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

Percentage Accurate: 99.4% → 99.8%

Time: 12.2s

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: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

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%

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

Alternative 2: 82.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+35} \lor \neg \left(t\_1 \leq 4 \cdot 10^{+129}\right):\\ \;\;\;\;60 \cdot \frac{y - x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 - 60 \cdot \frac{x}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (or (<= t_1 -5e+35) (not (<= t_1 4e+129)))
     (* 60.0 (/ (- y x) (- t z)))
     (- (* a 120.0) (* 60.0 (/ x (- t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if ((t_1 <= -5e+35) || !(t_1 <= 4e+129)) {
		tmp = 60.0 * ((y - x) / (t - z));
	} else {
		tmp = (a * 120.0) - (60.0 * (x / (t - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if ((t_1 <= (-5d+35)) .or. (.not. (t_1 <= 4d+129))) then
        tmp = 60.0d0 * ((y - x) / (t - z))
    else
        tmp = (a * 120.0d0) - (60.0d0 * (x / (t - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if ((t_1 <= -5e+35) || !(t_1 <= 4e+129)) {
		tmp = 60.0 * ((y - x) / (t - z));
	} else {
		tmp = (a * 120.0) - (60.0 * (x / (t - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if (t_1 <= -5e+35) or not (t_1 <= 4e+129):
		tmp = 60.0 * ((y - x) / (t - z))
	else:
		tmp = (a * 120.0) - (60.0 * (x / (t - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if ((t_1 <= -5e+35) || !(t_1 <= 4e+129))
		tmp = Float64(60.0 * Float64(Float64(y - x) / Float64(t - z)));
	else
		tmp = Float64(Float64(a * 120.0) - Float64(60.0 * Float64(x / Float64(t - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if ((t_1 <= -5e+35) || ~((t_1 <= 4e+129)))
		tmp = 60.0 * ((y - x) / (t - z));
	else
		tmp = (a * 120.0) - (60.0 * (x / (t - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+35], N[Not[LessEqual[t$95$1, 4e+129]], $MachinePrecision]], N[(60.0 * N[(N[(y - x), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] - N[(60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -5.00000000000000021e35 or 4e129 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 97.6%

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

      1. associate-/l* 99.8%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 83.7%

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

   if -5.00000000000000021e35 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4e129

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 86.8%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+35} \lor \neg \left(\frac{60 \cdot \left(x - y\right)}{z - t} \leq 4 \cdot 10^{+129}\right):\\ \;\;\;\;60 \cdot \frac{y - x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 - 60 \cdot \frac{x}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+79} \lor \neg \left(a \cdot 120 \leq 10^{-84}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y - x}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -1e+79) (not (<= (* a 120.0) 1e-84)))
   (* a 120.0)
   (* 60.0 (/ (- y x) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -1e+79) || !((a * 120.0) <= 1e-84)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((y - x) / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-1d+79)) .or. (.not. ((a * 120.0d0) <= 1d-84))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((y - x) / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -1e+79) || !((a * 120.0) <= 1e-84)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((y - x) / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -1e+79) or not ((a * 120.0) <= 1e-84):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((y - x) / (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -1e+79) || !(Float64(a * 120.0) <= 1e-84))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(y - x) / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -1e+79) || ~(((a * 120.0) <= 1e-84)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((y - x) / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -1e+79], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-84]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(y - x), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -9.99999999999999967e78 or 1e-84 < (*.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%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 77.9%

