Statistics.Distribution.Beta:$cdensity from math-functions-0.1.5.2

Percentage Accurate: 89.1% → 99.8%

Time: 15.6s

Alternatives: 15

Speedup: 1.9×

Specification

Math

\[\begin{array}{l} \\ \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t))

C

double code(double x, double y, double z, double t) {
	return (((x - 1.0) * log(y)) + ((z - 1.0) * log((1.0 - y)))) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x - 1.0d0) * log(y)) + ((z - 1.0d0) * log((1.0d0 - y)))) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((x - 1.0) * Math.log(y)) + ((z - 1.0) * Math.log((1.0 - y)))) - t;
}

Python

def code(x, y, z, t):
	return (((x - 1.0) * math.log(y)) + ((z - 1.0) * math.log((1.0 - y)))) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x - 1.0) * log(y)) + Float64(Float64(z - 1.0) * log(Float64(1.0 - y)))) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((x - 1.0) * log(y)) + ((z - 1.0) * log((1.0 - y)))) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[(z - 1.0), $MachinePrecision] * N[Log[N[(1.0 - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Initial Program: 89.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t))

C

double code(double x, double y, double z, double t) {
	return (((x - 1.0) * log(y)) + ((z - 1.0) * log((1.0 - y)))) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((x - 1.0d0) * log(y)) + ((z - 1.0d0) * log((1.0d0 - y)))) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((x - 1.0) * Math.log(y)) + ((z - 1.0) * Math.log((1.0 - y)))) - t;
}

Python

def code(x, y, z, t):
	return (((x - 1.0) * math.log(y)) + ((z - 1.0) * math.log((1.0 - y)))) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(x - 1.0) * log(y)) + Float64(Float64(z - 1.0) * log(Float64(1.0 - y)))) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((x - 1.0) * log(y)) + ((z - 1.0) * log((1.0 - y)))) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(x - 1.0), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[(z - 1.0), $MachinePrecision] * N[Log[N[(1.0 - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \mathsf{fma}\left(-1 + x, \log y, -t\right)\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (fma (+ z -1.0) (log1p (- y)) (fma (+ -1.0 x) (log y) (- t))))

C

double code(double x, double y, double z, double t) {
	return fma((z + -1.0), log1p(-y), fma((-1.0 + x), log(y), -t));
}

Julia

function code(x, y, z, t)
	return fma(Float64(z + -1.0), log1p(Float64(-y)), fma(Float64(-1.0 + x), log(y), Float64(-t)))
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(z + -1.0), $MachinePrecision] * N[Log[1 + (-y)], $MachinePrecision] + N[(N[(-1.0 + x), $MachinePrecision] * N[Log[y], $MachinePrecision] + (-t)), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 88.6%

   \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
2. Step-by-step derivation

   1. sub-neg 88.6%

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

   2. +-commutative 88.6%

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

   3. associate-+l+ 88.6%

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

   4. fma-define 88.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z - 1, \log \left(1 - y\right), \left(x - 1\right) \cdot \log y + \left(-t\right)\right)} \]

   5. sub-neg 88.6%

      \[\leadsto \mathsf{fma}\left(\color{blue}{z + \left(-1\right)}, \log \left(1 - y\right), \left(x - 1\right) \cdot \log y + \left(-t\right)\right) \]

   6. metadata-eval 88.6%

      \[\leadsto \mathsf{fma}\left(z + \color{blue}{-1}, \log \left(1 - y\right), \left(x - 1\right) \cdot \log y + \left(-t\right)\right) \]

   7. sub-neg 88.6%

      \[\leadsto \mathsf{fma}\left(z + -1, \log \color{blue}{\left(1 + \left(-y\right)\right)}, \left(x - 1\right) \cdot \log y + \left(-t\right)\right) \]

   8. log1p-define 99.9%

      \[\leadsto \mathsf{fma}\left(z + -1, \color{blue}{\mathsf{log1p}\left(-y\right)}, \left(x - 1\right) \cdot \log y + \left(-t\right)\right) \]

   9. fma-define 99.9%

      \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \color{blue}{\mathsf{fma}\left(x - 1, \log y, -t\right)}\right) \]

   10. sub-neg 99.9%

       \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \mathsf{fma}\left(\color{blue}{x + \left(-1\right)}, \log y, -t\right)\right) \]

   11. metadata-eval 99.9%

       \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \mathsf{fma}\left(x + \color{blue}{-1}, \log y, -t\right)\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \mathsf{fma}\left(x + -1, \log y, -t\right)\right)} \]
4. Add Preprocessing

5. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \mathsf{fma}\left(-1 + x, \log y, -t\right)\right) \]
6. Add Preprocessing

Alternative 2: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \left(-1 + x\right) \cdot \log y\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (fma (+ z -1.0) (log1p (- y)) (* (+ -1.0 x) (log y))) t))

C

double code(double x, double y, double z, double t) {
	return fma((z + -1.0), log1p(-y), ((-1.0 + x) * log(y))) - t;
}

Julia

function code(x, y, z, t)
	return Float64(fma(Float64(z + -1.0), log1p(Float64(-y)), Float64(Float64(-1.0 + x) * log(y))) - t)
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(z + -1.0), $MachinePrecision] * N[Log[1 + (-y)], $MachinePrecision] + N[(N[(-1.0 + x), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 88.6%

   \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
2. Step-by-step derivation

   1. +-commutative 88.6%

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

   2. fma-define 88.6%

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

   3. sub-neg 88.6%

      \[\leadsto \mathsf{fma}\left(\color{blue}{z + \left(-1\right)}, \log \left(1 - y\right), \left(x - 1\right) \cdot \log y\right) - t \]

