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

Percentage Accurate: 99.3% → 99.3%

Time: 13.1s

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: 99.3% 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]

Derivation

1. Initial program 99.8%

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

Alternative 2: 67.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x - y \leq -5 \cdot 10^{+111} \lor \neg \left(x - y \leq 2 \cdot 10^{+90}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- x y) -5e+111) (not (<= (- x y) 2e+90)))
   (* 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) <= -5e+111) || !((x - y) <= 2e+90)) {
		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) <= (-5d+111)) .or. (.not. ((x - y) <= 2d+90))) 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) <= -5e+111) || !((x - y) <= 2e+90)) {
		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) <= -5e+111) or not ((x - y) <= 2e+90):
		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) <= -5e+111) || !(Float64(x - y) <= 2e+90))
		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) <= -5e+111) || ~(((x - y) <= 2e+90)))
		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], -5e+111], N[Not[LessEqual[N[(x - y), $MachinePrecision], 2e+90]], $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) < -4.9999999999999997e111 or 1.99999999999999993e90 < (-.f64 x 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. +-commutative 99.6%

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

      2. fma-define 99.7%

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

      3. associate-*r/ 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/l* 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around 0 72.3%

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

   if -4.9999999999999997e111 < (-.f64 x y) < 1.99999999999999993e90

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 77.1%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - y \leq -5 \cdot 10^{+111} \lor \neg \left(x - y \leq 2 \cdot 10^{+90}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x - y \leq -5 \cdot 10^{+111}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;x - y \leq 2 \cdot 10^{+90}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- x y) -5e+111)
   (* 60.0 (/ (- x y) (- z t)))
   (if (<= (- x y) 2e+90) (* 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 ((x - y) <= -5e+111) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((x - y) <= 2e+90) {
		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 ((x - y) <= (-5d+111)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if ((x - y) <= 2d+90) 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 ((x - y) <= -5e+111) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((x - y) <= 2e+90) {
		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 (x - y) <= -5e+111:
		tmp = 60.0 * ((x - y) / (z - t))
	elif (x - y) <= 2e+90:
		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(x - y) <= -5e+111)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (Float64(x - y) <= 2e+90)
		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 ((x - y) <= -5e+111)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif ((x - y) <= 2e+90)
		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[LessEqual[N[(x - y), $MachinePrecision], -5e+111], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x - y), $MachinePrecision], 2e+90], N[(a * 120.0), $MachinePrecision], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.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* 99.6%

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

   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. +-commutative 99.6%

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

      2. fma-define 99.7%

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

      3. associate-*r/ 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/l* 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in a around 0 71.7%

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

   if -4.9999999999999997e111 < (-.f64 x y) < 1.99999999999999993e90

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 77.1%

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

   if 1.99999999999999993e90 < (-.f64 x 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. +-commutative 99.6%

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

      2. fma-define 99.7%

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

      3. associate-*r/ 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 72.8%

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

      1. clear-num 72.6%

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

      2. un-div-inv 72.9%

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

   9. Applied egg-rr 72.9%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - y \leq -5 \cdot 10^{+111}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;x - y \leq 2 \cdot 10^{+90}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+91} \lor \neg \left(x \leq 3.5 \cdot 10^{-60}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -3.2e+91) (not (<= x 3.5e-60)))
   (+ (* a 120.0) (* 60.0 (/ x (- z t))))
   (+ (* a 120.0) (/ (* y -60.0) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3.2e+91) || !(x <= 3.5e-60)) {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-3.2d+91)) .or. (.not. (x <= 3.5d-60))) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / (z - t)))
    else
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3.2e+91) || !(x <= 3.5e-60)) {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -3.2e+91) or not (x <= 3.5e-60):
		tmp = (a * 120.0) + (60.0 * (x / (z - t)))
	else:
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -3.2e+91) || !(x <= 3.5e-60))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / Float64(z - t))));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -3.2e+91) || ~((x <= 3.5e-60)))
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	else
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -3.2e+91], N[Not[LessEqual[x, 3.5e-60]], $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[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.19999999999999989e91 or 3.49999999999999976e-60 < x