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

   if -9.99999999999999967e78 < (*.f64 a #s(literal 120 binary64)) < 1e-84

   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* 99.7%

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

      2. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 78.9%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+79} \lor \neg \left(a \cdot 120 \leq 10^{-84}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y - x}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+79}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-123}:\\ \;\;\;\;60 \cdot \frac{y - x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -1e+79)
   (* a 120.0)
   (if (<= (* a 120.0) 2e-123)
     (* 60.0 (/ (- y x) (- t z)))
     (+ (* a 120.0) (* -60.0 (/ y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -1e+79) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e-123) {
		tmp = 60.0 * ((y - x) / (t - z));
	} else {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-1d+79)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 2d-123) then
        tmp = 60.0d0 * ((y - x) / (t - z))
    else
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -1e+79) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e-123) {
		tmp = 60.0 * ((y - x) / (t - z));
	} else {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -1e+79:
		tmp = a * 120.0
	elif (a * 120.0) <= 2e-123:
		tmp = 60.0 * ((y - x) / (t - z))
	else:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -1e+79)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 2e-123)
		tmp = Float64(60.0 * Float64(Float64(y - x) / Float64(t - z)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -1e+79)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 2e-123)
		tmp = 60.0 * ((y - x) / (t - z));
	else
		tmp = (a * 120.0) + (-60.0 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e+79], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-123], N[(60.0 * N[(N[(y - x), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -9.99999999999999967e78

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. fma-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 88.0%

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

   if -9.99999999999999967e78 < (*.f64 a #s(literal 120 binary64)) < 2.0000000000000001e-123

   1. Initial program 98.1%

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

      1. associate-/l* 99.7%

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

      2. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 80.5%

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

   if 2.0000000000000001e-123 < (*.f64 a #s(literal 120 binary64))

   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* 99.9%

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

   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 x around 0 85.5%

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

      1. neg-mul-1 85.5%

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

   7. Simplified 85.5%

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

   8. Taylor expanded in z around inf 69.4%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+79}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-123}:\\ \;\;\;\;60 \cdot \frac{y - x}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-35}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-207}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-132}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.15e-35)
   (* a 120.0)
   (if (<= a -3.7e-207)
     (* 60.0 (/ (- x y) z))
     (if (<= a 7e-132) (* 60.0 (/ (- y x) t)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.15e-35) {
		tmp = a * 120.0;
	} else if (a <= -3.7e-207) {
		tmp = 60.0 * ((x - y) / z);
	} else if (a <= 7e-132) {
		tmp = 60.0 * ((y - 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 <= (-1.15d-35)) then
        tmp = a * 120.0d0
    else if (a <= (-3.7d-207)) then
        tmp = 60.0d0 * ((x - y) / z)
    else if (a <= 7d-132) then
        tmp = 60.0d0 * ((y - 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 <= -1.15e-35) {
		tmp = a * 120.0;
	} else if (a <= -3.7e-207) {
		tmp = 60.0 * ((x - y) / z);
	} else if (a <= 7e-132) {
		tmp = 60.0 * ((y - x) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.15e-35:
		tmp = a * 120.0
	elif a <= -3.7e-207:
		tmp = 60.0 * ((x - y) / z)
	elif a <= 7e-132:
		tmp = 60.0 * ((y - x) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.15e-35)
		tmp = Float64(a * 120.0);
	elseif (a <= -3.7e-207)
		tmp = Float64(60.0 * Float64(Float64(x - y) / z));
	elseif (a <= 7e-132)
		tmp = Float64(60.0 * Float64(Float64(y - 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 <= -1.15e-35)
		tmp = a * 120.0;
	elseif (a <= -3.7e-207)
		tmp = 60.0 * ((x - y) / z);
	elseif (a <= 7e-132)
		tmp = 60.0 * ((y - x) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.15e-35], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -3.7e-207], N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7e-132], N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.1499999999999999e-35 or 6.9999999999999999e-132 < a

