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

Percentage Accurate: 99.3% → 99.8%

Time: 13.5s

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: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. *-commutative 99.4%

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

   2. associate-/l* 99.7%

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

   3. fma-define 99.8%

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

   4. sub-neg 99.8%

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

   5. +-commutative 99.8%

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

   6. neg-sub0 99.8%

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

   7. associate-+l- 99.8%

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

   8. sub0-neg 99.8%

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

   9. distribute-frac-neg2 99.8%

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

   10. distribute-neg-frac 99.8%

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

   11. metadata-eval 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5.5 \cdot 10^{-39} \lor \neg \left(a \cdot 120 \leq 10^{-34}\right):\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -5.5e-39) (not (<= (* a 120.0) 1e-34)))
   (+ (* a 120.0) (* y (/ -60.0 (- z t))))
   (* (- 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) <= -5.5e-39) || !((a * 120.0) <= 1e-34)) {
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	} 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) <= (-5.5d-39)) .or. (.not. ((a * 120.0d0) <= 1d-34))) then
        tmp = (a * 120.0d0) + (y * ((-60.0d0) / (z - t)))
    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) <= -5.5e-39) || !((a * 120.0) <= 1e-34)) {
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	} else {
		tmp = (x - y) * (60.0 / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -5.5e-39) or not ((a * 120.0) <= 1e-34):
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)))
	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) <= -5.5e-39) || !(Float64(a * 120.0) <= 1e-34))
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(-60.0 / Float64(z - t))));
	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) <= -5.5e-39) || ~(((a * 120.0) <= 1e-34)))
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	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], -5.5e-39], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-34]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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)) < -5.50000000000000018e-39 or 9.99999999999999928e-35 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.2%

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

      1. associate-/l* 99.9%

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

   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 85.8%

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

      1. associate-*r/ 85.1%

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

      2. *-commutative 85.1%

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

      3. *-lft-identity 85.1%

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

      4. times-frac 85.8%

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

      5. /-rgt-identity 85.8%

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

   7. Simplified 85.8%

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

   if -5.50000000000000018e-39 < (*.f64 a #s(literal 120 binary64)) < 9.99999999999999928e-35

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. fma-define 99.6%

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

      3. clear-num 99.5%

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

      4. un-div-inv 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 81.7%

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

      1. associate-*r/ 81.7%

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

      2. associate-*l/ 81.7%

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

      3. metadata-eval 81.7%

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

      4. associate-*r/ 81.6%

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

      5. *-commutative 81.6%

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

      6. associate-*r/ 81.7%

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

      7. metadata-eval 81.7%

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

   9. Simplified 81.7%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5.5 \cdot 10^{-39} \lor \neg \left(a \cdot 120 \leq 10^{-34}\right):\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2000000000000 \lor \neg \left(a \cdot 120 \leq 10^{+17}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -2000000000000.0) (not (<= (* a 120.0) 1e+17)))
   (* 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) <= -2000000000000.0) || !((a * 120.0) <= 1e+17)) {
		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) <= (-2000000000000.0d0)) .or. (.not. ((a * 120.0d0) <= 1d+17))) 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) <= -2000000000000.0) || !((a * 120.0) <= 1e+17)) {
		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) <= -2000000000000.0) or not ((a * 120.0) <= 1e+17):
		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) <= -2000000000000.0) || !(Float64(a * 120.0) <= 1e+17))
		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) <= -2000000000000.0) || ~(((a * 120.0) <= 1e+17)))
		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], -2000000000000.0], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 1e+17]], $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)) < -2e12 or 1e17 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. neg-sub0 99.9%

