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

Percentage Accurate: 99.4% → 99.7%

Time: 13.3s

Alternatives: 12

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: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. *-commutative 99.0%

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

   2. associate-/l* 99.8%

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

4. Applied egg-rr 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 72.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+31} \lor \neg \left(a \cdot 120 \leq -2 \cdot 10^{-85} \lor \neg \left(a \cdot 120 \leq -4 \cdot 10^{-139}\right) \land a \cdot 120 \leq 5 \cdot 10^{-76}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -1e+31)
         (not
          (or (<= (* a 120.0) -2e-85)
              (and (not (<= (* a 120.0) -4e-139)) (<= (* a 120.0) 5e-76)))))
   (* 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) <= -1e+31) || !(((a * 120.0) <= -2e-85) || (!((a * 120.0) <= -4e-139) && ((a * 120.0) <= 5e-76)))) {
		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) <= (-1d+31)) .or. (.not. ((a * 120.0d0) <= (-2d-85)) .or. (.not. ((a * 120.0d0) <= (-4d-139))) .and. ((a * 120.0d0) <= 5d-76))) 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) <= -1e+31) || !(((a * 120.0) <= -2e-85) || (!((a * 120.0) <= -4e-139) && ((a * 120.0) <= 5e-76)))) {
		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) <= -1e+31) or not (((a * 120.0) <= -2e-85) or (not ((a * 120.0) <= -4e-139) and ((a * 120.0) <= 5e-76))):
		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) <= -1e+31) || !((Float64(a * 120.0) <= -2e-85) || (!(Float64(a * 120.0) <= -4e-139) && (Float64(a * 120.0) <= 5e-76))))
		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) <= -1e+31) || ~((((a * 120.0) <= -2e-85) || (~(((a * 120.0) <= -4e-139)) && ((a * 120.0) <= 5e-76)))))
		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], -1e+31], N[Not[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-85], And[N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-139]], $MachinePrecision], LessEqual[N[(a * 120.0), $MachinePrecision], 5e-76]]]], $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)) < -9.9999999999999996e30 or -2e-85 < (*.f64 a #s(literal 120 binary64)) < -4.00000000000000012e-139 or 4.9999999999999998e-76 < (*.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 75.4%

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

   if -9.9999999999999996e30 < (*.f64 a #s(literal 120 binary64)) < -2e-85 or -4.00000000000000012e-139 < (*.f64 a #s(literal 120 binary64)) < 4.9999999999999998e-76

   1. Initial program 97.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in a around 0 82.5%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+31} \lor \neg \left(a \cdot 120 \leq -2 \cdot 10^{-85} \lor \neg \left(a \cdot 120 \leq -4 \cdot 10^{-139}\right) \land a \cdot 120 \leq 5 \cdot 10^{-76}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+31}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-85} \lor \neg \left(a \cdot 120 \leq -4 \cdot 10^{-139}\right) \land a \cdot 120 \leq 5 \cdot 10^{-76}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -1e+31)
   (+ (* a 120.0) (* -60.0 (/ y z)))
   (if (or (<= (* a 120.0) -2e-85)
           (and (not (<= (* a 120.0) -4e-139)) (<= (* a 120.0) 5e-76)))
     (* 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 ((a * 120.0) <= -1e+31) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (((a * 120.0) <= -2e-85) || (!((a * 120.0) <= -4e-139) && ((a * 120.0) <= 5e-76))) {
		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 ((a * 120.0d0) <= (-1d+31)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if (((a * 120.0d0) <= (-2d-85)) .or. (.not. ((a * 120.0d0) <= (-4d-139))) .and. ((a * 120.0d0) <= 5d-76)) 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 ((a * 120.0) <= -1e+31) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (((a * 120.0) <= -2e-85) || (!((a * 120.0) <= -4e-139) && ((a * 120.0) <= 5e-76))) {
		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 (a * 120.0) <= -1e+31:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif ((a * 120.0) <= -2e-85) or (not ((a * 120.0) <= -4e-139) and ((a * 120.0) <= 5e-76)):
		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(a * 120.0) <= -1e+31)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif ((Float64(a * 120.0) <= -2e-85) || (!(Float64(a * 120.0) <= -4e-139) && (Float64(a * 120.0) <= 5e-76)))
		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 ((a * 120.0) <= -1e+31)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif (((a * 120.0) <= -2e-85) || (~(((a * 120.0) <= -4e-139)) && ((a * 120.0) <= 5e-76)))
		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[LessEqual[N[(a * 120.0), $MachinePrecision], -1e+31], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-85], And[N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-139]], $MachinePrecision], LessEqual[N[(a * 120.0), $MachinePrecision], 5e-76]]], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -9.9999999999999996e30

