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

Percentage Accurate: 99.3% → 99.8%

Time: 14.2s

Alternatives: 19

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0 + N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $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. +-commutative 99.8%

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

   2. fma-def 99.8%

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

   3. associate-*l/ 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 73.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+24}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-20}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;t_1 \leq 1.2 \cdot 10^{+70}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+94}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -1e+24)
     (/ 60.0 (/ (- z t) (- x y)))
     (if (<= t_1 5e-20)
       (* a 120.0)
       (if (<= t_1 1.2e+70)
         (* 60.0 (/ (- x y) (- z t)))
         (if (<= t_1 5e+94) (* a 120.0) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+24) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (t_1 <= 5e-20) {
		tmp = a * 120.0;
	} else if (t_1 <= 1.2e+70) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t_1 <= 5e+94) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-1d+24)) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else if (t_1 <= 5d-20) then
        tmp = a * 120.0d0
    else if (t_1 <= 1.2d+70) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (t_1 <= 5d+94) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -1e+24) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if (t_1 <= 5e-20) {
		tmp = a * 120.0;
	} else if (t_1 <= 1.2e+70) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t_1 <= 5e+94) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -1e+24:
		tmp = 60.0 / ((z - t) / (x - y))
	elif t_1 <= 5e-20:
		tmp = a * 120.0
	elif t_1 <= 1.2e+70:
		tmp = 60.0 * ((x - y) / (z - t))
	elif t_1 <= 5e+94:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+24)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	elseif (t_1 <= 5e-20)
		tmp = Float64(a * 120.0);
	elseif (t_1 <= 1.2e+70)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (t_1 <= 5e+94)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+24)
		tmp = 60.0 / ((z - t) / (x - y));
	elseif (t_1 <= 5e-20)
		tmp = a * 120.0;
	elseif (t_1 <= 1.2e+70)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (t_1 <= 5e+94)
		tmp = a * 120.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+24], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-20], N[(a * 120.0), $MachinePrecision], If[LessEqual[t$95$1, 1.2e+70], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+94], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -9.9999999999999998e23

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. associate-/l* 99.6%

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

      2. clear-num 99.7%

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

      3. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.6%

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

      3. metadata-eval 99.6%

         \[\leadsto \color{blue}{\frac{1}{0.016666666666666666}} \cdot \left(\left(x - y\right) \cdot \frac{1}{z - t}\right) + a \cdot 120 \]

      4. div-inv 99.6%

         \[\leadsto \frac{1}{0.016666666666666666} \cdot \color{blue}{\frac{x - y}{z - t}} + a \cdot 120 \]

      5. times-frac 99.8%

         \[\leadsto \color{blue}{\frac{1 \cdot \left(x - y\right)}{0.016666666666666666 \cdot \left(z - t\right)}} + a \cdot 120 \]

      6. *-un-lft-identity 99.8%

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

      7. *-commutative 99.8%

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

   7. Applied egg-rr 99.8%

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

   8. Taylor expanded in a around 0 84.4%

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

      1. associate-*r/ 84.4%

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

      2. associate-/l* 84.6%

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

   10. Simplified 84.6%

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

   if -9.9999999999999998e23 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 4.9999999999999999e-20 or 1.19999999999999993e70 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 5.0000000000000001e94

   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 83.8%

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

   if 4.9999999999999999e-20 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 1.19999999999999993e70

   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* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in a around 0 67.3%

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

   if 5.0000000000000001e94 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

   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. Taylor expanded in a around 0 85.0%

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

      1. associate-*r/ 85.1%

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

   6. Applied egg-rr 85.1%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -1 \cdot 10^{+24}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{-20}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 1.2 \cdot 10^{+70}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 5 \cdot 10^{+94}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60 \cdot \left(x - y\right)}{z - t}\\ \end{array} \]

Alternative 3: 83.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60 \cdot \left(x - y\right)}{z - t}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+72}:\\ \;\;\;\;\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{elif}\;t_1 \leq 3 \cdot 10^{+186}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* 60.0 (- x y)) (- z t))))
   (if (<= t_1 -5e+72)
     (/ (- x y) (* (- z t) 0.016666666666666666))
     (if (<= t_1 3e+186)
       (+ (* a 120.0) (* 60.0 (/ x (- z t))))
       (* 60.0 (/ (- x y) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+72) {
		tmp = (x - y) / ((z - t) * 0.016666666666666666);
	} else if (t_1 <= 3e+186) {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (60.0d0 * (x - y)) / (z - t)
    if (t_1 <= (-5d+72)) then
        tmp = (x - y) / ((z - t) * 0.016666666666666666d0)
    else if (t_1 <= 3d+186) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / (z - t)))
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (60.0 * (x - y)) / (z - t);
	double tmp;
	if (t_1 <= -5e+72) {
		tmp = (x - y) / ((z - t) * 0.016666666666666666);
	} else if (t_1 <= 3e+186) {
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (60.0 * (x - y)) / (z - t)
	tmp = 0
	if t_1 <= -5e+72:
		tmp = (x - y) / ((z - t) * 0.016666666666666666)
	elif t_1 <= 3e+186:
		tmp = (a * 120.0) + (60.0 * (x / (z - t)))
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+72)
		tmp = Float64(Float64(x - y) / Float64(Float64(z - t) * 0.016666666666666666));
	elseif (t_1 <= 3e+186)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / Float64(z - t))));
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (60.0 * (x - y)) / (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+72)
		tmp = (x - y) / ((z - t) * 0.016666666666666666);
	elseif (t_1 <= 3e+186)
		tmp = (a * 120.0) + (60.0 * (x / (z - t)));
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+72], N[(N[(x - y), $MachinePrecision] / N[(N[(z - t), $MachinePrecision] * 0.016666666666666666), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 3e+186], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -4.99999999999999992e72