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 89.3%

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

   if -3.19999999999999989e91 < x < 3.49999999999999976e-60

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 97.0%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+91} \lor \neg \left(x \leq 3.5 \cdot 10^{-60}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+91} \lor \neg \left(x \leq 7.3 \cdot 10^{-60}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t - z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -5.4e+91) (not (<= x 7.3e-60)))
   (+ (* 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 <= -5.4e+91) || !(x <= 7.3e-60)) {
		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 <= (-5.4d+91)) .or. (.not. (x <= 7.3d-60))) 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 <= -5.4e+91) || !(x <= 7.3e-60)) {
		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 <= -5.4e+91) or not (x <= 7.3e-60):
		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 <= -5.4e+91) || !(x <= 7.3e-60))
		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 <= -5.4e+91) || ~((x <= 7.3e-60)))
		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, -5.4e+91], N[Not[LessEqual[x, 7.3e-60]], $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 < -5.4e91 or 7.2999999999999997e-60 < x

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 89.3%

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

   if -5.4e91 < x < 7.2999999999999997e-60

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 97.0%

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

      1. +-commutative 97.0%

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

      2. fma-define 97.0%

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

      3. associate-*r/ 97.0%

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

      4. remove-double-neg 97.0%

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

      5. neg-mul-1 97.0%

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

      6. times-frac 97.0%

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

      7. metadata-eval 97.0%

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

      8. neg-sub0 97.0%

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

      9. sub-neg 97.0%

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

      10. +-commutative 97.0%

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

      11. associate--r+ 97.0%

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

      12. neg-sub0 97.0%

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

      13. remove-double-neg 97.0%

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

   7. Simplified 97.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(120, a, 60 \cdot \frac{y}{t - z}\right)} \]
   8. Step-by-step derivation

      1. fma-undefine 97.0%

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

      2. *-commutative 97.0%

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

      3. +-commutative 97.0%

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

      4. clear-num 96.9%

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

      5. un-div-inv 97.0%

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

   9. Applied egg-rr 97.0%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+91} \lor \neg \left(x \leq 7.3 \cdot 10^{-60}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{t - z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-68} \lor \neg \left(t \leq 62000\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.2e-68) (not (<= t 62000.0)))
   (+ (* a 120.0) (* 60.0 (/ (- y x) t)))
   (+ (* a 120.0) (* 60.0 (/ (- x y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.2e-68) || !(t <= 62000.0)) {
		tmp = (a * 120.0) + (60.0 * ((y - x) / t));
	} else {
		tmp = (a * 120.0) + (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 ((t <= (-3.2d-68)) .or. (.not. (t <= 62000.0d0))) then
        tmp = (a * 120.0d0) + (60.0d0 * ((y - x) / t))
    else
        tmp = (a * 120.0d0) + (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 ((t <= -3.2e-68) || !(t <= 62000.0)) {
		tmp = (a * 120.0) + (60.0 * ((y - x) / t));
	} else {
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.2e-68) or not (t <= 62000.0):
		tmp = (a * 120.0) + (60.0 * ((y - x) / t))
	else:
		tmp = (a * 120.0) + (60.0 * ((x - y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.2e-68) || !(t <= 62000.0))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(y - x) / t)));
	else
		tmp = Float64(Float64(a * 120.0) + 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 ((t <= -3.2e-68) || ~((t <= 62000.0)))
		tmp = (a * 120.0) + (60.0 * ((y - x) / t));
	else
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.2e-68], N[Not[LessEqual[t, 62000.0]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.1999999999999999e-68 or 62000 < t

