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

Percentage Accurate: 99.3% → 99.8%

Time: 11.9s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. associate-/l* 99.4%

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

3. Simplified 99.4%

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

   1. clear-num 99.3%

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

   2. un-div-inv 99.4%

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

6. Applied egg-rr 99.4%

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

7. Final simplification 99.4%

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

Alternative 2: 67.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x - y \leq -1 \cdot 10^{+163} \lor \neg \left(x - y \leq 5 \cdot 10^{+111}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- x y) -1e+163) (not (<= (- x y) 5e+111)))
   (* 60.0 (/ (- x y) (- z t)))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x - y) <= -1e+163) || !((x - y) <= 5e+111)) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((x - y) <= (-1d+163)) .or. (.not. ((x - y) <= 5d+111))) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x - y) <= -1e+163) || !((x - y) <= 5e+111)) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((x - y) <= -1e+163) or not ((x - y) <= 5e+111):
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x - y) <= -1e+163) || !(Float64(x - y) <= 5e+111))
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((x - y) <= -1e+163) || ~(((x - y) <= 5e+111)))
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x - y), $MachinePrecision], -1e+163], N[Not[LessEqual[N[(x - y), $MachinePrecision], 5e+111]], $MachinePrecision]], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 x y) < -9.9999999999999994e162 or 4.9999999999999997e111 < (-.f64 x y)

   1. Initial program 98.1%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

      1. clear-num 98.9%

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

      2. un-div-inv 98.9%

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

   6. Applied egg-rr 98.9%

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

   7. Taylor expanded in a around 0 74.3%

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

   if -9.9999999999999994e162 < (-.f64 x y) < 4.9999999999999997e111

   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 73.7%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - y \leq -1 \cdot 10^{+163} \lor \neg \left(x - y \leq 5 \cdot 10^{+111}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -100000:\\ \;\;\;\;a \cdot 120 - \frac{60}{\frac{z}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-14}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -100000.0)
   (- (* a 120.0) (/ 60.0 (/ z y)))
   (if (<= (* a 120.0) 5e-14)
     (* (- y x) (/ 60.0 (- t z)))
     (+ (* a 120.0) (/ (* x -60.0) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -100000.0) {
		tmp = (a * 120.0) - (60.0 / (z / y));
	} else if ((a * 120.0) <= 5e-14) {
		tmp = (y - x) * (60.0 / (t - z));
	} else {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-100000.0d0)) then
        tmp = (a * 120.0d0) - (60.0d0 / (z / y))
    else if ((a * 120.0d0) <= 5d-14) then
        tmp = (y - x) * (60.0d0 / (t - z))
    else
        tmp = (a * 120.0d0) + ((x * (-60.0d0)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -100000.0) {
		tmp = (a * 120.0) - (60.0 / (z / y));
	} else if ((a * 120.0) <= 5e-14) {
		tmp = (y - x) * (60.0 / (t - z));
	} else {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -100000.0:
		tmp = (a * 120.0) - (60.0 / (z / y))
	elif (a * 120.0) <= 5e-14:
		tmp = (y - x) * (60.0 / (t - z))
	else:
		tmp = (a * 120.0) + ((x * -60.0) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -100000.0)
		tmp = Float64(Float64(a * 120.0) - Float64(60.0 / Float64(z / y)));
	elseif (Float64(a * 120.0) <= 5e-14)
		tmp = Float64(Float64(y - x) * Float64(60.0 / Float64(t - z)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * -60.0) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -100000.0)
		tmp = (a * 120.0) - (60.0 / (z / y));
	elseif ((a * 120.0) <= 5e-14)
		tmp = (y - x) * (60.0 / (t - z));
	else
		tmp = (a * 120.0) + ((x * -60.0) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -100000.0], N[(N[(a * 120.0), $MachinePrecision] - N[(60.0 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-14], N[(N[(y - x), $MachinePrecision] * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1e5

   1. Initial program 98.2%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

      1. clear-num 98.2%

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

      2. un-div-inv 98.3%

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

   6. Applied egg-rr 98.3%

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

   7. Taylor expanded in x around 0 86.7%

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

      1. neg-mul-1 86.7%

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

   9. Simplified 86.7%

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

   10. Taylor expanded in z around inf 78.5%

       \[\leadsto \frac{60}{\color{blue}{-1 \cdot \frac{z}{y}}} + a \cdot 120 \]
   11. Step-by-step derivation

