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

Percentage Accurate: 99.4% → 99.8%

Time: 13.7s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. associate-/l* 99.7%

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

   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: 70.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-73}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-58}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (/ (* y -60.0) z))))
   (if (<= (* a 120.0) -4e-30)
     t_1
     (if (<= (* a 120.0) -2e-73)
       (* 60.0 (/ x (- z t)))
       (if (<= (* a 120.0) -5e-125)
         t_1
         (if (<= (* a 120.0) 2e-58)
           (/ 60.0 (/ (- z t) (- x y)))
           (+ (* a 120.0) (* 60.0 (/ x z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((y * -60.0) / z);
	double tmp;
	if ((a * 120.0) <= -4e-30) {
		tmp = t_1;
	} else if ((a * 120.0) <= -2e-73) {
		tmp = 60.0 * (x / (z - t));
	} else if ((a * 120.0) <= -5e-125) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-58) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((y * (-60.0d0)) / z)
    if ((a * 120.0d0) <= (-4d-30)) then
        tmp = t_1
    else if ((a * 120.0d0) <= (-2d-73)) then
        tmp = 60.0d0 * (x / (z - t))
    else if ((a * 120.0d0) <= (-5d-125)) then
        tmp = t_1
    else if ((a * 120.0d0) <= 2d-58) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((y * -60.0) / z);
	double tmp;
	if ((a * 120.0) <= -4e-30) {
		tmp = t_1;
	} else if ((a * 120.0) <= -2e-73) {
		tmp = 60.0 * (x / (z - t));
	} else if ((a * 120.0) <= -5e-125) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-58) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + ((y * -60.0) / z)
	tmp = 0
	if (a * 120.0) <= -4e-30:
		tmp = t_1
	elif (a * 120.0) <= -2e-73:
		tmp = 60.0 * (x / (z - t))
	elif (a * 120.0) <= -5e-125:
		tmp = t_1
	elif (a * 120.0) <= 2e-58:
		tmp = 60.0 / ((z - t) / (x - y))
	else:
		tmp = (a * 120.0) + (60.0 * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / z))
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e-30)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= -2e-73)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (Float64(a * 120.0) <= -5e-125)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 2e-58)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + ((y * -60.0) / z);
	tmp = 0.0;
	if ((a * 120.0) <= -4e-30)
		tmp = t_1;
	elseif ((a * 120.0) <= -2e-73)
		tmp = 60.0 * (x / (z - t));
	elseif ((a * 120.0) <= -5e-125)
		tmp = t_1;
	elseif ((a * 120.0) <= 2e-58)
		tmp = 60.0 / ((z - t) / (x - y));
	else
		tmp = (a * 120.0) + (60.0 * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-30], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-73], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-125], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-58], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -4e-30 or -1.99999999999999999e-73 < (*.f64 a #s(literal 120 binary64)) < -4.99999999999999967e-125

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 89.5%

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

      1. associate-*r/ 89.4%

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

   7. Simplified 89.4%

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

   8. Taylor expanded in z around inf 80.8%

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

      1. associate-*r/ 80.8%

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

   10. Simplified 80.8%

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

   if -4e-30 < (*.f64 a #s(literal 120 binary64)) < -1.99999999999999999e-73

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 75.4%

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

   6. Taylor expanded in x around inf 75.4%

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

   if -4.99999999999999967e-125 < (*.f64 a #s(literal 120 binary64)) < 2.0000000000000001e-58

   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 84.9%

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

      1. clear-num 84.9%

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

      2. un-div-inv 85.0%

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

   7. Applied egg-rr 85.0%

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

   if 2.0000000000000001e-58 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   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 85.2%