   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 0 87.9%

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

      1. associate-*r/ 87.9%

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

      2. neg-mul-1 87.9%

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

      3. neg-sub0 87.9%

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

      4. sub-neg 87.9%

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

      5. +-commutative 87.9%

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

      6. associate--r+ 87.9%

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

      7. neg-sub0 87.9%

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

      8. remove-double-neg 87.9%

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

   7. Simplified 87.9%

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

   if -3.1999999999999999e-68 < t < 62000

   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 87.0%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-68} \lor \neg \left(t \leq 62000\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+92}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{+243}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.3e+92)
   (/ 60.0 (/ (- z t) (- x y)))
   (if (<= y 3.15e+243)
     (+ (* a 120.0) (* 60.0 (/ x (- z t))))
     (/ (* y -60.0) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.3e+92) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (y <= 3.15e+243) {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	} else {
		tmp = (y * -60.0) / (z - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-4.3d+92)) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else if (y <= 3.15d+243) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / (z - t)))
    else
        tmp = (y * (-60.0d0)) / (z - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.3e+92) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (y <= 3.15e+243) {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	} else {
		tmp = (y * -60.0) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.3e+92:
		tmp = 60.0 / ((z - t) / (x - y))
	elif y <= 3.15e+243:
		tmp = (a * 120.0) + (60.0 * (x / (z - t)))
	else:
		tmp = (y * -60.0) / (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.3e+92)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	elseif (y <= 3.15e+243)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / Float64(z - t))));
	else
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.3e+92)
		tmp = 60.0 / ((z - t) / (x - y));
	elseif (y <= 3.15e+243)
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	else
		tmp = (y * -60.0) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.3e+92], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.15e+243], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2999999999999998e92

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. fma-define 99.7%

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

      3. associate-*r/ 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/l* 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in a around 0 69.7%

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

      1. clear-num 69.6%

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

      2. un-div-inv 69.8%

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

   9. Applied egg-rr 69.8%

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

   if -4.2999999999999998e92 < y < 3.14999999999999989e243

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 89.7%

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

   if 3.14999999999999989e243 < 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* 99.3%

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

   3. Simplified 99.3%

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

      1. +-commutative 99.3%

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

      2. fma-define 99.4%

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

      3. associate-*r/ 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-/l* 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. clear-num 99.4%

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

      2. un-div-inv 99.8%

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

      3. div-inv 99.8%

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

      4. metadata-eval 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in y around inf 85.3%

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

       1. associate-*r/ 85.8%

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

       2. *-commutative 85.8%

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

   11. Simplified 85.8%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+92}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{+243}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{+141} \lor \neg \left(x \leq 4.05 \cdot 10^{+158}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.08e+141) (not (<= x 4.05e+158)))
   (* 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 <= -1.08e+141) || !(x <= 4.05e+158)) {
		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 <= (-1.08d+141)) .or. (.not. (x <= 4.05d+158))) 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 <= -1.08e+141) || !(x <= 4.05e+158)) {
		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 <= -1.08e+141) or not (x <= 4.05e+158):
		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 <= -1.08e+141) || !(x <= 4.05e+158))
		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 <= -1.08e+141) || ~((x <= 4.05e+158)))
		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, -1.08e+141], N[Not[LessEqual[x, 4.05e+158]], $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 < -1.08000000000000007e141 or 4.0499999999999999e158 < 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* 99.6%

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

   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. +-commutative 99.6%

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

      2. fma-define 99.6%

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

      3. associate-*r/ 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-/l* 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 73.9%

