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

Percentage Accurate: 99.4% → 99.8%

Time: 13.3s

Alternatives: 15

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 99.5%

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

   1. +-commutative 99.5%

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

   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: 74.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot 60}{z - t}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+79}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-96}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;t_1 \leq 0.2:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) 60.0) (- z t))))
   (if (<= t_1 -2e+79)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= t_1 -2e-96)
       (+ (* a 120.0) (* -60.0 (/ y z)))
       (if (<= t_1 0.2) (* a 120.0) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -2e+79) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t_1 <= -2e-96) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (t_1 <= 0.2) {
		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 = ((x - y) * 60.0d0) / (z - t)
    if (t_1 <= (-2d+79)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (t_1 <= (-2d-96)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    else if (t_1 <= 0.2d0) 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 = ((x - y) * 60.0) / (z - t);
	double tmp;
	if (t_1 <= -2e+79) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (t_1 <= -2e-96) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else if (t_1 <= 0.2) {
		tmp = a * 120.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((x - y) * 60.0) / (z - t)
	tmp = 0
	if t_1 <= -2e+79:
		tmp = 60.0 * ((x - y) / (z - t))
	elif t_1 <= -2e-96:
		tmp = (a * 120.0) + (-60.0 * (y / z))
	elif t_1 <= 0.2:
		tmp = a * 120.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x - y) * 60.0) / Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+79)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (t_1 <= -2e-96)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	elseif (t_1 <= 0.2)
		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 = ((x - y) * 60.0) / (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+79)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (t_1 <= -2e-96)
		tmp = (a * 120.0) + (-60.0 * (y / z));
	elseif (t_1 <= 0.2)
		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[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+79], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-96], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.2], 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)) < -1.99999999999999993e79

   1. Initial program 97.9%

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

      1. *-commutative 97.9%

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

      2. associate-/l* 99.6%

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

      3. div-inv 99.6%

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

      4. *-un-lft-identity 99.6%

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

      5. times-frac 97.7%

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

      6. metadata-eval 97.7%

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

   3. Applied egg-rr 97.7%

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

   4. Taylor expanded in a around 0 80.1%

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

   if -1.99999999999999993e79 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < -1.9999999999999998e-96

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf 71.3%

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

   3. Taylor expanded in x around 0 72.0%

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

   if -1.9999999999999998e-96 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t)) < 0.20000000000000001

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 85.4%

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

   if 0.20000000000000001 < (/.f64 (*.f64 60 (-.f64 x y)) (-.f64 z t))

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 99.8%

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

      3. div-inv 99.8%

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

      4. *-un-lft-identity 99.8%

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

      5. times-frac 99.6%

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

      6. metadata-eval 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in a around 0 76.1%

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

      1. expm1-log1p-u 71.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)\right)} \]

      2. expm1-udef 71.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)} - 1} \]

   6. Applied egg-rr 71.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)} - 1} \]
   7. Step-by-step derivation

      1. expm1-def 71.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(60 \cdot \frac{x - y}{z - t}\right)\right)} \]

      2. expm1-log1p 76.1%

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

      3. associate-*r/ 76.2%

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

   8. Simplified 76.2%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{+79}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq -2 \cdot 10^{-96}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\left(x - y\right) \cdot 60}{z - t} \leq 0.2:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot 60}{z - t}\\ \end{array} \]

