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

Percentage Accurate: 99.3% → 99.8%

Time: 13.0s

Alternatives: 17

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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

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

   1. associate-/l* 99.4%

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

3. Simplified 99.4%

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

Alternative 2: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z} + a \cdot 120\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-57}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;z \leq 0.28:\\ \;\;\;\;-60 \cdot \frac{x}{t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* 60.0 (/ (- x y) z)) (* a 120.0))))
   (if (<= z -1.95e-25)
     t_1
     (if (<= z 7.8e-57)
       (/ 60.0 (/ (- z t) (- x y)))
       (if (<= z 0.28) (+ (* -60.0 (/ x t)) (* 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)) + (a * 120.0);
	double tmp;
	if (z <= -1.95e-25) {
		tmp = t_1;
	} else if (z <= 7.8e-57) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (z <= 0.28) {
		tmp = (-60.0 * (x / t)) + (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)) + (a * 120.0d0)
    if (z <= (-1.95d-25)) then
        tmp = t_1
    else if (z <= 7.8d-57) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else if (z <= 0.28d0) then
        tmp = ((-60.0d0) * (x / t)) + (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)) + (a * 120.0);
	double tmp;
	if (z <= -1.95e-25) {
		tmp = t_1;
	} else if (z <= 7.8e-57) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (z <= 0.28) {
		tmp = (-60.0 * (x / t)) + (a * 120.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * ((x - y) / z)) + (a * 120.0)
	tmp = 0
	if z <= -1.95e-25:
		tmp = t_1
	elif z <= 7.8e-57:
		tmp = 60.0 / ((z - t) / (x - y))
	elif z <= 0.28:
		tmp = (-60.0 * (x / t)) + (a * 120.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(Float64(x - y) / z)) + Float64(a * 120.0))
	tmp = 0.0
	if (z <= -1.95e-25)
		tmp = t_1;
	elseif (z <= 7.8e-57)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	elseif (z <= 0.28)
		tmp = Float64(Float64(-60.0 * Float64(x / t)) + 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)) + (a * 120.0);
	tmp = 0.0;
	if (z <= -1.95e-25)
		tmp = t_1;
	elseif (z <= 7.8e-57)
		tmp = 60.0 / ((z - t) / (x - y));
	elseif (z <= 0.28)
		tmp = (-60.0 * (x / t)) + (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[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e-25], t$95$1, If[LessEqual[z, 7.8e-57], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.28], N[(N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.95e-25 or 0.28000000000000003 < z

   1. Initial program 99.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 87.2%

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

   if -1.95e-25 < z < 7.80000000000000013e-57

   1. Initial program 98.9%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in a around 0 69.6%

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

      1. associate-*r/ 69.6%

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

      2. *-rgt-identity 69.6%

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

      3. times-frac 69.5%

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

      4. /-rgt-identity 69.5%

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

      5. associate-/r/ 69.6%

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

   7. Simplified 69.6%

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

   if 7.80000000000000013e-57 < z < 0.28000000000000003

   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 0 91.3%

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

      1. neg-mul-1 91.3%

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

   5. Simplified 91.3%

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

   6. Taylor expanded in y around 0 91.4%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-25}:\\ \;\;\;\;60 \cdot \frac{x - y}{z} + a \cdot 120\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-57}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;z \leq 0.28:\\ \;\;\;\;-60 \cdot \frac{x}{t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x - y \leq -1 \cdot 10^{+163} \lor \neg \left(x - y \leq 5 \cdot 10^{+111}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- x y) -1e+163) (not (<= (- x y) 5e+111)))
   (* (- x y) (/ 60.0 (- z t)))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x - y) <= -1e+163) || !((x - y) <= 5e+111)) {
		tmp = (x - y) * (60.0 / (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 (((x - y) <= (-1d+163)) .or. (.not. ((x - y) <= 5d+111))) then
        tmp = (x - y) * (60.0d0 / (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 (((x - y) <= -1e+163) || !((x - y) <= 5e+111)) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((x - y) <= -1e+163) or not ((x - y) <= 5e+111):
		tmp = (x - y) * (60.0 / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(x - y) <= -1e+163) || !(Float64(x - y) <= 5e+111))
		tmp = Float64(Float64(x - y) * Float64(60.0 / 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 (((x - y) <= -1e+163) || ~(((x - y) <= 5e+111)))
		tmp = (x - y) * (60.0 / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(x - y), $MachinePrecision], -1e+163], N[Not[LessEqual[N[(x - y), $MachinePrecision], 5e+111]], $MachinePrecision]], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 x y) < -9.9999999999999994e162 or 4.9999999999999997e111 < (-.f64 x y)

