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

Percentage Accurate: 99.4% → 99.8%

Time: 15.2s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0 + N[(N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $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. +-commutative 99.0%

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

   2. fma-def 99.1%

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

   3. *-commutative 99.1%

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

   4. associate-*l/ 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0 + 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. Step-by-step derivation

   1. +-commutative 99.0%

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

   2. fma-def 99.1%

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

   3. associate-*l/ 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 3: 74.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-60}{\frac{t}{x - y}} + a \cdot 120\\ t_2 := \frac{x \cdot 60}{z} + a \cdot 120\\ \mathbf{if}\;z \leq -1 \cdot 10^{-93}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-21}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+170}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (/ -60.0 (/ t (- x y))) (* a 120.0)))
        (t_2 (+ (/ (* x 60.0) z) (* a 120.0))))
   (if (<= z -1e-93)
     t_2
     (if (<= z 4.8e-58)
       t_1
       (if (<= z 5.4e-21)
         (* 60.0 (/ (- x y) z))
         (if (<= z 1.75e+39)
           t_1
           (if (<= z 4.3e+170) t_2 (+ (* -60.0 (/ y z)) (* a 120.0)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 / (t / (x - y))) + (a * 120.0);
	double t_2 = ((x * 60.0) / z) + (a * 120.0);
	double tmp;
	if (z <= -1e-93) {
		tmp = t_2;
	} else if (z <= 4.8e-58) {
		tmp = t_1;
	} else if (z <= 5.4e-21) {
		tmp = 60.0 * ((x - y) / z);
	} else if (z <= 1.75e+39) {
		tmp = t_1;
	} else if (z <= 4.3e+170) {
		tmp = t_2;
	} else {
		tmp = (-60.0 * (y / z)) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((-60.0d0) / (t / (x - y))) + (a * 120.0d0)
    t_2 = ((x * 60.0d0) / z) + (a * 120.0d0)
    if (z <= (-1d-93)) then
        tmp = t_2
    else if (z <= 4.8d-58) then
        tmp = t_1
    else if (z <= 5.4d-21) then
        tmp = 60.0d0 * ((x - y) / z)
    else if (z <= 1.75d+39) then
        tmp = t_1
    else if (z <= 4.3d+170) then
        tmp = t_2
    else
        tmp = ((-60.0d0) * (y / z)) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (-60.0 / (t / (x - y))) + (a * 120.0);
	double t_2 = ((x * 60.0) / z) + (a * 120.0);
	double tmp;
	if (z <= -1e-93) {
		tmp = t_2;
	} else if (z <= 4.8e-58) {
		tmp = t_1;
	} else if (z <= 5.4e-21) {
		tmp = 60.0 * ((x - y) / z);
	} else if (z <= 1.75e+39) {
		tmp = t_1;
	} else if (z <= 4.3e+170) {
		tmp = t_2;
	} else {
		tmp = (-60.0 * (y / z)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-60.0 / (t / (x - y))) + (a * 120.0)
	t_2 = ((x * 60.0) / z) + (a * 120.0)
	tmp = 0
	if z <= -1e-93:
		tmp = t_2
	elif z <= 4.8e-58:
		tmp = t_1
	elif z <= 5.4e-21:
		tmp = 60.0 * ((x - y) / z)
	elif z <= 1.75e+39:
		tmp = t_1
	elif z <= 4.3e+170:
		tmp = t_2
	else:
		tmp = (-60.0 * (y / z)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-60.0 / Float64(t / Float64(x - y))) + Float64(a * 120.0))
	t_2 = Float64(Float64(Float64(x * 60.0) / z) + Float64(a * 120.0))
	tmp = 0.0
	if (z <= -1e-93)
		tmp = t_2;
	elseif (z <= 4.8e-58)
		tmp = t_1;
	elseif (z <= 5.4e-21)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (z <= 1.75e+39)
		tmp = t_1;
	elseif (z <= 4.3e+170)
		tmp = t_2;
	else
		tmp = Float64(Float64(-60.0 * Float64(y / z)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-60.0 / (t / (x - y))) + (a * 120.0);
	t_2 = ((x * 60.0) / z) + (a * 120.0);
	tmp = 0.0;
	if (z <= -1e-93)
		tmp = t_2;
	elseif (z <= 4.8e-58)
		tmp = t_1;
	elseif (z <= 5.4e-21)
		tmp = 60.0 * ((x - y) / z);
	elseif (z <= 1.75e+39)
		tmp = t_1;
	elseif (z <= 4.3e+170)
		tmp = t_2;
	else
		tmp = (-60.0 * (y / z)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(-60.0 / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * 60.0), $MachinePrecision] / z), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e-93], t$95$2, If[LessEqual[z, 4.8e-58], t$95$1, If[LessEqual[z, 5.4e-21], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+39], t$95$1, If[LessEqual[z, 4.3e+170], t$95$2, N[(N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.999999999999999e-94 or 1.7500000000000001e39 < z < 4.2999999999999999e170

