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

Percentage Accurate: 99.3% → 99.8%

Time: 13.9s

Alternatives: 18

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 99.8%

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

   1. associate-*r/ 99.9%

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

   2. fma-def 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 72.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -20000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-58}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{t \cdot -0.016666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= (* a 120.0) -20000000.0)
     (* a 120.0)
     (if (<= (* a 120.0) 1e-102)
       t_1
       (if (<= (* a 120.0) 2e-58)
         (* a 120.0)
         (if (<= (* a 120.0) 2e+21)
           t_1
           (+ (* a 120.0) (/ x (* t -0.016666666666666666)))))))))

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 ((a * 120.0) <= -20000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-102) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-58) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e+21) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (x / (t * -0.016666666666666666));
	}
	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 ((a * 120.0d0) <= (-20000000.0d0)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-102) then
        tmp = t_1
    else if ((a * 120.0d0) <= 2d-58) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 2d+21) then
        tmp = t_1
    else
        tmp = (a * 120.0d0) + (x / (t * (-0.016666666666666666d0)))
    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 ((a * 120.0) <= -20000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-102) {
		tmp = t_1;
	} else if ((a * 120.0) <= 2e-58) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e+21) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (x / (t * -0.016666666666666666));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if (a * 120.0) <= -20000000.0:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-102:
		tmp = t_1
	elif (a * 120.0) <= 2e-58:
		tmp = a * 120.0
	elif (a * 120.0) <= 2e+21:
		tmp = t_1
	else:
		tmp = (a * 120.0) + (x / (t * -0.016666666666666666))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -20000000.0)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-102)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= 2e-58)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 2e+21)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(t * -0.016666666666666666)));
	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 ((a * 120.0) <= -20000000.0)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-102)
		tmp = t_1;
	elseif ((a * 120.0) <= 2e-58)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 2e+21)
		tmp = t_1;
	else
		tmp = (a * 120.0) + (x / (t * -0.016666666666666666));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -20000000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-102], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-58], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+21], t$95$1, N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(t * -0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -2e7 or 9.99999999999999933e-103 < (*.f64 a 120) < 2.0000000000000001e-58

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 78.9%

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

   if -2e7 < (*.f64 a 120) < 9.99999999999999933e-103 or 2.0000000000000001e-58 < (*.f64 a 120) < 2e21

   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%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 76.8%

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

   if 2e21 < (*.f64 a 120)

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 93.6%

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

      1. associate-*r/ 93.6%

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

      2. *-commutative 93.6%

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

      3. associate-/l* 93.6%

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

   6. Simplified 93.6%

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

   7. Taylor expanded in z around 0 82.6%

      \[\leadsto \frac{x}{\color{blue}{-0.016666666666666666 \cdot t}} + a \cdot 120 \]
   8. Step-by-step derivation

      1. *-commutative 82.6%

         \[\leadsto \frac{x}{\color{blue}{t \cdot -0.016666666666666666}} + a \cdot 120 \]

   9. Simplified 82.6%

      \[\leadsto \frac{x}{\color{blue}{t \cdot -0.016666666666666666}} + a \cdot 120 \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -20000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-102}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-58}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+21}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{t \cdot -0.016666666666666666}\\ \end{array} \]

Alternative 3: 72.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -20000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-102}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-58}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+21}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{t \cdot -0.016666666666666666}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -20000000.0)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-102)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= (* a 120.0) 2e-58)
       (* a 120.0)
       (if (<= (* a 120.0) 2e+21)
         (/ 60.0 (/ (- z t) (- x y)))
         (+ (* a 120.0) (/ x (* t -0.016666666666666666))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -20000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-102) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 2e-58) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e+21) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (a * 120.0) + (x / (t * -0.016666666666666666));
	}
	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) <= (-20000000.0d0)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-102) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if ((a * 120.0d0) <= 2d-58) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 2d+21) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else
        tmp = (a * 120.0d0) + (x / (t * (-0.016666666666666666d0)))
    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) <= -20000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-102) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if ((a * 120.0) <= 2e-58) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 2e+21) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else {
		tmp = (a * 120.0) + (x / (t * -0.016666666666666666));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -20000000.0:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-102:
		tmp = 60.0 * ((x - y) / (z - t))
	elif (a * 120.0) <= 2e-58:
		tmp = a * 120.0
	elif (a * 120.0) <= 2e+21:
		tmp = 60.0 / ((z - t) / (x - y))
	else:
		tmp = (a * 120.0) + (x / (t * -0.016666666666666666))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -20000000.0)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-102)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (Float64(a * 120.0) <= 2e-58)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 2e+21)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(t * -0.016666666666666666)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -20000000.0)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-102)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif ((a * 120.0) <= 2e-58)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 2e+21)
		tmp = 60.0 / ((z - t) / (x - y));
	else
		tmp = (a * 120.0) + (x / (t * -0.016666666666666666));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -20000000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-102], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-58], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 2e+21], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(t * -0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a 120) < -2e7 or 9.99999999999999933e-103 < (*.f64 a 120) < 2.0000000000000001e-58

