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

Percentage Accurate: 99.3% → 99.8%

Time: 14.2s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. *-commutative 99.8%

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

   2. associate-/l* 99.8%

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

4. Applied egg-rr 99.8%

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

Alternative 2: 72.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+61}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -1.5 \cdot 10^{-80}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+46}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -5e+61)
   (+ (* a 120.0) (* y (/ -60.0 z)))
   (if (<= (* a 120.0) -1.5e-80)
     (+ (* a 120.0) (* -60.0 (/ x t)))
     (if (<= (* a 120.0) 1e+46) (* (- x y) (/ 60.0 (- z t))) (* a 120.0)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e+61) {
		tmp = (a * 120.0) + (y * (-60.0 / z));
	} else if ((a * 120.0) <= -1.5e-80) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else if ((a * 120.0) <= 1e+46) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a * 120.0d0) <= (-5d+61)) then
        tmp = (a * 120.0d0) + (y * ((-60.0d0) / z))
    else if ((a * 120.0d0) <= (-1.5d-80)) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (x / t))
    else if ((a * 120.0d0) <= 1d+46) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -5e+61) {
		tmp = (a * 120.0) + (y * (-60.0 / z));
	} else if ((a * 120.0) <= -1.5e-80) {
		tmp = (a * 120.0) + (-60.0 * (x / t));
	} else if ((a * 120.0) <= 1e+46) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -5e+61:
		tmp = (a * 120.0) + (y * (-60.0 / z))
	elif (a * 120.0) <= -1.5e-80:
		tmp = (a * 120.0) + (-60.0 * (x / t))
	elif (a * 120.0) <= 1e+46:
		tmp = (x - y) * (60.0 / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e+61)
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(-60.0 / z)));
	elseif (Float64(a * 120.0) <= -1.5e-80)
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(x / t)));
	elseif (Float64(a * 120.0) <= 1e+46)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -5e+61)
		tmp = (a * 120.0) + (y * (-60.0 / z));
	elseif ((a * 120.0) <= -1.5e-80)
		tmp = (a * 120.0) + (-60.0 * (x / t));
	elseif ((a * 120.0) <= 1e+46)
		tmp = (x - y) * (60.0 / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+61], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(-60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -1.5e-80], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+46], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -5.00000000000000018e61

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 93.4%

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

      1. associate-*r/ 93.3%

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

      2. *-commutative 93.3%

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

      3. *-lft-identity 93.3%

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

      4. times-frac 93.3%

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

      5. /-rgt-identity 93.3%

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

      6. metadata-eval 93.3%

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

      7. distribute-neg-frac 93.3%

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

      8. distribute-neg-frac2 93.3%

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

      9. neg-sub0 93.3%

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

      10. sub-neg 93.3%

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

      11. +-commutative 93.3%

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

      12. associate--r+ 93.3%

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

      13. neg-sub0 93.3%

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

      14. remove-double-neg 93.3%

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

   7. Simplified 93.3%

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

   8. Taylor expanded in t around 0 90.3%

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

   if -5.00000000000000018e61 < (*.f64 a #s(literal 120 binary64)) < -1.50000000000000004e-80

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 87.2%

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

      1. associate-*r/ 87.2%

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

   7. Simplified 87.2%

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

   8. Taylor expanded in z around 0 65.4%

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

   if -1.50000000000000004e-80 < (*.f64 a #s(literal 120 binary64)) < 9.9999999999999999e45

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. 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* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in a around 0 79.1%

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

      1. associate-*r/ 79.0%

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

   7. Simplified 79.0%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]
   8. 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* 99.8%

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

   9. Applied egg-rr 79.1%

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

   if 9.9999999999999999e45 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 85.0%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+61}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq -1.5 \cdot 10^{-80}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{+46}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1.5 \cdot 10^{-80} \lor \neg \left(a \cdot 120 \leq 10^{+46}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -1.5e-80) (not (<= (* a 120.0) 1e+46)))
   (* a 120.0)
   (* (- x y) (/ 60.0 (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -1.5e-80) || !((a * 120.0) <= 1e+46)) {
		tmp = a * 120.0;
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-1.5d-80)) .or. (.not. ((a * 120.0d0) <= 1d+46))) then
        tmp = a * 120.0d0
    else
        tmp = (x - y) * (60.0d0 / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -1.5e-80) || !((a * 120.0) <= 1e+46)) {
		tmp = a * 120.0;
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -1.5e-80) or not ((a * 120.0) <= 1e+46):
		tmp = a * 120.0
	else:
		tmp = (x - y) * (60.0 / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -1.5e-80) || !(Float64(a * 120.0) <= 1e+46))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -1.5e-80) || ~(((a * 120.0) <= 1e+46)))
		tmp = a * 120.0;
	else
		tmp = (x - y) * (60.0 / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -1.5e-80], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+46]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.50000000000000004e-80 or 9.9999999999999999e45 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 77.4%