   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* 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in a around 0 74.3%

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

      1. associate-*r/ 73.4%

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

      2. *-rgt-identity 73.4%

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

      3. times-frac 74.3%

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

      4. /-rgt-identity 74.3%

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

   7. Simplified 74.3%

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

   if -9.9999999999999994e162 < (-.f64 x y) < 4.9999999999999997e111

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 73.7%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - y \leq -1 \cdot 10^{+163} \lor \neg \left(x - y \leq 5 \cdot 10^{+111}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -100000:\\ \;\;\;\;a \cdot 120 - \frac{60}{\frac{z}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-14}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -100000.0)
   (- (* a 120.0) (/ 60.0 (/ z y)))
   (if (<= (* a 120.0) 5e-14)
     (* (- x y) (/ 60.0 (- z t)))
     (+ (* -60.0 (/ x t)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -100000.0) {
		tmp = (a * 120.0) - (60.0 / (z / y));
	} else if ((a * 120.0) <= 5e-14) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = (-60.0 * (x / t)) + (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) <= (-100000.0d0)) then
        tmp = (a * 120.0d0) - (60.0d0 / (z / y))
    else if ((a * 120.0d0) <= 5d-14) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else
        tmp = ((-60.0d0) * (x / t)) + (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) <= -100000.0) {
		tmp = (a * 120.0) - (60.0 / (z / y));
	} else if ((a * 120.0) <= 5e-14) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = (-60.0 * (x / t)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -100000.0:
		tmp = (a * 120.0) - (60.0 / (z / y))
	elif (a * 120.0) <= 5e-14:
		tmp = (x - y) * (60.0 / (z - t))
	else:
		tmp = (-60.0 * (x / t)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -100000.0)
		tmp = Float64(Float64(a * 120.0) - Float64(60.0 / Float64(z / y)));
	elseif (Float64(a * 120.0) <= 5e-14)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = Float64(Float64(-60.0 * Float64(x / t)) + 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) <= -100000.0)
		tmp = (a * 120.0) - (60.0 / (z / y));
	elseif ((a * 120.0) <= 5e-14)
		tmp = (x - y) * (60.0 / (z - t));
	else
		tmp = (-60.0 * (x / t)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -100000.0], N[(N[(a * 120.0), $MachinePrecision] - N[(60.0 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-14], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1e5

   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* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in z around inf 73.0%

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

      1. clear-num 73.0%

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

      2. un-div-inv 73.0%

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

   7. Applied egg-rr 73.0%

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

   8. Taylor expanded in x around 0 78.5%

      \[\leadsto \frac{60}{\color{blue}{-1 \cdot \frac{z}{y}}} + a \cdot 120 \]
   9. Step-by-step derivation

      1. associate-*r/ 78.5%

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

      2. neg-mul-1 78.5%

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

   10. Simplified 78.5%

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

   if -1e5 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000002e-14

   1. Initial program 99.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 71.2%

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

      1. associate-*r/ 70.5%

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

      2. *-rgt-identity 70.5%

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

      3. times-frac 71.2%

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

      4. /-rgt-identity 71.2%

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

   7. Simplified 71.2%

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

   if 5.0000000000000002e-14 < (*.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. Taylor expanded in z around 0 80.0%

