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

Percentage Accurate: 99.4% → 99.4%

Time: 14.4s

Alternatives: 21

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% 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: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (y - x)) / (t - z)) + (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 * (y - x)) / (t - z)) + (a * 120.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 2: 72.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{+54}:\\ \;\;\;\;\frac{60}{\frac{t}{y - x}}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-19}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(120 + 60 \cdot \frac{\frac{x}{a}}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e+94)
   (* a 120.0)
   (if (<= (* a 120.0) -4e+54)
     (/ 60.0 (/ t (- y x)))
     (if (<= (* a 120.0) -5e-52)
       (+ (* a 120.0) (/ (* x -60.0) t))
       (if (<= (* a 120.0) 5e-19)
         (* 60.0 (/ (- x y) (- z t)))
         (* a (+ 120.0 (* 60.0 (/ (/ x a) z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+94) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -4e+54) {
		tmp = 60.0 / (t / (y - x));
	} else if ((a * 120.0) <= -5e-52) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else if ((a * 120.0) <= 5e-19) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * (120.0 + (60.0 * ((x / a) / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d+94)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-4d+54)) then
        tmp = 60.0d0 / (t / (y - x))
    else if ((a * 120.0d0) <= (-5d-52)) then
        tmp = (a * 120.0d0) + ((x * (-60.0d0)) / t)
    else if ((a * 120.0d0) <= 5d-19) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = a * (120.0d0 + (60.0d0 * ((x / a) / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+94) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -4e+54) {
		tmp = 60.0 / (t / (y - x));
	} else if ((a * 120.0) <= -5e-52) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else if ((a * 120.0) <= 5e-19) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * (120.0 + (60.0 * ((x / a) / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e+94:
		tmp = a * 120.0
	elif (a * 120.0) <= -4e+54:
		tmp = 60.0 / (t / (y - x))
	elif (a * 120.0) <= -5e-52:
		tmp = (a * 120.0) + ((x * -60.0) / t)
	elif (a * 120.0) <= 5e-19:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * (120.0 + (60.0 * ((x / a) / z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+94)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -4e+54)
		tmp = Float64(60.0 / Float64(t / Float64(y - x)));
	elseif (Float64(a * 120.0) <= -5e-52)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * -60.0) / t));
	elseif (Float64(a * 120.0) <= 5e-19)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(a * Float64(120.0 + Float64(60.0 * Float64(Float64(x / a) / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e+94)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -4e+54)
		tmp = 60.0 / (t / (y - x));
	elseif ((a * 120.0) <= -5e-52)
		tmp = (a * 120.0) + ((x * -60.0) / t);
	elseif ((a * 120.0) <= 5e-19)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * (120.0 + (60.0 * ((x / a) / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+94], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e+54], N[(60.0 / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-52], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-19], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(120.0 + N[(60.0 * N[(N[(x / a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -2e94

   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 85.3%

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

   if -2e94 < (*.f64 a #s(literal 120 binary64)) < -4.0000000000000003e54

   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 72.2%

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

      1. clear-num 99.7%

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

      2. un-div-inv 100.0%

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

   7. Applied egg-rr 72.4%

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

   8. Taylor expanded in z around 0 72.4%

      \[\leadsto \frac{60}{\color{blue}{-1 \cdot \frac{t}{x - y}}} \]
   9. Step-by-step derivation

      1. neg-mul-1 72.4%

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

      2. distribute-neg-frac 72.4%

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

   10. Simplified 72.4%

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

   if -4.0000000000000003e54 < (*.f64 a #s(literal 120 binary64)) < -5e-52

   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 0 93.3%

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

      1. associate-*r/ 93.2%

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

      2. *-commutative 93.2%

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

      3. associate-/l* 93.2%

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

   7. Simplified 93.2%

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

   8. Taylor expanded in x around inf 81.0%

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

      1. associate-*r/ 81.0%

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

   10. Simplified 81.0%

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

   if -5e-52 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000004e-19

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   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 77.9%

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

   if 5.0000000000000004e-19 < (*.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 89.6%

