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

Percentage Accurate: 99.3% → 99.8%

Time: 12.6s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

   1. associate-/l* 99.8%

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

   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. Add Preprocessing

Alternative 2: 72.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+153}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+87}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+74}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+27}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+153)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= t_1 -2e+87)
       (+ (* a 120.0) (* 60.0 (/ x z)))
       (if (<= t_1 -2e+74)
         (* (- x y) (/ 60.0 (- z t)))
         (if (<= t_1 5e+27) (* a 120.0) t_1))))))

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 <= -1e+153) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t_1 <= -2e+87) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if (t_1 <= -2e+74) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if (t_1 <= 5e+27) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	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 <= (-1d+153)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (t_1 <= (-2d+87)) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    else if (t_1 <= (-2d+74)) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else if (t_1 <= 5d+27) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    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 <= -1e+153) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t_1 <= -2e+87) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if (t_1 <= -2e+74) {
		tmp = (x - y) * (60.0 / (z - t));
	} else if (t_1 <= 5e+27) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+153:
		tmp = 60.0 * ((x - y) / (z - t))
	elif t_1 <= -2e+87:
		tmp = (a * 120.0) + (60.0 * (x / z))
	elif t_1 <= -2e+74:
		tmp = (x - y) * (60.0 / (z - t))
	elif t_1 <= 5e+27:
		tmp = a * 120.0
	else:
		tmp = t_1
	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 <= -1e+153)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (t_1 <= -2e+87)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	elseif (t_1 <= -2e+74)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	elseif (t_1 <= 5e+27)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	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 <= -1e+153)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (t_1 <= -2e+87)
		tmp = (a * 120.0) + (60.0 * (x / z));
	elseif (t_1 <= -2e+74)
		tmp = (x - y) * (60.0 / (z - t));
	elseif (t_1 <= 5e+27)
		tmp = a * 120.0;
	else
		tmp = t_1;
	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[LessEqual[t$95$1, -1e+153], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e+87], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e+74], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+27], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1e153

   1. Initial program 97.2%

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

   3. Taylor expanded in a around 0 86.6%

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

   if -1e153 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.9999999999999999e87

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 84.2%

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

   4. Taylor expanded in z around inf 73.6%

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

   if -1.9999999999999999e87 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < -1.9999999999999999e74

   1. Initial program 99.7%

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

   3. Taylor expanded in a around 0 99.7%

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

      1. associate-*r/ 99.7%

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

   5. Simplified 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 100.0%

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

   7. Applied egg-rr 100.0%

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

   if -1.9999999999999999e74 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t)) < 4.99999999999999979e27

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.6%

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

   if 4.99999999999999979e27 < (/.f64 (*.f64 #s(literal 60 binary64) (-.f64 x y)) (-.f64 z t))