   4. metadata-eval 88.6%

      \[\leadsto \mathsf{fma}\left(z + \color{blue}{-1}, \log \left(1 - y\right), \left(x - 1\right) \cdot \log y\right) - t \]

   5. sub-neg 88.6%

      \[\leadsto \mathsf{fma}\left(z + -1, \log \color{blue}{\left(1 + \left(-y\right)\right)}, \left(x - 1\right) \cdot \log y\right) - t \]

   6. log1p-define 99.9%

      \[\leadsto \mathsf{fma}\left(z + -1, \color{blue}{\mathsf{log1p}\left(-y\right)}, \left(x - 1\right) \cdot \log y\right) - t \]

   7. sub-neg 99.9%

      \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \color{blue}{\left(x + \left(-1\right)\right)} \cdot \log y\right) - t \]

   8. metadata-eval 99.9%

      \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \left(x + \color{blue}{-1}\right) \cdot \log y\right) - t \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \left(x + -1\right) \cdot \log y\right) - t} \]
4. Add Preprocessing

5. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \left(-1 + x\right) \cdot \log y\right) - t \]
6. Add Preprocessing

Alternative 3: 99.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z + -1 \leq -5 \cdot 10^{+20} \lor \neg \left(z + -1 \leq 2 \cdot 10^{+29}\right):\\ \;\;\;\;z \cdot \left(\log y \cdot \frac{-1 + x}{z} - y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(-1 + x\right) \cdot \log y - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (+ z -1.0) -5e+20) (not (<= (+ z -1.0) 2e+29)))
   (- (* z (- (* (log y) (/ (+ -1.0 x) z)) y)) t)
   (- (* (+ -1.0 x) (log y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z + -1.0) <= -5e+20) || !((z + -1.0) <= 2e+29)) {
		tmp = (z * ((log(y) * ((-1.0 + x) / z)) - y)) - t;
	} else {
		tmp = ((-1.0 + x) * log(y)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z + (-1.0d0)) <= (-5d+20)) .or. (.not. ((z + (-1.0d0)) <= 2d+29))) then
        tmp = (z * ((log(y) * (((-1.0d0) + x) / z)) - y)) - t
    else
        tmp = (((-1.0d0) + x) * log(y)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z + -1.0) <= -5e+20) || !((z + -1.0) <= 2e+29)) {
		tmp = (z * ((Math.log(y) * ((-1.0 + x) / z)) - y)) - t;
	} else {
		tmp = ((-1.0 + x) * Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z + -1.0) <= -5e+20) or not ((z + -1.0) <= 2e+29):
		tmp = (z * ((math.log(y) * ((-1.0 + x) / z)) - y)) - t
	else:
		tmp = ((-1.0 + x) * math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z + -1.0) <= -5e+20) || !(Float64(z + -1.0) <= 2e+29))
		tmp = Float64(Float64(z * Float64(Float64(log(y) * Float64(Float64(-1.0 + x) / z)) - y)) - t);
	else
		tmp = Float64(Float64(Float64(-1.0 + x) * log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z + -1.0) <= -5e+20) || ~(((z + -1.0) <= 2e+29)))
		tmp = (z * ((log(y) * ((-1.0 + x) / z)) - y)) - t;
	else
		tmp = ((-1.0 + x) * log(y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z + -1.0), $MachinePrecision], -5e+20], N[Not[LessEqual[N[(z + -1.0), $MachinePrecision], 2e+29]], $MachinePrecision]], N[(N[(z * N[(N[(N[Log[y], $MachinePrecision] * N[(N[(-1.0 + x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[(-1.0 + x), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z #s(literal 1 binary64)) < -5e20 or 1.99999999999999983e29 < (-.f64 z #s(literal 1 binary64))

   1. Initial program 75.2%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.2%

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \color{blue}{\left(y \cdot \left(-0.5 \cdot y - 1\right)\right)}\right) - t \]

   4. Taylor expanded in y around 0 99.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
   5. Step-by-step derivation

      1. associate-*r* 99.1%

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

      2. mul-1-neg 99.1%

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

      3. sub-neg 99.1%

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

      4. metadata-eval 99.1%

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

      5. *-commutative 99.1%

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

      6. fma-define 99.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z - 1, \left(x + -1\right) \cdot \log y\right)} - t \]

      7. sub-neg 99.2%

         \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z + \left(-1\right)}, \left(x + -1\right) \cdot \log y\right) - t \]

      8. metadata-eval 99.2%

         \[\leadsto \mathsf{fma}\left(-y, z + \color{blue}{-1}, \left(x + -1\right) \cdot \log y\right) - t \]

      9. +-commutative 99.2%

         \[\leadsto \mathsf{fma}\left(-y, \color{blue}{-1 + z}, \left(x + -1\right) \cdot \log y\right) - t \]

      10. *-commutative 99.2%

          \[\leadsto \mathsf{fma}\left(-y, -1 + z, \color{blue}{\log y \cdot \left(x + -1\right)}\right) - t \]

      11. +-commutative 99.2%

          \[\leadsto \mathsf{fma}\left(-y, -1 + z, \log y \cdot \color{blue}{\left(-1 + x\right)}\right) - t \]

   6. Simplified 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, -1 + z, \log y \cdot \left(-1 + x\right)\right)} - t \]