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

      1. associate-*r/ 89.6%

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

   7. Simplified 89.6%

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

   8. Taylor expanded in a around inf 89.6%

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

   9. Taylor expanded in z around inf 72.7%

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

       1. associate-/r* 72.7%

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

   11. Simplified 72.7%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{+54}:\\ \;\;\;\;\frac{60}{\frac{t}{y - x}}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-19}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(120 + 60 \cdot \frac{\frac{x}{a}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{+54}:\\ \;\;\;\;\frac{60}{\frac{t}{y - x}}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-19}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e+94)
   (* a 120.0)
   (if (<= (* a 120.0) -4e+54)
     (/ 60.0 (/ t (- y x)))
     (if (<= (* a 120.0) -5e-52)
       (+ (* a 120.0) (/ (* x -60.0) t))
       (if (<= (* a 120.0) 5e-19)
         (* 60.0 (/ (- x y) (- z t)))
         (+ (* a 120.0) (* 60.0 (/ x z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+94) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -4e+54) {
		tmp = 60.0 / (t / (y - x));
	} else if ((a * 120.0) <= -5e-52) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else if ((a * 120.0) <= 5e-19) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d+94)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-4d+54)) then
        tmp = 60.0d0 / (t / (y - x))
    else if ((a * 120.0d0) <= (-5d-52)) then
        tmp = (a * 120.0d0) + ((x * (-60.0d0)) / t)
    else if ((a * 120.0d0) <= 5d-19) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+94) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -4e+54) {
		tmp = 60.0 / (t / (y - x));
	} else if ((a * 120.0) <= -5e-52) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else if ((a * 120.0) <= 5e-19) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e+94:
		tmp = a * 120.0
	elif (a * 120.0) <= -4e+54:
		tmp = 60.0 / (t / (y - x))
	elif (a * 120.0) <= -5e-52:
		tmp = (a * 120.0) + ((x * -60.0) / t)
	elif (a * 120.0) <= 5e-19:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + (60.0 * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+94)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -4e+54)
		tmp = Float64(60.0 / Float64(t / Float64(y - x)));
	elseif (Float64(a * 120.0) <= -5e-52)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * -60.0) / t));
	elseif (Float64(a * 120.0) <= 5e-19)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e+94)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -4e+54)
		tmp = 60.0 / (t / (y - x));
	elseif ((a * 120.0) <= -5e-52)
		tmp = (a * 120.0) + ((x * -60.0) / t);
	elseif ((a * 120.0) <= 5e-19)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + (60.0 * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+94], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e+54], N[(60.0 / N[(t / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-52], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-19], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -2e94

   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 85.3%

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

   if -2e94 < (*.f64 a #s(literal 120 binary64)) < -4.0000000000000003e54

   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 72.2%

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

      1. clear-num 99.7%

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

      2. un-div-inv 100.0%

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

   7. Applied egg-rr 72.4%

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

   8. Taylor expanded in z around 0 72.4%

      \[\leadsto \frac{60}{\color{blue}{-1 \cdot \frac{t}{x - y}}} \]
   9. Step-by-step derivation

      1. neg-mul-1 72.4%

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

      2. distribute-neg-frac 72.4%

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

   10. Simplified 72.4%

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

   if -4.0000000000000003e54 < (*.f64 a #s(literal 120 binary64)) < -5e-52

   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 0 93.3%

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

      1. associate-*r/ 93.2%

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

      2. *-commutative 93.2%

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

      3. associate-/l* 93.2%

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

   7. Simplified 93.2%

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

   8. Taylor expanded in x around inf 81.0%

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

      1. associate-*r/ 81.0%

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

   10. Simplified 81.0%

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

   if -5e-52 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000004e-19

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   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 77.9%

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

   if 5.0000000000000004e-19 < (*.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 89.6%

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

      1. associate-*r/ 89.6%

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

   7. Simplified 89.6%

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

   8. Taylor expanded in z around inf 72.7%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{+54}:\\ \;\;\;\;\frac{60}{\frac{t}{y - x}}\\ \mathbf{elif}\;a \cdot 120 \leq -5 \cdot 10^{-52}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-19}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot 120 \leq -6.1 \cdot 10^{-25}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= (* a 120.0) -2e+94)
     (* a 120.0)
     (if (<= (* a 120.0) -1e+60)
       t_1
       (if (<= (* a 120.0) -6.1e-25)
         (+ (* a 120.0) (* 60.0 (/ y t)))
         (if (<= (* a 120.0) 5e-19) t_1 (+ (* a 120.0) (* 60.0 (/ x z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -2e+94) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -1e+60) {
		tmp = t_1;
	} else if ((a * 120.0) <= -6.1e-25) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= 5e-19) {
		tmp = t_1;
	} 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 = 60.0d0 * ((x - y) / (z - t))
    if ((a * 120.0d0) <= (-2d+94)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-1d+60)) then
        tmp = t_1
    else if ((a * 120.0d0) <= (-6.1d-25)) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / t))
    else if ((a * 120.0d0) <= 5d-19) then
        tmp = t_1
    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 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -2e+94) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -1e+60) {
		tmp = t_1;
	} else if ((a * 120.0) <= -6.1e-25) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else if ((a * 120.0) <= 5e-19) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if (a * 120.0) <= -2e+94:
		tmp = a * 120.0
	elif (a * 120.0) <= -1e+60:
		tmp = t_1
	elif (a * 120.0) <= -6.1e-25:
		tmp = (a * 120.0) + (60.0 * (y / t))
	elif (a * 120.0) <= 5e-19:
		tmp = t_1
	else:
		tmp = (a * 120.0) + (60.0 * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+94)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -1e+60)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= -6.1e-25)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	elseif (Float64(a * 120.0) <= 5e-19)
		tmp = t_1;
	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 = 60.0 * ((x - y) / (z - t));
	tmp = 0.0;
	if ((a * 120.0) <= -2e+94)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -1e+60)
		tmp = t_1;
	elseif ((a * 120.0) <= -6.1e-25)
		tmp = (a * 120.0) + (60.0 * (y / t));
	elseif ((a * 120.0) <= 5e-19)
		tmp = t_1;
	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[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+94], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e+60], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], -6.1e-25], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-19], t$95$1, 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)) < -2e94

