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

Percentage Accurate: 99.4% → 99.8%

Time: 13.0s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. +-commutative 99.4%

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

   2. fma-def 99.5%

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

   3. *-commutative 99.5%

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

   4. associate-/l* 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 73.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+127}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{+14}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-77} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-52}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -4e+127)
   (* a 120.0)
   (if (<= (* a 120.0) -4e+14)
     (+ (* a 120.0) (* -60.0 (/ y z)))
     (if (or (<= (* a 120.0) -2e-77) (not (<= (* a 120.0) 5e-52)))
       (* a 120.0)
       (* 60.0 (/ (- x y) (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e+127) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -4e+14) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (((a * 120.0) <= -2e-77) || !((a * 120.0) <= 5e-52)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-4d+127)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-4d+14)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if (((a * 120.0d0) <= (-2d-77)) .or. (.not. ((a * 120.0d0) <= 5d-52))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -4e+127) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -4e+14) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (((a * 120.0) <= -2e-77) || !((a * 120.0) <= 5e-52)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -4e+127:
		tmp = a * 120.0
	elif (a * 120.0) <= -4e+14:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif ((a * 120.0) <= -2e-77) or not ((a * 120.0) <= 5e-52):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -4e+127)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -4e+14)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif ((Float64(a * 120.0) <= -2e-77) || !(Float64(a * 120.0) <= 5e-52))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -4e+127)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -4e+14)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif (((a * 120.0) <= -2e-77) || ~(((a * 120.0) <= 5e-52)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e+127], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e+14], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -2e-77], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-52]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -3.99999999999999982e127 or -4e14 < (*.f64 a 120) < -1.9999999999999999e-77 or 5e-52 < (*.f64 a 120)