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in a around 0 90.5%

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

      1. metadata-eval 90.5%

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

      2. times-frac 90.8%

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

      3. *-un-lft-identity 90.8%

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

      4. *-commutative 90.8%

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

   6. Applied egg-rr 90.8%

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

   if -4.99999999999999992e72 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 2.99999999999999982e186

   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 y around 0 87.8%

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

   if 2.99999999999999982e186 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

   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. Taylor expanded in a around 0 93.4%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq -5 \cdot 10^{+72}:\\ \;\;\;\;\frac{x - y}{\left(z - t\right) \cdot 0.016666666666666666}\\ \mathbf{elif}\;\frac{60 \cdot \left(x - y\right)}{z - t} \leq 3 \cdot 10^{+186}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 4: 66.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;x - y \leq -5 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x - y \leq 2 \cdot 10^{-34}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x - y \leq 4 \cdot 10^{+203}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= (- x y) -5e+75)
     t_1
     (if (<= (- x y) 2e-34)
       (* a 120.0)
       (if (<= (- x y) 4e+203) (+ (* a 120.0) (* 60.0 (/ y t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((x - y) <= -5e+75) {
		tmp = t_1;
	} else if ((x - y) <= 2e-34) {
		tmp = a * 120.0;
	} else if ((x - y) <= 4e+203) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    if ((x - y) <= (-5d+75)) then
        tmp = t_1
    else if ((x - y) <= 2d-34) then
        tmp = a * 120.0d0
    else if ((x - y) <= 4d+203) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((x - y) <= -5e+75) {
		tmp = t_1;
	} else if ((x - y) <= 2e-34) {
		tmp = a * 120.0;
	} else if ((x - y) <= 4e+203) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if (x - y) <= -5e+75:
		tmp = t_1
	elif (x - y) <= 2e-34:
		tmp = a * 120.0
	elif (x - y) <= 4e+203:
		tmp = (a * 120.0) + (60.0 * (y / t))
	else:
		tmp = t_1
	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(x - y) <= -5e+75)
		tmp = t_1;
	elseif (Float64(x - y) <= 2e-34)
		tmp = Float64(a * 120.0);
	elseif (Float64(x - y) <= 4e+203)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	tmp = 0.0;
	if ((x - y) <= -5e+75)
		tmp = t_1;
	elseif ((x - y) <= 2e-34)
		tmp = a * 120.0;
	elseif ((x - y) <= 4e+203)
		tmp = (a * 120.0) + (60.0 * (y / t));
	else
		tmp = t_1;
	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[(x - y), $MachinePrecision], -5e+75], t$95$1, If[LessEqual[N[(x - y), $MachinePrecision], 2e-34], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(x - y), $MachinePrecision], 4e+203], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 x y) < -5.0000000000000002e75 or 4e203 < (-.f64 x y)

   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 69.8%

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

   if -5.0000000000000002e75 < (-.f64 x y) < 1.99999999999999986e-34

   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 89.1%

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

   if 1.99999999999999986e-34 < (-.f64 x y) < 4e203

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 81.7%

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

      1. associate-*r/ 27.4%

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

   6. Simplified 81.7%

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

   7. Taylor expanded in z around 0 67.9%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - y \leq -5 \cdot 10^{+75}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;x - y \leq 2 \cdot 10^{-34}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x - y \leq 4 \cdot 10^{+203}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 5: 66.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x - y \leq -5 \cdot 10^{+75}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;x - y \leq 2 \cdot 10^{-34}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x - y \leq 4 \cdot 10^{+203}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- x y) -5e+75)
   (/ 60.0 (/ (- z t) (- x y)))
   (if (<= (- x y) 2e-34)
     (* a 120.0)
     (if (<= (- x y) 4e+203)
       (+ (* a 120.0) (* 60.0 (/ y t)))
       (* 60.0 (/ (- x y) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x - y) <= -5e+75) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if ((x - y) <= 2e-34) {
		tmp = a * 120.0;
	} else if ((x - y) <= 4e+203) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x - y) <= (-5d+75)) then
        tmp = 60.0d0 / ((z - t) / (x - y))
    else if ((x - y) <= 2d-34) then
        tmp = a * 120.0d0
    else if ((x - y) <= 4d+203) then
        tmp = (a * 120.0d0) + (60.0d0 * (y / t))
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x - y) <= -5e+75) {
		tmp = 60.0 / ((z - t) / (x - y));
	} else if ((x - y) <= 2e-34) {
		tmp = a * 120.0;
	} else if ((x - y) <= 4e+203) {
		tmp = (a * 120.0) + (60.0 * (y / t));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x - y) <= -5e+75:
		tmp = 60.0 / ((z - t) / (x - y))
	elif (x - y) <= 2e-34:
		tmp = a * 120.0
	elif (x - y) <= 4e+203:
		tmp = (a * 120.0) + (60.0 * (y / t))
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x - y) <= -5e+75)
		tmp = Float64(60.0 / Float64(Float64(z - t) / Float64(x - y)));
	elseif (Float64(x - y) <= 2e-34)
		tmp = Float64(a * 120.0);
	elseif (Float64(x - y) <= 4e+203)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)));
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x - y) <= -5e+75)
		tmp = 60.0 / ((z - t) / (x - y));
	elseif ((x - y) <= 2e-34)
		tmp = a * 120.0;
	elseif ((x - y) <= 4e+203)
		tmp = (a * 120.0) + (60.0 * (y / t));
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x - y), $MachinePrecision], -5e+75], N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x - y), $MachinePrecision], 2e-34], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(x - y), $MachinePrecision], 4e+203], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 x y) < -5.0000000000000002e75

   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-/l* 99.7%

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

      2. clear-num 99.6%

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

      3. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l* 99.6%

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

      3. metadata-eval 99.6%

         \[\leadsto \color{blue}{\frac{1}{0.016666666666666666}} \cdot \left(\left(x - y\right) \cdot \frac{1}{z - t}\right) + a \cdot 120 \]

