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

Percentage Accurate: 99.3% → 99.8%

Time: 13.4s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (- x y) (* (- z t) 0.016666666666666666)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((x - y) / ((z - t) * 0.016666666666666666)) + (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 = ((x - y) / ((z - t) * 0.016666666666666666d0)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((x - y) / ((z - t) * 0.016666666666666666)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((x - y) / ((z - t) * 0.016666666666666666)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x - y) / Float64(Float64(z - t) * 0.016666666666666666)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x - y) / ((z - t) * 0.016666666666666666)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(x - y), $MachinePrecision] / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.0%

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

   1. *-commutative 99.0%

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

   2. associate-/l* 99.8%

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

4. Applied egg-rr 99.8%

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

   1. clear-num 99.8%

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

   2. un-div-inv 99.8%

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

   3. div-inv 99.8%

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

   4. metadata-eval 99.8%

      \[\leadsto \frac{x - y}{\left(z - t\right) \cdot \color{blue}{0.016666666666666666}} + a \cdot 120 \]

6. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]
7. Add Preprocessing

Alternative 2: 72.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+175}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-41}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-44}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e+175)
   (* a 120.0)
   (if (<= (* a 120.0) -5e+76)
     (+ (* a 120.0) (* -60.0 (/ y z)))
     (if (<= (* a 120.0) -1e-41)
       (+ (* a 120.0) (* 60.0 (/ y t)))
       (if (<= (* a 120.0) 1e-44)
         (* 60.0 (/ (- x y) (- z t)))
         (+ (* a 120.0) (/ 60.0 (/ z x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+175) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -5e+76) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= -1e-41) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= 1e-44) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 / (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d+175)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-5d+76)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if ((a * 120.0d0) <= (-1d-41)) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / t))
    else if ((a * 120.0d0) <= 1d-44) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + (60.0d0 / (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+175) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -5e+76) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= -1e-41) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= 1e-44) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 / (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e+175:
		tmp = a * 120.0
	elif (a * 120.0) <= -5e+76:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif (a * 120.0) <= -1e-41:
		tmp = (a * 120.0) + (60.0 * (y / t))
	elif (a * 120.0) <= 1e-44:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + (60.0 / (z / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+175)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -5e+76)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (Float64(a * 120.0) <= -1e-41)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	elseif (Float64(a * 120.0) <= 1e-44)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e+175)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -5e+76)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif ((a * 120.0) <= -1e-41)
		tmp = (a * 120.0) + (60.0 * (y / t));
	elseif ((a * 120.0) <= 1e-44)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + (60.0 / (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+175], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+76], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-41], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-44], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.9999999999999999e175

   1. Initial program 96.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 89.7%

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

   if -1.9999999999999999e175 < (*.f64 a #s(literal 120 binary64)) < -4.99999999999999991e76

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 81.3%

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

   6. Taylor expanded in x around 0 85.3%

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

   if -4.99999999999999991e76 < (*.f64 a #s(literal 120 binary64)) < -1.00000000000000001e-41

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 84.4%

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

      1. associate-*r/ 84.3%

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

   7. Simplified 84.3%

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

   8. Taylor expanded in z around 0 77.1%

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

   if -1.00000000000000001e-41 < (*.f64 a #s(literal 120 binary64)) < 9.99999999999999953e-45

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

      3. div-inv 99.7%

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

      4. metadata-eval 99.7%

         \[\leadsto \frac{x - y}{\left(z - t\right) \cdot \color{blue}{0.016666666666666666}} + a \cdot 120 \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]

   7. Taylor expanded in a around 0 85.9%

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

   if 9.99999999999999953e-45 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

         \[\leadsto 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}} + a \cdot 120 \]