   7. Taylor expanded in z around inf 99.1%

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

      1. +-commutative 99.1%

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

      2. mul-1-neg 99.1%

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

      3. unsub-neg 99.1%

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

      4. +-commutative 99.1%

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

      5. associate-/l* 99.0%

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

      6. fma-define 99.0%

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

      7. sub-neg 99.0%

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

      8. metadata-eval 99.0%

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

   9. Simplified 99.0%

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

   10. Taylor expanded in y around 0 99.1%

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

       1. sub-neg 99.1%

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

       2. metadata-eval 99.1%

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

       3. associate-*r/ 99.0%

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

   12. Simplified 99.0%

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

   if -5e20 < (-.f64 z #s(literal 1 binary64)) < 1.99999999999999983e29

   1. Initial program 99.9%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.6%

      \[\leadsto \color{blue}{\log y \cdot \left(x - 1\right) - t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z + -1 \leq -5 \cdot 10^{+20} \lor \neg \left(z + -1 \leq 2 \cdot 10^{+29}\right):\\ \;\;\;\;z \cdot \left(\log y \cdot \frac{-1 + x}{z} - y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(-1 + x\right) \cdot \log y - t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-1 + x \leq -1 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{elif}\;-1 + x \leq -0.4:\\ \;\;\;\;y \cdot \left(1 - z\right) - \left(\log y + t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-1 + x\right) \cdot \log y - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ -1.0 x) -1e+47)
   (- (* x (log y)) t)
   (if (<= (+ -1.0 x) -0.4)
     (- (* y (- 1.0 z)) (+ (log y) t))
     (- (* (+ -1.0 x) (log y)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((-1.0 + x) <= -1e+47) {
		tmp = (x * log(y)) - t;
	} else if ((-1.0 + x) <= -0.4) {
		tmp = (y * (1.0 - z)) - (log(y) + t);
	} else {
		tmp = ((-1.0 + x) * log(y)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((-1.0d0) + x) <= (-1d+47)) then
        tmp = (x * log(y)) - t
    else if (((-1.0d0) + x) <= (-0.4d0)) then
        tmp = (y * (1.0d0 - z)) - (log(y) + t)
    else
        tmp = (((-1.0d0) + x) * log(y)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((-1.0 + x) <= -1e+47) {
		tmp = (x * Math.log(y)) - t;
	} else if ((-1.0 + x) <= -0.4) {
		tmp = (y * (1.0 - z)) - (Math.log(y) + t);
	} else {
		tmp = ((-1.0 + x) * Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (-1.0 + x) <= -1e+47:
		tmp = (x * math.log(y)) - t
	elif (-1.0 + x) <= -0.4:
		tmp = (y * (1.0 - z)) - (math.log(y) + t)
	else:
		tmp = ((-1.0 + x) * math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(-1.0 + x) <= -1e+47)
		tmp = Float64(Float64(x * log(y)) - t);
	elseif (Float64(-1.0 + x) <= -0.4)
		tmp = Float64(Float64(y * Float64(1.0 - z)) - Float64(log(y) + t));
	else
		tmp = Float64(Float64(Float64(-1.0 + x) * log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((-1.0 + x) <= -1e+47)
		tmp = (x * log(y)) - t;
	elseif ((-1.0 + x) <= -0.4)
		tmp = (y * (1.0 - z)) - (log(y) + t);
	else
		tmp = ((-1.0 + x) * log(y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(-1.0 + x), $MachinePrecision], -1e+47], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[N[(-1.0 + x), $MachinePrecision], -0.4], N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[(N[Log[y], $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-1.0 + x), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 x #s(literal 1 binary64)) < -1e47

   1. Initial program 94.9%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.6%

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \color{blue}{\left(y \cdot \left(-0.5 \cdot y - 1\right)\right)}\right) - t \]

   4. Taylor expanded in x around inf 94.9%

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

      1. *-commutative 94.9%

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

   6. Simplified 94.9%

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

   if -1e47 < (-.f64 x #s(literal 1 binary64)) < -0.40000000000000002

   1. Initial program 84.1%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Step-by-step derivation

      1. sub-neg 84.1%

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

      2. +-commutative 84.1%

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

      3. associate-+l+ 84.1%

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

      4. fma-define 84.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z - 1, \log \left(1 - y\right), \left(x - 1\right) \cdot \log y + \left(-t\right)\right)} \]

      5. sub-neg 84.1%

         \[\leadsto \mathsf{fma}\left(\color{blue}{z + \left(-1\right)}, \log \left(1 - y\right), \left(x - 1\right) \cdot \log y + \left(-t\right)\right) \]

      6. metadata-eval 84.1%

         \[\leadsto \mathsf{fma}\left(z + \color{blue}{-1}, \log \left(1 - y\right), \left(x - 1\right) \cdot \log y + \left(-t\right)\right) \]

      7. sub-neg 84.1%

         \[\leadsto \mathsf{fma}\left(z + -1, \log \color{blue}{\left(1 + \left(-y\right)\right)}, \left(x - 1\right) \cdot \log y + \left(-t\right)\right) \]

      8. log1p-define 100.0%

         \[\leadsto \mathsf{fma}\left(z + -1, \color{blue}{\mathsf{log1p}\left(-y\right)}, \left(x - 1\right) \cdot \log y + \left(-t\right)\right) \]

      9. fma-define 100.0%

         \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \color{blue}{\mathsf{fma}\left(x - 1, \log y, -t\right)}\right) \]

      10. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \mathsf{fma}\left(\color{blue}{x + \left(-1\right)}, \log y, -t\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \mathsf{fma}\left(x + \color{blue}{-1}, \log y, -t\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \mathsf{fma}\left(x + -1, \log y, -t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.3%

      \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \color{blue}{-1 \cdot \log y - t}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 99.3%

         \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \color{blue}{\left(-\log y\right)} - t\right) \]

   7. Simplified 99.3%

      \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \color{blue}{\left(-\log y\right) - t}\right) \]

   8. Taylor expanded in y around 0 98.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z - 1\right)\right) - \left(t + \log y\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 98.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot \left(z - 1\right)} - \left(t + \log y\right) \]