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

   if -1.50000000000000004e-80 < (*.f64 a #s(literal 120 binary64)) < 9.9999999999999999e45

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Add Preprocessing
   3. 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* 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in a around 0 79.1%

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

      1. associate-*r/ 79.0%

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

   7. Simplified 79.0%

      \[\leadsto \color{blue}{\frac{60 \cdot \left(x - y\right)}{z - t}} \]
   8. 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* 99.8%

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

   9. Applied egg-rr 79.1%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1.5 \cdot 10^{-80} \lor \neg \left(a \cdot 120 \leq 10^{+46}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+32} \lor \neg \left(y \leq 3.5 \cdot 10^{-41}\right):\\ \;\;\;\;a \cdot 120 + y \cdot \frac{60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.4e+32) (not (<= y 3.5e-41)))
   (+ (* a 120.0) (* y (/ 60.0 (- t z))))
   (+ (* a 120.0) (* x (/ 60.0 (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.4e+32) || !(y <= 3.5e-41)) {
		tmp = (a * 120.0) + (y * (60.0 / (t - z)));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.4d+32)) .or. (.not. (y <= 3.5d-41))) then
        tmp = (a * 120.0d0) + (y * (60.0d0 / (t - z)))
    else
        tmp = (a * 120.0d0) + (x * (60.0d0 / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.4e+32) || !(y <= 3.5e-41)) {
		tmp = (a * 120.0) + (y * (60.0 / (t - z)));
	} else {
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.4e+32) or not (y <= 3.5e-41):
		tmp = (a * 120.0) + (y * (60.0 / (t - z)))
	else:
		tmp = (a * 120.0) + (x * (60.0 / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.4e+32) || !(y <= 3.5e-41))
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(60.0 / Float64(t - z))));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(x * Float64(60.0 / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.4e+32) || ~((y <= 3.5e-41)))
		tmp = (a * 120.0) + (y * (60.0 / (t - z)));
	else
		tmp = (a * 120.0) + (x * (60.0 / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.4e+32], N[Not[LessEqual[y, 3.5e-41]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(x * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.39999999999999991e32 or 3.5e-41 < y

