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

Percentage Accurate: 99.4% → 99.8%

Time: 10.9s

Alternatives: 15

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/ 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $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-*r/ 99.8%

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

   2. fma-def 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 3: 83.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{+82}:\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+75)
     t_1
     (if (<= t_1 1e+82)
       (+ (* (/ 60.0 (- z t)) x) (* a 120.0))
       (* 60.0 (/ (- x y) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+75) {
		tmp = t_1;
	} else if (t_1 <= 1e+82) {
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	} else {
		tmp = 60.0 * ((x - y) / (z - 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) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-5d+75)) then
        tmp = t_1
    else if (t_1 <= 1d+82) then
        tmp = ((60.0d0 / (z - t)) * x) + (a * 120.0d0)
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    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 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+75) {
		tmp = t_1;
	} else if (t_1 <= 1e+82) {
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e+75:
		tmp = t_1
	elif t_1 <= 1e+82:
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0)
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+75)
		tmp = t_1;
	elseif (t_1 <= 1e+82)
		tmp = Float64(Float64(Float64(60.0 / Float64(z - t)) * x) + Float64(a * 120.0));
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+75)
		tmp = t_1;
	elseif (t_1 <= 1e+82)
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+75], t$95$1, If[LessEqual[t$95$1, 1e+82], N[(N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -5.0000000000000002e75

   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. Taylor expanded in a around 0 82.8%

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

      1. associate-*r/ 82.9%

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

   6. Applied egg-rr 82.9%

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

   if -5.0000000000000002e75 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 9.9999999999999996e81

   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 x around inf 90.1%

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

      1. associate-*r/ 90.1%

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

      2. associate-*l/ 90.1%

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

      3. *-commutative 90.1%

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

   6. Simplified 90.1%

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

   if 9.9999999999999996e81 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

   1. Initial program 94.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 a around 0 90.1%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+75}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+82}:\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 4: 73.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+69}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+71)
     t_1
     (if (<= t_1 2e+69) (* a 120.0) (* 60.0 (/ (- x y) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+71) {
		tmp = t_1;
	} else if (t_1 <= 2e+69) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - 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) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+71)) then
        tmp = t_1
    else if (t_1 <= 2d+69) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    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 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+71) {
		tmp = t_1;
	} else if (t_1 <= 2e+69) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+71:
		tmp = t_1
	elif t_1 <= 2e+69:
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+71)
		tmp = t_1;
	elseif (t_1 <= 2e+69)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+71)
		tmp = t_1;
	elseif (t_1 <= 2e+69)
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+71], t$95$1, If[LessEqual[t$95$1, 2e+69], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -1e71

   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. Taylor expanded in a around 0 83.2%

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

      1. associate-*r/ 83.3%

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

   6. Applied egg-rr 83.3%

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

   if -1e71 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 2.0000000000000001e69

   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 78.4%

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

   if 2.0000000000000001e69 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

   1. Initial program 95.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 88.3%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+71}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 2 \cdot 10^{+69}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 5: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-58}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+31}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e-58)
   (+ (* a 120.0) (* -60.0 (/ y z)))
   (if (<= (* a 120.0) 5e+31) (* 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 * 120.0) <= -4e-58) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 5e+31) {
		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 * 120.0d0) <= (-4d-58)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if ((a * 120.0d0) <= 5d+31) 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 * 120.0) <= -4e-58) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 5e+31) {
		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 * 120.0) <= -4e-58:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif (a * 120.0) <= 5e+31:
		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 (Float64(a * 120.0) <= -4e-58)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (Float64(a * 120.0) <= 5e+31)
		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 * 120.0) <= -4e-58)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif ((a * 120.0) <= 5e+31)
		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[N[(a * 120.0), $MachinePrecision], -4e-58], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e+31], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -4.0000000000000001e-58

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 88.9%

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

   3. Taylor expanded in t around 0 78.6%

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

   if -4.0000000000000001e-58 < (*.f64 a 120) < 5.00000000000000027e31

   1. Initial program 97.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 a around 0 81.1%

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

   if 5.00000000000000027e31 < (*.f64 a 120)