   1. Initial program 98.0%

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

   3. Taylor expanded in a around 0 78.0%

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

      1. associate-*r/ 78.1%

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

   5. Simplified 78.1%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+153}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{+87}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -2 \cdot 10^{+74}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+27}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+107}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{+22}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -20:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-68}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e+107)
   (+ (* a 120.0) (/ (* 60.0 y) t))
   (if (<= (* a 120.0) -2e+22)
     (+ (* a 120.0) (/ (* 60.0 x) z))
     (if (<= (* a 120.0) -20.0)
       (+ (* a 120.0) (* -60.0 (/ x t)))
       (if (<= (* a 120.0) 1e-68) (* 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) <= -5e+107) {
		tmp = (a * 120.0) + ((60.0 * y) / t);
	} else if ((a * 120.0) <= -2e+22) {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	} else if ((a * 120.0) <= -20.0) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else if ((a * 120.0) <= 1e-68) {
		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) <= (-5d+107)) then
        tmp = (a * 120.0d0) + ((60.0d0 * y) / t)
    else if ((a * 120.0d0) <= (-2d+22)) then
        tmp = (a * 120.0d0) + ((60.0d0 * x) / z)
    else if ((a * 120.0d0) <= (-20.0d0)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (x / t))
    else if ((a * 120.0d0) <= 1d-68) 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) <= -5e+107) {
		tmp = (a * 120.0) + ((60.0 * y) / t);
	} else if ((a * 120.0) <= -2e+22) {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	} else if ((a * 120.0) <= -20.0) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else if ((a * 120.0) <= 1e-68) {
		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) <= -5e+107:
		tmp = (a * 120.0) + ((60.0 * y) / t)
	elif (a * 120.0) <= -2e+22:
		tmp = (a * 120.0) + ((60.0 * x) / z)
	elif (a * 120.0) <= -20.0:
		tmp = (a * 120.0) + (-60.0 * (x / t))
	elif (a * 120.0) <= 1e-68:
		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) <= -5e+107)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * y) / t));
	elseif (Float64(a * 120.0) <= -2e+22)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / z));
	elseif (Float64(a * 120.0) <= -20.0)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)));
	elseif (Float64(a * 120.0) <= 1e-68)
		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) <= -5e+107)
		tmp = (a * 120.0) + ((60.0 * y) / t);
	elseif ((a * 120.0) <= -2e+22)
		tmp = (a * 120.0) + ((60.0 * x) / z);
	elseif ((a * 120.0) <= -20.0)
		tmp = (a * 120.0) + (-60.0 * (x / t));
	elseif ((a * 120.0) <= 1e-68)
		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], -5e+107], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -2e+22], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -20.0], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-68], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.0000000000000002e107

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 93.0%

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

   4. Taylor expanded in z around 0 85.8%

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

      1. associate-*r/ 85.8%

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

      2. *-commutative 85.8%

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

   6. Simplified 85.8%

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

   if -5.0000000000000002e107 < (*.f64 a #s(literal 120 binary64)) < -2e22

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 91.7%

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

   4. Taylor expanded in z around inf 85.6%

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

      1. associate-*r/ 85.7%

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

   6. Applied egg-rr 85.7%

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

   if -2e22 < (*.f64 a #s(literal 120 binary64)) < -20

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.1%

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

   4. Taylor expanded in z around 0 80.1%

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

   if -20 < (*.f64 a #s(literal 120 binary64)) < 1.00000000000000007e-68

   1. Initial program 98.8%

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

   3. Taylor expanded in a around 0 76.5%

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

   if 1.00000000000000007e-68 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf 75.7%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+107}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{+22}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -20:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-68}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+33}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-68}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+91}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+219}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e+33)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-68)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= (* a 120.0) 2e+91)
       (+ (* a 120.0) (/ (* 60.0 x) z))
       (if (<= (* a 120.0) 2e+219)
         (+ (* a 120.0) (/ -60.0 (/ z y)))
         (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e+33) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-68) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 2e+91) {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	} else if ((a * 120.0) <= 2e+219) {
		tmp = (a * 120.0) + (-60.0 / (z / y));
	} 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) <= (-4d+33)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-68) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if ((a * 120.0d0) <= 2d+91) then
        tmp = (a * 120.0d0) + ((60.0d0 * x) / z)
    else if ((a * 120.0d0) <= 2d+219) then
        tmp = (a * 120.0d0) + ((-60.0d0) / (z / y))
    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) <= -4e+33) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-68) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 2e+91) {
		tmp = (a * 120.0) + ((60.0 * x) / z);
	} else if ((a * 120.0) <= 2e+219) {
		tmp = (a * 120.0) + (-60.0 / (z / y));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -4e+33:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-68:
		tmp = 60.0 * ((x - y) / (z - t))
	elif (a * 120.0) <= 2e+91:
		tmp = (a * 120.0) + ((60.0 * x) / z)
	elif (a * 120.0) <= 2e+219:
		tmp = (a * 120.0) + (-60.0 / (z / y))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e+33)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-68)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 2e+91)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / z));
	elseif (Float64(a * 120.0) <= 2e+219)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 / Float64(z / y)));
	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) <= -4e+33)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-68)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif ((a * 120.0) <= 2e+91)
		tmp = (a * 120.0) + ((60.0 * x) / z);
	elseif ((a * 120.0) <= 2e+219)
		tmp = (a * 120.0) + (-60.0 / (z / y));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e+33], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-68], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+91], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(60.0 * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+219], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -3.9999999999999998e33 or 1.99999999999999993e219 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf 83.9%

