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

Percentage Accurate: 99.6% → 99.8%

Time: 15.7s

Alternatives: 21

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: 99.6% 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

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

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 99.8%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 70.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+76}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-234}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-210}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-48}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-18}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+23}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+110}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{-t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e+76)
   (* a 120.0)
   (if (<= (* a 120.0) 5e-234)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= (* a 120.0) 4e-210)
       (* a 120.0)
       (if (<= (* a 120.0) 1e-48)
         (/ (* 60.0 (- x y)) (- z t))
         (if (<= (* a 120.0) 2e-18)
           (+ (* a 120.0) (* x (/ -60.0 t)))
           (if (<= (* a 120.0) 2e+23)
             (+ (* a 120.0) (* 60.0 (/ y t)))
             (if (<= (* a 120.0) 2e+110)
               (* a 120.0)
               (+ (* a 120.0) (/ -60.0 (/ (- t) y)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+76) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e-234) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 4e-210) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-48) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else if ((a * 120.0) <= 2e-18) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else if ((a * 120.0) <= 2e+23) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= 2e+110) {
		tmp = a * 120.0;
	} else {
		tmp = (a * 120.0) + (-60.0 / (-t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d+76)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 5d-234) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if ((a * 120.0d0) <= 4d-210) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-48) then
        tmp = (60.0d0 * (x - y)) / (z - t)
    else if ((a * 120.0d0) <= 2d-18) then
        tmp = (a * 120.0d0) + (x * ((-60.0d0) / t))
    else if ((a * 120.0d0) <= 2d+23) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / t))
    else if ((a * 120.0d0) <= 2d+110) then
        tmp = a * 120.0d0
    else
        tmp = (a * 120.0d0) + ((-60.0d0) / (-t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+76) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e-234) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 4e-210) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-48) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else if ((a * 120.0) <= 2e-18) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else if ((a * 120.0) <= 2e+23) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= 2e+110) {
		tmp = a * 120.0;
	} else {
		tmp = (a * 120.0) + (-60.0 / (-t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e+76:
		tmp = a * 120.0
	elif (a * 120.0) <= 5e-234:
		tmp = 60.0 * ((x - y) / (z - t))
	elif (a * 120.0) <= 4e-210:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-48:
		tmp = (60.0 * (x - y)) / (z - t)
	elif (a * 120.0) <= 2e-18:
		tmp = (a * 120.0) + (x * (-60.0 / t))
	elif (a * 120.0) <= 2e+23:
		tmp = (a * 120.0) + (60.0 * (y / t))
	elif (a * 120.0) <= 2e+110:
		tmp = a * 120.0
	else:
		tmp = (a * 120.0) + (-60.0 / (-t / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+76)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 5e-234)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 4e-210)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-48)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	elseif (Float64(a * 120.0) <= 2e-18)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)));
	elseif (Float64(a * 120.0) <= 2e+23)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	elseif (Float64(a * 120.0) <= 2e+110)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 / Float64(Float64(-t) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e+76)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 5e-234)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif ((a * 120.0) <= 4e-210)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-48)
		tmp = (60.0 * (x - y)) / (z - t);
	elseif ((a * 120.0) <= 2e-18)
		tmp = (a * 120.0) + (x * (-60.0 / t));
	elseif ((a * 120.0) <= 2e+23)
		tmp = (a * 120.0) + (60.0 * (y / t));
	elseif ((a * 120.0) <= 2e+110)
		tmp = a * 120.0;
	else
		tmp = (a * 120.0) + (-60.0 / (-t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+76], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-234], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 4e-210], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-48], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-18], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+23], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+110], N[(a * 120.0), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 / N[((-t) / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if (*.f64 a 120) < -2.0000000000000001e76 or 4.99999999999999979e-234 < (*.f64 a 120) < 4.0000000000000002e-210 or 1.9999999999999998e23 < (*.f64 a 120) < 2e110

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 86.4%

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

   if -2.0000000000000001e76 < (*.f64 a 120) < 4.99999999999999979e-234

   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 76.4%

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

   if 4.0000000000000002e-210 < (*.f64 a 120) < 9.9999999999999997e-49

   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. Taylor expanded in a around 0 77.1%

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

      1. expm1-log1p-u 41.7%

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

      2. expm1-udef 23.6%

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

   6. Applied egg-rr 23.6%

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

      1. expm1-def 41.7%

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

      2. expm1-log1p 77.1%

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

      3. associate-*r/ 77.1%

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

   8. Simplified 77.1%

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

   if 9.9999999999999997e-49 < (*.f64 a 120) < 2.0000000000000001e-18

   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* 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 inf 99.7%

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

      1. associate-*r/ 99.7%

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

      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 2.0000000000000001e-18 < (*.f64 a 120) < 1.9999999999999998e23

   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 71.8%

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

   5. Taylor expanded in z around 0 71.8%

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

   if 2e110 < (*.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 0 96.2%

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

      1. associate-*r/ 96.2%

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

      2. associate-/l* 96.3%

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

   6. Simplified 96.3%

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

   7. Taylor expanded in z around 0 87.1%

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

      1. neg-mul-1 87.1%

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

      2. distribute-neg-frac 87.1%

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

   9. Simplified 87.1%

      \[\leadsto \frac{-60}{\color{blue}{\frac{-t}{y}}} + a \cdot 120 \]
3. Recombined 6 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+76}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-234}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-210}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-48}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-18}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+23}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+110}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{-t}{y}}\\ \end{array} \]

Alternative 3: 70.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+76}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-210}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-18}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+23} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{+110}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= (* a 120.0) -2e+76)
     (* a 120.0)
     (if (<= (* a 120.0) 5e-234)
       t_1
       (if (<= (* a 120.0) 4e-210)
         (* a 120.0)
         (if (<= (* a 120.0) 1e-49)
           t_1
           (if (<= (* a 120.0) 2e-18)
             (+ (* a 120.0) (* x (/ -60.0 t)))
             (if (or (<= (* a 120.0) 2e+23) (not (<= (* a 120.0) 2e+110)))
               (+ (* a 120.0) (* 60.0 (/ y t)))
               (* a 120.0)))))))))