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

   6. Taylor expanded in z around inf 70.0%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-30}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-73}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-125}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-58}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-73}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-58}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (/ (* y -60.0) z))))
   (if (<= (* a 120.0) -4e-30)
     t_1
     (if (<= (* a 120.0) -2e-73)
       (* 60.0 (/ x (- z t)))
       (if (<= (* a 120.0) -5e-125)
         t_1
         (if (<= (* a 120.0) 2e-58)
           (* 60.0 (/ (- x y) (- z t)))
           (+ (* a 120.0) (* 60.0 (/ x z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((y * -60.0) / z);
	double tmp;
	if ((a * 120.0) <= -4e-30) {
		tmp = t_1;
	} else if ((a * 120.0) <= -2e-73) {
		tmp = 60.0 * (x / (z - t));
	} else if ((a * 120.0) <= -5e-125) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-58) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((y * (-60.0d0)) / z)
    if ((a * 120.0d0) <= (-4d-30)) then
        tmp = t_1
    else if ((a * 120.0d0) <= (-2d-73)) then
        tmp = 60.0d0 * (x / (z - t))
    else if ((a * 120.0d0) <= (-5d-125)) then
        tmp = t_1
    else if ((a * 120.0d0) <= 2d-58) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + ((y * -60.0) / z);
	double tmp;
	if ((a * 120.0) <= -4e-30) {
		tmp = t_1;
	} else if ((a * 120.0) <= -2e-73) {
		tmp = 60.0 * (x / (z - t));
	} else if ((a * 120.0) <= -5e-125) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-58) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + ((y * -60.0) / z)
	tmp = 0
	if (a * 120.0) <= -4e-30:
		tmp = t_1
	elif (a * 120.0) <= -2e-73:
		tmp = 60.0 * (x / (z - t))
	elif (a * 120.0) <= -5e-125:
		tmp = t_1
	elif (a * 120.0) <= 2e-58:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + (60.0 * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / z))
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e-30)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= -2e-73)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (Float64(a * 120.0) <= -5e-125)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 2e-58)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + ((y * -60.0) / z);
	tmp = 0.0;
	if ((a * 120.0) <= -4e-30)
		tmp = t_1;
	elseif ((a * 120.0) <= -2e-73)
		tmp = 60.0 * (x / (z - t));
	elseif ((a * 120.0) <= -5e-125)
		tmp = t_1;
	elseif ((a * 120.0) <= 2e-58)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + (60.0 * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-30], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-73], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-125], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-58], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -4e-30 or -1.99999999999999999e-73 < (*.f64 a #s(literal 120 binary64)) < -4.99999999999999967e-125

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 89.5%

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

      1. associate-*r/ 89.4%

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

   7. Simplified 89.4%

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

   8. Taylor expanded in z around inf 80.8%

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

      1. associate-*r/ 80.8%

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

   10. Simplified 80.8%

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

   if -4e-30 < (*.f64 a #s(literal 120 binary64)) < -1.99999999999999999e-73

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 75.4%

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

   6. Taylor expanded in x around inf 75.4%

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

   if -4.99999999999999967e-125 < (*.f64 a #s(literal 120 binary64)) < 2.0000000000000001e-58

   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 84.9%

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

   if 2.0000000000000001e-58 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   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 85.2%

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

   6. Taylor expanded in z around inf 70.0%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-30}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-73}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-125}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-58}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+143}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-126}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-216}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;y \leq 75000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+118}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.85e+143)
   (* -60.0 (/ y (- z t)))
   (if (<= y -4.2e-126)
     (* a 120.0)
     (if (<= y -6e-216)
       (* x (/ 60.0 (- z t)))
       (if (<= y 75000000.0)
         (* a 120.0)
         (if (<= y 6e+118) (/ (* 60.0 x) (- z t)) (/ (* y -60.0) (- z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.85e+143) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= -4.2e-126) {
		tmp = a * 120.0;
	} else if (y <= -6e-216) {
		tmp = x * (60.0 / (z - t));
	} else if (y <= 75000000.0) {
		tmp = a * 120.0;
	} else if (y <= 6e+118) {
		tmp = (60.0 * x) / (z - t);
	} else {
		tmp = (y * -60.0) / (z - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.85d+143)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (y <= (-4.2d-126)) then
        tmp = a * 120.0d0
    else if (y <= (-6d-216)) then
        tmp = x * (60.0d0 / (z - t))
    else if (y <= 75000000.0d0) then
        tmp = a * 120.0d0
    else if (y <= 6d+118) then
        tmp = (60.0d0 * x) / (z - t)
    else
        tmp = (y * (-60.0d0)) / (z - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.85e+143) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= -4.2e-126) {
		tmp = a * 120.0;
	} else if (y <= -6e-216) {
		tmp = x * (60.0 / (z - t));
	} else if (y <= 75000000.0) {
		tmp = a * 120.0;
	} else if (y <= 6e+118) {
		tmp = (60.0 * x) / (z - t);
	} else {
		tmp = (y * -60.0) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.85e+143:
		tmp = -60.0 * (y / (z - t))
	elif y <= -4.2e-126:
		tmp = a * 120.0
	elif y <= -6e-216:
		tmp = x * (60.0 / (z - t))
	elif y <= 75000000.0:
		tmp = a * 120.0
	elif y <= 6e+118:
		tmp = (60.0 * x) / (z - t)
	else:
		tmp = (y * -60.0) / (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.85e+143)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (y <= -4.2e-126)
		tmp = Float64(a * 120.0);
	elseif (y <= -6e-216)
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	elseif (y <= 75000000.0)
		tmp = Float64(a * 120.0);
	elseif (y <= 6e+118)
		tmp = Float64(Float64(60.0 * x) / Float64(z - t));
	else
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.85e+143)
		tmp = -60.0 * (y / (z - t));
	elseif (y <= -4.2e-126)
		tmp = a * 120.0;
	elseif (y <= -6e-216)
		tmp = x * (60.0 / (z - t));
	elseif (y <= 75000000.0)
		tmp = a * 120.0;
	elseif (y <= 6e+118)
		tmp = (60.0 * x) / (z - t);
	else
		tmp = (y * -60.0) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.85e+143], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.2e-126], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -6e-216], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 75000000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, 6e+118], N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.8500000000000001e143

