Initial program 99.3%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 65.6%

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

   if -5.0000000000000003e-34 < (-.f64 z t) < 5.00000000000000041e-6

   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%

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

   3. Simplified 99.8%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 89.5%

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

      1. associate-*r/ 89.6%

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

      2. *-commutative 89.6%

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

      3. associate-*r/ 89.5%

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

   8. Simplified 89.5%

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

   9. Taylor expanded in z around inf 62.8%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -5 \cdot 10^{-34}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 5 \cdot 10^{-6}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6: 88.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+147}:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+47}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.5e+147)
   (+ (/ x (/ (- z t) 60.0)) (* a 120.0))
   (if (<= x 1.6e+47)
     (+ (/ (* y -60.0) (- z t)) (* a 120.0))
     (+ (* (/ 60.0 (- z t)) x) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.5e+147) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else if (x <= 1.6e+47) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = ((60.0 / (z - t)) * x) + (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 <= (-4.5d+147)) then
        tmp = (x / ((z - t) / 60.0d0)) + (a * 120.0d0)
    else if (x <= 1.6d+47) then
        tmp = ((y * (-60.0d0)) / (z - t)) + (a * 120.0d0)
    else
        tmp = ((60.0d0 / (z - t)) * x) + (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 <= -4.5e+147) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else if (x <= 1.6e+47) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.5e+147:
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0)
	elif x <= 1.6e+47:
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	else:
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.5e+147)
		tmp = Float64(Float64(x / Float64(Float64(z - t) / 60.0)) + Float64(a * 120.0));
	elseif (x <= 1.6e+47)
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(Float64(60.0 / Float64(z - t)) * x) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4.5e+147)
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	elseif (x <= 1.6e+47)
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	else
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.5e+147], N[(N[(x / N[(N[(z - t), $MachinePrecision] / 60.0), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e+47], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.50000000000000008e147

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 90.8%

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

      1. associate-*r/ 90.9%

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

      2. *-commutative 90.9%

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

      3. associate-/l* 90.8%

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

   6. Simplified 90.8%

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

   if -4.50000000000000008e147 < x < 1.6e47

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0 94.3%

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

   if 1.6e47 < x

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 93.2%

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

      1. associate-*r/ 93.2%

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

      2. associate-*l/ 93.3%

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

      3. *-commutative 93.3%

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

   6. Simplified 93.3%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+147}:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+47}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \end{array} \]

Alternative 7: 88.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+147}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4e+147)
   (+ (/ (* 60.0 x) (- z t)) (* a 120.0))
   (if (<= x 2.4e+47)
     (+ (/ (* y -60.0) (- z t)) (* a 120.0))
     (+ (* (/ 60.0 (- z t)) x) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4e+147) {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	} else if (x <= 2.4e+47) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = ((60.0 / (z - t)) * x) + (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 <= (-4d+147)) then
        tmp = ((60.0d0 * x) / (z - t)) + (a * 120.0d0)
    else if (x <= 2.4d+47) then
        tmp = ((y * (-60.0d0)) / (z - t)) + (a * 120.0d0)
    else
        tmp = ((60.0d0 / (z - t)) * x) + (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 <= -4e+147) {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	} else if (x <= 2.4e+47) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4e+147:
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0)
	elif x <= 2.4e+47:
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	else:
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4e+147)
		tmp = Float64(Float64(Float64(60.0 * x) / Float64(z - t)) + Float64(a * 120.0));
	elseif (x <= 2.4e+47)
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(Float64(60.0 / Float64(z - t)) * x) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4e+147)
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	elseif (x <= 2.4e+47)
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	else
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4e+147], N[(N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e+47], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.9999999999999999e147

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 90.9%

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

      1. *-commutative 90.9%

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

   4. Simplified 90.9%

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

   if -3.9999999999999999e147 < x < 2.40000000000000019e47

   1. Initial program 99.3%

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

   2. Taylor expanded in x around 0 94.3%

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

   if 2.40000000000000019e47 < x

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 93.2%

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

      1. associate-*r/ 93.2%

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

      2. associate-*l/ 93.3%

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

      3. *-commutative 93.3%

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

   6. Simplified 93.3%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+147}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+47}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \end{array} \]