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 ((a * 120.0) <= -2e+76) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e-234) {
		tmp = t_1;
	} else if ((a * 120.0) <= 4e-210) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-49) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-18) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else if (((a * 120.0) <= 2e+23) || !((a * 120.0) <= 2e+110)) {
		tmp = (a * 120.0) + (60.0 * (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) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    if ((a * 120.0d0) <= (-2d+76)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 5d-234) then
        tmp = t_1
    else if ((a * 120.0d0) <= 4d-210) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-49) then
        tmp = t_1
    else if ((a * 120.0d0) <= 2d-18) then
        tmp = (a * 120.0d0) + (x * ((-60.0d0) / t))
    else if (((a * 120.0d0) <= 2d+23) .or. (.not. ((a * 120.0d0) <= 2d+110))) then
        tmp = (a * 120.0d0) + (60.0d0 * (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 t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -2e+76) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e-234) {
		tmp = t_1;
	} else if ((a * 120.0) <= 4e-210) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-49) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-18) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else if (((a * 120.0) <= 2e+23) || !((a * 120.0) <= 2e+110)) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if (a * 120.0) <= -2e+76:
		tmp = a * 120.0
	elif (a * 120.0) <= 5e-234:
		tmp = t_1
	elif (a * 120.0) <= 4e-210:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-49:
		tmp = t_1
	elif (a * 120.0) <= 2e-18:
		tmp = (a * 120.0) + (x * (-60.0 / t))
	elif ((a * 120.0) <= 2e+23) or not ((a * 120.0) <= 2e+110):
		tmp = (a * 120.0) + (60.0 * (y / t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+76)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 5e-234)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 4e-210)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-49)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 2e-18)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)));
	elseif ((Float64(a * 120.0) <= 2e+23) || !(Float64(a * 120.0) <= 2e+110))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	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 - y) / (z - t));
	tmp = 0.0;
	if ((a * 120.0) <= -2e+76)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 5e-234)
		tmp = t_1;
	elseif ((a * 120.0) <= 4e-210)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-49)
		tmp = t_1;
	elseif ((a * 120.0) <= 2e-18)
		tmp = (a * 120.0) + (x * (-60.0 / t));
	elseif (((a * 120.0) <= 2e+23) || ~(((a * 120.0) <= 2e+110)))
		tmp = (a * 120.0) + (60.0 * (y / t));
	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[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+76], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-234], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 4e-210], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-49], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-18], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+23], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+110]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a 120) < -2.0000000000000001e76 or 4.99999999999999979e-234 < (*.f64 a 120) < 4.0000000000000002e-210 or 1.9999999999999998e23 < (*.f64 a 120) < 2e110

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 86.4%

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

   if -2.0000000000000001e76 < (*.f64 a 120) < 4.99999999999999979e-234 or 4.0000000000000002e-210 < (*.f64 a 120) < 9.99999999999999936e-50

   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 76.4%

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

   if 9.99999999999999936e-50 < (*.f64 a 120) < 2.0000000000000001e-18

   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* 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 inf 99.6%

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

      1. associate-*r/ 99.8%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around 0 99.8%

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

   if 2.0000000000000001e-18 < (*.f64 a 120) < 1.9999999999999998e23 or 2e110 < (*.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 0 93.2%

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

   5. Taylor expanded in z around 0 85.2%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+76}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-234}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-210}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-49}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-18}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+23} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{+110}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 4: 70.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+76}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-234}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-210}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-48}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-18}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+23} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{+110}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e+76)
   (* a 120.0)
   (if (<= (* a 120.0) 5e-234)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= (* a 120.0) 4e-210)
       (* a 120.0)
       (if (<= (* a 120.0) 1e-48)
         (/ (* 60.0 (- x y)) (- z t))
         (if (<= (* a 120.0) 2e-18)
           (+ (* a 120.0) (* x (/ -60.0 t)))
           (if (or (<= (* a 120.0) 2e+23) (not (<= (* a 120.0) 2e+110)))
             (+ (* a 120.0) (* 60.0 (/ y t)))
             (* a 120.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+76) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e-234) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 4e-210) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-48) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else if ((a * 120.0) <= 2e-18) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else if (((a * 120.0) <= 2e+23) || !((a * 120.0) <= 2e+110)) {
		tmp = (a * 120.0) + (60.0 * (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 * 120.0d0) <= (-2d+76)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 5d-234) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if ((a * 120.0d0) <= 4d-210) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-48) then
        tmp = (60.0d0 * (x - y)) / (z - t)
    else if ((a * 120.0d0) <= 2d-18) then
        tmp = (a * 120.0d0) + (x * ((-60.0d0) / t))
    else if (((a * 120.0d0) <= 2d+23) .or. (.not. ((a * 120.0d0) <= 2d+110))) then
        tmp = (a * 120.0d0) + (60.0d0 * (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 * 120.0) <= -2e+76) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e-234) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 4e-210) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-48) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else if ((a * 120.0) <= 2e-18) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else if (((a * 120.0) <= 2e+23) || !((a * 120.0) <= 2e+110)) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e+76:
		tmp = a * 120.0
	elif (a * 120.0) <= 5e-234:
		tmp = 60.0 * ((x - y) / (z - t))
	elif (a * 120.0) <= 4e-210:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-48:
		tmp = (60.0 * (x - y)) / (z - t)
	elif (a * 120.0) <= 2e-18:
		tmp = (a * 120.0) + (x * (-60.0 / t))
	elif ((a * 120.0) <= 2e+23) or not ((a * 120.0) <= 2e+110):
		tmp = (a * 120.0) + (60.0 * (y / t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+76)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 5e-234)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 4e-210)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-48)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	elseif (Float64(a * 120.0) <= 2e-18)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)));
	elseif ((Float64(a * 120.0) <= 2e+23) || !(Float64(a * 120.0) <= 2e+110))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(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 * 120.0) <= -2e+76)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 5e-234)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif ((a * 120.0) <= 4e-210)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-48)
		tmp = (60.0 * (x - y)) / (z - t);
	elseif ((a * 120.0) <= 2e-18)
		tmp = (a * 120.0) + (x * (-60.0 / t));
	elseif (((a * 120.0) <= 2e+23) || ~(((a * 120.0) <= 2e+110)))
		tmp = (a * 120.0) + (60.0 * (y / 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], -2e+76], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-234], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 4e-210], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-48], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-18], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+23], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+110]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a 120) < -2.0000000000000001e76 or 4.99999999999999979e-234 < (*.f64 a 120) < 4.0000000000000002e-210 or 1.9999999999999998e23 < (*.f64 a 120) < 2e110