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

   if -3.9999999999999998e33 < (*.f64 a #s(literal 120 binary64)) < 1.00000000000000007e-68

   1. Initial program 98.9%

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

   3. Taylor expanded in a around 0 74.6%

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

   if 1.00000000000000007e-68 < (*.f64 a #s(literal 120 binary64)) < 2.00000000000000016e91

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 92.3%

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

   4. Taylor expanded in z around inf 77.0%

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

      1. associate-*r/ 77.1%

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

   6. Applied egg-rr 77.1%

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

   if 2.00000000000000016e91 < (*.f64 a #s(literal 120 binary64)) < 1.99999999999999993e219

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.2%

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

   4. Taylor expanded in z around inf 77.8%

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

      1. *-commutative 77.8%

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

      2. associate-*l/ 77.8%

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

      3. associate-*r/ 77.8%

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

      4. *-commutative 77.8%

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

      5. associate-/r/ 77.7%

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

   6. Simplified 77.7%

      \[\leadsto \color{blue}{\frac{-60}{\frac{z}{y}}} + a \cdot 120 \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+33}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-68}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+91}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+219}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+33}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-68}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+91}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+219}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e+33)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-68)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= (* a 120.0) 2e+91)
       (+ (* a 120.0) (* 60.0 (/ x z)))
       (if (<= (* a 120.0) 2e+219)
         (+ (* a 120.0) (/ -60.0 (/ z y)))
         (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e+33) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-68) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 2e+91) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if ((a * 120.0) <= 2e+219) {
		tmp = (a * 120.0) + (-60.0 / (z / y));
	} 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) <= (-4d+33)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-68) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if ((a * 120.0d0) <= 2d+91) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    else if ((a * 120.0d0) <= 2d+219) then
        tmp = (a * 120.0d0) + ((-60.0d0) / (z / y))
    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) <= -4e+33) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-68) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 2e+91) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if ((a * 120.0) <= 2e+219) {
		tmp = (a * 120.0) + (-60.0 / (z / y));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -4e+33:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-68:
		tmp = 60.0 * ((x - y) / (z - t))
	elif (a * 120.0) <= 2e+91:
		tmp = (a * 120.0) + (60.0 * (x / z))
	elif (a * 120.0) <= 2e+219:
		tmp = (a * 120.0) + (-60.0 / (z / y))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e+33)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-68)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 2e+91)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	elseif (Float64(a * 120.0) <= 2e+219)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 / Float64(z / y)));
	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) <= -4e+33)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-68)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif ((a * 120.0) <= 2e+91)
		tmp = (a * 120.0) + (60.0 * (x / z));
	elseif ((a * 120.0) <= 2e+219)
		tmp = (a * 120.0) + (-60.0 / (z / y));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e+33], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-68], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+91], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+219], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -3.9999999999999998e33 or 1.99999999999999993e219 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.7%

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

   3. Taylor expanded in z around inf 83.9%

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

   if -3.9999999999999998e33 < (*.f64 a #s(literal 120 binary64)) < 1.00000000000000007e-68

   1. Initial program 98.9%

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

   3. Taylor expanded in a around 0 74.6%

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

   if 1.00000000000000007e-68 < (*.f64 a #s(literal 120 binary64)) < 2.00000000000000016e91

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 92.3%

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

   4. Taylor expanded in z around inf 77.0%

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

   if 2.00000000000000016e91 < (*.f64 a #s(literal 120 binary64)) < 1.99999999999999993e219