   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* 99.6%

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

   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 77.7%

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

   6. Taylor expanded in x around 0 71.4%

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

   if -1.8500000000000001e143 < y < -4.1999999999999997e-126 or -6.00000000000000025e-216 < y < 7.5e7

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   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 58.9%

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

   if -4.1999999999999997e-126 < y < -6.00000000000000025e-216

   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* 99.7%

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

   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 72.0%

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

   6. Taylor expanded in x around inf 72.1%

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

      1. associate-*r/ 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*r/ 99.9%

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

   8. Simplified 72.2%

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

   if 7.5e7 < y < 6e118

   1. Initial program 99.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 73.2%

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

   6. Taylor expanded in x around inf 56.6%

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

      1. associate-*r/ 56.7%

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

   8. Simplified 56.7%

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

   if 6e118 < y

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   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 82.8%

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

   6. Taylor expanded in x around 0 71.1%

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

      1. associate-*r/ 87.9%

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

   8. Simplified 71.1%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+143}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-126}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-216}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;y \leq 75000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+118}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+144}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-126}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-216}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;y \leq 80000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+118}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.4e+144)
   (* -60.0 (/ y (- z t)))
   (if (<= y -5.2e-126)
     (* a 120.0)
     (if (<= y -3e-216)
       (* x (/ 60.0 (- z t)))
       (if (<= y 80000000.0)
         (* a 120.0)
         (if (<= y 6e+118) (* 60.0 (/ x (- z t))) (/ (* y -60.0) (- z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.4e+144) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= -5.2e-126) {
		tmp = a * 120.0;
	} else if (y <= -3e-216) {
		tmp = x * (60.0 / (z - t));
	} else if (y <= 80000000.0) {
		tmp = a * 120.0;
	} else if (y <= 6e+118) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = (y * -60.0) / (z - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.4d+144)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (y <= (-5.2d-126)) then
        tmp = a * 120.0d0
    else if (y <= (-3d-216)) then
        tmp = x * (60.0d0 / (z - t))
    else if (y <= 80000000.0d0) then
        tmp = a * 120.0d0
    else if (y <= 6d+118) then
        tmp = 60.0d0 * (x / (z - t))
    else
        tmp = (y * (-60.0d0)) / (z - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.4e+144) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= -5.2e-126) {
		tmp = a * 120.0;
	} else if (y <= -3e-216) {
		tmp = x * (60.0 / (z - t));
	} else if (y <= 80000000.0) {
		tmp = a * 120.0;
	} else if (y <= 6e+118) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = (y * -60.0) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.4e+144:
		tmp = -60.0 * (y / (z - t))
	elif y <= -5.2e-126:
		tmp = a * 120.0
	elif y <= -3e-216:
		tmp = x * (60.0 / (z - t))
	elif y <= 80000000.0:
		tmp = a * 120.0
	elif y <= 6e+118:
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = (y * -60.0) / (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.4e+144)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (y <= -5.2e-126)
		tmp = Float64(a * 120.0);
	elseif (y <= -3e-216)
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	elseif (y <= 80000000.0)
		tmp = Float64(a * 120.0);
	elseif (y <= 6e+118)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	else
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.4e+144)
		tmp = -60.0 * (y / (z - t));
	elseif (y <= -5.2e-126)
		tmp = a * 120.0;
	elseif (y <= -3e-216)
		tmp = x * (60.0 / (z - t));
	elseif (y <= 80000000.0)
		tmp = a * 120.0;
	elseif (y <= 6e+118)
		tmp = 60.0 * (x / (z - t));
	else
		tmp = (y * -60.0) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.4e+144], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.2e-126], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -3e-216], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 80000000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, 6e+118], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.40000000000000003e144