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around inf 89.9%

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

   8. Taylor expanded in z around inf 75.2%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+175}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-41}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-44}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+175}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-41}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-44}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e+175)
   (* a 120.0)
   (if (<= (* a 120.0) -5e+76)
     (+ (* a 120.0) (* -60.0 (/ y z)))
     (if (<= (* a 120.0) -1e-41)
       (+ (* a 120.0) (* 60.0 (/ y t)))
       (if (<= (* a 120.0) 1e-44)
         (* 60.0 (/ (- x y) (- z t)))
         (+ (* a 120.0) (* 60.0 (/ x z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+175) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -5e+76) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= -1e-41) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= 1e-44) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d+175)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-5d+76)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if ((a * 120.0d0) <= (-1d-41)) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / t))
    else if ((a * 120.0d0) <= 1d-44) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+175) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -5e+76) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= -1e-41) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= 1e-44) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e+175:
		tmp = a * 120.0
	elif (a * 120.0) <= -5e+76:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif (a * 120.0) <= -1e-41:
		tmp = (a * 120.0) + (60.0 * (y / t))
	elif (a * 120.0) <= 1e-44:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + (60.0 * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+175)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -5e+76)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (Float64(a * 120.0) <= -1e-41)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	elseif (Float64(a * 120.0) <= 1e-44)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e+175)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -5e+76)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif ((a * 120.0) <= -1e-41)
		tmp = (a * 120.0) + (60.0 * (y / t));
	elseif ((a * 120.0) <= 1e-44)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + (60.0 * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+175], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+76], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-41], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-44], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.9999999999999999e175

   1. Initial program 96.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 89.7%

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

   if -1.9999999999999999e175 < (*.f64 a #s(literal 120 binary64)) < -4.99999999999999991e76

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 81.3%

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

   6. Taylor expanded in x around 0 85.3%

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

   if -4.99999999999999991e76 < (*.f64 a #s(literal 120 binary64)) < -1.00000000000000001e-41

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 84.4%

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

      1. associate-*r/ 84.3%

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

   7. Simplified 84.3%

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

   8. Taylor expanded in z around 0 77.1%

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

   if -1.00000000000000001e-41 < (*.f64 a #s(literal 120 binary64)) < 9.99999999999999953e-45

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

      3. div-inv 99.7%

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

      4. metadata-eval 99.7%

         \[\leadsto \frac{x - y}{\left(z - t\right) \cdot \color{blue}{0.016666666666666666}} + a \cdot 120 \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]

   7. Taylor expanded in a around 0 85.9%

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

   if 9.99999999999999953e-45 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 74.7%

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

   6. Taylor expanded in x around inf 75.2%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+175}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{+76}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{-41}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-44}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-41} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-106}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -1e-41) (not (<= (* a 120.0) 5e-106)))
   (+ (* a 120.0) (* 60.0 (/ y (- t z))))
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -1e-41) || !((a * 120.0) <= 5e-106)) {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	} 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 * 120.0d0) <= (-1d-41)) .or. (.not. ((a * 120.0d0) <= 5d-106))) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / (t - z)))
    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 * 120.0) <= -1e-41) || !((a * 120.0) <= 5e-106)) {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -1e-41) or not ((a * 120.0) <= 5e-106):
		tmp = (a * 120.0) + (60.0 * (y / (t - z)))
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -1e-41) || !(Float64(a * 120.0) <= 5e-106))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / Float64(t - z))));
	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 * 120.0) <= -1e-41) || ~(((a * 120.0) <= 5e-106)))
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-41], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-106]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.00000000000000001e-41 or 4.99999999999999983e-106 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 86.0%

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

      1. neg-mul-1 86.0%

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

      2. distribute-neg-frac2 86.0%

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

      3. neg-sub0 86.0%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{0 - \left(z - t\right)}} + a \cdot 120 \]

      4. sub-neg 86.0%

         \[\leadsto 60 \cdot \frac{y}{0 - \color{blue}{\left(z + \left(-t\right)\right)}} + a \cdot 120 \]

      5. +-commutative 86.0%

         \[\leadsto 60 \cdot \frac{y}{0 - \color{blue}{\left(\left(-t\right) + z\right)}} + a \cdot 120 \]

      6. associate--r+ 86.0%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{\left(0 - \left(-t\right)\right) - z}} + a \cdot 120 \]

      7. neg-sub0 86.0%

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

      8. remove-double-neg 86.0%

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

   7. Simplified 86.0%

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

   if -1.00000000000000001e-41 < (*.f64 a #s(literal 120 binary64)) < 4.99999999999999983e-106