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

      7. associate-+l- 99.9%

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

      8. sub0-neg 99.9%

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

      9. distribute-frac-neg2 99.9%

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

      10. distribute-neg-frac 99.9%

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

      11. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 77.4%

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

   if -2e12 < (*.f64 a #s(literal 120 binary64)) < 1e17

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. fma-define 99.6%

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

      3. clear-num 99.5%

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

      4. un-div-inv 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 78.3%

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

      1. associate-*r/ 78.4%

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

      2. associate-*l/ 78.4%

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

      3. metadata-eval 78.4%

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

      4. associate-*r/ 78.2%

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

      5. *-commutative 78.2%

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

      6. associate-*r/ 78.4%

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

      7. metadata-eval 78.4%

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

   9. Simplified 78.4%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2000000000000 \lor \neg \left(a \cdot 120 \leq 10^{+17}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+36}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot 60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-34}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -1e+36)
   (+ (* a 120.0) (/ (* x 60.0) z))
   (if (<= (* a 120.0) 1e-34)
     (* (- x y) (/ 60.0 (- z t)))
     (+ (* a 120.0) (* y (/ -60.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -1e+36) {
		tmp = (a * 120.0) + ((x * 60.0) / z);
	} else if ((a * 120.0) <= 1e-34) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = (a * 120.0) + (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 ((a * 120.0d0) <= (-1d+36)) then
        tmp = (a * 120.0d0) + ((x * 60.0d0) / z)
    else if ((a * 120.0d0) <= 1d-34) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else
        tmp = (a * 120.0d0) + (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 ((a * 120.0) <= -1e+36) {
		tmp = (a * 120.0) + ((x * 60.0) / z);
	} else if ((a * 120.0) <= 1e-34) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = (a * 120.0) + (y * (-60.0 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -1e+36:
		tmp = (a * 120.0) + ((x * 60.0) / z)
	elif (a * 120.0) <= 1e-34:
		tmp = (x - y) * (60.0 / (z - t))
	else:
		tmp = (a * 120.0) + (y * (-60.0 / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -1e+36)
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x * 60.0) / z));
	elseif (Float64(a * 120.0) <= 1e-34)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(-60.0 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -1e+36)
		tmp = (a * 120.0) + ((x * 60.0) / z);
	elseif ((a * 120.0) <= 1e-34)
		tmp = (x - y) * (60.0 / (z - t));
	else
		tmp = (a * 120.0) + (y * (-60.0 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -1e+36], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x * 60.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-34], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(-60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -1.00000000000000004e36

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 79.4%

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

   4. Taylor expanded in x around inf 83.3%

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

   if -1.00000000000000004e36 < (*.f64 a #s(literal 120 binary64)) < 9.99999999999999928e-35

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. fma-define 99.6%

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

      3. clear-num 99.5%

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

      4. un-div-inv 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 79.6%

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

      1. associate-*r/ 79.6%

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

      2. associate-*l/ 79.7%

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

      3. metadata-eval 79.7%

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

      4. associate-*r/ 79.5%

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

      5. *-commutative 79.5%

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

      6. associate-*r/ 79.7%

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

      7. metadata-eval 79.7%

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

   9. Simplified 79.7%

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

   if 9.99999999999999928e-35 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 86.6%

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

      1. associate-*r/ 85.2%

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

      2. *-commutative 85.2%

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

      3. *-lft-identity 85.2%

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

      4. times-frac 86.6%

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

      5. /-rgt-identity 86.6%

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

   7. Simplified 86.6%

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

   8. Taylor expanded in z around inf 72.6%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -1 \cdot 10^{+36}:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot 60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-34}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2000000000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-34}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* a 120.0) -2000000000000.0)
   (* a 120.0)
   (if (<= (* a 120.0) 1e-34)
     (* (- x y) (/ 60.0 (- z t)))
     (+ (* a 120.0) (* y (/ -60.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a * 120.0) <= -2000000000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-34) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = (a * 120.0) + (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 ((a * 120.0d0) <= (-2000000000000.0d0)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= 1d-34) then
        tmp = (x - y) * (60.0d0 / (z - t))
    else
        tmp = (a * 120.0d0) + (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 ((a * 120.0) <= -2000000000000.0) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= 1e-34) {
		tmp = (x - y) * (60.0 / (z - t));
	} else {
		tmp = (a * 120.0) + (y * (-60.0 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a * 120.0) <= -2000000000000.0:
		tmp = a * 120.0
	elif (a * 120.0) <= 1e-34:
		tmp = (x - y) * (60.0 / (z - t))
	else:
		tmp = (a * 120.0) + (y * (-60.0 / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(a * 120.0) <= -2000000000000.0)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= 1e-34)
		tmp = Float64(Float64(x - y) * Float64(60.0 / Float64(z - t)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(-60.0 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a * 120.0) <= -2000000000000.0)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= 1e-34)
		tmp = (x - y) * (60.0 / (z - t));
	else
		tmp = (a * 120.0) + (y * (-60.0 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(a * 120.0), $MachinePrecision], -2000000000000.0], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 1e-34], N[(N[(x - y), $MachinePrecision] * N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(-60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a #s(literal 120 binary64)) < -2e12