   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 z around inf 84.0%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-58}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{+31}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6: 59.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-73}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-162}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-136}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-45}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.05e-73)
   (* a 120.0)
   (if (<= a 1.85e-162)
     (* (- x y) (/ -60.0 t))
     (if (<= a 9e-136)
       (/ (* y -60.0) (- z t))
       (if (<= a 1.7e-45) (* -60.0 (/ (- x y) t)) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.05e-73) {
		tmp = a * 120.0;
	} else if (a <= 1.85e-162) {
		tmp = (x - y) * (-60.0 / t);
	} else if (a <= 9e-136) {
		tmp = (y * -60.0) / (z - t);
	} else if (a <= 1.7e-45) {
		tmp = -60.0 * ((x - y) / 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 <= (-1.05d-73)) then
        tmp = a * 120.0d0
    else if (a <= 1.85d-162) then
        tmp = (x - y) * ((-60.0d0) / t)
    else if (a <= 9d-136) then
        tmp = (y * (-60.0d0)) / (z - t)
    else if (a <= 1.7d-45) then
        tmp = (-60.0d0) * ((x - y) / 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 <= -1.05e-73) {
		tmp = a * 120.0;
	} else if (a <= 1.85e-162) {
		tmp = (x - y) * (-60.0 / t);
	} else if (a <= 9e-136) {
		tmp = (y * -60.0) / (z - t);
	} else if (a <= 1.7e-45) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.05e-73:
		tmp = a * 120.0
	elif a <= 1.85e-162:
		tmp = (x - y) * (-60.0 / t)
	elif a <= 9e-136:
		tmp = (y * -60.0) / (z - t)
	elif a <= 1.7e-45:
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.05e-73)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.85e-162)
		tmp = Float64(Float64(x - y) * Float64(-60.0 / t));
	elseif (a <= 9e-136)
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	elseif (a <= 1.7e-45)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / 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 <= -1.05e-73)
		tmp = a * 120.0;
	elseif (a <= 1.85e-162)
		tmp = (x - y) * (-60.0 / t);
	elseif (a <= 9e-136)
		tmp = (y * -60.0) / (z - t);
	elseif (a <= 1.7e-45)
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.05e-73], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.85e-162], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e-136], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-45], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.0499999999999999e-73 or 1.70000000000000002e-45 < 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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 76.0%

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

   if -1.0499999999999999e-73 < a < 1.8500000000000001e-162

   1. Initial program 98.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 87.5%

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

   5. Taylor expanded in z around 0 55.8%

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

      1. *-commutative 55.8%

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

      2. metadata-eval 55.8%

         \[\leadsto \frac{x - y}{t} \cdot \color{blue}{\frac{1}{-0.016666666666666666}} \]

      3. times-frac 55.8%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot 1}{t \cdot -0.016666666666666666}} \]

      4. associate-*r/ 55.9%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{1}{t \cdot -0.016666666666666666}} \]

      5. *-commutative 55.9%

         \[\leadsto \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot t}} \]

      6. associate-/r* 56.0%

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{t}} \]

      7. metadata-eval 56.0%

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

   7. Simplified 56.0%

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

   if 1.8500000000000001e-162 < a < 8.99999999999999944e-136

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 78.8%

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

      1. associate-*r/ 78.8%

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

   6. Applied egg-rr 78.8%

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

   7. Taylor expanded in x around 0 78.7%

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

      1. associate-*r/ 78.7%

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

      2. *-commutative 78.7%

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

   9. Simplified 78.7%

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

   if 8.99999999999999944e-136 < a < 1.70000000000000002e-45

   1. Initial program 93.5%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in a around 0 74.8%

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

   5. Taylor expanded in z around 0 49.2%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-73}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-162}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-136}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-45}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7: 89.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+25} \lor \neg \left(x \leq 6.4 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -3e+25) (not (<= x 6.4e-57)))
   (+ (* (/ 60.0 (- z t)) x) (* a 120.0))
   (+ (/ (* y -60.0) (- z t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3e+25) || !(x <= 6.4e-57)) {
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	} else {
		tmp = ((y * -60.0) / (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) :: tmp
    if ((x <= (-3d+25)) .or. (.not. (x <= 6.4d-57))) then
        tmp = ((60.0d0 / (z - t)) * x) + (a * 120.0d0)
    else
        tmp = ((y * (-60.0d0)) / (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 tmp;
	if ((x <= -3e+25) || !(x <= 6.4e-57)) {
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	} else {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -3e+25) or not (x <= 6.4e-57):
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0)
	else:
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -3e+25) || !(x <= 6.4e-57))
		tmp = Float64(Float64(Float64(60.0 / Float64(z - t)) * x) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -3e+25) || ~((x <= 6.4e-57)))
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	else
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -3e+25], N[Not[LessEqual[x, 6.4e-57]], $MachinePrecision]], N[(N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.00000000000000006e25 or 6.4000000000000002e-57 < x