Alternative 3: 76.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+73}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;z \leq -0.000175 \lor \neg \left(z \leq 3.6 \cdot 10^{-72}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* -60.0 (/ y z)))))
   (if (<= z -2.1e+194)
     t_1
     (if (<= z -6e+73)
       (+ (* a 120.0) (/ x (* z 0.016666666666666666)))
       (if (or (<= z -0.000175) (not (<= z 3.6e-72)))
         t_1
         (+ (* a 120.0) (* -60.0 (/ (- x y) t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (-60.0 * (y / z));
	double tmp;
	if (z <= -2.1e+194) {
		tmp = t_1;
	} else if (z <= -6e+73) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if ((z <= -0.000175) || !(z <= 3.6e-72)) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (a * 120.0d0) + ((-60.0d0) * (y / z))
    if (z <= (-2.1d+194)) then
        tmp = t_1
    else if (z <= (-6d+73)) then
        tmp = (a * 120.0d0) + (x / (z * 0.016666666666666666d0))
    else if ((z <= (-0.000175d0)) .or. (.not. (z <= 3.6d-72))) then
        tmp = t_1
    else
        tmp = (a * 120.0d0) + ((-60.0d0) * ((x - y) / 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 = (a * 120.0) + (-60.0 * (y / z));
	double tmp;
	if (z <= -2.1e+194) {
		tmp = t_1;
	} else if (z <= -6e+73) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if ((z <= -0.000175) || !(z <= 3.6e-72)) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (-60.0 * (y / z))
	tmp = 0
	if z <= -2.1e+194:
		tmp = t_1
	elif z <= -6e+73:
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666))
	elif (z <= -0.000175) or not (z <= 3.6e-72):
		tmp = t_1
	else:
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)))
	tmp = 0.0
	if (z <= -2.1e+194)
		tmp = t_1;
	elseif (z <= -6e+73)
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(z * 0.016666666666666666)));
	elseif ((z <= -0.000175) || !(z <= 3.6e-72))
		tmp = t_1;
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (-60.0 * (y / z));
	tmp = 0.0;
	if (z <= -2.1e+194)
		tmp = t_1;
	elseif (z <= -6e+73)
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	elseif ((z <= -0.000175) || ~((z <= 3.6e-72)))
		tmp = t_1;
	else
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+194], t$95$1, If[LessEqual[z, -6e+73], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -0.000175], N[Not[LessEqual[z, 3.6e-72]], $MachinePrecision]], t$95$1, N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.10000000000000016e194 or -6.00000000000000021e73 < z < -1.74999999999999998e-4 or 3.6e-72 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 87.8%

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

   3. Taylor expanded in x around 0 80.2%

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

   if -2.10000000000000016e194 < z < -6.00000000000000021e73

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 88.5%

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

   3. Taylor expanded in x around inf 87.3%

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

      1. associate-*r/ 87.4%

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

      2. *-commutative 87.4%

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

   5. Simplified 87.4%

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

   6. Taylor expanded in x around 0 87.3%

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

      1. *-commutative 87.3%

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

      2. metadata-eval 87.3%

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

      3. times-frac 87.4%

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

      4. *-rgt-identity 87.4%

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

   8. Simplified 87.4%

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

   if -1.74999999999999998e-4 < z < 3.6e-72

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 89.2%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+194}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+73}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;z \leq -0.000175 \lor \neg \left(z \leq 3.6 \cdot 10^{-72}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 4: 66.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+73}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-8} \lor \neg \left(z \leq 1.85 \cdot 10^{-72}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* -60.0 (/ y z)))))
   (if (<= z -4.2e+193)
     t_1
     (if (<= z -2.9e+73)
       (+ (* a 120.0) (/ x (* z 0.016666666666666666)))
       (if (or (<= z -6.6e-8) (not (<= z 1.85e-72)))
         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 = (a * 120.0) + (-60.0 * (y / z));
	double tmp;
	if (z <= -4.2e+193) {
		tmp = t_1;
	} else if (z <= -2.9e+73) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if ((z <= -6.6e-8) || !(z <= 1.85e-72)) {
		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 = (a * 120.0d0) + ((-60.0d0) * (y / z))
    if (z <= (-4.2d+193)) then
        tmp = t_1
    else if (z <= (-2.9d+73)) then
        tmp = (a * 120.0d0) + (x / (z * 0.016666666666666666d0))
    else if ((z <= (-6.6d-8)) .or. (.not. (z <= 1.85d-72))) 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 = (a * 120.0) + (-60.0 * (y / z));
	double tmp;
	if (z <= -4.2e+193) {
		tmp = t_1;
	} else if (z <= -2.9e+73) {
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	} else if ((z <= -6.6e-8) || !(z <= 1.85e-72)) {
		tmp = t_1;
	} else {
		tmp = (a * 120.0) + (-60.0 / (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (-60.0 * (y / z))
	tmp = 0
	if z <= -4.2e+193:
		tmp = t_1
	elif z <= -2.9e+73:
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666))
	elif (z <= -6.6e-8) or not (z <= 1.85e-72):
		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(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)))
	tmp = 0.0
	if (z <= -4.2e+193)
		tmp = t_1;
	elseif (z <= -2.9e+73)
		tmp = Float64(Float64(a * 120.0) + Float64(x / Float64(z * 0.016666666666666666)));
	elseif ((z <= -6.6e-8) || !(z <= 1.85e-72))
		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 = (a * 120.0) + (-60.0 * (y / z));
	tmp = 0.0;
	if (z <= -4.2e+193)
		tmp = t_1;
	elseif (z <= -2.9e+73)
		tmp = (a * 120.0) + (x / (z * 0.016666666666666666));
	elseif ((z <= -6.6e-8) || ~((z <= 1.85e-72)))
		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[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+193], t$95$1, If[LessEqual[z, -2.9e+73], N[(N[(a * 120.0), $MachinePrecision] + N[(x / N[(z * 0.016666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -6.6e-8], N[Not[LessEqual[z, 1.85e-72]], $MachinePrecision]], t$95$1, N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2e193 or -2.9000000000000002e73 < z < -6.59999999999999954e-8 or 1.8499999999999999e-72 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 87.8%