   1. Initial program 99.2%

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

   2. Taylor expanded in z around inf 74.6%

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

   if -3.99999999999999982e127 < (*.f64 a 120) < -4e14

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 81.3%

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

      1. associate-*r/ 81.2%

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

   4. Simplified 81.2%

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

   5. Taylor expanded in z around inf 72.1%

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

   if -1.9999999999999999e-77 < (*.f64 a 120) < 5e-52

   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* 99.6%

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

      2. associate-/r/ 99.7%

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

   3. Applied egg-rr 99.7%

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

      1. *-commutative 99.7%

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

      2. clear-num 99.6%

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

      3. un-div-inv 99.6%

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

      4. div-inv 99.6%

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

      5. metadata-eval 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 80.2%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{+127}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{+14}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -2 \cdot 10^{-77} \lor \neg \left(a \cdot 120 \leq 5 \cdot 10^{-52}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 3: 66.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ t_2 := a \cdot 120 + 60 \cdot \frac{y}{t}\\ t_3 := a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{if}\;t \leq -2300:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{-210}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+110}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t))))
        (t_2 (+ (* a 120.0) (* 60.0 (/ y t))))
        (t_3 (+ (* a 120.0) (* -60.0 (/ y z)))))
   (if (<= t -2300.0)
     t_2
     (if (<= t 1.4e-305)
       t_1
       (if (<= t 2.95e-210)
         t_3
         (if (<= t 6.6e-88)
           t_1
           (if (<= t 2.5e+97) t_3 (if (<= t 1.1e+110) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double t_2 = (a * 120.0) + (60.0 * (y / t));
	double t_3 = (a * 120.0) + (-60.0 * (y / z));
	double tmp;
	if (t <= -2300.0) {
		tmp = t_2;
	} else if (t <= 1.4e-305) {
		tmp = t_1;
	} else if (t <= 2.95e-210) {
		tmp = t_3;
	} else if (t <= 6.6e-88) {
		tmp = t_1;
	} else if (t <= 2.5e+97) {
		tmp = t_3;
	} else if (t <= 1.1e+110) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    t_2 = (a * 120.0d0) + (60.0d0 * (y / t))
    t_3 = (a * 120.0d0) + ((-60.0d0) * (y / z))
    if (t <= (-2300.0d0)) then
        tmp = t_2
    else if (t <= 1.4d-305) then
        tmp = t_1
    else if (t <= 2.95d-210) then
        tmp = t_3
    else if (t <= 6.6d-88) then
        tmp = t_1
    else if (t <= 2.5d+97) then
        tmp = t_3
    else if (t <= 1.1d+110) then
        tmp = t_1
    else
        tmp = t_2
    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 t_2 = (a * 120.0) + (60.0 * (y / t));
	double t_3 = (a * 120.0) + (-60.0 * (y / z));
	double tmp;
	if (t <= -2300.0) {
		tmp = t_2;
	} else if (t <= 1.4e-305) {
		tmp = t_1;
	} else if (t <= 2.95e-210) {
		tmp = t_3;
	} else if (t <= 6.6e-88) {
		tmp = t_1;
	} else if (t <= 2.5e+97) {
		tmp = t_3;
	} else if (t <= 1.1e+110) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	t_2 = (a * 120.0) + (60.0 * (y / t))
	t_3 = (a * 120.0) + (-60.0 * (y / z))
	tmp = 0
	if t <= -2300.0:
		tmp = t_2
	elif t <= 1.4e-305:
		tmp = t_1
	elif t <= 2.95e-210:
		tmp = t_3
	elif t <= 6.6e-88:
		tmp = t_1
	elif t <= 2.5e+97:
		tmp = t_3
	elif t <= 1.1e+110:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	t_2 = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(y / t)))
	t_3 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)))
	tmp = 0.0
	if (t <= -2300.0)
		tmp = t_2;
	elseif (t <= 1.4e-305)
		tmp = t_1;
	elseif (t <= 2.95e-210)
		tmp = t_3;
	elseif (t <= 6.6e-88)
		tmp = t_1;
	elseif (t <= 2.5e+97)
		tmp = t_3;
	elseif (t <= 1.1e+110)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	t_2 = (a * 120.0) + (60.0 * (y / t));
	t_3 = (a * 120.0) + (-60.0 * (y / z));
	tmp = 0.0;
	if (t <= -2300.0)
		tmp = t_2;
	elseif (t <= 1.4e-305)
		tmp = t_1;
	elseif (t <= 2.95e-210)
		tmp = t_3;
	elseif (t <= 6.6e-88)
		tmp = t_1;
	elseif (t <= 2.5e+97)
		tmp = t_3;
	elseif (t <= 1.1e+110)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2300.0], t$95$2, If[LessEqual[t, 1.4e-305], t$95$1, If[LessEqual[t, 2.95e-210], t$95$3, If[LessEqual[t, 6.6e-88], t$95$1, If[LessEqual[t, 2.5e+97], t$95$3, If[LessEqual[t, 1.1e+110], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2300 or 1.09999999999999996e110 < t

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 92.5%

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

   3. Taylor expanded in x around 0 82.4%

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

   if -2300 < t < 1.40000000000000007e-305 or 2.9499999999999999e-210 < t < 6.59999999999999987e-88 or 2.49999999999999999e97 < t < 1.09999999999999996e110

   1. Initial program 98.6%

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

      1. associate-/l* 99.6%

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

      2. associate-/r/ 99.8%

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

   3. Applied egg-rr 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.6%

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

      3. un-div-inv 99.7%

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

      4. div-inv 99.7%

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

      5. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in a around 0 80.3%

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

   if 1.40000000000000007e-305 < t < 2.9499999999999999e-210 or 6.59999999999999987e-88 < t < 2.49999999999999999e97

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 85.4%

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

      1. associate-*r/ 85.3%

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

   4. Simplified 85.3%

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

   5. Taylor expanded in z around inf 75.0%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2300:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-305}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{-210}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{-88}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+97}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+110}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 4: 67.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ t_2 := a \cdot 120 + \frac{-60}{\frac{t}{x}}\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-210}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t))))
        (t_2 (+ (* a 120.0) (/ -60.0 (/ t x)))))
   (if (<= t -9.5e-30)
     t_2
     (if (<= t -3.2e-300)
       t_1
       (if (<= t 4.8e-210)
         (+ (* a 120.0) (* -60.0 (/ y z)))
         (if (<= t 6.4e-87) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double t_2 = (a * 120.0) + (-60.0 / (t / x));
	double tmp;
	if (t <= -9.5e-30) {
		tmp = t_2;
	} else if (t <= -3.2e-300) {
		tmp = t_1;
	} else if (t <= 4.8e-210) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (t <= 6.4e-87) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    t_2 = (a * 120.0d0) + ((-60.0d0) / (t / x))
    if (t <= (-9.5d-30)) then
        tmp = t_2
    else if (t <= (-3.2d-300)) then
        tmp = t_1
    else if (t <= 4.8d-210) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if (t <= 6.4d-87) then
        tmp = t_1
    else
        tmp = t_2
    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 t_2 = (a * 120.0) + (-60.0 / (t / x));
	double tmp;
	if (t <= -9.5e-30) {
		tmp = t_2;
	} else if (t <= -3.2e-300) {
		tmp = t_1;
	} else if (t <= 4.8e-210) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (t <= 6.4e-87) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	t_2 = (a * 120.0) + (-60.0 / (t / x))
	tmp = 0
	if t <= -9.5e-30:
		tmp = t_2
	elif t <= -3.2e-300:
		tmp = t_1
	elif t <= 4.8e-210:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif t <= 6.4e-87:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	t_2 = Float64(Float64(a * 120.0) + Float64(-60.0 / Float64(t / x)))
	tmp = 0.0
	if (t <= -9.5e-30)
		tmp = t_2;
	elseif (t <= -3.2e-300)
		tmp = t_1;
	elseif (t <= 4.8e-210)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (t <= 6.4e-87)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	t_2 = (a * 120.0) + (-60.0 / (t / x));
	tmp = 0.0;
	if (t <= -9.5e-30)
		tmp = t_2;
	elseif (t <= -3.2e-300)
		tmp = t_1;
	elseif (t <= 4.8e-210)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif (t <= 6.4e-87)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e-30], t$95$2, If[LessEqual[t, -3.2e-300], t$95$1, If[LessEqual[t, 4.8e-210], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.4e-87], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.49999999999999939e-30 or 6.39999999999999958e-87 < t