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 78.9%

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

   if -2e7 < (*.f64 a 120) < 9.99999999999999933e-103

   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%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 77.5%

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

   if 2.0000000000000001e-58 < (*.f64 a 120) < 2e21

   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%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.5%

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

   5. Applied egg-rr 99.5%

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

   6. Taylor expanded in a around 0 72.0%

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

      1. associate-*r/ 72.3%

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

      2. associate-/l* 72.3%

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

   8. Simplified 72.3%

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

   if 2e21 < (*.f64 a 120)

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 93.6%

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

      1. associate-*r/ 93.6%

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

      2. *-commutative 93.6%

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

      3. associate-/l* 93.6%

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

   6. Simplified 93.6%

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

   7. Taylor expanded in z around 0 82.6%

      \[\leadsto \frac{x}{\color{blue}{-0.016666666666666666 \cdot t}} + a \cdot 120 \]
   8. Step-by-step derivation

      1. *-commutative 82.6%

         \[\leadsto \frac{x}{\color{blue}{t \cdot -0.016666666666666666}} + a \cdot 120 \]

   9. Simplified 82.6%

      \[\leadsto \frac{x}{\color{blue}{t \cdot -0.016666666666666666}} + a \cdot 120 \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -20000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-102}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{-58}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 2 \cdot 10^{+21}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{x}{t \cdot -0.016666666666666666}\\ \end{array} \]

Alternative 4: 58.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{-78}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-104}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-54}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= a -2.3e-78)
     (* a 120.0)
     (if (<= a -3e-264)
       t_1
       (if (<= a 2.05e-104)
         (* 60.0 (/ x (- z t)))
         (if (<= a 2.1e-54)
           (* a 120.0)
           (if (<= a 3.2e-11) t_1 (* a 120.0))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (a <= -2.3e-78) {
		tmp = a * 120.0;
	} else if (a <= -3e-264) {
		tmp = t_1;
	} else if (a <= 2.05e-104) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= 2.1e-54) {
		tmp = a * 120.0;
	} else if (a <= 3.2e-11) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * (y / (z - t))
    if (a <= (-2.3d-78)) then
        tmp = a * 120.0d0
    else if (a <= (-3d-264)) then
        tmp = t_1
    else if (a <= 2.05d-104) then
        tmp = 60.0d0 * (x / (z - t))
    else if (a <= 2.1d-54) then
        tmp = a * 120.0d0
    else if (a <= 3.2d-11) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (y / (z - t));
	double tmp;
	if (a <= -2.3e-78) {
		tmp = a * 120.0;
	} else if (a <= -3e-264) {
		tmp = t_1;
	} else if (a <= 2.05e-104) {
		tmp = 60.0 * (x / (z - t));
	} else if (a <= 2.1e-54) {
		tmp = a * 120.0;
	} else if (a <= 3.2e-11) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (y / (z - t))
	tmp = 0
	if a <= -2.3e-78:
		tmp = a * 120.0
	elif a <= -3e-264:
		tmp = t_1
	elif a <= 2.05e-104:
		tmp = 60.0 * (x / (z - t))
	elif a <= 2.1e-54:
		tmp = a * 120.0
	elif a <= 3.2e-11:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(y / Float64(z - t)))
	tmp = 0.0
	if (a <= -2.3e-78)
		tmp = Float64(a * 120.0);
	elseif (a <= -3e-264)
		tmp = t_1;
	elseif (a <= 2.05e-104)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	elseif (a <= 2.1e-54)
		tmp = Float64(a * 120.0);
	elseif (a <= 3.2e-11)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	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 (a <= -2.3e-78)
		tmp = a * 120.0;
	elseif (a <= -3e-264)
		tmp = t_1;
	elseif (a <= 2.05e-104)
		tmp = 60.0 * (x / (z - t));
	elseif (a <= 2.1e-54)
		tmp = a * 120.0;
	elseif (a <= 3.2e-11)
		tmp = t_1;
	else
		tmp = a * 120.0;
	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[a, -2.3e-78], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -3e-264], t$95$1, If[LessEqual[a, 2.05e-104], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e-54], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 3.2e-11], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.3000000000000002e-78 or 2.04999999999999992e-104 < a < 2.1e-54 or 3.19999999999999994e-11 < a