       1. associate-*r/ 78.5%

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

       2. neg-mul-1 78.5%

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

   12. Simplified 78.5%

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

   if -1e5 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000002e-14

   1. Initial program 99.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around 0 71.2%

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

      1. associate-*r/ 70.5%

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

      2. associate-*l/ 71.2%

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

      3. metadata-eval 71.2%

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

      4. associate-*r/ 71.2%

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

      5. *-commutative 71.2%

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

      6. associate-*r/ 71.2%

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

      7. metadata-eval 71.2%

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

   9. Simplified 71.2%

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

   if 5.0000000000000002e-14 < (*.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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 89.5%

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

      1. associate-*r/ 89.5%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in z around 0 80.2%

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

      1. associate-*r/ 80.2%

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

   10. Simplified 80.2%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -100000:\\ \;\;\;\;a \cdot 120 - \frac{60}{\frac{z}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-14}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -100000:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-14}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -100000.0)
   (+ (* a 120.0) (* -60.0 (/ y z)))
   (if (<= (* a 120.0) 5e-14)
     (* (- y x) (/ 60.0 (- t z)))
     (+ (* a 120.0) (/ (* x -60.0) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -100000.0) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 5e-14) {
		tmp = (y - x) * (60.0 / (t - z));
	} else {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-100000.0d0)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if ((a * 120.0d0) <= 5d-14) then
        tmp = (y - x) * (60.0d0 / (t - z))
    else
        tmp = (a * 120.0d0) + ((x * (-60.0d0)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -100000.0) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 5e-14) {
		tmp = (y - x) * (60.0 / (t - z));
	} else {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -100000.0:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif (a * 120.0) <= 5e-14:
		tmp = (y - x) * (60.0 / (t - z))
	else:
		tmp = (a * 120.0) + ((x * -60.0) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -100000.0)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (Float64(a * 120.0) <= 5e-14)
		tmp = Float64(Float64(y - x) * Float64(60.0 / Float64(t - z)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * -60.0) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -100000.0)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif ((a * 120.0) <= 5e-14)
		tmp = (y - x) * (60.0 / (t - z));
	else
		tmp = (a * 120.0) + ((x * -60.0) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -100000.0], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-14], N[(N[(y - x), $MachinePrecision] * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1e5

   1. Initial program 98.2%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in z around inf 73.0%

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

   6. Taylor expanded in x around 0 78.5%

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

   if -1e5 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000002e-14

   1. Initial program 99.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around 0 71.2%

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

      1. associate-*r/ 70.5%

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

      2. associate-*l/ 71.2%

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

      3. metadata-eval 71.2%

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

      4. associate-*r/ 71.2%

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

      5. *-commutative 71.2%

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

      6. associate-*r/ 71.2%

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

      7. metadata-eval 71.2%

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

   9. Simplified 71.2%

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

   if 5.0000000000000002e-14 < (*.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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 89.5%

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

      1. associate-*r/ 89.5%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in z around 0 80.2%

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

      1. associate-*r/ 80.2%

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

   10. Simplified 80.2%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -100000:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-14}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -100000:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+30}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -100000.0)
   (+ (* a 120.0) (* -60.0 (/ y z)))
   (if (<= (* a 120.0) 1e+30) (* (- y x) (/ 60.0 (- t z))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -100000.0) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 1e+30) {
		tmp = (y - x) * (60.0 / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-100000.0d0)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if ((a * 120.0d0) <= 1d+30) then
        tmp = (y - x) * (60.0d0 / (t - z))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -100000.0) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 1e+30) {
		tmp = (y - x) * (60.0 / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -100000.0:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif (a * 120.0) <= 1e+30:
		tmp = (y - x) * (60.0 / (t - z))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -100000.0)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (Float64(a * 120.0) <= 1e+30)
		tmp = Float64(Float64(y - x) * Float64(60.0 / Float64(t - z)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -100000.0)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif ((a * 120.0) <= 1e+30)
		tmp = (y - x) * (60.0 / (t - z));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -100000.0], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+30], N[(N[(y - x), $MachinePrecision] * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1e5