   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 85.3%

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

   if -2e94 < (*.f64 a #s(literal 120 binary64)) < -9.9999999999999995e59 or -6.10000000000000018e-25 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000004e-19

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   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 77.3%

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

   if -9.9999999999999995e59 < (*.f64 a #s(literal 120 binary64)) < -6.10000000000000018e-25

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 91.9%

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

   6. Taylor expanded in z around 0 75.4%

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

   if 5.0000000000000004e-19 < (*.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 89.6%

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

      1. associate-*r/ 89.6%

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

   7. Simplified 89.6%

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

   8. Taylor expanded in z around inf 72.7%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -1 \cdot 10^{+60}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq -6.1 \cdot 10^{-25}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-19}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 56.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+110}:\\ \;\;\;\;\frac{60}{\frac{t - z}{y}}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-120}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-190}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+177}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.5e+110)
   (/ 60.0 (/ (- t z) y))
   (if (<= y -1.7e-120)
     (* a 120.0)
     (if (<= y -2.2e-190)
       (/ (* 60.0 x) (- z t))
       (if (<= y 1.02e+177) (* a 120.0) (/ (* y -60.0) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.5e+110) {
		tmp = 60.0 / ((t - z) / y);
	} else if (y <= -1.7e-120) {
		tmp = a * 120.0;
	} else if (y <= -2.2e-190) {
		tmp = (60.0 * x) / (z - t);
	} else if (y <= 1.02e+177) {
		tmp = a * 120.0;
	} 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 <= (-3.5d+110)) then
        tmp = 60.0d0 / ((t - z) / y)
    else if (y <= (-1.7d-120)) then
        tmp = a * 120.0d0
    else if (y <= (-2.2d-190)) then
        tmp = (60.0d0 * x) / (z - t)
    else if (y <= 1.02d+177) then
        tmp = a * 120.0d0
    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 <= -3.5e+110) {
		tmp = 60.0 / ((t - z) / y);
	} else if (y <= -1.7e-120) {
		tmp = a * 120.0;
	} else if (y <= -2.2e-190) {
		tmp = (60.0 * x) / (z - t);
	} else if (y <= 1.02e+177) {
		tmp = a * 120.0;
	} else {
		tmp = (y * -60.0) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.5e+110:
		tmp = 60.0 / ((t - z) / y)
	elif y <= -1.7e-120:
		tmp = a * 120.0
	elif y <= -2.2e-190:
		tmp = (60.0 * x) / (z - t)
	elif y <= 1.02e+177:
		tmp = a * 120.0
	else:
		tmp = (y * -60.0) / (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.5e+110)
		tmp = Float64(60.0 / Float64(Float64(t - z) / y));
	elseif (y <= -1.7e-120)
		tmp = Float64(a * 120.0);
	elseif (y <= -2.2e-190)
		tmp = Float64(Float64(60.0 * x) / Float64(z - t));
	elseif (y <= 1.02e+177)
		tmp = Float64(a * 120.0);
	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 <= -3.5e+110)
		tmp = 60.0 / ((t - z) / y);
	elseif (y <= -1.7e-120)
		tmp = a * 120.0;
	elseif (y <= -2.2e-190)
		tmp = (60.0 * x) / (z - t);
	elseif (y <= 1.02e+177)
		tmp = a * 120.0;
	else
		tmp = (y * -60.0) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.5e+110], N[(60.0 / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e-120], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -2.2e-190], N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e+177], N[(a * 120.0), $MachinePrecision], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.4999999999999999e110

   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 73.3%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.8%

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

   7. Applied egg-rr 73.3%

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

   8. Taylor expanded in x around 0 64.4%

      \[\leadsto \frac{60}{\color{blue}{-1 \cdot \frac{z - t}{y}}} \]
   9. Step-by-step derivation

      1. mul-1-neg 64.4%

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

      2. distribute-neg-frac2 64.4%

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

   10. Simplified 64.4%

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

   if -3.4999999999999999e110 < y < -1.70000000000000005e-120 or -2.20000000000000004e-190 < y < 1.02e177

   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 62.0%

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

   if -1.70000000000000005e-120 < y < -2.20000000000000004e-190

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 74.3%

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

   6. Taylor expanded in x around inf 74.4%

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

      1. associate-*r/ 74.5%

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

   8. Simplified 74.5%

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

   if 1.02e177 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   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 89.0%