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

      1. neg-mul-1 80.0%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in y around 0 80.2%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -100000:\\ \;\;\;\;a \cdot 120 - \frac{60}{\frac{z}{y}}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-14}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -100000:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-14}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -100000.0)
   (+ (* a 120.0) (* -60.0 (/ y z)))
   (if (<= (* a 120.0) 5e-14)
     (* (- x y) (/ 60.0 (- z t)))
     (+ (* -60.0 (/ x t)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -100000.0) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 5e-14) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = (-60.0 * (x / t)) + (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) <= (-100000.0d0)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if ((a * 120.0d0) <= 5d-14) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else
        tmp = ((-60.0d0) * (x / t)) + (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) <= -100000.0) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if ((a * 120.0) <= 5e-14) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = (-60.0 * (x / t)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -100000.0:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif (a * 120.0) <= 5e-14:
		tmp = (x - y) * (60.0 / (z - t))
	else:
		tmp = (-60.0 * (x / t)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -100000.0)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (Float64(a * 120.0) <= 5e-14)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = Float64(Float64(-60.0 * Float64(x / t)) + 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) <= -100000.0)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif ((a * 120.0) <= 5e-14)
		tmp = (x - y) * (60.0 / (z - t));
	else
		tmp = (-60.0 * (x / t)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -100000.0], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-14], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1e5

   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* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in z around inf 73.0%

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

   6. Taylor expanded in x around 0 78.5%

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

   if -1e5 < (*.f64 a #s(literal 120 binary64)) < 5.0000000000000002e-14

   1. Initial program 99.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 71.2%

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

      1. associate-*r/ 70.5%

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

      2. *-rgt-identity 70.5%

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

      3. times-frac 71.2%

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

      4. /-rgt-identity 71.2%

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

   7. Simplified 71.2%

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

   if 5.0000000000000002e-14 < (*.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. Taylor expanded in z around 0 80.0%

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

      1. neg-mul-1 80.0%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in y around 0 80.2%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -100000:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-14}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1000000000 \lor \neg \left(z \leq 7800000\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y - x}{t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1000000000.0) (not (<= z 7800000.0)))
   (+ (* 60.0 (/ (- x y) z)) (* a 120.0))
   (+ (* 60.0 (/ (- y x) t)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1000000000.0) || !(z <= 7800000.0)) {
		tmp = (60.0 * ((x - y) / z)) + (a * 120.0);
	} else {
		tmp = (60.0 * ((y - x) / t)) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1000000000.0d0)) .or. (.not. (z <= 7800000.0d0))) then
        tmp = (60.0d0 * ((x - y) / z)) + (a * 120.0d0)
    else
        tmp = (60.0d0 * ((y - x) / t)) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1000000000.0) || !(z <= 7800000.0)) {
		tmp = (60.0 * ((x - y) / z)) + (a * 120.0);
	} else {
		tmp = (60.0 * ((y - x) / t)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1000000000.0) or not (z <= 7800000.0):
		tmp = (60.0 * ((x - y) / z)) + (a * 120.0)
	else:
		tmp = (60.0 * ((y - x) / t)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1000000000.0) || !(z <= 7800000.0))
		tmp = Float64(Float64(60.0 * Float64(Float64(x - y) / z)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(60.0 * Float64(Float64(y - x) / t)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1000000000.0) || ~((z <= 7800000.0)))
		tmp = (60.0 * ((x - y) / z)) + (a * 120.0);
	else
		tmp = (60.0 * ((y - x) / t)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1000000000.0], N[Not[LessEqual[z, 7800000.0]], $MachinePrecision]], N[(N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1e9 or 7.8e6 < z

   1. Initial program 99.0%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 90.9%

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

   if -1e9 < z < 7.8e6

   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* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around 0 82.0%