   1. Initial program 98.2%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in z around inf 73.0%

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

   6. Taylor expanded in x around 0 78.5%

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

   if -1e5 < (*.f64 a #s(literal 120 binary64)) < 1e30

   1. Initial program 99.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.6%

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

      2. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around 0 70.1%

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

      1. associate-*r/ 69.4%

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

      2. associate-*l/ 70.1%

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

      3. metadata-eval 70.1%

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

      4. associate-*r/ 70.1%

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

      5. *-commutative 70.1%

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

      6. associate-*r/ 70.1%

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

      7. metadata-eval 70.1%

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

   9. Simplified 70.1%

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

   if 1e30 < (*.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* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 83.8%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -100000:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+30}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x - y \leq -1 \cdot 10^{+163}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{60}{t - z}\\ \mathbf{elif}\;x - y \leq 5 \cdot 10^{+111}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- x y) -1e+163)
   (* (- y x) (/ 60.0 (- t z)))
   (if (<= (- x y) 5e+111) (* 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 ((x - y) <= -1e+163) {
		tmp = (y - x) * (60.0 / (t - z));
	} else if ((x - y) <= 5e+111) {
		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 ((x - y) <= (-1d+163)) then
        tmp = (y - x) * (60.0d0 / (t - z))
    else if ((x - y) <= 5d+111) 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 ((x - y) <= -1e+163) {
		tmp = (y - x) * (60.0 / (t - z));
	} else if ((x - y) <= 5e+111) {
		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 (x - y) <= -1e+163:
		tmp = (y - x) * (60.0 / (t - z))
	elif (x - y) <= 5e+111:
		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(x - y) <= -1e+163)
		tmp = Float64(Float64(y - x) * Float64(60.0 / Float64(t - z)));
	elseif (Float64(x - y) <= 5e+111)
		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 ((x - y) <= -1e+163)
		tmp = (y - x) * (60.0 / (t - z));
	elseif ((x - y) <= 5e+111)
		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[LessEqual[N[(x - y), $MachinePrecision], -1e+163], N[(N[(y - x), $MachinePrecision] * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x - y), $MachinePrecision], 5e+111], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 x y) < -9.9999999999999994e162

   1. Initial program 97.3%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

      1. clear-num 97.2%

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

      2. un-div-inv 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in a around 0 83.7%

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

      1. associate-*r/ 83.7%

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

      2. associate-*l/ 83.8%

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

      3. metadata-eval 83.8%

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

      4. associate-*r/ 83.8%

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

      5. *-commutative 83.8%

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

      6. associate-*r/ 83.8%

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

      7. metadata-eval 83.8%

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

   9. Simplified 83.8%

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

   if -9.9999999999999994e162 < (-.f64 x y) < 4.9999999999999997e111

   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 73.7%

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

   if 4.9999999999999997e111 < (-.f64 x y)

   1. Initial program 98.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. 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 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around 0 69.5%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - y \leq -1 \cdot 10^{+163}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{60}{t - z}\\ \mathbf{elif}\;x - y \leq 5 \cdot 10^{+111}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+115} \lor \neg \left(x \leq 3.7 \cdot 10^{+99}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.2e+115) (not (<= x 3.7e+99)))
   (+ (* a 120.0) (* 60.0 (/ x (- z t))))
   (+ (* a 120.0) (/ 60.0 (/ (- t z) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.2e+115) || !(x <= 3.7e+99)) {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	} else {
		tmp = (a * 120.0) + (60.0 / ((t - z) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.2d+115)) .or. (.not. (x <= 3.7d+99))) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / (z - t)))
    else
        tmp = (a * 120.0d0) + (60.0d0 / ((t - z) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.2e+115) || !(x <= 3.7e+99)) {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	} else {
		tmp = (a * 120.0) + (60.0 / ((t - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.2e+115) or not (x <= 3.7e+99):
		tmp = (a * 120.0) + (60.0 * (x / (z - t)))
	else:
		tmp = (a * 120.0) + (60.0 / ((t - z) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.2e+115) || !(x <= 3.7e+99))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / Float64(z - t))));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(t - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.2e+115) || ~((x <= 3.7e+99)))
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	else
		tmp = (a * 120.0) + (60.0 / ((t - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.2e+115], N[Not[LessEqual[x, 3.7e+99]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2e115 or 3.7000000000000001e99 < x

