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

Percentage Accurate: 99.3% → 99.8%

Time: 15.8s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 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 99.0%

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

   1. +-commutative 99.0%

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

   2. fma-def 99.1%

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

   3. associate-*l/ 99.8%

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

   4. *-commutative 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 82.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+143} \lor \neg \left(t_1 \leq 10^{+28}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (or (<= t_1 -2e+143) (not (<= t_1 1e+28)))
     (* 60.0 (/ (- x y) (- z t)))
     (+ (/ 60.0 (/ (- z t) x)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if ((t_1 <= -2e+143) || !(t_1 <= 1e+28)) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (60.0 / ((z - t) / x)) + (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) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    if ((t_1 <= (-2d+143)) .or. (.not. (t_1 <= 1d+28))) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (60.0d0 / ((z - t) / x)) + (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 t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if ((t_1 <= -2e+143) || !(t_1 <= 1e+28)) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if (t_1 <= -2e+143) or not (t_1 <= 1e+28):
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if ((t_1 <= -2e+143) || !(t_1 <= 1e+28))
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(60.0 / Float64(Float64(z - t) / x)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if ((t_1 <= -2e+143) || ~((t_1 <= 1e+28)))
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+143], N[Not[LessEqual[t$95$1, 1e+28]], $MachinePrecision]], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -2e143 or 9.99999999999999958e27 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 86.6%

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

   if -2e143 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 9.99999999999999958e27

   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%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 88.9%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+143} \lor \neg \left(\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{+28}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \end{array} \]

Alternative 3: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t_1 \leq -0.0002 \lor \neg \left(t_1 \leq 10^{+16}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (or (<= t_1 -0.0002) (not (<= t_1 1e+16)))
     (* 60.0 (/ (- x y) (- z t)))
     (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if ((t_1 <= -0.0002) || !(t_1 <= 1e+16)) {
		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) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) * 60.0d0) / (z - t)
    if ((t_1 <= (-0.0002d0)) .or. (.not. (t_1 <= 1d+16))) 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 t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if ((t_1 <= -0.0002) || !(t_1 <= 1e+16)) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if (t_1 <= -0.0002) or not (t_1 <= 1e+16):
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if ((t_1 <= -0.0002) || !(t_1 <= 1e+16))
		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)
	t_1 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if ((t_1 <= -0.0002) || ~((t_1 <= 1e+16)))
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -0.0002], N[Not[LessEqual[t$95$1, 1e+16]], $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 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -2.0000000000000001e-4 or 1e16 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 82.3%

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

   if -2.0000000000000001e-4 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 1e16

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 75.7%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -0.0002 \lor \neg \left(\frac{\left(x - y\right) \cdot 60}{z - t} \leq 10^{+16}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 4: 53.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -2 \cdot 10^{+159}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq -1 \cdot 10^{+108} \lor \neg \left(z - t \leq -5 \cdot 10^{+66}\right) \land z - t \leq 5 \cdot 10^{+110}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- z t) -2e+159)
   (* a 120.0)
   (if (or (<= (- z t) -1e+108)
           (and (not (<= (- z t) -5e+66)) (<= (- z t) 5e+110)))
     (* -60.0 (/ (- x y) t))
     (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -2e+159) {
		tmp = a * 120.0;
	} else if (((z - t) <= -1e+108) || (!((z - t) <= -5e+66) && ((z - t) <= 5e+110))) {
		tmp = -60.0 * ((x - y) / 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 ((z - t) <= (-2d+159)) then
        tmp = a * 120.0d0
    else if (((z - t) <= (-1d+108)) .or. (.not. ((z - t) <= (-5d+66))) .and. ((z - t) <= 5d+110)) then
        tmp = (-60.0d0) * ((x - y) / 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 ((z - t) <= -2e+159) {
		tmp = a * 120.0;
	} else if (((z - t) <= -1e+108) || (!((z - t) <= -5e+66) && ((z - t) <= 5e+110))) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z - t) <= -2e+159:
		tmp = a * 120.0
	elif ((z - t) <= -1e+108) or (not ((z - t) <= -5e+66) and ((z - t) <= 5e+110)):
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z - t) <= -2e+159)
		tmp = Float64(a * 120.0);
	elseif ((Float64(z - t) <= -1e+108) || (!(Float64(z - t) <= -5e+66) && (Float64(z - t) <= 5e+110)))
		tmp = Float64(-60.0 * Float64(Float64(x - y) / 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 ((z - t) <= -2e+159)
		tmp = a * 120.0;
	elseif (((z - t) <= -1e+108) || (~(((z - t) <= -5e+66)) && ((z - t) <= 5e+110)))
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z - t), $MachinePrecision], -2e+159], N[(a * 120.0), $MachinePrecision], If[Or[LessEqual[N[(z - t), $MachinePrecision], -1e+108], And[N[Not[LessEqual[N[(z - t), $MachinePrecision], -5e+66]], $MachinePrecision], LessEqual[N[(z - t), $MachinePrecision], 5e+110]]], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z t) < -1.9999999999999999e159 or -1e108 < (-.f64 z t) < -4.99999999999999991e66 or 4.99999999999999978e110 < (-.f64 z t)