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

      1. associate-*r/ 82.0%

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

      2. neg-mul-1 82.0%

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

      3. neg-sub0 82.0%

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

      4. sub-neg 82.0%

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

      5. +-commutative 82.0%

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

      6. associate--r+ 82.0%

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

      7. neg-sub0 82.0%

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

      8. remove-double-neg 82.0%

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

   7. Simplified 82.0%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1000000000 \lor \neg \left(z \leq 7800000\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y - x}{t} + a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+163}:\\ \;\;\;\;\frac{60 \cdot \left(y - x\right)}{t} + a \cdot 120\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+156}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.3e+163)
   (+ (/ (* 60.0 (- y x)) t) (* a 120.0))
   (if (<= y 1.35e+156)
     (+ (/ (* 60.0 x) (- z t)) (* a 120.0))
     (* (- x y) (/ 60.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.3e+163) {
		tmp = ((60.0 * (y - x)) / t) + (a * 120.0);
	} else if (y <= 1.35e+156) {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	} 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 (y <= (-4.3d+163)) then
        tmp = ((60.0d0 * (y - x)) / t) + (a * 120.0d0)
    else if (y <= 1.35d+156) then
        tmp = ((60.0d0 * x) / (z - t)) + (a * 120.0d0)
    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 (y <= -4.3e+163) {
		tmp = ((60.0 * (y - x)) / t) + (a * 120.0);
	} else if (y <= 1.35e+156) {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.3e+163:
		tmp = ((60.0 * (y - x)) / t) + (a * 120.0)
	elif y <= 1.35e+156:
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0)
	else:
		tmp = (x - y) * (60.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.3e+163)
		tmp = Float64(Float64(Float64(60.0 * Float64(y - x)) / t) + Float64(a * 120.0));
	elseif (y <= 1.35e+156)
		tmp = Float64(Float64(Float64(60.0 * x) / Float64(z - t)) + Float64(a * 120.0));
	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 (y <= -4.3e+163)
		tmp = ((60.0 * (y - x)) / t) + (a * 120.0);
	elseif (y <= 1.35e+156)
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	else
		tmp = (x - y) * (60.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.3e+163], N[(N[(N[(60.0 * N[(y - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+156], N[(N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.3000000000000002e163

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 71.0%

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

      1. associate-*r/ 71.0%

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

      2. neg-mul-1 71.0%

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

      3. neg-sub0 71.0%

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

      4. sub-neg 71.0%

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

      5. +-commutative 71.0%

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

      6. associate--r+ 71.0%

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

      7. neg-sub0 71.0%

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

      8. remove-double-neg 71.0%

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

   7. Simplified 71.0%

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

      1. *-commutative 71.0%

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

      2. associate-*l/ 71.1%

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

   9. Applied egg-rr 71.1%

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

   if -4.3000000000000002e163 < y < 1.35e156

   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 89.3%

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

   if 1.35e156 < y

   1. Initial program 95.3%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in a around 0 90.5%

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

      1. associate-*r/ 90.6%

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

      2. *-rgt-identity 90.6%

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

      3. times-frac 90.7%

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

      4. /-rgt-identity 90.7%

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

   7. Simplified 90.7%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+163}:\\ \;\;\;\;\frac{60 \cdot \left(y - x\right)}{t} + a \cdot 120\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+156}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+163}:\\ \;\;\;\;60 \cdot \frac{y - x}{t} + a \cdot 120\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+153}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -7e+163)
   (+ (* 60.0 (/ (- y x) t)) (* a 120.0))
   (if (<= y 1.7e+153)
     (+ (/ (* 60.0 x) (- z t)) (* a 120.0))
     (* (- x y) (/ 60.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7e+163) {
		tmp = (60.0 * ((y - x) / t)) + (a * 120.0);
	} else if (y <= 1.7e+153) {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	} 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 (y <= (-7d+163)) then
        tmp = (60.0d0 * ((y - x) / t)) + (a * 120.0d0)
    else if (y <= 1.7d+153) then
        tmp = ((60.0d0 * x) / (z - t)) + (a * 120.0d0)
    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 (y <= -7e+163) {
		tmp = (60.0 * ((y - x) / t)) + (a * 120.0);
	} else if (y <= 1.7e+153) {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -7e+163:
		tmp = (60.0 * ((y - x) / t)) + (a * 120.0)
	elif y <= 1.7e+153:
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0)
	else:
		tmp = (x - y) * (60.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -7e+163)
		tmp = Float64(Float64(60.0 * Float64(Float64(y - x) / t)) + Float64(a * 120.0));
	elseif (y <= 1.7e+153)
		tmp = Float64(Float64(Float64(60.0 * x) / Float64(z - t)) + Float64(a * 120.0));
	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 (y <= -7e+163)
		tmp = (60.0 * ((y - x) / t)) + (a * 120.0);
	elseif (y <= 1.7e+153)
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	else
		tmp = (x - y) * (60.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -7e+163], N[(N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+153], N[(N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.0000000000000005e163