      2. mul-1-neg 98.6%

         \[\leadsto \color{blue}{\left(-y\right)} \cdot \left(z - 1\right) - \left(t + \log y\right) \]

      3. sub-neg 98.6%

         \[\leadsto \left(-y\right) \cdot \color{blue}{\left(z + \left(-1\right)\right)} - \left(t + \log y\right) \]

      4. metadata-eval 98.6%

         \[\leadsto \left(-y\right) \cdot \left(z + \color{blue}{-1}\right) - \left(t + \log y\right) \]

      5. +-commutative 98.6%

         \[\leadsto \left(-y\right) \cdot \color{blue}{\left(-1 + z\right)} - \left(t + \log y\right) \]

      6. +-commutative 98.6%

         \[\leadsto \left(-y\right) \cdot \left(-1 + z\right) - \color{blue}{\left(\log y + t\right)} \]

   10. Simplified 98.6%

       \[\leadsto \color{blue}{\left(-y\right) \cdot \left(-1 + z\right) - \left(\log y + t\right)} \]

   11. Taylor expanded in y around inf 76.5%

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

       1. mul-1-neg 76.5%

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

       2. unsub-neg 76.5%

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

       3. mul-1-neg 76.5%

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

       4. sub-neg 76.5%

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

       5. metadata-eval 76.5%

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

       6. +-commutative 76.5%

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

       7. distribute-neg-in 76.5%

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

       8. metadata-eval 76.5%

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

       9. log-rec 76.5%

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

       10. mul-1-neg 76.5%

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

       11. remove-double-neg 76.5%

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

       12. +-commutative 76.5%

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

   13. Simplified 76.5%

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

   14. Taylor expanded in y around 0 98.6%

       \[\leadsto \color{blue}{-1 \cdot \left(t + \log y\right) + y \cdot \left(1 - z\right)} \]
   15. Step-by-step derivation

       1. mul-1-neg 98.6%

          \[\leadsto \color{blue}{\left(-\left(t + \log y\right)\right)} + y \cdot \left(1 - z\right) \]

       2. +-commutative 98.6%

          \[\leadsto \color{blue}{y \cdot \left(1 - z\right) + \left(-\left(t + \log y\right)\right)} \]

       3. sub-neg 98.6%

          \[\leadsto \color{blue}{y \cdot \left(1 - z\right) - \left(t + \log y\right)} \]

       4. +-commutative 98.6%

          \[\leadsto y \cdot \left(1 - z\right) - \color{blue}{\left(\log y + t\right)} \]

   16. Simplified 98.6%

       \[\leadsto \color{blue}{y \cdot \left(1 - z\right) - \left(\log y + t\right)} \]

   if -0.40000000000000002 < (-.f64 x #s(literal 1 binary64))

   1. Initial program 93.0%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 92.8%

      \[\leadsto \color{blue}{\log y \cdot \left(x - 1\right) - t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-1 + x \leq -1 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{elif}\;-1 + x \leq -0.4:\\ \;\;\;\;y \cdot \left(1 - z\right) - \left(\log y + t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-1 + x\right) \cdot \log y - t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \left(\left(z + -1\right) \cdot \left(y \cdot \left(-1 + y \cdot -0.5\right)\right) + \left(-1 + x\right) \cdot \log y\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (+ (* (+ z -1.0) (* y (+ -1.0 (* y -0.5)))) (* (+ -1.0 x) (log y))) t))

C

double code(double x, double y, double z, double t) {
	return (((z + -1.0) * (y * (-1.0 + (y * -0.5)))) + ((-1.0 + x) * log(y))) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((z + (-1.0d0)) * (y * ((-1.0d0) + (y * (-0.5d0))))) + (((-1.0d0) + x) * log(y))) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((z + -1.0) * (y * (-1.0 + (y * -0.5)))) + ((-1.0 + x) * Math.log(y))) - t;
}

Python

def code(x, y, z, t):
	return (((z + -1.0) * (y * (-1.0 + (y * -0.5)))) + ((-1.0 + x) * math.log(y))) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(z + -1.0) * Float64(y * Float64(-1.0 + Float64(y * -0.5)))) + Float64(Float64(-1.0 + x) * log(y))) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((z + -1.0) * (y * (-1.0 + (y * -0.5)))) + ((-1.0 + x) * log(y))) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(z + -1.0), $MachinePrecision] * N[(y * N[(-1.0 + N[(y * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 + x), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 88.6%

   \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
2. Add Preprocessing

3. Taylor expanded in y around 0 99.5%

   \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \color{blue}{\left(y \cdot \left(-0.5 \cdot y - 1\right)\right)}\right) - t \]

4. Final simplification 99.5%

   \[\leadsto \left(\left(z + -1\right) \cdot \left(y \cdot \left(-1 + y \cdot -0.5\right)\right) + \left(-1 + x\right) \cdot \log y\right) - t \]
5. Add Preprocessing

Alternative 6: 87.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -242000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) - \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -242000.0) (not (<= x 1.0)))
   (- (* x (log y)) t)
   (- (- t) (log y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -242000.0) || !(x <= 1.0)) {
		tmp = (x * log(y)) - t;
	} else {
		tmp = -t - log(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-242000.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = (x * log(y)) - t
    else
        tmp = -t - log(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -242000.0) || !(x <= 1.0)) {
		tmp = (x * Math.log(y)) - t;
	} else {
		tmp = -t - Math.log(y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -242000.0) or not (x <= 1.0):
		tmp = (x * math.log(y)) - t
	else:
		tmp = -t - math.log(y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -242000.0) || !(x <= 1.0))
		tmp = Float64(Float64(x * log(y)) - t);
	else
		tmp = Float64(Float64(-t) - log(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -242000.0) || ~((x <= 1.0)))
		tmp = (x * log(y)) - t;
	else
		tmp = -t - log(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -242000.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[((-t) - N[Log[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -242000 or 1 < x

