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

Percentage Accurate: 99.4% → 99.7%

Time: 16.4s

Alternatives: 19

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: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.6%

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

   1. associate-/l* 99.8%

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

   2. fma-define 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 81.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-165}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-98}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 10000:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* x (/ 60.0 (- z t))))))
   (if (<= (* a 120.0) -4e-78)
     t_1
     (if (<= (* a 120.0) 2e-165)
       (* 60.0 (/ (- x y) (- z t)))
       (if (<= (* a 120.0) 4e-98)
         (+ (* a 120.0) (* (- x y) (/ -60.0 t)))
         (if (<= (* a 120.0) 10000.0) (/ (* 60.0 (- x y)) (- z t)) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (x * (60.0 / (z - t)));
	double tmp;
	if ((a * 120.0) <= -4e-78) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-165) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 4e-98) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else if ((a * 120.0) <= 10000.0) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + (x * (60.0d0 / (z - t)))
    if ((a * 120.0d0) <= (-4d-78)) then
        tmp = t_1
    else if ((a * 120.0d0) <= 2d-165) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if ((a * 120.0d0) <= 4d-98) then
        tmp = (a * 120.0d0) + ((x - y) * ((-60.0d0) / t))
    else if ((a * 120.0d0) <= 10000.0d0) then
        tmp = (60.0d0 * (x - y)) / (z - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (x * (60.0 / (z - t)));
	double tmp;
	if ((a * 120.0) <= -4e-78) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-165) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 4e-98) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else if ((a * 120.0) <= 10000.0) {
		tmp = (60.0 * (x - y)) / (z - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (x * (60.0 / (z - t)))
	tmp = 0
	if (a * 120.0) <= -4e-78:
		tmp = t_1
	elif (a * 120.0) <= 2e-165:
		tmp = 60.0 * ((x - y) / (z - t))
	elif (a * 120.0) <= 4e-98:
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t))
	elif (a * 120.0) <= 10000.0:
		tmp = (60.0 * (x - y)) / (z - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))))
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e-78)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 2e-165)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 4e-98)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(-60.0 / t)));
	elseif (Float64(a * 120.0) <= 10000.0)
		tmp = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (x * (60.0 / (z - t)));
	tmp = 0.0;
	if ((a * 120.0) <= -4e-78)
		tmp = t_1;
	elseif ((a * 120.0) <= 2e-165)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif ((a * 120.0) <= 4e-98)
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	elseif ((a * 120.0) <= 10000.0)
		tmp = (60.0 * (x - y)) / (z - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-78], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-165], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 4e-98], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 10000.0], N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -4e-78 or 1e4 < (*.f64 a #s(literal 120 binary64))

   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 inf 85.4%

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

      1. associate-*r/ 84.7%

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

      2. *-commutative 84.7%

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

      3. associate-*r/ 85.4%

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

   7. Simplified 85.4%

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

   if -4e-78 < (*.f64 a #s(literal 120 binary64)) < 2e-165

   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%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 89.3%

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

   if 2e-165 < (*.f64 a #s(literal 120 binary64)) < 3.99999999999999976e-98

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

      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. Taylor expanded in z around 0 96.1%

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

   if 3.99999999999999976e-98 < (*.f64 a #s(literal 120 binary64)) < 1e4

   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* 99.6%

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

   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 0 81.5%

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

      1. associate-*r/ 81.6%

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

   7. Simplified 81.6%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-78}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-165}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 4 \cdot 10^{-98}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 10000:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+173}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{+21}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-78}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 10000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e+173)
   (+ (* a 120.0) (* x (/ -60.0 t)))
   (if (<= (* a 120.0) -2e+21)
     (+ (* a 120.0) (* 60.0 (/ x z)))
     (if (<= (* a 120.0) -4e-78)
       (+ (* a 120.0) (* 60.0 (/ y t)))
       (if (<= (* a 120.0) 10000.0)
         (* 60.0 (/ (- x y) (- z t)))
         (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e+173) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else if ((a * 120.0) <= -2e+21) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if ((a * 120.0) <= -4e-78) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= 10000.0) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-5d+173)) then
        tmp = (a * 120.0d0) + (x * ((-60.0d0) / t))
    else if ((a * 120.0d0) <= (-2d+21)) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    else if ((a * 120.0d0) <= (-4d-78)) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / t))
    else if ((a * 120.0d0) <= 10000.0d0) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e+173) {
		tmp = (a * 120.0) + (x * (-60.0 / t));
	} else if ((a * 120.0) <= -2e+21) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if ((a * 120.0) <= -4e-78) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= 10000.0) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -5e+173:
		tmp = (a * 120.0) + (x * (-60.0 / t))
	elif (a * 120.0) <= -2e+21:
		tmp = (a * 120.0) + (60.0 * (x / z))
	elif (a * 120.0) <= -4e-78:
		tmp = (a * 120.0) + (60.0 * (y / t))
	elif (a * 120.0) <= 10000.0:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e+173)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / t)));
	elseif (Float64(a * 120.0) <= -2e+21)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	elseif (Float64(a * 120.0) <= -4e-78)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	elseif (Float64(a * 120.0) <= 10000.0)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -5e+173)
		tmp = (a * 120.0) + (x * (-60.0 / t));
	elseif ((a * 120.0) <= -2e+21)
		tmp = (a * 120.0) + (60.0 * (x / z));
	elseif ((a * 120.0) <= -4e-78)
		tmp = (a * 120.0) + (60.0 * (y / t));
	elseif ((a * 120.0) <= 10000.0)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+173], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+21], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-78], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 10000.0], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.00000000000000034e173