   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* 99.9%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. neg-sub0 99.9%

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

      7. associate-+l- 99.9%

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

      8. sub0-neg 99.9%

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

      9. distribute-frac-neg2 99.9%

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

      10. distribute-neg-frac 99.9%

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

      11. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 78.2%

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

   if -2e12 < (*.f64 a #s(literal 120 binary64)) < 9.99999999999999928e-35

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. fma-define 99.6%

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

      3. clear-num 99.5%

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

      4. un-div-inv 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in a around 0 80.5%

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

      1. associate-*r/ 80.5%

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

      2. associate-*l/ 80.5%

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

      3. metadata-eval 80.5%

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

      4. associate-*r/ 80.3%

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

      5. *-commutative 80.3%

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

      6. associate-*r/ 80.5%

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

      7. metadata-eval 80.5%

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

   9. Simplified 80.5%

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

   if 9.99999999999999928e-35 < (*.f64 a #s(literal 120 binary64))

   1. Initial program 98.5%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   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 86.6%

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

      1. associate-*r/ 85.2%

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

      2. *-commutative 85.2%

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

      3. *-lft-identity 85.2%

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

      4. times-frac 86.6%

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

      5. /-rgt-identity 86.6%

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

   7. Simplified 86.6%

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

   8. Taylor expanded in z around inf 72.6%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -2000000000000:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq 10^{-34}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -680000 \lor \neg \left(z \leq 9.2 \cdot 10^{+34}\right):\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -680000.0) (not (<= z 9.2e+34)))
   (+ (* a 120.0) (* (- x y) (/ 60.0 z)))
   (+ (* a 120.0) (* (- x y) (/ -60.0 t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -680000.0) || !(z <= 9.2e+34)) {
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	} else {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / 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 <= (-680000.0d0)) .or. (.not. (z <= 9.2d+34))) then
        tmp = (a * 120.0d0) + ((x - y) * (60.0d0 / z))
    else
        tmp = (a * 120.0d0) + ((x - y) * ((-60.0d0) / 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 <= -680000.0) || !(z <= 9.2e+34)) {
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	} else {
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -680000.0) or not (z <= 9.2e+34):
		tmp = (a * 120.0) + ((x - y) * (60.0 / z))
	else:
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -680000.0) || !(z <= 9.2e+34))
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(60.0 / z)));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(Float64(x - y) * Float64(-60.0 / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -680000.0) || ~((z <= 9.2e+34)))
		tmp = (a * 120.0) + ((x - y) * (60.0 / z));
	else
		tmp = (a * 120.0) + ((x - y) * (-60.0 / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -680000.0], N[Not[LessEqual[z, 9.2e+34]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] * N[(-60.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.8e5 or 9.1999999999999993e34 < z

   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. Taylor expanded in z around inf 92.4%

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

   if -6.8e5 < z < 9.1999999999999993e34

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-/l* 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in z around 0 80.0%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -680000 \lor \neg \left(z \leq 9.2 \cdot 10^{+34}\right):\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{60}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \left(x - y\right) \cdot \frac{-60}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+122}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;y \leq 0.14:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot 60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.3e+122)
   (+ (* a 120.0) (* y (/ -60.0 (- z t))))
   (if (<= y 0.14)
     (+ (* 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 (y <= -1.3e+122) {
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	} else if (y <= 0.14) {
		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 (y <= (-1.3d+122)) then
        tmp = (a * 120.0d0) + (y * ((-60.0d0) / (z - t)))
    else if (y <= 0.14d0) 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 (y <= -1.3e+122) {
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	} else if (y <= 0.14) {
		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 y <= -1.3e+122:
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)))
	elif y <= 0.14:
		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 (y <= -1.3e+122)
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(-60.0 / Float64(z - t))));
	elseif (y <= 0.14)
		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 (y <= -1.3e+122)
		tmp = (a * 120.0) + (y * (-60.0 / (z - t)));
	elseif (y <= 0.14)
		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[LessEqual[y, -1.3e+122], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(-60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.14], 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 3 regimes

