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

Percentage Accurate: 99.3% → 99.8%

Time: 11.3s

Alternatives: 13

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: 99.3% 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 99.8%

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

   1. +-commutative 99.8%

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

   2. fma-def 99.8%

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

   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: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{if}\;a \cdot 120 \leq -50000000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-107}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-114}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ 60.0 (- z t)) (- x y))))
   (if (<= (* a 120.0) -50000000000.0)
     (* a 120.0)
     (if (<= (* a 120.0) -1e-70)
       t_1
       (if (<= (* a 120.0) -2e-107)
         (+ (* a 120.0) (* x (/ -60.0 t)))
         (if (<= (* a 120.0) -2e-114)
           (+ (* a 120.0) (/ 60.0 (/ t y)))
           (if (<= (* a 120.0) 2e+18) t_1 (* a 120.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 / (z - t)) * (x - y);
	double tmp;
	if ((a * 120.0) <= -50000000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -1e-70) {
		tmp = t_1;
	} else if ((a * 120.0) <= -2e-107) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else if ((a * 120.0) <= -2e-114) {
		tmp = (a * 120.0) + (60.0 / (t / y));
	} else if ((a * 120.0) <= 2e+18) {
		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 / (z - t)) * (x - y)
    if ((a * 120.0d0) <= (-50000000000.0d0)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-1d-70)) then
        tmp = t_1
    else if ((a * 120.0d0) <= (-2d-107)) then
        tmp = (a * 120.0d0) + (x * ((-60.0d0) / t))
    else if ((a * 120.0d0) <= (-2d-114)) then
        tmp = (a * 120.0d0) + (60.0d0 / (t / y))
    else if ((a * 120.0d0) <= 2d+18) 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 / (z - t)) * (x - y);
	double tmp;
	if ((a * 120.0) <= -50000000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -1e-70) {
		tmp = t_1;
	} else if ((a * 120.0) <= -2e-107) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else if ((a * 120.0) <= -2e-114) {
		tmp = (a * 120.0) + (60.0 / (t / y));
	} else if ((a * 120.0) <= 2e+18) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 / (z - t)) * (x - y)
	tmp = 0
	if (a * 120.0) <= -50000000000.0:
		tmp = a * 120.0
	elif (a * 120.0) <= -1e-70:
		tmp = t_1
	elif (a * 120.0) <= -2e-107:
		tmp = (a * 120.0) + (x * (-60.0 / t))
	elif (a * 120.0) <= -2e-114:
		tmp = (a * 120.0) + (60.0 / (t / y))
	elif (a * 120.0) <= 2e+18:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y))
	tmp = 0.0
	if (Float64(a * 120.0) <= -50000000000.0)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -1e-70)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= -2e-107)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)));
	elseif (Float64(a * 120.0) <= -2e-114)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(t / y)));
	elseif (Float64(a * 120.0) <= 2e+18)
		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 / (z - t)) * (x - y);
	tmp = 0.0;
	if ((a * 120.0) <= -50000000000.0)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -1e-70)
		tmp = t_1;
	elseif ((a * 120.0) <= -2e-107)
		tmp = (a * 120.0) + (x * (-60.0 / t));
	elseif ((a * 120.0) <= -2e-114)
		tmp = (a * 120.0) + (60.0 / (t / y));
	elseif ((a * 120.0) <= 2e+18)
		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[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -50000000000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-70], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-107], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-114], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+18], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a 120) < -5e10 or 2e18 < (*.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 86.1%

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

   if -5e10 < (*.f64 a 120) < -9.99999999999999996e-71 or -2.0000000000000001e-114 < (*.f64 a 120) < 2e18

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 80.0%

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

      1. associate-*r/ 80.1%

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

      2. *-commutative 80.1%

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

      3. associate-*r/ 80.1%

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

   8. Simplified 80.1%

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

   if -9.99999999999999996e-71 < (*.f64 a 120) < -2e-107

   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 x around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. associate-*l/ 100.0%

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

      3. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around 0 100.0%

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

   if -2e-107 < (*.f64 a 120) < -2.0000000000000001e-114

   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* 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 x around 0 100.0%

      \[\leadsto \frac{60}{\color{blue}{-1 \cdot \frac{z - t}{y}}} + a \cdot 120 \]
   5. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \frac{60}{\color{blue}{\frac{-1 \cdot \left(z - t\right)}{y}}} + a \cdot 120 \]