   1. Initial program 93.0%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.7%

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \color{blue}{\left(y \cdot \left(-0.5 \cdot y - 1\right)\right)}\right) - t \]

   4. Taylor expanded in x around inf 92.9%

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

      1. *-commutative 92.9%

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

   6. Simplified 92.9%

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

   if -242000 < x < 1

   1. Initial program 84.5%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.5%

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

   4. Taylor expanded in x around 0 82.7%

      \[\leadsto \color{blue}{-1 \cdot \log y} - t \]
   5. Step-by-step derivation

      1. mul-1-neg 82.7%

         \[\leadsto \color{blue}{\left(-\log y\right)} - t \]

   6. Simplified 82.7%

      \[\leadsto \color{blue}{\left(-\log y\right)} - t \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -242000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) - \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -242000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\left(y - t\right) - \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -242000.0) (not (<= x 1.0)))
   (- (* x (log y)) t)
   (- (- y t) (log y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -242000.0) || !(x <= 1.0)) {
		tmp = (x * log(y)) - t;
	} else {
		tmp = (y - t) - log(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-242000.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = (x * log(y)) - t
    else
        tmp = (y - t) - log(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -242000.0) || !(x <= 1.0)) {
		tmp = (x * Math.log(y)) - t;
	} else {
		tmp = (y - t) - Math.log(y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -242000.0) or not (x <= 1.0):
		tmp = (x * math.log(y)) - t
	else:
		tmp = (y - t) - math.log(y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -242000.0) || !(x <= 1.0))
		tmp = Float64(Float64(x * log(y)) - t);
	else
		tmp = Float64(Float64(y - t) - log(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -242000.0) || ~((x <= 1.0)))
		tmp = (x * log(y)) - t;
	else
		tmp = (y - t) - log(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -242000.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(y - t), $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -242000 or 1 < x

   1. Initial program 93.0%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.7%

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \color{blue}{\left(y \cdot \left(-0.5 \cdot y - 1\right)\right)}\right) - t \]

   4. Taylor expanded in x around inf 92.9%

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

      1. *-commutative 92.9%

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

   6. Simplified 92.9%

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

   if -242000 < x < 1

   1. Initial program 84.5%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Step-by-step derivation

      1. sub-neg 84.5%

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

      2. +-commutative 84.5%

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

      3. associate-+l+ 84.5%

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

      4. fma-define 84.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z - 1, \log \left(1 - y\right), \left(x - 1\right) \cdot \log y + \left(-t\right)\right)} \]

      5. sub-neg 84.5%

         \[\leadsto \mathsf{fma}\left(\color{blue}{z + \left(-1\right)}, \log \left(1 - y\right), \left(x - 1\right) \cdot \log y + \left(-t\right)\right) \]

      6. metadata-eval 84.5%

         \[\leadsto \mathsf{fma}\left(z + \color{blue}{-1}, \log \left(1 - y\right), \left(x - 1\right) \cdot \log y + \left(-t\right)\right) \]

      7. sub-neg 84.5%

         \[\leadsto \mathsf{fma}\left(z + -1, \log \color{blue}{\left(1 + \left(-y\right)\right)}, \left(x - 1\right) \cdot \log y + \left(-t\right)\right) \]

      8. log1p-define 100.0%

         \[\leadsto \mathsf{fma}\left(z + -1, \color{blue}{\mathsf{log1p}\left(-y\right)}, \left(x - 1\right) \cdot \log y + \left(-t\right)\right) \]

      9. fma-define 100.0%

         \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \color{blue}{\mathsf{fma}\left(x - 1, \log y, -t\right)}\right) \]

      10. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \mathsf{fma}\left(\color{blue}{x + \left(-1\right)}, \log y, -t\right)\right) \]

      11. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \mathsf{fma}\left(x + \color{blue}{-1}, \log y, -t\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \mathsf{fma}\left(x + -1, \log y, -t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.2%

      \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \color{blue}{-1 \cdot \log y - t}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 99.2%

         \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \color{blue}{\left(-\log y\right)} - t\right) \]

   7. Simplified 99.2%

      \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \color{blue}{\left(-\log y\right) - t}\right) \]

   8. Taylor expanded in y around 0 98.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z - 1\right)\right) - \left(t + \log y\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 98.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot \left(z - 1\right)} - \left(t + \log y\right) \]

      2. mul-1-neg 98.6%

         \[\leadsto \color{blue}{\left(-y\right)} \cdot \left(z - 1\right) - \left(t + \log y\right) \]

      3. sub-neg 98.6%

         \[\leadsto \left(-y\right) \cdot \color{blue}{\left(z + \left(-1\right)\right)} - \left(t + \log y\right) \]

      4. metadata-eval 98.6%

         \[\leadsto \left(-y\right) \cdot \left(z + \color{blue}{-1}\right) - \left(t + \log y\right) \]

      5. +-commutative 98.6%

         \[\leadsto \left(-y\right) \cdot \color{blue}{\left(-1 + z\right)} - \left(t + \log y\right) \]

      6. +-commutative 98.6%

         \[\leadsto \left(-y\right) \cdot \left(-1 + z\right) - \color{blue}{\left(\log y + t\right)} \]

   10. Simplified 98.6%

       \[\leadsto \color{blue}{\left(-y\right) \cdot \left(-1 + z\right) - \left(\log y + t\right)} \]

   11. Taylor expanded in z around 0 83.0%

       \[\leadsto \color{blue}{y - \left(t + \log y\right)} \]
   12. Step-by-step derivation

       1. associate--r+ 83.0%

          \[\leadsto \color{blue}{\left(y - t\right) - \log y} \]