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   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 inf 97.1%

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

      1. associate-*r/ 97.1%

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

      2. *-commutative 97.1%

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

      3. associate-*r/ 97.0%

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

   7. Simplified 97.0%

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

   8. Taylor expanded in z around 0 93.5%

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

   if -5.00000000000000034e173 < (*.f64 a #s(literal 120 binary64)) < -2e21

   1. Initial program 95.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 75.6%

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

      1. associate-*r/ 71.7%

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

      2. *-commutative 71.7%

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

      3. associate-*r/ 75.5%

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

   7. Simplified 75.5%

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

   8. Taylor expanded in z around inf 71.5%

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

   if -2e21 < (*.f64 a #s(literal 120 binary64)) < -4e-78

   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* 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around 0 75.8%

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

   6. Taylor expanded in x around 0 68.0%

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

   if -4e-78 < (*.f64 a #s(literal 120 binary64)) < 1e4

   1. Initial program 98.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 a around 0 85.0%

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

   if 1e4 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 100.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 76.8%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+173}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{+21}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-78}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 10000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z}\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{-80}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-189}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-240}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-87}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 43:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) z))))
   (if (<= a -1.6e-80)
     (* a 120.0)
     (if (<= a -2.6e-189)
       (/ (* y -60.0) (- z t))
       (if (<= a 7.5e-240)
         t_1
         (if (<= a 5e-87)
           (* -60.0 (/ (- x y) t))
           (if (<= a 43.0) t_1 (* a 120.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / z);
	double tmp;
	if (a <= -1.6e-80) {
		tmp = a * 120.0;
	} else if (a <= -2.6e-189) {
		tmp = (y * -60.0) / (z - t);
	} else if (a <= 7.5e-240) {
		tmp = t_1;
	} else if (a <= 5e-87) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 43.0) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / z)
    if (a <= (-1.6d-80)) then
        tmp = a * 120.0d0
    else if (a <= (-2.6d-189)) then
        tmp = (y * (-60.0d0)) / (z - t)
    else if (a <= 7.5d-240) then
        tmp = t_1
    else if (a <= 5d-87) then
        tmp = (-60.0d0) * ((x - y) / t)
    else if (a <= 43.0d0) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / z);
	double tmp;
	if (a <= -1.6e-80) {
		tmp = a * 120.0;
	} else if (a <= -2.6e-189) {
		tmp = (y * -60.0) / (z - t);
	} else if (a <= 7.5e-240) {
		tmp = t_1;
	} else if (a <= 5e-87) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 43.0) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / z)
	tmp = 0
	if a <= -1.6e-80:
		tmp = a * 120.0
	elif a <= -2.6e-189:
		tmp = (y * -60.0) / (z - t)
	elif a <= 7.5e-240:
		tmp = t_1
	elif a <= 5e-87:
		tmp = -60.0 * ((x - y) / t)
	elif a <= 43.0:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / z))
	tmp = 0.0
	if (a <= -1.6e-80)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.6e-189)
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	elseif (a <= 7.5e-240)
		tmp = t_1;
	elseif (a <= 5e-87)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	elseif (a <= 43.0)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / z);
	tmp = 0.0;
	if (a <= -1.6e-80)
		tmp = a * 120.0;
	elseif (a <= -2.6e-189)
		tmp = (y * -60.0) / (z - t);
	elseif (a <= 7.5e-240)
		tmp = t_1;
	elseif (a <= 5e-87)
		tmp = -60.0 * ((x - y) / t);
	elseif (a <= 43.0)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6e-80], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.6e-189], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e-240], t$95$1, If[LessEqual[a, 5e-87], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 43.0], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.5999999999999999e-80 or 43 < 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* 99.8%

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

   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 71.9%

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

   if -1.5999999999999999e-80 < a < -2.5999999999999999e-189

   1. Initial program 94.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 88.5%

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

   6. Taylor expanded in x around 0 65.9%

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

      1. associate-*r/ 65.9%

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

   8. Simplified 65.9%

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

   if -2.5999999999999999e-189 < a < 7.4999999999999995e-240 or 5.00000000000000042e-87 < a < 43