   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* 99.6%

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

   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 77.7%

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

   6. Taylor expanded in x around 0 71.4%

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

   if -1.40000000000000003e144 < y < -5.19999999999999998e-126 or -3.00000000000000013e-216 < y < 8e7

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   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 58.9%

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

   if -5.19999999999999998e-126 < y < -3.00000000000000013e-216

   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* 99.7%

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

   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 72.0%

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

   6. Taylor expanded in x around inf 72.1%

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

      1. associate-*r/ 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*r/ 99.9%

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

   8. Simplified 72.2%

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

   if 8e7 < y < 6e118

   1. Initial program 99.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 73.2%

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

   6. Taylor expanded in x around inf 56.6%

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

   if 6e118 < y

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   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 82.8%

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

   6. Taylor expanded in x around 0 71.1%

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

      1. associate-*r/ 87.9%

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

   8. Simplified 71.1%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+144}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-126}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-216}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;y \leq 80000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+118}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -4 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-126}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-216}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;y \leq 850000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+118}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= y -4e+141)
     t_1
     (if (<= y -3.3e-126)
       (* a 120.0)
       (if (<= y -6e-216)
         (* x (/ 60.0 (- z t)))
         (if (<= y 850000.0)
           (* a 120.0)
           (if (<= y 6e+118) (* 60.0 (/ x (- z t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -4e+141) {
		tmp = t_1;
	} else if (y <= -3.3e-126) {
		tmp = a * 120.0;
	} else if (y <= -6e-216) {
		tmp = x * (60.0 / (z - t));
	} else if (y <= 850000.0) {
		tmp = a * 120.0;
	} else if (y <= 6e+118) {
		tmp = 60.0 * (x / (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 = (-60.0d0) * (y / (z - t))
    if (y <= (-4d+141)) then
        tmp = t_1
    else if (y <= (-3.3d-126)) then
        tmp = a * 120.0d0
    else if (y <= (-6d-216)) then
        tmp = x * (60.0d0 / (z - t))
    else if (y <= 850000.0d0) then
        tmp = a * 120.0d0
    else if (y <= 6d+118) then
        tmp = 60.0d0 * (x / (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 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -4e+141) {
		tmp = t_1;
	} else if (y <= -3.3e-126) {
		tmp = a * 120.0;
	} else if (y <= -6e-216) {
		tmp = x * (60.0 / (z - t));
	} else if (y <= 850000.0) {
		tmp = a * 120.0;
	} else if (y <= 6e+118) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	tmp = 0
	if y <= -4e+141:
		tmp = t_1
	elif y <= -3.3e-126:
		tmp = a * 120.0
	elif y <= -6e-216:
		tmp = x * (60.0 / (z - t))
	elif y <= 850000.0:
		tmp = a * 120.0
	elif y <= 6e+118:
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (y <= -4e+141)
		tmp = t_1;
	elseif (y <= -3.3e-126)
		tmp = Float64(a * 120.0);
	elseif (y <= -6e-216)
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	elseif (y <= 850000.0)
		tmp = Float64(a * 120.0);
	elseif (y <= 6e+118)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (y <= -4e+141)
		tmp = t_1;
	elseif (y <= -3.3e-126)
		tmp = a * 120.0;
	elseif (y <= -6e-216)
		tmp = x * (60.0 / (z - t));
	elseif (y <= 850000.0)
		tmp = a * 120.0;
	elseif (y <= 6e+118)
		tmp = 60.0 * (x / (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e+141], t$95$1, If[LessEqual[y, -3.3e-126], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -6e-216], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 850000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, 6e+118], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.00000000000000007e141 or 6e118 < y