      2. neg-mul-1 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in z around 0 100.0%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -50000000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-70}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-107}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-114}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+18}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 3: 81.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-97} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{+18}\right):\\ \;\;\;\;a \cdot 120 + t_1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 60.0 (- z t))))
   (if (or (<= (* a 120.0) -2e-97) (not (<= (* a 120.0) 2e+18)))
     (+ (* a 120.0) (* t_1 x))
     (* 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) <= -2e-97) || !((a * 120.0) <= 2e+18)) {
		tmp = (a * 120.0) + (t_1 * x);
	} 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) <= (-2d-97)) .or. (.not. ((a * 120.0d0) <= 2d+18))) then
        tmp = (a * 120.0d0) + (t_1 * x)
    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) <= -2e-97) || !((a * 120.0) <= 2e+18)) {
		tmp = (a * 120.0) + (t_1 * x);
	} 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) <= -2e-97) or not ((a * 120.0) <= 2e+18):
		tmp = (a * 120.0) + (t_1 * x)
	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) <= -2e-97) || !(Float64(a * 120.0) <= 2e+18))
		tmp = Float64(Float64(a * 120.0) + Float64(t_1 * x));
	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) <= -2e-97) || ~(((a * 120.0) <= 2e+18)))
		tmp = (a * 120.0) + (t_1 * x);
	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], -2e-97], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+18]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(t$95$1 * x), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(x - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -2.00000000000000007e-97 or 2e18 < (*.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 x around inf 91.9%

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

      1. associate-*r/ 91.9%

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

      2. associate-*l/ 91.9%

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

      3. *-commutative 91.9%

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

   6. Simplified 91.9%

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

   if -2.00000000000000007e-97 < (*.f64 a 120) < 2e18

   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/ 99.7%

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

   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 81.3%

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

      1. associate-*r/ 81.4%

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

      2. *-commutative 81.4%

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

      3. associate-*r/ 81.4%

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

   8. Simplified 81.4%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-97} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{+18}\right):\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \end{array} \]

Alternative 4: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -50000000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+18}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -50000000000.0)
   (* a 120.0)
   (if (<= (* a 120.0) 2e+18) (* (/ 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) <= -50000000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e+18) {
		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) <= (-50000000000.0d0)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 2d+18) 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) <= -50000000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e+18) {
		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) <= -50000000000.0:
		tmp = a * 120.0
	elif (a * 120.0) <= 2e+18:
		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) <= -50000000000.0)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 2e+18)
		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) <= -50000000000.0)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 2e+18)
		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], -50000000000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+18], 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 (*.f64 a 120) < -5e10 or 2e18 < (*.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 86.1%

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

   if -5e10 < (*.f64 a 120) < 2e18

   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/ 99.7%

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

   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 77.5%

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

      1. associate-*r/ 77.6%

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

      2. *-commutative 77.6%

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

      3. associate-*r/ 77.7%

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

   8. Simplified 77.7%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -50000000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+18}:\\ \;\;\;\;\frac{60}{z - t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 5: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+23} \lor \neg \left(y \leq 10^{+73}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.2e+23) (not (<= y 1e+73)))
   (+ (* a 120.0) (/ (* y -60.0) (- z t)))
   (+ (* a 120.0) (* (/ 60.0 (- z t)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.2e+23) || !(y <= 1e+73)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.2d+23)) .or. (.not. (y <= 1d+73))) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else
        tmp = (a * 120.0d0) + ((60.0d0 / (z - t)) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.2e+23) || !(y <= 1e+73)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.2e+23) or not (y <= 1e+73):
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	else:
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.2e+23) || !(y <= 1e+73))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 / Float64(z - t)) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.2e+23) || ~((y <= 1e+73)))
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	else
		tmp = (a * 120.0) + ((60.0 / (z - t)) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.2e+23], N[Not[LessEqual[y, 1e+73]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e23 or 9.99999999999999983e72 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 91.8%

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

   if -1.2e23 < y < 9.99999999999999983e72

   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 94.5%

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

      1. associate-*r/ 94.5%

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

      2. associate-*l/ 94.5%

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

      3. *-commutative 94.5%

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

   6. Simplified 94.5%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+23} \lor \neg \left(y \leq 10^{+73}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{z - t} \cdot x\\ \end{array} \]