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 88.7%

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

      1. associate-*r/ 88.7%

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

      2. *-commutative 88.7%

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

      3. *-lft-identity 88.7%

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

      4. times-frac 88.7%

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

      5. /-rgt-identity 88.7%

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

      6. metadata-eval 88.7%

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

      7. distribute-neg-frac 88.7%

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

      8. distribute-neg-frac2 88.7%

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

      9. neg-sub0 88.7%

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

      10. sub-neg 88.7%

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

      11. +-commutative 88.7%

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

      12. associate--r+ 88.7%

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

      13. neg-sub0 88.7%

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

      14. remove-double-neg 88.7%

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

   7. Simplified 88.7%

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

   if -2.39999999999999991e32 < y < 3.5e-41

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf 98.1%

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

      1. associate-*r/ 98.1%

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

      2. *-commutative 98.1%

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

      3. associate-*r/ 98.2%

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

   7. Simplified 98.2%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+32} \lor \neg \left(y \leq 3.5 \cdot 10^{-41}\right):\\ \;\;\;\;a \cdot 120 + y \cdot \frac{60}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{60}{z - t}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+181}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+143}:\\ \;\;\;\;a \cdot 120 + x \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ 60.0 (- z t))))
   (if (<= y -2.5e+181)
     (* 60.0 (/ (- x y) (- z t)))
     (if (<= y 1.12e+143) (+ (* a 120.0) (* x t_1)) (* (- x y) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 / (z - t);
	double tmp;
	if (y <= -2.5e+181) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (y <= 1.12e+143) {
		tmp = (a * 120.0) + (x * t_1);
	} else {
		tmp = (x - y) * 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 / (z - t)
    if (y <= (-2.5d+181)) then
        tmp = 60.0d0 * ((x - y) / (z - t))
    else if (y <= 1.12d+143) then
        tmp = (a * 120.0d0) + (x * t_1)
    else
        tmp = (x - y) * 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 / (z - t);
	double tmp;
	if (y <= -2.5e+181) {
		tmp = 60.0 * ((x - y) / (z - t));
	} else if (y <= 1.12e+143) {
		tmp = (a * 120.0) + (x * t_1);
	} else {
		tmp = (x - y) * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 / (z - t)
	tmp = 0
	if y <= -2.5e+181:
		tmp = 60.0 * ((x - y) / (z - t))
	elif y <= 1.12e+143:
		tmp = (a * 120.0) + (x * t_1)
	else:
		tmp = (x - y) * t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 / Float64(z - t))
	tmp = 0.0
	if (y <= -2.5e+181)
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	elseif (y <= 1.12e+143)
		tmp = Float64(Float64(a * 120.0) + Float64(x * t_1));
	else
		tmp = Float64(Float64(x - y) * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 / (z - t);
	tmp = 0.0;
	if (y <= -2.5e+181)
		tmp = 60.0 * ((x - y) / (z - t));
	elseif (y <= 1.12e+143)
		tmp = (a * 120.0) + (x * t_1);
	else
		tmp = (x - y) * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e+181], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e+143], N[(N[(a * 120.0), $MachinePrecision] + N[(x * t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5000000000000002e181

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 76.2%

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

   if -2.5000000000000002e181 < y < 1.12e143

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf 89.6%

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

      1. associate-*r/ 89.6%

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

      2. *-commutative 89.6%

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

      3. associate-*r/ 89.6%

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

   7. Simplified 89.6%

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

   if 1.12e143 < y

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

      2. associate-/l* 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in a around 0 81.9%

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

      1. associate-*r/ 81.8%

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

   7. Simplified 81.8%

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

      1. *-commutative 99.5%

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

      2. associate-/l* 99.9%

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

   9. Applied egg-rr 82.1%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+181}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+143}:\\ \;\;\;\;a \cdot 120 + x \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-82} \lor \neg \left(a \leq 5.2 \cdot 10^{+45}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.4e-82) (not (<= a 5.2e+45)))
   (* 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 <= -1.4e-82) || !(a <= 5.2e+45)) {
		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 <= (-1.4d-82)) .or. (.not. (a <= 5.2d+45))) 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 <= -1.4e-82) || !(a <= 5.2e+45)) {
		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 <= -1.4e-82) or not (a <= 5.2e+45):
		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 <= -1.4e-82) || !(a <= 5.2e+45))
		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 <= -1.4e-82) || ~((a <= 5.2e+45)))
		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, -1.4e-82], N[Not[LessEqual[a, 5.2e+45]], $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 < -1.40000000000000012e-82 or 5.20000000000000014e45 < a

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 77.4%

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

   if -1.40000000000000012e-82 < a < 5.20000000000000014e45

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 79.1%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-82} \lor \neg \left(a \leq 5.2 \cdot 10^{+45}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 58.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+181} \lor \neg \left(y \leq 1.2 \cdot 10^{+144}\right):\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.2e+181) (not (<= y 1.2e+144)))
   (* 60.0 (/ y (- t z)))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.2e+181) || !(y <= 1.2e+144)) {
		tmp = 60.0 * (y / (t - 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 <= (-3.2d+181)) .or. (.not. (y <= 1.2d+144))) then
        tmp = 60.0d0 * (y / (t - 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 <= -3.2e+181) || !(y <= 1.2e+144)) {
		tmp = 60.0 * (y / (t - z));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.2e+181) or not (y <= 1.2e+144):
		tmp = 60.0 * (y / (t - z))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.2e+181) || !(y <= 1.2e+144))
		tmp = Float64(60.0 * Float64(y / Float64(t - 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 <= -3.2e+181) || ~((y <= 1.2e+144)))
		tmp = 60.0 * (y / (t - z));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.2e+181], N[Not[LessEqual[y, 1.2e+144]], $MachinePrecision]], N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2e181 or 1.2e144 < y