      4. div-inv 99.6%

         \[\leadsto \frac{1}{0.016666666666666666} \cdot \color{blue}{\frac{x - y}{z - t}} + a \cdot 120 \]

      5. times-frac 99.8%

         \[\leadsto \color{blue}{\frac{1 \cdot \left(x - y\right)}{0.016666666666666666 \cdot \left(z - t\right)}} + a \cdot 120 \]

      6. *-un-lft-identity 99.8%

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

      7. *-commutative 99.8%

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

   7. Applied egg-rr 99.8%

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

   8. Taylor expanded in a around 0 67.6%

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

      1. associate-*r/ 67.6%

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

      2. associate-/l* 67.6%

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

   10. Simplified 67.6%

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

   if -5.0000000000000002e75 < (-.f64 x y) < 1.99999999999999986e-34

   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 89.1%

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

   if 1.99999999999999986e-34 < (-.f64 x y) < 4e203

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 81.7%

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

      1. associate-*r/ 27.4%

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

   6. Simplified 81.7%

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

   7. Taylor expanded in z around 0 67.9%

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

   if 4e203 < (-.f64 x y)

   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. Taylor expanded in a around 0 75.1%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x - y \leq -5 \cdot 10^{+75}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x - y}}\\ \mathbf{elif}\;x - y \leq 2 \cdot 10^{-34}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;x - y \leq 4 \cdot 10^{+203}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 6: 57.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -1 \cdot 10^{-45}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 2 \cdot 10^{-152}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;z - t \leq 10^{-23}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- z t) -1e-45)
   (* a 120.0)
   (if (<= (- z t) 2e-152)
     (* -60.0 (/ (- x y) t))
     (if (<= (- z t) 1e-23) (* (/ 60.0 (- z t)) x) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -1e-45) {
		tmp = a * 120.0;
	} else if ((z - t) <= 2e-152) {
		tmp = -60.0 * ((x - y) / t);
	} else if ((z - t) <= 1e-23) {
		tmp = (60.0 / (z - t)) * x;
	} 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 ((z - t) <= (-1d-45)) then
        tmp = a * 120.0d0
    else if ((z - t) <= 2d-152) then
        tmp = (-60.0d0) * ((x - y) / t)
    else if ((z - t) <= 1d-23) then
        tmp = (60.0d0 / (z - t)) * x
    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 ((z - t) <= -1e-45) {
		tmp = a * 120.0;
	} else if ((z - t) <= 2e-152) {
		tmp = -60.0 * ((x - y) / t);
	} else if ((z - t) <= 1e-23) {
		tmp = (60.0 / (z - t)) * x;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z - t) <= -1e-45:
		tmp = a * 120.0
	elif (z - t) <= 2e-152:
		tmp = -60.0 * ((x - y) / t)
	elif (z - t) <= 1e-23:
		tmp = (60.0 / (z - t)) * x
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z - t) <= -1e-45)
		tmp = Float64(a * 120.0);
	elseif (Float64(z - t) <= 2e-152)
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	elseif (Float64(z - t) <= 1e-23)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z - t) <= -1e-45)
		tmp = a * 120.0;
	elseif ((z - t) <= 2e-152)
		tmp = -60.0 * ((x - y) / t);
	elseif ((z - t) <= 1e-23)
		tmp = (60.0 / (z - t)) * x;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z - t), $MachinePrecision], -1e-45], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 2e-152], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 1e-23], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 z t) < -9.99999999999999984e-46 or 9.9999999999999996e-24 < (-.f64 z t)

   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 65.6%

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

   if -9.99999999999999984e-46 < (-.f64 z t) < 2.00000000000000013e-152

   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* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in a around 0 90.4%

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

   5. Taylor expanded in z around 0 55.4%

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

   if 2.00000000000000013e-152 < (-.f64 z t) < 9.9999999999999996e-24

   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-/l* 99.7%

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

      2. clear-num 99.4%

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

      3. associate-/r/ 99.6%

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

   5. Applied egg-rr 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.6%

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

      3. metadata-eval 99.6%

         \[\leadsto \color{blue}{\frac{1}{0.016666666666666666}} \cdot \left(\left(x - y\right) \cdot \frac{1}{z - t}\right) + a \cdot 120 \]

      4. div-inv 99.8%

         \[\leadsto \frac{1}{0.016666666666666666} \cdot \color{blue}{\frac{x - y}{z - t}} + a \cdot 120 \]

      5. times-frac 99.8%

         \[\leadsto \color{blue}{\frac{1 \cdot \left(x - y\right)}{0.016666666666666666 \cdot \left(z - t\right)}} + a \cdot 120 \]