Alternative 6: 89.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+25} \lor \neg \left(y \leq 2.3 \cdot 10^{+70}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.2e+25) (not (<= y 2.3e+70)))
   (+ (* a 120.0) (/ (* y -60.0) (- z t)))
   (+ (* a 120.0) (/ (* 60.0 x) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.2e+25) || !(y <= 2.3e+70)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / (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) :: tmp
    if ((y <= (-5.2d+25)) .or. (.not. (y <= 2.3d+70))) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else
        tmp = (a * 120.0d0) + ((60.0d0 * x) / (z - 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 <= -5.2e+25) || !(y <= 2.3e+70)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5.2e+25) or not (y <= 2.3e+70):
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	else:
		tmp = (a * 120.0) + ((60.0 * x) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5.2e+25) || !(y <= 2.3e+70))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -5.2e+25) || ~((y <= 2.3e+70)))
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	else
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5.2e+25], N[Not[LessEqual[y, 2.3e+70]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.1999999999999997e25 or 2.29999999999999994e70 < y

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 91.8%

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

   if -5.1999999999999997e25 < y < 2.29999999999999994e70

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 94.5%

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

      1. *-commutative 94.5%

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

   4. Simplified 94.5%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+25} \lor \neg \left(y \leq 2.3 \cdot 10^{+70}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \end{array} \]

Alternative 7: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+23} \lor \neg \left(y \leq 1.3 \cdot 10^{+70}\right):\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.25e+23) (not (<= y 1.3e+70)))
   (+ (* a 120.0) (/ 60.0 (/ (- t z) y)))
   (+ (* a 120.0) (/ (* 60.0 x) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.25e+23) || !(y <= 1.3e+70)) {
		tmp = (a * 120.0) + (60.0 / ((t - z) / y));
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / (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) :: tmp
    if ((y <= (-1.25d+23)) .or. (.not. (y <= 1.3d+70))) then
        tmp = (a * 120.0d0) + (60.0d0 / ((t - z) / y))
    else
        tmp = (a * 120.0d0) + ((60.0d0 * x) / (z - 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 <= -1.25e+23) || !(y <= 1.3e+70)) {
		tmp = (a * 120.0) + (60.0 / ((t - z) / y));
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.25e+23) or not (y <= 1.3e+70):
		tmp = (a * 120.0) + (60.0 / ((t - z) / y))
	else:
		tmp = (a * 120.0) + ((60.0 * x) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.25e+23) || !(y <= 1.3e+70))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(t - z) / y)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.25e+23) || ~((y <= 1.3e+70)))
		tmp = (a * 120.0) + (60.0 / ((t - z) / y));
	else
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.25e+23], N[Not[LessEqual[y, 1.3e+70]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25e23 or 1.3e70 < y

   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 0 91.8%

      \[\leadsto \frac{60}{\color{blue}{-1 \cdot \frac{z - t}{y}}} + a \cdot 120 \]
   5. Step-by-step derivation

      1. associate-*r/ 91.8%

         \[\leadsto \frac{60}{\color{blue}{\frac{-1 \cdot \left(z - t\right)}{y}}} + a \cdot 120 \]

      2. neg-mul-1 91.8%

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

   6. Simplified 91.8%

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

   if -1.25e23 < y < 1.3e70

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 94.5%

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

      1. *-commutative 94.5%

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

   4. Simplified 94.5%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+23} \lor \neg \left(y \leq 1.3 \cdot 10^{+70}\right):\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \end{array} \]

Alternative 8: 74.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5000000 \lor \neg \left(a \leq 1.95 \cdot 10^{+17}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5000000.0) (not (<= a 1.95e+17)))
   (* a 120.0)
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5000000.0) || !(a <= 1.95e+17)) {
		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) :: tmp
    if ((a <= (-5000000.0d0)) .or. (.not. (a <= 1.95d+17))) 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 tmp;
	if ((a <= -5000000.0) || !(a <= 1.95e+17)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5000000.0) or not (a <= 1.95e+17):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5000000.0) || !(a <= 1.95e+17))
		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)
	tmp = 0.0;
	if ((a <= -5000000.0) || ~((a <= 1.95e+17)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5000000.0], N[Not[LessEqual[a, 1.95e+17]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5e6 or 1.95e17 < 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 86.1%