2. if y < -1.30000000000000004e122

   1. Initial program 96.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 90.6%

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

      1. associate-*r/ 87.7%

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

      2. *-commutative 87.7%

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

      3. *-lft-identity 87.7%

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

      4. times-frac 90.5%

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

      5. /-rgt-identity 90.5%

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

   7. Simplified 90.5%

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

   if -1.30000000000000004e122 < y < 0.14000000000000001

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 92.3%

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

      1. associate-*r/ 92.3%

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

   7. Simplified 92.3%

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

   if 0.14000000000000001 < y

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 87.8%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+122}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z - t}\\ \mathbf{elif}\;y \leq 0.14:\\ \;\;\;\;a \cdot 120 + \frac{x \cdot 60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + \frac{y \cdot -60}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -0.5 \lor \neg \left(a \leq 8.2 \cdot 10^{+18}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -0.5) (not (<= a 8.2e+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 <= -0.5) || !(a <= 8.2e+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 <= (-0.5d0)) .or. (.not. (a <= 8.2d+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 <= -0.5) || !(a <= 8.2e+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 <= -0.5) or not (a <= 8.2e+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 ((a <= -0.5) || !(a <= 8.2e+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 <= -0.5) || ~((a <= 8.2e+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[a, -0.5], N[Not[LessEqual[a, 8.2e+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 a < -0.5 or 8.2e18 < a

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. neg-sub0 99.9%

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

      7. associate-+l- 99.9%

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

      8. sub0-neg 99.9%

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

      9. distribute-frac-neg2 99.9%

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

      10. distribute-neg-frac 99.9%

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

      11. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 77.4%

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

   if -0.5 < a < 8.2e18

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

   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 78.3%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -0.5 \lor \neg \left(a \leq 8.2 \cdot 10^{+18}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+172} \lor \neg \left(x \leq 5.2 \cdot 10^{+111}\right):\\ \;\;\;\;\frac{x \cdot 60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -9.5e+172) (not (<= x 5.2e+111)))
   (/ (* x 60.0) (- z t))
   (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -9.5e+172) || !(x <= 5.2e+111)) {
		tmp = (x * 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 ((x <= (-9.5d+172)) .or. (.not. (x <= 5.2d+111))) then
        tmp = (x * 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 ((x <= -9.5e+172) || !(x <= 5.2e+111)) {
		tmp = (x * 60.0) / (z - t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -9.5e+172) or not (x <= 5.2e+111):
		tmp = (x * 60.0) / (z - t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -9.5e+172) || !(x <= 5.2e+111))
		tmp = Float64(Float64(x * 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 ((x <= -9.5e+172) || ~((x <= 5.2e+111)))
		tmp = (x * 60.0) / (z - t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -9.5e+172], N[Not[LessEqual[x, 5.2e+111]], $MachinePrecision]], N[(N[(x * 60.0), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.50000000000000027e172 or 5.1999999999999997e111 < x

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

      3. clear-num 99.5%

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

      4. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 71.0%

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

      1. associate-*r/ 71.1%

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

   9. Simplified 71.1%

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

   if -9.50000000000000027e172 < x < 5.1999999999999997e111

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. distribute-frac-neg2 99.8%

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

      10. distribute-neg-frac 99.8%

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

      11. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 54.4%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+172} \lor \neg \left(x \leq 5.2 \cdot 10^{+111}\right):\\ \;\;\;\;\frac{x \cdot 60}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+172} \lor \neg \left(x \leq 5.2 \cdot 10^{+111}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -6.8e+172) (not (<= x 5.2e+111)))
   (* 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 <= -6.8e+172) || !(x <= 5.2e+111)) {
		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 <= (-6.8d+172)) .or. (.not. (x <= 5.2d+111))) 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 <= -6.8e+172) || !(x <= 5.2e+111)) {
		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 <= -6.8e+172) or not (x <= 5.2e+111):
		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 <= -6.8e+172) || !(x <= 5.2e+111))
		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 <= -6.8e+172) || ~((x <= 5.2e+111)))
		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, -6.8e+172], N[Not[LessEqual[x, 5.2e+111]], $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 < -6.7999999999999996e172 or 5.1999999999999997e111 < x

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.7%

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

      3. clear-num 99.5%

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

      4. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 71.0%

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

   if -6.7999999999999996e172 < x < 5.1999999999999997e111

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. distribute-frac-neg2 99.8%