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 86.7%

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

   6. Taylor expanded in z around inf 56.7%

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

   if 7.4999999999999995e-240 < a < 5.00000000000000042e-87

   1. Initial program 97.2%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 80.7%

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

   6. Taylor expanded in z around 0 63.4%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-80}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-189}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-240}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-87}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 43:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z}\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{-80}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-240}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-87}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 43:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) z))))
   (if (<= a -1.6e-80)
     (* a 120.0)
     (if (<= a -1.1e-187)
       (* y (/ -60.0 (- z t)))
       (if (<= a 1.15e-240)
         t_1
         (if (<= a 7.2e-87)
           (* -60.0 (/ (- x y) t))
           (if (<= a 43.0) t_1 (* a 120.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / z);
	double tmp;
	if (a <= -1.6e-80) {
		tmp = a * 120.0;
	} else if (a <= -1.1e-187) {
		tmp = y * (-60.0 / (z - t));
	} else if (a <= 1.15e-240) {
		tmp = t_1;
	} else if (a <= 7.2e-87) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 43.0) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / z)
    if (a <= (-1.6d-80)) then
        tmp = a * 120.0d0
    else if (a <= (-1.1d-187)) then
        tmp = y * ((-60.0d0) / (z - t))
    else if (a <= 1.15d-240) then
        tmp = t_1
    else if (a <= 7.2d-87) then
        tmp = (-60.0d0) * ((x - y) / t)
    else if (a <= 43.0d0) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / z);
	double tmp;
	if (a <= -1.6e-80) {
		tmp = a * 120.0;
	} else if (a <= -1.1e-187) {
		tmp = y * (-60.0 / (z - t));
	} else if (a <= 1.15e-240) {
		tmp = t_1;
	} else if (a <= 7.2e-87) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 43.0) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / z)
	tmp = 0
	if a <= -1.6e-80:
		tmp = a * 120.0
	elif a <= -1.1e-187:
		tmp = y * (-60.0 / (z - t))
	elif a <= 1.15e-240:
		tmp = t_1
	elif a <= 7.2e-87:
		tmp = -60.0 * ((x - y) / t)
	elif a <= 43.0:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / z))
	tmp = 0.0
	if (a <= -1.6e-80)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.1e-187)
		tmp = Float64(y * Float64(-60.0 / Float64(z - t)));
	elseif (a <= 1.15e-240)
		tmp = t_1;
	elseif (a <= 7.2e-87)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	elseif (a <= 43.0)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / z);
	tmp = 0.0;
	if (a <= -1.6e-80)
		tmp = a * 120.0;
	elseif (a <= -1.1e-187)
		tmp = y * (-60.0 / (z - t));
	elseif (a <= 1.15e-240)
		tmp = t_1;
	elseif (a <= 7.2e-87)
		tmp = -60.0 * ((x - y) / t);
	elseif (a <= 43.0)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.6e-80], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.1e-187], N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e-240], t$95$1, If[LessEqual[a, 7.2e-87], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 43.0], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.5999999999999999e-80 or 43 < 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* 99.8%

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

   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 71.9%

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

   if -1.5999999999999999e-80 < a < -1.10000000000000004e-187

   1. Initial program 94.1%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around inf 82.9%

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

      1. *-commutative 82.9%

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

   7. Simplified 82.9%

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

   8. Taylor expanded in y around inf 87.9%

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

      1. associate-/l* 82.2%

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

      2. associate-/r* 65.2%

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

      3. associate-*r/ 65.3%

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

      4. metadata-eval 65.3%

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

   10. Simplified 65.3%

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

   11. Taylor expanded in y around inf 65.9%

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

       1. associate-*r/ 65.9%

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

       2. *-rgt-identity 65.9%

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

       3. *-commutative 65.9%

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

       4. associate-*r/ 65.6%

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

       5. associate-*l* 65.5%

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

       6. metadata-eval 65.5%

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

       7. distribute-lft-neg-in 65.5%

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

       8. associate-*r/ 65.6%

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

       9. metadata-eval 65.6%

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

       10. distribute-neg-frac 65.6%

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

       11. metadata-eval 65.6%

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

   13. Simplified 65.6%

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

   if -1.10000000000000004e-187 < a < 1.14999999999999996e-240 or 7.19999999999999986e-87 < a < 43

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 86.7%

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

   6. Taylor expanded in z around inf 56.7%

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

   if 1.14999999999999996e-240 < a < 7.19999999999999986e-87

   1. Initial program 97.2%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 80.7%

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

   6. Taylor expanded in z around 0 63.4%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-80}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-187}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-240}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-87}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 43:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z}\\ t_2 := -60 \cdot \frac{x - y}{t}\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{-80}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-187}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 4.35 \cdot 10^{-240}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-88}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 64000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) z))) (t_2 (* -60.0 (/ (- x y) t))))
   (if (<= a -1.65e-80)
     (* a 120.0)
     (if (<= a -1.25e-187)
       t_2
       (if (<= a 4.35e-240)
         t_1
         (if (<= a 2.6e-88) t_2 (if (<= a 64000.0) t_1 (* a 120.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / z);
	double t_2 = -60.0 * ((x - y) / t);
	double tmp;
	if (a <= -1.65e-80) {
		tmp = a * 120.0;
	} else if (a <= -1.25e-187) {
		tmp = t_2;
	} else if (a <= 4.35e-240) {
		tmp = t_1;
	} else if (a <= 2.6e-88) {
		tmp = t_2;
	} else if (a <= 64000.0) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / z)
    t_2 = (-60.0d0) * ((x - y) / t)
    if (a <= (-1.65d-80)) then
        tmp = a * 120.0d0
    else if (a <= (-1.25d-187)) then
        tmp = t_2
    else if (a <= 4.35d-240) then
        tmp = t_1
    else if (a <= 2.6d-88) then
        tmp = t_2
    else if (a <= 64000.0d0) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / z);
	double t_2 = -60.0 * ((x - y) / t);
	double tmp;
	if (a <= -1.65e-80) {
		tmp = a * 120.0;
	} else if (a <= -1.25e-187) {
		tmp = t_2;
	} else if (a <= 4.35e-240) {
		tmp = t_1;
	} else if (a <= 2.6e-88) {
		tmp = t_2;
	} else if (a <= 64000.0) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / z)
	t_2 = -60.0 * ((x - y) / t)
	tmp = 0
	if a <= -1.65e-80:
		tmp = a * 120.0
	elif a <= -1.25e-187:
		tmp = t_2
	elif a <= 4.35e-240:
		tmp = t_1
	elif a <= 2.6e-88:
		tmp = t_2
	elif a <= 64000.0:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / z))
	t_2 = Float64(-60.0 * Float64(Float64(x - y) / t))
	tmp = 0.0
	if (a <= -1.65e-80)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.25e-187)
		tmp = t_2;
	elseif (a <= 4.35e-240)
		tmp = t_1;
	elseif (a <= 2.6e-88)
		tmp = t_2;
	elseif (a <= 64000.0)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / z);
	t_2 = -60.0 * ((x - y) / t);
	tmp = 0.0;
	if (a <= -1.65e-80)
		tmp = a * 120.0;
	elseif (a <= -1.25e-187)
		tmp = t_2;
	elseif (a <= 4.35e-240)
		tmp = t_1;
	elseif (a <= 2.6e-88)
		tmp = t_2;
	elseif (a <= 64000.0)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.65e-80], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.25e-187], t$95$2, If[LessEqual[a, 4.35e-240], t$95$1, If[LessEqual[a, 2.6e-88], t$95$2, If[LessEqual[a, 64000.0], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.65e-80 or 64000 < 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* 99.8%