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   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 80.6%

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

   6. Taylor expanded in x around 0 71.2%

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

   if -4.00000000000000007e141 < y < -3.3000000000000001e-126 or -6.00000000000000025e-216 < y < 8.5e5

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   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 58.9%

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

   if -3.3000000000000001e-126 < y < -6.00000000000000025e-216

   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* 99.7%

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

   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 72.0%

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

   6. Taylor expanded in x around inf 72.1%

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

      1. associate-*r/ 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*r/ 99.9%

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

   8. Simplified 72.2%

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

   if 8.5e5 < y < 6e118

   1. Initial program 99.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 73.2%

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

   6. Taylor expanded in x around inf 56.6%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+141}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-126}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-216}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;y \leq 850000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+118}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ t_2 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+142}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-126}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 14000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x (- z t)))) (t_2 (* -60.0 (/ y (- z t)))))
   (if (<= y -1.5e+142)
     t_2
     (if (<= y -4.2e-126)
       (* a 120.0)
       (if (<= y -6e-216)
         t_1
         (if (<= y 14000000.0) (* a 120.0) (if (<= y 7.2e+118) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double t_2 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -1.5e+142) {
		tmp = t_2;
	} else if (y <= -4.2e-126) {
		tmp = a * 120.0;
	} else if (y <= -6e-216) {
		tmp = t_1;
	} else if (y <= 14000000.0) {
		tmp = a * 120.0;
	} else if (y <= 7.2e+118) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 / (z - t))
    t_2 = (-60.0d0) * (y / (z - t))
    if (y <= (-1.5d+142)) then
        tmp = t_2
    else if (y <= (-4.2d-126)) then
        tmp = a * 120.0d0
    else if (y <= (-6d-216)) then
        tmp = t_1
    else if (y <= 14000000.0d0) then
        tmp = a * 120.0d0
    else if (y <= 7.2d+118) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double t_2 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -1.5e+142) {
		tmp = t_2;
	} else if (y <= -4.2e-126) {
		tmp = a * 120.0;
	} else if (y <= -6e-216) {
		tmp = t_1;
	} else if (y <= 14000000.0) {
		tmp = a * 120.0;
	} else if (y <= 7.2e+118) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (x / (z - t))
	t_2 = -60.0 * (y / (z - t))
	tmp = 0
	if y <= -1.5e+142:
		tmp = t_2
	elif y <= -4.2e-126:
		tmp = a * 120.0
	elif y <= -6e-216:
		tmp = t_1
	elif y <= 14000000.0:
		tmp = a * 120.0
	elif y <= 7.2e+118:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(x / Float64(z - t)))
	t_2 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (y <= -1.5e+142)
		tmp = t_2;
	elseif (y <= -4.2e-126)
		tmp = Float64(a * 120.0);
	elseif (y <= -6e-216)
		tmp = t_1;
	elseif (y <= 14000000.0)
		tmp = Float64(a * 120.0);
	elseif (y <= 7.2e+118)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * (x / (z - t));
	t_2 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (y <= -1.5e+142)
		tmp = t_2;
	elseif (y <= -4.2e-126)
		tmp = a * 120.0;
	elseif (y <= -6e-216)
		tmp = t_1;
	elseif (y <= 14000000.0)
		tmp = a * 120.0;
	elseif (y <= 7.2e+118)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.5e+142], t$95$2, If[LessEqual[y, -4.2e-126], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -6e-216], t$95$1, If[LessEqual[y, 14000000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, 7.2e+118], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.49999999999999987e142 or 7.2e118 < y

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   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 80.6%

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

   6. Taylor expanded in x around 0 71.2%

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

   if -1.49999999999999987e142 < y < -4.1999999999999997e-126 or -6.00000000000000025e-216 < y < 1.4e7

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   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 58.9%

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

   if -4.1999999999999997e-126 < y < -6.00000000000000025e-216 or 1.4e7 < y < 7.2e118

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   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 72.6%