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 71.0%

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

      1. associate-*r/ 71.0%

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

      2. neg-mul-1 71.0%

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

      3. neg-sub0 71.0%

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

      4. sub-neg 71.0%

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

      5. +-commutative 71.0%

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

      6. associate--r+ 71.0%

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

      7. neg-sub0 71.0%

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

      8. remove-double-neg 71.0%

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

   7. Simplified 71.0%

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

   if -7.0000000000000005e163 < y < 1.6999999999999999e153

   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 89.3%

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

   if 1.6999999999999999e153 < y

   1. Initial program 95.3%

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

      1. associate-/l* 95.3%

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

   3. Simplified 95.3%

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

   5. Taylor expanded in a around 0 90.5%

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

      1. associate-*r/ 90.6%

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

      2. *-rgt-identity 90.6%

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

      3. times-frac 90.7%

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

      4. /-rgt-identity 90.7%

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

   7. Simplified 90.7%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+163}:\\ \;\;\;\;60 \cdot \frac{y - x}{t} + a \cdot 120\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+153}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -62000000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z} + a \cdot 120\\ \mathbf{elif}\;z \leq 3400000000:\\ \;\;\;\;60 \cdot \frac{y - x}{t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z}{x - y}} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -62000000000.0)
   (+ (* 60.0 (/ (- x y) z)) (* a 120.0))
   (if (<= z 3400000000.0)
     (+ (* 60.0 (/ (- y x) t)) (* a 120.0))
     (+ (/ 60.0 (/ z (- x y))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -62000000000.0) {
		tmp = (60.0 * ((x - y) / z)) + (a * 120.0);
	} else if (z <= 3400000000.0) {
		tmp = (60.0 * ((y - x) / t)) + (a * 120.0);
	} else {
		tmp = (60.0 / (z / (x - y))) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-62000000000.0d0)) then
        tmp = (60.0d0 * ((x - y) / z)) + (a * 120.0d0)
    else if (z <= 3400000000.0d0) then
        tmp = (60.0d0 * ((y - x) / t)) + (a * 120.0d0)
    else
        tmp = (60.0d0 / (z / (x - y))) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -62000000000.0) {
		tmp = (60.0 * ((x - y) / z)) + (a * 120.0);
	} else if (z <= 3400000000.0) {
		tmp = (60.0 * ((y - x) / t)) + (a * 120.0);
	} else {
		tmp = (60.0 / (z / (x - y))) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -62000000000.0:
		tmp = (60.0 * ((x - y) / z)) + (a * 120.0)
	elif z <= 3400000000.0:
		tmp = (60.0 * ((y - x) / t)) + (a * 120.0)
	else:
		tmp = (60.0 / (z / (x - y))) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -62000000000.0)
		tmp = Float64(Float64(60.0 * Float64(Float64(x - y) / z)) + Float64(a * 120.0));
	elseif (z <= 3400000000.0)
		tmp = Float64(Float64(60.0 * Float64(Float64(y - x) / t)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(60.0 / Float64(z / Float64(x - y))) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -62000000000.0)
		tmp = (60.0 * ((x - y) / z)) + (a * 120.0);
	elseif (z <= 3400000000.0)
		tmp = (60.0 * ((y - x) / t)) + (a * 120.0);
	else
		tmp = (60.0 / (z / (x - y))) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -62000000000.0], N[(N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3400000000.0], N[(N[(60.0 * N[(N[(y - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2e10

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 91.1%

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

   if -6.2e10 < z < 3.4e9

   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* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in z around 0 82.0%