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

      3. div-inv 99.7%

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

      4. metadata-eval 99.7%

         \[\leadsto \frac{x - y}{\left(z - t\right) \cdot \color{blue}{0.016666666666666666}} + a \cdot 120 \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]

   7. Taylor expanded in a around 0 88.6%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-41} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-106}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-41}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-106}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -1e-41)
   (+ (* a 120.0) (* 60.0 (/ y (- t z))))
   (if (<= (* a 120.0) 5e-106)
     (* 60.0 (/ (- x y) (- z t)))
     (+ (* a 120.0) (* y (/ -60.0 (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -1e-41) {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	} else if ((a * 120.0) <= 5e-106) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (y * (-60.0 / (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 * 120.0d0) <= (-1d-41)) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / (t - z)))
    else if ((a * 120.0d0) <= 5d-106) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + (y * ((-60.0d0) / (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 * 120.0) <= -1e-41) {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	} else if ((a * 120.0) <= 5e-106) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -1e-41:
		tmp = (a * 120.0) + (60.0 * (y / (t - z)))
	elif (a * 120.0) <= 5e-106:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -1e-41)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / Float64(t - z))));
	elseif (Float64(a * 120.0) <= 5e-106)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(-60.0 / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -1e-41)
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	elseif ((a * 120.0) <= 5e-106)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-41], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-106], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.00000000000000001e-41

   1. Initial program 98.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 89.3%

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

      1. neg-mul-1 89.3%

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

      2. distribute-neg-frac2 89.3%

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

      3. neg-sub0 89.3%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{0 - \left(z - t\right)}} + a \cdot 120 \]

      4. sub-neg 89.3%

         \[\leadsto 60 \cdot \frac{y}{0 - \color{blue}{\left(z + \left(-t\right)\right)}} + a \cdot 120 \]

      5. +-commutative 89.3%

         \[\leadsto 60 \cdot \frac{y}{0 - \color{blue}{\left(\left(-t\right) + z\right)}} + a \cdot 120 \]

      6. associate--r+ 89.3%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{\left(0 - \left(-t\right)\right) - z}} + a \cdot 120 \]

      7. neg-sub0 89.3%

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

      8. remove-double-neg 89.3%

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

   7. Simplified 89.3%

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

   if -1.00000000000000001e-41 < (*.f64 a #s(literal 120 binary64)) < 4.99999999999999983e-106

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

      3. div-inv 99.7%

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

      4. metadata-eval 99.7%

         \[\leadsto \frac{x - y}{\left(z - t\right) \cdot \color{blue}{0.016666666666666666}} + a \cdot 120 \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]

   7. Taylor expanded in a around 0 88.6%

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

   if 4.99999999999999983e-106 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 83.1%

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

      1. associate-*r/ 83.2%

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

   7. Simplified 83.2%

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

      1. *-commutative 83.2%

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

      2. associate-/l* 83.2%

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

   9. Applied egg-rr 83.2%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-41}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-106}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-32} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-44}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -2e-32) (not (<= (* a 120.0) 5e-44)))
   (* 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 * 120.0) <= -2e-32) || !((a * 120.0) <= 5e-44)) {
		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 * 120.0d0) <= (-2d-32)) .or. (.not. ((a * 120.0d0) <= 5d-44))) 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 * 120.0) <= -2e-32) || !((a * 120.0) <= 5e-44)) {
		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 * 120.0) <= -2e-32) or not ((a * 120.0) <= 5e-44):
		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 ((Float64(a * 120.0) <= -2e-32) || !(Float64(a * 120.0) <= 5e-44))
		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 * 120.0) <= -2e-32) || ~(((a * 120.0) <= 5e-44)))
		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[N[(a * 120.0), $MachinePrecision], -2e-32], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-44]], $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 (*.f64 a #s(literal 120 binary64)) < -2.00000000000000011e-32 or 5.00000000000000039e-44 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 74.7%

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

   if -2.00000000000000011e-32 < (*.f64 a #s(literal 120 binary64)) < 5.00000000000000039e-44

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.7%

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

      3. div-inv 99.7%

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

      4. metadata-eval 99.7%

         \[\leadsto \frac{x - y}{\left(z - t\right) \cdot \color{blue}{0.016666666666666666}} + a \cdot 120 \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]