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 91.2%

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

   4. Taylor expanded in z around inf 77.8%

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

      1. *-commutative 77.8%

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

      2. associate-*l/ 77.8%

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

      3. associate-*r/ 77.8%

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

      4. *-commutative 77.8%

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

      5. associate-/r/ 77.7%

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

   6. Simplified 77.7%

      \[\leadsto \color{blue}{\frac{-60}{\frac{z}{y}}} + a \cdot 120 \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+33}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-68}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+91}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+219}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+217}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-202}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-180}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+172}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.2e+217)
   (* -60.0 (/ y (- z t)))
   (if (<= y 2.5e-202)
     (* a 120.0)
     (if (<= y 2.15e-180)
       (/ 60.0 (/ (- z t) x))
       (if (<= y 6e+172) (* a 120.0) (/ (* y -60.0) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.2e+217) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= 2.5e-202) {
		tmp = a * 120.0;
	} else if (y <= 2.15e-180) {
		tmp = 60.0 / ((z - t) / x);
	} else if (y <= 6e+172) {
		tmp = a * 120.0;
	} else {
		tmp = (y * -60.0) / (z - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.2d+217)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if (y <= 2.5d-202) then
        tmp = a * 120.0d0
    else if (y <= 2.15d-180) then
        tmp = 60.0d0 / ((z - t) / x)
    else if (y <= 6d+172) then
        tmp = a * 120.0d0
    else
        tmp = (y * (-60.0d0)) / (z - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.2e+217) {
		tmp = -60.0 * (y / (z - t));
	} else if (y <= 2.5e-202) {
		tmp = a * 120.0;
	} else if (y <= 2.15e-180) {
		tmp = 60.0 / ((z - t) / x);
	} else if (y <= 6e+172) {
		tmp = a * 120.0;
	} else {
		tmp = (y * -60.0) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.2e+217:
		tmp = -60.0 * (y / (z - t))
	elif y <= 2.5e-202:
		tmp = a * 120.0
	elif y <= 2.15e-180:
		tmp = 60.0 / ((z - t) / x)
	elif y <= 6e+172:
		tmp = a * 120.0
	else:
		tmp = (y * -60.0) / (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.2e+217)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (y <= 2.5e-202)
		tmp = Float64(a * 120.0);
	elseif (y <= 2.15e-180)
		tmp = Float64(60.0 / Float64(Float64(z - t) / x));
	elseif (y <= 6e+172)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.2e+217)
		tmp = -60.0 * (y / (z - t));
	elseif (y <= 2.5e-202)
		tmp = a * 120.0;
	elseif (y <= 2.15e-180)
		tmp = 60.0 / ((z - t) / x);
	elseif (y <= 6e+172)
		tmp = a * 120.0;
	else
		tmp = (y * -60.0) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.2e+217], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-202], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, 2.15e-180], N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+172], N[(a * 120.0), $MachinePrecision], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.1999999999999999e217

   1. Initial program 92.8%

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

   3. Taylor expanded in y around inf 60.3%

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

   if -1.1999999999999999e217 < y < 2.49999999999999986e-202 or 2.1499999999999998e-180 < y < 5.9999999999999998e172

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 66.2%

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

   if 2.49999999999999986e-202 < y < 2.1499999999999998e-180

   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 inf 80.5%

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

      1. clear-num 80.5%

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

      2. un-div-inv 80.6%

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

   5. Applied egg-rr 80.6%

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

   if 5.9999999999999998e172 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 79.6%

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

      1. associate-*r/ 79.7%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in x around 0 76.4%