Alternative 8: 58.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{-195}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-304}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-78}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.25e-195)
   (* a 120.0)
   (if (<= a -9.5e-304)
     (* (- x y) (/ -60.0 t))
     (if (<= a 2.05e-78) (* -60.0 (/ y (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.25e-195) {
		tmp = a * 120.0;
	} else if (a <= -9.5e-304) {
		tmp = (x - y) * (-60.0 / t);
	} else if (a <= 2.05e-78) {
		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 (a <= (-1.25d-195)) then
        tmp = a * 120.0d0
    else if (a <= (-9.5d-304)) then
        tmp = (x - y) * ((-60.0d0) / t)
    else if (a <= 2.05d-78) 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 (a <= -1.25e-195) {
		tmp = a * 120.0;
	} else if (a <= -9.5e-304) {
		tmp = (x - y) * (-60.0 / t);
	} else if (a <= 2.05e-78) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.25e-195:
		tmp = a * 120.0
	elif a <= -9.5e-304:
		tmp = (x - y) * (-60.0 / t)
	elif a <= 2.05e-78:
		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 (a <= -1.25e-195)
		tmp = Float64(a * 120.0);
	elseif (a <= -9.5e-304)
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	elseif (a <= 2.05e-78)
		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 (a <= -1.25e-195)
		tmp = a * 120.0;
	elseif (a <= -9.5e-304)
		tmp = (x - y) * (-60.0 / t);
	elseif (a <= 2.05e-78)
		tmp = -60.0 * (y / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.25e-195], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -9.5e-304], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.05e-78], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.25000000000000002e-195 or 2.0499999999999999e-78 < a

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 68.5%

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

   if -1.25000000000000002e-195 < a < -9.50000000000000023e-304

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 83.9%

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

      1. associate-*r/ 84.3%

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

      2. *-commutative 84.3%

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

      3. associate-*r/ 84.2%

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

   8. Simplified 84.2%

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

   9. Taylor expanded in z around 0 60.9%

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

   if -9.50000000000000023e-304 < a < 2.0499999999999999e-78

   1. Initial program 97.7%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 51.8%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.25 \cdot 10^{-195}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-304}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-78}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-19}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 225000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.05e-19)
   (* a 120.0)
   (if (<= a 225000000.0) (* 60.0 (/ (- x y) (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.05e-19) {
		tmp = a * 120.0;
	} else if (a <= 225000000.0) {
		tmp = 60.0 * ((x - 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 (a <= (-2.05d-19)) then
        tmp = a * 120.0d0
    else if (a <= 225000000.0d0) then
        tmp = 60.0d0 * ((x - 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 (a <= -2.05e-19) {
		tmp = a * 120.0;
	} else if (a <= 225000000.0) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.05e-19:
		tmp = a * 120.0
	elif a <= 225000000.0:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.05e-19)
		tmp = Float64(a * 120.0);
	elseif (a <= 225000000.0)
		tmp = Float64(60.0 * Float64(Float64(x - 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 (a <= -2.05e-19)
		tmp = a * 120.0;
	elseif (a <= 225000000.0)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.05e-19], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 225000000.0], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.04999999999999993e-19 or 2.25e8 < a

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 77.8%

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

   if -2.04999999999999993e-19 < a < 2.25e8

   1. Initial program 99.0%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 75.4%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-19}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 225000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 10: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{-15}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 225000000:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.8e-15)
   (* a 120.0)
   (if (<= a 225000000.0) (* (/ 60.0 (- z t)) (- x y)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.8e-15) {
		tmp = a * 120.0;
	} else if (a <= 225000000.0) {
		tmp = (60.0 / (z - t)) * (x - y);
	} 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 (a <= (-8.8d-15)) then
        tmp = a * 120.0d0
    else if (a <= 225000000.0d0) then
        tmp = (60.0d0 / (z - t)) * (x - y)
    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 (a <= -8.8e-15) {
		tmp = a * 120.0;
	} else if (a <= 225000000.0) {
		tmp = (60.0 / (z - t)) * (x - y);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.8e-15:
		tmp = a * 120.0
	elif a <= 225000000.0:
		tmp = (60.0 / (z - t)) * (x - y)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.8e-15)
		tmp = Float64(a * 120.0);
	elseif (a <= 225000000.0)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8.8e-15)
		tmp = a * 120.0;
	elseif (a <= 225000000.0)
		tmp = (60.0 / (z - t)) * (x - y);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.8e-15], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 225000000.0], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -8.79999999999999942e-15 or 2.25e8 < a