   7. Taylor expanded in a around 0 85.4%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-32} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-44}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-32}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-44}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e-32)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-44)
     (* 60.0 (/ (- x y) (- z t)))
     (+ (* a 120.0) (* 60.0 (/ x z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-32) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-44) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d-32)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-44) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e-32) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-44) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e-32:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-44:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + (60.0 * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e-32)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-44)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e-32)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-44)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + (60.0 * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-32], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-44], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -2.00000000000000011e-32

   1. Initial program 98.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 74.6%

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

   if -2.00000000000000011e-32 < (*.f64 a #s(literal 120 binary64)) < 9.99999999999999953e-45

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.7%

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

      3. div-inv 99.7%

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

      4. metadata-eval 99.7%

         \[\leadsto \frac{x - y}{\left(z - t\right) \cdot \color{blue}{0.016666666666666666}} + a \cdot 120 \]

   6. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]

   7. Taylor expanded in a around 0 85.2%

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

   if 9.99999999999999953e-45 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 74.7%

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

   6. Taylor expanded in x around inf 75.2%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-32}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-44}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-36}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-248}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{-105}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.12e-36)
   (* a 120.0)
   (if (<= a -6.5e-248)
     (* -60.0 (/ y (- z t)))
     (if (<= a 1.32e-105) (* 60.0 (/ x (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.12e-36) {
		tmp = a * 120.0;
	} else if (a <= -6.5e-248) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 1.32e-105) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.12d-36)) then
        tmp = a * 120.0d0
    else if (a <= (-6.5d-248)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (a <= 1.32d-105) then
        tmp = 60.0d0 * (x / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.12e-36) {
		tmp = a * 120.0;
	} else if (a <= -6.5e-248) {
		tmp = -60.0 * (y / (z - t));
	} else if (a <= 1.32e-105) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.12e-36:
		tmp = a * 120.0
	elif a <= -6.5e-248:
		tmp = -60.0 * (y / (z - t))
	elif a <= 1.32e-105:
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.12e-36)
		tmp = Float64(a * 120.0);
	elseif (a <= -6.5e-248)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (a <= 1.32e-105)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.12e-36)
		tmp = a * 120.0;
	elseif (a <= -6.5e-248)
		tmp = -60.0 * (y / (z - t));
	elseif (a <= 1.32e-105)
		tmp = 60.0 * (x / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.12e-36], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -6.5e-248], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.32e-105], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.12e-36 or 1.32000000000000006e-105 < a

   1. Initial program 98.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 72.6%

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

   if -1.12e-36 < a < -6.5e-248

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in a around inf 78.8%

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

      1. associate-*r/ 78.8%

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

      2. *-commutative 78.8%

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

   7. Simplified 78.8%

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

   8. Taylor expanded in y around inf 53.0%

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

   if -6.5e-248 < a < 1.32000000000000006e-105

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in a around inf 67.3%

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

      1. associate-*r/ 67.4%

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

      2. *-commutative 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in x around inf 54.9%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.12 \cdot 10^{-36}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-248}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{-105}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.3 \cdot 10^{+81} \lor \neg \left(x \leq 1.65 \cdot 10^{+89}\right):\\ \;\;\;\;a \cdot 120 + \frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -6.3e+81) (not (<= x 1.65e+89)))
   (+ (* a 120.0) (/ x (* (- z t) 0.016666666666666666)))
   (+ (* a 120.0) (* 60.0 (/ y (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -6.3e+81) || !(x <= 1.65e+89)) {
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666));
	} else {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-6.3d+81)) .or. (.not. (x <= 1.65d+89))) then
        tmp = (a * 120.0d0) + (x / ((z - t) * 0.016666666666666666d0))
    else
        tmp = (a * 120.0d0) + (60.0d0 * (y / (t - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -6.3e+81) || !(x <= 1.65e+89)) {
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666));
	} else {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -6.3e+81) or not (x <= 1.65e+89):
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666))
	else:
		tmp = (a * 120.0) + (60.0 * (y / (t - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -6.3e+81) || !(x <= 1.65e+89))
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(Float64(z - t) * 0.016666666666666666)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / Float64(t - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -6.3e+81) || ~((x <= 1.65e+89)))
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666));
	else
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -6.3e+81], N[Not[LessEqual[x, 1.65e+89]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.3000000000000004e81 or 1.64999999999999987e89 < x