   1. Initial program 98.2%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 88.9%

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

      1. associate-*r/ 87.2%

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

      2. associate-*l/ 88.9%

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

      3. *-commutative 88.9%

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

   6. Simplified 88.9%

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

   if -3.00000000000000006e25 < x < 6.4000000000000002e-57

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 96.4%

      \[\leadsto \frac{\color{blue}{-60 \cdot y}}{z - t} + a \cdot 120 \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+25} \lor \neg \left(x \leq 6.4 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 8: 52.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x}{t}\\ \mathbf{if}\;a \leq -1.12 \cdot 10^{-69}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-194}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ x t))))
   (if (<= a -1.12e-69)
     (* a 120.0)
     (if (<= a -1.15e-258)
       t_1
       (if (<= a 4.1e-194)
         (* 60.0 (/ y t))
         (if (<= a 9.5e-163) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / t);
	double tmp;
	if (a <= -1.12e-69) {
		tmp = a * 120.0;
	} else if (a <= -1.15e-258) {
		tmp = t_1;
	} else if (a <= 4.1e-194) {
		tmp = 60.0 * (y / t);
	} else if (a <= 9.5e-163) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * (x / t)
    if (a <= (-1.12d-69)) then
        tmp = a * 120.0d0
    else if (a <= (-1.15d-258)) then
        tmp = t_1
    else if (a <= 4.1d-194) then
        tmp = 60.0d0 * (y / t)
    else if (a <= 9.5d-163) then
        tmp = t_1
    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 t_1 = -60.0 * (x / t);
	double tmp;
	if (a <= -1.12e-69) {
		tmp = a * 120.0;
	} else if (a <= -1.15e-258) {
		tmp = t_1;
	} else if (a <= 4.1e-194) {
		tmp = 60.0 * (y / t);
	} else if (a <= 9.5e-163) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (x / t)
	tmp = 0
	if a <= -1.12e-69:
		tmp = a * 120.0
	elif a <= -1.15e-258:
		tmp = t_1
	elif a <= 4.1e-194:
		tmp = 60.0 * (y / t)
	elif a <= 9.5e-163:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(x / t))
	tmp = 0.0
	if (a <= -1.12e-69)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.15e-258)
		tmp = t_1;
	elseif (a <= 4.1e-194)
		tmp = Float64(60.0 * Float64(y / t));
	elseif (a <= 9.5e-163)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (x / t);
	tmp = 0.0;
	if (a <= -1.12e-69)
		tmp = a * 120.0;
	elseif (a <= -1.15e-258)
		tmp = t_1;
	elseif (a <= 4.1e-194)
		tmp = 60.0 * (y / t);
	elseif (a <= 9.5e-163)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.12e-69], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.15e-258], t$95$1, If[LessEqual[a, 4.1e-194], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e-163], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.12e-69 or 9.50000000000000012e-163 < a

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 70.3%

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

   if -1.12e-69 < a < -1.14999999999999996e-258 or 4.1000000000000003e-194 < a < 9.50000000000000012e-163