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

   6. Taylor expanded in x around 0 85.5%

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

      1. associate-*r/ 96.2%

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

   8. Simplified 85.7%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+110}:\\ \;\;\;\;\frac{60}{\frac{t - z}{y}}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-120}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-190}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+177}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+110}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-120}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-186}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+177}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.4e+110)
   (* -60.0 (/ y (- z t)))
   (if (<= y -2e-120)
     (* a 120.0)
     (if (<= y -3.5e-186)
       (/ (* 60.0 x) (- z t))
       (if (<= y 3.7e+177) (* a 120.0) (/ (* y -60.0) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.4e+110) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= -2e-120) {
		tmp = a * 120.0;
	} else if (y <= -3.5e-186) {
		tmp = (60.0 * x) / (z - t);
	} else if (y <= 3.7e+177) {
		tmp = a * 120.0;
	} 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 <= (-5.4d+110)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (y <= (-2d-120)) then
        tmp = a * 120.0d0
    else if (y <= (-3.5d-186)) then
        tmp = (60.0d0 * x) / (z - t)
    else if (y <= 3.7d+177) then
        tmp = a * 120.0d0
    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 <= -5.4e+110) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= -2e-120) {
		tmp = a * 120.0;
	} else if (y <= -3.5e-186) {
		tmp = (60.0 * x) / (z - t);
	} else if (y <= 3.7e+177) {
		tmp = a * 120.0;
	} else {
		tmp = (y * -60.0) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.4e+110:
		tmp = -60.0 * (y / (z - t))
	elif y <= -2e-120:
		tmp = a * 120.0
	elif y <= -3.5e-186:
		tmp = (60.0 * x) / (z - t)
	elif y <= 3.7e+177:
		tmp = a * 120.0
	else:
		tmp = (y * -60.0) / (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.4e+110)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (y <= -2e-120)
		tmp = Float64(a * 120.0);
	elseif (y <= -3.5e-186)
		tmp = Float64(Float64(60.0 * x) / Float64(z - t));
	elseif (y <= 3.7e+177)
		tmp = Float64(a * 120.0);
	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 <= -5.4e+110)
		tmp = -60.0 * (y / (z - t));
	elseif (y <= -2e-120)
		tmp = a * 120.0;
	elseif (y <= -3.5e-186)
		tmp = (60.0 * x) / (z - t);
	elseif (y <= 3.7e+177)
		tmp = a * 120.0;
	else
		tmp = (y * -60.0) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.4e+110], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2e-120], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -3.5e-186], N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e+177], N[(a * 120.0), $MachinePrecision], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.40000000000000019e110

   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 y around inf 95.3%

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

   6. Taylor expanded in y around inf 64.4%

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

   if -5.40000000000000019e110 < y < -1.99999999999999996e-120 or -3.49999999999999989e-186 < y < 3.70000000000000014e177

   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 62.0%

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

   if -1.99999999999999996e-120 < y < -3.49999999999999989e-186

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 74.3%

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

   6. Taylor expanded in x around inf 74.4%

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

      1. associate-*r/ 74.5%

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

   8. Simplified 74.5%

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

   if 3.70000000000000014e177 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   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 89.0%

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

   6. Taylor expanded in x around 0 85.5%

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

      1. associate-*r/ 96.2%

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

   8. Simplified 85.7%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+110}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-120}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-186}:\\ \;\;\;\;\frac{60 \cdot x}{z - t}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+177}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 55.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+112}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-87}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-186}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+177}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6.2e+112)
   (* -60.0 (/ y (- z t)))
   (if (<= y -1.95e-87)
     (* a 120.0)
     (if (<= y -3.5e-186)
       (/ 60.0 (/ (- z t) x))
       (if (<= y 1.02e+177) (* a 120.0) (/ (* y -60.0) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.2e+112) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= -1.95e-87) {
		tmp = a * 120.0;
	} else if (y <= -3.5e-186) {
		tmp = 60.0 / ((z - t) / x);
	} else if (y <= 1.02e+177) {
		tmp = a * 120.0;
	} 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 <= (-6.2d+112)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (y <= (-1.95d-87)) then
        tmp = a * 120.0d0
    else if (y <= (-3.5d-186)) then
        tmp = 60.0d0 / ((z - t) / x)
    else if (y <= 1.02d+177) then
        tmp = a * 120.0d0
    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 <= -6.2e+112) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= -1.95e-87) {
		tmp = a * 120.0;
	} else if (y <= -3.5e-186) {
		tmp = 60.0 / ((z - t) / x);
	} else if (y <= 1.02e+177) {
		tmp = a * 120.0;
	} else {
		tmp = (y * -60.0) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -6.2e+112:
		tmp = -60.0 * (y / (z - t))
	elif y <= -1.95e-87:
		tmp = a * 120.0
	elif y <= -3.5e-186:
		tmp = 60.0 / ((z - t) / x)
	elif y <= 1.02e+177:
		tmp = a * 120.0
	else:
		tmp = (y * -60.0) / (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6.2e+112)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (y <= -1.95e-87)
		tmp = Float64(a * 120.0);
	elseif (y <= -3.5e-186)
		tmp = Float64(60.0 / Float64(Float64(z - t) / x));
	elseif (y <= 1.02e+177)
		tmp = Float64(a * 120.0);
	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 <= -6.2e+112)
		tmp = -60.0 * (y / (z - t));
	elseif (y <= -1.95e-87)
		tmp = a * 120.0;
	elseif (y <= -3.5e-186)
		tmp = 60.0 / ((z - t) / x);
	elseif (y <= 1.02e+177)
		tmp = a * 120.0;
	else
		tmp = (y * -60.0) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6.2e+112], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.95e-87], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -3.5e-186], N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e+177], N[(a * 120.0), $MachinePrecision], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.19999999999999965e112