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

   6. Taylor expanded in x around inf 64.9%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+142}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-126}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-216}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;y \leq 14000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+118}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+102}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{+71} \lor \neg \left(y \leq 1.86 \cdot 10^{+87}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= y -1.35e+143)
     t_1
     (if (<= y -2.4e+102)
       (+ (* a 120.0) (* 60.0 (/ y t)))
       (if (or (<= y -2.05e+71) (not (<= y 1.86e+87)))
         t_1
         (+ (* a 120.0) (* 60.0 (/ x (- z t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if (y <= -1.35e+143) {
		tmp = t_1;
	} else if (y <= -2.4e+102) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((y <= -2.05e+71) || !(y <= 1.86e+87)) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    if (y <= (-1.35d+143)) then
        tmp = t_1
    else if (y <= (-2.4d+102)) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / t))
    else if ((y <= (-2.05d+71)) .or. (.not. (y <= 1.86d+87))) then
        tmp = t_1
    else
        tmp = (a * 120.0d0) + (60.0d0 * (x / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if (y <= -1.35e+143) {
		tmp = t_1;
	} else if (y <= -2.4e+102) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((y <= -2.05e+71) || !(y <= 1.86e+87)) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if y <= -1.35e+143:
		tmp = t_1
	elif y <= -2.4e+102:
		tmp = (a * 120.0) + (60.0 * (y / t))
	elif (y <= -2.05e+71) or not (y <= 1.86e+87):
		tmp = t_1
	else:
		tmp = (a * 120.0) + (60.0 * (x / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (y <= -1.35e+143)
		tmp = t_1;
	elseif (y <= -2.4e+102)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	elseif ((y <= -2.05e+71) || !(y <= 1.86e+87))
		tmp = t_1;
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	tmp = 0.0;
	if (y <= -1.35e+143)
		tmp = t_1;
	elseif (y <= -2.4e+102)
		tmp = (a * 120.0) + (60.0 * (y / t));
	elseif ((y <= -2.05e+71) || ~((y <= 1.86e+87)))
		tmp = t_1;
	else
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e+143], t$95$1, If[LessEqual[y, -2.4e+102], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -2.05e+71], N[Not[LessEqual[y, 1.86e+87]], $MachinePrecision]], t$95$1, N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3500000000000001e143 or -2.39999999999999994e102 < y < -2.0500000000000001e71 or 1.86000000000000011e87 < y

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   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 82.0%

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

   if -1.3500000000000001e143 < y < -2.39999999999999994e102

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   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 99.8%

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

      1. associate-*r/ 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around 0 99.8%

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

   if -2.0500000000000001e71 < y < 1.86000000000000011e87

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 91.6%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+143}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+102}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{+71} \lor \neg \left(y \leq 1.86 \cdot 10^{+87}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;y \leq -1.22 \cdot 10^{+142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+100}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-21}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+87}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= y -1.22e+142)
     t_1
     (if (<= y -3.4e+100)
       (+ (* a 120.0) (* 60.0 (/ y t)))
       (if (<= y -2e-21)
         (+ (* a 120.0) (* (- x y) (/ 60.0 z)))
         (if (<= y 2.2e+87) (+ (* a 120.0) (* 60.0 (/ x (- z t)))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if (y <= -1.22e+142) {
		tmp = t_1;
	} else if (y <= -3.4e+100) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if (y <= -2e-21) {
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	} else if (y <= 2.2e+87) {
		tmp = (a * 120.0) + (60.0 * (x / (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 = 60.0d0 * ((x - y) / (z - t))
    if (y <= (-1.22d+142)) then
        tmp = t_1
    else if (y <= (-3.4d+100)) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / t))
    else if (y <= (-2d-21)) then
        tmp = (a * 120.0d0) + ((x - y) * (60.0d0 / z))
    else if (y <= 2.2d+87) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / (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 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if (y <= -1.22e+142) {
		tmp = t_1;
	} else if (y <= -3.4e+100) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if (y <= -2e-21) {
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	} else if (y <= 2.2e+87) {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if y <= -1.22e+142:
		tmp = t_1
	elif y <= -3.4e+100:
		tmp = (a * 120.0) + (60.0 * (y / t))
	elif y <= -2e-21:
		tmp = (a * 120.0) + ((x - y) * (60.0 / z))
	elif y <= 2.2e+87:
		tmp = (a * 120.0) + (60.0 * (x / (z - t)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (y <= -1.22e+142)
		tmp = t_1;
	elseif (y <= -3.4e+100)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	elseif (y <= -2e-21)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(60.0 / z)));
	elseif (y <= 2.2e+87)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / Float64(z - t))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	tmp = 0.0;
	if (y <= -1.22e+142)
		tmp = t_1;
	elseif (y <= -3.4e+100)
		tmp = (a * 120.0) + (60.0 * (y / t));
	elseif (y <= -2e-21)
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	elseif (y <= 2.2e+87)
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.22e+142], t$95$1, If[LessEqual[y, -3.4e+100], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2e-21], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+87], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.21999999999999998e142 or 2.2000000000000001e87 < y