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 68.9%

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

   if -1.1499999999999999e-35 < a < -3.69999999999999984e-207

   1. Initial program 92.4%

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

      1. associate-/l* 99.7%

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

      2. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 65.7%

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

   6. Taylor expanded in z around inf 55.5%

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

   if -3.69999999999999984e-207 < a < 6.9999999999999999e-132

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 91.6%

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

   6. Taylor expanded in z around 0 60.0%

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

      1. associate-*r/ 60.0%

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

      2. neg-mul-1 60.0%

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

      3. neg-sub0 60.0%

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

      4. sub-neg 60.0%

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

      5. +-commutative 60.0%

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

      6. associate--r+ 60.0%

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

      7. neg-sub0 60.0%

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

      8. remove-double-neg 60.0%

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

   8. Simplified 60.0%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-35}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-207}:\\ \;\;\;\;60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-132}:\\ \;\;\;\;60 \cdot \frac{y - x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-176}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-233}:\\ \;\;\;\;60 \cdot \frac{y}{-z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-132}:\\ \;\;\;\;\frac{x \cdot \left(-60\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.6e-176)
   (* a 120.0)
   (if (<= a -1.35e-233)
     (* 60.0 (/ y (- z)))
     (if (<= a 1.15e-132) (/ (* x (- 60.0)) t) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.6e-176) {
		tmp = a * 120.0;
	} else if (a <= -1.35e-233) {
		tmp = 60.0 * (y / -z);
	} else if (a <= 1.15e-132) {
		tmp = (x * -60.0) / 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 <= (-5.6d-176)) then
        tmp = a * 120.0d0
    else if (a <= (-1.35d-233)) then
        tmp = 60.0d0 * (y / -z)
    else if (a <= 1.15d-132) then
        tmp = (x * -60.0d0) / 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 <= -5.6e-176) {
		tmp = a * 120.0;
	} else if (a <= -1.35e-233) {
		tmp = 60.0 * (y / -z);
	} else if (a <= 1.15e-132) {
		tmp = (x * -60.0) / t;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.6e-176:
		tmp = a * 120.0
	elif a <= -1.35e-233:
		tmp = 60.0 * (y / -z)
	elif a <= 1.15e-132:
		tmp = (x * -60.0) / t
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.6e-176)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.35e-233)
		tmp = Float64(60.0 * Float64(y / Float64(-z)));
	elseif (a <= 1.15e-132)
		tmp = Float64(Float64(x * Float64(-60.0)) / 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 <= -5.6e-176)
		tmp = a * 120.0;
	elseif (a <= -1.35e-233)
		tmp = 60.0 * (y / -z);
	elseif (a <= 1.15e-132)
		tmp = (x * -60.0) / t;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.6e-176], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.35e-233], N[(60.0 * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.15e-132], N[(N[(x * (-60.0)), $MachinePrecision] / t), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.6000000000000003e-176 or 1.15000000000000002e-132 < a

   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%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 65.2%

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

   if -5.6000000000000003e-176 < a < -1.35e-233

   1. Initial program 92.8%

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

      1. associate-/l* 99.6%

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

      2. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 88.7%

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

   6. Taylor expanded in x around 0 73.6%

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

      1. associate-*r/ 73.5%

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

      2. remove-double-neg 73.5%

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

      3. neg-mul-1 73.5%

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

      4. times-frac 73.6%

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

      5. metadata-eval 73.6%

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

      6. neg-sub0 73.6%

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

      7. sub-neg 73.6%

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

      8. +-commutative 73.6%

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

      9. associate--r+ 73.6%

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

      10. neg-sub0 73.6%

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

      11. remove-double-neg 73.6%

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

   8. Simplified 73.6%

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

   9. Taylor expanded in t around 0 45.8%

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

       1. associate-*r/ 45.8%

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

       2. mul-1-neg 45.8%

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

   11. Simplified 45.8%

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

   if -1.35e-233 < a < 1.15000000000000002e-132

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 90.4%

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

   6. Taylor expanded in x around inf 50.2%

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

      1. associate-*r/ 50.2%

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

   8. Simplified 50.2%

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

   9. Taylor expanded in z around 0 40.3%

      \[\leadsto \frac{60 \cdot x}{\color{blue}{-1 \cdot t}} \]
   10. Step-by-step derivation