      \[\leadsto \frac{\color{blue}{-60 \cdot y}}{z - t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+217}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-202}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-180}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+172}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-201}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-180}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+172}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= y -9e+216)
     t_1
     (if (<= y 1.32e-201)
       (* a 120.0)
       (if (<= y 2.15e-180)
         (/ 60.0 (/ (- z t) x))
         (if (<= y 1.45e+172) (* a 120.0) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -9e+216) {
		tmp = t_1;
	} else if (y <= 1.32e-201) {
		tmp = a * 120.0;
	} else if (y <= 2.15e-180) {
		tmp = 60.0 / ((z - t) / x);
	} else if (y <= 1.45e+172) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	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) * (y / (z - t))
    if (y <= (-9d+216)) then
        tmp = t_1
    else if (y <= 1.32d-201) then
        tmp = a * 120.0d0
    else if (y <= 2.15d-180) then
        tmp = 60.0d0 / ((z - t) / x)
    else if (y <= 1.45d+172) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    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 * (y / (z - t));
	double tmp;
	if (y <= -9e+216) {
		tmp = t_1;
	} else if (y <= 1.32e-201) {
		tmp = a * 120.0;
	} else if (y <= 2.15e-180) {
		tmp = 60.0 / ((z - t) / x);
	} else if (y <= 1.45e+172) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	tmp = 0
	if y <= -9e+216:
		tmp = t_1
	elif y <= 1.32e-201:
		tmp = a * 120.0
	elif y <= 2.15e-180:
		tmp = 60.0 / ((z - t) / x)
	elif y <= 1.45e+172:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (y <= -9e+216)
		tmp = t_1;
	elseif (y <= 1.32e-201)
		tmp = Float64(a * 120.0);
	elseif (y <= 2.15e-180)
		tmp = Float64(60.0 / Float64(Float64(z - t) / x));
	elseif (y <= 1.45e+172)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (y <= -9e+216)
		tmp = t_1;
	elseif (y <= 1.32e-201)
		tmp = a * 120.0;
	elseif (y <= 2.15e-180)
		tmp = 60.0 / ((z - t) / x);
	elseif (y <= 1.45e+172)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+216], t$95$1, If[LessEqual[y, 1.32e-201], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, 2.15e-180], N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+172], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.0000000000000005e216 or 1.45e172 < y

   1. Initial program 97.8%

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

   3. Taylor expanded in y around inf 71.6%

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

   if -9.0000000000000005e216 < y < 1.31999999999999996e-201 or 2.1499999999999998e-180 < y < 1.45e172

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 66.2%

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

   if 1.31999999999999996e-201 < y < 2.1499999999999998e-180

   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 inf 80.5%

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

      1. clear-num 80.5%

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

      2. un-div-inv 80.6%

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

   5. Applied egg-rr 80.6%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+216}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-201}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-180}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+172}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 56.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.75 \cdot 10^{-202}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-180}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+173}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= y -9e+216)
     t_1
     (if (<= y 3.75e-202)
       (* a 120.0)
       (if (<= y 2.15e-180)
         (* 60.0 (/ x (- z t)))
         (if (<= y 2.9e+173) (* a 120.0) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (y <= -9e+216) {
		tmp = t_1;
	} else if (y <= 3.75e-202) {
		tmp = a * 120.0;
	} else if (y <= 2.15e-180) {
		tmp = 60.0 * (x / (z - t));
	} else if (y <= 2.9e+173) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	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) * (y / (z - t))
    if (y <= (-9d+216)) then
        tmp = t_1
    else if (y <= 3.75d-202) then
        tmp = a * 120.0d0
    else if (y <= 2.15d-180) then
        tmp = 60.0d0 * (x / (z - t))
    else if (y <= 2.9d+173) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    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 * (y / (z - t));
	double tmp;
	if (y <= -9e+216) {
		tmp = t_1;
	} else if (y <= 3.75e-202) {
		tmp = a * 120.0;
	} else if (y <= 2.15e-180) {
		tmp = 60.0 * (x / (z - t));
	} else if (y <= 2.9e+173) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	tmp = 0
	if y <= -9e+216:
		tmp = t_1
	elif y <= 3.75e-202:
		tmp = a * 120.0
	elif y <= 2.15e-180:
		tmp = 60.0 * (x / (z - t))
	elif y <= 2.9e+173:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (y <= -9e+216)
		tmp = t_1;
	elseif (y <= 3.75e-202)
		tmp = Float64(a * 120.0);
	elseif (y <= 2.15e-180)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (y <= 2.9e+173)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (y / (z - t));
	tmp = 0.0;
	if (y <= -9e+216)
		tmp = t_1;
	elseif (y <= 3.75e-202)
		tmp = a * 120.0;
	elseif (y <= 2.15e-180)
		tmp = 60.0 * (x / (z - t));
	elseif (y <= 2.9e+173)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e+216], t$95$1, If[LessEqual[y, 3.75e-202], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, 2.15e-180], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+173], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.0000000000000005e216 or 2.90000000000000007e173 < y