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 73.2%

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

   if -2.3000000000000002e-78 < a < -3e-264 or 2.1e-54 < a < 3.19999999999999994e-11

   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%

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

   3. Simplified 99.7%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 49.0%

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

   if -3e-264 < a < 2.04999999999999992e-104

   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* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 61.3%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-78}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-264}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-104}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-54}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-11}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 5: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -46000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-102} \lor \neg \left(a \leq 1.35 \cdot 10^{-60}\right) \land a \leq 4.7 \cdot 10^{-11}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -46000.0)
   (* a 120.0)
   (if (or (<= a 3.1e-102) (and (not (<= a 1.35e-60)) (<= a 4.7e-11)))
     (* 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 <= -46000.0) {
		tmp = a * 120.0;
	} else if ((a <= 3.1e-102) || (!(a <= 1.35e-60) && (a <= 4.7e-11))) {
		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 <= (-46000.0d0)) then
        tmp = a * 120.0d0
    else if ((a <= 3.1d-102) .or. (.not. (a <= 1.35d-60)) .and. (a <= 4.7d-11)) 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 <= -46000.0) {
		tmp = a * 120.0;
	} else if ((a <= 3.1e-102) || (!(a <= 1.35e-60) && (a <= 4.7e-11))) {
		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 <= -46000.0:
		tmp = a * 120.0
	elif (a <= 3.1e-102) or (not (a <= 1.35e-60) and (a <= 4.7e-11)):
		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 (a <= -46000.0)
		tmp = Float64(a * 120.0);
	elseif ((a <= 3.1e-102) || (!(a <= 1.35e-60) && (a <= 4.7e-11)))
		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 <= -46000.0)
		tmp = a * 120.0;
	elseif ((a <= 3.1e-102) || (~((a <= 1.35e-60)) && (a <= 4.7e-11)))
		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[a, -46000.0], N[(a * 120.0), $MachinePrecision], If[Or[LessEqual[a, 3.1e-102], And[N[Not[LessEqual[a, 1.35e-60]], $MachinePrecision], LessEqual[a, 4.7e-11]]], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -46000 or 3.10000000000000013e-102 < a < 1.35e-60 or 4.69999999999999993e-11 < a

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 78.1%

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

   if -46000 < a < 3.10000000000000013e-102 or 1.35e-60 < a < 4.69999999999999993e-11

   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%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 78.5%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -46000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-102} \lor \neg \left(a \leq 1.35 \cdot 10^{-60}\right) \land a \leq 4.7 \cdot 10^{-11}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6: 76.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -2.05 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -0.00056:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+25}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* 60.0 (/ y t)))))
   (if (<= t -2.05e+71)
     t_1
     (if (<= t -0.00056)
       (* 60.0 (/ (- x y) (- z t)))
       (if (<= t 1.15e+25) (+ (* a 120.0) (* (- x y) (/ 60.0 z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * (y / t));
	double tmp;
	if (t <= -2.05e+71) {
		tmp = t_1;
	} else if (t <= -0.00056) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t <= 1.15e+25) {
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	} 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 = (a * 120.0d0) + (60.0d0 * (y / t))
    if (t <= (-2.05d+71)) then
        tmp = t_1
    else if (t <= (-0.00056d0)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (t <= 1.15d+25) then
        tmp = (a * 120.0d0) + ((x - y) * (60.0d0 / z))
    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 = (a * 120.0) + (60.0 * (y / t));
	double tmp;
	if (t <= -2.05e+71) {
		tmp = t_1;
	} else if (t <= -0.00056) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t <= 1.15e+25) {
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (60.0 * (y / t))
	tmp = 0
	if t <= -2.05e+71:
		tmp = t_1
	elif t <= -0.00056:
		tmp = 60.0 * ((x - y) / (z - t))
	elif t <= 1.15e+25:
		tmp = (a * 120.0) + ((x - y) * (60.0 / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)))
	tmp = 0.0
	if (t <= -2.05e+71)
		tmp = t_1;
	elseif (t <= -0.00056)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (t <= 1.15e+25)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(60.0 / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (60.0 * (y / t));
	tmp = 0.0;
	if (t <= -2.05e+71)
		tmp = t_1;
	elseif (t <= -0.00056)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (t <= 1.15e+25)
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.05e+71], t$95$1, If[LessEqual[t, -0.00056], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+25], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.0500000000000001e71 or 1.1499999999999999e25 < t