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

   if -1.08000000000000007e141 < x < 4.0499999999999999e158

   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 63.2%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.08 \cdot 10^{+141} \lor \neg \left(x \leq 4.05 \cdot 10^{+158}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+158}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.45e+139)
   (* x (/ 60.0 (- z t)))
   (if (<= x 7.4e+158) (* a 120.0) (/ x (* (- z t) 0.016666666666666666)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.45e+139) {
		tmp = x * (60.0 / (z - t));
	} else if (x <= 7.4e+158) {
		tmp = a * 120.0;
	} else {
		tmp = x / ((z - t) * 0.016666666666666666);
	}
	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 <= (-1.45d+139)) then
        tmp = x * (60.0d0 / (z - t))
    else if (x <= 7.4d+158) then
        tmp = a * 120.0d0
    else
        tmp = x / ((z - t) * 0.016666666666666666d0)
    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 <= -1.45e+139) {
		tmp = x * (60.0 / (z - t));
	} else if (x <= 7.4e+158) {
		tmp = a * 120.0;
	} else {
		tmp = x / ((z - t) * 0.016666666666666666);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.45e+139:
		tmp = x * (60.0 / (z - t))
	elif x <= 7.4e+158:
		tmp = a * 120.0
	else:
		tmp = x / ((z - t) * 0.016666666666666666)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.45e+139)
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	elseif (x <= 7.4e+158)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(x / Float64(Float64(z - t) * 0.016666666666666666));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.45e+139)
		tmp = x * (60.0 / (z - t));
	elseif (x <= 7.4e+158)
		tmp = a * 120.0;
	else
		tmp = x / ((z - t) * 0.016666666666666666);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.45e+139], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.4e+158], N[(a * 120.0), $MachinePrecision], N[(x / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4499999999999999e139

   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. +-commutative 99.6%

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

      2. fma-define 99.6%

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

      3. associate-*r/ 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-/l* 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 75.1%

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

      1. associate-*r/ 75.1%

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

      2. associate-*l/ 75.3%

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

      3. *-commutative 75.3%

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

   9. Simplified 75.3%

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

   if -1.4499999999999999e139 < x < 7.40000000000000021e158

   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 63.2%

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

   if 7.40000000000000021e158 < 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* 99.6%

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

   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. +-commutative 99.6%

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

      2. fma-define 99.6%

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

      3. associate-*r/ 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in x around inf 72.7%

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

      1. metadata-eval 72.7%

         \[\leadsto \color{blue}{\frac{1}{0.016666666666666666}} \cdot \frac{x}{z - t} \]

      2. times-frac 72.7%

         \[\leadsto \color{blue}{\frac{1 \cdot x}{0.016666666666666666 \cdot \left(z - t\right)}} \]

      3. *-un-lft-identity 72.7%

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

      4. *-commutative 72.7%

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

   9. Applied egg-rr 72.7%

      \[\leadsto \color{blue}{\frac{x}{\left(z - t\right) \cdot 0.016666666666666666}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+139}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+158}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.76 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+159}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.76e+146)
   (* x (/ 60.0 (- z t)))
   (if (<= x 1.9e+159) (* a 120.0) (* 60.0 (/ x (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.76e+146) {
		tmp = x * (60.0 / (z - t));
	} else if (x <= 1.9e+159) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (x / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.76d+146)) then
        tmp = x * (60.0d0 / (z - t))
    else if (x <= 1.9d+159) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (x / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.76e+146) {
		tmp = x * (60.0 / (z - t));
	} else if (x <= 1.9e+159) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (x / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.76e+146:
		tmp = x * (60.0 / (z - t))
	elif x <= 1.9e+159:
		tmp = a * 120.0
	else:
		tmp = 60.0 * (x / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.76e+146)
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	elseif (x <= 1.9e+159)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.76e+146)
		tmp = x * (60.0 / (z - t));
	elseif (x <= 1.9e+159)
		tmp = a * 120.0;
	else
		tmp = 60.0 * (x / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.76e+146], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+159], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.76000000000000007e146

   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. +-commutative 99.6%

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

      2. fma-define 99.6%

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

      3. associate-*r/ 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-/l* 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 75.1%

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

      1. associate-*r/ 75.1%

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

      2. associate-*l/ 75.3%

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

      3. *-commutative 75.3%

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

   9. Simplified 75.3%

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

   if -1.76000000000000007e146 < x < 1.89999999999999983e159

   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 63.2%

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

   if 1.89999999999999983e159 < 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* 99.6%

