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

Percentage Accurate: 99.3% → 99.8%

Time: 12.7s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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 99.8%

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

6. Applied egg-rr 99.8%

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

Alternative 2: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-74} \lor \neg \left(a \cdot 120 \leq 10^{-158}\right):\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -2e-74) (not (<= (* a 120.0) 1e-158)))
   (+ (* x (/ 60.0 (- z t))) (* a 120.0))
   (/ 60.0 (/ (- z t) (- x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e-74) || !((a * 120.0) <= 1e-158)) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else {
		tmp = 60.0 / ((z - t) / (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-2d-74)) .or. (.not. ((a * 120.0d0) <= 1d-158))) then
        tmp = (x * (60.0d0 / (z - t))) + (a * 120.0d0)
    else
        tmp = 60.0d0 / ((z - t) / (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e-74) || !((a * 120.0) <= 1e-158)) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else {
		tmp = 60.0 / ((z - t) / (x - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -2e-74) or not ((a * 120.0) <= 1e-158):
		tmp = (x * (60.0 / (z - t))) + (a * 120.0)
	else:
		tmp = 60.0 / ((z - t) / (x - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -2e-74) || !(Float64(a * 120.0) <= 1e-158))
		tmp = Float64(Float64(x * Float64(60.0 / Float64(z - t))) + Float64(a * 120.0));
	else
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -2e-74) || ~(((a * 120.0) <= 1e-158)))
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	else
		tmp = 60.0 / ((z - t) / (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-74], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-158]], $MachinePrecision]], N[(N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.99999999999999992e-74 or 1.00000000000000006e-158 < (*.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. 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 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around inf 88.1%

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

      1. associate-*r/ 88.1%

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

      2. associate-*l/ 88.1%

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

      3. metadata-eval 88.1%

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

      4. associate-*r/ 88.1%

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

      5. *-commutative 88.1%

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

      6. associate-*r/ 88.1%

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

      7. metadata-eval 88.1%

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

   9. Simplified 88.1%

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

   if -1.99999999999999992e-74 < (*.f64 a #s(literal 120 binary64)) < 1.00000000000000006e-158

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

      2. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 88.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   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 99.7%

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

   7. Applied egg-rr 88.1%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-74} \lor \neg \left(a \cdot 120 \leq 10^{-158}\right):\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-74} \lor \neg \left(a \cdot 120 \leq 1000000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -2e-74) (not (<= (* a 120.0) 1000000.0)))
   (* a 120.0)
   (/ 60.0 (/ (- z t) (- x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e-74) || !((a * 120.0) <= 1000000.0)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 / ((z - t) / (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-2d-74)) .or. (.not. ((a * 120.0d0) <= 1000000.0d0))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 / ((z - t) / (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e-74) || !((a * 120.0) <= 1000000.0)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 / ((z - t) / (x - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -2e-74) or not ((a * 120.0) <= 1000000.0):
		tmp = a * 120.0
	else:
		tmp = 60.0 / ((z - t) / (x - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -2e-74) || !(Float64(a * 120.0) <= 1000000.0))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -2e-74) || ~(((a * 120.0) <= 1000000.0)))
		tmp = a * 120.0;
	else
		tmp = 60.0 / ((z - t) / (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-74], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1000000.0]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.99999999999999992e-74 or 1e6 < (*.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%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 83.9%

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

   if -1.99999999999999992e-74 < (*.f64 a #s(literal 120 binary64)) < 1e6

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 77.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   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 99.8%

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

   7. Applied egg-rr 77.1%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-74} \lor \neg \left(a \cdot 120 \leq 1000000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-74} \lor \neg \left(a \cdot 120 \leq 1000000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -2e-74) (not (<= (* a 120.0) 1000000.0)))
   (* a 120.0)
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e-74) || !((a * 120.0) <= 1000000.0)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-2d-74)) .or. (.not. ((a * 120.0d0) <= 1000000.0d0))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -2e-74) || !((a * 120.0) <= 1000000.0)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -2e-74) or not ((a * 120.0) <= 1000000.0):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -2e-74) || !(Float64(a * 120.0) <= 1000000.0))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -2e-74) || ~(((a * 120.0) <= 1000000.0)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-74], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1000000.0]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.99999999999999992e-74 or 1e6 < (*.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%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 83.9%