       1. neg-mul-1 40.3%

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

   11. Simplified 40.3%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{-176}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.35 \cdot 10^{-233}:\\ \;\;\;\;60 \cdot \frac{y}{-z}\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-132}:\\ \;\;\;\;\frac{x \cdot \left(-60\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 90.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+59}:\\ \;\;\;\;a \cdot 120 - 60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \frac{60}{t - z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 - \frac{60}{\frac{t - z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.8e+59)
   (- (* a 120.0) (* 60.0 (/ x (- t z))))
   (if (<= x 1.9e+57)
     (+ (* y (/ 60.0 (- t z))) (* a 120.0))
     (- (* a 120.0) (/ 60.0 (/ (- t z) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.8e+59) {
		tmp = (a * 120.0) - (60.0 * (x / (t - z)));
	} else if (x <= 1.9e+57) {
		tmp = (y * (60.0 / (t - z))) + (a * 120.0);
	} else {
		tmp = (a * 120.0) - (60.0 / ((t - z) / x));
	}
	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 <= (-4.8d+59)) then
        tmp = (a * 120.0d0) - (60.0d0 * (x / (t - z)))
    else if (x <= 1.9d+57) then
        tmp = (y * (60.0d0 / (t - z))) + (a * 120.0d0)
    else
        tmp = (a * 120.0d0) - (60.0d0 / ((t - z) / x))
    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 <= -4.8e+59) {
		tmp = (a * 120.0) - (60.0 * (x / (t - z)));
	} else if (x <= 1.9e+57) {
		tmp = (y * (60.0 / (t - z))) + (a * 120.0);
	} else {
		tmp = (a * 120.0) - (60.0 / ((t - z) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.8e+59:
		tmp = (a * 120.0) - (60.0 * (x / (t - z)))
	elif x <= 1.9e+57:
		tmp = (y * (60.0 / (t - z))) + (a * 120.0)
	else:
		tmp = (a * 120.0) - (60.0 / ((t - z) / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.8e+59)
		tmp = Float64(Float64(a * 120.0) - Float64(60.0 * Float64(x / Float64(t - z))));
	elseif (x <= 1.9e+57)
		tmp = Float64(Float64(y * Float64(60.0 / Float64(t - z))) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(a * 120.0) - Float64(60.0 / Float64(Float64(t - z) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4.8e+59)
		tmp = (a * 120.0) - (60.0 * (x / (t - z)));
	elseif (x <= 1.9e+57)
		tmp = (y * (60.0 / (t - z))) + (a * 120.0);
	else
		tmp = (a * 120.0) - (60.0 / ((t - z) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.8e+59], N[(N[(a * 120.0), $MachinePrecision] - N[(60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+57], N[(N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] - N[(60.0 / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.8000000000000004e59