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

   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 71.9%

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

   if -1.65e-80 < a < -1.2499999999999999e-187 or 4.3500000000000003e-240 < a < 2.60000000000000014e-88

   1. Initial program 96.3%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 83.0%

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

   6. Taylor expanded in z around 0 63.6%

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

   if -1.2499999999999999e-187 < a < 4.3500000000000003e-240 or 2.60000000000000014e-88 < a < 64000

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 86.7%

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

   6. Taylor expanded in z around inf 56.7%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-80}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-187}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 4.35 \cdot 10^{-240}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-88}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 64000:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-81}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-268}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-135}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-91}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 53:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.5e-81)
   (* a 120.0)
   (if (<= a 9.6e-268)
     (/ (* 60.0 y) t)
     (if (<= a 5e-135)
       (* -60.0 (/ x t))
       (if (<= a 4.2e-91)
         (* 60.0 (/ y t))
         (if (<= a 53.0) (/ (* y -60.0) z) (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.5e-81) {
		tmp = a * 120.0;
	} else if (a <= 9.6e-268) {
		tmp = (60.0 * y) / t;
	} else if (a <= 5e-135) {
		tmp = -60.0 * (x / t);
	} else if (a <= 4.2e-91) {
		tmp = 60.0 * (y / t);
	} else if (a <= 53.0) {
		tmp = (y * -60.0) / 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 <= (-3.5d-81)) then
        tmp = a * 120.0d0
    else if (a <= 9.6d-268) then
        tmp = (60.0d0 * y) / t
    else if (a <= 5d-135) then
        tmp = (-60.0d0) * (x / t)
    else if (a <= 4.2d-91) then
        tmp = 60.0d0 * (y / t)
    else if (a <= 53.0d0) then
        tmp = (y * (-60.0d0)) / 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 <= -3.5e-81) {
		tmp = a * 120.0;
	} else if (a <= 9.6e-268) {
		tmp = (60.0 * y) / t;
	} else if (a <= 5e-135) {
		tmp = -60.0 * (x / t);
	} else if (a <= 4.2e-91) {
		tmp = 60.0 * (y / t);
	} else if (a <= 53.0) {
		tmp = (y * -60.0) / z;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.5e-81:
		tmp = a * 120.0
	elif a <= 9.6e-268:
		tmp = (60.0 * y) / t
	elif a <= 5e-135:
		tmp = -60.0 * (x / t)
	elif a <= 4.2e-91:
		tmp = 60.0 * (y / t)
	elif a <= 53.0:
		tmp = (y * -60.0) / z
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.5e-81)
		tmp = Float64(a * 120.0);
	elseif (a <= 9.6e-268)
		tmp = Float64(Float64(60.0 * y) / t);
	elseif (a <= 5e-135)
		tmp = Float64(-60.0 * Float64(x / t));
	elseif (a <= 4.2e-91)
		tmp = Float64(60.0 * Float64(y / t));
	elseif (a <= 53.0)
		tmp = Float64(Float64(y * -60.0) / 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 <= -3.5e-81)
		tmp = a * 120.0;
	elseif (a <= 9.6e-268)
		tmp = (60.0 * y) / t;
	elseif (a <= 5e-135)
		tmp = -60.0 * (x / t);
	elseif (a <= 4.2e-91)
		tmp = 60.0 * (y / t);
	elseif (a <= 53.0)
		tmp = (y * -60.0) / z;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.5e-81], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 9.6e-268], N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 5e-135], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.2e-91], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 53.0], N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.49999999999999986e-81 or 53 < 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* 99.8%

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

   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 71.9%

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

   if -3.49999999999999986e-81 < a < 9.5999999999999996e-268

   1. Initial program 97.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 a around 0 92.5%

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

   6. Taylor expanded in z around 0 50.7%

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

   7. Taylor expanded in x around 0 38.2%

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

      1. associate-*r/ 38.2%

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

   9. Simplified 38.2%

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

   if 9.5999999999999996e-268 < a < 5.0000000000000002e-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* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 79.5%

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

   6. Taylor expanded in z around 0 53.3%

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

   7. Taylor expanded in x around inf 35.2%

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

   if 5.0000000000000002e-135 < a < 4.1999999999999998e-91

   1. Initial program 88.7%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around 0 78.0%

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

   6. Taylor expanded in z around 0 60.7%

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

   7. Taylor expanded in x around 0 45.7%

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

   if 4.1999999999999998e-91 < a < 53

   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* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around 0 79.1%