   1. Initial program 97.7%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around inf 90.4%

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

   if -1.2e115 < x < 3.7000000000000001e99

   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 0 91.7%

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

      1. neg-mul-1 91.7%

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

   9. Simplified 91.7%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+115} \lor \neg \left(x \leq 3.7 \cdot 10^{+99}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+115} \lor \neg \left(x \leq 2.55 \cdot 10^{+99}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.2e+115) (not (<= x 2.55e+99)))
   (+ (* a 120.0) (* 60.0 (/ x (- z t))))
   (+ (* a 120.0) (* 60.0 (/ y (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.2e+115) || !(x <= 2.55e+99)) {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	} else {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-1.2d+115)) .or. (.not. (x <= 2.55d+99))) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / (z - t)))
    else
        tmp = (a * 120.0d0) + (60.0d0 * (y / (t - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.2e+115) || !(x <= 2.55e+99)) {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	} else {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.2e+115) or not (x <= 2.55e+99):
		tmp = (a * 120.0) + (60.0 * (x / (z - t)))
	else:
		tmp = (a * 120.0) + (60.0 * (y / (t - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.2e+115) || !(x <= 2.55e+99))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / Float64(z - t))));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / Float64(t - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.2e+115) || ~((x <= 2.55e+99)))
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	else
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.2e+115], N[Not[LessEqual[x, 2.55e+99]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2e115 or 2.54999999999999976e99 < x

   1. Initial program 97.7%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around inf 90.4%

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

   if -1.2e115 < x < 2.54999999999999976e99

   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 91.7%

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

      1. associate-*r/ 91.7%

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

      2. remove-double-neg 91.7%

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

      3. neg-mul-1 91.7%

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

      4. times-frac 91.7%

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

      5. metadata-eval 91.7%

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

      6. neg-sub0 91.7%

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

      7. sub-neg 91.7%

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

      8. +-commutative 91.7%

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

      9. associate--r+ 91.7%

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

      10. neg-sub0 91.7%

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

      11. remove-double-neg 91.7%

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

   7. Simplified 91.7%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+115} \lor \neg \left(x \leq 2.55 \cdot 10^{+99}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+180}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t}{y}}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+153}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{60}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.1e+180)
   (+ (* a 120.0) (/ 60.0 (/ t y)))
   (if (<= y 1.6e+153)
     (+ (* a 120.0) (* 60.0 (/ x (- z t))))
     (* (- y x) (/ 60.0 (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.1e+180) {
		tmp = (a * 120.0) + (60.0 / (t / y));
	} else if (y <= 1.6e+153) {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	} else {
		tmp = (y - x) * (60.0 / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.1d+180)) then
        tmp = (a * 120.0d0) + (60.0d0 / (t / y))
    else if (y <= 1.6d+153) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / (z - t)))
    else
        tmp = (y - x) * (60.0d0 / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.1e+180) {
		tmp = (a * 120.0) + (60.0 / (t / y));
	} else if (y <= 1.6e+153) {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	} else {
		tmp = (y - x) * (60.0 / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.1e+180:
		tmp = (a * 120.0) + (60.0 / (t / y))
	elif y <= 1.6e+153:
		tmp = (a * 120.0) + (60.0 * (x / (z - t)))
	else:
		tmp = (y - x) * (60.0 / (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.1e+180)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(t / y)));
	elseif (y <= 1.6e+153)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / Float64(z - t))));
	else
		tmp = Float64(Float64(y - x) * Float64(60.0 / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.1e+180)
		tmp = (a * 120.0) + (60.0 / (t / y));
	elseif (y <= 1.6e+153)
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	else
		tmp = (y - x) * (60.0 / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.1e+180], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+153], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e180

   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. 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 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around 0 96.4%

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

      1. neg-mul-1 96.4%

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

   9. Simplified 96.4%

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

   10. Taylor expanded in z around 0 74.0%

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

   if -1.1e180 < y < 1.6000000000000001e153

   1. Initial program 99.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 88.2%

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

   if 1.6000000000000001e153 < y

   1. Initial program 95.3%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

      1. clear-num 95.4%

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

      2. un-div-inv 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in a around 0 90.5%