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 86.4%

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

   if -2.0000000000000001e76 < (*.f64 a 120) < 4.99999999999999979e-234

   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 76.4%

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

   if 4.0000000000000002e-210 < (*.f64 a 120) < 9.9999999999999997e-49

   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. Taylor expanded in a around 0 77.1%

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

      1. expm1-log1p-u 41.7%

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

      2. expm1-udef 23.6%

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

   6. Applied egg-rr 23.6%

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

      1. expm1-def 41.7%

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

      2. expm1-log1p 77.1%

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

      3. associate-*r/ 77.1%

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

   8. Simplified 77.1%

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

   if 9.9999999999999997e-49 < (*.f64 a 120) < 2.0000000000000001e-18

   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* 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 inf 99.7%

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

      1. associate-*r/ 99.7%

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

      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 2.0000000000000001e-18 < (*.f64 a 120) < 1.9999999999999998e23 or 2e110 < (*.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 0 93.2%

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

   5. Taylor expanded in z around 0 85.2%

      \[\leadsto 120 \cdot a + \color{blue}{60 \cdot \frac{y}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+76}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-234}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-210}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-48}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-18}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+23} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{+110}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 5: 83.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{+115}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+87)
     t_1
     (if (<= t_1 1e+115)
       (+ (* a 120.0) (* -60.0 (/ y (- z t))))
       (* 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+87) {
		tmp = t_1;
	} else if (t_1 <= 1e+115) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} 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+87)) then
        tmp = t_1
    else if (t_1 <= 1d+115) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    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+87) {
		tmp = t_1;
	} else if (t_1 <= 1e+115) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} 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+87:
		tmp = t_1
	elif t_1 <= 1e+115:
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	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+87)
		tmp = t_1;
	elseif (t_1 <= 1e+115)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	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+87)
		tmp = t_1;
	elseif (t_1 <= 1e+115)
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	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+87], t$95$1, If[LessEqual[t$95$1, 1e+115], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $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)) < -9.9999999999999996e86

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 82.2%

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

      1. expm1-log1p-u 0.0%

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

      2. expm1-udef 0.0%

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

   6. Applied egg-rr 0.0%

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

      1. expm1-def 0.0%

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

      2. expm1-log1p 82.2%

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

      3. associate-*r/ 82.3%

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

   8. Simplified 82.3%

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

   if -9.9999999999999996e86 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 1e115

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 85.9%

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

   if 1e115 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

   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. Taylor expanded in a around 0 89.7%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+87}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 10^{+115}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 6: 70.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{+68}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-212}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-17}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+21} \lor \neg \left(a \leq 3.8 \cdot 10^{+110}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= a -7.8e+68)
     (* a 120.0)
     (if (<= a 6.6e-231)
       t_1
       (if (<= a 1.8e-212)
         (* a 120.0)
         (if (<= a 2.1e-51)
           t_1
           (if (<= a 9.2e-17)
             (+ (* a 120.0) (* -60.0 (/ x t)))
             (if (or (<= a 3.5e+21) (not (<= a 3.8e+110)))
               (+ (* a 120.0) (* 60.0 (/ y t)))
               (* a 120.0)))))))))

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 (a <= -7.8e+68) {
		tmp = a * 120.0;
	} else if (a <= 6.6e-231) {
		tmp = t_1;
	} else if (a <= 1.8e-212) {
		tmp = a * 120.0;
	} else if (a <= 2.1e-51) {
		tmp = t_1;
	} else if (a <= 9.2e-17) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else if ((a <= 3.5e+21) || !(a <= 3.8e+110)) {
		tmp = (a * 120.0) + (60.0 * (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) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    if (a <= (-7.8d+68)) then
        tmp = a * 120.0d0
    else if (a <= 6.6d-231) then
        tmp = t_1
    else if (a <= 1.8d-212) then
        tmp = a * 120.0d0
    else if (a <= 2.1d-51) then
        tmp = t_1
    else if (a <= 9.2d-17) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (x / t))
    else if ((a <= 3.5d+21) .or. (.not. (a <= 3.8d+110))) then
        tmp = (a * 120.0d0) + (60.0d0 * (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 t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if (a <= -7.8e+68) {
		tmp = a * 120.0;
	} else if (a <= 6.6e-231) {
		tmp = t_1;
	} else if (a <= 1.8e-212) {
		tmp = a * 120.0;
	} else if (a <= 2.1e-51) {
		tmp = t_1;
	} else if (a <= 9.2e-17) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else if ((a <= 3.5e+21) || !(a <= 3.8e+110)) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if a <= -7.8e+68:
		tmp = a * 120.0
	elif a <= 6.6e-231:
		tmp = t_1
	elif a <= 1.8e-212:
		tmp = a * 120.0
	elif a <= 2.1e-51:
		tmp = t_1
	elif a <= 9.2e-17:
		tmp = (a * 120.0) + (-60.0 * (x / t))
	elif (a <= 3.5e+21) or not (a <= 3.8e+110):
		tmp = (a * 120.0) + (60.0 * (y / t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (a <= -7.8e+68)
		tmp = Float64(a * 120.0);
	elseif (a <= 6.6e-231)
		tmp = t_1;
	elseif (a <= 1.8e-212)
		tmp = Float64(a * 120.0);
	elseif (a <= 2.1e-51)
		tmp = t_1;
	elseif (a <= 9.2e-17)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)));
	elseif ((a <= 3.5e+21) || !(a <= 3.8e+110))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	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 - y) / (z - t));
	tmp = 0.0;
	if (a <= -7.8e+68)
		tmp = a * 120.0;
	elseif (a <= 6.6e-231)
		tmp = t_1;
	elseif (a <= 1.8e-212)
		tmp = a * 120.0;
	elseif (a <= 2.1e-51)
		tmp = t_1;
	elseif (a <= 9.2e-17)
		tmp = (a * 120.0) + (-60.0 * (x / t));
	elseif ((a <= 3.5e+21) || ~((a <= 3.8e+110)))
		tmp = (a * 120.0) + (60.0 * (y / t));
	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[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.8e+68], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 6.6e-231], t$95$1, If[LessEqual[a, 1.8e-212], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 2.1e-51], t$95$1, If[LessEqual[a, 9.2e-17], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 3.5e+21], N[Not[LessEqual[a, 3.8e+110]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.80000000000000037e68 or 6.60000000000000056e-231 < a < 1.8e-212 or 3.5e21 < a < 3.79999999999999989e110