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

   6. Taylor expanded in x around 0 50.0%

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

      1. associate-*r/ 50.2%

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

   8. Simplified 50.2%

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

   9. Taylor expanded in z around inf 41.9%

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

       1. associate-*r/ 42.1%

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

   11. Simplified 42.1%

       \[\leadsto \color{blue}{\frac{-60 \cdot y}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-81}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{-268}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-135}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-91}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 53:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{y}{t}\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{-81}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-268}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-134}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 64000000:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ y t))))
   (if (<= a -3.9e-81)
     (* a 120.0)
     (if (<= a 1.02e-268)
       t_1
       (if (<= a 1.95e-134)
         (* -60.0 (/ x t))
         (if (<= a 4.1e-91)
           t_1
           (if (<= a 64000000.0) (/ (* y -60.0) z) (* a 120.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (y / t);
	double tmp;
	if (a <= -3.9e-81) {
		tmp = a * 120.0;
	} else if (a <= 1.02e-268) {
		tmp = t_1;
	} else if (a <= 1.95e-134) {
		tmp = -60.0 * (x / t);
	} else if (a <= 4.1e-91) {
		tmp = t_1;
	} else if (a <= 64000000.0) {
		tmp = (y * -60.0) / 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) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * (y / t)
    if (a <= (-3.9d-81)) then
        tmp = a * 120.0d0
    else if (a <= 1.02d-268) then
        tmp = t_1
    else if (a <= 1.95d-134) then
        tmp = (-60.0d0) * (x / t)
    else if (a <= 4.1d-91) then
        tmp = t_1
    else if (a <= 64000000.0d0) then
        tmp = (y * (-60.0d0)) / 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 t_1 = 60.0 * (y / t);
	double tmp;
	if (a <= -3.9e-81) {
		tmp = a * 120.0;
	} else if (a <= 1.02e-268) {
		tmp = t_1;
	} else if (a <= 1.95e-134) {
		tmp = -60.0 * (x / t);
	} else if (a <= 4.1e-91) {
		tmp = t_1;
	} else if (a <= 64000000.0) {
		tmp = (y * -60.0) / z;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (y / t)
	tmp = 0
	if a <= -3.9e-81:
		tmp = a * 120.0
	elif a <= 1.02e-268:
		tmp = t_1
	elif a <= 1.95e-134:
		tmp = -60.0 * (x / t)
	elif a <= 4.1e-91:
		tmp = t_1
	elif a <= 64000000.0:
		tmp = (y * -60.0) / z
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(y / t))
	tmp = 0.0
	if (a <= -3.9e-81)
		tmp = Float64(a * 120.0);
	elseif (a <= 1.02e-268)
		tmp = t_1;
	elseif (a <= 1.95e-134)
		tmp = Float64(-60.0 * Float64(x / t));
	elseif (a <= 4.1e-91)
		tmp = t_1;
	elseif (a <= 64000000.0)
		tmp = Float64(Float64(y * -60.0) / z);
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * (y / t);
	tmp = 0.0;
	if (a <= -3.9e-81)
		tmp = a * 120.0;
	elseif (a <= 1.02e-268)
		tmp = t_1;
	elseif (a <= 1.95e-134)
		tmp = -60.0 * (x / t);
	elseif (a <= 4.1e-91)
		tmp = t_1;
	elseif (a <= 64000000.0)
		tmp = (y * -60.0) / z;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.9e-81], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 1.02e-268], t$95$1, If[LessEqual[a, 1.95e-134], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.1e-91], t$95$1, If[LessEqual[a, 64000000.0], N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.89999999999999985e-81 or 6.4e7 < 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* 99.8%

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

   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 71.9%

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

   if -3.89999999999999985e-81 < a < 1.0200000000000001e-268 or 1.95e-134 < a < 4.10000000000000024e-91

   1. Initial program 96.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in a around 0 90.4%

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

   6. Taylor expanded in z around 0 52.1%

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

   7. Taylor expanded in x around 0 39.3%

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

   if 1.0200000000000001e-268 < a < 1.95e-134

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 79.5%

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

   6. Taylor expanded in z around 0 53.3%

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

   7. Taylor expanded in x around inf 35.2%

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

   if 4.10000000000000024e-91 < a < 6.4e7

   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* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around 0 79.1%