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

   3. Taylor expanded in x around 0 80.2%

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

   if -4.2e193 < z < -2.9000000000000002e73

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 88.5%

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

   3. Taylor expanded in x around inf 87.3%

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

      1. associate-*r/ 87.4%

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

      2. *-commutative 87.4%

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

   5. Simplified 87.4%

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

   6. Taylor expanded in x around 0 87.3%

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

      1. *-commutative 87.3%

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

      2. metadata-eval 87.3%

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

      3. times-frac 87.4%

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

      4. *-rgt-identity 87.4%

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

   8. Simplified 87.4%

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

   if -6.59999999999999954e-8 < z < 1.8499999999999999e-72

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 89.2%

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

      1. associate-*r/ 88.3%

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

      2. associate-/l* 89.2%

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

   4. Simplified 89.2%

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

   5. Taylor expanded in x around inf 73.9%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+193}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+73}:\\ \;\;\;\;a \cdot 120 + \frac{x}{z \cdot 0.016666666666666666}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-8} \lor \neg \left(z \leq 1.85 \cdot 10^{-72}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{t}{x}}\\ \end{array} \]

Alternative 5: 85.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-85}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+62}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ (* a 120.0) (* 60.0 (/ (- x y) z)))))
   (if (<= z -2.4e-8)
     t_1
     (if (<= z 2.9e-85)
       (+ (* a 120.0) (* -60.0 (/ (- x y) t)))
       (if (<= z 2.85e+62) (+ (* a 120.0) (/ (* y -60.0) (- z t))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (a * 120.0) + (60.0 * ((x - y) / z));
	double tmp;
	if (z <= -2.4e-8) {
		tmp = t_1;
	} else if (z <= 2.9e-85) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else if (z <= 2.85e+62) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - 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 = (a * 120.0d0) + (60.0d0 * ((x - y) / z))
    if (z <= (-2.4d-8)) then
        tmp = t_1
    else if (z <= 2.9d-85) then
        tmp = (a * 120.0d0) + ((-60.0d0) * ((x - y) / t))
    else if (z <= 2.85d+62) then
        tmp = (a * 120.0d0) + ((y * (-60.0d0)) / (z - 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 = (a * 120.0) + (60.0 * ((x - y) / z));
	double tmp;
	if (z <= -2.4e-8) {
		tmp = t_1;
	} else if (z <= 2.9e-85) {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	} else if (z <= 2.85e+62) {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (a * 120.0) + (60.0 * ((x - y) / z))
	tmp = 0
	if z <= -2.4e-8:
		tmp = t_1
	elif z <= 2.9e-85:
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t))
	elif z <= 2.85e+62:
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(x - y) / z)))
	tmp = 0.0
	if (z <= -2.4e-8)
		tmp = t_1;
	elseif (z <= 2.9e-85)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(Float64(x - y) / t)));
	elseif (z <= 2.85e+62)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(y * -60.0) / Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (a * 120.0) + (60.0 * ((x - y) / z));
	tmp = 0.0;
	if (z <= -2.4e-8)
		tmp = t_1;
	elseif (z <= 2.9e-85)
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	elseif (z <= 2.85e+62)
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e-8], t$95$1, If[LessEqual[z, 2.9e-85], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.85e+62], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.39999999999999998e-8 or 2.84999999999999999e62 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 92.3%

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

   if -2.39999999999999998e-8 < z < 2.9000000000000002e-85

   1. Initial program 98.9%

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

   2. Taylor expanded in z around 0 89.1%

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

   if 2.9000000000000002e-85 < z < 2.84999999999999999e62

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 89.2%

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

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-8}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-85}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+62}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \end{array} \]