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 86.4%

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

   if -7.80000000000000037e68 < a < 6.60000000000000056e-231 or 1.8e-212 < a < 2.10000000000000002e-51

   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 76.4%

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

   if 2.10000000000000002e-51 < a < 9.20000000000000035e-17

   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* 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 inf 99.6%

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

      1. associate-*r/ 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around 0 99.6%

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

   if 9.20000000000000035e-17 < a < 3.5e21 or 3.79999999999999989e110 < 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 x around 0 93.2%

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

   5. Taylor expanded in z around 0 85.2%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+68}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-231}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-212}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-51}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-17}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+21} \lor \neg \left(a \leq 3.8 \cdot 10^{+110}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7: 71.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \leq -1.75 \cdot 10^{+70}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-212}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-18}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= a -1.75e+70)
     (* a 120.0)
     (if (<= a 6.6e-231)
       t_1
       (if (<= a 1.8e-212)
         (* a 120.0)
         (if (<= a 4.5e-51)
           t_1
           (if (<= a 5.3e-18)
             (+ (* a 120.0) (* -60.0 (/ x t)))
             (if (<= a 1.85e+21) t_1 (* a 120.0)))))))))

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 (a <= -1.75e+70) {
		tmp = a * 120.0;
	} else if (a <= 6.6e-231) {
		tmp = t_1;
	} else if (a <= 1.8e-212) {
		tmp = a * 120.0;
	} else if (a <= 4.5e-51) {
		tmp = t_1;
	} else if (a <= 5.3e-18) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else if (a <= 1.85e+21) {
		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 - y) / (z - t))
    if (a <= (-1.75d+70)) then
        tmp = a * 120.0d0
    else if (a <= 6.6d-231) then
        tmp = t_1
    else if (a <= 1.8d-212) then
        tmp = a * 120.0d0
    else if (a <= 4.5d-51) then
        tmp = t_1
    else if (a <= 5.3d-18) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (x / t))
    else if (a <= 1.85d+21) 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 - y) / (z - t));
	double tmp;
	if (a <= -1.75e+70) {
		tmp = a * 120.0;
	} else if (a <= 6.6e-231) {
		tmp = t_1;
	} else if (a <= 1.8e-212) {
		tmp = a * 120.0;
	} else if (a <= 4.5e-51) {
		tmp = t_1;
	} else if (a <= 5.3e-18) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else if (a <= 1.85e+21) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if a <= -1.75e+70:
		tmp = a * 120.0
	elif a <= 6.6e-231:
		tmp = t_1
	elif a <= 1.8e-212:
		tmp = a * 120.0
	elif a <= 4.5e-51:
		tmp = t_1
	elif a <= 5.3e-18:
		tmp = (a * 120.0) + (-60.0 * (x / t))
	elif a <= 1.85e+21:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (a <= -1.75e+70)
		tmp = Float64(a * 120.0);
	elseif (a <= 6.6e-231)
		tmp = t_1;
	elseif (a <= 1.8e-212)
		tmp = Float64(a * 120.0);
	elseif (a <= 4.5e-51)
		tmp = t_1;
	elseif (a <= 5.3e-18)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)));
	elseif (a <= 1.85e+21)
		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 - y) / (z - t));
	tmp = 0.0;
	if (a <= -1.75e+70)
		tmp = a * 120.0;
	elseif (a <= 6.6e-231)
		tmp = t_1;
	elseif (a <= 1.8e-212)
		tmp = a * 120.0;
	elseif (a <= 4.5e-51)
		tmp = t_1;
	elseif (a <= 5.3e-18)
		tmp = (a * 120.0) + (-60.0 * (x / t));
	elseif (a <= 1.85e+21)
		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[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.75e+70], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 6.6e-231], t$95$1, If[LessEqual[a, 1.8e-212], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 4.5e-51], t$95$1, If[LessEqual[a, 5.3e-18], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.85e+21], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.75000000000000001e70 or 6.60000000000000056e-231 < a < 1.8e-212 or 1.85e21 < 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 84.7%

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

   if -1.75000000000000001e70 < a < 6.60000000000000056e-231 or 1.8e-212 < a < 4.49999999999999974e-51 or 5.3000000000000003e-18 < a < 1.85e21

   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 75.9%

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

   if 4.49999999999999974e-51 < a < 5.3000000000000003e-18

   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* 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 inf 99.6%

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

      1. associate-*r/ 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-/l* 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around 0 99.6%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.75 \cdot 10^{+70}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-231}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-212}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-51}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-18}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+21}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8: 53.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{60}{z - t}\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{+68}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.18 \cdot 10^{-45}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{-291}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-231}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-162} \lor \neg \left(a \leq 4.5 \cdot 10^{-47}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ 60.0 (- z t)))))
   (if (<= a -7.8e+68)
     (* a 120.0)
     (if (<= a -1.18e-45)
       (* 60.0 (/ (- x y) z))
       (if (<= a 3.05e-291)
         t_1
         (if (<= a 6.6e-231)
           (* -60.0 (/ y (- z t)))
           (if (or (<= a 8e-162) (not (<= a 4.5e-47))) (* a 120.0) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (60.0 / (z - t));
	double tmp;
	if (a <= -7.8e+68) {
		tmp = a * 120.0;
	} else if (a <= -1.18e-45) {
		tmp = 60.0 * ((x - y) / z);
	} else if (a <= 3.05e-291) {
		tmp = t_1;
	} else if (a <= 6.6e-231) {
		tmp = -60.0 * (y / (z - t));
	} else if ((a <= 8e-162) || !(a <= 4.5e-47)) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (60.0d0 / (z - t))
    if (a <= (-7.8d+68)) then
        tmp = a * 120.0d0
    else if (a <= (-1.18d-45)) then
        tmp = 60.0d0 * ((x - y) / z)
    else if (a <= 3.05d-291) then
        tmp = t_1
    else if (a <= 6.6d-231) then
        tmp = (-60.0d0) * (y / (z - t))
    else if ((a <= 8d-162) .or. (.not. (a <= 4.5d-47))) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (60.0 / (z - t));
	double tmp;
	if (a <= -7.8e+68) {
		tmp = a * 120.0;
	} else if (a <= -1.18e-45) {
		tmp = 60.0 * ((x - y) / z);
	} else if (a <= 3.05e-291) {
		tmp = t_1;
	} else if (a <= 6.6e-231) {
		tmp = -60.0 * (y / (z - t));
	} else if ((a <= 8e-162) || !(a <= 4.5e-47)) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (60.0 / (z - t))
	tmp = 0
	if a <= -7.8e+68:
		tmp = a * 120.0
	elif a <= -1.18e-45:
		tmp = 60.0 * ((x - y) / z)
	elif a <= 3.05e-291:
		tmp = t_1
	elif a <= 6.6e-231:
		tmp = -60.0 * (y / (z - t))
	elif (a <= 8e-162) or not (a <= 4.5e-47):
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(60.0 / Float64(z - t)))
	tmp = 0.0
	if (a <= -7.8e+68)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.18e-45)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (a <= 3.05e-291)
		tmp = t_1;
	elseif (a <= 6.6e-231)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif ((a <= 8e-162) || !(a <= 4.5e-47))
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (60.0 / (z - t));
	tmp = 0.0;
	if (a <= -7.8e+68)
		tmp = a * 120.0;
	elseif (a <= -1.18e-45)
		tmp = 60.0 * ((x - y) / z);
	elseif (a <= 3.05e-291)
		tmp = t_1;
	elseif (a <= 6.6e-231)
		tmp = -60.0 * (y / (z - t));
	elseif ((a <= 8e-162) || ~((a <= 4.5e-47)))
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.8e+68], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.18e-45], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.05e-291], t$95$1, If[LessEqual[a, 6.6e-231], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 8e-162], N[Not[LessEqual[a, 4.5e-47]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.80000000000000037e68 or 6.60000000000000056e-231 < a < 7.99999999999999963e-162 or 4.5e-47 < 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 80.8%