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

   6. Taylor expanded in x around 0 50.0%

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

      1. associate-*r/ 50.2%

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

   8. Simplified 50.2%

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

   9. Taylor expanded in z around inf 41.9%

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

       1. associate-*r/ 42.1%

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

   11. Simplified 42.1%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-81}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-268}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-134}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-91}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 64000000:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{y}{t}\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{-81}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-268}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-135}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 43:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ y t))))
   (if (<= a -4.5e-81)
     (* a 120.0)
     (if (<= a 8.5e-268)
       t_1
       (if (<= a 7.5e-135)
         (* -60.0 (/ x t))
         (if (<= a 2.8e-91)
           t_1
           (if (<= a 43.0) (* -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 * (y / t);
	double tmp;
	if (a <= -4.5e-81) {
		tmp = a * 120.0;
	} else if (a <= 8.5e-268) {
		tmp = t_1;
	} else if (a <= 7.5e-135) {
		tmp = -60.0 * (x / t);
	} else if (a <= 2.8e-91) {
		tmp = t_1;
	} else if (a <= 43.0) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * (y / t)
    if (a <= (-4.5d-81)) then
        tmp = a * 120.0d0
    else if (a <= 8.5d-268) then
        tmp = t_1
    else if (a <= 7.5d-135) then
        tmp = (-60.0d0) * (x / t)
    else if (a <= 2.8d-91) then
        tmp = t_1
    else if (a <= 43.0d0) then
        tmp = (-60.0d0) * (y / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (y / t);
	double tmp;
	if (a <= -4.5e-81) {
		tmp = a * 120.0;
	} else if (a <= 8.5e-268) {
		tmp = t_1;
	} else if (a <= 7.5e-135) {
		tmp = -60.0 * (x / t);
	} else if (a <= 2.8e-91) {
		tmp = t_1;
	} else if (a <= 43.0) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (y / t)
	tmp = 0
	if a <= -4.5e-81:
		tmp = a * 120.0
	elif a <= 8.5e-268:
		tmp = t_1
	elif a <= 7.5e-135:
		tmp = -60.0 * (x / t)
	elif a <= 2.8e-91:
		tmp = t_1
	elif a <= 43.0:
		tmp = -60.0 * (y / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(y / t))
	tmp = 0.0
	if (a <= -4.5e-81)
		tmp = Float64(a * 120.0);
	elseif (a <= 8.5e-268)
		tmp = t_1;
	elseif (a <= 7.5e-135)
		tmp = Float64(-60.0 * Float64(x / t));
	elseif (a <= 2.8e-91)
		tmp = t_1;
	elseif (a <= 43.0)
		tmp = Float64(-60.0 * Float64(y / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * (y / t);
	tmp = 0.0;
	if (a <= -4.5e-81)
		tmp = a * 120.0;
	elseif (a <= 8.5e-268)
		tmp = t_1;
	elseif (a <= 7.5e-135)
		tmp = -60.0 * (x / t);
	elseif (a <= 2.8e-91)
		tmp = t_1;
	elseif (a <= 43.0)
		tmp = -60.0 * (y / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.5e-81], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 8.5e-268], t$95$1, If[LessEqual[a, 7.5e-135], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-91], t$95$1, If[LessEqual[a, 43.0], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -4.5e-81 or 43 < 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* 99.8%

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

   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 71.9%

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

   if -4.5e-81 < a < 8.50000000000000052e-268 or 7.5e-135 < a < 2.8e-91

   1. Initial program 96.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in a around 0 90.4%

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

   6. Taylor expanded in z around 0 52.1%

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

   7. Taylor expanded in x around 0 39.3%

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

   if 8.50000000000000052e-268 < a < 7.5e-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* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 79.5%

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

   6. Taylor expanded in z around 0 53.3%

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

   7. Taylor expanded in x around inf 35.2%

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

   if 2.8e-91 < a < 43

   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* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around 0 79.1%

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

   6. Taylor expanded in x around 0 50.0%

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

      1. associate-*r/ 50.2%

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

   8. Simplified 50.2%

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

   9. Taylor expanded in z around inf 41.9%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.5 \cdot 10^{-81}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-268}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-135}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-91}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 43:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-80}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-87}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 1.76 \cdot 10^{-9}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \mathbf{elif}\;a \leq 43:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.35e-80)
   (* a 120.0)
   (if (<= a 4.4e-87)
     (* -60.0 (/ (- x y) t))
     (if (<= a 1.76e-9)
       (/ (* y -60.0) z)
       (if (<= a 43.0) (/ (* 60.0 y) t) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.35e-80) {
		tmp = a * 120.0;
	} else if (a <= 4.4e-87) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 1.76e-9) {
		tmp = (y * -60.0) / z;
	} else if (a <= 43.0) {
		tmp = (60.0 * y) / t;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.35d-80)) then
        tmp = a * 120.0d0
    else if (a <= 4.4d-87) then
        tmp = (-60.0d0) * ((x - y) / t)
    else if (a <= 1.76d-9) then
        tmp = (y * (-60.0d0)) / z
    else if (a <= 43.0d0) then
        tmp = (60.0d0 * y) / t
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.35e-80) {
		tmp = a * 120.0;
	} else if (a <= 4.4e-87) {
		tmp = -60.0 * ((x - y) / t);
	} else if (a <= 1.76e-9) {
		tmp = (y * -60.0) / z;
	} else if (a <= 43.0) {
		tmp = (60.0 * y) / t;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.35e-80:
		tmp = a * 120.0
	elif a <= 4.4e-87:
		tmp = -60.0 * ((x - y) / t)
	elif a <= 1.76e-9:
		tmp = (y * -60.0) / z
	elif a <= 43.0:
		tmp = (60.0 * y) / t
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.35e-80)
		tmp = Float64(a * 120.0);
	elseif (a <= 4.4e-87)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	elseif (a <= 1.76e-9)
		tmp = Float64(Float64(y * -60.0) / z);
	elseif (a <= 43.0)
		tmp = Float64(Float64(60.0 * y) / t);
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.35e-80)
		tmp = a * 120.0;
	elseif (a <= 4.4e-87)
		tmp = -60.0 * ((x - y) / t);
	elseif (a <= 1.76e-9)
		tmp = (y * -60.0) / z;
	elseif (a <= 43.0)
		tmp = (60.0 * y) / t;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.35e-80], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 4.4e-87], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.76e-9], N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[a, 43.0], N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.3500000000000001e-80 or 43 < 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* 99.8%

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

   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 71.9%

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

   if -1.3500000000000001e-80 < a < 4.39999999999999976e-87

   1. Initial program 97.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 86.8%

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

   6. Taylor expanded in z around 0 52.6%

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

   if 4.39999999999999976e-87 < a < 1.75999999999999992e-9

   1. Initial program 99.5%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around 0 71.9%

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

   6. Taylor expanded in x around 0 43.6%

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

      1. associate-*r/ 43.8%

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

   8. Simplified 43.8%

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

   9. Taylor expanded in z around inf 43.9%

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

       1. associate-*r/ 44.1%

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

   11. Simplified 44.1%

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

   if 1.75999999999999992e-9 < a < 43

   1. Initial program 100.0%

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

      1. associate-/l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around 0 99.5%