      6. *-un-lft-identity 99.8%

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

      7. *-commutative 99.8%

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

   7. Applied egg-rr 99.8%

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

   8. Taylor expanded in a around 0 93.6%

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

      1. associate-*r/ 93.4%

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

      2. associate-/l* 93.5%

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

   10. Simplified 93.5%

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

   11. Taylor expanded in x around inf 73.5%

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

       1. associate-*r/ 79.5%

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

       2. associate-*l/ 79.7%

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

       3. *-commutative 79.7%

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

   13. Simplified 73.5%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -1 \cdot 10^{-45}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq 2 \cdot 10^{-152}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;z - t \leq 10^{-23}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7: 73.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-13} \lor \neg \left(a \leq -1.25 \cdot 10^{-30}\right) \land a \leq 2.9 \cdot 10^{-79}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.4e+42)
   (* a 120.0)
   (if (or (<= a -6.8e-13) (and (not (<= a -1.25e-30)) (<= a 2.9e-79)))
     (* 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 <= -3.4e+42) {
		tmp = a * 120.0;
	} else if ((a <= -6.8e-13) || (!(a <= -1.25e-30) && (a <= 2.9e-79))) {
		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 <= (-3.4d+42)) then
        tmp = a * 120.0d0
    else if ((a <= (-6.8d-13)) .or. (.not. (a <= (-1.25d-30))) .and. (a <= 2.9d-79)) 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 <= -3.4e+42) {
		tmp = a * 120.0;
	} else if ((a <= -6.8e-13) || (!(a <= -1.25e-30) && (a <= 2.9e-79))) {
		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 <= -3.4e+42:
		tmp = a * 120.0
	elif (a <= -6.8e-13) or (not (a <= -1.25e-30) and (a <= 2.9e-79)):
		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 <= -3.4e+42)
		tmp = Float64(a * 120.0);
	elseif ((a <= -6.8e-13) || (!(a <= -1.25e-30) && (a <= 2.9e-79)))
		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 <= -3.4e+42)
		tmp = a * 120.0;
	elseif ((a <= -6.8e-13) || (~((a <= -1.25e-30)) && (a <= 2.9e-79)))
		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, -3.4e+42], N[(a * 120.0), $MachinePrecision], If[Or[LessEqual[a, -6.8e-13], And[N[Not[LessEqual[a, -1.25e-30]], $MachinePrecision], LessEqual[a, 2.9e-79]]], 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 < -3.39999999999999975e42 or -6.80000000000000031e-13 < a < -1.24999999999999993e-30 or 2.9000000000000001e-79 < 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 80.0%

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

   if -3.39999999999999975e42 < a < -6.80000000000000031e-13 or -1.24999999999999993e-30 < a < 2.9000000000000001e-79

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 76.3%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-13} \lor \neg \left(a \leq -1.25 \cdot 10^{-30}\right) \land a \leq 2.9 \cdot 10^{-79}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8: 74.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{+42}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-30}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= a -2.6e+42)
     (* a 120.0)
     (if (<= a -4.2e+23)
       t_1
       (if (<= a -5.5e-30)
         (+ (* a 120.0) (* -60.0 (/ y z)))
         (if (<= a 2.8e-79) t_1 (* a 120.0)))))))

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 <= -2.6e+42) {
		tmp = a * 120.0;
	} else if (a <= -4.2e+23) {
		tmp = t_1;
	} else if (a <= -5.5e-30) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (a <= 2.8e-79) {
		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 * ((x - y) / (z - t))
    if (a <= (-2.6d+42)) then
        tmp = a * 120.0d0
    else if (a <= (-4.2d+23)) then
        tmp = t_1
    else if (a <= (-5.5d-30)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if (a <= 2.8d-79) 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 * ((x - y) / (z - t));
	double tmp;
	if (a <= -2.6e+42) {
		tmp = a * 120.0;
	} else if (a <= -4.2e+23) {
		tmp = t_1;
	} else if (a <= -5.5e-30) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (a <= 2.8e-79) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if a <= -2.6e+42:
		tmp = a * 120.0
	elif a <= -4.2e+23:
		tmp = t_1
	elif a <= -5.5e-30:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif a <= 2.8e-79:
		tmp = t_1
	else:
		tmp = a * 120.0
	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 (a <= -2.6e+42)
		tmp = Float64(a * 120.0);
	elseif (a <= -4.2e+23)
		tmp = t_1;
	elseif (a <= -5.5e-30)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (a <= 2.8e-79)
		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 * ((x - y) / (z - t));
	tmp = 0.0;
	if (a <= -2.6e+42)
		tmp = a * 120.0;
	elseif (a <= -4.2e+23)
		tmp = t_1;
	elseif (a <= -5.5e-30)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif (a <= 2.8e-79)
		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[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.6e+42], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -4.2e+23], t$95$1, If[LessEqual[a, -5.5e-30], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e-79], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.5999999999999999e42 or 2.80000000000000012e-79 < 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 79.5%

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

   if -2.5999999999999999e42 < a < -4.2000000000000003e23 or -5.49999999999999976e-30 < a < 2.80000000000000012e-79

   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 78.2%

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

   if -4.2000000000000003e23 < a < -5.49999999999999976e-30

   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* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 89.4%

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

      1. associate-*r/ 25.1%

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

   6. Simplified 89.1%

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

   7. Taylor expanded in t around 0 77.1%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+42}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{+23}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-30}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-79}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 9: 59.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-30}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-65} \lor \neg \left(a \leq -5.3 \cdot 10^{-134}\right) \land a \leq 2.6 \cdot 10^{-79}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.15e-30)
   (* a 120.0)
   (if (or (<= a -1.85e-65) (and (not (<= a -5.3e-134)) (<= a 2.6e-79)))
     (* -60.0 (/ (- x y) t))
     (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.15e-30) {
		tmp = a * 120.0;
	} else if ((a <= -1.85e-65) || (!(a <= -5.3e-134) && (a <= 2.6e-79))) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.15d-30)) then
        tmp = a * 120.0d0
    else if ((a <= (-1.85d-65)) .or. (.not. (a <= (-5.3d-134))) .and. (a <= 2.6d-79)) then
        tmp = (-60.0d0) * ((x - y) / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.15e-30) {
		tmp = a * 120.0;
	} else if ((a <= -1.85e-65) || (!(a <= -5.3e-134) && (a <= 2.6e-79))) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.15e-30:
		tmp = a * 120.0
	elif (a <= -1.85e-65) or (not (a <= -5.3e-134) and (a <= 2.6e-79)):
		tmp = -60.0 * ((x - y) / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.15e-30)
		tmp = Float64(a * 120.0);
	elseif ((a <= -1.85e-65) || (!(a <= -5.3e-134) && (a <= 2.6e-79)))
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.15e-30)
		tmp = a * 120.0;
	elseif ((a <= -1.85e-65) || (~((a <= -5.3e-134)) && (a <= 2.6e-79)))
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.15e-30], N[(a * 120.0), $MachinePrecision], If[Or[LessEqual[a, -1.85e-65], And[N[Not[LessEqual[a, -5.3e-134]], $MachinePrecision], LessEqual[a, 2.6e-79]]], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.14999999999999992e-30 or -1.85e-65 < a < -5.30000000000000003e-134 or 2.59999999999999994e-79 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 73.1%