   1. Initial program 98.8%

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

      1. *-commutative 98.8%

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

      2. associate-/l* 99.8%

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

   4. Applied egg-rr 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

      3. div-inv 99.8%

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

      4. metadata-eval 99.8%

         \[\leadsto \frac{x - y}{\left(z - t\right) \cdot \color{blue}{0.016666666666666666}} + a \cdot 120 \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]

   7. Taylor expanded in x around inf 91.6%

      \[\leadsto \frac{\color{blue}{x}}{\left(z - t\right) \cdot 0.016666666666666666} + a \cdot 120 \]

   if -6.3000000000000004e81 < x < 1.64999999999999987e89

   1. Initial program 99.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 93.5%

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

      1. neg-mul-1 93.5%

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

      2. distribute-neg-frac2 93.5%

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

      3. neg-sub0 93.5%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{0 - \left(z - t\right)}} + a \cdot 120 \]

      4. sub-neg 93.5%

         \[\leadsto 60 \cdot \frac{y}{0 - \color{blue}{\left(z + \left(-t\right)\right)}} + a \cdot 120 \]

      5. +-commutative 93.5%

         \[\leadsto 60 \cdot \frac{y}{0 - \color{blue}{\left(\left(-t\right) + z\right)}} + a \cdot 120 \]

      6. associate--r+ 93.5%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{\left(0 - \left(-t\right)\right) - z}} + a \cdot 120 \]

      7. neg-sub0 93.5%

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

      8. remove-double-neg 93.5%

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

   7. Simplified 93.5%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.3 \cdot 10^{+81} \lor \neg \left(x \leq 1.65 \cdot 10^{+89}\right):\\ \;\;\;\;a \cdot 120 + \frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+82} \lor \neg \left(x \leq 4.3 \cdot 10^{+89}\right):\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -7e+82) (not (<= x 4.3e+89)))
   (+ (* a 120.0) (/ 60.0 (/ (- z t) x)))
   (+ (* a 120.0) (* 60.0 (/ y (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -7e+82) || !(x <= 4.3e+89)) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} else {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-7d+82)) .or. (.not. (x <= 4.3d+89))) then
        tmp = (a * 120.0d0) + (60.0d0 / ((z - t) / x))
    else
        tmp = (a * 120.0d0) + (60.0d0 * (y / (t - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -7e+82) || !(x <= 4.3e+89)) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} else {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -7e+82) or not (x <= 4.3e+89):
		tmp = (a * 120.0) + (60.0 / ((z - t) / x))
	else:
		tmp = (a * 120.0) + (60.0 * (y / (t - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -7e+82) || !(x <= 4.3e+89))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(z - t) / x)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / Float64(t - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -7e+82) || ~((x <= 4.3e+89)))
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	else
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -7e+82], N[Not[LessEqual[x, 4.3e+89]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.0000000000000001e82 or 4.3000000000000002e89 < x

   1. Initial program 98.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

         \[\leadsto 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}} + a \cdot 120 \]

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 91.6%

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

   if -7.0000000000000001e82 < x < 4.3000000000000002e89

   1. Initial program 99.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 93.5%

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

      1. neg-mul-1 93.5%

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

      2. distribute-neg-frac2 93.5%

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

      3. neg-sub0 93.5%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{0 - \left(z - t\right)}} + a \cdot 120 \]

      4. sub-neg 93.5%

         \[\leadsto 60 \cdot \frac{y}{0 - \color{blue}{\left(z + \left(-t\right)\right)}} + a \cdot 120 \]

      5. +-commutative 93.5%

         \[\leadsto 60 \cdot \frac{y}{0 - \color{blue}{\left(\left(-t\right) + z\right)}} + a \cdot 120 \]

      6. associate--r+ 93.5%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{\left(0 - \left(-t\right)\right) - z}} + a \cdot 120 \]