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

   6. Taylor expanded in z around 0 99.5%

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

   7. Taylor expanded in x around 0 99.5%

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

      1. associate-*r/ 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{-80}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-87}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;a \leq 1.76 \cdot 10^{-9}:\\ \;\;\;\;\frac{y \cdot -60}{z}\\ \mathbf{elif}\;a \leq 43:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 82.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-78} \lor \neg \left(a \cdot 120 \leq 10000\right):\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -4e-78) (not (<= (* a 120.0) 10000.0)))
   (+ (* a 120.0) (* x (/ 60.0 (- z t))))
   (* 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) <= -4e-78) || !((a * 120.0) <= 10000.0)) {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-4d-78)) .or. (.not. ((a * 120.0d0) <= 10000.0d0))) then
        tmp = (a * 120.0d0) + (x * (60.0d0 / (z - t)))
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -4e-78) || !((a * 120.0) <= 10000.0)) {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -4e-78) or not ((a * 120.0) <= 10000.0):
		tmp = (a * 120.0) + (x * (60.0 / (z - t)))
	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) <= -4e-78) || !(Float64(a * 120.0) <= 10000.0))
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))));
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -4e-78) || ~(((a * 120.0) <= 10000.0)))
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	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], -4e-78], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 10000.0]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -4e-78 or 1e4 < (*.f64 a #s(literal 120 binary64))

   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 inf 85.4%

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

      1. associate-*r/ 84.7%

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

      2. *-commutative 84.7%

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

      3. associate-*r/ 85.4%

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

   7. Simplified 85.4%

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

   if -4e-78 < (*.f64 a #s(literal 120 binary64)) < 1e4

   1. Initial program 98.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 a around 0 85.0%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-78} \lor \neg \left(a \cdot 120 \leq 10000\right):\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-20} \lor \neg \left(a \cdot 120 \leq 10000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -5e-20) (not (<= (* a 120.0) 10000.0)))
   (* 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) <= -5e-20) || !((a * 120.0) <= 10000.0)) {
		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) <= (-5d-20)) .or. (.not. ((a * 120.0d0) <= 10000.0d0))) 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) <= -5e-20) || !((a * 120.0) <= 10000.0)) {
		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) <= -5e-20) or not ((a * 120.0) <= 10000.0):
		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) <= -5e-20) || !(Float64(a * 120.0) <= 10000.0))
		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) <= -5e-20) || ~(((a * 120.0) <= 10000.0)))
		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], -5e-20], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 10000.0]], $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)) < -4.9999999999999999e-20 or 1e4 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.1%

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

      1. associate-/l* 99.8%

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

   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 73.9%

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

   if -4.9999999999999999e-20 < (*.f64 a #s(literal 120 binary64)) < 1e4

   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%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 82.1%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-20} \lor \neg \left(a \cdot 120 \leq 10000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-78}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 10000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e-78)
   (+ (* a 120.0) (* 60.0 (/ y t)))
   (if (<= (* a 120.0) 10000.0) (* 60.0 (/ (- x y) (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e-78) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= 10000.0) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-4d-78)) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / t))
    else if ((a * 120.0d0) <= 10000.0d0) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e-78) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= 10000.0) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -4e-78:
		tmp = (a * 120.0) + (60.0 * (y / t))
	elif (a * 120.0) <= 10000.0:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e-78)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	elseif (Float64(a * 120.0) <= 10000.0)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -4e-78)
		tmp = (a * 120.0) + (60.0 * (y / t));
	elseif ((a * 120.0) <= 10000.0)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-78], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 10000.0], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -4e-78

   1. Initial program 98.5%

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

      1. *-commutative 98.5%

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

      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 z around 0 76.1%

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

   6. Taylor expanded in x around 0 70.3%

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

   if -4e-78 < (*.f64 a #s(literal 120 binary64)) < 1e4

   1. Initial program 98.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 a around 0 85.0%

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

   if 1e4 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 100.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 76.8%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-78}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 10000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-41} \lor \neg \left(t \leq 1.52 \cdot 10^{-61}\right):\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.6e-41) (not (<= t 1.52e-61)))
   (+ (* a 120.0) (* (- x y) (/ -60.0 t)))
   (+ (* a 120.0) (* (- x y) (/ 60.0 z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.6e-41) || !(t <= 1.52e-61)) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else {
		tmp = (a * 120.0) + ((x - y) * (60.0 / 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 ((t <= (-2.6d-41)) .or. (.not. (t <= 1.52d-61))) then
        tmp = (a * 120.0d0) + ((x - y) * ((-60.0d0) / t))
    else
        tmp = (a * 120.0d0) + ((x - y) * (60.0d0 / 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 ((t <= -2.6e-41) || !(t <= 1.52e-61)) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else {
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.6e-41) or not (t <= 1.52e-61):
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t))
	else:
		tmp = (a * 120.0) + ((x - y) * (60.0 / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.6e-41) || !(t <= 1.52e-61))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(-60.0 / t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(60.0 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.6e-41) || ~((t <= 1.52e-61)))
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	else
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.6e-41], N[Not[LessEqual[t, 1.52e-61]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.5999999999999999e-41 or 1.52000000000000003e-61 < t