Alternative 6: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-7} \lor \neg \left(a \cdot 120 \leq 4 \cdot 10^{+18}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -1e-7) (not (<= (* a 120.0) 4e+18)))
   (* 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) <= -1e-7) || !((a * 120.0) <= 4e+18)) {
		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) <= (-1d-7)) .or. (.not. ((a * 120.0d0) <= 4d+18))) 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) <= -1e-7) || !((a * 120.0) <= 4e+18)) {
		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) <= -1e-7) or not ((a * 120.0) <= 4e+18):
		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) <= -1e-7) || !(Float64(a * 120.0) <= 4e+18))
		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) <= -1e-7) || ~(((a * 120.0) <= 4e+18)))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -1e-7], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 4e+18]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -9.9999999999999995e-8 or 4e18 < (*.f64 a 120)

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 78.2%

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

   if -9.9999999999999995e-8 < (*.f64 a 120) < 4e18

   1. Initial program 99.0%

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

      1. *-commutative 99.0%

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

      2. associate-/l* 99.7%

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

      3. div-inv 99.6%

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

      4. *-un-lft-identity 99.6%

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

      5. times-frac 98.8%

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

      6. metadata-eval 98.8%

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

   3. Applied egg-rr 98.8%

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

   4. Taylor expanded in a around 0 70.5%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{-7} \lor \neg \left(a \cdot 120 \leq 4 \cdot 10^{+18}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 7: 84.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-7} \lor \neg \left(z \leq 1.9 \cdot 10^{-64}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.8e-7) (not (<= z 1.9e-64)))
   (+ (* a 120.0) (* 60.0 (/ (- x y) z)))
   (+ (* a 120.0) (* -60.0 (/ (- x y) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.8e-7) || !(z <= 1.9e-64)) {
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	} else {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.8d-7)) .or. (.not. (z <= 1.9d-64))) then
        tmp = (a * 120.0d0) + (60.0d0 * ((x - y) / z))
    else
        tmp = (a * 120.0d0) + ((-60.0d0) * ((x - y) / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.8e-7) || !(z <= 1.9e-64)) {
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	} else {
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.8e-7) or not (z <= 1.9e-64):
		tmp = (a * 120.0) + (60.0 * ((x - y) / z))
	else:
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.8e-7) || !(z <= 1.9e-64))
		tmp = Float64(Float64(a * 120.0) + Float64(60.0 * Float64(Float64(x - y) / z)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(Float64(x - y) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.8e-7) || ~((z <= 1.9e-64)))
		tmp = (a * 120.0) + (60.0 * ((x - y) / z));
	else
		tmp = (a * 120.0) + (-60.0 * ((x - y) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.8e-7], N[Not[LessEqual[z, 1.9e-64]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(60.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.79999999999999957e-7 or 1.9000000000000001e-64 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 88.5%

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

   if -4.79999999999999957e-7 < z < 1.9000000000000001e-64

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 89.4%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-7} \lor \neg \left(z \leq 1.9 \cdot 10^{-64}\right):\\ \;\;\;\;a \cdot 120 + 60 \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 8: 89.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -440 \lor \neg \left(x \leq 3350000\right):\\ \;\;\;\;a \cdot 120 + \frac{x \cdot 60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -440.0) (not (<= x 3350000.0)))
   (+ (* a 120.0) (/ (* x 60.0) (- z t)))
   (+ (* a 120.0) (/ (* y -60.0) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -440.0) || !(x <= 3350000.0)) {
		tmp = (a * 120.0) + ((x * 60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + ((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 ((x <= (-440.0d0)) .or. (.not. (x <= 3350000.0d0))) then
        tmp = (a * 120.0d0) + ((x * 60.0d0) / (z - t))
    else
        tmp = (a * 120.0d0) + ((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 ((x <= -440.0) || !(x <= 3350000.0)) {
		tmp = (a * 120.0) + ((x * 60.0) / (z - t));
	} else {
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -440.0) or not (x <= 3350000.0):
		tmp = (a * 120.0) + ((x * 60.0) / (z - t))
	else:
		tmp = (a * 120.0) + ((y * -60.0) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -440.0) || !(x <= 3350000.0))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * 60.0) / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + 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 ((x <= -440.0) || ~((x <= 3350000.0)))
		tmp = (a * 120.0) + ((x * 60.0) / (z - t));
	else
		tmp = (a * 120.0) + ((y * -60.0) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -440.0], N[Not[LessEqual[x, 3350000.0]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(y * -60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -440 or 3.35e6 < x