   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* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 85.2%

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

      1. associate-*r/ 84.2%

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

      2. *-commutative 84.2%

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

      3. associate-/l* 85.1%

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

   7. Simplified 85.1%

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

   8. Taylor expanded in z around inf 80.9%

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

      1. *-commutative 80.9%

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

      2. associate-*l/ 80.0%

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

   10. Simplified 80.0%

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

   if -9.999999999999999e-94 < z < 4.8000000000000001e-58 or 5.4000000000000002e-21 < z < 1.7500000000000001e39

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 88.5%

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

      1. associate-*r/ 88.5%

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

      2. associate-/l* 88.6%

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

   7. Simplified 88.6%

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

   if 4.8000000000000001e-58 < z < 5.4000000000000002e-21

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 85.9%

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

   6. Taylor expanded in z around inf 86.5%

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

   if 4.2999999999999999e170 < z

   1. Initial program 97.1%

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

   3. Taylor expanded in x around 0 89.9%

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

   4. Taylor expanded in z around inf 87.4%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-93}:\\ \;\;\;\;\frac{x \cdot 60}{z} + a \cdot 120\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-58}:\\ \;\;\;\;\frac{-60}{\frac{t}{x - y}} + a \cdot 120\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-21}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+39}:\\ \;\;\;\;\frac{-60}{\frac{t}{x - y}} + a \cdot 120\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+170}:\\ \;\;\;\;\frac{x \cdot 60}{z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-34} \lor \neg \left(a \cdot 120 \leq 4 \cdot 10^{-177}\right):\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -5e-34) (not (<= (* a 120.0) 4e-177)))
   (+ (/ 60.0 (/ (- z t) x)) (* a 120.0))
   (* (/ (- x y) (- z t)) 60.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -5e-34) || !((a * 120.0) <= 4e-177)) {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	} else {
		tmp = ((x - y) / (z - t)) * 60.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-5d-34)) .or. (.not. ((a * 120.0d0) <= 4d-177))) then
        tmp = (60.0d0 / ((z - t) / x)) + (a * 120.0d0)
    else
        tmp = ((x - y) / (z - t)) * 60.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -5e-34) || !((a * 120.0) <= 4e-177)) {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	} else {
		tmp = ((x - y) / (z - t)) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -5e-34) or not ((a * 120.0) <= 4e-177):
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0)
	else:
		tmp = ((x - y) / (z - t)) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -5e-34) || !(Float64(a * 120.0) <= 4e-177))
		tmp = Float64(Float64(60.0 / Float64(Float64(z - t) / x)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(Float64(x - y) / Float64(z - t)) * 60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -5e-34) || ~(((a * 120.0) <= 4e-177)))
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	else
		tmp = ((x - y) / (z - t)) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-34], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 4e-177]], $MachinePrecision]], N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -5.0000000000000003e-34 or 3.99999999999999981e-177 < (*.f64 a 120)