   1. Initial program 98.5%

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

      1. *-commutative 98.5%

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

      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 z around 0 88.7%

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

   if -2.5999999999999999e-41 < t < 1.52000000000000003e-61

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

      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 z around inf 88.0%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-41} \lor \neg \left(t \leq 1.52 \cdot 10^{-61}\right):\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 89.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+28}:\\ \;\;\;\;a \cdot 120 + \frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-8}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.8e+28)
   (+ (* a 120.0) (/ x (* (- z t) 0.016666666666666666)))
   (if (<= x 1.32e-8)
     (+ (* a 120.0) (/ (* y -60.0) (- z t)))
     (+ (* 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 <= -1.8e+28) {
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666));
	} else if (x <= 1.32e-8) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} 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 <= (-1.8d+28)) then
        tmp = (a * 120.0d0) + (x / ((z - t) * 0.016666666666666666d0))
    else if (x <= 1.32d-8) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    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 <= -1.8e+28) {
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666));
	} else if (x <= 1.32e-8) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.8e+28:
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666))
	elif x <= 1.32e-8:
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	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 <= -1.8e+28)
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(Float64(z - t) * 0.016666666666666666)));
	elseif (x <= 1.32e-8)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.8e+28)
		tmp = (a * 120.0) + (x / ((z - t) * 0.016666666666666666));
	elseif (x <= 1.32e-8)
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	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, -1.8e+28], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.32e-8], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.8e28

   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* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 86.2%

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

      1. associate-*r/ 84.5%

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

      2. *-commutative 84.5%

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

      3. associate-*r/ 86.2%

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

   7. Simplified 86.2%

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

      1. clear-num 86.1%

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

      2. un-div-inv 86.2%

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

      3. div-inv 86.2%

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

      4. metadata-eval 86.2%

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

   9. Applied egg-rr 86.2%

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

   if -1.8e28 < x < 1.32000000000000007e-8

   1. Initial program 99.1%

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

      1. associate-/l* 99.8%

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

   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 96.6%

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

      1. associate-*r/ 95.9%

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

   7. Simplified 95.9%

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

   if 1.32000000000000007e-8 < x

   1. Initial program 98.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 x around inf 89.9%

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

      1. associate-*r/ 88.2%

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

      2. *-commutative 88.2%

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

      3. associate-*r/ 89.9%

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

   7. Simplified 89.9%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+28}:\\ \;\;\;\;a \cdot 120 + \frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-8}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-115}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-240}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-114}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.5e-115)
   (* a 120.0)
   (if (<= a 8.6e-240)
     (* -60.0 (/ y z))
     (if (<= a 1.02e-114) (* -60.0 (/ x t)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e-115) {
		tmp = a * 120.0;
	} else if (a <= 8.6e-240) {
		tmp = -60.0 * (y / z);
	} else if (a <= 1.02e-114) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9.5d-115)) then
        tmp = a * 120.0d0
    else if (a <= 8.6d-240) then
        tmp = (-60.0d0) * (y / z)
    else if (a <= 1.02d-114) then
        tmp = (-60.0d0) * (x / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.5e-115) {
		tmp = a * 120.0;
	} else if (a <= 8.6e-240) {
		tmp = -60.0 * (y / z);
	} else if (a <= 1.02e-114) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.5e-115:
		tmp = a * 120.0
	elif a <= 8.6e-240:
		tmp = -60.0 * (y / z)
	elif a <= 1.02e-114:
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.5e-115)
		tmp = Float64(a * 120.0);
	elseif (a <= 8.6e-240)
		tmp = Float64(-60.0 * Float64(y / z));
	elseif (a <= 1.02e-114)
		tmp = Float64(-60.0 * Float64(x / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.5e-115)
		tmp = a * 120.0;
	elseif (a <= 8.6e-240)
		tmp = -60.0 * (y / z);
	elseif (a <= 1.02e-114)
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.5e-115], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 8.6e-240], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e-114], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.4999999999999996e-115 or 1.0199999999999999e-114 < 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%

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

   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 62.6%

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

   if -9.4999999999999996e-115 < a < 8.60000000000000027e-240

   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%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 93.0%

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

   6. Taylor expanded in x around 0 51.1%

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

      1. associate-*r/ 51.2%

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

   8. Simplified 51.2%

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

   9. Taylor expanded in z around inf 22.6%

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

   if 8.60000000000000027e-240 < a < 1.0199999999999999e-114

   1. Initial program 96.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in a around 0 81.9%

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

   6. Taylor expanded in z around 0 67.9%

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

   7. Taylor expanded in x around inf 40.9%

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

4. Final simplification 50.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9.5 \cdot 10^{-115}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-240}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-114}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 53.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-151} \lor \neg \left(a \leq 2.35 \cdot 10^{-114}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.2e-151) (not (<= a 2.35e-114)))
   (* a 120.0)
   (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.2e-151) || !(a <= 2.35e-114)) {
		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 <= (-1.2d-151)) .or. (.not. (a <= 2.35d-114))) 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 <= -1.2e-151) || !(a <= 2.35e-114)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.2e-151) or not (a <= 2.35e-114):
		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 <= -1.2e-151) || !(a <= 2.35e-114))
		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 <= -1.2e-151) || ~((a <= 2.35e-114)))
		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, -1.2e-151], N[Not[LessEqual[a, 2.35e-114]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.2e-151 or 2.35000000000000003e-114 < 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 60.8%

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

   if -1.2e-151 < a < 2.35000000000000003e-114

   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%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 88.4%

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

   6. Taylor expanded in z around 0 52.8%

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

   7. Taylor expanded in x around inf 25.2%

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

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{-151} \lor \neg \left(a \leq 2.35 \cdot 10^{-114}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 99.7% 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 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. Final simplification 99.8%

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

Alternative 19: 51.6% 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 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 45.4%

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

6. Final simplification 45.4%

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

Developer target: 99.7% 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 2024101 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

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

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