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

   if -1.99999999999999992e-74 < (*.f64 a #s(literal 120 binary64)) < 1e6

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 77.1%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2 \cdot 10^{-74} \lor \neg \left(a \cdot 120 \leq 1000000\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{-109}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-244}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-160}:\\ \;\;\;\;\frac{60}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.06e-109)
   (* a 120.0)
   (if (<= a -3.4e-244)
     (* 60.0 (/ (- y x) t))
     (if (<= a 1.75e-160) (/ 60.0 (/ z (- x y))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.06e-109) {
		tmp = a * 120.0;
	} else if (a <= -3.4e-244) {
		tmp = 60.0 * ((y - x) / t);
	} else if (a <= 1.75e-160) {
		tmp = 60.0 / (z / (x - y));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.06d-109)) then
        tmp = a * 120.0d0
    else if (a <= (-3.4d-244)) then
        tmp = 60.0d0 * ((y - x) / t)
    else if (a <= 1.75d-160) then
        tmp = 60.0d0 / (z / (x - y))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.06e-109) {
		tmp = a * 120.0;
	} else if (a <= -3.4e-244) {
		tmp = 60.0 * ((y - x) / t);
	} else if (a <= 1.75e-160) {
		tmp = 60.0 / (z / (x - y));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.06e-109:
		tmp = a * 120.0
	elif a <= -3.4e-244:
		tmp = 60.0 * ((y - x) / t)
	elif a <= 1.75e-160:
		tmp = 60.0 / (z / (x - y))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.06e-109)
		tmp = Float64(a * 120.0);
	elseif (a <= -3.4e-244)
		tmp = Float64(60.0 * Float64(Float64(y - x) / t));
	elseif (a <= 1.75e-160)
		tmp = Float64(60.0 / Float64(z / Float64(x - y)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.06e-109)
		tmp = a * 120.0;
	elseif (a <= -3.4e-244)
		tmp = 60.0 * ((y - x) / t);
	elseif (a <= 1.75e-160)
		tmp = 60.0 / (z / (x - y));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.06e-109], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -3.4e-244], N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.75e-160], N[(60.0 / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.06e-109 or 1.7500000000000001e-160 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 72.8%

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

   if -1.06e-109 < a < -3.40000000000000009e-244

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 93.4%

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

   6. Taylor expanded in z around 0 71.0%

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

      1. associate-*r/ 71.0%

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

      2. neg-mul-1 71.0%

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

      3. neg-sub0 71.0%

         \[\leadsto 60 \cdot \frac{\color{blue}{0 - \left(x - y\right)}}{t} \]

      4. sub-neg 71.0%

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

      5. +-commutative 71.0%

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

      6. associate--r+ 71.0%

         \[\leadsto 60 \cdot \frac{\color{blue}{\left(0 - \left(-y\right)\right) - x}}{t} \]

      7. neg-sub0 71.0%

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

      8. remove-double-neg 71.0%

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

   8. Simplified 71.0%

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

   if -3.40000000000000009e-244 < a < 1.7500000000000001e-160

   1. Initial program 99.5%

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

      1. associate-/l* 99.7%

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

      2. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 90.5%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   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 99.7%