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

      1. associate-*r/ 82.0%

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

      2. neg-mul-1 82.0%

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

      3. neg-sub0 82.0%

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

      4. sub-neg 82.0%

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

      5. +-commutative 82.0%

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

      6. associate--r+ 82.0%

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

      7. neg-sub0 82.0%

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

      8. remove-double-neg 82.0%

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

   7. Simplified 82.0%

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

   if 3.4e9 < z

   1. Initial program 98.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 90.7%

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

      1. clear-num 90.7%

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

      2. un-div-inv 90.8%

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

   7. Applied egg-rr 90.8%

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

Alternative 10: 72.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-52} \lor \neg \left(a \leq 3.1 \cdot 10^{-16}\right):\\ \;\;\;\;-60 \cdot \frac{x}{t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.5e-52) (not (<= a 3.1e-16)))
   (+ (* -60.0 (/ x t)) (* a 120.0))
   (* (- x y) (/ 60.0 (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.5e-52) || !(a <= 3.1e-16)) {
		tmp = (-60.0 * (x / t)) + (a * 120.0);
	} 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 <= (-7.5d-52)) .or. (.not. (a <= 3.1d-16))) then
        tmp = ((-60.0d0) * (x / t)) + (a * 120.0d0)
    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 <= -7.5e-52) || !(a <= 3.1e-16)) {
		tmp = (-60.0 * (x / t)) + (a * 120.0);
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.5e-52) or not (a <= 3.1e-16):
		tmp = (-60.0 * (x / t)) + (a * 120.0)
	else:
		tmp = (x - y) * (60.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.5e-52) || !(a <= 3.1e-16))
		tmp = Float64(Float64(-60.0 * Float64(x / t)) + Float64(a * 120.0));
	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 <= -7.5e-52) || ~((a <= 3.1e-16)))
		tmp = (-60.0 * (x / t)) + (a * 120.0);
	else
		tmp = (x - y) * (60.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7.5e-52], N[Not[LessEqual[a, 3.1e-16]], $MachinePrecision]], N[(N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $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 a < -7.50000000000000006e-52 or 3.1000000000000001e-16 < a

   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 0 76.0%

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

      1. neg-mul-1 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in y around 0 75.8%

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

   if -7.50000000000000006e-52 < a < 3.1000000000000001e-16

   1. Initial program 98.9%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 73.3%

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

      1. associate-*r/ 72.5%

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

      2. *-rgt-identity 72.5%

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

      3. times-frac 73.3%

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

      4. /-rgt-identity 73.3%

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

   7. Simplified 73.3%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-52} \lor \neg \left(a \leq 3.1 \cdot 10^{-16}\right):\\ \;\;\;\;-60 \cdot \frac{x}{t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{+173} \lor \neg \left(x \leq 7.4 \cdot 10^{+112}\right):\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -9.4e+173) (not (<= x 7.4e+112)))
   (/ x (* (- z t) 0.016666666666666666))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -9.4e+173) || !(x <= 7.4e+112)) {
		tmp = x / ((z - t) * 0.016666666666666666);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-9.4d+173)) .or. (.not. (x <= 7.4d+112))) then
        tmp = x / ((z - t) * 0.016666666666666666d0)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -9.4e+173) || !(x <= 7.4e+112)) {
		tmp = x / ((z - t) * 0.016666666666666666);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -9.4e+173) or not (x <= 7.4e+112):
		tmp = x / ((z - t) * 0.016666666666666666)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -9.4e+173) || !(x <= 7.4e+112))
		tmp = Float64(x / Float64(Float64(z - t) * 0.016666666666666666));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -9.4e+173) || ~((x <= 7.4e+112)))
		tmp = x / ((z - t) * 0.016666666666666666);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -9.4e+173], N[Not[LessEqual[x, 7.4e+112]], $MachinePrecision]], N[(x / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.4000000000000003e173 or 7.40000000000000008e112 < x