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

   if -5e6 < a < 1.95e17

   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 77.5%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5000000 \lor \neg \left(a \leq 1.95 \cdot 10^{+17}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 9: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + ((60.0d0 / (z - t)) * (x - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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/ 99.8%

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

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%

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

Alternative 10: 58.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-99}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+16}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.35e-99)
   (* a 120.0)
   (if (<= a 1.55e+16) (* -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 <= -1.35e-99) {
		tmp = a * 120.0;
	} else if (a <= 1.55e+16) {
		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 <= (-1.35d-99)) then
        tmp = a * 120.0d0
    else if (a <= 1.55d+16) 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 <= -1.35e-99) {
		tmp = a * 120.0;
	} else if (a <= 1.55e+16) {
		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 <= -1.35e-99:
		tmp = a * 120.0
	elif a <= 1.55e+16:
		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 <= -1.35e-99)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.55e+16)
		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 <= -1.35e-99)
		tmp = a * 120.0;
	elseif (a <= 1.55e+16)
		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, -1.35e-99], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.55e+16], 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 < -1.35e-99 or 1.55e16 < 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 81.3%

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

   if -1.35e-99 < a < 1.55e16

   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 81.3%

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

   5. Taylor expanded in z around 0 47.7%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-99}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+16}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11: 58.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-99}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+16}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.45e-99)
   (* a 120.0)
   (if (<= a 1.55e+16) (* (- 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 <= -1.45e-99) {
		tmp = a * 120.0;
	} else if (a <= 1.55e+16) {
		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 <= (-1.45d-99)) then
        tmp = a * 120.0d0
    else if (a <= 1.55d+16) 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 <= -1.45e-99) {
		tmp = a * 120.0;
	} else if (a <= 1.55e+16) {
		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 <= -1.45e-99:
		tmp = a * 120.0
	elif a <= 1.55e+16:
		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 <= -1.45e-99)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.55e+16)
		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 <= -1.45e-99)
		tmp = a * 120.0;
	elseif (a <= 1.55e+16)
		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, -1.45e-99], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.55e+16], 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 < -1.44999999999999993e-99 or 1.55e16 < 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 81.3%

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

   if -1.44999999999999993e-99 < a < 1.55e16

   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 81.3%

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

   5. Taylor expanded in z around 0 47.7%

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

      1. expm1-log1p-u 29.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-60 \cdot \frac{x - y}{t}\right)\right)} \]

      2. expm1-udef 13.9%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-60 \cdot \frac{x - y}{t}\right)} - 1} \]

   7. Applied egg-rr 13.9%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-60 \cdot \frac{x - y}{t}\right)} - 1} \]
   8. Step-by-step derivation

      1. expm1-def 29.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-60 \cdot \frac{x - y}{t}\right)\right)} \]

      2. expm1-log1p 47.7%

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

      3. associate-*r/ 47.8%

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

      4. associate-*l/ 47.8%

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

   9. Simplified 47.8%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-99}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+16}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 12: 50.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-205}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-225}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e-205)
   (* a 120.0)
   (if (<= z 2.7e-225) (* -60.0 (/ x t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e-205) {
		tmp = a * 120.0;
	} else if (z <= 2.7e-225) {
		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 (z <= (-1.3d-205)) then
        tmp = a * 120.0d0
    else if (z <= 2.7d-225) 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 (z <= -1.3e-205) {
		tmp = a * 120.0;
	} else if (z <= 2.7e-225) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e-205:
		tmp = a * 120.0
	elif z <= 2.7e-225:
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e-205)
		tmp = Float64(a * 120.0);
	elseif (z <= 2.7e-225)
		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 (z <= -1.3e-205)
		tmp = a * 120.0;
	elseif (z <= 2.7e-225)
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e-205], N[(a * 120.0), $MachinePrecision], If[LessEqual[z, 2.7e-225], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2999999999999999e-205 or 2.69999999999999992e-225 < z

   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 61.8%

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

   if -1.2999999999999999e-205 < z < 2.69999999999999992e-225

   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 79.4%

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

   5. Taylor expanded in z around 0 76.7%

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

   6. Taylor expanded in x around inf 52.6%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-205}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-225}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13: 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 99.8%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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 56.1%

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

5. Final simplification 56.1%

   \[\leadsto a \cdot 120 \]

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 2023200 
(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)))