      7. neg-sub0 93.5%

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

      8. remove-double-neg 93.5%

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

   7. Simplified 93.5%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+82} \lor \neg \left(x \leq 4.3 \cdot 10^{+89}\right):\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+81}:\\ \;\;\;\;a \cdot 120 + \frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+89}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot 60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.65e+81)
   (+ (* a 120.0) (/ x (* (- z t) 0.016666666666666666)))
   (if (<= x 1.75e+89)
     (+ (* a 120.0) (* 60.0 (/ y (- t z))))
     (+ (* a 120.0) (/ (* x 60.0) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.65e+81) {
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666));
	} else if (x <= 1.75e+89) {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	} else {
		tmp = (a * 120.0) + ((x * 60.0) / (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 (x <= (-1.65d+81)) then
        tmp = (a * 120.0d0) + (x / ((z - t) * 0.016666666666666666d0))
    else if (x <= 1.75d+89) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / (t - z)))
    else
        tmp = (a * 120.0d0) + ((x * 60.0d0) / (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 (x <= -1.65e+81) {
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666));
	} else if (x <= 1.75e+89) {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	} else {
		tmp = (a * 120.0) + ((x * 60.0) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.65e+81:
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666))
	elif x <= 1.75e+89:
		tmp = (a * 120.0) + (60.0 * (y / (t - z)))
	else:
		tmp = (a * 120.0) + ((x * 60.0) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.65e+81)
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(Float64(z - t) * 0.016666666666666666)));
	elseif (x <= 1.75e+89)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / Float64(t - z))));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * 60.0) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.65e+81)
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666));
	elseif (x <= 1.75e+89)
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	else
		tmp = (a * 120.0) + ((x * 60.0) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.65e+81], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75e+89], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.65e81

   1. Initial program 97.8%

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

      1. *-commutative 97.8%

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

      2. associate-/l* 99.8%

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

   4. Applied egg-rr 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

      3. div-inv 99.8%

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

      4. metadata-eval 99.8%

         \[\leadsto \frac{x - y}{\left(z - t\right) \cdot \color{blue}{0.016666666666666666}} + a \cdot 120 \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]

   7. Taylor expanded in x around inf 92.2%

      \[\leadsto \frac{\color{blue}{x}}{\left(z - t\right) \cdot 0.016666666666666666} + a \cdot 120 \]

   if -1.65e81 < x < 1.75e89

   1. Initial program 99.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 93.5%

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

      1. neg-mul-1 93.5%

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

      2. distribute-neg-frac2 93.5%

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

      3. neg-sub0 93.5%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{0 - \left(z - t\right)}} + a \cdot 120 \]

      4. sub-neg 93.5%

         \[\leadsto 60 \cdot \frac{y}{0 - \color{blue}{\left(z + \left(-t\right)\right)}} + a \cdot 120 \]

      5. +-commutative 93.5%

         \[\leadsto 60 \cdot \frac{y}{0 - \color{blue}{\left(\left(-t\right) + z\right)}} + a \cdot 120 \]

      6. associate--r+ 93.5%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{\left(0 - \left(-t\right)\right) - z}} + a \cdot 120 \]

      7. neg-sub0 93.5%

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

      8. remove-double-neg 93.5%

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

   7. Simplified 93.5%

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

   if 1.75e89 < x

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 91.0%

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

      1. associate-*r/ 91.1%

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

   7. Simplified 91.1%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+81}:\\ \;\;\;\;a \cdot 120 + \frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+89}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot 60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{-37} \lor \neg \left(a \leq 1.65 \cdot 10^{-63}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.45e-37) (not (<= a 1.65e-63)))
   (* a 120.0)
   (* -60.0 (/ y (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.45e-37) || !(a <= 1.65e-63)) {
		tmp = a * 120.0;
	} else {
		tmp = -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 ((a <= (-2.45d-37)) .or. (.not. (a <= 1.65d-63))) then
        tmp = a * 120.0d0
    else
        tmp = (-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 ((a <= -2.45e-37) || !(a <= 1.65e-63)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.45e-37) or not (a <= 1.65e-63):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.45e-37) || !(a <= 1.65e-63))
		tmp = Float64(a * 120.0);
	else
		tmp = 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 ((a <= -2.45e-37) || ~((a <= 1.65e-63)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.45e-37], N[Not[LessEqual[a, 1.65e-63]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.45000000000000009e-37 or 1.64999999999999997e-63 < a