   1. Initial program 98.5%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 74.9%

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

      1. associate-*r/ 73.6%

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

      2. *-rgt-identity 73.6%

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

      3. times-frac 74.9%

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

      4. /-rgt-identity 74.9%

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

   7. Simplified 74.9%

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

   8. Taylor expanded in x around inf 69.5%

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

      1. *-commutative 69.5%

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

      2. metadata-eval 69.5%

         \[\leadsto \frac{x}{z - t} \cdot \color{blue}{\frac{1}{0.016666666666666666}} \]

      3. times-frac 69.6%

         \[\leadsto \color{blue}{\frac{x \cdot 1}{\left(z - t\right) \cdot 0.016666666666666666}} \]

      4. *-rgt-identity 69.6%

         \[\leadsto \frac{\color{blue}{x}}{\left(z - t\right) \cdot 0.016666666666666666} \]

   10. Simplified 69.6%

       \[\leadsto \color{blue}{\frac{x}{\left(z - t\right) \cdot 0.016666666666666666}} \]

   if -9.4000000000000003e173 < x < 7.40000000000000008e112

   1. Initial program 99.2%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 61.9%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.4 \cdot 10^{+173} \lor \neg \left(x \leq 7.4 \cdot 10^{+112}\right):\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 57.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+171} \lor \neg \left(x \leq 1.5 \cdot 10^{+113}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -7.6e+171) (not (<= x 1.5e+113)))
   (* 60.0 (/ x (- z t)))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -7.6e+171) || !(x <= 1.5e+113)) {
		tmp = 60.0 * (x / (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 ((x <= (-7.6d+171)) .or. (.not. (x <= 1.5d+113))) then
        tmp = 60.0d0 * (x / (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 ((x <= -7.6e+171) || !(x <= 1.5e+113)) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -7.6e+171) or not (x <= 1.5e+113):
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -7.6e+171) || !(x <= 1.5e+113))
		tmp = Float64(60.0 * Float64(x / 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 ((x <= -7.6e+171) || ~((x <= 1.5e+113)))
		tmp = 60.0 * (x / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -7.6e+171], N[Not[LessEqual[x, 1.5e+113]], $MachinePrecision]], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.6000000000000004e171 or 1.5e113 < x

   1. Initial program 98.5%

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

      1. associate-/l* 99.7%

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

   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 69.5%

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

   if -7.6000000000000004e171 < x < 1.5e113

   1. Initial program 99.2%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 61.9%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+171} \lor \neg \left(x \leq 1.5 \cdot 10^{+113}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+163} \lor \neg \left(y \leq 9.7 \cdot 10^{+154}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.8e+163) (not (<= y 9.7e+154)))
   (* -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 <= -5.8e+163) || !(y <= 9.7e+154)) {
		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 <= (-5.8d+163)) .or. (.not. (y <= 9.7d+154))) 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 <= -5.8e+163) || !(y <= 9.7e+154)) {
		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 <= -5.8e+163) or not (y <= 9.7e+154):
		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 <= -5.8e+163) || !(y <= 9.7e+154))
		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 <= -5.8e+163) || ~((y <= 9.7e+154)))
		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, -5.8e+163], N[Not[LessEqual[y, 9.7e+154]], $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 < -5.79999999999999996e163 or 9.69999999999999987e154 < y

   1. Initial program 98.0%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in y around inf 62.9%

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

   if -5.79999999999999996e163 < y < 9.69999999999999987e154

   1. Initial program 99.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 59.0%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+163} \lor \neg \left(y \leq 9.7 \cdot 10^{+154}\right):\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+171}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+112}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -9.2e+171)
   (* 60.0 (/ x (- z t)))
   (if (<= x 2.8e+112) (* a 120.0) (* x (/ 60.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -9.2e+171) {
		tmp = 60.0 * (x / (z - t));
	} else if (x <= 2.8e+112) {
		tmp = a * 120.0;
	} else {
		tmp = x * (60.0 / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-9.2d+171)) then
        tmp = 60.0d0 * (x / (z - t))
    else if (x <= 2.8d+112) then
        tmp = a * 120.0d0
    else
        tmp = x * (60.0d0 / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -9.2e+171) {
		tmp = 60.0 * (x / (z - t));
	} else if (x <= 2.8e+112) {
		tmp = a * 120.0;
	} else {
		tmp = x * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -9.2e+171:
		tmp = 60.0 * (x / (z - t))
	elif x <= 2.8e+112:
		tmp = a * 120.0
	else:
		tmp = x * (60.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -9.2e+171)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (x <= 2.8e+112)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(x * Float64(60.0 / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -9.2e+171)
		tmp = 60.0 * (x / (z - t));
	elseif (x <= 2.8e+112)
		tmp = a * 120.0;
	else
		tmp = x * (60.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -9.2e+171], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+112], N[(a * 120.0), $MachinePrecision], N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.20000000000000069e171