   1. Initial program 99.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 87.4%

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

   if -5.0000000000000003e-34 < (*.f64 a 120) < 3.99999999999999981e-177

   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* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 85.6%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-34} \lor \neg \left(a \cdot 120 \leq 4 \cdot 10^{-177}\right):\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x - y \leq -5 \cdot 10^{+82} \lor \neg \left(x - y \leq 10^{+103}\right):\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- x y) -5e+82) (not (<= (- x y) 1e+103)))
   (* (/ (- x y) (- z t)) 60.0)
   (+ (* -60.0 (/ y z)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x - y) <= -5e+82) || !((x - y) <= 1e+103)) {
		tmp = ((x - y) / (z - t)) * 60.0;
	} else {
		tmp = (-60.0 * (y / z)) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((x - y) <= (-5d+82)) .or. (.not. ((x - y) <= 1d+103))) then
        tmp = ((x - y) / (z - t)) * 60.0d0
    else
        tmp = ((-60.0d0) * (y / z)) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x - y) <= -5e+82) || !((x - y) <= 1e+103)) {
		tmp = ((x - y) / (z - t)) * 60.0;
	} else {
		tmp = (-60.0 * (y / z)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((x - y) <= -5e+82) or not ((x - y) <= 1e+103):
		tmp = ((x - y) / (z - t)) * 60.0
	else:
		tmp = (-60.0 * (y / z)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x - y) <= -5e+82) || !(Float64(x - y) <= 1e+103))
		tmp = Float64(Float64(Float64(x - y) / Float64(z - t)) * 60.0);
	else
		tmp = Float64(Float64(-60.0 * Float64(y / z)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x - y) <= -5e+82) || ~(((x - y) <= 1e+103)))
		tmp = ((x - y) / (z - t)) * 60.0;
	else
		tmp = (-60.0 * (y / z)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x - y), $MachinePrecision], -5e+82], N[Not[LessEqual[N[(x - y), $MachinePrecision], 1e+103]], $MachinePrecision]], N[(N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision], N[(N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 x y) < -5.00000000000000015e82 or 1e103 < (-.f64 x y)

   1. Initial program 98.3%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 70.9%

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

   if -5.00000000000000015e82 < (-.f64 x y) < 1e103

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 93.6%

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

   4. Taylor expanded in z around inf 83.2%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - y \leq -5 \cdot 10^{+82} \lor \neg \left(x - y \leq 10^{+103}\right):\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x - y \leq -5 \cdot 10^{+82}:\\ \;\;\;\;\frac{-60}{\frac{t - z}{x - y}}\\ \mathbf{elif}\;x - y \leq 10^{+103}:\\ \;\;\;\;-60 \cdot \frac{y}{z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- x y) -5e+82)
   (/ -60.0 (/ (- t z) (- x y)))
   (if (<= (- x y) 1e+103)
     (+ (* -60.0 (/ y z)) (* a 120.0))
     (* (/ (- x y) (- z t)) 60.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x - y) <= -5e+82) {
		tmp = -60.0 / ((t - z) / (x - y));
	} else if ((x - y) <= 1e+103) {
		tmp = (-60.0 * (y / z)) + (a * 120.0);
	} else {
		tmp = ((x - y) / (z - t)) * 60.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x - y) <= (-5d+82)) then
        tmp = (-60.0d0) / ((t - z) / (x - y))
    else if ((x - y) <= 1d+103) then
        tmp = ((-60.0d0) * (y / z)) + (a * 120.0d0)
    else
        tmp = ((x - y) / (z - t)) * 60.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x - y) <= -5e+82) {
		tmp = -60.0 / ((t - z) / (x - y));
	} else if ((x - y) <= 1e+103) {
		tmp = (-60.0 * (y / z)) + (a * 120.0);
	} else {
		tmp = ((x - y) / (z - t)) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x - y) <= -5e+82:
		tmp = -60.0 / ((t - z) / (x - y))
	elif (x - y) <= 1e+103:
		tmp = (-60.0 * (y / z)) + (a * 120.0)
	else:
		tmp = ((x - y) / (z - t)) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x - y) <= -5e+82)
		tmp = Float64(-60.0 / Float64(Float64(t - z) / Float64(x - y)));
	elseif (Float64(x - y) <= 1e+103)
		tmp = Float64(Float64(-60.0 * Float64(y / z)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(Float64(x - y) / Float64(z - t)) * 60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x - y) <= -5e+82)
		tmp = -60.0 / ((t - z) / (x - y));
	elseif ((x - y) <= 1e+103)
		tmp = (-60.0 * (y / z)) + (a * 120.0);
	else
		tmp = ((x - y) / (z - t)) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x - y), $MachinePrecision], -5e+82], N[(-60.0 / N[(N[(t - z), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x - y), $MachinePrecision], 1e+103], N[(N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 x y) < -5.00000000000000015e82