   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 y around inf 95.3%

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

   6. Taylor expanded in y around inf 64.4%

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

   if -6.19999999999999965e112 < y < -1.9499999999999999e-87 or -3.49999999999999989e-186 < y < 1.02e177

   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 62.2%

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

   if -1.9499999999999999e-87 < y < -3.49999999999999989e-186

   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 70.0%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   7. Applied egg-rr 70.0%

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

   8. Taylor expanded in x around inf 69.9%

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

   if 1.02e177 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   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 89.0%

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

   6. Taylor expanded in x around 0 85.5%

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

      1. associate-*r/ 96.2%

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

   8. Simplified 85.7%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+112}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-87}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-186}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+177}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-87}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-190}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+180}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= y -1e+113)
     t_1
     (if (<= y -1.95e-87)
       (* a 120.0)
       (if (<= y -3.1e-190)
         (/ 60.0 (/ (- z t) x))
         (if (<= y 1.95e+180) (* a 120.0) 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 <= -1e+113) {
		tmp = t_1;
	} else if (y <= -1.95e-87) {
		tmp = a * 120.0;
	} else if (y <= -3.1e-190) {
		tmp = 60.0 / ((z - t) / x);
	} else if (y <= 1.95e+180) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * (y / (z - t))
    if (y <= (-1d+113)) then
        tmp = t_1
    else if (y <= (-1.95d-87)) then
        tmp = a * 120.0d0
    else if (y <= (-3.1d-190)) then
        tmp = 60.0d0 / ((z - t) / x)
    else if (y <= 1.95d+180) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -1e+113) {
		tmp = t_1;
	} else if (y <= -1.95e-87) {
		tmp = a * 120.0;
	} else if (y <= -3.1e-190) {
		tmp = 60.0 / ((z - t) / x);
	} else if (y <= 1.95e+180) {
		tmp = a * 120.0;
	} 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 <= -1e+113:
		tmp = t_1
	elif y <= -1.95e-87:
		tmp = a * 120.0
	elif y <= -3.1e-190:
		tmp = 60.0 / ((z - t) / x)
	elif y <= 1.95e+180:
		tmp = a * 120.0
	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 <= -1e+113)
		tmp = t_1;
	elseif (y <= -1.95e-87)
		tmp = Float64(a * 120.0);
	elseif (y <= -3.1e-190)
		tmp = Float64(60.0 / Float64(Float64(z - t) / x));
	elseif (y <= 1.95e+180)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (y <= -1e+113)
		tmp = t_1;
	elseif (y <= -1.95e-87)
		tmp = a * 120.0;
	elseif (y <= -3.1e-190)
		tmp = 60.0 / ((z - t) / x);
	elseif (y <= 1.95e+180)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+113], t$95$1, If[LessEqual[y, -1.95e-87], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -3.1e-190], N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e+180], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1e113 or 1.95e180 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 95.5%

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

   6. Taylor expanded in y around inf 71.6%

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

   if -1e113 < y < -1.9499999999999999e-87 or -3.09999999999999993e-190 < y < 1.95e180

   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 62.2%

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

   if -1.9499999999999999e-87 < y < -3.09999999999999993e-190

   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 70.0%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

   7. Applied egg-rr 70.0%

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

   8. Taylor expanded in x around inf 69.9%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+113}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-87}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-190}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+180}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -5 \cdot 10^{+111}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-86}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-186}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+178}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= y -5e+111)
     t_1
     (if (<= y -2.4e-86)
       (* a 120.0)
       (if (<= y -1.75e-186)
         (* 60.0 (/ x (- z t)))
         (if (<= y 2.6e+178) (* a 120.0) 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 <= -5e+111) {
		tmp = t_1;
	} else if (y <= -2.4e-86) {
		tmp = a * 120.0;
	} else if (y <= -1.75e-186) {
		tmp = 60.0 * (x / (z - t));
	} else if (y <= 2.6e+178) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * (y / (z - t))
    if (y <= (-5d+111)) then
        tmp = t_1
    else if (y <= (-2.4d-86)) then
        tmp = a * 120.0d0
    else if (y <= (-1.75d-186)) then
        tmp = 60.0d0 * (x / (z - t))
    else if (y <= 2.6d+178) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -5e+111) {
		tmp = t_1;
	} else if (y <= -2.4e-86) {
		tmp = a * 120.0;
	} else if (y <= -1.75e-186) {
		tmp = 60.0 * (x / (z - t));
	} else if (y <= 2.6e+178) {
		tmp = a * 120.0;
	} 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 <= -5e+111:
		tmp = t_1
	elif y <= -2.4e-86:
		tmp = a * 120.0
	elif y <= -1.75e-186:
		tmp = 60.0 * (x / (z - t))
	elif y <= 2.6e+178:
		tmp = a * 120.0
	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 <= -5e+111)
		tmp = t_1;
	elseif (y <= -2.4e-86)
		tmp = Float64(a * 120.0);
	elseif (y <= -1.75e-186)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (y <= 2.6e+178)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (y <= -5e+111)
		tmp = t_1;
	elseif (y <= -2.4e-86)
		tmp = a * 120.0;
	elseif (y <= -1.75e-186)
		tmp = 60.0 * (x / (z - t));
	elseif (y <= 2.6e+178)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+111], t$95$1, If[LessEqual[y, -2.4e-86], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -1.75e-186], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+178], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9999999999999997e111 or 2.6000000000000001e178 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 95.5%