   1. Initial program 99.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 a around 0 87.1%

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

   5. Taylor expanded in z around 0 49.0%

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

   6. Taylor expanded in x around inf 41.6%

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

   if -1.14999999999999996e-258 < a < 4.1000000000000003e-194

   1. Initial program 95.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 a around 0 88.5%

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

   5. Taylor expanded in z around 0 64.3%

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

   6. Taylor expanded in x around 0 41.5%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-69}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-258}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-194}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-163}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9: 52.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{-60}{t}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{-69}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-193}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ -60.0 t))))
   (if (<= a -1.15e-69)
     (* a 120.0)
     (if (<= a -2.2e-258)
       t_1
       (if (<= a 1.55e-193)
         (* 60.0 (/ y t))
         (if (<= a 6e-163) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (-60.0 / t);
	double tmp;
	if (a <= -1.15e-69) {
		tmp = a * 120.0;
	} else if (a <= -2.2e-258) {
		tmp = t_1;
	} else if (a <= 1.55e-193) {
		tmp = 60.0 * (y / t);
	} else if (a <= 6e-163) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * ((-60.0d0) / t)
    if (a <= (-1.15d-69)) then
        tmp = a * 120.0d0
    else if (a <= (-2.2d-258)) then
        tmp = t_1
    else if (a <= 1.55d-193) then
        tmp = 60.0d0 * (y / t)
    else if (a <= 6d-163) then
        tmp = t_1
    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 t_1 = x * (-60.0 / t);
	double tmp;
	if (a <= -1.15e-69) {
		tmp = a * 120.0;
	} else if (a <= -2.2e-258) {
		tmp = t_1;
	} else if (a <= 1.55e-193) {
		tmp = 60.0 * (y / t);
	} else if (a <= 6e-163) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (-60.0 / t)
	tmp = 0
	if a <= -1.15e-69:
		tmp = a * 120.0
	elif a <= -2.2e-258:
		tmp = t_1
	elif a <= 1.55e-193:
		tmp = 60.0 * (y / t)
	elif a <= 6e-163:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(-60.0 / t))
	tmp = 0.0
	if (a <= -1.15e-69)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.2e-258)
		tmp = t_1;
	elseif (a <= 1.55e-193)
		tmp = Float64(60.0 * Float64(y / t));
	elseif (a <= 6e-163)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (-60.0 / t);
	tmp = 0.0;
	if (a <= -1.15e-69)
		tmp = a * 120.0;
	elseif (a <= -2.2e-258)
		tmp = t_1;
	elseif (a <= 1.55e-193)
		tmp = 60.0 * (y / t);
	elseif (a <= 6e-163)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e-69], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.2e-258], t$95$1, If[LessEqual[a, 1.55e-193], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6e-163], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.15e-69 or 6.0000000000000005e-163 < a

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 70.3%

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

   if -1.15e-69 < a < -2.20000000000000015e-258 or 1.5500000000000001e-193 < a < 6.0000000000000005e-163

   1. Initial program 99.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 a around 0 87.1%

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

   5. Taylor expanded in z around 0 49.0%

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

   6. Taylor expanded in x around inf 41.6%

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

      1. associate-*r/ 41.5%

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

      2. associate-*l/ 41.7%

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

      3. *-commutative 41.7%

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

   8. Simplified 41.7%

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

   if -2.20000000000000015e-258 < a < 1.5500000000000001e-193

   1. Initial program 95.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 a around 0 88.5%

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

   5. Taylor expanded in z around 0 64.3%

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

   6. Taylor expanded in x around 0 41.5%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-69}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-258}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-193}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-163}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 10: 75.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{-7}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+29}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.2e-7)
   (* a 120.0)
   (if (<= a 2.2e+29) (* 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 <= -8.2e-7) {
		tmp = a * 120.0;
	} else if (a <= 2.2e+29) {
		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 <= (-8.2d-7)) then
        tmp = a * 120.0d0
    else if (a <= 2.2d+29) 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 <= -8.2e-7) {
		tmp = a * 120.0;
	} else if (a <= 2.2e+29) {
		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 <= -8.2e-7:
		tmp = a * 120.0
	elif a <= 2.2e+29:
		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 <= -8.2e-7)
		tmp = Float64(a * 120.0);
	elseif (a <= 2.2e+29)
		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 <= -8.2e-7)
		tmp = a * 120.0;
	elseif (a <= 2.2e+29)
		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, -8.2e-7], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 2.2e+29], 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 < -8.1999999999999998e-7 or 2.2000000000000001e29 < 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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 82.8%

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

   if -8.1999999999999998e-7 < a < 2.2000000000000001e29

   1. Initial program 98.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 a around 0 78.0%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{-7}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+29}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11: 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]