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0 87.5%

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

      1. associate-*r/ 86.9%

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

      2. associate-/l* 87.4%

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

   4. Simplified 87.4%

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

   5. Taylor expanded in x around inf 79.7%

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

   if -9.49999999999999939e-30 < t < -3.20000000000000021e-300 or 4.80000000000000008e-210 < t < 6.39999999999999958e-87

   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%

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

      2. associate-/r/ 99.8%

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

   3. Applied egg-rr 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.6%

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

      3. un-div-inv 99.7%

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

      4. div-inv 99.6%

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

      5. metadata-eval 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 83.7%

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

   if -3.20000000000000021e-300 < t < 4.80000000000000008e-210

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 89.4%

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

      1. associate-*r/ 89.2%

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

   4. Simplified 89.2%

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

   5. Taylor expanded in z around inf 85.6%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-30}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{t}{x}}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-300}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-210}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-87}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{t}{x}}\\ \end{array} \]

Alternative 5: 67.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;t \leq -9.6 \cdot 10^{-32}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-210}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= t -9.6e-32)
     (+ (* a 120.0) (/ (* x -60.0) t))
     (if (<= t -2.9e-306)
       t_1
       (if (<= t 4.6e-210)
         (+ (* a 120.0) (* -60.0 (/ y z)))
         (if (<= t 1.36e-87) t_1 (+ (* a 120.0) (/ -60.0 (/ t x)))))))))

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 <= -9.6e-32) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else if (t <= -2.9e-306) {
		tmp = t_1;
	} else if (t <= 4.6e-210) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (t <= 1.36e-87) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (-60.0 / (t / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    if (t <= (-9.6d-32)) then
        tmp = (a * 120.0d0) + ((x * (-60.0d0)) / t)
    else if (t <= (-2.9d-306)) then
        tmp = t_1
    else if (t <= 4.6d-210) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if (t <= 1.36d-87) then
        tmp = t_1
    else
        tmp = (a * 120.0d0) + ((-60.0d0) / (t / x))
    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 <= -9.6e-32) {
		tmp = (a * 120.0) + ((x * -60.0) / t);
	} else if (t <= -2.9e-306) {
		tmp = t_1;
	} else if (t <= 4.6e-210) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (t <= 1.36e-87) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (-60.0 / (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if t <= -9.6e-32:
		tmp = (a * 120.0) + ((x * -60.0) / t)
	elif t <= -2.9e-306:
		tmp = t_1
	elif t <= 4.6e-210:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif t <= 1.36e-87:
		tmp = t_1
	else:
		tmp = (a * 120.0) + (-60.0 / (t / x))
	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 (t <= -9.6e-32)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * -60.0) / t));
	elseif (t <= -2.9e-306)
		tmp = t_1;
	elseif (t <= 4.6e-210)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (t <= 1.36e-87)
		tmp = t_1;
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 / Float64(t / x)));
	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 <= -9.6e-32)
		tmp = (a * 120.0) + ((x * -60.0) / t);
	elseif (t <= -2.9e-306)
		tmp = t_1;
	elseif (t <= 4.6e-210)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif (t <= 1.36e-87)
		tmp = t_1;
	else
		tmp = (a * 120.0) + (-60.0 / (t / x));
	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[t, -9.6e-32], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.9e-306], t$95$1, If[LessEqual[t, 4.6e-210], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.36e-87], t$95$1, N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.6000000000000005e-32