   1. Initial program 98.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 74.1%

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

   if -2.45000000000000009e-37 < a < 1.64999999999999997e-63

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in a around inf 74.5%

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

      1. associate-*r/ 74.6%

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

      2. *-commutative 74.6%

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

   7. Simplified 74.6%

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

   8. Taylor expanded in y around inf 45.0%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.45 \cdot 10^{-37} \lor \neg \left(a \leq 1.65 \cdot 10^{-63}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-46} \lor \neg \left(a \leq 1.85 \cdot 10^{-137}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.6e-46) (not (<= a 1.85e-137)))
   (* a 120.0)
   (* x (/ -60.0 t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.6e-46) || !(a <= 1.85e-137)) {
		tmp = a * 120.0;
	} else {
		tmp = x * (-60.0 / 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 <= (-5.6d-46)) .or. (.not. (a <= 1.85d-137))) then
        tmp = a * 120.0d0
    else
        tmp = x * ((-60.0d0) / 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 <= -5.6e-46) || !(a <= 1.85e-137)) {
		tmp = a * 120.0;
	} else {
		tmp = x * (-60.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.6e-46) or not (a <= 1.85e-137):
		tmp = a * 120.0
	else:
		tmp = x * (-60.0 / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.6e-46) || !(a <= 1.85e-137))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(x * Float64(-60.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.6e-46) || ~((a <= 1.85e-137)))
		tmp = a * 120.0;
	else
		tmp = x * (-60.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.6e-46], N[Not[LessEqual[a, 1.85e-137]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.5999999999999997e-46 or 1.85e-137 < a

   1. Initial program 98.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 70.6%

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

   if -5.5999999999999997e-46 < a < 1.85e-137

   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* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

         \[\leadsto 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}} + a \cdot 120 \]

      2. un-div-inv 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in x around inf 54.7%

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

   8. Taylor expanded in z around 0 33.2%

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

   9. Taylor expanded in x around inf 26.7%

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

       1. associate-*r/ 26.7%

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

       2. *-commutative 26.7%

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

       3. associate-/l* 26.7%

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

   11. Simplified 26.7%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-46} \lor \neg \left(a \leq 1.85 \cdot 10^{-137}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-45} \lor \neg \left(a \leq 1.05 \cdot 10^{-141}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.1e-45) (not (<= a 1.05e-141)))
   (* a 120.0)
   (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.1e-45) || !(a <= 1.05e-141)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / 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 <= (-2.1d-45)) .or. (.not. (a <= 1.05d-141))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (x / 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 <= -2.1e-45) || !(a <= 1.05e-141)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.1e-45) or not (a <= 1.05e-141):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (x / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.1e-45) || !(a <= 1.05e-141))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.1e-45) || ~((a <= 1.05e-141)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.1e-45], N[Not[LessEqual[a, 1.05e-141]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.09999999999999995e-45 or 1.05e-141 < a

   1. Initial program 98.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 70.6%

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

   if -2.09999999999999995e-45 < a < 1.05e-141

   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* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

         \[\leadsto 60 \cdot \color{blue}{\frac{1}{\frac{z - t}{x - y}}} + a \cdot 120 \]

      2. un-div-inv 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in x around inf 54.7%

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

   8. Taylor expanded in z around 0 33.2%

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

   9. Taylor expanded in x around inf 26.7%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-45} \lor \neg \left(a \leq 1.05 \cdot 10^{-141}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. *-commutative 99.0%

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

   2. associate-/l* 99.8%

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

4. Applied egg-rr 99.8%

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

5. Final simplification 99.8%

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

Alternative 16: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. associate-/l* 99.7%

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

3. Simplified 99.7%

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

5. Final simplification 99.7%

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

Alternative 17: 50.2% 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 99.0%

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

   1. associate-/l* 99.7%

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

3. Simplified 99.7%

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

5. Taylor expanded in z around inf 50.0%

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

6. Final simplification 50.0%

   \[\leadsto a \cdot 120 \]
7. Add Preprocessing

Developer Target 1: 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 2024135 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (/ 60 (/ (- z t) (- x y))) (* a 120)))

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