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%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 12: 59.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-71}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-46}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.7e-71)
   (* a 120.0)
   (if (<= a 1.8e-46) (* -60.0 (/ (- x y) t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.7e-71) {
		tmp = a * 120.0;
	} else if (a <= 1.8e-46) {
		tmp = -60.0 * ((x - y) / 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 <= (-2.7d-71)) then
        tmp = a * 120.0d0
    else if (a <= 1.8d-46) then
        tmp = (-60.0d0) * ((x - y) / 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 <= -2.7e-71) {
		tmp = a * 120.0;
	} else if (a <= 1.8e-46) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.7e-71:
		tmp = a * 120.0
	elif a <= 1.8e-46:
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.7e-71)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.8e-46)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / 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 <= -2.7e-71)
		tmp = a * 120.0;
	elseif (a <= 1.8e-46)
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.7e-71], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.8e-46], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.7000000000000001e-71 or 1.8e-46 < 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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 76.0%

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

   if -2.7000000000000001e-71 < a < 1.8e-46

   1. Initial program 97.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 a around 0 84.4%

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

   5. Taylor expanded in z around 0 51.9%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-71}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-46}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13: 59.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-73}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-59}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.5e-73)
   (* a 120.0)
   (if (<= a 6.5e-59) (* (- x y) (/ -60.0 t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.5e-73) {
		tmp = a * 120.0;
	} else if (a <= 6.5e-59) {
		tmp = (x - y) * (-60.0 / 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 <= (-2.5d-73)) then
        tmp = a * 120.0d0
    else if (a <= 6.5d-59) then
        tmp = (x - y) * ((-60.0d0) / 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 <= -2.5e-73) {
		tmp = a * 120.0;
	} else if (a <= 6.5e-59) {
		tmp = (x - y) * (-60.0 / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.5e-73:
		tmp = a * 120.0
	elif a <= 6.5e-59:
		tmp = (x - y) * (-60.0 / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.5e-73)
		tmp = Float64(a * 120.0);
	elseif (a <= 6.5e-59)
		tmp = Float64(Float64(x - y) * Float64(-60.0 / 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 <= -2.5e-73)
		tmp = a * 120.0;
	elseif (a <= 6.5e-59)
		tmp = (x - y) * (-60.0 / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.5e-73], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 6.5e-59], N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -2.4999999999999999e-73 or 6.50000000000000017e-59 < 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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 76.0%

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

   if -2.4999999999999999e-73 < a < 6.50000000000000017e-59

   1. Initial program 97.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 a around 0 84.4%

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

   5. Taylor expanded in z around 0 51.9%

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

      1. *-commutative 51.9%

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

      2. metadata-eval 51.9%

         \[\leadsto \frac{x - y}{t} \cdot \color{blue}{\frac{1}{-0.016666666666666666}} \]

      3. times-frac 51.9%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot 1}{t \cdot -0.016666666666666666}} \]

      4. associate-*r/ 51.9%

         \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{1}{t \cdot -0.016666666666666666}} \]

      5. *-commutative 51.9%

         \[\leadsto \left(x - y\right) \cdot \frac{1}{\color{blue}{-0.016666666666666666 \cdot t}} \]

      6. associate-/r* 52.0%

         \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{\frac{1}{-0.016666666666666666}}{t}} \]

      7. metadata-eval 52.0%

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

   7. Simplified 52.0%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-73}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-59}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14: 52.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-66}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-220}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.8e-66)
   (* a 120.0)
   (if (<= a 3.2e-220) (* -60.0 (/ x t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.8e-66) {
		tmp = a * 120.0;
	} else if (a <= 3.2e-220) {
		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 (a <= (-6.8d-66)) then
        tmp = a * 120.0d0
    else if (a <= 3.2d-220) 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 (a <= -6.8e-66) {
		tmp = a * 120.0;
	} else if (a <= 3.2e-220) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.8e-66:
		tmp = a * 120.0
	elif a <= 3.2e-220:
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.8e-66)
		tmp = Float64(a * 120.0);
	elseif (a <= 3.2e-220)
		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 (a <= -6.8e-66)
		tmp = a * 120.0;
	elseif (a <= 3.2e-220)
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.8e-66], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 3.2e-220], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.79999999999999994e-66 or 3.20000000000000005e-220 < a

   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 67.8%

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

   if -6.79999999999999994e-66 < a < 3.20000000000000005e-220

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 91.5%

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

   5. Taylor expanded in z around 0 58.0%

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

   6. Taylor expanded in x around inf 36.7%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{-66}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-220}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 15: 50.7% 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. 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 56.0%

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

5. Final simplification 56.0%

   \[\leadsto a \cdot 120 \]

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 2023199 
(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)))