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

   if -1.14999999999999992e-30 < a < -1.85e-65 or -5.30000000000000003e-134 < a < 2.59999999999999994e-79

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in a around 0 85.2%

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

   5. Taylor expanded in z around 0 48.4%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-30}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-65} \lor \neg \left(a \leq -5.3 \cdot 10^{-134}\right) \land a \leq 2.6 \cdot 10^{-79}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 10: 56.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-60}{z - t}\\ \mathbf{if}\;y \leq -2.55 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-112}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-81}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+88}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ -60.0 (- z t)))))
   (if (<= y -2.55e+103)
     t_1
     (if (<= y 1.6e-112)
       (* a 120.0)
       (if (<= y 1.15e-81)
         (* (/ 60.0 (- z t)) x)
         (if (<= y 4e+88) (* a 120.0) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-60.0 / (z - t));
	double tmp;
	if (y <= -2.55e+103) {
		tmp = t_1;
	} else if (y <= 1.6e-112) {
		tmp = a * 120.0;
	} else if (y <= 1.15e-81) {
		tmp = (60.0 / (z - t)) * x;
	} else if (y <= 4e+88) {
		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 = y * ((-60.0d0) / (z - t))
    if (y <= (-2.55d+103)) then
        tmp = t_1
    else if (y <= 1.6d-112) then
        tmp = a * 120.0d0
    else if (y <= 1.15d-81) then
        tmp = (60.0d0 / (z - t)) * x
    else if (y <= 4d+88) 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 = y * (-60.0 / (z - t));
	double tmp;
	if (y <= -2.55e+103) {
		tmp = t_1;
	} else if (y <= 1.6e-112) {
		tmp = a * 120.0;
	} else if (y <= 1.15e-81) {
		tmp = (60.0 / (z - t)) * x;
	} else if (y <= 4e+88) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (-60.0 / (z - t))
	tmp = 0
	if y <= -2.55e+103:
		tmp = t_1
	elif y <= 1.6e-112:
		tmp = a * 120.0
	elif y <= 1.15e-81:
		tmp = (60.0 / (z - t)) * x
	elif y <= 4e+88:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(-60.0 / Float64(z - t)))
	tmp = 0.0
	if (y <= -2.55e+103)
		tmp = t_1;
	elseif (y <= 1.6e-112)
		tmp = Float64(a * 120.0);
	elseif (y <= 1.15e-81)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	elseif (y <= 4e+88)
		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 = y * (-60.0 / (z - t));
	tmp = 0.0;
	if (y <= -2.55e+103)
		tmp = t_1;
	elseif (y <= 1.6e-112)
		tmp = a * 120.0;
	elseif (y <= 1.15e-81)
		tmp = (60.0 / (z - t)) * x;
	elseif (y <= 4e+88)
		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[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.55e+103], t$95$1, If[LessEqual[y, 1.6e-112], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, 1.15e-81], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 4e+88], N[(a * 120.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5500000000000001e103 or 3.99999999999999984e88 < y

   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-/l* 99.7%

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

      2. clear-num 99.7%

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

      3. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l* 99.6%

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

      3. metadata-eval 99.6%

         \[\leadsto \color{blue}{\frac{1}{0.016666666666666666}} \cdot \left(\left(x - y\right) \cdot \frac{1}{z - t}\right) + a \cdot 120 \]

      4. div-inv 99.6%

         \[\leadsto \frac{1}{0.016666666666666666} \cdot \color{blue}{\frac{x - y}{z - t}} + a \cdot 120 \]

      5. times-frac 99.7%

         \[\leadsto \color{blue}{\frac{1 \cdot \left(x - y\right)}{0.016666666666666666 \cdot \left(z - t\right)}} + a \cdot 120 \]

      6. *-un-lft-identity 99.7%

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

      7. *-commutative 99.7%

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

   7. Applied egg-rr 99.7%

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

   8. Taylor expanded in y around inf 60.0%

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

      1. associate-*r/ 60.1%

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

      2. *-commutative 60.1%

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

      3. associate-*r/ 60.2%

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

   10. Simplified 60.2%

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

   if -2.5500000000000001e103 < y < 1.59999999999999997e-112 or 1.14999999999999996e-81 < y < 3.99999999999999984e88

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 71.5%

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

   if 1.59999999999999997e-112 < y < 1.14999999999999996e-81

   1. Initial program 99.1%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

      1. associate-/l* 99.1%

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

      2. clear-num 98.8%

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

      3. associate-/r/ 99.4%

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

   5. Applied egg-rr 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l* 99.4%

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

      3. metadata-eval 99.4%

         \[\leadsto \color{blue}{\frac{1}{0.016666666666666666}} \cdot \left(\left(x - y\right) \cdot \frac{1}{z - t}\right) + a \cdot 120 \]

      4. div-inv 99.7%

         \[\leadsto \frac{1}{0.016666666666666666} \cdot \color{blue}{\frac{x - y}{z - t}} + a \cdot 120 \]

      5. times-frac 99.4%

         \[\leadsto \color{blue}{\frac{1 \cdot \left(x - y\right)}{0.016666666666666666 \cdot \left(z - t\right)}} + a \cdot 120 \]

      6. *-un-lft-identity 99.4%

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

      7. *-commutative 99.4%

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

   7. Applied egg-rr 99.4%

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

   8. Taylor expanded in a around 0 99.7%

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

      1. associate-*r/ 99.1%

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

      2. associate-/l* 99.4%

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

   10. Simplified 99.4%

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

   11. Taylor expanded in x around inf 99.7%

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

       1. associate-*r/ 99.1%

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

       2. associate-*l/ 99.7%

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

       3. *-commutative 99.7%

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

   13. Simplified 99.7%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+103}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-112}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-81}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+88}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \end{array} \]