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 83.4%

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

      1. associate-*r/ 83.4%

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

      2. associate-/l* 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in z around 0 76.7%

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

      1. associate-*r/ 76.7%

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

   7. Simplified 76.7%

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

   if -9.6000000000000005e-32 < t < -2.8999999999999999e-306 or 4.6e-210 < t < 1.3599999999999999e-87

   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%

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

      2. associate-/r/ 99.8%

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

   3. Applied egg-rr 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.6%

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

      3. un-div-inv 99.7%

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

      4. div-inv 99.6%

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

      5. metadata-eval 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 83.7%

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

   if -2.8999999999999999e-306 < t < 4.6e-210

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 89.4%

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

      1. associate-*r/ 89.2%

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

   4. Simplified 89.2%

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

   5. Taylor expanded in z around inf 85.6%

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

   if 1.3599999999999999e-87 < t

   1. Initial program 98.9%

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

   2. Taylor expanded in z around 0 87.5%

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

      1. associate-*r/ 86.4%

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

      2. associate-/l* 87.4%

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

   4. Simplified 87.4%

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

   5. Taylor expanded in x around inf 81.9%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{-32}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot -60}{t}\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-306}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-210}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-87}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{t}{x}}\\ \end{array} \]

Alternative 6: 80.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{+246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+167}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+223}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= x -2.9e+246)
     t_1
     (if (<= x 5.6e+167)
       (+ (* a 120.0) (* -60.0 (/ y (- z t))))
       (if (<= x 1.08e+223) (+ (* a 120.0) (/ -60.0 (/ t x))) 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 <= -2.9e+246) {
		tmp = t_1;
	} else if (x <= 5.6e+167) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else if (x <= 1.08e+223) {
		tmp = (a * 120.0) + (-60.0 / (t / x));
	} 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 <= (-2.9d+246)) then
        tmp = t_1
    else if (x <= 5.6d+167) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    else if (x <= 1.08d+223) then
        tmp = (a * 120.0d0) + ((-60.0d0) / (t / x))
    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 <= -2.9e+246) {
		tmp = t_1;
	} else if (x <= 5.6e+167) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else if (x <= 1.08e+223) {
		tmp = (a * 120.0) + (-60.0 / (t / x));
	} 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 <= -2.9e+246:
		tmp = t_1
	elif x <= 5.6e+167:
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	elif x <= 1.08e+223:
		tmp = (a * 120.0) + (-60.0 / (t / x))
	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 (x <= -2.9e+246)
		tmp = t_1;
	elseif (x <= 5.6e+167)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	elseif (x <= 1.08e+223)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 / Float64(t / x)));
	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 <= -2.9e+246)
		tmp = t_1;
	elseif (x <= 5.6e+167)
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	elseif (x <= 1.08e+223)
		tmp = (a * 120.0) + (-60.0 / (t / x));
	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[x, -2.9e+246], t$95$1, If[LessEqual[x, 5.6e+167], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.08e+223], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.90000000000000014e246 or 1.08000000000000005e223 < x

   1. Initial program 95.6%

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

      1. associate-/l* 99.6%

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

      2. associate-/r/ 99.6%

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

   3. Applied egg-rr 99.6%

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

      1. *-commutative 99.6%

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

      2. clear-num 99.5%

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

      3. un-div-inv 99.7%

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

      4. div-inv 99.6%

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

      5. metadata-eval 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 95.4%

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

   if -2.90000000000000014e246 < x < 5.5999999999999998e167

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 85.2%

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

   if 5.5999999999999998e167 < x < 1.08000000000000005e223

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. associate-/l* 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+246}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+167}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+223}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 7: 79.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+139} \lor \neg \left(x \leq 1.25 \cdot 10^{+166}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -5.2e+139) (not (<= x 1.25e+166)))
   (+ (* a 120.0) (* -60.0 (/ (- x y) t)))
   (+ (* a 120.0) (* -60.0 (/ y (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -5.2e+139) || !(x <= 1.25e+166)) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else {
		tmp = (a * 120.0) + (-60.0 * (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 <= (-5.2d+139)) .or. (.not. (x <= 1.25d+166))) then
        tmp = (a * 120.0d0) + ((-60.0d0) * ((x - y) / t))
    else
        tmp = (a * 120.0d0) + ((-60.0d0) * (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 <= -5.2e+139) || !(x <= 1.25e+166)) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -5.2e+139) or not (x <= 1.25e+166):
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t))
	else:
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -5.2e+139) || !(x <= 1.25e+166))
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(Float64(x - y) / t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -5.2e+139) || ~((x <= 1.25e+166)))
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	else
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -5.2e+139], N[Not[LessEqual[x, 1.25e+166]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.20000000000000044e139 or 1.25e166 < x