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

   7. Applied egg-rr 90.5%

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

   8. Taylor expanded in z around inf 64.5%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{-109}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-244}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-160}:\\ \;\;\;\;\frac{60}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{-110}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-242}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-160}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.22e-110)
   (* a 120.0)
   (if (<= a -1.7e-242)
     (* 60.0 (/ (- y x) t))
     (if (<= a 2.7e-160) (* 60.0 (/ (- x y) z)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.22e-110) {
		tmp = a * 120.0;
	} else if (a <= -1.7e-242) {
		tmp = 60.0 * ((y - x) / t);
	} else if (a <= 2.7e-160) {
		tmp = 60.0 * ((x - y) / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.22d-110)) then
        tmp = a * 120.0d0
    else if (a <= (-1.7d-242)) then
        tmp = 60.0d0 * ((y - x) / t)
    else if (a <= 2.7d-160) then
        tmp = 60.0d0 * ((x - y) / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.22e-110) {
		tmp = a * 120.0;
	} else if (a <= -1.7e-242) {
		tmp = 60.0 * ((y - x) / t);
	} else if (a <= 2.7e-160) {
		tmp = 60.0 * ((x - y) / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.22e-110:
		tmp = a * 120.0
	elif a <= -1.7e-242:
		tmp = 60.0 * ((y - x) / t)
	elif a <= 2.7e-160:
		tmp = 60.0 * ((x - y) / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.22e-110)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.7e-242)
		tmp = Float64(60.0 * Float64(Float64(y - x) / t));
	elseif (a <= 2.7e-160)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.22e-110)
		tmp = a * 120.0;
	elseif (a <= -1.7e-242)
		tmp = 60.0 * ((y - x) / t);
	elseif (a <= 2.7e-160)
		tmp = 60.0 * ((x - y) / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.22e-110], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.7e-242], N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.7e-160], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.22e-110 or 2.7000000000000001e-160 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 72.8%

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

   if -1.22e-110 < a < -1.7e-242

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 93.4%

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

   6. Taylor expanded in z around 0 71.0%

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

      1. associate-*r/ 71.0%

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

      2. neg-mul-1 71.0%

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

      3. neg-sub0 71.0%

         \[\leadsto 60 \cdot \frac{\color{blue}{0 - \left(x - y\right)}}{t} \]

      4. sub-neg 71.0%

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

      5. +-commutative 71.0%

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

      6. associate--r+ 71.0%

         \[\leadsto 60 \cdot \frac{\color{blue}{\left(0 - \left(-y\right)\right) - x}}{t} \]

      7. neg-sub0 71.0%

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

      8. remove-double-neg 71.0%

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

   8. Simplified 71.0%

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

   if -1.7e-242 < a < 2.7000000000000001e-160

   1. Initial program 99.5%

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

      1. associate-/l* 99.7%

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

      2. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 90.5%

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

   6. Taylor expanded in z around inf 64.4%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.22 \cdot 10^{-110}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-242}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-160}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+68} \lor \neg \left(y \leq 6.4 \cdot 10^{+89}\right):\\ \;\;\;\;y \cdot \frac{-60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -8.8e+68) (not (<= y 6.4e+89)))
   (+ (* y (/ -60.0 (- z t))) (* a 120.0))
   (+ (* x (/ 60.0 (- z t))) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -8.8e+68) || !(y <= 6.4e+89)) {
		tmp = (y * (-60.0 / (z - t))) + (a * 120.0);
	} else {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-8.8d+68)) .or. (.not. (y <= 6.4d+89))) then
        tmp = (y * ((-60.0d0) / (z - t))) + (a * 120.0d0)
    else
        tmp = (x * (60.0d0 / (z - t))) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -8.8e+68) || !(y <= 6.4e+89)) {
		tmp = (y * (-60.0 / (z - t))) + (a * 120.0);
	} else {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -8.8e+68) or not (y <= 6.4e+89):
		tmp = (y * (-60.0 / (z - t))) + (a * 120.0)
	else:
		tmp = (x * (60.0 / (z - t))) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -8.8e+68) || !(y <= 6.4e+89))
		tmp = Float64(Float64(y * Float64(-60.0 / Float64(z - t))) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(x * Float64(60.0 / Float64(z - t))) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -8.8e+68) || ~((y <= 6.4e+89)))
		tmp = (y * (-60.0 / (z - t))) + (a * 120.0);
	else
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -8.8e+68], N[Not[LessEqual[y, 6.4e+89]], $MachinePrecision]], N[(N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.79999999999999949e68 or 6.39999999999999974e89 < 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. 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 95.2%