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf 75.4%

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

   6. Taylor expanded in x around 0 78.3%

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

   if -9.9999999999999996e30 < (*.f64 a #s(literal 120 binary64)) < -2e-85 or -4.00000000000000012e-139 < (*.f64 a #s(literal 120 binary64)) < 4.9999999999999998e-76

   1. Initial program 97.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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. Taylor expanded in a around 0 82.5%

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

   if -2e-85 < (*.f64 a #s(literal 120 binary64)) < -4.00000000000000012e-139 or 4.9999999999999998e-76 < (*.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 74.0%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+31}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-85} \lor \neg \left(a \cdot 120 \leq -4 \cdot 10^{-139}\right) \land a \cdot 120 \leq 5 \cdot 10^{-76}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+28} \lor \neg \left(a \leq -1.42 \cdot 10^{-37}\right) \land \left(a \leq -1.15 \cdot 10^{-151} \lor \neg \left(a \leq 1.1 \cdot 10^{-74}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.1e+28)
         (and (not (<= a -1.42e-37))
              (or (<= a -1.15e-151) (not (<= a 1.1e-74)))))
   (* a 120.0)
   (* x (/ 60.0 (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.1e+28) || (!(a <= -1.42e-37) && ((a <= -1.15e-151) || !(a <= 1.1e-74)))) {
		tmp = a * 120.0;
	} else {
		tmp = x * (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 ((a <= (-3.1d+28)) .or. (.not. (a <= (-1.42d-37))) .and. (a <= (-1.15d-151)) .or. (.not. (a <= 1.1d-74))) then
        tmp = a * 120.0d0
    else
        tmp = x * (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 ((a <= -3.1e+28) || (!(a <= -1.42e-37) && ((a <= -1.15e-151) || !(a <= 1.1e-74)))) {
		tmp = a * 120.0;
	} else {
		tmp = x * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.1e+28) or (not (a <= -1.42e-37) and ((a <= -1.15e-151) or not (a <= 1.1e-74))):
		tmp = a * 120.0
	else:
		tmp = x * (60.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.1e+28) || (!(a <= -1.42e-37) && ((a <= -1.15e-151) || !(a <= 1.1e-74))))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.1e+28) || (~((a <= -1.42e-37)) && ((a <= -1.15e-151) || ~((a <= 1.1e-74)))))
		tmp = a * 120.0;
	else
		tmp = x * (60.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.1e+28], And[N[Not[LessEqual[a, -1.42e-37]], $MachinePrecision], Or[LessEqual[a, -1.15e-151], N[Not[LessEqual[a, 1.1e-74]], $MachinePrecision]]]], N[(a * 120.0), $MachinePrecision], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.1000000000000001e28 or -1.42e-37 < a < -1.14999999999999998e-151 or 1.10000000000000005e-74 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   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 71.3%

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

   if -3.1000000000000001e28 < a < -1.42e-37 or -1.14999999999999998e-151 < a < 1.10000000000000005e-74

   1. Initial program 97.4%

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

      1. associate-/l* 99.6%

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

   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 89.5%

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

   6. Taylor expanded in x around inf 56.2%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{+28} \lor \neg \left(a \leq -1.42 \cdot 10^{-37}\right) \land \left(a \leq -1.15 \cdot 10^{-151} \lor \neg \left(a \leq 1.1 \cdot 10^{-74}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-139} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-138}\right):\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -4e-139) (not (<= (* a 120.0) 5e-138)))
   (+ (* a 120.0) (* x (/ 60.0 (- z t))))
   (* 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) <= -4e-139) || !((a * 120.0) <= 5e-138)) {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	} 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) <= (-4d-139)) .or. (.not. ((a * 120.0d0) <= 5d-138))) then
        tmp = (a * 120.0d0) + (x * (60.0d0 / (z - t)))
    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) <= -4e-139) || !((a * 120.0) <= 5e-138)) {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -4e-139) or not ((a * 120.0) <= 5e-138):
		tmp = (a * 120.0) + (x * (60.0 / (z - t)))
	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) <= -4e-139) || !(Float64(a * 120.0) <= 5e-138))
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))));
	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) <= -4e-139) || ~(((a * 120.0) <= 5e-138)))
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	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], -4e-139], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-138]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $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)) < -4.00000000000000012e-139 or 4.99999999999999989e-138 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 86.6%