Alternative 11: 56.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-113}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-82}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+89}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.5e+102)
   (* y (/ -60.0 (- z t)))
   (if (<= y 2.3e-113)
     (* a 120.0)
     (if (<= y 6e-82)
       (* (/ 60.0 (- z t)) x)
       (if (<= y 1.7e+89) (* a 120.0) (/ (* y -60.0) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.5e+102) {
		tmp = y * (-60.0 / (z - t));
	} else if (y <= 2.3e-113) {
		tmp = a * 120.0;
	} else if (y <= 6e-82) {
		tmp = (60.0 / (z - t)) * x;
	} else if (y <= 1.7e+89) {
		tmp = a * 120.0;
	} else {
		tmp = (y * -60.0) / (z - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-4.5d+102)) then
        tmp = y * ((-60.0d0) / (z - t))
    else if (y <= 2.3d-113) then
        tmp = a * 120.0d0
    else if (y <= 6d-82) then
        tmp = (60.0d0 / (z - t)) * x
    else if (y <= 1.7d+89) then
        tmp = a * 120.0d0
    else
        tmp = (y * (-60.0d0)) / (z - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.5e+102) {
		tmp = y * (-60.0 / (z - t));
	} else if (y <= 2.3e-113) {
		tmp = a * 120.0;
	} else if (y <= 6e-82) {
		tmp = (60.0 / (z - t)) * x;
	} else if (y <= 1.7e+89) {
		tmp = a * 120.0;
	} else {
		tmp = (y * -60.0) / (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.5e+102:
		tmp = y * (-60.0 / (z - t))
	elif y <= 2.3e-113:
		tmp = a * 120.0
	elif y <= 6e-82:
		tmp = (60.0 / (z - t)) * x
	elif y <= 1.7e+89:
		tmp = a * 120.0
	else:
		tmp = (y * -60.0) / (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.5e+102)
		tmp = Float64(y * Float64(-60.0 / Float64(z - t)));
	elseif (y <= 2.3e-113)
		tmp = Float64(a * 120.0);
	elseif (y <= 6e-82)
		tmp = Float64(Float64(60.0 / Float64(z - t)) * x);
	elseif (y <= 1.7e+89)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(y * -60.0) / Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.5e+102)
		tmp = y * (-60.0 / (z - t));
	elseif (y <= 2.3e-113)
		tmp = a * 120.0;
	elseif (y <= 6e-82)
		tmp = (60.0 / (z - t)) * x;
	elseif (y <= 1.7e+89)
		tmp = a * 120.0;
	else
		tmp = (y * -60.0) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.5e+102], N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-113], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, 6e-82], N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[y, 1.7e+89], N[(a * 120.0), $MachinePrecision], N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.50000000000000021e102

   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-/l* 99.7%

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

      2. clear-num 99.8%

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

      3. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l* 99.6%

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

      3. metadata-eval 99.6%

         \[\leadsto \color{blue}{\frac{1}{0.016666666666666666}} \cdot \left(\left(x - y\right) \cdot \frac{1}{z - t}\right) + a \cdot 120 \]

      4. div-inv 99.6%

         \[\leadsto \frac{1}{0.016666666666666666} \cdot \color{blue}{\frac{x - y}{z - t}} + a \cdot 120 \]

      5. times-frac 99.7%

         \[\leadsto \color{blue}{\frac{1 \cdot \left(x - y\right)}{0.016666666666666666 \cdot \left(z - t\right)}} + a \cdot 120 \]

      6. *-un-lft-identity 99.7%

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

      7. *-commutative 99.7%

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

   7. Applied egg-rr 99.7%

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

   8. Taylor expanded in y around inf 52.7%

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

      1. associate-*r/ 52.7%

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

      2. *-commutative 52.7%

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

      3. associate-*r/ 52.9%

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

   10. Simplified 52.9%

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

   if -4.50000000000000021e102 < y < 2.30000000000000008e-113 or 5.9999999999999998e-82 < y < 1.7000000000000001e89

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 71.5%

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

   if 2.30000000000000008e-113 < y < 5.9999999999999998e-82

   1. Initial program 99.1%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

      1. associate-/l* 99.1%

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

      2. clear-num 98.8%

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

      3. associate-/r/ 99.4%

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

   5. Applied egg-rr 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l* 99.4%

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

      3. metadata-eval 99.4%

         \[\leadsto \color{blue}{\frac{1}{0.016666666666666666}} \cdot \left(\left(x - y\right) \cdot \frac{1}{z - t}\right) + a \cdot 120 \]

      4. div-inv 99.7%

         \[\leadsto \frac{1}{0.016666666666666666} \cdot \color{blue}{\frac{x - y}{z - t}} + a \cdot 120 \]

      5. times-frac 99.4%

         \[\leadsto \color{blue}{\frac{1 \cdot \left(x - y\right)}{0.016666666666666666 \cdot \left(z - t\right)}} + a \cdot 120 \]

      6. *-un-lft-identity 99.4%

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

      7. *-commutative 99.4%

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

   7. Applied egg-rr 99.4%

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

   8. Taylor expanded in a around 0 99.7%

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

      1. associate-*r/ 99.1%

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

      2. associate-/l* 99.4%

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

   10. Simplified 99.4%

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

   11. Taylor expanded in x around inf 99.7%

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

       1. associate-*r/ 99.1%

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

       2. associate-*l/ 99.7%

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

       3. *-commutative 99.7%

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

   13. Simplified 99.7%

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

   if 1.7000000000000001e89 < y

   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-/l* 99.7%

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

      2. clear-num 99.6%

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

      3. associate-/r/ 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l* 99.6%

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

      3. metadata-eval 99.6%

         \[\leadsto \color{blue}{\frac{1}{0.016666666666666666}} \cdot \left(\left(x - y\right) \cdot \frac{1}{z - t}\right) + a \cdot 120 \]