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

      1. associate-*r/ 95.3%

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

      2. *-commutative 95.3%

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

      3. associate-*r/ 95.3%

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

   9. Simplified 95.3%

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

   if -8.79999999999999949e68 < y < 6.39999999999999974e89

   1. Initial program 99.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

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

   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 95.4%

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

      1. associate-*r/ 95.3%

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

      2. associate-*l/ 95.3%

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

      3. metadata-eval 95.3%

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

      4. associate-*r/ 95.3%

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

      5. *-commutative 95.3%

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

      6. associate-*r/ 95.3%

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

      7. metadata-eval 95.3%

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

   9. Simplified 95.3%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+68} \lor \neg \left(y \leq 6.4 \cdot 10^{+89}\right):\\ \;\;\;\;y \cdot \frac{-60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+69}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-60}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.32e+69)
   (+ (/ (* y -60.0) (- z t)) (* a 120.0))
   (if (<= y 5.2e+89)
     (+ (* x (/ 60.0 (- z t))) (* a 120.0))
     (+ (* y (/ -60.0 (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.32e+69) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else if (y <= 5.2e+89) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else {
		tmp = (y * (-60.0 / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.32d+69)) then
        tmp = ((y * (-60.0d0)) / (z - t)) + (a * 120.0d0)
    else if (y <= 5.2d+89) then
        tmp = (x * (60.0d0 / (z - t))) + (a * 120.0d0)
    else
        tmp = (y * ((-60.0d0) / (z - t))) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.32e+69) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else if (y <= 5.2e+89) {
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	} else {
		tmp = (y * (-60.0 / (z - t))) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.32e+69:
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	elif y <= 5.2e+89:
		tmp = (x * (60.0 / (z - t))) + (a * 120.0)
	else:
		tmp = (y * (-60.0 / (z - t))) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.32e+69)
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	elseif (y <= 5.2e+89)
		tmp = Float64(Float64(x * Float64(60.0 / Float64(z - t))) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(y * Float64(-60.0 / Float64(z - t))) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.32e+69)
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	elseif (y <= 5.2e+89)
		tmp = (x * (60.0 / (z - t))) + (a * 120.0);
	else
		tmp = (y * (-60.0 / (z - t))) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.32e+69], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+89], N[(N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.32e69

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 93.9%

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

   if -1.32e69 < y < 5.2000000000000001e89

   1. Initial program 99.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

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

   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 95.4%

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

      1. associate-*r/ 95.3%

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

      2. associate-*l/ 95.3%

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

      3. metadata-eval 95.3%

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

      4. associate-*r/ 95.3%

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

      5. *-commutative 95.3%

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

      6. associate-*r/ 95.3%

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

      7. metadata-eval 95.3%

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

   9. Simplified 95.3%

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

   if 5.2000000000000001e89 < y

   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. 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%

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

   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 97.1%

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

      1. associate-*r/ 97.2%

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

      2. *-commutative 97.2%

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

      3. associate-*r/ 97.3%

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

   9. Simplified 97.3%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+69}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+89}:\\ \;\;\;\;x \cdot \frac{60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-60}{z - t} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-107} \lor \neg \left(a \leq 1.6 \cdot 10^{-160}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8.5e-107) (not (<= a 1.6e-160)))
   (* a 120.0)
   (* 60.0 (/ (- x y) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.5e-107) || !(a <= 1.6e-160)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-8.5d-107)) .or. (.not. (a <= 1.6d-160))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.5e-107) || !(a <= 1.6e-160)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8.5e-107) or not (a <= 1.6e-160):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8.5e-107) || !(a <= 1.6e-160))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -8.5e-107) || ~((a <= 1.6e-160)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8.5e-107], N[Not[LessEqual[a, 1.6e-160]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.49999999999999956e-107 or 1.60000000000000004e-160 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 72.8%

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

   if -8.49999999999999956e-107 < a < 1.60000000000000004e-160

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

      2. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 91.5%

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

   6. Taylor expanded in z around inf 56.0%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-107} \lor \neg \left(a \leq 1.6 \cdot 10^{-160}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-82} \lor \neg \left(a \leq 2.6 \cdot 10^{-160}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.1e-82) (not (<= a 2.6e-160)))
   (* a 120.0)
   (* 60.0 (/ y (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.1e-82) || !(a <= 2.6e-160)) {
		tmp = a * 120.0;
	} else {
		tmp = 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 ((a <= (-2.1d-82)) .or. (.not. (a <= 2.6d-160))) then
        tmp = a * 120.0d0
    else
        tmp = 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 ((a <= -2.1e-82) || !(a <= 2.6e-160)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.1e-82) or not (a <= 2.6e-160):
		tmp = a * 120.0
	else:
		tmp = 60.0 * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.1e-82) || !(a <= 2.6e-160))
		tmp = Float64(a * 120.0);
	else
		tmp = 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 ((a <= -2.1e-82) || ~((a <= 2.6e-160)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.1e-82], N[Not[LessEqual[a, 2.6e-160]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.1e-82 or 2.60000000000000003e-160 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 73.9%

