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

Percentage Accurate: 99.4% → 99.8%

Time: 10.4s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0 + N[(N[(x - y), $MachinePrecision] * N[(60.0 / 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. Step-by-step derivation

   1. +-commutative 99.8%

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

   2. fma-define 99.8%

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

   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. Add Preprocessing

Alternative 2: 82.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-28} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-83}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -1e-28) (not (<= (* a 120.0) 5e-83)))
   (+ (* a 120.0) (* 60.0 (/ y (- t z))))
   (* 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) <= -1e-28) || !((a * 120.0) <= 5e-83)) {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	} 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) <= (-1d-28)) .or. (.not. ((a * 120.0d0) <= 5d-83))) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / (t - z)))
    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) <= -1e-28) || !((a * 120.0) <= 5e-83)) {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -1e-28) or not ((a * 120.0) <= 5e-83):
		tmp = (a * 120.0) + (60.0 * (y / (t - z)))
	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) <= -1e-28) || !(Float64(a * 120.0) <= 5e-83))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / Float64(t - z))));
	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) <= -1e-28) || ~(((a * 120.0) <= 5e-83)))
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	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], -1e-28], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-83]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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)) < -9.99999999999999971e-29 or 5e-83 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 92.1%

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

      1. associate-*r/ 92.1%

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

      2. remove-double-neg 92.1%

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

      3. neg-mul-1 92.1%

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

      4. times-frac 92.1%

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

      5. metadata-eval 92.1%

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

      6. neg-sub0 92.1%

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

      7. sub-neg 92.1%

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

      8. +-commutative 92.1%

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

      9. associate--r+ 92.1%

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

      10. neg-sub0 92.1%

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

      11. remove-double-neg 92.1%

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

   7. Simplified 92.1%

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

   if -9.99999999999999971e-29 < (*.f64 a #s(literal 120 binary64)) < 5e-83

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 84.5%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-28} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-83}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-25} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-10}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -5e-25) (not (<= (* a 120.0) 5e-10)))
   (* 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) <= -5e-25) || !((a * 120.0) <= 5e-10)) {
		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) <= (-5d-25)) .or. (.not. ((a * 120.0d0) <= 5d-10))) 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) <= -5e-25) || !((a * 120.0) <= 5e-10)) {
		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) <= -5e-25) or not ((a * 120.0) <= 5e-10):
		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) <= -5e-25) || !(Float64(a * 120.0) <= 5e-10))
		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) <= -5e-25) || ~(((a * 120.0) <= 5e-10)))
		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], -5e-25], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-10]], $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)) < -4.99999999999999962e-25 or 5.00000000000000031e-10 < (*.f64 a #s(literal 120 binary64))

   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 80.7%

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

   if -4.99999999999999962e-25 < (*.f64 a #s(literal 120 binary64)) < 5.00000000000000031e-10

   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%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 82.0%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-25} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-10}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-25}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-57}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e-25)
   (* a 120.0)
   (if (<= (* a 120.0) 5e-57)
     (* 60.0 (/ (- x y) (- z t)))
     (+ (* a 120.0) (* 60.0 (/ y t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e-25) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e-57) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (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 * 120.0d0) <= (-5d-25)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 5d-57) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (a * 120.0d0) + (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 * 120.0) <= -5e-25) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 5e-57) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (a * 120.0) + (60.0 * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -5e-25:
		tmp = a * 120.0
	elif (a * 120.0) <= 5e-57:
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (a * 120.0) + (60.0 * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e-25)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 5e-57)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + 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 * 120.0) <= -5e-25)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 5e-57)
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (a * 120.0) + (60.0 * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e-25], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-57], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -4.99999999999999962e-25

   1. Initial program 99.9%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 83.1%

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

   if -4.99999999999999962e-25 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000002e-57

   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%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 82.9%

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

   if 5.0000000000000002e-57 < (*.f64 a #s(literal 120 binary64))

   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 y around inf 75.7%

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

   6. Taylor expanded in x around 0 70.9%

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

   7. Taylor expanded in t around inf 76.4%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{-25}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-57}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+32} \lor \neg \left(x \leq 1.9 \cdot 10^{+152}\right):\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -5e+32) (not (<= x 1.9e+152)))
   (+ (* a 120.0) (* x (/ -60.0 (- t z))))
   (+ (* 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 <= -5e+32) || !(x <= 1.9e+152)) {
		tmp = (a * 120.0) + (x * (-60.0 / (t - z)));
	} 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 <= (-5d+32)) .or. (.not. (x <= 1.9d+152))) then
        tmp = (a * 120.0d0) + (x * ((-60.0d0) / (t - z)))
    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 <= -5e+32) || !(x <= 1.9e+152)) {
		tmp = (a * 120.0) + (x * (-60.0 / (t - z)));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -5e+32) or not (x <= 1.9e+152):
		tmp = (a * 120.0) + (x * (-60.0 / (t - z)))
	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 <= -5e+32) || !(x <= 1.9e+152))
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / Float64(t - z))));
	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 <= -5e+32) || ~((x <= 1.9e+152)))
		tmp = (a * 120.0) + (x * (-60.0 / (t - z)));
	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, -5e+32], N[Not[LessEqual[x, 1.9e+152]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / N[(t - z), $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 < -4.9999999999999997e32 or 1.9e152 < x