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

      1. associate-*r/ 86.1%

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

      2. *-commutative 86.1%

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

      3. associate-*r/ 86.6%

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

   7. Simplified 86.6%

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

   if -4.00000000000000012e-139 < (*.f64 a #s(literal 120 binary64)) < 4.99999999999999989e-138

   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* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in a around 0 88.8%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-139} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-138}\right):\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.7 \cdot 10^{-240}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-163}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+102}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 7.7e-240)
   (* a 120.0)
   (if (<= y 5.5e-163)
     (* 60.0 (/ x z))
     (if (<= y 3.3e+102) (* a 120.0) (* -60.0 (/ y (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 7.7e-240) {
		tmp = a * 120.0;
	} else if (y <= 5.5e-163) {
		tmp = 60.0 * (x / z);
	} else if (y <= 3.3e+102) {
		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 (y <= 7.7d-240) then
        tmp = a * 120.0d0
    else if (y <= 5.5d-163) then
        tmp = 60.0d0 * (x / z)
    else if (y <= 3.3d+102) 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 (y <= 7.7e-240) {
		tmp = a * 120.0;
	} else if (y <= 5.5e-163) {
		tmp = 60.0 * (x / z);
	} else if (y <= 3.3e+102) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 7.7e-240:
		tmp = a * 120.0
	elif y <= 5.5e-163:
		tmp = 60.0 * (x / z)
	elif y <= 3.3e+102:
		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 (y <= 7.7e-240)
		tmp = Float64(a * 120.0);
	elseif (y <= 5.5e-163)
		tmp = Float64(60.0 * Float64(x / z));
	elseif (y <= 3.3e+102)
		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 (y <= 7.7e-240)
		tmp = a * 120.0;
	elseif (y <= 5.5e-163)
		tmp = 60.0 * (x / z);
	elseif (y <= 3.3e+102)
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 7.7e-240], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, 5.5e-163], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+102], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 7.7e-240 or 5.4999999999999998e-163 < y < 3.29999999999999999e102

   1. Initial program 99.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 60.3%

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

   if 7.7e-240 < y < 5.4999999999999998e-163

   1. Initial program 93.6%

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

      1. *-commutative 93.6%

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

      2. associate-/l* 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around inf 70.2%

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

   6. Taylor expanded in x around inf 70.2%

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

   7. Taylor expanded in x around inf 60.4%

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

   if 3.29999999999999999e102 < y

   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* 99.8%

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

   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 73.7%

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

   6. Taylor expanded in a around inf 60.9%

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

   7. Taylor expanded in y around inf 60.6%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.7 \cdot 10^{-240}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-163}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+102}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+218} \lor \neg \left(y \leq 5.5 \cdot 10^{+42}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.25e+218) (not (<= y 5.5e+42)))
   (+ (* a 120.0) (/ (* y -60.0) (- z t)))
   (+ (* a 120.0) (* x (/ 60.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.25e+218) || !(y <= 5.5e+42)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (x * (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 <= (-2.25d+218)) .or. (.not. (y <= 5.5d+42))) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else
        tmp = (a * 120.0d0) + (x * (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 <= -2.25e+218) || !(y <= 5.5e+42)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.25e+218) or not (y <= 5.5e+42):
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	else:
		tmp = (a * 120.0) + (x * (60.0 / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.25e+218) || !(y <= 5.5e+42))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.25e+218) || ~((y <= 5.5e+42)))
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	else
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.25e+218], N[Not[LessEqual[y, 5.5e+42]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.25000000000000004e218 or 5.50000000000000001e42 < y