   1. Initial program 99.0%

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

   2. Taylor expanded in x around inf 87.1%

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

      1. associate-*r/ 86.4%

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

   4. Simplified 86.4%

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

   if -440 < x < 3.35e6

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 98.0%

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

      1. associate-*r/ 98.0%

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

   4. Simplified 98.0%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -440 \lor \neg \left(x \leq 3350000\right):\\ \;\;\;\;a \cdot 120 + \frac{x \cdot 60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \]

Alternative 9: 67.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-7} \lor \neg \left(z \leq 3.6 \cdot 10^{-72}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.2e-7) (not (<= z 3.6e-72)))
   (+ (* a 120.0) (* -60.0 (/ y z)))
   (+ (* a 120.0) (/ -60.0 (/ t x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e-7) || !(z <= 3.6e-72)) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} 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) :: tmp
    if ((z <= (-1.2d-7)) .or. (.not. (z <= 3.6d-72))) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / z))
    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 tmp;
	if ((z <= -1.2e-7) || !(z <= 3.6e-72)) {
		tmp = (a * 120.0) + (-60.0 * (y / z));
	} else {
		tmp = (a * 120.0) + (-60.0 / (t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.2e-7) or not (z <= 3.6e-72):
		tmp = (a * 120.0) + (-60.0 * (y / z))
	else:
		tmp = (a * 120.0) + (-60.0 / (t / x))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.2e-7) || !(z <= 3.6e-72))
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / z)));
	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)
	tmp = 0.0;
	if ((z <= -1.2e-7) || ~((z <= 3.6e-72)))
		tmp = (a * 120.0) + (-60.0 * (y / z));
	else
		tmp = (a * 120.0) + (-60.0 / (t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.2e-7], N[Not[LessEqual[z, 3.6e-72]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.19999999999999989e-7 or 3.6e-72 < z

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 87.9%

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

   3. Taylor expanded in x around 0 77.5%

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

   if -1.19999999999999989e-7 < z < 3.6e-72

   1. Initial program 99.0%

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

   2. Taylor expanded in z around 0 89.2%

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

      1. associate-*r/ 88.3%

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

      2. associate-/l* 89.2%

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

   4. Simplified 89.2%

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

   5. Taylor expanded in x around inf 73.9%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-7} \lor \neg \left(z \leq 3.6 \cdot 10^{-72}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{-60}{\frac{t}{x}}\\ \end{array} \]

Alternative 10: 99.4% accurate, 1.0× speedup

Math

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

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(Float64(x - y) * 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[(N[(x - y), $MachinePrecision] * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

2. Final simplification 99.5%

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

Alternative 11: 52.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+256} \lor \neg \left(x \leq 1.75 \cdot 10^{+102}\right):\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.3e+256) (not (<= x 1.75e+102)))
   (* -60.0 (/ (- x y) t))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.3e+256) || !(x <= 1.75e+102)) {
		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 ((x <= (-2.3d+256)) .or. (.not. (x <= 1.75d+102))) 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 ((x <= -2.3e+256) || !(x <= 1.75e+102)) {
		tmp = -60.0 * ((x - y) / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.3e+256) or not (x <= 1.75e+102):
		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 ((x <= -2.3e+256) || !(x <= 1.75e+102))
		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 ((x <= -2.3e+256) || ~((x <= 1.75e+102)))
		tmp = -60.0 * ((x - y) / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.3e+256], N[Not[LessEqual[x, 1.75e+102]], $MachinePrecision]], 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 x < -2.2999999999999999e256 or 1.75000000000000005e102 < x