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.9%

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

      4. div-inv 99.9%

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

      5. metadata-eval 99.9%

         \[\leadsto \frac{x - y}{\left(z - t\right) \cdot \color{blue}{0.016666666666666666}} + a \cdot 120 \]

   7. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]

   8. Taylor expanded in z around 0 95.4%

      \[\leadsto \frac{x - y}{\color{blue}{-0.016666666666666666 \cdot t}} + a \cdot 120 \]
   9. Step-by-step derivation

      1. *-commutative 95.4%

         \[\leadsto \frac{x - y}{\color{blue}{t \cdot -0.016666666666666666}} + a \cdot 120 \]

   10. Simplified 95.4%

       \[\leadsto \frac{x - y}{\color{blue}{t \cdot -0.016666666666666666}} + a \cdot 120 \]

   11. Taylor expanded in x around 0 82.8%

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

   if -2.0500000000000001e71 < t < -5.5999999999999995e-4

   1. Initial program 99.5%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in a around 0 85.0%

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

   if -5.5999999999999995e-4 < t < 1.1499999999999999e25

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 83.2%

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

      1. associate-/r/ 83.2%

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

   6. Applied egg-rr 83.2%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{+71}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -0.00056:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+25}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 7: 76.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -9.8 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -0.13:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+25}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* 60.0 (/ y t)))))
   (if (<= t -9.8e+70)
     t_1
     (if (<= t -0.13)
       (* 60.0 (/ (- x y) (- z t)))
       (if (<= t 1.55e+25) (+ (* a 120.0) (/ 60.0 (/ z (- x y)))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * (y / t));
	double tmp;
	if (t <= -9.8e+70) {
		tmp = t_1;
	} else if (t <= -0.13) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t <= 1.55e+25) {
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	} 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 = (a * 120.0d0) + (60.0d0 * (y / t))
    if (t <= (-9.8d+70)) then
        tmp = t_1
    else if (t <= (-0.13d0)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (t <= 1.55d+25) then
        tmp = (a * 120.0d0) + (60.0d0 / (z / (x - y)))
    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 = (a * 120.0) + (60.0 * (y / t));
	double tmp;
	if (t <= -9.8e+70) {
		tmp = t_1;
	} else if (t <= -0.13) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t <= 1.55e+25) {
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (60.0 * (y / t))
	tmp = 0
	if t <= -9.8e+70:
		tmp = t_1
	elif t <= -0.13:
		tmp = 60.0 * ((x - y) / (z - t))
	elif t <= 1.55e+25:
		tmp = (a * 120.0) + (60.0 / (z / (x - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)))
	tmp = 0.0
	if (t <= -9.8e+70)
		tmp = t_1;
	elseif (t <= -0.13)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (t <= 1.55e+25)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(z / Float64(x - y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (60.0 * (y / t));
	tmp = 0.0;
	if (t <= -9.8e+70)
		tmp = t_1;
	elseif (t <= -0.13)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (t <= 1.55e+25)
		tmp = (a * 120.0) + (60.0 / (z / (x - y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.8e+70], t$95$1, If[LessEqual[t, -0.13], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e+25], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(z / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.80000000000000056e70 or 1.5499999999999999e25 < t

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.9%

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

      4. div-inv 99.9%

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

      5. metadata-eval 99.9%

         \[\leadsto \frac{x - y}{\left(z - t\right) \cdot \color{blue}{0.016666666666666666}} + a \cdot 120 \]

   7. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}} + a \cdot 120 \]

   8. Taylor expanded in z around 0 95.4%

      \[\leadsto \frac{x - y}{\color{blue}{-0.016666666666666666 \cdot t}} + a \cdot 120 \]
   9. Step-by-step derivation