   1. Initial program 98.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 89.1%

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

      1. associate-*r/ 89.1%

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

   7. Simplified 89.1%

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

   if -2.25000000000000004e218 < y < 5.50000000000000001e42

   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* 99.8%

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

   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 92.7%

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

      1. associate-*r/ 92.1%

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

      2. *-commutative 92.1%

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

      3. associate-*r/ 92.7%

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

   7. Simplified 92.7%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+218} \lor \neg \left(y \leq 5.5 \cdot 10^{+42}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+32}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-56}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.15e+32)
   (+ (* a 120.0) (* (- x y) (/ -60.0 t)))
   (if (<= t 1.8e-56)
     (+ (* a 120.0) (* (- x y) (/ 60.0 z)))
     (+ (* a 120.0) (* x (/ 60.0 (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e+32) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else if (t <= 1.8e-56) {
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	} else {
		tmp = (a * 120.0) + (x * (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 (t <= (-1.15d+32)) then
        tmp = (a * 120.0d0) + ((x - y) * ((-60.0d0) / t))
    else if (t <= 1.8d-56) then
        tmp = (a * 120.0d0) + ((x - y) * (60.0d0 / z))
    else
        tmp = (a * 120.0d0) + (x * (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 (t <= -1.15e+32) {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	} else if (t <= 1.8e-56) {
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.15e+32:
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t))
	elif t <= 1.8e-56:
		tmp = (a * 120.0) + ((x - y) * (60.0 / z))
	else:
		tmp = (a * 120.0) + (x * (60.0 / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.15e+32)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(-60.0 / t)));
	elseif (t <= 1.8e-56)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(60.0 / z)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.15e+32)
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	elseif (t <= 1.8e-56)
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	else
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.15e+32], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.8e-56], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15e32

   1. Initial program 97.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 z around 0 94.2%

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

      1. associate-*r/ 92.3%

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

      2. *-commutative 92.3%

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

      3. associate-/l* 94.2%

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

   7. Simplified 94.2%

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

   if -1.15e32 < t < 1.79999999999999989e-56

   1. Initial program 99.0%

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

      1. *-commutative 99.0%

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

      2. associate-/l* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in z around inf 87.9%

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

   if 1.79999999999999989e-56 < t

   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 87.2%

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

      1. associate-*r/ 87.2%

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

      2. *-commutative 87.2%

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

      3. associate-*r/ 87.2%

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

   7. Simplified 87.2%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+32}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-56}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-260} \lor \neg \left(a \leq 2.3 \cdot 10^{-133}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.8e-260) (not (<= a 2.3e-133)))
   (* a 120.0)
   (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e-260) || !(a <= 2.3e-133)) {
		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 <= (-2.8d-260)) .or. (.not. (a <= 2.3d-133))) 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 <= -2.8e-260) || !(a <= 2.3e-133)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.8e-260) or not (a <= 2.3e-133):
		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 <= -2.8e-260) || !(a <= 2.3e-133))
		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 <= -2.8e-260) || ~((a <= 2.3e-133)))
		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, -2.8e-260], N[Not[LessEqual[a, 2.3e-133]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.7999999999999998e-260 or 2.3e-133 < a

   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* 99.8%

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

   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 60.9%

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

   if -2.7999999999999998e-260 < a < 2.3e-133

   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* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around 0 49.0%

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

      1. associate-*r/ 49.0%

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

      2. *-commutative 49.0%

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

      3. associate-/l* 49.2%

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

   7. Simplified 49.2%

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

   8. Taylor expanded in x around inf 34.8%

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

   9. Taylor expanded in x around inf 28.5%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-260} \lor \neg \left(a \leq 2.3 \cdot 10^{-133}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. associate-/l* 99.8%

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

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 11: 51.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+197}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.9e+197) (* 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+197) {
		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+197)) 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+197) {
		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+197:
		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+197)
		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+197)
		tmp = 60.0 * (x / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.9e+197], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.90000000000000026e197

   1. Initial program 96.2%

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

      1. *-commutative 96.2%

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

      2. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf 78.4%

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

   6. Taylor expanded in x around inf 74.9%

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

   7. Taylor expanded in x around inf 58.9%

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

   if -4.90000000000000026e197 < x

   1. Initial program 99.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 55.9%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.9 \cdot 10^{+197}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.7% 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%

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

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 52.2%

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

6. Final simplification 52.2%

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

Developer target: 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 2024078 
(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)))