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

   if -7.80000000000000037e68 < a < -1.18e-45

   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 72.6%

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

   5. Taylor expanded in z around inf 59.9%

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

   if -1.18e-45 < a < 3.05e-291 or 7.99999999999999963e-162 < a < 4.5e-47

   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 77.8%

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

   5. Taylor expanded in x around inf 48.6%

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

      1. *-commutative 48.6%

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

      2. metadata-eval 48.6%

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

      3. times-frac 48.6%

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

      4. associate-*r/ 48.5%

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

      5. *-commutative 48.5%

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

      6. associate-/r* 48.7%

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

      7. metadata-eval 48.7%

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

   7. Simplified 48.7%

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

   if 3.05e-291 < a < 6.60000000000000056e-231

   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* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in a around 0 79.5%

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

   5. Taylor expanded in x around 0 64.5%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+68}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.18 \cdot 10^{-45}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 3.05 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-231}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-162} \lor \neg \left(a \leq 4.5 \cdot 10^{-47}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \end{array} \]

Alternative 9: 53.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{+68}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-46}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-232}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-162}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x (- z t)))))
   (if (<= a -7.8e+68)
     (* a 120.0)
     (if (<= a -6.8e-46)
       (* 60.0 (/ (- x y) z))
       (if (<= a 4.2e-308)
         t_1
         (if (<= a 2.8e-232)
           (* -60.0 (/ y (- z t)))
           (if (<= a 8.4e-162)
             (* a 120.0)
             (if (<= a 1.5e-47) t_1 (* a 120.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double tmp;
	if (a <= -7.8e+68) {
		tmp = a * 120.0;
	} else if (a <= -6.8e-46) {
		tmp = 60.0 * ((x - y) / z);
	} else if (a <= 4.2e-308) {
		tmp = t_1;
	} else if (a <= 2.8e-232) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 8.4e-162) {
		tmp = a * 120.0;
	} else if (a <= 1.5e-47) {
		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 / (z - t))
    if (a <= (-7.8d+68)) then
        tmp = a * 120.0d0
    else if (a <= (-6.8d-46)) then
        tmp = 60.0d0 * ((x - y) / z)
    else if (a <= 4.2d-308) then
        tmp = t_1
    else if (a <= 2.8d-232) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (a <= 8.4d-162) then
        tmp = a * 120.0d0
    else if (a <= 1.5d-47) 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 / (z - t));
	double tmp;
	if (a <= -7.8e+68) {
		tmp = a * 120.0;
	} else if (a <= -6.8e-46) {
		tmp = 60.0 * ((x - y) / z);
	} else if (a <= 4.2e-308) {
		tmp = t_1;
	} else if (a <= 2.8e-232) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 8.4e-162) {
		tmp = a * 120.0;
	} else if (a <= 1.5e-47) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (x / (z - t))
	tmp = 0
	if a <= -7.8e+68:
		tmp = a * 120.0
	elif a <= -6.8e-46:
		tmp = 60.0 * ((x - y) / z)
	elif a <= 4.2e-308:
		tmp = t_1
	elif a <= 2.8e-232:
		tmp = -60.0 * (y / (z - t))
	elif a <= 8.4e-162:
		tmp = a * 120.0
	elif a <= 1.5e-47:
		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 / Float64(z - t)))
	tmp = 0.0
	if (a <= -7.8e+68)
		tmp = Float64(a * 120.0);
	elseif (a <= -6.8e-46)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (a <= 4.2e-308)
		tmp = t_1;
	elseif (a <= 2.8e-232)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (a <= 8.4e-162)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.5e-47)
		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 / (z - t));
	tmp = 0.0;
	if (a <= -7.8e+68)
		tmp = a * 120.0;
	elseif (a <= -6.8e-46)
		tmp = 60.0 * ((x - y) / z);
	elseif (a <= 4.2e-308)
		tmp = t_1;
	elseif (a <= 2.8e-232)
		tmp = -60.0 * (y / (z - t));
	elseif (a <= 8.4e-162)
		tmp = a * 120.0;
	elseif (a <= 1.5e-47)
		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 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.8e+68], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -6.8e-46], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e-308], t$95$1, If[LessEqual[a, 2.8e-232], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.4e-162], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.5e-47], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.80000000000000037e68 or 2.79999999999999993e-232 < a < 8.4e-162 or 1.50000000000000008e-47 < 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 80.8%

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

   if -7.80000000000000037e68 < a < -6.79999999999999992e-46

   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 72.6%

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

   5. Taylor expanded in z around inf 59.9%

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

   if -6.79999999999999992e-46 < a < 4.2e-308 or 8.4e-162 < a < 1.50000000000000008e-47

   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 78.1%

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

   5. Taylor expanded in x around inf 49.0%

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

   if 4.2e-308 < a < 2.79999999999999993e-232

   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* 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in a around 0 77.7%