   1. Initial program 97.8%

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

      1. *-commutative 97.8%

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

      2. associate-/l* 99.7%

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

      3. div-inv 99.6%

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

      4. *-un-lft-identity 99.6%

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

      5. times-frac 97.7%

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

      6. metadata-eval 97.7%

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

   3. Applied egg-rr 97.7%

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

   4. Taylor expanded in a around 0 75.7%

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

   5. Taylor expanded in z around 0 51.0%

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

   if -2.2999999999999999e256 < x < 1.75000000000000005e102

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 62.7%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+256} \lor \neg \left(x \leq 1.75 \cdot 10^{+102}\right):\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 12: 57.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+242} \lor \neg \left(x \leq 3.6 \cdot 10^{+139}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -3.6e+242) (not (<= x 3.6e+139)))
   (* 60.0 (/ x (- z t)))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3.6e+242) || !(x <= 3.6e+139)) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x <= (-3.6d+242)) .or. (.not. (x <= 3.6d+139))) then
        tmp = 60.0d0 * (x / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -3.6e+242) || !(x <= 3.6e+139)) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -3.6e+242) or not (x <= 3.6e+139):
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -3.6e+242) || !(x <= 3.6e+139))
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -3.6e+242) || ~((x <= 3.6e+139)))
		tmp = 60.0 * (x / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -3.6e+242], N[Not[LessEqual[x, 3.6e+139]], $MachinePrecision]], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.59999999999999995e242 or 3.59999999999999985e139 < x

   1. Initial program 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-/l* 99.7%

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

      3. div-inv 99.6%

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

      4. *-un-lft-identity 99.6%

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

      5. times-frac 97.4%

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

      6. metadata-eval 97.4%

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

   3. Applied egg-rr 97.4%

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

   4. Taylor expanded in a around 0 79.4%

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

   5. Taylor expanded in x around inf 72.7%

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

   if -3.59999999999999995e242 < x < 3.59999999999999985e139

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 62.3%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+242} \lor \neg \left(x \leq 3.6 \cdot 10^{+139}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 13: 51.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+129}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.6e+129) (* -60.0 (/ y z)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.6e+129) {
		tmp = -60.0 * (y / 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 (y <= (-2.6d+129)) then
        tmp = (-60.0d0) * (y / 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 (y <= -2.6e+129) {
		tmp = -60.0 * (y / z);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.6e+129:
		tmp = -60.0 * (y / z)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.6e+129)
		tmp = Float64(-60.0 * Float64(y / 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 (y <= -2.6e+129)
		tmp = -60.0 * (y / z);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.6e+129], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.60000000000000012e129

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 99.6%

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

      3. div-inv 99.6%

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

      4. *-un-lft-identity 99.6%

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

      5. times-frac 99.6%

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

      6. metadata-eval 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in a around 0 73.5%

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

   5. Taylor expanded in x around 0 55.5%

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

      1. associate-*r/ 55.6%

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

      2. associate-/l* 55.5%

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

   7. Simplified 55.5%

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

   8. Taylor expanded in z around inf 43.6%

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

   if -2.60000000000000012e129 < y

   1. Initial program 99.4%

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

   2. Taylor expanded in z around inf 60.3%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+129}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 14: 51.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+129}:\\ \;\;\;\;\frac{y}{\frac{z}{-60}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.6e+129) (/ y (/ z -60.0)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.6e+129) {
		tmp = y / (z / -60.0);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.6d+129)) then
        tmp = y / (z / (-60.0d0))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.6e+129) {
		tmp = y / (z / -60.0);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.6e+129:
		tmp = y / (z / -60.0)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.6e+129)
		tmp = Float64(y / Float64(z / -60.0));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.6e+129)
		tmp = y / (z / -60.0);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.6e+129], N[(y / N[(z / -60.0), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.60000000000000012e129

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 99.6%

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

      3. div-inv 99.6%

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

      4. *-un-lft-identity 99.6%

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

      5. times-frac 99.6%

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

      6. metadata-eval 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in a around 0 73.5%

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

   5. Taylor expanded in x around 0 55.5%

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

      1. associate-*r/ 55.6%

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

      2. associate-/l* 55.5%

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

   7. Simplified 55.5%

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

   8. Taylor expanded in z around inf 43.6%

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

      1. associate-*r/ 43.6%

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

      2. *-commutative 43.6%

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

      3. associate-/l* 43.6%

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

   10. Simplified 43.6%

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

   if -2.60000000000000012e129 < y

   1. Initial program 99.4%

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

   2. Taylor expanded in z around inf 60.3%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+129}:\\ \;\;\;\;\frac{y}{\frac{z}{-60}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 15: 51.0% 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 99.5%

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

2. Taylor expanded in z around inf 54.6%

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

3. Final simplification 54.6%

   \[\leadsto a \cdot 120 \]

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 2023309 
(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)))