   1. Initial program 99.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 75.5%

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

   if -1.9999999999999999e159 < (-.f64 z t) < -1e108 or -4.99999999999999991e66 < (-.f64 z t) < 4.99999999999999978e110

   1. Initial program 99.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 81.7%

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

   5. Taylor expanded in z around 0 58.9%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -2 \cdot 10^{+159}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq -1 \cdot 10^{+108} \lor \neg \left(z - t \leq -5 \cdot 10^{+66}\right) \land z - t \leq 5 \cdot 10^{+110}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 5: 53.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -2 \cdot 10^{+159}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq -1 \cdot 10^{+108}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot -60}{t}\\ \mathbf{elif}\;z - t \leq -5 \cdot 10^{+66}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 5 \cdot 10^{+110}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- z t) -2e+159)
   (* a 120.0)
   (if (<= (- z t) -1e+108)
     (/ (* (- x y) -60.0) t)
     (if (<= (- z t) -5e+66)
       (* a 120.0)
       (if (<= (- z t) 5e+110) (* -60.0 (/ (- x y) t)) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -2e+159) {
		tmp = a * 120.0;
	} else if ((z - t) <= -1e+108) {
		tmp = ((x - y) * -60.0) / t;
	} else if ((z - t) <= -5e+66) {
		tmp = a * 120.0;
	} else if ((z - t) <= 5e+110) {
		tmp = -60.0 * ((x - y) / 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 ((z - t) <= (-2d+159)) then
        tmp = a * 120.0d0
    else if ((z - t) <= (-1d+108)) then
        tmp = ((x - y) * (-60.0d0)) / t
    else if ((z - t) <= (-5d+66)) then
        tmp = a * 120.0d0
    else if ((z - t) <= 5d+110) then
        tmp = (-60.0d0) * ((x - y) / 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 ((z - t) <= -2e+159) {
		tmp = a * 120.0;
	} else if ((z - t) <= -1e+108) {
		tmp = ((x - y) * -60.0) / t;
	} else if ((z - t) <= -5e+66) {
		tmp = a * 120.0;
	} else if ((z - t) <= 5e+110) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z - t) <= -2e+159:
		tmp = a * 120.0
	elif (z - t) <= -1e+108:
		tmp = ((x - y) * -60.0) / t
	elif (z - t) <= -5e+66:
		tmp = a * 120.0
	elif (z - t) <= 5e+110:
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z - t) <= -2e+159)
		tmp = Float64(a * 120.0);
	elseif (Float64(z - t) <= -1e+108)
		tmp = Float64(Float64(Float64(x - y) * -60.0) / t);
	elseif (Float64(z - t) <= -5e+66)
		tmp = Float64(a * 120.0);
	elseif (Float64(z - t) <= 5e+110)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / 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 ((z - t) <= -2e+159)
		tmp = a * 120.0;
	elseif ((z - t) <= -1e+108)
		tmp = ((x - y) * -60.0) / t;
	elseif ((z - t) <= -5e+66)
		tmp = a * 120.0;
	elseif ((z - t) <= 5e+110)
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z - t), $MachinePrecision], -2e+159], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], -1e+108], N[(N[(N[(x - y), $MachinePrecision] * -60.0), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], -5e+66], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 5e+110], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 z t) < -1.9999999999999999e159 or -1e108 < (-.f64 z t) < -4.99999999999999991e66 or 4.99999999999999978e110 < (-.f64 z t)