   13. Simplified 83.0%

       \[\leadsto \color{blue}{\left(y - t\right) - \log y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -242000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\left(y - t\right) - \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -1 + y \cdot -0.5\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+167}:\\ \;\;\;\;z \cdot \left(y \cdot t\_1 - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+93}:\\ \;\;\;\;\left(-t\right) - \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot t\_1\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -1.0 (* y -0.5))))
   (if (<= z -1.05e+167)
     (* z (- (* y t_1) (/ t z)))
     (if (<= z 1.4e+93) (- (- t) (log y)) (- (* y (* z t_1)) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -1.0 + (y * -0.5);
	double tmp;
	if (z <= -1.05e+167) {
		tmp = z * ((y * t_1) - (t / z));
	} else if (z <= 1.4e+93) {
		tmp = -t - log(y);
	} else {
		tmp = (y * (z * t_1)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-1.0d0) + (y * (-0.5d0))
    if (z <= (-1.05d+167)) then
        tmp = z * ((y * t_1) - (t / z))
    else if (z <= 1.4d+93) then
        tmp = -t - log(y)
    else
        tmp = (y * (z * t_1)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -1.0 + (y * -0.5);
	double tmp;
	if (z <= -1.05e+167) {
		tmp = z * ((y * t_1) - (t / z));
	} else if (z <= 1.4e+93) {
		tmp = -t - Math.log(y);
	} else {
		tmp = (y * (z * t_1)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -1.0 + (y * -0.5)
	tmp = 0
	if z <= -1.05e+167:
		tmp = z * ((y * t_1) - (t / z))
	elif z <= 1.4e+93:
		tmp = -t - math.log(y)
	else:
		tmp = (y * (z * t_1)) - t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-1.0 + Float64(y * -0.5))
	tmp = 0.0
	if (z <= -1.05e+167)
		tmp = Float64(z * Float64(Float64(y * t_1) - Float64(t / z)));
	elseif (z <= 1.4e+93)
		tmp = Float64(Float64(-t) - log(y));
	else
		tmp = Float64(Float64(y * Float64(z * t_1)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -1.0 + (y * -0.5);
	tmp = 0.0;
	if (z <= -1.05e+167)
		tmp = z * ((y * t_1) - (t / z));
	elseif (z <= 1.4e+93)
		tmp = -t - log(y);
	else
		tmp = (y * (z * t_1)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-1.0 + N[(y * -0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.05e+167], N[(z * N[(N[(y * t$95$1), $MachinePrecision] - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+93], N[((-t) - N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(z * t$95$1), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e167

   1. Initial program 62.1%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.6%

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \color{blue}{\left(y \cdot \left(-0.5 \cdot y - 1\right)\right)}\right) - t \]

   4. Taylor expanded in z around inf 53.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(-0.5 \cdot y - 1\right)\right)} - t \]

   5. Taylor expanded in z around inf 53.6%

      \[\leadsto \color{blue}{z \cdot \left(-1 \cdot \frac{t}{z} + y \cdot \left(-0.5 \cdot y - 1\right)\right)} \]

   if -1.05e167 < z < 1.39999999999999994e93

   1. Initial program 97.5%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 96.8%

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

   4. Taylor expanded in x around 0 59.5%

      \[\leadsto \color{blue}{-1 \cdot \log y} - t \]
   5. Step-by-step derivation

      1. mul-1-neg 59.5%

         \[\leadsto \color{blue}{\left(-\log y\right)} - t \]

   6. Simplified 59.5%

      \[\leadsto \color{blue}{\left(-\log y\right)} - t \]

   if 1.39999999999999994e93 < z

   1. Initial program 66.1%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.9%

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \color{blue}{\left(y \cdot \left(-0.5 \cdot y - 1\right)\right)}\right) - t \]

   4. Taylor expanded in z around inf 68.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(-0.5 \cdot y - 1\right)\right)} - t \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+167}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-1 + y \cdot -0.5\right) - \frac{t}{z}\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+93}:\\ \;\;\;\;\left(-t\right) - \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z + -1 \leq 2 \cdot 10^{+229}:\\ \;\;\;\;\left(-1 + x\right) \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ z -1.0) 2e+229) (- (* (+ -1.0 x) (log y)) t) (- (- t) (* z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z + -1.0) <= 2e+229) {
		tmp = ((-1.0 + x) * log(y)) - t;
	} else {
		tmp = -t - (z * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z + (-1.0d0)) <= 2d+229) then
        tmp = (((-1.0d0) + x) * log(y)) - t
    else
        tmp = -t - (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z + -1.0) <= 2e+229) {
		tmp = ((-1.0 + x) * Math.log(y)) - t;
	} else {
		tmp = -t - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z + -1.0) <= 2e+229:
		tmp = ((-1.0 + x) * math.log(y)) - t
	else:
		tmp = -t - (z * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z + -1.0) <= 2e+229)
		tmp = Float64(Float64(Float64(-1.0 + x) * log(y)) - t);
	else
		tmp = Float64(Float64(-t) - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z + -1.0) <= 2e+229)
		tmp = ((-1.0 + x) * log(y)) - t;
	else
		tmp = -t - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z + -1.0), $MachinePrecision], 2e+229], N[(N[(N[(-1.0 + x), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[((-t) - N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z #s(literal 1 binary64)) < 2e229

   1. Initial program 91.1%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 90.4%

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

   if 2e229 < (-.f64 z #s(literal 1 binary64))

   1. Initial program 45.7%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 100.0%

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \color{blue}{\left(y \cdot \left(-0.5 \cdot y - 1\right)\right)}\right) - t \]

   4. Taylor expanded in z around inf 86.4%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(-0.5 \cdot y - 1\right)\right)} - t \]