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 79.5%

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

   6. Taylor expanded in x around 0 71.5%

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

      1. neg-mul-1 71.5%

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

      2. distribute-neg-frac2 71.5%

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

      3. neg-sub0 71.5%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{0 - \left(z - t\right)}} \]

      4. sub-neg 71.5%

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

      5. +-commutative 71.5%

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

      6. associate--r+ 71.5%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{\left(0 - \left(-t\right)\right) - z}} \]

      7. neg-sub0 71.5%

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

      8. remove-double-neg 71.5%

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

   8. Simplified 71.5%

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

   if -3.2e181 < y < 1.2e144

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 63.8%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+181} \lor \neg \left(y \leq 1.2 \cdot 10^{+144}\right):\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+181}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+143}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.2e+181)
   (* 60.0 (/ y (- t z)))
   (if (<= y 3.9e+143) (* a 120.0) (* y (/ 60.0 (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.2e+181) {
		tmp = 60.0 * (y / (t - z));
	} else if (y <= 3.9e+143) {
		tmp = a * 120.0;
	} else {
		tmp = y * (60.0 / (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-5.2d+181)) then
        tmp = 60.0d0 * (y / (t - z))
    else if (y <= 3.9d+143) then
        tmp = a * 120.0d0
    else
        tmp = y * (60.0d0 / (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.2e+181) {
		tmp = 60.0 * (y / (t - z));
	} else if (y <= 3.9e+143) {
		tmp = a * 120.0;
	} else {
		tmp = y * (60.0 / (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.2e+181:
		tmp = 60.0 * (y / (t - z))
	elif y <= 3.9e+143:
		tmp = a * 120.0
	else:
		tmp = y * (60.0 / (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.2e+181)
		tmp = Float64(60.0 * Float64(y / Float64(t - z)));
	elseif (y <= 3.9e+143)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(y * Float64(60.0 / Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5.2e+181)
		tmp = 60.0 * (y / (t - z));
	elseif (y <= 3.9e+143)
		tmp = a * 120.0;
	else
		tmp = y * (60.0 / (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.2e+181], N[(60.0 * N[(y / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e+143], N[(a * 120.0), $MachinePrecision], N[(y * N[(60.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.2e181

   1. Initial program 99.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 76.2%

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

   6. Taylor expanded in x around 0 74.6%

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

      1. neg-mul-1 74.6%

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

      2. distribute-neg-frac2 74.6%

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

      3. neg-sub0 74.6%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{0 - \left(z - t\right)}} \]

      4. sub-neg 74.6%

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

      5. +-commutative 74.6%

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

      6. associate--r+ 74.6%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{\left(0 - \left(-t\right)\right) - z}} \]