   1. Initial program 99.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 75.5%

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

   if -1.9999999999999999e159 < (-.f64 z t) < -1e108

   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%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 87.4%

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

   5. Taylor expanded in z around 0 63.8%

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

      1. associate-*r/ 63.9%

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

   7. Applied egg-rr 63.9%

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

   if -4.99999999999999991e66 < (-.f64 z t) < 4.99999999999999978e110

   1. Initial program 98.9%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 80.8%

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

   5. Taylor expanded in z around 0 58.2%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -2 \cdot 10^{+159}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq -1 \cdot 10^{+108}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot -60}{t}\\ \mathbf{elif}\;z - t \leq -5 \cdot 10^{+66}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 5 \cdot 10^{+110}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6: 89.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+101} \lor \neg \left(y \leq 9.5 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.05e+101) (not (<= y 9.5e+76)))
   (+ (/ (* y -60.0) (- z t)) (* a 120.0))
   (+ (/ 60.0 (/ (- z t) x)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.05e+101) || !(y <= 9.5e+76)) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.05d+101)) .or. (.not. (y <= 9.5d+76))) then
        tmp = ((y * (-60.0d0)) / (z - t)) + (a * 120.0d0)
    else
        tmp = (60.0d0 / ((z - t) / x)) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.05e+101) || !(y <= 9.5e+76)) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.05e+101) or not (y <= 9.5e+76):
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	else:
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.05e+101) || !(y <= 9.5e+76))
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(60.0 / Float64(Float64(z - t) / x)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.05e+101) || ~((y <= 9.5e+76)))
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	else
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.05e+101], N[Not[LessEqual[y, 9.5e+76]], $MachinePrecision]], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e101 or 9.5000000000000003e76 < y

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 87.8%

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

   if -1.05e101 < y < 9.5000000000000003e76

   1. Initial program 98.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 91.0%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+101} \lor \neg \left(y \leq 9.5 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \end{array} \]

Alternative 7: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 8: 50.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-63}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-226}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-61}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.6e-63)
   (* a 120.0)
   (if (<= a -8.5e-226)
     (* 60.0 (/ y t))
     (if (<= a 6.5e-61) (* -60.0 (/ x t)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.6e-63) {
		tmp = a * 120.0;
	} else if (a <= -8.5e-226) {
		tmp = 60.0 * (y / t);
	} else if (a <= 6.5e-61) {
		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 (a <= (-1.6d-63)) then
        tmp = a * 120.0d0
    else if (a <= (-8.5d-226)) then
        tmp = 60.0d0 * (y / t)
    else if (a <= 6.5d-61) 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 (a <= -1.6e-63) {
		tmp = a * 120.0;
	} else if (a <= -8.5e-226) {
		tmp = 60.0 * (y / t);
	} else if (a <= 6.5e-61) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.6e-63:
		tmp = a * 120.0
	elif a <= -8.5e-226:
		tmp = 60.0 * (y / t)
	elif a <= 6.5e-61:
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.6e-63)
		tmp = Float64(a * 120.0);
	elseif (a <= -8.5e-226)
		tmp = Float64(60.0 * Float64(y / t));
	elseif (a <= 6.5e-61)
		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 (a <= -1.6e-63)
		tmp = a * 120.0;
	elseif (a <= -8.5e-226)
		tmp = 60.0 * (y / t);
	elseif (a <= 6.5e-61)
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.6e-63], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -8.5e-226], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-61], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.59999999999999994e-63 or 6.4999999999999994e-61 < a