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

      10. distribute-neg-frac 99.8%

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

      11. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 54.4%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+172} \lor \neg \left(x \leq 5.2 \cdot 10^{+111}\right):\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-201} \lor \neg \left(a \leq 2.4 \cdot 10^{-74}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.05e-201) (not (<= a 2.4e-74)))
   (* a 120.0)
   (* y (/ -60.0 z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.05e-201) || !(a <= 2.4e-74)) {
		tmp = a * 120.0;
	} 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 ((a <= (-1.05d-201)) .or. (.not. (a <= 2.4d-74))) then
        tmp = a * 120.0d0
    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 ((a <= -1.05e-201) || !(a <= 2.4e-74)) {
		tmp = a * 120.0;
	} else {
		tmp = y * (-60.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.05e-201) or not (a <= 2.4e-74):
		tmp = a * 120.0
	else:
		tmp = y * (-60.0 / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.05e-201) || !(a <= 2.4e-74))
		tmp = Float64(a * 120.0);
	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 ((a <= -1.05e-201) || ~((a <= 2.4e-74)))
		tmp = a * 120.0;
	else
		tmp = y * (-60.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.05e-201], N[Not[LessEqual[a, 2.4e-74]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(y * N[(-60.0 / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.05000000000000006e-201 or 2.3999999999999999e-74 < a

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. distribute-frac-neg2 99.8%

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

      10. distribute-neg-frac 99.8%

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

      11. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 59.7%

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

   if -1.05000000000000006e-201 < a < 2.3999999999999999e-74

   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%

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

      2. associate-/l* 99.5%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. neg-sub0 99.6%

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

      7. associate-+l- 99.6%

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

      8. sub0-neg 99.6%

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

      9. distribute-frac-neg2 99.6%

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

      10. distribute-neg-frac 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 44.2%

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

   6. Taylor expanded in t around 0 30.9%

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

      1. associate-*r/ 30.9%

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

      2. *-commutative 30.9%

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

      3. associate-*r/ 30.9%

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

   8. Simplified 30.9%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{-201} \lor \neg \left(a \leq 2.4 \cdot 10^{-74}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-60}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-200} \lor \neg \left(a \leq 6.5 \cdot 10^{-76}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.3e-200) (not (<= a 6.5e-76))) (* a 120.0) (* -60.0 (/ y z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.3e-200) || !(a <= 6.5e-76)) {
		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 ((a <= (-2.3d-200)) .or. (.not. (a <= 6.5d-76))) 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 ((a <= -2.3e-200) || !(a <= 6.5e-76)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.3e-200) or not (a <= 6.5e-76):
		tmp = a * 120.0
	else:
		tmp = -60.0 * (y / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.3e-200) || !(a <= 6.5e-76))
		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 ((a <= -2.3e-200) || ~((a <= 6.5e-76)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.3e-200], N[Not[LessEqual[a, 6.5e-76]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.30000000000000007e-200 or 6.5e-76 < a

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. neg-sub0 99.8%

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

      7. associate-+l- 99.8%

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

      8. sub0-neg 99.8%

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

      9. distribute-frac-neg2 99.8%

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

      10. distribute-neg-frac 99.8%

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

      11. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 59.7%

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

   if -2.30000000000000007e-200 < a < 6.5e-76

   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%

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

      2. associate-/l* 99.5%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. neg-sub0 99.6%

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

      7. associate-+l- 99.6%

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

      8. sub0-neg 99.6%

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

      9. distribute-frac-neg2 99.6%

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

      10. distribute-neg-frac 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 44.2%

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

   6. Taylor expanded in t around 0 30.9%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-200} \lor \neg \left(a \leq 6.5 \cdot 10^{-76}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return (a * 120.0) + ((x - y) * (60.0 / (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) + ((x - y) * (60.0d0 / (z - t)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. *-commutative 99.4%

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

   2. associate-/l* 99.7%

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

4. Applied egg-rr 99.7%

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

5. Final simplification 99.7%

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

Alternative 14: 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 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
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. Final simplification 99.7%

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

Alternative 15: 50.6% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. *-commutative 99.4%

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

   2. associate-/l* 99.7%

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

   3. fma-define 99.8%

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

   4. sub-neg 99.8%

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

   5. +-commutative 99.8%

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

   6. neg-sub0 99.8%

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

   7. associate-+l- 99.8%

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

   8. sub0-neg 99.8%

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

   9. distribute-frac-neg2 99.8%

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

   10. distribute-neg-frac 99.8%

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

   11. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in t around inf 46.1%

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

6. Final simplification 46.1%

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

Developer Target 1: 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 2024160 
(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)))