      1. *-commutative 95.4%

         \[\leadsto \frac{x - y}{\color{blue}{t \cdot -0.016666666666666666}} + a \cdot 120 \]

   10. Simplified 95.4%

       \[\leadsto \frac{x - y}{\color{blue}{t \cdot -0.016666666666666666}} + a \cdot 120 \]

   11. Taylor expanded in x around 0 82.8%

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

   if -9.80000000000000056e70 < t < -0.13

   1. Initial program 99.5%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in a around 0 85.0%

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

   if -0.13 < t < 1.5499999999999999e25

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 83.2%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.8 \cdot 10^{+70}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -0.13:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+25}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 8: 56.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-20}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{60}{\frac{-t}{x}}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+136}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= y -1.06e+102)
     t_1
     (if (<= y 6.6e-20)
       (* a 120.0)
       (if (<= y 9.5e+24)
         (/ 60.0 (/ (- t) x))
         (if (<= y 1.08e+136) (* 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 <= -1.06e+102) {
		tmp = t_1;
	} else if (y <= 6.6e-20) {
		tmp = a * 120.0;
	} else if (y <= 9.5e+24) {
		tmp = 60.0 / (-t / x);
	} else if (y <= 1.08e+136) {
		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 <= (-1.06d+102)) then
        tmp = t_1
    else if (y <= 6.6d-20) then
        tmp = a * 120.0d0
    else if (y <= 9.5d+24) then
        tmp = 60.0d0 / (-t / x)
    else if (y <= 1.08d+136) 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 <= -1.06e+102) {
		tmp = t_1;
	} else if (y <= 6.6e-20) {
		tmp = a * 120.0;
	} else if (y <= 9.5e+24) {
		tmp = 60.0 / (-t / x);
	} else if (y <= 1.08e+136) {
		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 <= -1.06e+102:
		tmp = t_1
	elif y <= 6.6e-20:
		tmp = a * 120.0
	elif y <= 9.5e+24:
		tmp = 60.0 / (-t / x)
	elif y <= 1.08e+136:
		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 <= -1.06e+102)
		tmp = t_1;
	elseif (y <= 6.6e-20)
		tmp = Float64(a * 120.0);
	elseif (y <= 9.5e+24)
		tmp = Float64(60.0 / Float64(Float64(-t) / x));
	elseif (y <= 1.08e+136)
		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 <= -1.06e+102)
		tmp = t_1;
	elseif (y <= 6.6e-20)
		tmp = a * 120.0;
	elseif (y <= 9.5e+24)
		tmp = 60.0 / (-t / x);
	elseif (y <= 1.08e+136)
		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, -1.06e+102], t$95$1, If[LessEqual[y, 6.6e-20], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, 9.5e+24], N[(60.0 / N[((-t) / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.08e+136], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.06000000000000001e102 or 1.07999999999999994e136 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 59.8%

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

   if -1.06000000000000001e102 < y < 6.6e-20 or 9.5000000000000001e24 < y < 1.07999999999999994e136

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 63.6%

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

   if 6.6e-20 < y < 9.5000000000000001e24

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around 0 100.0%

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

      1. associate-*r/ 99.8%

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

      2. associate-/l* 99.6%

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

   8. Simplified 99.6%

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

   9. Taylor expanded in x around inf 75.6%

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

   10. Taylor expanded in z around 0 64.4%

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

       1. neg-mul-1 64.4%

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

       2. distribute-neg-frac 64.4%

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

   12. Simplified 64.4%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+102}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-20}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{60}{\frac{-t}{x}}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+136}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]