   1. Initial program 98.2%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 71.9%

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

      1. associate-*r/ 71.8%

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

      2. frac-2neg 71.8%

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

      3. sub-neg 71.8%

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

      4. distribute-neg-in 71.8%

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

      5. remove-double-neg 71.8%

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

   7. Applied egg-rr 71.8%

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

      1. distribute-lft-neg-in 71.8%

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

      2. metadata-eval 71.8%

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

      3. associate-/l* 71.9%

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

      4. +-commutative 71.9%

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

      5. unsub-neg 71.9%

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

   9. Simplified 71.9%

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

   if -5.00000000000000015e82 < (-.f64 x y) < 1e103

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 93.6%

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

   4. Taylor expanded in z around inf 83.2%

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

   if 1e103 < (-.f64 x y)

   1. Initial program 98.3%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 69.9%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - y \leq -5 \cdot 10^{+82}:\\ \;\;\;\;\frac{-60}{\frac{t - z}{x - y}}\\ \mathbf{elif}\;x - y \leq 10^{+103}:\\ \;\;\;\;-60 \cdot \frac{y}{z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-37}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-284}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-135}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.5e-37)
   (* a 120.0)
   (if (<= a 2.4e-284)
     (* -60.0 (/ (- x y) t))
     (if (<= a 2.7e-135) (* 60.0 (/ (- x y) z)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e-37) {
		tmp = a * 120.0;
	} else if (a <= 2.4e-284) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 2.7e-135) {
		tmp = 60.0 * ((x - y) / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-5.5d-37)) then
        tmp = a * 120.0d0
    else if (a <= 2.4d-284) then
        tmp = (-60.0d0) * ((x - y) / t)
    else if (a <= 2.7d-135) then
        tmp = 60.0d0 * ((x - y) / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.5e-37) {
		tmp = a * 120.0;
	} else if (a <= 2.4e-284) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 2.7e-135) {
		tmp = 60.0 * ((x - y) / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.5e-37:
		tmp = a * 120.0
	elif a <= 2.4e-284:
		tmp = -60.0 * ((x - y) / t)
	elif a <= 2.7e-135:
		tmp = 60.0 * ((x - y) / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.5e-37)
		tmp = Float64(a * 120.0);
	elseif (a <= 2.4e-284)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	elseif (a <= 2.7e-135)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.5e-37)
		tmp = a * 120.0;
	elseif (a <= 2.4e-284)
		tmp = -60.0 * ((x - y) / t);
	elseif (a <= 2.7e-135)
		tmp = 60.0 * ((x - y) / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.5e-37], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 2.4e-284], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e-135], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.4999999999999998e-37 or 2.69999999999999999e-135 < a