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

   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. +-commutative 99.6%

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

      2. fma-define 99.6%

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

      3. associate-*r/ 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in x around inf 72.7%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.76 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+159}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+147} \lor \neg \left(x \leq 2.35 \cdot 10^{+166}\right):\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.95e+147) (not (<= x 2.35e+166)))
   (/ (* 60.0 x) z)
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.95e+147) || !(x <= 2.35e+166)) {
		tmp = (60.0 * x) / 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 ((x <= (-1.95d+147)) .or. (.not. (x <= 2.35d+166))) then
        tmp = (60.0d0 * x) / 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 ((x <= -1.95e+147) || !(x <= 2.35e+166)) {
		tmp = (60.0 * x) / z;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.95e+147) or not (x <= 2.35e+166):
		tmp = (60.0 * x) / z
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.95e+147) || !(x <= 2.35e+166))
		tmp = Float64(Float64(60.0 * x) / 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 ((x <= -1.95e+147) || ~((x <= 2.35e+166)))
		tmp = (60.0 * x) / z;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.95e+147], N[Not[LessEqual[x, 2.35e+166]], $MachinePrecision]], N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.95000000000000008e147 or 2.35e166 < 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* 99.6%

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

   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. +-commutative 99.6%

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

      2. fma-define 99.6%

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

      3. associate-*r/ 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in x around inf 74.6%

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

   8. Taylor expanded in z around inf 41.7%

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

      1. associate-*r/ 41.8%

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

   10. Simplified 41.8%

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

   if -1.95000000000000008e147 < x < 2.35e166

   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 63.1%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+147} \lor \neg \left(x \leq 2.35 \cdot 10^{+166}\right):\\ \;\;\;\;\frac{60 \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+147} \lor \neg \left(x \leq 4.3 \cdot 10^{+166}\right):\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -4.9e+147) (not (<= x 4.3e+166))) (* 60.0 (/ x z)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4.9e+147) || !(x <= 4.3e+166)) {
		tmp = 60.0 * (x / 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 ((x <= (-4.9d+147)) .or. (.not. (x <= 4.3d+166))) then
        tmp = 60.0d0 * (x / 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 ((x <= -4.9e+147) || !(x <= 4.3e+166)) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -4.9e+147) or not (x <= 4.3e+166):
		tmp = 60.0 * (x / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -4.9e+147) || !(x <= 4.3e+166))
		tmp = Float64(60.0 * Float64(x / 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 ((x <= -4.9e+147) || ~((x <= 4.3e+166)))
		tmp = 60.0 * (x / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -4.9e+147], N[Not[LessEqual[x, 4.3e+166]], $MachinePrecision]], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8999999999999998e147 or 4.3e166 < 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* 99.6%

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

   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. +-commutative 99.6%

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

      2. fma-define 99.6%

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

      3. associate-*r/ 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in x around inf 74.6%

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

   8. Taylor expanded in z around inf 41.7%

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

   if -4.8999999999999998e147 < x < 4.3e166

   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 63.1%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+147} \lor \neg \left(x \leq 4.3 \cdot 10^{+166}\right):\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+178} \lor \neg \left(x \leq 1.8 \cdot 10^{+163}\right):\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.9e+178) (not (<= x 1.8e+163)))
   (* -60.0 (/ x t))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.9e+178) || !(x <= 1.8e+163)) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-2.9d+178)) .or. (.not. (x <= 1.8d+163))) then
        tmp = (-60.0d0) * (x / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.9e+178) || !(x <= 1.8e+163)) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.9e+178) or not (x <= 1.8e+163):
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.9e+178) || !(x <= 1.8e+163))
		tmp = Float64(-60.0 * Float64(x / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2.9e+178) || ~((x <= 1.8e+163)))
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.9e+178], N[Not[LessEqual[x, 1.8e+163]], $MachinePrecision]], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9e178 or 1.79999999999999989e163 < 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* 99.6%

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

   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. +-commutative 99.6%

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

      2. fma-define 99.6%

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

      3. associate-*r/ 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-/l* 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in x around inf 76.0%

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

   8. Taylor expanded in z around 0 38.8%

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

   if -2.9e178 < x < 1.79999999999999989e163

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 62.4%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+178} \lor \neg \left(x \leq 1.8 \cdot 10^{+163}\right):\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 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 99.8%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 15: 49.8% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in z around inf 52.5%

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

6. Final simplification 52.5%

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

Developer Target 1: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024139 
(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)))