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 77.8%

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

   if -8.79999999999999942e-15 < a < 2.25e8

   1. Initial program 99.0%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 75.4%

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

      1. associate-*r/ 74.7%

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

      2. *-commutative 74.7%

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

      3. associate-*r/ 75.4%

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

   8. Simplified 75.4%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{-15}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 225000000:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11: 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 99.4%

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

   1. associate-/l* 99.7%

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

3. Simplified 99.7%

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

   1. associate-/r/ 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 12: 52.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{+196}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+260} \lor \neg \left(y \leq 1.35 \cdot 10^{+303}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 6.5e+196)
   (* a 120.0)
   (if (or (<= y 4.3e+260) (not (<= y 1.35e+303)))
     (* -60.0 (/ y z))
     (* 60.0 (/ y t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 6.5e+196) {
		tmp = a * 120.0;
	} else if ((y <= 4.3e+260) || !(y <= 1.35e+303)) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = 60.0 * (y / t);
	}
	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 <= 6.5d+196) then
        tmp = a * 120.0d0
    else if ((y <= 4.3d+260) .or. (.not. (y <= 1.35d+303))) then
        tmp = (-60.0d0) * (y / z)
    else
        tmp = 60.0d0 * (y / t)
    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 <= 6.5e+196) {
		tmp = a * 120.0;
	} else if ((y <= 4.3e+260) || !(y <= 1.35e+303)) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 6.5e+196:
		tmp = a * 120.0
	elif (y <= 4.3e+260) or not (y <= 1.35e+303):
		tmp = -60.0 * (y / z)
	else:
		tmp = 60.0 * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 6.5e+196)
		tmp = Float64(a * 120.0);
	elseif ((y <= 4.3e+260) || !(y <= 1.35e+303))
		tmp = Float64(-60.0 * Float64(y / z));
	else
		tmp = Float64(60.0 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 6.5e+196)
		tmp = a * 120.0;
	elseif ((y <= 4.3e+260) || ~((y <= 1.35e+303)))
		tmp = -60.0 * (y / z);
	else
		tmp = 60.0 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 6.5e+196], N[(a * 120.0), $MachinePrecision], If[Or[LessEqual[y, 4.3e+260], N[Not[LessEqual[y, 1.35e+303]], $MachinePrecision]], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 6.49999999999999968e196

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 57.9%

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

   if 6.49999999999999968e196 < y < 4.30000000000000024e260 or 1.35000000000000005e303 < y

   1. Initial program 94.8%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 75.7%

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

      1. associate-*r/ 71.0%

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

   8. Simplified 71.0%

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

   9. Taylor expanded in z around inf 70.7%

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

   if 4.30000000000000024e260 < y < 1.35000000000000005e303

   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* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around inf 82.6%

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

      1. associate-*r/ 82.6%

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

   8. Simplified 82.6%

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

   9. Taylor expanded in z around 0 83.3%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.5 \cdot 10^{+196}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+260} \lor \neg \left(y \leq 1.35 \cdot 10^{+303}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 13: 58.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-156}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-78}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.8e-156)
   (* a 120.0)
   (if (<= a 1.85e-78) (* -60.0 (/ y (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.8e-156) {
		tmp = a * 120.0;
	} else if (a <= 1.85e-78) {
		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 (a <= (-1.8d-156)) then
        tmp = a * 120.0d0
    else if (a <= 1.85d-78) 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 (a <= -1.8e-156) {
		tmp = a * 120.0;
	} else if (a <= 1.85e-78) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.8e-156:
		tmp = a * 120.0
	elif a <= 1.85e-78:
		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 (a <= -1.8e-156)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.85e-78)
		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 (a <= -1.8e-156)
		tmp = a * 120.0;
	elseif (a <= 1.85e-78)
		tmp = -60.0 * (y / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.8e-156], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.85e-78], 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 a < -1.79999999999999999e-156 or 1.85000000000000003e-78 < a