   1. Initial program 98.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 87.4%

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

   if -4.8000000000000004e59 < x < 1.8999999999999999e57

   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* 99.9%

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

   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 x around 0 95.2%

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

      1. neg-mul-1 95.2%

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

   7. Simplified 95.2%

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

   if 1.8999999999999999e57 < x

   1. Initial program 98.1%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 86.6%

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

      1. clear-num 86.6%

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

      2. un-div-inv 86.7%

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

   7. Applied egg-rr 86.7%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+59}:\\ \;\;\;\;a \cdot 120 - 60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+57}:\\ \;\;\;\;y \cdot \frac{60}{t - z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 - \frac{60}{\frac{t - z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+59}:\\ \;\;\;\;a \cdot 120 - 60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120 - \frac{y \cdot -60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 - \frac{60}{\frac{t - z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.3e+59)
   (- (* a 120.0) (* 60.0 (/ x (- t z))))
   (if (<= x 4.8e+53)
     (- (* a 120.0) (/ (* y -60.0) (- t z)))
     (- (* a 120.0) (/ 60.0 (/ (- t z) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.3e+59) {
		tmp = (a * 120.0) - (60.0 * (x / (t - z)));
	} else if (x <= 4.8e+53) {
		tmp = (a * 120.0) - ((y * -60.0) / (t - z));
	} else {
		tmp = (a * 120.0) - (60.0 / ((t - z) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.3d+59)) then
        tmp = (a * 120.0d0) - (60.0d0 * (x / (t - z)))
    else if (x <= 4.8d+53) then
        tmp = (a * 120.0d0) - ((y * (-60.0d0)) / (t - z))
    else
        tmp = (a * 120.0d0) - (60.0d0 / ((t - z) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.3e+59) {
		tmp = (a * 120.0) - (60.0 * (x / (t - z)));
	} else if (x <= 4.8e+53) {
		tmp = (a * 120.0) - ((y * -60.0) / (t - z));
	} else {
		tmp = (a * 120.0) - (60.0 / ((t - z) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.3e+59:
		tmp = (a * 120.0) - (60.0 * (x / (t - z)))
	elif x <= 4.8e+53:
		tmp = (a * 120.0) - ((y * -60.0) / (t - z))
	else:
		tmp = (a * 120.0) - (60.0 / ((t - z) / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.3e+59)
		tmp = Float64(Float64(a * 120.0) - Float64(60.0 * Float64(x / Float64(t - z))));
	elseif (x <= 4.8e+53)
		tmp = Float64(Float64(a * 120.0) - Float64(Float64(y * -60.0) / Float64(t - z)));
	else
		tmp = Float64(Float64(a * 120.0) - Float64(60.0 / Float64(Float64(t - z) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.3e+59)
		tmp = (a * 120.0) - (60.0 * (x / (t - z)));
	elseif (x <= 4.8e+53)
		tmp = (a * 120.0) - ((y * -60.0) / (t - z));
	else
		tmp = (a * 120.0) - (60.0 / ((t - z) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.3e+59], N[(N[(a * 120.0), $MachinePrecision] - N[(60.0 * N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8e+53], N[(N[(a * 120.0), $MachinePrecision] - N[(N[(y * -60.0), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] - N[(60.0 / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3e59

   1. Initial program 98.1%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 87.4%

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

   if -1.3e59 < x < 4.8e53

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 95.2%

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

   if 4.8e53 < x

   1. Initial program 98.1%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 86.6%

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

      1. clear-num 86.6%

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

      2. un-div-inv 86.7%

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

   7. Applied egg-rr 86.7%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+59}:\\ \;\;\;\;a \cdot 120 - 60 \cdot \frac{x}{t - z}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+53}:\\ \;\;\;\;a \cdot 120 - \frac{y \cdot -60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 - \frac{60}{\frac{t - z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.18 \cdot 10^{-173} \lor \neg \left(a \leq 1.15 \cdot 10^{-115}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.18e-173) (not (<= a 1.15e-115)))
   (* a 120.0)
   (* 60.0 (/ y (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.18e-173) || !(a <= 1.15e-115)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.18d-173)) .or. (.not. (a <= 1.15d-115))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (y / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.18e-173) || !(a <= 1.15e-115)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.18e-173) or not (a <= 1.15e-115):
		tmp = a * 120.0
	else:
		tmp = 60.0 * (y / (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.18e-173) || !(a <= 1.15e-115))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(y / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.18e-173) || ~((a <= 1.15e-115)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * (y / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.18e-173], N[Not[LessEqual[a, 1.15e-115]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.1800000000000001e-173 or 1.14999999999999992e-115 < a

   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%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 66.8%