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

   5. Taylor expanded in x around 0 59.5%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+68}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-46}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-308}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-232}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-162}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-47}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 10: 53.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+68}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-45}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-231}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-162}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-45}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.8e+68)
   (* a 120.0)
   (if (<= a -2.9e-45)
     (* 60.0 (/ (- x y) z))
     (if (<= a 1.45e-291)
       (* x (/ 60.0 (- z t)))
       (if (<= a 6.6e-231)
         (* -60.0 (/ y (- z t)))
         (if (<= a 8e-162)
           (* a 120.0)
           (if (<= a 1.1e-45) (* 60.0 (/ (- y x) t)) (* a 120.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.8e+68) {
		tmp = a * 120.0;
	} else if (a <= -2.9e-45) {
		tmp = 60.0 * ((x - y) / z);
	} else if (a <= 1.45e-291) {
		tmp = x * (60.0 / (z - t));
	} else if (a <= 6.6e-231) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 8e-162) {
		tmp = a * 120.0;
	} else if (a <= 1.1e-45) {
		tmp = 60.0 * ((y - 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 <= (-7.8d+68)) then
        tmp = a * 120.0d0
    else if (a <= (-2.9d-45)) then
        tmp = 60.0d0 * ((x - y) / z)
    else if (a <= 1.45d-291) then
        tmp = x * (60.0d0 / (z - t))
    else if (a <= 6.6d-231) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (a <= 8d-162) then
        tmp = a * 120.0d0
    else if (a <= 1.1d-45) then
        tmp = 60.0d0 * ((y - 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 <= -7.8e+68) {
		tmp = a * 120.0;
	} else if (a <= -2.9e-45) {
		tmp = 60.0 * ((x - y) / z);
	} else if (a <= 1.45e-291) {
		tmp = x * (60.0 / (z - t));
	} else if (a <= 6.6e-231) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 8e-162) {
		tmp = a * 120.0;
	} else if (a <= 1.1e-45) {
		tmp = 60.0 * ((y - x) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.8e+68:
		tmp = a * 120.0
	elif a <= -2.9e-45:
		tmp = 60.0 * ((x - y) / z)
	elif a <= 1.45e-291:
		tmp = x * (60.0 / (z - t))
	elif a <= 6.6e-231:
		tmp = -60.0 * (y / (z - t))
	elif a <= 8e-162:
		tmp = a * 120.0
	elif a <= 1.1e-45:
		tmp = 60.0 * ((y - x) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.8e+68)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.9e-45)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (a <= 1.45e-291)
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	elseif (a <= 6.6e-231)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (a <= 8e-162)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.1e-45)
		tmp = Float64(60.0 * Float64(Float64(y - 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 <= -7.8e+68)
		tmp = a * 120.0;
	elseif (a <= -2.9e-45)
		tmp = 60.0 * ((x - y) / z);
	elseif (a <= 1.45e-291)
		tmp = x * (60.0 / (z - t));
	elseif (a <= 6.6e-231)
		tmp = -60.0 * (y / (z - t));
	elseif (a <= 8e-162)
		tmp = a * 120.0;
	elseif (a <= 1.1e-45)
		tmp = 60.0 * ((y - x) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.8e+68], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.9e-45], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e-291], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.6e-231], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e-162], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.1e-45], N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7.80000000000000037e68 or 6.60000000000000056e-231 < a < 7.99999999999999963e-162 or 1.09999999999999997e-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 80.8%

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

   if -7.80000000000000037e68 < a < -2.9e-45

   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 72.6%

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

   5. Taylor expanded in z around inf 59.9%

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

   if -2.9e-45 < a < 1.45000000000000001e-291

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 77.0%

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

   5. Taylor expanded in x around inf 51.4%

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

      1. *-commutative 51.4%

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

      2. metadata-eval 51.4%

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

      3. times-frac 51.4%

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

      4. associate-*r/ 51.4%

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

      5. *-commutative 51.4%

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

      6. associate-/r* 51.4%

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

      7. metadata-eval 51.4%

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

   7. Simplified 51.4%

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

   if 1.45000000000000001e-291 < a < 6.60000000000000056e-231

   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* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in a around 0 79.5%

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

   5. Taylor expanded in x around 0 64.5%

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

   if 7.99999999999999963e-162 < a < 1.09999999999999997e-45

   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. Taylor expanded in a around 0 79.5%

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

   5. Taylor expanded in z around 0 59.3%

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

      1. associate-*r/ 59.3%

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

      2. neg-mul-1 59.3%

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

   7. Simplified 59.3%

      \[\leadsto 60 \cdot \color{blue}{\frac{-\left(x - y\right)}{t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.8 \cdot 10^{+68}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-45}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-231}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-162}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-45}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 11: 53.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+64}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-231}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-162}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x (- z t)))))
   (if (<= a -4.5e+64)
     (* a 120.0)
     (if (<= a 1.45e-304)
       t_1
       (if (<= a 6.3e-231)
         (* -60.0 (/ y (- z t)))
         (if (<= a 8.4e-162)
           (* a 120.0)
           (if (<= a 1.35e-46) t_1 (* a 120.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double tmp;
	if (a <= -4.5e+64) {
		tmp = a * 120.0;
	} else if (a <= 1.45e-304) {
		tmp = t_1;
	} else if (a <= 6.3e-231) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 8.4e-162) {
		tmp = a * 120.0;
	} else if (a <= 1.35e-46) {
		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 / (z - t))
    if (a <= (-4.5d+64)) then
        tmp = a * 120.0d0
    else if (a <= 1.45d-304) then
        tmp = t_1
    else if (a <= 6.3d-231) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (a <= 8.4d-162) then
        tmp = a * 120.0d0
    else if (a <= 1.35d-46) 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 / (z - t));
	double tmp;
	if (a <= -4.5e+64) {
		tmp = a * 120.0;
	} else if (a <= 1.45e-304) {
		tmp = t_1;
	} else if (a <= 6.3e-231) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 8.4e-162) {
		tmp = a * 120.0;
	} else if (a <= 1.35e-46) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (x / (z - t))
	tmp = 0
	if a <= -4.5e+64:
		tmp = a * 120.0
	elif a <= 1.45e-304:
		tmp = t_1
	elif a <= 6.3e-231:
		tmp = -60.0 * (y / (z - t))
	elif a <= 8.4e-162:
		tmp = a * 120.0
	elif a <= 1.35e-46:
		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 / Float64(z - t)))
	tmp = 0.0
	if (a <= -4.5e+64)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.45e-304)
		tmp = t_1;
	elseif (a <= 6.3e-231)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (a <= 8.4e-162)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.35e-46)
		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 / (z - t));
	tmp = 0.0;
	if (a <= -4.5e+64)
		tmp = a * 120.0;
	elseif (a <= 1.45e-304)
		tmp = t_1;
	elseif (a <= 6.3e-231)
		tmp = -60.0 * (y / (z - t));
	elseif (a <= 8.4e-162)
		tmp = a * 120.0;
	elseif (a <= 1.35e-46)
		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 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e+64], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.45e-304], t$95$1, If[LessEqual[a, 6.3e-231], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.4e-162], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.35e-46], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.49999999999999973e64 or 6.3e-231 < a < 8.4e-162 or 1.35e-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 80.2%