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

      1. associate-*r/ 90.6%

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

      2. associate-*l/ 90.7%

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

      3. metadata-eval 90.7%

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

      4. associate-*r/ 90.6%

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

      5. *-commutative 90.6%

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

      6. associate-*r/ 90.7%

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

      7. metadata-eval 90.7%

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

   9. Simplified 90.7%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+180}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t}{y}}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+153}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+175} \lor \neg \left(x \leq 1.4 \cdot 10^{+113}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -3e+175) (not (<= x 1.4e+113)))
   (* 60.0 (/ x (- z t)))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3e+175) || !(x <= 1.4e+113)) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-3d+175)) .or. (.not. (x <= 1.4d+113))) then
        tmp = 60.0d0 * (x / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3e+175) || !(x <= 1.4e+113)) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -3e+175) or not (x <= 1.4e+113):
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -3e+175) || !(x <= 1.4e+113))
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -3e+175) || ~((x <= 1.4e+113)))
		tmp = 60.0 * (x / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -3e+175], N[Not[LessEqual[x, 1.4e+113]], $MachinePrecision]], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.0000000000000002e175 or 1.39999999999999999e113 < x

   1. Initial program 98.5%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t} + a \cdot 120} \]
   4. Add Preprocessing
   5. 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 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around 0 74.9%

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

   8. Taylor expanded in x around inf 69.5%

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

   if -3.0000000000000002e175 < x < 1.39999999999999999e113

   1. Initial program 99.2%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 61.9%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+175} \lor \neg \left(x \leq 1.4 \cdot 10^{+113}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. associate-/l* 99.4%

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

3. Simplified 99.4%

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

5. Final simplification 99.4%

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

Alternative 12: 51.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.6 \cdot 10^{+157}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 5.6e+157) (* a 120.0) (* 60.0 (/ y t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 5.6e+157) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 5.6d+157) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 5.6e+157) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 5.6e+157:
		tmp = a * 120.0
	else:
		tmp = 60.0 * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 5.6e+157)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 5.6e+157)
		tmp = a * 120.0;
	else
		tmp = 60.0 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 5.6e+157], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.6000000000000005e157

   1. Initial program 99.4%

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

      1. associate-/l* 99.8%

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

   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 55.1%

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

   if 5.6000000000000005e157 < y

   1. Initial program 95.3%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

      1. clear-num 95.4%

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

      2. un-div-inv 95.4%

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

   6. Applied egg-rr 95.4%

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

   7. Taylor expanded in a around 0 90.5%

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

   8. Taylor expanded in x around 0 64.9%

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

      1. associate-*r/ 70.0%

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

      2. remove-double-neg 70.0%

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

      3. neg-mul-1 70.0%

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

      4. times-frac 69.9%

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

      5. metadata-eval 69.9%

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

      6. neg-sub0 69.9%

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

      7. sub-neg 69.9%

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

      8. +-commutative 69.9%

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

      9. associate--r+ 69.9%

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

      10. neg-sub0 69.9%

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

      11. remove-double-neg 69.9%

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

   10. Simplified 64.9%

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

   11. Taylor expanded in t around inf 52.7%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.6 \cdot 10^{+157}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{+137}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 1.5e+137) (* a 120.0) (* 60.0 (/ x z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 1.5e+137) {
		tmp = a * 120.0;
	} else {
		tmp = 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 (x <= 1.5d+137) then
        tmp = a * 120.0d0
    else
        tmp = 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 (x <= 1.5e+137) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 1.5e+137:
		tmp = a * 120.0
	else:
		tmp = 60.0 * (x / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= 1.5e+137)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= 1.5e+137)
		tmp = a * 120.0;
	else
		tmp = 60.0 * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, 1.5e+137], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.5e137

   1. Initial program 99.3%

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

      1. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around inf 56.2%

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

   if 1.5e137 < x

   1. Initial program 97.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 59.5%

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

   6. Taylor expanded in x around inf 59.5%

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

   7. Taylor expanded in x around inf 42.8%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{+137}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.1% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. associate-/l* 99.4%

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

3. Simplified 99.4%

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

5. Taylor expanded in z around inf 51.2%

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

6. Final simplification 51.2%

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

Developer Target 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024137 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

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

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