   1. Initial program 97.8%

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

   3. Taylor expanded in y around inf 71.6%

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

   if -9.0000000000000005e216 < y < 3.75000000000000002e-202 or 2.1499999999999998e-180 < y < 2.90000000000000007e173

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 66.2%

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

   if 3.75000000000000002e-202 < y < 2.1499999999999998e-180

   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 inf 80.5%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+216}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq 3.75 \cdot 10^{-202}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-180}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+173}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -20 \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-125}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -20.0) (not (<= (* a 120.0) 5e-125)))
   (+ (* a 120.0) (/ (* y -60.0) (- z t)))
   (* (- x y) (/ 60.0 (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -20.0) || !((a * 120.0) <= 5e-125)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-20.0d0)) .or. (.not. ((a * 120.0d0) <= 5d-125))) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else
        tmp = (x - y) * (60.0d0 / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -20.0) || !((a * 120.0) <= 5e-125)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -20.0) or not ((a * 120.0) <= 5e-125):
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	else:
		tmp = (x - y) * (60.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -20.0) || !(Float64(a * 120.0) <= 5e-125))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(x - y) * 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 * 120.0) <= -20.0) || ~(((a * 120.0) <= 5e-125)))
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	else
		tmp = (x - y) * (60.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -20.0], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-125]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -20 or 4.99999999999999967e-125 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.4%

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

   3. Taylor expanded in x around 0 87.3%

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

   if -20 < (*.f64 a #s(literal 120 binary64)) < 4.99999999999999967e-125

   1. Initial program 98.6%

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

   3. Taylor expanded in a around 0 79.0%

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

      1. associate-*r/ 77.9%

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

   5. Simplified 77.9%

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

      1. *-commutative 98.6%

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

      2. associate-/l* 99.7%

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

   7. Applied egg-rr 79.0%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -20 \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-125}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+33} \lor \neg \left(a \cdot 120 \leq 10^{-68}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -4e+33) (not (<= (* a 120.0) 1e-68)))
   (* 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) <= -4e+33) || !((a * 120.0) <= 1e-68)) {
		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) <= (-4d+33)) .or. (.not. ((a * 120.0d0) <= 1d-68))) 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) <= -4e+33) || !((a * 120.0) <= 1e-68)) {
		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) <= -4e+33) or not ((a * 120.0) <= 1e-68):
		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) <= -4e+33) || !(Float64(a * 120.0) <= 1e-68))
		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) <= -4e+33) || ~(((a * 120.0) <= 1e-68)))
		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], -4e+33], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-68]], $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)) < -3.9999999999999998e33 or 1.00000000000000007e-68 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.3%

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

   3. Taylor expanded in z around inf 78.0%

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

   if -3.9999999999999998e33 < (*.f64 a #s(literal 120 binary64)) < 1.00000000000000007e-68

   1. Initial program 98.9%

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

   3. Taylor expanded in a around 0 74.6%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+33} \lor \neg \left(a \cdot 120 \leq 10^{-68}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+81} \lor \neg \left(y \leq 8 \cdot 10^{+95}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -7e+81) (not (<= y 8e+95)))
   (+ (* a 120.0) (/ (* y -60.0) (- z t)))
   (+ (* a 120.0) (/ (* 60.0 x) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -7e+81) || !(y <= 8e+95)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-7d+81)) .or. (.not. (y <= 8d+95))) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - t))
    else
        tmp = (a * 120.0d0) + ((60.0d0 * x) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -7e+81) || !(y <= 8e+95)) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -7e+81) or not (y <= 8e+95):
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	else:
		tmp = (a * 120.0) + ((60.0 * x) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -7e+81) || !(y <= 8e+95))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(60.0 * x) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -7e+81) || ~((y <= 8e+95)))
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	else
		tmp = (a * 120.0) + ((60.0 * x) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -7e+81], N[Not[LessEqual[y, 8e+95]], $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[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.0000000000000001e81 or 8.00000000000000016e95 < y