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

   if -4.49999999999999973e64 < a < 1.45e-304 or 8.4e-162 < a < 1.35e-46

   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 76.8%

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

   5. Taylor expanded in x around inf 47.1%

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

   if 1.45e-304 < a < 6.3e-231

   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* 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in a around 0 77.7%

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

   5. Taylor expanded in x around 0 59.5%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{+64}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-304}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 6.3 \cdot 10^{-231}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-162}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-46}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 12: 72.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+71} \lor \neg \left(a \leq 6.6 \cdot 10^{-231} \lor \neg \left(a \leq 1.8 \cdot 10^{-212}\right) \land a \leq 4.4 \cdot 10^{-45}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.8e+71)
         (not (or (<= a 6.6e-231) (and (not (<= a 1.8e-212)) (<= a 4.4e-45)))))
   (* 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 <= -3.8e+71) || !((a <= 6.6e-231) || (!(a <= 1.8e-212) && (a <= 4.4e-45)))) {
		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 <= (-3.8d+71)) .or. (.not. (a <= 6.6d-231) .or. (.not. (a <= 1.8d-212)) .and. (a <= 4.4d-45))) 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 <= -3.8e+71) || !((a <= 6.6e-231) || (!(a <= 1.8e-212) && (a <= 4.4e-45)))) {
		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 <= -3.8e+71) or not ((a <= 6.6e-231) or (not (a <= 1.8e-212) and (a <= 4.4e-45))):
		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 <= -3.8e+71) || !((a <= 6.6e-231) || (!(a <= 1.8e-212) && (a <= 4.4e-45))))
		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 <= -3.8e+71) || ~(((a <= 6.6e-231) || (~((a <= 1.8e-212)) && (a <= 4.4e-45)))))
		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, -3.8e+71], N[Not[Or[LessEqual[a, 6.6e-231], And[N[Not[LessEqual[a, 1.8e-212]], $MachinePrecision], LessEqual[a, 4.4e-45]]]], $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 < -3.8000000000000001e71 or 6.60000000000000056e-231 < a < 1.8e-212 or 4.39999999999999987e-45 < a

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 81.7%

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

   if -3.8000000000000001e71 < a < 6.60000000000000056e-231 or 1.8e-212 < a < 4.39999999999999987e-45

   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. Taylor expanded in a around 0 76.3%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+71} \lor \neg \left(a \leq 6.6 \cdot 10^{-231} \lor \neg \left(a \leq 1.8 \cdot 10^{-212}\right) \land a \leq 4.4 \cdot 10^{-45}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 13: 88.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.000135 \lor \neg \left(y \leq 4.2 \cdot 10^{+26}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -0.000135) (not (<= y 4.2e+26)))
   (+ (* a 120.0) (* -60.0 (/ y (- z t))))
   (+ (* x (/ 60.0 (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -0.000135) || !(y <= 4.2e+26)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = (x * (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 ((y <= (-0.000135d0)) .or. (.not. (y <= 4.2d+26))) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    else
        tmp = (x * (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 ((y <= -0.000135) || !(y <= 4.2e+26)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -0.000135) or not (y <= 4.2e+26):
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	else:
		tmp = (x * (60.0 / (z - t))) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -0.000135) || !(y <= 4.2e+26))
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	else
		tmp = Float64(Float64(x * Float64(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 ((y <= -0.000135) || ~((y <= 4.2e+26)))
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	else
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -0.000135], N[Not[LessEqual[y, 4.2e+26]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35000000000000002e-4 or 4.2000000000000002e26 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 88.6%

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

   if -1.35000000000000002e-4 < y < 4.2000000000000002e26

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 93.9%

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

      1. associate-*r/ 93.9%

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

      2. associate-*l/ 93.9%

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

      3. *-commutative 93.9%

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

   6. Simplified 93.9%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.000135 \lor \neg \left(y \leq 4.2 \cdot 10^{+26}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 14: 88.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{-5}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6.1e-5)
   (+ (/ -60.0 (/ (- z t) y)) (* a 120.0))
   (if (<= y 3e+26)
     (+ (* x (/ 60.0 (- z t))) (* a 120.0))
     (+ (* a 120.0) (* -60.0 (/ y (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.1e-5) {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	} else if (y <= 3e+26) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else {
		tmp = (a * 120.0) + (-60.0 * (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 (y <= (-6.1d-5)) then
        tmp = ((-60.0d0) / ((z - t) / y)) + (a * 120.0d0)
    else if (y <= 3d+26) then
        tmp = (x * (60.0d0 / (z - t))) + (a * 120.0d0)
    else
        tmp = (a * 120.0d0) + ((-60.0d0) * (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 (y <= -6.1e-5) {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	} else if (y <= 3e+26) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -6.1e-5:
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0)
	elif y <= 3e+26:
		tmp = (x * (60.0 / (z - t))) + (a * 120.0)
	else:
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6.1e-5)
		tmp = Float64(Float64(-60.0 / Float64(Float64(z - t) / y)) + Float64(a * 120.0));
	elseif (y <= 3e+26)
		tmp = Float64(Float64(x * Float64(60.0 / Float64(z - t))) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -6.1e-5)
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	elseif (y <= 3e+26)
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	else
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6.1e-5], N[(N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3e+26], N[(N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.09999999999999987e-5

   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 89.0%

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

      1. associate-*r/ 89.0%

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

      2. associate-/l* 89.1%

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

   6. Simplified 89.1%

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

   if -6.09999999999999987e-5 < y < 2.99999999999999997e26

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 93.9%

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

      1. associate-*r/ 93.9%

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

      2. associate-*l/ 93.9%

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

      3. *-commutative 93.9%

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

   6. Simplified 93.9%

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

   if 2.99999999999999997e26 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 88.0%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{-5}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \end{array} \]