   1. Initial program 99.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 70.9%

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

   if -5.4999999999999998e-37 < a < 2.40000000000000003e-284

   1. Initial program 98.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 85.1%

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

   6. Taylor expanded in z around 0 53.1%

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

   if 2.40000000000000003e-284 < a < 2.69999999999999999e-135

   1. Initial program 99.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 85.8%

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

   6. Taylor expanded in z around inf 57.7%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-37}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-284}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-135}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+42} \lor \neg \left(x \leq 3.2 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -5.5e+42) (not (<= x 3.2e+63)))
   (+ (/ 60.0 (/ (- z t) x)) (* a 120.0))
   (+ (/ (* y -60.0) (- z t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -5.5e+42) || !(x <= 3.2e+63)) {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	} else {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-5.5d+42)) .or. (.not. (x <= 3.2d+63))) then
        tmp = (60.0d0 / ((z - t) / x)) + (a * 120.0d0)
    else
        tmp = ((y * (-60.0d0)) / (z - t)) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -5.5e+42) || !(x <= 3.2e+63)) {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	} else {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -5.5e+42) or not (x <= 3.2e+63):
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0)
	else:
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -5.5e+42) || !(x <= 3.2e+63))
		tmp = Float64(Float64(60.0 / Float64(Float64(z - t) / x)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -5.5e+42) || ~((x <= 3.2e+63)))
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	else
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -5.5e+42], N[Not[LessEqual[x, 3.2e+63]], $MachinePrecision]], N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.50000000000000001e42 or 3.20000000000000011e63 < x

   1. Initial program 97.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 90.3%

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

   if -5.50000000000000001e42 < x < 3.20000000000000011e63

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 97.5%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+42} \lor \neg \left(x \leq 3.2 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{-36} \lor \neg \left(a \leq 4.6 \cdot 10^{-36}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -5.1e-36) (not (<= a 4.6e-36)))
   (* a 120.0)
   (* (/ (- x y) (- z t)) 60.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.1e-36) || !(a <= 4.6e-36)) {
		tmp = a * 120.0;
	} else {
		tmp = ((x - y) / (z - t)) * 60.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-5.1d-36)) .or. (.not. (a <= 4.6d-36))) then
        tmp = a * 120.0d0
    else
        tmp = ((x - y) / (z - t)) * 60.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -5.1e-36) || !(a <= 4.6e-36)) {
		tmp = a * 120.0;
	} else {
		tmp = ((x - y) / (z - t)) * 60.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -5.1e-36) or not (a <= 4.6e-36):
		tmp = a * 120.0
	else:
		tmp = ((x - y) / (z - t)) * 60.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -5.1e-36) || !(a <= 4.6e-36))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(Float64(x - y) / Float64(z - t)) * 60.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -5.1e-36) || ~((a <= 4.6e-36)))
		tmp = a * 120.0;
	else
		tmp = ((x - y) / (z - t)) * 60.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -5.1e-36], N[Not[LessEqual[a, 4.6e-36]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] * 60.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.09999999999999973e-36 or 4.59999999999999993e-36 < a

   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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 74.8%

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

   if -5.09999999999999973e-36 < a < 4.59999999999999993e-36

   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* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 80.4%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{-36} \lor \neg \left(a \leq 4.6 \cdot 10^{-36}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - t} \cdot 60\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-37} \lor \neg \left(a \leq 4.1 \cdot 10^{-187}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.8e-37) (not (<= a 4.1e-187)))
   (* a 120.0)
   (* -60.0 (/ (- x y) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e-37) || !(a <= 4.1e-187)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.8d-37)) .or. (.not. (a <= 4.1d-187))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * ((x - y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e-37) || !(a <= 4.1e-187)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.8e-37) or not (a <= 4.1e-187):
		tmp = a * 120.0
	else:
		tmp = -60.0 * ((x - y) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.8e-37) || !(a <= 4.1e-187))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.8e-37) || ~((a <= 4.1e-187)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * ((x - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.8e-37], N[Not[LessEqual[a, 4.1e-187]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.79999999999999982e-37 or 4.1000000000000002e-187 < a