      4. div-inv 99.6%

         \[\leadsto \frac{1}{0.016666666666666666} \cdot \color{blue}{\frac{x - y}{z - t}} + a \cdot 120 \]

      5. times-frac 99.7%

         \[\leadsto \color{blue}{\frac{1 \cdot \left(x - y\right)}{0.016666666666666666 \cdot \left(z - t\right)}} + a \cdot 120 \]

      6. *-un-lft-identity 99.7%

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

      7. *-commutative 99.7%

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

   7. Applied egg-rr 99.7%

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

   8. Taylor expanded in a around 0 81.0%

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

      1. associate-*r/ 81.1%

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

      2. associate-/l* 81.1%

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

   10. Simplified 81.1%

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

   11. Taylor expanded in x around 0 67.1%

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

       1. associate-*r/ 67.2%

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

   13. Simplified 67.2%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-113}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-82}:\\ \;\;\;\;\frac{60}{z - t} \cdot x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+89}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t}\\ \end{array} \]

Alternative 12: 63.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;y \leq -3 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-80}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+73}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= y -3e+23)
     t_1
     (if (<= y 1.6e-80)
       (+ (* a 120.0) (* 60.0 (/ x z)))
       (if (<= y 2.4e+73) (* a 120.0) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if (y <= -3e+23) {
		tmp = t_1;
	} else if (y <= 1.6e-80) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if (y <= 2.4e+73) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    if (y <= (-3d+23)) then
        tmp = t_1
    else if (y <= 1.6d-80) then
        tmp = (a * 120.0d0) + (60.0d0 * (x / z))
    else if (y <= 2.4d+73) then
        tmp = a * 120.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if (y <= -3e+23) {
		tmp = t_1;
	} else if (y <= 1.6e-80) {
		tmp = (a * 120.0) + (60.0 * (x / z));
	} else if (y <= 2.4e+73) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if y <= -3e+23:
		tmp = t_1
	elif y <= 1.6e-80:
		tmp = (a * 120.0) + (60.0 * (x / z))
	elif y <= 2.4e+73:
		tmp = a * 120.0
	else:
		tmp = t_1
	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 (y <= -3e+23)
		tmp = t_1;
	elseif (y <= 1.6e-80)
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(x / z)));
	elseif (y <= 2.4e+73)
		tmp = Float64(a * 120.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	tmp = 0.0;
	if (y <= -3e+23)
		tmp = t_1;
	elseif (y <= 1.6e-80)
		tmp = (a * 120.0) + (60.0 * (x / z));
	elseif (y <= 2.4e+73)
		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[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3e+23], t$95$1, If[LessEqual[y, 1.6e-80], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+73], N[(a * 120.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.0000000000000001e23 or 2.40000000000000002e73 < y

   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 71.4%

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

   if -3.0000000000000001e23 < y < 1.5999999999999999e-80

   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 x around inf 96.8%

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

      1. associate-*r/ 96.8%

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

      2. associate-*l/ 96.8%

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

      3. *-commutative 96.8%

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

   6. Simplified 96.8%

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

   7. Taylor expanded in z around inf 75.6%

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

   if 1.5999999999999999e-80 < y < 2.40000000000000002e73

   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 82.1%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+23}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-80}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+73}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 13: 89.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+77} \lor \neg \left(y \leq 3 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.3e+77) (not (<= y 3e+83)))
   (+ (/ (* y -60.0) (- z t)) (* a 120.0))
   (+ (* (/ 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 <= -1.3e+77) || !(y <= 3e+83)) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} 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 <= (-1.3d+77)) .or. (.not. (y <= 3d+83))) then
        tmp = ((y * (-60.0d0)) / (z - t)) + (a * 120.0d0)
    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 <= -1.3e+77) || !(y <= 3e+83)) {
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	} else {
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.3e+77) or not (y <= 3e+83):
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0)
	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 <= -1.3e+77) || !(y <= 3e+83))
		tmp = Float64(Float64(Float64(y * -60.0) / Float64(z - t)) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(Float64(60.0 / 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 <= -1.3e+77) || ~((y <= 3e+83)))
		tmp = ((y * -60.0) / (z - t)) + (a * 120.0);
	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, -1.3e+77], N[Not[LessEqual[y, 3e+83]], $MachinePrecision]], N[(N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3000000000000001e77 or 3e83 < y

   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 x around 0 85.3%

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

      1. associate-*r/ 58.3%

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

   6. Simplified 85.4%

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

   if -1.3000000000000001e77 < y < 3e83

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 95.9%

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

      1. associate-*r/ 95.9%

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

      2. associate-*l/ 95.9%

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

      3. *-commutative 95.9%

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

   6. Simplified 95.9%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+77} \lor \neg \left(y \leq 3 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \end{array} \]

Alternative 14: 89.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+76}:\\ \;\;\;\;\frac{60}{\frac{t - z}{y}} + a \cdot 120\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+78}:\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3e+76)
   (+ (/ 60.0 (/ (- t z) y)) (* a 120.0))
   (if (<= y 4e+78)
     (+ (* (/ 60.0 (- z t)) x) (* 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 (y <= -3e+76) {
		tmp = (60.0 / ((t - z) / y)) + (a * 120.0);
	} else if (y <= 4e+78) {
		tmp = ((60.0 / (z - t)) * x) + (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 (y <= (-3d+76)) then
        tmp = (60.0d0 / ((t - z) / y)) + (a * 120.0d0)
    else if (y <= 4d+78) then
        tmp = ((60.0d0 / (z - t)) * x) + (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 (y <= -3e+76) {
		tmp = (60.0 / ((t - z) / y)) + (a * 120.0);
	} else if (y <= 4e+78) {
		tmp = ((60.0 / (z - t)) * x) + (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 y <= -3e+76:
		tmp = (60.0 / ((t - z) / y)) + (a * 120.0)
	elif y <= 4e+78:
		tmp = ((60.0 / (z - t)) * x) + (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 (y <= -3e+76)
		tmp = Float64(Float64(60.0 / Float64(Float64(t - z) / y)) + Float64(a * 120.0));
	elseif (y <= 4e+78)
		tmp = Float64(Float64(Float64(60.0 / Float64(z - t)) * x) + 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 (y <= -3e+76)
		tmp = (60.0 / ((t - z) / y)) + (a * 120.0);
	elseif (y <= 4e+78)
		tmp = ((60.0 / (z - t)) * x) + (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[LessEqual[y, -3e+76], N[(N[(60.0 / N[(N[(t - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+78], N[(N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $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 3 regimes