Alternative 9: 56.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{y}{z - t}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-20}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+24}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+139}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ y (- z t)))))
   (if (<= y -1.05e+101)
     t_1
     (if (<= y 6.6e-20)
       (* a 120.0)
       (if (<= y 2.8e+24)
         (* -60.0 (/ (- x y) t))
         (if (<= y 1.18e+139) (* 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 <= -1.05e+101) {
		tmp = t_1;
	} else if (y <= 6.6e-20) {
		tmp = a * 120.0;
	} else if (y <= 2.8e+24) {
		tmp = -60.0 * ((x - y) / t);
	} else if (y <= 1.18e+139) {
		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 <= (-1.05d+101)) then
        tmp = t_1
    else if (y <= 6.6d-20) then
        tmp = a * 120.0d0
    else if (y <= 2.8d+24) then
        tmp = (-60.0d0) * ((x - y) / t)
    else if (y <= 1.18d+139) 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 <= -1.05e+101) {
		tmp = t_1;
	} else if (y <= 6.6e-20) {
		tmp = a * 120.0;
	} else if (y <= 2.8e+24) {
		tmp = -60.0 * ((x - y) / t);
	} else if (y <= 1.18e+139) {
		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 <= -1.05e+101:
		tmp = t_1
	elif y <= 6.6e-20:
		tmp = a * 120.0
	elif y <= 2.8e+24:
		tmp = -60.0 * ((x - y) / t)
	elif y <= 1.18e+139:
		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 <= -1.05e+101)
		tmp = t_1;
	elseif (y <= 6.6e-20)
		tmp = Float64(a * 120.0);
	elseif (y <= 2.8e+24)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	elseif (y <= 1.18e+139)
		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 <= -1.05e+101)
		tmp = t_1;
	elseif (y <= 6.6e-20)
		tmp = a * 120.0;
	elseif (y <= 2.8e+24)
		tmp = -60.0 * ((x - y) / t);
	elseif (y <= 1.18e+139)
		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, -1.05e+101], t$95$1, If[LessEqual[y, 6.6e-20], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, 2.8e+24], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.18e+139], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e101 or 1.18e139 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 59.8%

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

   if -1.05e101 < y < 6.6e-20 or 2.8000000000000002e24 < y < 1.18e139

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 63.6%

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

   if 6.6e-20 < y < 2.8000000000000002e24

   1. Initial program 99.8%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in a around 0 100.0%

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

      1. associate-*r/ 99.8%

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

      2. associate-/l* 99.6%

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

   8. Simplified 99.6%

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

   9. Taylor expanded in z around 0 76.9%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+101}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-20}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+24}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+139}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \end{array} \]

Alternative 10: 82.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+101} \lor \neg \left(y \leq 5 \cdot 10^{+141}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.25e+101) (not (<= y 5e+141)))
   (* 60.0 (/ (- x y) (- z t)))
   (+ (/ 60.0 (/ (- z t) x)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.25e+101) || !(y <= 5e+141)) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.25d+101)) .or. (.not. (y <= 5d+141))) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (60.0d0 / ((z - t) / x)) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.25e+101) || !(y <= 5e+141)) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.25e+101) or not (y <= 5e+141):
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.25e+101) || !(y <= 5e+141))
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(60.0 / Float64(Float64(z - t) / x)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.25e+101) || ~((y <= 5e+141)))
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (60.0 / ((z - t) / x)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.25e+101], N[Not[LessEqual[y, 5e+141]], $MachinePrecision]], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.24999999999999997e101 or 5.00000000000000025e141 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 74.6%

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

   if -1.24999999999999997e101 < y < 5.00000000000000025e141

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 91.6%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+101} \lor \neg \left(y \leq 5 \cdot 10^{+141}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}} + a \cdot 120\\ \end{array} \]

Alternative 11: 82.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+102} \lor \neg \left(y \leq 9.2 \cdot 10^{+139}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.06e+102) (not (<= y 9.2e+139)))
   (* 60.0 (/ (- x y) (- z t)))
   (+ (/ x (/ (- z t) 60.0)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.06e+102) || !(y <= 9.2e+139)) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.06d+102)) .or. (.not. (y <= 9.2d+139))) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else
        tmp = (x / ((z - t) / 60.0d0)) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.06e+102) || !(y <= 9.2e+139)) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.06e+102) or not (y <= 9.2e+139):
		tmp = 60.0 * ((x - y) / (z - t))
	else:
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.06e+102) || !(y <= 9.2e+139))
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	else
		tmp = Float64(Float64(x / Float64(Float64(z - t) / 60.0)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.06e+102) || ~((y <= 9.2e+139)))
		tmp = 60.0 * ((x - y) / (z - t));
	else
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.06e+102], N[Not[LessEqual[y, 9.2e+139]], $MachinePrecision]], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(N[(z - t), $MachinePrecision] / 60.0), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.06000000000000001e102 or 9.2e139 < y

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 74.6%

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

   if -1.06000000000000001e102 < y < 9.2e139

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 91.6%

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

      1. associate-*r/ 91.6%

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

      2. *-commutative 91.6%

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

      3. associate-/l* 91.6%

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

   6. Simplified 91.6%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+102} \lor \neg \left(y \leq 9.2 \cdot 10^{+139}\right):\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \end{array} \]