   1. Initial program 99.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 69.0%

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

   if -4.79999999999999982e-37 < a < 4.1000000000000002e-187

   1. Initial program 98.4%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 86.3%

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

   6. Taylor expanded in z around 0 50.2%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-37} \lor \neg \left(a \leq 4.1 \cdot 10^{-187}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-43} \lor \neg \left(a \leq 4.1 \cdot 10^{-167}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.7e-43) (not (<= a 4.1e-167)))
   (* a 120.0)
   (/ -60.0 (/ (- z t) y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.7e-43) || !(a <= 4.1e-167)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / ((z - t) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.7d-43)) .or. (.not. (a <= 4.1d-167))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) / ((z - t) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.7e-43) || !(a <= 4.1e-167)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 / ((z - t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.7e-43) or not (a <= 4.1e-167):
		tmp = a * 120.0
	else:
		tmp = -60.0 / ((z - t) / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.7e-43) || !(a <= 4.1e-167))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 / Float64(Float64(z - t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.7e-43) || ~((a <= 4.1e-167)))
		tmp = a * 120.0;
	else
		tmp = -60.0 / ((z - t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.7e-43], N[Not[LessEqual[a, 4.1e-167]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.7000000000000001e-43 or 4.10000000000000018e-167 < a

   1. Initial program 99.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 69.2%

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

   if -4.7000000000000001e-43 < a < 4.10000000000000018e-167

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0 68.0%

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

      1. +-commutative 68.0%

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

      2. fma-def 68.0%

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

   5. Applied egg-rr 68.0%

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

   6. Taylor expanded in a around 0 54.4%

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

      1. associate-*r/ 54.4%

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

      2. associate-/l* 54.4%

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

   8. Simplified 54.4%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.7 \cdot 10^{-43} \lor \neg \left(a \leq 4.1 \cdot 10^{-167}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-85} \lor \neg \left(a \leq 2 \cdot 10^{-225}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.3e-85) (not (<= a 2e-225))) (* a 120.0) (* -60.0 (/ y z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.3e-85) || !(a <= 2e-225)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.3d-85)) .or. (.not. (a <= 2d-225))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.3e-85) || !(a <= 2e-225)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.3e-85) or not (a <= 2e-225):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.3e-85) || !(a <= 2e-225))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.3e-85) || ~((a <= 2e-225)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.3e-85], N[Not[LessEqual[a, 2e-225]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.29999999999999973e-85 or 1.9999999999999999e-225 < a

   1. Initial program 99.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 65.6%

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

   if -3.29999999999999973e-85 < a < 1.9999999999999999e-225

   1. Initial program 98.0%

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

   3. Taylor expanded in x around 0 65.0%

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

      1. +-commutative 65.0%

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

      2. fma-def 65.0%

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

   5. Applied egg-rr 65.0%

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

   6. Taylor expanded in a around 0 55.3%

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

      1. associate-*r/ 55.3%

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

      2. associate-/l* 55.3%

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

   8. Simplified 55.3%

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

   9. Taylor expanded in z around inf 30.4%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.3 \cdot 10^{-85} \lor \neg \left(a \leq 2 \cdot 10^{-225}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{-43} \lor \neg \left(a \leq 6.8 \cdot 10^{-192}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.46e-43) (not (<= a 6.8e-192))) (* a 120.0) (* 60.0 (/ y t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.46e-43) || !(a <= 6.8e-192)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.46d-43)) .or. (.not. (a <= 6.8d-192))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.46e-43) || !(a <= 6.8e-192)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.46e-43) or not (a <= 6.8e-192):
		tmp = a * 120.0
	else:
		tmp = 60.0 * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.46e-43) || !(a <= 6.8e-192))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.46e-43) || ~((a <= 6.8e-192)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.46e-43], N[Not[LessEqual[a, 6.8e-192]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.45999999999999997e-43 or 6.80000000000000003e-192 < a

   1. Initial program 99.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 68.7%

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

   if -1.45999999999999997e-43 < a < 6.80000000000000003e-192

   1. Initial program 98.4%

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

   3. Taylor expanded in x around 0 66.7%

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

   4. Taylor expanded in z around 0 42.1%

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

   5. Taylor expanded in y around inf 33.0%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.46 \cdot 10^{-43} \lor \neg \left(a \leq 6.8 \cdot 10^{-192}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 15: 51.3% 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* 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in z around inf 53.5%

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

6. Final simplification 53.5%

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

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024040 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

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

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