   1. Initial program 99.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 66.3%

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

   if -1.59999999999999994e-63 < a < -8.4999999999999998e-226

   1. Initial program 99.5%

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

      1. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in a around 0 90.5%

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

   5. Taylor expanded in z around 0 65.8%

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

   6. Taylor expanded in x around 0 47.1%

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

   if -8.4999999999999998e-226 < a < 6.4999999999999994e-61

   1. Initial program 98.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 88.2%

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

   5. Taylor expanded in z around 0 58.0%

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

   6. Taylor expanded in x around inf 41.1%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-63}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-226}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-61}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9: 50.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-64}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-225}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-68}:\\ \;\;\;\;\frac{-60}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.5e-64)
   (* a 120.0)
   (if (<= a -1.9e-225)
     (* 60.0 (/ y t))
     (if (<= a 7.2e-68) (/ -60.0 (/ t x)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.5e-64) {
		tmp = a * 120.0;
	} else if (a <= -1.9e-225) {
		tmp = 60.0 * (y / t);
	} else if (a <= 7.2e-68) {
		tmp = -60.0 / (t / x);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7.5d-64)) then
        tmp = a * 120.0d0
    else if (a <= (-1.9d-225)) then
        tmp = 60.0d0 * (y / t)
    else if (a <= 7.2d-68) then
        tmp = (-60.0d0) / (t / x)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.5e-64) {
		tmp = a * 120.0;
	} else if (a <= -1.9e-225) {
		tmp = 60.0 * (y / t);
	} else if (a <= 7.2e-68) {
		tmp = -60.0 / (t / x);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.5e-64:
		tmp = a * 120.0
	elif a <= -1.9e-225:
		tmp = 60.0 * (y / t)
	elif a <= 7.2e-68:
		tmp = -60.0 / (t / x)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.5e-64)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.9e-225)
		tmp = Float64(60.0 * Float64(y / t));
	elseif (a <= 7.2e-68)
		tmp = Float64(-60.0 / Float64(t / x));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.5e-64)
		tmp = a * 120.0;
	elseif (a <= -1.9e-225)
		tmp = 60.0 * (y / t);
	elseif (a <= 7.2e-68)
		tmp = -60.0 / (t / x);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.5e-64], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.9e-225], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.2e-68], N[(-60.0 / N[(t / x), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.49999999999999949e-64 or 7.20000000000000015e-68 < a

   1. Initial program 99.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 66.3%

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

   if -7.49999999999999949e-64 < a < -1.9000000000000001e-225

   1. Initial program 99.5%

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

      1. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in a around 0 90.5%

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

   5. Taylor expanded in z around 0 65.8%

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

   6. Taylor expanded in x around 0 47.1%

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

   if -1.9000000000000001e-225 < a < 7.20000000000000015e-68

   1. Initial program 98.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 88.2%

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

   5. Taylor expanded in z around 0 58.0%

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

   6. Taylor expanded in x around inf 41.1%

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

      1. associate-*r/ 41.2%

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

      2. associate-/l* 41.2%

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

   8. Simplified 41.2%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-64}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-225}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-68}:\\ \;\;\;\;\frac{-60}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 10: 49.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-8} \lor \neg \left(a \leq 2.3 \cdot 10^{-65}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2e-8) (not (<= a 2.3e-65))) (* a 120.0) (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2e-8) || !(a <= 2.3e-65)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2d-8)) .or. (.not. (a <= 2.3d-65))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2e-8) || !(a <= 2.3e-65)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2e-8) or not (a <= 2.3e-65):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (x / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2e-8) || !(a <= 2.3e-65))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2e-8) || ~((a <= 2.3e-65)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2e-8], N[Not[LessEqual[a, 2.3e-65]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2e-8 or 2.3e-65 < a

   1. Initial program 99.2%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 70.5%

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

   if -2e-8 < a < 2.3e-65

   1. Initial program 98.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 87.0%

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

   5. Taylor expanded in z around 0 56.8%

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

   6. Taylor expanded in x around inf 33.4%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-8} \lor \neg \left(a \leq 2.3 \cdot 10^{-65}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]

Alternative 11: 50.3% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in z around inf 47.8%

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

5. Final simplification 47.8%

   \[\leadsto a \cdot 120 \]

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 2023280 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

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

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