Alternative 12: 89.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-5} \lor \neg \left(x \leq 4.1 \cdot 10^{+51}\right):\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.25e-5) (not (<= x 4.1e+51)))
   (+ (/ x (/ (- z t) 60.0)) (* a 120.0))
   (+ (/ (* 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 <= -2.25e-5) || !(x <= 4.1e+51)) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else {
		tmp = ((y * -60.0) / (z - 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 ((x <= (-2.25d-5)) .or. (.not. (x <= 4.1d+51))) then
        tmp = (x / ((z - t) / 60.0d0)) + (a * 120.0d0)
    else
        tmp = ((y * (-60.0d0)) / (z - 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 ((x <= -2.25e-5) || !(x <= 4.1e+51)) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.25e-5) or not (x <= 4.1e+51):
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0)
	else:
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.25e-5) || !(x <= 4.1e+51))
		tmp = Float64(Float64(x / Float64(Float64(z - t) / 60.0)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -2.25e-5) || ~((x <= 4.1e+51)))
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	else
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.25e-5], N[Not[LessEqual[x, 4.1e+51]], $MachinePrecision]], N[(N[(x / N[(N[(z - t), $MachinePrecision] / 60.0), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.25000000000000014e-5 or 4.10000000000000011e51 < x

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 89.5%

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

      1. associate-*r/ 89.4%

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

      2. *-commutative 89.4%

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

      3. associate-/l* 89.4%

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

   6. Simplified 89.4%

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

   if -2.25000000000000014e-5 < x < 4.10000000000000011e51

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 94.9%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-5} \lor \neg \left(x \leq 4.1 \cdot 10^{+51}\right):\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 13: 89.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+47}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.6e-5)
   (+ (/ x (/ (- z t) 60.0)) (* a 120.0))
   (if (<= x 1.9e+47)
     (+ (/ (* y -60.0) (- z t)) (* a 120.0))
     (+ (/ (* 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 <= -4.6e-5) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else if (x <= 1.9e+47) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = ((60.0 * x) / (z - 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 (x <= (-4.6d-5)) then
        tmp = (x / ((z - t) / 60.0d0)) + (a * 120.0d0)
    else if (x <= 1.9d+47) then
        tmp = ((y * (-60.0d0)) / (z - t)) + (a * 120.0d0)
    else
        tmp = ((60.0d0 * x) / (z - 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 (x <= -4.6e-5) {
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	} else if (x <= 1.9e+47) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.6e-5:
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0)
	elif x <= 1.9e+47:
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	else:
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.6e-5)
		tmp = Float64(Float64(x / Float64(Float64(z - t) / 60.0)) + Float64(a * 120.0));
	elseif (x <= 1.9e+47)
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(Float64(60.0 * x) / Float64(z - t)) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4.6e-5)
		tmp = (x / ((z - t) / 60.0)) + (a * 120.0);
	elseif (x <= 1.9e+47)
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	else
		tmp = ((60.0 * x) / (z - t)) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.6e-5], N[(N[(x / N[(N[(z - t), $MachinePrecision] / 60.0), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e+47], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(60.0 * x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.6e-5