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 69.3%

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

   if -1.79999999999999999e-156 < a < 1.85000000000000003e-78

   1. Initial program 98.4%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 48.0%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-156}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-78}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14: 51.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.8 \cdot 10^{+182}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+225}:\\ \;\;\;\;\frac{x}{t \cdot -0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot 0.016666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 2.8e+182)
   (* a 120.0)
   (if (<= x 1.9e+225)
     (/ x (* t -0.016666666666666666))
     (/ x (* z 0.016666666666666666)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 2.8e+182) {
		tmp = a * 120.0;
	} else if (x <= 1.9e+225) {
		tmp = x / (t * -0.016666666666666666);
	} else {
		tmp = x / (z * 0.016666666666666666);
	}
	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 <= 2.8d+182) then
        tmp = a * 120.0d0
    else if (x <= 1.9d+225) then
        tmp = x / (t * (-0.016666666666666666d0))
    else
        tmp = x / (z * 0.016666666666666666d0)
    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 <= 2.8e+182) {
		tmp = a * 120.0;
	} else if (x <= 1.9e+225) {
		tmp = x / (t * -0.016666666666666666);
	} else {
		tmp = x / (z * 0.016666666666666666);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 2.8e+182:
		tmp = a * 120.0
	elif x <= 1.9e+225:
		tmp = x / (t * -0.016666666666666666)
	else:
		tmp = x / (z * 0.016666666666666666)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 2.8e+182)
		tmp = Float64(a * 120.0);
	elseif (x <= 1.9e+225)
		tmp = Float64(x / Float64(t * -0.016666666666666666));
	else
		tmp = Float64(x / Float64(z * 0.016666666666666666));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 2.8e+182)
		tmp = a * 120.0;
	elseif (x <= 1.9e+225)
		tmp = x / (t * -0.016666666666666666);
	else
		tmp = x / (z * 0.016666666666666666);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, 2.8e+182], N[(a * 120.0), $MachinePrecision], If[LessEqual[x, 1.9e+225], N[(x / N[(t * -0.016666666666666666), $MachinePrecision]), $MachinePrecision], N[(x / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 2.80000000000000006e182

   1. Initial program 99.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 57.9%

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

   if 2.80000000000000006e182 < x < 1.9e225

   1. Initial program 100.0%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 77.1%

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

      1. *-commutative 77.1%

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

      2. associate-*l/ 77.3%

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

      3. associate-/l* 77.1%

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

   8. Simplified 77.1%

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

   9. Taylor expanded in z around 0 70.1%

      \[\leadsto \frac{x}{\color{blue}{-0.016666666666666666 \cdot t}} \]
   10. Step-by-step derivation

       1. *-commutative 70.1%

          \[\leadsto \frac{x}{\color{blue}{t \cdot -0.016666666666666666}} \]

   11. Simplified 70.1%

       \[\leadsto \frac{x}{\color{blue}{t \cdot -0.016666666666666666}} \]

   if 1.9e225 < x

   1. Initial program 99.3%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in x around inf 84.6%

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

      1. *-commutative 84.6%

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

      2. associate-*l/ 84.2%

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

      3. associate-/l* 84.5%

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

   8. Simplified 84.5%

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

   9. Taylor expanded in z around inf 69.8%

      \[\leadsto \frac{x}{\color{blue}{0.016666666666666666 \cdot z}} \]
   10. Step-by-step derivation

       1. *-commutative 69.8%

          \[\leadsto \frac{x}{\color{blue}{z \cdot 0.016666666666666666}} \]

   11. Simplified 69.8%

       \[\leadsto \frac{x}{\color{blue}{z \cdot 0.016666666666666666}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.8 \cdot 10^{+182}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+225}:\\ \;\;\;\;\frac{x}{t \cdot -0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot 0.016666666666666666}\\ \end{array} \]