Alternative 15: 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 99.8%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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. Final simplification 99.8%

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

Alternative 16: 99.6% 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]

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 17: 57.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+187} \lor \neg \left(y \leq 6.2 \cdot 10^{+207}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -9.5e+187) (not (<= y 6.2e+207)))
   (* -60.0 (/ y (- z t)))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -9.5e+187) || !(y <= 6.2e+207)) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-9.5d+187)) .or. (.not. (y <= 6.2d+207))) then
        tmp = (-60.0d0) * (y / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -9.5e+187) || !(y <= 6.2e+207)) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -9.5e+187) or not (y <= 6.2e+207):
		tmp = -60.0 * (y / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -9.5e+187) || !(y <= 6.2e+207))
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -9.5e+187) || ~((y <= 6.2e+207)))
		tmp = -60.0 * (y / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -9.5e+187], N[Not[LessEqual[y, 6.2e+207]], $MachinePrecision]], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.4999999999999996e187 or 6.2000000000000005e207 < 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* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 81.5%

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

   5. Taylor expanded in x around 0 71.1%

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

   if -9.4999999999999996e187 < y < 6.2000000000000005e207

   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 59.8%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+187} \lor \neg \left(y \leq 6.2 \cdot 10^{+207}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 18: 52.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+271} \lor \neg \left(y \leq 1.15 \cdot 10^{+225}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -7e+271) (not (<= y 1.15e+225))) (* -60.0 (/ y z)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -7e+271) || !(y <= 1.15e+225)) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-7d+271)) .or. (.not. (y <= 1.15d+225))) then
        tmp = (-60.0d0) * (y / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -7e+271) || !(y <= 1.15e+225)) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -7e+271) or not (y <= 1.15e+225):
		tmp = -60.0 * (y / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -7e+271) || !(y <= 1.15e+225))
		tmp = Float64(-60.0 * Float64(y / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -7e+271) || ~((y <= 1.15e+225)))
		tmp = -60.0 * (y / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -7e+271], N[Not[LessEqual[y, 1.15e+225]], $MachinePrecision]], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.9999999999999999e271 or 1.15e225 < y

   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. Taylor expanded in a around 0 95.4%

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

   5. Taylor expanded in x around 0 88.0%

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

      1. associate-*r/ 87.9%

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

   7. Simplified 87.9%

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

   8. Taylor expanded in z around inf 57.4%

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

   if -6.9999999999999999e271 < y < 1.15e225

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 57.8%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+271} \lor \neg \left(y \leq 1.15 \cdot 10^{+225}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 19: 52.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+271}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+224}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.06e+271)
   (* -60.0 (/ y z))
   (if (<= y 7e+224) (* a 120.0) (* 60.0 (/ y t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.06e+271) {
		tmp = -60.0 * (y / z);
	} else if (y <= 7e+224) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.06d+271)) then
        tmp = (-60.0d0) * (y / z)
    else if (y <= 7d+224) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.06e+271) {
		tmp = -60.0 * (y / z);
	} else if (y <= 7e+224) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.06e+271:
		tmp = -60.0 * (y / z)
	elif y <= 7e+224:
		tmp = a * 120.0
	else:
		tmp = 60.0 * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.06e+271)
		tmp = Float64(-60.0 * Float64(y / z));
	elseif (y <= 7e+224)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.06e+271)
		tmp = -60.0 * (y / z);
	elseif (y <= 7e+224)
		tmp = a * 120.0;
	else
		tmp = 60.0 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.06e+271], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+224], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05999999999999991e271

   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* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in a around 0 99.8%

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

   5. Taylor expanded in x around 0 99.8%

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

      1. associate-*r/ 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in z around inf 79.3%

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

   if -1.05999999999999991e271 < y < 7e224

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 57.8%

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

   if 7e224 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 92.3%

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

   5. Taylor expanded in x around 0 79.8%

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

      1. associate-*r/ 79.9%

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

   7. Simplified 79.9%

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

   8. Taylor expanded in z around 0 62.6%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+271}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+224}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 20: 52.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+273}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+225}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{60}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.05e+273)
   (* -60.0 (/ y z))
   (if (<= y 7.2e+225) (* a 120.0) (/ y (/ t 60.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.05e+273) {
		tmp = -60.0 * (y / z);
	} else if (y <= 7.2e+225) {
		tmp = a * 120.0;
	} else {
		tmp = y / (t / 60.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.05d+273)) then
        tmp = (-60.0d0) * (y / z)
    else if (y <= 7.2d+225) then
        tmp = a * 120.0d0
    else
        tmp = y / (t / 60.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.05e+273) {
		tmp = -60.0 * (y / z);
	} else if (y <= 7.2e+225) {
		tmp = a * 120.0;
	} else {
		tmp = y / (t / 60.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.05e+273:
		tmp = -60.0 * (y / z)
	elif y <= 7.2e+225:
		tmp = a * 120.0
	else:
		tmp = y / (t / 60.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.05e+273)
		tmp = Float64(-60.0 * Float64(y / z));
	elseif (y <= 7.2e+225)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(y / Float64(t / 60.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.05e+273)
		tmp = -60.0 * (y / z);
	elseif (y <= 7.2e+225)
		tmp = a * 120.0;
	else
		tmp = y / (t / 60.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.05e+273], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+225], N[(a * 120.0), $MachinePrecision], N[(y / N[(t / 60.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05000000000000001e273

   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* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in a around 0 99.8%

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

   5. Taylor expanded in x around 0 99.8%

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

      1. associate-*r/ 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in z around inf 79.3%

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

   if -1.05000000000000001e273 < y < 7.1999999999999996e225

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 57.8%

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

   if 7.1999999999999996e225 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 92.3%

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

   5. Taylor expanded in x around 0 79.8%

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

      1. associate-*r/ 79.9%

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

   7. Simplified 79.9%

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

   8. Taylor expanded in z around 0 62.6%

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

      1. associate-*r/ 62.7%

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

      2. *-commutative 62.7%

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

      3. associate-/l* 62.8%

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

   10. Simplified 62.8%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+273}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+225}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t}{60}}\\ \end{array} \]

Alternative 21: 51.0% 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 53.4%

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

5. Final simplification 53.4%

   \[\leadsto a \cdot 120 \]

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 2023257 
(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)))