      7. neg-sub0 74.6%

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

      8. remove-double-neg 74.6%

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

   8. Simplified 74.6%

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

   if -5.2e181 < y < 3.8999999999999998e143

   1. Initial program 99.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 63.8%

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

   if 3.8999999999999998e143 < y

   1. Initial program 99.5%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 81.9%

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

   6. Taylor expanded in x around 0 69.2%

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

      1. associate-*r/ 87.0%

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

      2. *-commutative 87.0%

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

      3. *-lft-identity 87.0%

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

      4. times-frac 87.2%

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

      5. /-rgt-identity 87.2%

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

      6. metadata-eval 87.2%

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

      7. distribute-neg-frac 87.2%

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

      8. distribute-neg-frac2 87.2%

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

      9. neg-sub0 87.2%

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

      10. sub-neg 87.2%

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

      11. +-commutative 87.2%

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

      12. associate--r+ 87.2%

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

      13. neg-sub0 87.2%

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

      14. remove-double-neg 87.2%

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

   8. Simplified 69.4%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+181}:\\ \;\;\;\;60 \cdot \frac{y}{t - z}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+143}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{60}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.2 \cdot 10^{+144}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+159}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 7.2e+144)
   (* a 120.0)
   (if (<= y 3.8e+159) (* y (/ 60.0 t)) (* y (/ -60.0 z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 7.2e+144) {
		tmp = a * 120.0;
	} else if (y <= 3.8e+159) {
		tmp = y * (60.0 / t);
	} else {
		tmp = y * (-60.0 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 7.2d+144) then
        tmp = a * 120.0d0
    else if (y <= 3.8d+159) then
        tmp = y * (60.0d0 / t)
    else
        tmp = y * ((-60.0d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 7.2e+144) {
		tmp = a * 120.0;
	} else if (y <= 3.8e+159) {
		tmp = y * (60.0 / t);
	} else {
		tmp = y * (-60.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 7.2e+144:
		tmp = a * 120.0
	elif y <= 3.8e+159:
		tmp = y * (60.0 / t)
	else:
		tmp = y * (-60.0 / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 7.2e+144)
		tmp = Float64(a * 120.0);
	elseif (y <= 3.8e+159)
		tmp = Float64(y * Float64(60.0 / t));
	else
		tmp = Float64(y * Float64(-60.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 7.2e+144)
		tmp = a * 120.0;
	elseif (y <= 3.8e+159)
		tmp = y * (60.0 / t);
	else
		tmp = y * (-60.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 7.2e+144], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, 3.8e+159], N[(y * N[(60.0 / t), $MachinePrecision]), $MachinePrecision], N[(y * N[(-60.0 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 7.1999999999999995e144

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 59.1%

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

   if 7.1999999999999995e144 < y < 3.79999999999999965e159

   1. Initial program 99.3%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 99.6%

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

   6. Taylor expanded in x around 0 86.2%

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

      1. associate-*r/ 86.0%

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

      2. *-commutative 86.0%

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

      3. *-lft-identity 86.0%

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

      4. times-frac 86.7%

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

      5. /-rgt-identity 86.7%

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

      6. metadata-eval 86.7%

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

      7. distribute-neg-frac 86.7%

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

      8. distribute-neg-frac2 86.7%

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

      9. neg-sub0 86.7%

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

      10. sub-neg 86.7%

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

      11. +-commutative 86.7%

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

      12. associate--r+ 86.7%

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

      13. neg-sub0 86.7%

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

      14. remove-double-neg 86.7%

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

   8. Simplified 86.7%

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

   9. Taylor expanded in t around inf 85.8%

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

   if 3.79999999999999965e159 < y

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 77.9%

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

   6. Taylor expanded in x around 0 65.4%

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

      1. associate-*r/ 87.2%

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

      2. *-commutative 87.2%

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

      3. *-lft-identity 87.2%

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

      4. times-frac 87.3%

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

      5. /-rgt-identity 87.3%

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

      6. metadata-eval 87.3%

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

      7. distribute-neg-frac 87.3%

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

      8. distribute-neg-frac2 87.3%

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

      9. neg-sub0 87.3%

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

      10. sub-neg 87.3%

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

      11. +-commutative 87.3%

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

      12. associate--r+ 87.3%

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

      13. neg-sub0 87.3%

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

      14. remove-double-neg 87.3%

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

   8. Simplified 65.5%

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

   9. Taylor expanded in t around 0 46.6%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.2 \cdot 10^{+144}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+159}:\\ \;\;\;\;y \cdot \frac{60}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.2 \cdot 10^{+145}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+160}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 8.2e+145)
   (* a 120.0)
   (if (<= y 1.1e+160) (* 60.0 (/ y t)) (* y (/ -60.0 z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 8.2e+145) {
		tmp = a * 120.0;
	} else if (y <= 1.1e+160) {
		tmp = 60.0 * (y / t);
	} else {
		tmp = y * (-60.0 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 8.2d+145) then
        tmp = a * 120.0d0
    else if (y <= 1.1d+160) then
        tmp = 60.0d0 * (y / t)
    else
        tmp = y * ((-60.0d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 8.2e+145) {
		tmp = a * 120.0;
	} else if (y <= 1.1e+160) {
		tmp = 60.0 * (y / t);
	} else {
		tmp = y * (-60.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 8.2e+145:
		tmp = a * 120.0
	elif y <= 1.1e+160:
		tmp = 60.0 * (y / t)
	else:
		tmp = y * (-60.0 / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 8.2e+145)
		tmp = Float64(a * 120.0);
	elseif (y <= 1.1e+160)
		tmp = Float64(60.0 * Float64(y / t));
	else
		tmp = Float64(y * Float64(-60.0 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 8.2e+145)
		tmp = a * 120.0;
	elseif (y <= 1.1e+160)
		tmp = 60.0 * (y / t);
	else
		tmp = y * (-60.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 8.2e+145], N[(a * 120.0), $MachinePrecision], If[LessEqual[y, 1.1e+160], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(y * N[(-60.0 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 8.2000000000000003e145