Alternative 15: 51.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.8 \cdot 10^{+182}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+225}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot 0.016666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 3.8e+182)
   (* a 120.0)
   (if (<= x 2.7e+225) (/ (* x -60.0) t) (/ x (* z 0.016666666666666666)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 3.8e+182) {
		tmp = a * 120.0;
	} else if (x <= 2.7e+225) {
		tmp = (x * -60.0) / t;
	} else {
		tmp = x / (z * 0.016666666666666666);
	}
	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 <= 3.8d+182) then
        tmp = a * 120.0d0
    else if (x <= 2.7d+225) then
        tmp = (x * (-60.0d0)) / t
    else
        tmp = x / (z * 0.016666666666666666d0)
    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 <= 3.8e+182) {
		tmp = a * 120.0;
	} else if (x <= 2.7e+225) {
		tmp = (x * -60.0) / t;
	} else {
		tmp = x / (z * 0.016666666666666666);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 3.8e+182:
		tmp = a * 120.0
	elif x <= 2.7e+225:
		tmp = (x * -60.0) / t
	else:
		tmp = x / (z * 0.016666666666666666)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 3.8e+182)
		tmp = Float64(a * 120.0);
	elseif (x <= 2.7e+225)
		tmp = Float64(Float64(x * -60.0) / t);
	else
		tmp = Float64(x / Float64(z * 0.016666666666666666));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 3.8e+182)
		tmp = a * 120.0;
	elseif (x <= 2.7e+225)
		tmp = (x * -60.0) / t;
	else
		tmp = x / (z * 0.016666666666666666);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, 3.8e+182], N[(a * 120.0), $MachinePrecision], If[LessEqual[x, 2.7e+225], N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision], N[(x / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 3.80000000000000013e182

   1. Initial program 99.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 57.9%

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

   if 3.80000000000000013e182 < x < 2.6999999999999999e225

   1. Initial program 100.0%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around 0 77.1%

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

      1. associate-*r/ 77.3%

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

      2. *-commutative 77.3%

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

      3. associate-*r/ 77.1%

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

   8. Simplified 77.1%

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

   9. Taylor expanded in z around 0 70.1%

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

   10. Taylor expanded in x around inf 70.0%

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

       1. associate-*r/ 70.2%

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

   12. Simplified 70.2%

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

   if 2.6999999999999999e225 < x

   1. Initial program 99.3%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

      1. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in x around inf 84.6%

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

      1. *-commutative 84.6%

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

      2. associate-*l/ 84.2%

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

      3. associate-/l* 84.5%

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

   8. Simplified 84.5%

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

   9. Taylor expanded in z around inf 69.8%

      \[\leadsto \frac{x}{\color{blue}{0.016666666666666666 \cdot z}} \]
   10. Step-by-step derivation

       1. *-commutative 69.8%

          \[\leadsto \frac{x}{\color{blue}{z \cdot 0.016666666666666666}} \]

   11. Simplified 69.8%

       \[\leadsto \frac{x}{\color{blue}{z \cdot 0.016666666666666666}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.8 \cdot 10^{+182}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+225}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot 0.016666666666666666}\\ \end{array} \]

Alternative 16: 52.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{+196}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 7.5e+196) (* a 120.0) (* -60.0 (/ y z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 7.5e+196) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / 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 <= 7.5d+196) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (y / 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 <= 7.5e+196) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 7.5e+196:
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 7.5e+196)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 7.5e+196)
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 7.5e+196], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.5000000000000005e196

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 57.9%

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

   if 7.5000000000000005e196 < y

   1. Initial program 96.6%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 78.2%

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

      1. associate-*r/ 75.1%

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

   8. Simplified 75.1%

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

   9. Taylor expanded in z around inf 56.3%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{+196}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 17: 50.8% 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 99.4%

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

   1. associate-/l* 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in z around inf 53.1%

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

5. Final simplification 53.1%

   \[\leadsto a \cdot 120 \]

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 2023175 
(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)))