   5. Taylor expanded in y around 0 86.4%

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

      1. associate-*r* 86.4%

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

      2. mul-1-neg 86.4%

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

   7. Simplified 86.4%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z + -1 \leq 2 \cdot 10^{+229}:\\ \;\;\;\;\left(-1 + x\right) \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) - z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \left(\left(-1 + x\right) \cdot \log y - \left(z + -1\right) \cdot y\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (- (* (+ -1.0 x) (log y)) (* (+ z -1.0) y)) t))

C

double code(double x, double y, double z, double t) {
	return (((-1.0 + x) * log(y)) - ((z + -1.0) * y)) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((((-1.0d0) + x) * log(y)) - ((z + (-1.0d0)) * y)) - t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((-1.0 + x) * Math.log(y)) - ((z + -1.0) * y)) - t;
}

Python

def code(x, y, z, t):
	return (((-1.0 + x) * math.log(y)) - ((z + -1.0) * y)) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(-1.0 + x) * log(y)) - Float64(Float64(z + -1.0) * y)) - t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((-1.0 + x) * log(y)) - ((z + -1.0) * y)) - t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(-1.0 + x), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(N[(z + -1.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 88.6%

   \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
2. Add Preprocessing

3. Taylor expanded in y around 0 99.5%

   \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
4. Step-by-step derivation

   1. +-commutative 99.5%

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

   2. sub-neg 99.5%

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

   3. metadata-eval 99.5%

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

   4. fma-define 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x + -1, -1 \cdot \left(y \cdot \left(z - 1\right)\right)\right)} - t \]

   5. mul-1-neg 99.5%

      \[\leadsto \mathsf{fma}\left(\log y, x + -1, \color{blue}{-y \cdot \left(z - 1\right)}\right) - t \]

   6. fma-neg 99.5%

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

   7. +-commutative 99.5%

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

   8. sub-neg 99.5%

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

   9. metadata-eval 99.5%

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

   10. +-commutative 99.5%

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

5. Simplified 99.5%

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

6. Final simplification 99.5%

   \[\leadsto \left(\left(-1 + x\right) \cdot \log y - \left(z + -1\right) \cdot y\right) - t \]
7. Add Preprocessing

Alternative 11: 43.1% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-13} \lor \neg \left(t \leq 5400\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.6e-13) (not (<= t 5400.0))) (- t) (* y (- 1.0 z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.6e-13) || !(t <= 5400.0)) {
		tmp = -t;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.6d-13)) .or. (.not. (t <= 5400.0d0))) then
        tmp = -t
    else
        tmp = y * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.6e-13) || !(t <= 5400.0)) {
		tmp = -t;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.6e-13) or not (t <= 5400.0):
		tmp = -t
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.6e-13) || !(t <= 5400.0))
		tmp = Float64(-t);
	else
		tmp = Float64(y * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.6e-13) || ~((t <= 5400.0)))
		tmp = -t;
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.6e-13], N[Not[LessEqual[t, 5400.0]], $MachinePrecision]], (-t), N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6e-13 or 5400 < t

   1. Initial program 94.9%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 64.3%

      \[\leadsto \color{blue}{-1 \cdot t} \]
   4. Step-by-step derivation

      1. mul-1-neg 64.3%

         \[\leadsto \color{blue}{-t} \]

   5. Simplified 64.3%

      \[\leadsto \color{blue}{-t} \]

   if -1.6e-13 < t < 5400

   1. Initial program 82.2%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Step-by-step derivation

      1. sub-neg 82.2%

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

      2. +-commutative 82.2%

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

      3. associate-+l+ 82.2%

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

      4. fma-define 82.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z - 1, \log \left(1 - y\right), \left(x - 1\right) \cdot \log y + \left(-t\right)\right)} \]

      5. sub-neg 82.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{z + \left(-1\right)}, \log \left(1 - y\right), \left(x - 1\right) \cdot \log y + \left(-t\right)\right) \]

      6. metadata-eval 82.2%

         \[\leadsto \mathsf{fma}\left(z + \color{blue}{-1}, \log \left(1 - y\right), \left(x - 1\right) \cdot \log y + \left(-t\right)\right) \]

      7. sub-neg 82.2%

         \[\leadsto \mathsf{fma}\left(z + -1, \log \color{blue}{\left(1 + \left(-y\right)\right)}, \left(x - 1\right) \cdot \log y + \left(-t\right)\right) \]

      8. log1p-define 99.9%

         \[\leadsto \mathsf{fma}\left(z + -1, \color{blue}{\mathsf{log1p}\left(-y\right)}, \left(x - 1\right) \cdot \log y + \left(-t\right)\right) \]

      9. fma-define 99.9%

         \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \color{blue}{\mathsf{fma}\left(x - 1, \log y, -t\right)}\right) \]

      10. sub-neg 99.9%

          \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \mathsf{fma}\left(\color{blue}{x + \left(-1\right)}, \log y, -t\right)\right) \]

      11. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \mathsf{fma}\left(x + \color{blue}{-1}, \log y, -t\right)\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \mathsf{fma}\left(x + -1, \log y, -t\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 59.6%

      \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \color{blue}{-1 \cdot \log y - t}\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 59.6%

         \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \color{blue}{\left(-\log y\right)} - t\right) \]

   7. Simplified 59.6%

      \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \color{blue}{\left(-\log y\right) - t}\right) \]

   8. Taylor expanded in y around 0 58.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z - 1\right)\right) - \left(t + \log y\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 58.9%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot \left(z - 1\right)} - \left(t + \log y\right) \]

      2. mul-1-neg 58.9%

         \[\leadsto \color{blue}{\left(-y\right)} \cdot \left(z - 1\right) - \left(t + \log y\right) \]