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 59.1%

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

   if 8.2000000000000003e145 < y < 1.09999999999999996e160

   1. Initial program 99.3%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in a around 0 99.6%

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

   6. Taylor expanded in x around 0 86.2%

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

      1. neg-mul-1 86.2%

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

      2. distribute-neg-frac2 86.2%

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

      3. neg-sub0 86.2%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{0 - \left(z - t\right)}} \]

      4. sub-neg 86.2%

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

      5. +-commutative 86.2%

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

      6. associate--r+ 86.2%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{\left(0 - \left(-t\right)\right) - z}} \]

      7. neg-sub0 86.2%

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

      8. remove-double-neg 86.2%

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

   8. Simplified 86.2%

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

   9. Taylor expanded in t around inf 85.4%

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

   if 1.09999999999999996e160 < y

   1. Initial program 99.6%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 77.9%

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

   6. Taylor expanded in x around 0 65.4%

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

      1. associate-*r/ 87.2%

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

      2. *-commutative 87.2%

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

      3. *-lft-identity 87.2%

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

      4. times-frac 87.3%

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

      5. /-rgt-identity 87.3%

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

      6. metadata-eval 87.3%

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

      7. distribute-neg-frac 87.3%

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

      8. distribute-neg-frac2 87.3%

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

      9. neg-sub0 87.3%

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

      10. sub-neg 87.3%

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

      11. +-commutative 87.3%

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

      12. associate--r+ 87.3%

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

      13. neg-sub0 87.3%

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

      14. remove-double-neg 87.3%

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

   8. Simplified 65.5%

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

   9. Taylor expanded in t around 0 46.6%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.2 \cdot 10^{+145}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+160}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + (60.0d0 * ((x - y) / (z - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 12: 51.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.5 \cdot 10^{+145}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 4.5e+145) (* a 120.0) (* 60.0 (/ y t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 4.5e+145) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (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 (y <= 4.5d+145) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * (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 (y <= 4.5e+145) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 4.5e+145:
		tmp = a * 120.0
	else:
		tmp = 60.0 * (y / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 4.5e+145)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 4.5e+145)
		tmp = a * 120.0;
	else
		tmp = 60.0 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 4.5e+145], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.4999999999999998e145

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 59.1%

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

   if 4.4999999999999998e145 < y

   1. Initial program 99.5%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 81.9%

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

   6. Taylor expanded in x around 0 69.2%

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

      1. neg-mul-1 69.2%

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

      2. distribute-neg-frac2 69.2%

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

      3. neg-sub0 69.2%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{0 - \left(z - t\right)}} \]

      4. sub-neg 69.2%

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

      5. +-commutative 69.2%

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

      6. associate--r+ 69.2%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{\left(0 - \left(-t\right)\right) - z}} \]

      7. neg-sub0 69.2%

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

      8. remove-double-neg 69.2%

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

   8. Simplified 69.2%

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

   9. Taylor expanded in t around inf 43.2%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.5 \cdot 10^{+145}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 50.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{+145}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 2.4e+145) (* a 120.0) (* -60.0 (/ y z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 2.4e+145) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= 2.4d+145) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 2.4e+145) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 2.4e+145:
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 2.4e+145)
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 2.4e+145)
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 2.4e+145], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.39999999999999992e145

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 59.1%

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

   if 2.39999999999999992e145 < y

   1. Initial program 99.5%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in a around 0 81.9%

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

   6. Taylor expanded in x around 0 69.2%

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

      1. neg-mul-1 69.2%

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

      2. distribute-neg-frac2 69.2%

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

      3. neg-sub0 69.2%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{0 - \left(z - t\right)}} \]

      4. sub-neg 69.2%

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

      5. +-commutative 69.2%

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

      6. associate--r+ 69.2%

         \[\leadsto 60 \cdot \frac{y}{\color{blue}{\left(0 - \left(-t\right)\right) - z}} \]

      7. neg-sub0 69.2%

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

      8. remove-double-neg 69.2%

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

   8. Simplified 69.2%

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

   9. Taylor expanded in t around 0 41.1%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{+145}:\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.1% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-/l* 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in z around inf 53.4%

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

6. Final simplification 53.4%

   \[\leadsto a \cdot 120 \]
7. Add Preprocessing

Developer Target 1: 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 2024114 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (/ 60 (/ (- z t) (- x y))) (* a 120)))

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