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

   if -2.1e-82 < a < 2.60000000000000003e-160

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

      2. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 88.1%

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

   6. Taylor expanded in x around 0 49.2%

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

      1. associate-*r/ 49.2%

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

      2. remove-double-neg 49.2%

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

      3. neg-mul-1 49.2%

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

      4. times-frac 49.2%

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

      5. metadata-eval 49.2%

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

      6. neg-sub0 49.2%

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

      7. sub-neg 49.2%

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

      8. +-commutative 49.2%

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

      9. associate--r+ 49.2%

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

      10. neg-sub0 49.2%

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

      11. remove-double-neg 49.2%

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

   8. Simplified 49.2%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-82} \lor \neg \left(a \leq 2.6 \cdot 10^{-160}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{-110} \lor \neg \left(a \leq 1.25 \cdot 10^{-160}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.25e-110) (not (<= a 1.25e-160)))
   (* a 120.0)
   (* 60.0 (/ y t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.25e-110) || !(a <= 1.25e-160)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.25d-110)) .or. (.not. (a <= 1.25d-160))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.25e-110) || !(a <= 1.25e-160)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.25e-110) or not (a <= 1.25e-160):
		tmp = a * 120.0
	else:
		tmp = 60.0 * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.25e-110) || !(a <= 1.25e-160))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.25e-110) || ~((a <= 1.25e-160)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.25e-110], N[Not[LessEqual[a, 1.25e-160]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.25e-110 or 1.24999999999999999e-160 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 72.8%

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

   if -2.25e-110 < a < 1.24999999999999999e-160

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

      2. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 91.5%

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

   6. Taylor expanded in z around 0 48.2%

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

      1. associate-*r/ 48.2%

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

      2. neg-mul-1 48.2%

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

      3. neg-sub0 48.2%

         \[\leadsto 60 \cdot \frac{\color{blue}{0 - \left(x - y\right)}}{t} \]

      4. sub-neg 48.2%

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

      5. +-commutative 48.2%

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

      6. associate--r+ 48.2%

         \[\leadsto 60 \cdot \frac{\color{blue}{\left(0 - \left(-y\right)\right) - x}}{t} \]

      7. neg-sub0 48.2%

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

      8. remove-double-neg 48.2%

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

   8. Simplified 48.2%

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

   9. Taylor expanded in y around inf 29.3%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{-110} \lor \neg \left(a \leq 1.25 \cdot 10^{-160}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. *-commutative 99.7%

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

   2. associate-/l* 99.8%

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

4. Applied egg-rr 99.8%

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

Alternative 13: 99.8% accurate, 1.0× speedup

Math

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

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(60.0 * Float64(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[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

Alternative 14: 50.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.35 \cdot 10^{+247}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x 1.35e+247) (* a 120.0) (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= 1.35e+247) {
		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 <= 1.35d+247) 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 <= 1.35e+247) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= 1.35e+247:
		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 <= 1.35e+247)
		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 <= 1.35e+247)
		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, 1.35e+247], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.35e247

   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%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 60.2%

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

   if 1.35e247 < x

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

      2. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around inf 86.0%

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

      1. *-commutative 86.0%

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

   7. Simplified 86.0%

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

   8. Taylor expanded in z around 0 65.5%

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

      1. +-commutative 65.5%

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

      2. *-commutative 65.5%

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

   10. Simplified 65.5%

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

   11. Taylor expanded in x around inf 64.7%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.35 \cdot 10^{+247}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.0% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. associate-/l* 99.8%

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

   2. fma-define 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in z around inf 58.1%

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

6. Final simplification 58.1%

   \[\leadsto a \cdot 120 \]
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 2024123 
(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)))