2. if y < -2.9999999999999998e76

   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. Taylor expanded in x around 0 84.9%

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

      1. associate-*r/ 84.9%

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

      2. neg-mul-1 84.9%

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

   6. Simplified 84.9%

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

   if -2.9999999999999998e76 < y < 4.00000000000000003e78

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 95.9%

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

      1. associate-*r/ 95.9%

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

      2. associate-*l/ 95.9%

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

      3. *-commutative 95.9%

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

   6. Simplified 95.9%

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

   if 4.00000000000000003e78 < y

   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. Taylor expanded in x around 0 85.9%

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

      1. associate-*r/ 65.8%

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

   6. Simplified 86.1%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+76}:\\ \;\;\;\;\frac{60}{\frac{t - z}{y}} + a \cdot 120\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+78}:\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -60}{z - t} + a \cdot 120\\ \end{array} \]

Alternative 15: 99.8% accurate, 1.0× speedup

Math

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

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(Float64(60.0 / 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[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $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%

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

Alternative 16: 53.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-137}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-306}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-177}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4e-137)
   (* a 120.0)
   (if (<= a 2.6e-306)
     (* -60.0 (/ x t))
     (if (<= a 6.5e-177) (* 60.0 (/ x z)) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4e-137) {
		tmp = a * 120.0;
	} else if (a <= 2.6e-306) {
		tmp = -60.0 * (x / t);
	} else if (a <= 6.5e-177) {
		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 <= (-4d-137)) then
        tmp = a * 120.0d0
    else if (a <= 2.6d-306) then
        tmp = (-60.0d0) * (x / t)
    else if (a <= 6.5d-177) 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 <= -4e-137) {
		tmp = a * 120.0;
	} else if (a <= 2.6e-306) {
		tmp = -60.0 * (x / t);
	} else if (a <= 6.5e-177) {
		tmp = 60.0 * (x / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4e-137:
		tmp = a * 120.0
	elif a <= 2.6e-306:
		tmp = -60.0 * (x / t)
	elif a <= 6.5e-177:
		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 <= -4e-137)
		tmp = Float64(a * 120.0);
	elseif (a <= 2.6e-306)
		tmp = Float64(-60.0 * Float64(x / t));
	elseif (a <= 6.5e-177)
		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 <= -4e-137)
		tmp = a * 120.0;
	elseif (a <= 2.6e-306)
		tmp = -60.0 * (x / t);
	elseif (a <= 6.5e-177)
		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, -4e-137], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, 2.6e-306], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-177], N[(60.0 * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.99999999999999991e-137 or 6.4999999999999998e-177 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 66.1%

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

   if -3.99999999999999991e-137 < a < 2.6e-306

   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* 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 69.8%

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

      1. associate-*r/ 69.8%

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

      2. associate-*l/ 69.9%

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

      3. *-commutative 69.9%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in z around 0 55.6%

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

      1. fma-def 55.6%

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

   9. Simplified 55.6%

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

   10. Taylor expanded in a around 0 44.7%

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

   if 2.6e-306 < a < 6.4999999999999998e-177

   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 x around inf 65.7%

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

      1. associate-*r/ 65.7%

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

      2. associate-*l/ 65.6%

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

      3. *-commutative 65.6%

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

   6. Simplified 65.6%

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

   7. Taylor expanded in z around inf 51.7%

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

   8. Taylor expanded in a around 0 41.1%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-137}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-306}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-177}:\\ \;\;\;\;60 \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 17: 53.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.9 \cdot 10^{-137} \lor \neg \left(a \leq 2.25 \cdot 10^{-274}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.9e-137) (not (<= a 2.25e-274)))
   (* a 120.0)
   (* -60.0 (/ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.9e-137) || !(a <= 2.25e-274)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.9d-137)) .or. (.not. (a <= 2.25d-274))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.9e-137) || !(a <= 2.25e-274)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.9e-137) or not (a <= 2.25e-274):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (x / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.9e-137) || !(a <= 2.25e-274))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.9e-137) || ~((a <= 2.25e-274)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.9e-137], N[Not[LessEqual[a, 2.25e-274]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.8999999999999996e-137 or 2.24999999999999996e-274 < a

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 61.4%

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

   if -4.8999999999999996e-137 < a < 2.24999999999999996e-274

   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* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 70.5%

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

      1. associate-*r/ 70.5%

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

      2. associate-*l/ 70.6%

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

      3. *-commutative 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in z around 0 51.7%

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

      1. fma-def 51.7%

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

   9. Simplified 51.7%

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

   10. Taylor expanded in a around 0 42.3%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.9 \cdot 10^{-137} \lor \neg \left(a \leq 2.25 \cdot 10^{-274}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \end{array} \]

Alternative 18: 51.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{+167}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 1.7e+167) (* a 120.0) (* -60.0 (/ y z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.7e+167) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 1.7d+167) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.7e+167) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 1.7e+167:
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.7e+167)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 1.7e+167)
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.7e+167], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.7e167

   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 61.6%

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

   if 1.7e167 < y

   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. Taylor expanded in a around 0 89.5%

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

   5. Taylor expanded in z around inf 49.3%

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

   6. Taylor expanded in x around 0 39.7%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{+167}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 19: 51.4% 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 55.8%

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

5. Final simplification 55.8%

   \[\leadsto a \cdot 120 \]

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023173 
(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)))