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

   6. Taylor expanded in y around inf 71.6%

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

   if -4.9999999999999997e111 < y < -2.40000000000000013e-86 or -1.74999999999999995e-186 < y < 2.6000000000000001e178

   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 62.2%

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

   if -2.40000000000000013e-86 < y < -1.74999999999999995e-186

   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 y around inf 79.6%

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

   6. Taylor expanded in x around inf 69.9%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+111}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-86}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-186}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+178}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-128}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-144}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{elif}\;y \leq 1.82 \cdot 10^{+180}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= y -1.7e+112)
     t_1
     (if (<= y -1.9e-128)
       (* a 120.0)
       (if (<= y -5.4e-144)
         (* x (/ 60.0 z))
         (if (<= y 1.82e+180) (* a 120.0) 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 <= -1.7e+112) {
		tmp = t_1;
	} else if (y <= -1.9e-128) {
		tmp = a * 120.0;
	} else if (y <= -5.4e-144) {
		tmp = x * (60.0 / z);
	} else if (y <= 1.82e+180) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * (y / (z - t))
    if (y <= (-1.7d+112)) then
        tmp = t_1
    else if (y <= (-1.9d-128)) then
        tmp = a * 120.0d0
    else if (y <= (-5.4d-144)) then
        tmp = x * (60.0d0 / z)
    else if (y <= 1.82d+180) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -1.7e+112) {
		tmp = t_1;
	} else if (y <= -1.9e-128) {
		tmp = a * 120.0;
	} else if (y <= -5.4e-144) {
		tmp = x * (60.0 / z);
	} else if (y <= 1.82e+180) {
		tmp = a * 120.0;
	} 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 <= -1.7e+112:
		tmp = t_1
	elif y <= -1.9e-128:
		tmp = a * 120.0
	elif y <= -5.4e-144:
		tmp = x * (60.0 / z)
	elif y <= 1.82e+180:
		tmp = a * 120.0
	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 <= -1.7e+112)
		tmp = t_1;
	elseif (y <= -1.9e-128)
		tmp = Float64(a * 120.0);
	elseif (y <= -5.4e-144)
		tmp = Float64(x * Float64(60.0 / z));
	elseif (y <= 1.82e+180)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (y <= -1.7e+112)
		tmp = t_1;
	elseif (y <= -1.9e-128)
		tmp = a * 120.0;
	elseif (y <= -5.4e-144)
		tmp = x * (60.0 / z);
	elseif (y <= 1.82e+180)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+112], t$95$1, If[LessEqual[y, -1.9e-128], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, -5.4e-144], N[(x * N[(60.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.82e+180], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.69999999999999997e112 or 1.8199999999999999e180 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 95.5%

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

   6. Taylor expanded in y around inf 71.6%

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

   if -1.69999999999999997e112 < y < -1.9000000000000001e-128 or -5.3999999999999995e-144 < y < 1.8199999999999999e180

   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 61.3%

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

   if -1.9000000000000001e-128 < y < -5.3999999999999995e-144

   1. Initial program 100.0%

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

      1. associate-/l* 99.8%

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

   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 87.7%

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

   6. Taylor expanded in x around inf 87.6%

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

      1. associate-*r/ 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*r/ 99.8%

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

   8. Simplified 87.6%

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

   9. Taylor expanded in z around inf 76.1%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+112}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-128}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-144}:\\ \;\;\;\;x \cdot \frac{60}{z}\\ \mathbf{elif}\;y \leq 1.82 \cdot 10^{+180}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+94} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{-9}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -2e+94) (not (<= (* a 120.0) 2e-9)))
   (* a 120.0)
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e+94) || !((a * 120.0) <= 2e-9)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-2d+94)) .or. (.not. ((a * 120.0d0) <= 2d-9))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e+94) || !((a * 120.0) <= 2e-9)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -2e+94) or not ((a * 120.0) <= 2e-9):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -2e+94) || !(Float64(a * 120.0) <= 2e-9))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -2e+94) || ~(((a * 120.0) <= 2e-9)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+94], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-9]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -2e94 or 2.00000000000000012e-9 < (*.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 77.5%