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

   if -1.1800000000000001e-173 < a < 1.14999999999999992e-115

   1. Initial program 98.4%

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

      1. associate-/l* 99.7%

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

      2. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 89.6%

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

   6. Taylor expanded in x around 0 49.4%

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

      1. associate-*r/ 49.3%

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

      2. remove-double-neg 49.3%

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

      3. neg-mul-1 49.3%

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

      4. times-frac 49.4%

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

      5. metadata-eval 49.4%

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

      6. neg-sub0 49.4%

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

      7. sub-neg 49.4%

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

      8. +-commutative 49.4%

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

      9. associate--r+ 49.4%

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

      10. neg-sub0 49.4%

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

      11. remove-double-neg 49.4%

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

   8. Simplified 49.4%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.18 \cdot 10^{-173} \lor \neg \left(a \leq 1.15 \cdot 10^{-115}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-207} \lor \neg \left(a \leq 4.7 \cdot 10^{-132}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.2e-207) (not (<= a 4.7e-132))) (* a 120.0) (* 60.0 (/ y t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.2e-207) || !(a <= 4.7e-132)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.2d-207)) .or. (.not. (a <= 4.7d-132))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.2e-207) || !(a <= 4.7e-132)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.2e-207) or not (a <= 4.7e-132):
		tmp = a * 120.0
	else:
		tmp = 60.0 * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.2e-207) || !(a <= 4.7e-132))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.2e-207) || ~((a <= 4.7e-132)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.2e-207], N[Not[LessEqual[a, 4.7e-132]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.20000000000000007e-207 or 4.7000000000000002e-132 < a

   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* 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 64.1%

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

   if -4.20000000000000007e-207 < a < 4.7000000000000002e-132

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 91.6%

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

   6. Taylor expanded in x around 0 49.4%

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

      1. associate-*r/ 49.4%

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

      2. remove-double-neg 49.4%

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

      3. neg-mul-1 49.4%

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

      4. times-frac 49.4%

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

      5. metadata-eval 49.4%

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

      6. neg-sub0 49.4%

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

      7. sub-neg 49.4%

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

      8. +-commutative 49.4%

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

      9. associate--r+ 49.4%

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

      10. neg-sub0 49.4%

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

      11. remove-double-neg 49.4%

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

   8. Simplified 49.4%

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

   9. Taylor expanded in t around inf 28.0%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-207} \lor \neg \left(a \leq 4.7 \cdot 10^{-132}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+201}:\\ \;\;\;\;60 \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -6.2e+201) (* 60.0 (/ y (- z))) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.2e+201) {
		tmp = 60.0 * (y / -z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-6.2d+201)) then
        tmp = 60.0d0 * (y / -z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -6.2e+201) {
		tmp = 60.0 * (y / -z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -6.2e+201:
		tmp = 60.0 * (y / -z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -6.2e+201)
		tmp = Float64(60.0 * Float64(y / Float64(-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 (y <= -6.2e+201)
		tmp = 60.0 * (y / -z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -6.2e+201], N[(60.0 * N[(y / (-z)), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.19999999999999961e201

   1. Initial program 96.2%

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

      1. associate-/l* 99.9%

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

      2. fma-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in a around 0 85.6%

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

   6. Taylor expanded in x around 0 78.0%

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

      1. associate-*r/ 74.2%

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

      2. remove-double-neg 74.2%

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

      3. neg-mul-1 74.2%

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

      4. times-frac 78.0%

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

      5. metadata-eval 78.0%

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

      6. neg-sub0 78.0%

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

      7. sub-neg 78.0%

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

      8. +-commutative 78.0%

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

      9. associate--r+ 78.0%

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

      10. neg-sub0 78.0%

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

      11. remove-double-neg 78.0%

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

   8. Simplified 78.0%

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

   9. Taylor expanded in t around 0 52.0%

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

       1. associate-*r/ 52.0%

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

       2. mul-1-neg 52.0%

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

   11. Simplified 52.0%

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

   if -6.19999999999999961e201 < y

   1. Initial program 99.4%

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

      1. associate-/l* 99.8%

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

      2. fma-define 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 53.6%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+201}:\\ \;\;\;\;60 \cdot \frac{y}{-z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.8% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. associate-/l* 99.8%

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

   2. fma-define 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in z around inf 50.0%

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

6. Final simplification 50.0%

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

Developer Target 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024146 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (/ 60 (/ (- z t) (- x y))) (* a 120)))

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