   1. Initial program 98.7%

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

   3. Taylor expanded in x around 0 91.2%

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

   if -7.0000000000000001e81 < y < 8.00000000000000016e95

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf 94.8%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+81} \lor \neg \left(y \leq 8 \cdot 10^{+95}\right):\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60 \cdot x}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+219} \lor \neg \left(y \leq 1.6 \cdot 10^{+172}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.55e+219) (not (<= y 1.6e+172)))
   (* -60.0 (/ y (- z t)))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.55e+219) || !(y <= 1.6e+172)) {
		tmp = -60.0 * (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 ((y <= (-2.55d+219)) .or. (.not. (y <= 1.6d+172))) then
        tmp = (-60.0d0) * (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 ((y <= -2.55e+219) || !(y <= 1.6e+172)) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.55e+219) or not (y <= 1.6e+172):
		tmp = -60.0 * (y / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.55e+219) || !(y <= 1.6e+172))
		tmp = Float64(-60.0 * Float64(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 ((y <= -2.55e+219) || ~((y <= 1.6e+172)))
		tmp = -60.0 * (y / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.55e+219], N[Not[LessEqual[y, 1.6e+172]], $MachinePrecision]], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.54999999999999997e219 or 1.59999999999999993e172 < y

   1. Initial program 97.8%

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

   3. Taylor expanded in y around inf 71.6%

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

   if -2.54999999999999997e219 < y < 1.59999999999999993e172

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 64.1%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+219} \lor \neg \left(y \leq 1.6 \cdot 10^{+172}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-91} \lor \neg \left(a \leq 1.6 \cdot 10^{-127}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.8e-91) (not (<= a 1.6e-127))) (* a 120.0) (* -60.0 (/ y z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e-91) || !(a <= 1.6e-127)) {
		tmp = a * 120.0;
	} else {
		tmp = -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 <= (-2.8d-91)) .or. (.not. (a <= 1.6d-127))) then
        tmp = a * 120.0d0
    else
        tmp = (-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 <= -2.8e-91) || !(a <= 1.6e-127)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.8e-91) or not (a <= 1.6e-127):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.8e-91) || !(a <= 1.6e-127))
		tmp = Float64(a * 120.0);
	else
		tmp = 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 <= -2.8e-91) || ~((a <= 1.6e-127)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.8e-91], N[Not[LessEqual[a, 1.6e-127]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.8e-91 or 1.60000000000000009e-127 < a

   1. Initial program 99.4%

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

   3. Taylor expanded in z around inf 69.8%

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

   if -2.8e-91 < a < 1.60000000000000009e-127

   1. Initial program 98.3%

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

   3. Taylor expanded in a around 0 83.7%

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

      1. associate-*r/ 82.2%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in z around inf 53.1%

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

   7. Taylor expanded in x around 0 34.6%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-91} \lor \neg \left(a \leq 1.6 \cdot 10^{-127}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.1%

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

   1. *-commutative 99.1%

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

   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%

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

Alternative 15: 51.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.5 \cdot 10^{+173}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 3.5e+173) (* a 120.0) (* 60.0 (/ y t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 3.5e+173) {
		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 (y <= 3.5d+173) 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 (y <= 3.5e+173) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 3.5e+173:
		tmp = a * 120.0
	else:
		tmp = 60.0 * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 3.5e+173)
		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 (y <= 3.5e+173)
		tmp = a * 120.0;
	else
		tmp = 60.0 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 3.5e+173], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.4999999999999999e173

   1. Initial program 99.0%

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

   3. Taylor expanded in z around inf 61.5%

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

   if 3.4999999999999999e173 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in a around 0 79.6%

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

      1. associate-*r/ 79.7%

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

   5. Simplified 79.7%

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

   6. Taylor expanded in z around 0 56.9%

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

   7. Taylor expanded in x around 0 53.5%

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

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.5 \cdot 10^{+173}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.6% 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 99.1%

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

3. Taylor expanded in z around inf 56.1%

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

4. Final simplification 56.1%

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

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024097 
(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)))