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

   if -2e94 < (*.f64 a #s(literal 120 binary64)) < 2.00000000000000012e-9

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   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 73.8%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+94} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{-9}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 73.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-19}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2e+94)
   (* a 120.0)
   (if (<= (* a 120.0) 5e-19)
     (* 60.0 (/ (- x y) (- z t)))
     (+ (* a 120.0) (* 60.0 (/ x z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+94) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e-19) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-2d+94)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 5d-19) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2e+94) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e-19) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 * (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2e+94:
		tmp = a * 120.0
	elif (a * 120.0) <= 5e-19:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + (60.0 * (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2e+94)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 5e-19)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2e+94)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 5e-19)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + (60.0 * (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+94], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-19], 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)) < -2e94

   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 85.3%

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

   if -2e94 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000004e-19

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   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 74.1%

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

   if 5.0000000000000004e-19 < (*.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 89.6%

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

      1. associate-*r/ 89.6%

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

   7. Simplified 89.6%

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

   8. Taylor expanded in z around inf 72.7%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-19}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 89.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+59} \lor \neg \left(y \leq 7.8 \cdot 10^{+118}\right):\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.9e+59) (not (<= y 7.8e+118)))
   (+ (* a 120.0) (/ -60.0 (/ (- z t) y)))
   (+ (* a 120.0) (/ 60.0 (/ (- z t) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.9e+59) || !(y <= 7.8e+118)) {
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y));
	} else {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.9d+59)) .or. (.not. (y <= 7.8d+118))) then
        tmp = (a * 120.0d0) + ((-60.0d0) / ((z - t) / y))
    else
        tmp = (a * 120.0d0) + (60.0d0 / ((z - t) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.9e+59) || !(y <= 7.8e+118)) {
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y));
	} else {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.9e+59) or not (y <= 7.8e+118):
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y))
	else:
		tmp = (a * 120.0) + (60.0 / ((z - t) / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.9e+59) || !(y <= 7.8e+118))
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 / Float64(Float64(z - t) / y)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(z - t) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.9e+59) || ~((y <= 7.8e+118)))
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y));
	else
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.9e+59], N[Not[LessEqual[y, 7.8e+118]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.89999999999999991e59 or 7.8e118 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   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 0 90.1%

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

      1. clear-num 90.0%

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

      2. un-div-inv 90.2%

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

   7. Applied egg-rr 90.2%

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

   if -2.89999999999999991e59 < y < 7.8e118

   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. Step-by-step derivation

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 94.0%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+59} \lor \neg \left(y \leq 7.8 \cdot 10^{+118}\right):\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 89.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+62} \lor \neg \left(y \leq 4.2 \cdot 10^{+119}\right):\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.6e+62) (not (<= y 4.2e+119)))
   (+ (* a 120.0) (/ -60.0 (/ (- z t) y)))
   (+ (* a 120.0) (* x (/ 60.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.6e+62) || !(y <= 4.2e+119)) {
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-4.6d+62)) .or. (.not. (y <= 4.2d+119))) then
        tmp = (a * 120.0d0) + ((-60.0d0) / ((z - t) / y))
    else
        tmp = (a * 120.0d0) + (x * (60.0d0 / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.6e+62) || !(y <= 4.2e+119)) {
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.6e+62) or not (y <= 4.2e+119):
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y))
	else:
		tmp = (a * 120.0) + (x * (60.0 / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.6e+62) || !(y <= 4.2e+119))
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 / Float64(Float64(z - t) / y)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4.6e+62) || ~((y <= 4.2e+119)))
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y));
	else
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.6e+62], N[Not[LessEqual[y, 4.2e+119]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.59999999999999968e62 or 4.19999999999999966e119 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   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 0 90.1%

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

      1. clear-num 90.0%

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

      2. un-div-inv 90.2%

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

   7. Applied egg-rr 90.2%

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

   if -4.59999999999999968e62 < y < 4.19999999999999966e119

   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 94.0%

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

      1. associate-*r/ 94.0%

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

      2. *-commutative 94.0%

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

      3. associate-*r/ 93.9%

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

   7. Simplified 93.9%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+62} \lor \neg \left(y \leq 4.2 \cdot 10^{+119}\right):\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z - t}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 89.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+61} \lor \neg \left(y \leq 1.25 \cdot 10^{+119}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -7.6e+61) (not (<= y 1.25e+119)))
   (+ (* a 120.0) (* -60.0 (/ y (- z t))))
   (+ (* a 120.0) (* x (/ 60.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -7.6e+61) || !(y <= 1.25e+119)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-7.6d+61)) .or. (.not. (y <= 1.25d+119))) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    else
        tmp = (a * 120.0d0) + (x * (60.0d0 / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -7.6e+61) || !(y <= 1.25e+119)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -7.6e+61) or not (y <= 1.25e+119):
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	else:
		tmp = (a * 120.0) + (x * (60.0 / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -7.6e+61) || !(y <= 1.25e+119))
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -7.6e+61) || ~((y <= 1.25e+119)))
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	else
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -7.6e+61], N[Not[LessEqual[y, 1.25e+119]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5999999999999999e61 or 1.25e119 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   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 0 90.1%