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 87.7%

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

      1. associate-*r/ 87.6%

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

      2. *-commutative 87.6%

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

      3. associate-/l* 87.6%

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

   6. Simplified 87.6%

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

   if -4.6e-5 < x < 1.9000000000000002e47

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 95.5%

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

   if 1.9000000000000002e47 < x

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 90.6%

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

      1. *-commutative 90.6%

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

   4. Simplified 90.6%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{\frac{z - t}{60}} + a \cdot 120\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+47}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot x}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 14: 52.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-78}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-128}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-138}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-103}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.1e-78)
   (* a 120.0)
   (if (<= a -1.25e-128)
     (* 60.0 (/ y t))
     (if (<= a -2.9e-138)
       (* -60.0 (/ y z))
       (if (<= a 9.2e-103) (* 60.0 (/ x z)) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e-78) {
		tmp = a * 120.0;
	} else if (a <= -1.25e-128) {
		tmp = 60.0 * (y / t);
	} else if (a <= -2.9e-138) {
		tmp = -60.0 * (y / z);
	} else if (a <= 9.2e-103) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.1d-78)) then
        tmp = a * 120.0d0
    else if (a <= (-1.25d-128)) then
        tmp = 60.0d0 * (y / t)
    else if (a <= (-2.9d-138)) then
        tmp = (-60.0d0) * (y / z)
    else if (a <= 9.2d-103) then
        tmp = 60.0d0 * (x / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.1e-78) {
		tmp = a * 120.0;
	} else if (a <= -1.25e-128) {
		tmp = 60.0 * (y / t);
	} else if (a <= -2.9e-138) {
		tmp = -60.0 * (y / z);
	} else if (a <= 9.2e-103) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.1e-78:
		tmp = a * 120.0
	elif a <= -1.25e-128:
		tmp = 60.0 * (y / t)
	elif a <= -2.9e-138:
		tmp = -60.0 * (y / z)
	elif a <= 9.2e-103:
		tmp = 60.0 * (x / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.1e-78)
		tmp = Float64(a * 120.0);
	elseif (a <= -1.25e-128)
		tmp = Float64(60.0 * Float64(y / t));
	elseif (a <= -2.9e-138)
		tmp = Float64(-60.0 * Float64(y / z));
	elseif (a <= 9.2e-103)
		tmp = Float64(60.0 * Float64(x / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.1e-78)
		tmp = a * 120.0;
	elseif (a <= -1.25e-128)
		tmp = 60.0 * (y / t);
	elseif (a <= -2.9e-138)
		tmp = -60.0 * (y / z);
	elseif (a <= 9.2e-103)
		tmp = 60.0 * (x / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.1e-78], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -1.25e-128], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.9e-138], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.2e-103], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.1000000000000001e-78 or 9.2000000000000003e-103 < a

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 69.7%

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

   if -2.1000000000000001e-78 < a < -1.25e-128

   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%

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

   3. Simplified 99.8%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 56.2%

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

   7. Taylor expanded in z around 0 50.0%

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

   if -1.25e-128 < a < -2.89999999999999973e-138

   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%

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

   3. Simplified 99.2%

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

      1. associate-/r/ 99.2%

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

   5. Applied egg-rr 99.2%

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

   6. Taylor expanded in y around inf 52.3%

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

   7. Taylor expanded in z around inf 52.3%

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

   if -2.89999999999999973e-138 < a < 9.2000000000000003e-103

   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* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 84.8%

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

      1. associate-*r/ 84.7%

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

      2. associate-/l* 84.6%

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

   8. Simplified 84.6%

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

   9. Taylor expanded in x around inf 52.3%

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

   10. Taylor expanded in z around inf 38.0%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{-78}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-128}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-138}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-103}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 15: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

   1. associate-/r/ 99.8%

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

5. Applied egg-rr 99.8%

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

6. Final simplification 99.8%

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

Alternative 16: 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]

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

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

Alternative 17: 52.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-137}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-105}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.2e-137)
   (* a 120.0)
   (if (<= a 7.6e-105) (* 60.0 (/ x z)) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e-137) {
		tmp = a * 120.0;
	} else if (a <= 7.6e-105) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.2d-137)) then
        tmp = a * 120.0d0
    else if (a <= 7.6d-105) then
        tmp = 60.0d0 * (x / z)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.2e-137) {
		tmp = a * 120.0;
	} else if (a <= 7.6e-105) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.2e-137:
		tmp = a * 120.0
	elif a <= 7.6e-105:
		tmp = 60.0 * (x / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.2e-137)
		tmp = Float64(a * 120.0);
	elseif (a <= 7.6e-105)
		tmp = Float64(60.0 * Float64(x / z));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.2e-137)
		tmp = a * 120.0;
	elseif (a <= 7.6e-105)
		tmp = 60.0 * (x / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.2e-137], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 7.6e-105], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -6.19999999999999955e-137 or 7.5999999999999995e-105 < a

   1. Initial program 99.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 66.0%

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

   if -6.19999999999999955e-137 < a < 7.5999999999999995e-105

   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* 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 85.0%

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

      1. associate-*r/ 84.9%

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

      2. associate-/l* 84.8%

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

   8. Simplified 84.8%

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

   9. Taylor expanded in x around inf 51.7%

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

   10. Taylor expanded in z around inf 37.5%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.2 \cdot 10^{-137}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-105}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 18: 50.1% 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 99.8%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in z around inf 51.9%

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

5. Final simplification 51.9%

   \[\leadsto a \cdot 120 \]

Developer target: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023192 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

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

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