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   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 81.3%

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

   if -1.21999999999999998e142 < y < -3.39999999999999994e100

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   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 99.8%

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

      1. associate-*r/ 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around 0 99.8%

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

   if -3.39999999999999994e100 < y < -1.99999999999999982e-21

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      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 86.4%

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

   if -1.99999999999999982e-21 < y < 2.2000000000000001e87

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   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 92.7%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+142}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{+100}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-21}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+87}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -0.0002:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-58}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+129}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -0.0002)
   (* a 120.0)
   (if (<= (* a 120.0) 2e-58)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= (* a 120.0) 1e+129)
       (+ (* a 120.0) (* -60.0 (/ x t)))
       (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -0.0002) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e-58) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 1e+129) {
		tmp = (a * 120.0) + (-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 * 120.0d0) <= (-0.0002d0)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 2d-58) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if ((a * 120.0d0) <= 1d+129) then
        tmp = (a * 120.0d0) + ((-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 * 120.0) <= -0.0002) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e-58) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 1e+129) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -0.0002:
		tmp = a * 120.0
	elif (a * 120.0) <= 2e-58:
		tmp = 60.0 * ((x - y) / (z - t))
	elif (a * 120.0) <= 1e+129:
		tmp = (a * 120.0) + (-60.0 * (x / t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -0.0002)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 2e-58)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 1e+129)
		tmp = Float64(Float64(a * 120.0) + 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 * 120.0) <= -0.0002)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 2e-58)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif ((a * 120.0) <= 1e+129)
		tmp = (a * 120.0) + (-60.0 * (x / 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], -0.0002], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-58], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+129], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -2.0000000000000001e-4 or 1e129 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 74.5%

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

   if -2.0000000000000001e-4 < (*.f64 a #s(literal 120 binary64)) < 2.0000000000000001e-58

   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 79.8%

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

   if 2.0000000000000001e-58 < (*.f64 a #s(literal 120 binary64)) < 1e129

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 90.3%

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

   6. Taylor expanded in z around 0 76.1%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -0.0002:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-58}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+129}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -0.0002:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-58}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -0.0002)
   (* a 120.0)
   (if (<= (* a 120.0) 2e-58)
     (* 60.0 (/ (- x y) (- z t)))
     (+ (* a 120.0) (* 60.0 (/ x z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -0.0002) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e-58) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-0.0002d0)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 2d-58) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -0.0002) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e-58) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -0.0002:
		tmp = a * 120.0
	elif (a * 120.0) <= 2e-58:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + (60.0 * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -0.0002)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 2e-58)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -0.0002)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 2e-58)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + (60.0 * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -0.0002], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-58], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -2.0000000000000001e-4

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 77.9%

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

   if -2.0000000000000001e-4 < (*.f64 a #s(literal 120 binary64)) < 2.0000000000000001e-58

   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 79.8%

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

   if 2.0000000000000001e-58 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   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 85.2%

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

   6. Taylor expanded in z around inf 70.0%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -0.0002:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-58}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 89.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+65}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+24}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.4e+65)
   (+ (* a 120.0) (* x (/ 60.0 (- z t))))
   (if (<= x 2.15e+24)
     (+ (* a 120.0) (/ (* y -60.0) (- z t)))
     (+ (* a 120.0) (* 60.0 (/ x (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.4e+65) {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	} else if (x <= 2.15e+24) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.4d+65)) then
        tmp = (a * 120.0d0) + (x * (60.0d0 / (z - t)))
    else if (x <= 2.15d+24) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else
        tmp = (a * 120.0d0) + (60.0d0 * (x / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.4e+65) {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	} else if (x <= 2.15e+24) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.4e+65:
		tmp = (a * 120.0) + (x * (60.0 / (z - t)))
	elif x <= 2.15e+24:
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	else:
		tmp = (a * 120.0) + (60.0 * (x / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.4e+65)
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))));
	elseif (x <= 2.15e+24)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.4e+65)
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	elseif (x <= 2.15e+24)
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	else
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.4e+65], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.15e+24], 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[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3999999999999999e65