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

   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 71.9%

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

   if -9.20000000000000069e171 < x < 2.8000000000000001e112

   1. Initial program 99.2%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 61.9%

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

   if 2.8000000000000001e112 < x

   1. Initial program 97.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 74.7%

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

      1. associate-*r/ 72.8%

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

      2. *-rgt-identity 72.8%

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

      3. times-frac 74.8%

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

      4. /-rgt-identity 74.8%

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

   7. Simplified 74.8%

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

   8. Taylor expanded in x around inf 68.3%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+171}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+112}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+187} \lor \neg \left(x \leq 6.5 \cdot 10^{+133}\right):\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -7.5e+187) (not (<= x 6.5e+133)))
   (* -60.0 (/ x t))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -7.5e+187) || !(x <= 6.5e+133)) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-7.5d+187)) .or. (.not. (x <= 6.5d+133))) then
        tmp = (-60.0d0) * (x / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -7.5e+187) || !(x <= 6.5e+133)) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -7.5e+187) or not (x <= 6.5e+133):
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -7.5e+187) || !(x <= 6.5e+133))
		tmp = Float64(-60.0 * Float64(x / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -7.5e+187) || ~((x <= 6.5e+133)))
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -7.5e+187], N[Not[LessEqual[x, 6.5e+133]], $MachinePrecision]], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5000000000000002e187 or 6.5000000000000004e133 < x

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0 63.8%

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

      1. neg-mul-1 63.8%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in x around inf 43.4%

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

   if -7.5000000000000002e187 < x < 6.5000000000000004e133

   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* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around inf 60.4%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+187} \lor \neg \left(x \leq 6.5 \cdot 10^{+133}\right):\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 51.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+183}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+139}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -7.5e+183)
   (* -60.0 (/ x t))
   (if (<= x 2.35e+139) (* a 120.0) (* 60.0 (/ x z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -7.5e+183) {
		tmp = -60.0 * (x / t);
	} else if (x <= 2.35e+139) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-7.5d+183)) then
        tmp = (-60.0d0) * (x / t)
    else if (x <= 2.35d+139) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -7.5e+183) {
		tmp = -60.0 * (x / t);
	} else if (x <= 2.35e+139) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -7.5e+183:
		tmp = -60.0 * (x / t)
	elif x <= 2.35e+139:
		tmp = a * 120.0
	else:
		tmp = 60.0 * (x / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -7.5e+183)
		tmp = Float64(-60.0 * Float64(x / t));
	elseif (x <= 2.35e+139)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -7.5e+183)
		tmp = -60.0 * (x / t);
	elseif (x <= 2.35e+139)
		tmp = a * 120.0;
	else
		tmp = 60.0 * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -7.5e+183], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.35e+139], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.49999999999999966e183

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 69.8%

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

      1. neg-mul-1 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in x around inf 52.0%

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

   if -7.49999999999999966e183 < x < 2.35e139

   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* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around inf 60.1%

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

   if 2.35e139 < x

   1. Initial program 97.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 59.5%

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

   6. Taylor expanded in x around inf 42.8%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+183}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+139}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.1% 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* 99.4%

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

3. Simplified 99.4%

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

5. Taylor expanded in z around inf 51.2%

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

6. Final simplification 51.2%

   \[\leadsto a \cdot 120 \]
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 2024137 
(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)))