   1. Initial program 98.2%

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

   2. Taylor expanded in z around 0 74.6%

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

   if -5.20000000000000044e139 < x < 1.25e166

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 88.6%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+139} \lor \neg \left(x \leq 1.25 \cdot 10^{+166}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \end{array} \]

Alternative 8: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-38} \lor \neg \left(y \leq 5.4 \cdot 10^{+97}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.75e-38) (not (<= y 5.4e+97)))
   (+ (* a 120.0) (* -60.0 (/ y (- z t))))
   (+ (* a 120.0) (/ 60.0 (/ (- z t) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.75e-38) || !(y <= 5.4e+97)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.75d-38)) .or. (.not. (y <= 5.4d+97))) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    else
        tmp = (a * 120.0d0) + (60.0d0 / ((z - t) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.75e-38) || !(y <= 5.4e+97)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.75e-38) or not (y <= 5.4e+97):
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	else:
		tmp = (a * 120.0) + (60.0 / ((z - t) / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.75e-38) || !(y <= 5.4e+97))
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 / Float64(Float64(z - t) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.75e-38) || ~((y <= 5.4e+97)))
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	else
		tmp = (a * 120.0) + (60.0 / ((z - t) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.75e-38], N[Not[LessEqual[y, 5.4e+97]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7500000000000001e-38 or 5.39999999999999987e97 < y

   1. Initial program 99.0%

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

   2. Taylor expanded in x around 0 89.9%

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

   if -1.7500000000000001e-38 < y < 5.39999999999999987e97

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 94.9%

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

      1. associate-*r/ 94.9%

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

      2. associate-/l* 94.9%

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

   4. Simplified 94.9%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-38} \lor \neg \left(y \leq 5.4 \cdot 10^{+97}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{60}{\frac{z - t}{x}}\\ \end{array} \]

Alternative 9: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-79} \lor \neg \left(a \leq 7.2 \cdot 10^{-53}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2e-79) (not (<= a 7.2e-53)))
   (* a 120.0)
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2e-79) || !(a <= 7.2e-53)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2d-79)) .or. (.not. (a <= 7.2d-53))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2e-79) || !(a <= 7.2e-53)) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2e-79) or not (a <= 7.2e-53):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2e-79) || !(a <= 7.2e-53))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2e-79) || ~((a <= 7.2e-53)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2e-79], N[Not[LessEqual[a, 7.2e-53]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2e-79 or 7.1999999999999998e-53 < a

   1. Initial program 99.3%

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

   2. Taylor expanded in z around inf 71.0%

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

   if -2e-79 < a < 7.1999999999999998e-53

   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* 99.6%

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

      2. associate-/r/ 99.7%

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

   3. Applied egg-rr 99.7%

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

      1. *-commutative 99.7%

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

      2. clear-num 99.6%

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

      3. un-div-inv 99.6%

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

      4. div-inv 99.6%

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

      5. metadata-eval 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in a around 0 80.2%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-79} \lor \neg \left(a \leq 7.2 \cdot 10^{-53}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 10: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-/l* 99.8%

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

   2. associate-/r/ 99.8%

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

3. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

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

Alternative 11: 52.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+246} \lor \neg \left(x \leq 1.1 \cdot 10^{+224}\right):\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -7e+246) (not (<= x 1.1e+224))) (* -60.0 (/ x t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -7e+246) || !(x <= 1.1e+224)) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-7d+246)) .or. (.not. (x <= 1.1d+224))) then
        tmp = (-60.0d0) * (x / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -7e+246) || !(x <= 1.1e+224)) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -7e+246) or not (x <= 1.1e+224):
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -7e+246) || !(x <= 1.1e+224))
		tmp = Float64(-60.0 * Float64(x / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -7e+246) || ~((x <= 1.1e+224)))
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -7e+246], N[Not[LessEqual[x, 1.1e+224]], $MachinePrecision]], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.99999999999999951e246 or 1.1e224 < x

   1. Initial program 95.6%

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

   2. Taylor expanded in z around 0 73.4%

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

   3. Taylor expanded in x around inf 66.8%

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

   if -6.99999999999999951e246 < x < 1.1e224

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 56.7%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{+246} \lor \neg \left(x \leq 1.1 \cdot 10^{+224}\right):\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 12: 51.1% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

2. Taylor expanded in z around inf 52.5%

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

3. Final simplification 52.5%

   \[\leadsto a \cdot 120 \]

Developer target: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023310 
(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)))