   1. Initial program 99.7%

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

      1. associate-/l* 99.6%

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

   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 92.5%

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

      1. associate-*r/ 92.6%

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

      2. *-commutative 92.6%

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

      3. associate-*r/ 92.6%

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

   7. Simplified 92.6%

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

   if -1.3999999999999999e65 < x < 2.14999999999999994e24

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   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 92.9%

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

      1. associate-*r/ 92.9%

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

   7. Simplified 92.9%

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

   if 2.14999999999999994e24 < x

   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 x around inf 85.7%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+65}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+24}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 70.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-11} \lor \neg \left(a \leq 10^{+196}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.8e-11) (not (<= a 1e+196)))
   (* 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 <= -4.8e-11) || !(a <= 1e+196)) {
		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 <= (-4.8d-11)) .or. (.not. (a <= 1d+196))) 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 <= -4.8e-11) || !(a <= 1e+196)) {
		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 <= -4.8e-11) or not (a <= 1e+196):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.8e-11) || !(a <= 1e+196))
		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 <= -4.8e-11) || ~((a <= 1e+196)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.8e-11], N[Not[LessEqual[a, 1e+196]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.8000000000000002e-11 or 9.9999999999999995e195 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 81.2%

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

   if -4.8000000000000002e-11 < a < 9.9999999999999995e195

   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 73.1%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-11} \lor \neg \left(a \leq 10^{+196}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+142} \lor \neg \left(y \leq 4.5 \cdot 10^{+92}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.4e+142) (not (<= y 4.5e+92)))
   (* -60.0 (/ y (- z t)))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.4e+142) || !(y <= 4.5e+92)) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.4d+142)) .or. (.not. (y <= 4.5d+92))) then
        tmp = (-60.0d0) * (y / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.4e+142) || !(y <= 4.5e+92)) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.4e+142) or not (y <= 4.5e+92):
		tmp = -60.0 * (y / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.4e+142) || !(y <= 4.5e+92))
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.4e+142) || ~((y <= 4.5e+92)))
		tmp = -60.0 * (y / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.4e+142], N[Not[LessEqual[y, 4.5e+92]], $MachinePrecision]], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e142 or 4.4999999999999999e92 < y

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   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 81.1%

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

   6. Taylor expanded in x around 0 70.6%

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

   if -1.4e142 < y < 4.4999999999999999e92

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   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 53.0%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+142} \lor \neg \left(y \leq 4.5 \cdot 10^{+92}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+177} \lor \neg \left(y \leq 3.3 \cdot 10^{+78}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.7e+177) (not (<= y 3.3e+78))) (* -60.0 (/ y z)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.7e+177) || !(y <= 3.3e+78)) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-5.7d+177)) .or. (.not. (y <= 3.3d+78))) then
        tmp = (-60.0d0) * (y / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.7e+177) || !(y <= 3.3e+78)) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5.7e+177) or not (y <= 3.3e+78):
		tmp = -60.0 * (y / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5.7e+177) || !(y <= 3.3e+78))
		tmp = Float64(-60.0 * Float64(y / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -5.7e+177) || ~((y <= 3.3e+78)))
		tmp = -60.0 * (y / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5.7e+177], N[Not[LessEqual[y, 3.3e+78]], $MachinePrecision]], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.70000000000000015e177 or 3.3e78 < y

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   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 81.7%

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

   6. Taylor expanded in x around 0 66.7%

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

   7. Taylor expanded in z around inf 46.9%

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

   if -5.70000000000000015e177 < y < 3.3e78

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   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 52.8%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+177} \lor \neg \left(y \leq 3.3 \cdot 10^{+78}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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. Final simplification 99.7%

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

Alternative 17: 50.9% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* a 120.0))

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t, a):
	return a * 120.0

Julia

function code(x, y, z, t, a)
	return Float64(a * 120.0)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0), $MachinePrecision]

Derivation

1. Initial program 99.7%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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 z around inf 43.9%

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

6. Final simplification 43.9%

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

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024108 
(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)))