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 94.2%

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

      1. associate-*r/ 94.1%

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

      2. *-commutative 94.1%

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

      3. *-lft-identity 94.1%

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

      4. times-frac 94.1%

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

      5. /-rgt-identity 94.1%

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

      6. remove-double-neg 94.1%

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

      7. distribute-frac-neg2 94.1%

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

      8. distribute-neg-frac2 94.1%

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

      9. distribute-neg-frac 94.1%

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

      10. metadata-eval 94.1%

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

      11. distribute-frac-neg2 94.1%

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

      12. neg-sub0 94.1%

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

      13. sub-neg 94.1%

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

      14. +-commutative 94.1%

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

      15. associate--r+ 94.1%

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

      16. neg-sub0 94.1%

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

      17. remove-double-neg 94.1%

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

   7. Simplified 94.1%

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

   if -4.9999999999999997e32 < x < 1.9e152

   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 93.7%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+32} \lor \neg \left(x \leq 1.9 \cdot 10^{+152}\right):\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+32} \lor \neg \left(x \leq 1.9 \cdot 10^{+152}\right):\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.9e+32) (not (<= x 1.9e+152)))
   (+ (* a 120.0) (* x (/ -60.0 (- t z))))
   (+ (* a 120.0) (* 60.0 (/ y (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.9e+32) || !(x <= 1.9e+152)) {
		tmp = (a * 120.0) + (x * (-60.0 / (t - z)));
	} else {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-2.9d+32)) .or. (.not. (x <= 1.9d+152))) then
        tmp = (a * 120.0d0) + (x * ((-60.0d0) / (t - z)))
    else
        tmp = (a * 120.0d0) + (60.0d0 * (y / (t - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.9e+32) || !(x <= 1.9e+152)) {
		tmp = (a * 120.0) + (x * (-60.0 / (t - z)));
	} else {
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.9e+32) or not (x <= 1.9e+152):
		tmp = (a * 120.0) + (x * (-60.0 / (t - z)))
	else:
		tmp = (a * 120.0) + (60.0 * (y / (t - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.9e+32) || !(x <= 1.9e+152))
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(-60.0 / Float64(t - z))));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / Float64(t - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2.9e+32) || ~((x <= 1.9e+152)))
		tmp = (a * 120.0) + (x * (-60.0 / (t - z)));
	else
		tmp = (a * 120.0) + (60.0 * (y / (t - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.9e+32], N[Not[LessEqual[x, 1.9e+152]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(-60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.90000000000000003e32 or 1.9e152 < x

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 94.2%

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

      1. associate-*r/ 94.1%

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

      2. *-commutative 94.1%

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

      3. *-lft-identity 94.1%

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

      4. times-frac 94.1%

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

      5. /-rgt-identity 94.1%

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

      6. remove-double-neg 94.1%

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

      7. distribute-frac-neg2 94.1%

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

      8. distribute-neg-frac2 94.1%

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

      9. distribute-neg-frac 94.1%

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

      10. metadata-eval 94.1%

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

      11. distribute-frac-neg2 94.1%

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

      12. neg-sub0 94.1%

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

      13. sub-neg 94.1%

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

      14. +-commutative 94.1%

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

      15. associate--r+ 94.1%

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

      16. neg-sub0 94.1%

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

      17. remove-double-neg 94.1%

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

   7. Simplified 94.1%

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

   if -2.90000000000000003e32 < x < 1.9e152

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 93.7%

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

      1. associate-*r/ 93.7%

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

      2. remove-double-neg 93.7%

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

      3. neg-mul-1 93.7%

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

      4. times-frac 93.7%

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

      5. metadata-eval 93.7%

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

      6. neg-sub0 93.7%

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

      7. sub-neg 93.7%

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

      8. +-commutative 93.7%

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

      9. associate--r+ 93.7%

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

      10. neg-sub0 93.7%

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

      11. remove-double-neg 93.7%

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

   7. Simplified 93.7%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+32} \lor \neg \left(x \leq 1.9 \cdot 10^{+152}\right):\\ \;\;\;\;a \cdot 120 + x \cdot \frac{-60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-40} \lor \neg \left(a \leq 1.45 \cdot 10^{-77}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7e-40) (not (<= a 1.45e-77)))
   (* a 120.0)
   (* 60.0 (/ x (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7e-40) || !(a <= 1.45e-77)) {
		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 ((a <= (-7d-40)) .or. (.not. (a <= 1.45d-77))) 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 ((a <= -7e-40) || !(a <= 1.45e-77)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (x / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7e-40) or not (a <= 1.45e-77):
		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 ((a <= -7e-40) || !(a <= 1.45e-77))
		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 ((a <= -7e-40) || ~((a <= 1.45e-77)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * (x / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7e-40], N[Not[LessEqual[a, 1.45e-77]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.0000000000000003e-40 or 1.4499999999999999e-77 < a

   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 77.6%

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

   if -7.0000000000000003e-40 < a < 1.4499999999999999e-77

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 92.0%

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

   6. Taylor expanded in x around inf 49.6%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-40} \lor \neg \left(a \leq 1.45 \cdot 10^{-77}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-95} \lor \neg \left(a \leq 4.4 \cdot 10^{-88}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.5e-95) (not (<= a 4.4e-88)))
   (* a 120.0)
   (* -60.0 (/ y (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.5e-95) || !(a <= 4.4e-88)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (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 <= (-3.5d-95)) .or. (.not. (a <= 4.4d-88))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (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 <= -3.5e-95) || !(a <= 4.4e-88)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.5e-95) or not (a <= 4.4e-88):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.5e-95) || !(a <= 4.4e-88))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.5e-95) || ~((a <= 4.4e-88)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.5e-95], N[Not[LessEqual[a, 4.4e-88]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.4999999999999997e-95 or 4.4000000000000001e-88 < a

   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 75.3%

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

   if -3.4999999999999997e-95 < a < 4.4000000000000001e-88

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 91.2%

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

   6. Taylor expanded in y around inf 41.7%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{-95} \lor \neg \left(a \leq 4.4 \cdot 10^{-88}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 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 99.8%

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

Alternative 10: 50.2% 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 52.7%

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

6. Final simplification 52.7%

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

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024111 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

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

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