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

   if -7.5999999999999999e61 < y < 1.25e119

   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 94.0%

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

      1. associate-*r/ 94.0%

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

      2. *-commutative 94.0%

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

      3. associate-*r/ 93.9%

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

   7. Simplified 93.9%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+61} \lor \neg \left(y \leq 1.25 \cdot 10^{+119}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 89.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+61}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z - t}{y}}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+119}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.6e+61)
   (+ (* a 120.0) (/ -60.0 (/ (- z t) y)))
   (if (<= y 2.6e+119)
     (+ (* a 120.0) (/ 60.0 (/ (- z t) x)))
     (+ (* a 120.0) (/ (* y -60.0) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.6e+61) {
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y));
	} else if (y <= 2.6e+119) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.6d+61)) then
        tmp = (a * 120.0d0) + ((-60.0d0) / ((z - t) / y))
    else if (y <= 2.6d+119) then
        tmp = (a * 120.0d0) + (60.0d0 / ((z - t) / x))
    else
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.6e+61) {
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y));
	} else if (y <= 2.6e+119) {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.6e+61:
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y))
	elif y <= 2.6e+119:
		tmp = (a * 120.0) + (60.0 / ((z - t) / x))
	else:
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.6e+61)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 / Float64(Float64(z - t) / y)));
	elseif (y <= 2.6e+119)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(z - t) / x)));
	else
		tmp = Float64(Float64(a * 120.0) + 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 <= -1.6e+61)
		tmp = (a * 120.0) + (-60.0 / ((z - t) / y));
	elseif (y <= 2.6e+119)
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	else
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.6e+61], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+119], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5999999999999999e61

   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 89.4%

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

      1. clear-num 89.3%

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

      2. un-div-inv 89.5%

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

   7. Applied egg-rr 89.5%

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

   if -1.5999999999999999e61 < y < 2.6e119

   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. Step-by-step derivation

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 94.0%

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

   if 2.6e119 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   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 0 91.2%

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

      1. associate-*r/ 91.4%

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

   7. Simplified 91.4%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+61}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z - t}{y}}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+119}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 82.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+207}:\\ \;\;\;\;\frac{60}{\frac{t - z}{y - x}}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+117}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.8e+207)
   (/ 60.0 (/ (- t z) (- y x)))
   (if (<= x 2.4e+117)
     (+ (* a 120.0) (* -60.0 (/ y (- z t))))
     (* 60.0 (/ (- x y) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.8e+207) {
		tmp = 60.0 / ((t - z) / (y - x));
	} else if (x <= 2.4e+117) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-6.8d+207)) then
        tmp = 60.0d0 / ((t - z) / (y - x))
    else if (x <= 2.4d+117) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.8e+207) {
		tmp = 60.0 / ((t - z) / (y - x));
	} else if (x <= 2.4e+117) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.8e+207:
		tmp = 60.0 / ((t - z) / (y - x))
	elif x <= 2.4e+117:
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.8e+207)
		tmp = Float64(60.0 / Float64(Float64(t - z) / Float64(y - x)));
	elseif (x <= 2.4e+117)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -6.8e+207)
		tmp = 60.0 / ((t - z) / (y - x));
	elseif (x <= 2.4e+117)
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.8e+207], N[(60.0 / N[(N[(t - z), $MachinePrecision] / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e+117], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.7999999999999997e207

   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 a around 0 73.3%

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

      1. clear-num 99.4%

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

      2. un-div-inv 99.7%

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

   7. Applied egg-rr 73.4%

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

   if -6.7999999999999997e207 < x < 2.3999999999999999e117

   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 85.5%

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

   if 2.3999999999999999e117 < 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* 99.8%

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

   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 79.3%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+207}:\\ \;\;\;\;\frac{60}{\frac{t - z}{y - x}}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+117}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 / ((t - z) / (y - x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

   1. clear-num 99.7%

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

   2. un-div-inv 99.8%

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

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

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

Alternative 19: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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. Final simplification 99.8%

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

Alternative 20: 52.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6.9 \cdot 10^{+233}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 6.9e+233) (* a 120.0) (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 6.9e+233) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= 6.9d+233) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 6.9e+233) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 6.9e+233:
		tmp = a * 120.0
	else:
		tmp = -60.0 * (x / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 6.9e+233)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 6.9e+233)
		tmp = a * 120.0;
	else
		tmp = -60.0 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, 6.9e+233], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.8999999999999996e233

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   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 53.6%

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

   if 6.8999999999999996e233 < x

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   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 95.3%

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

   6. Taylor expanded in x around inf 87.2%

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

      1. associate-*r/ 91.8%

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

      2. *-commutative 91.8%

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

      3. associate-*r/ 91.6%

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

   8. Simplified 87.0%

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

   9. Taylor expanded in z around 0 57.7%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6.9 \cdot 10^{+233}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 50.8% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-/l* 99.8%

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

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 50.2%

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

6. Final simplification 50.2%

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

Developer target: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024103 
(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)))