      3. sub-neg 58.9%

         \[\leadsto \left(-y\right) \cdot \color{blue}{\left(z + \left(-1\right)\right)} - \left(t + \log y\right) \]

      4. metadata-eval 58.9%

         \[\leadsto \left(-y\right) \cdot \left(z + \color{blue}{-1}\right) - \left(t + \log y\right) \]

      5. +-commutative 58.9%

         \[\leadsto \left(-y\right) \cdot \color{blue}{\left(-1 + z\right)} - \left(t + \log y\right) \]

      6. +-commutative 58.9%

         \[\leadsto \left(-y\right) \cdot \left(-1 + z\right) - \color{blue}{\left(\log y + t\right)} \]

   10. Simplified 58.9%

       \[\leadsto \color{blue}{\left(-y\right) \cdot \left(-1 + z\right) - \left(\log y + t\right)} \]

   11. Taylor expanded in y around inf 58.9%

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

       1. mul-1-neg 58.9%

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

       2. unsub-neg 58.9%

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

       3. mul-1-neg 58.9%

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

       4. sub-neg 58.9%

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

       5. metadata-eval 58.9%

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

       6. +-commutative 58.9%

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

       7. distribute-neg-in 58.9%

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

       8. metadata-eval 58.9%

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

       9. log-rec 58.9%

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

       10. mul-1-neg 58.9%

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

       11. remove-double-neg 58.9%

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

       12. +-commutative 58.9%

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

   13. Simplified 58.9%

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

   14. Taylor expanded in y around inf 20.0%

       \[\leadsto \color{blue}{y \cdot \left(1 - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 42.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-13} \lor \neg \left(t \leq 5400\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.8% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-13} \lor \neg \left(t \leq 62000\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.6e-13) (not (<= t 62000.0))) (- t) (* z (- y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.6e-13) || !(t <= 62000.0)) {
		tmp = -t;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.6d-13)) .or. (.not. (t <= 62000.0d0))) then
        tmp = -t
    else
        tmp = z * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.6e-13) || !(t <= 62000.0)) {
		tmp = -t;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.6e-13) or not (t <= 62000.0):
		tmp = -t
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.6e-13) || !(t <= 62000.0))
		tmp = Float64(-t);
	else
		tmp = Float64(z * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.6e-13) || ~((t <= 62000.0)))
		tmp = -t;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.6e-13], N[Not[LessEqual[t, 62000.0]], $MachinePrecision]], (-t), N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6e-13 or 62000 < t

   1. Initial program 94.9%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 64.3%

      \[\leadsto \color{blue}{-1 \cdot t} \]
   4. Step-by-step derivation

      1. mul-1-neg 64.3%

         \[\leadsto \color{blue}{-t} \]

   5. Simplified 64.3%

      \[\leadsto \color{blue}{-t} \]

   if -1.6e-13 < t < 62000

   1. Initial program 82.2%

      \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.2%

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \color{blue}{\left(y \cdot \left(-0.5 \cdot y - 1\right)\right)}\right) - t \]

   4. Taylor expanded in y around 0 99.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
   5. Step-by-step derivation

      1. associate-*r* 99.2%

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

      2. mul-1-neg 99.2%

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

      3. sub-neg 99.2%

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

      4. metadata-eval 99.2%

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

      5. *-commutative 99.2%

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

      6. fma-define 99.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z - 1, \left(x + -1\right) \cdot \log y\right)} - t \]

      7. sub-neg 99.2%

         \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z + \left(-1\right)}, \left(x + -1\right) \cdot \log y\right) - t \]

      8. metadata-eval 99.2%

         \[\leadsto \mathsf{fma}\left(-y, z + \color{blue}{-1}, \left(x + -1\right) \cdot \log y\right) - t \]

      9. +-commutative 99.2%

         \[\leadsto \mathsf{fma}\left(-y, \color{blue}{-1 + z}, \left(x + -1\right) \cdot \log y\right) - t \]

      10. *-commutative 99.2%

          \[\leadsto \mathsf{fma}\left(-y, -1 + z, \color{blue}{\log y \cdot \left(x + -1\right)}\right) - t \]

      11. +-commutative 99.2%

          \[\leadsto \mathsf{fma}\left(-y, -1 + z, \log y \cdot \color{blue}{\left(-1 + x\right)}\right) - t \]

   6. Simplified 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, -1 + z, \log y \cdot \left(-1 + x\right)\right)} - t \]

   7. Taylor expanded in z around inf 19.4%

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

      1. associate-*r* 19.4%

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

      2. mul-1-neg 19.4%

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

   9. Simplified 19.4%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-13} \lor \neg \left(t \leq 62000\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 46.1% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ z \cdot \left(\frac{y}{z} - y\right) - t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (* z (- (/ y z) y)) t))

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (z * ((y / z) - y)) - t
end function

Java

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

Python

def code(x, y, z, t):
	return (z * ((y / z) - y)) - t

Julia

function code(x, y, z, t)
	return Float64(Float64(z * Float64(Float64(y / z) - y)) - t)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(z * N[(N[(y / z), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 88.6%

   \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
2. Add Preprocessing

3. Taylor expanded in y around 0 99.5%

   \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \color{blue}{\left(y \cdot \left(-0.5 \cdot y - 1\right)\right)}\right) - t \]

4. Taylor expanded in y around 0 99.5%

   \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot \left(z - 1\right)\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
5. Step-by-step derivation

   1. associate-*r* 99.5%

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

   2. mul-1-neg 99.5%

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

   3. sub-neg 99.5%

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

   4. metadata-eval 99.5%

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

   5. *-commutative 99.5%

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

   6. fma-define 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z - 1, \left(x + -1\right) \cdot \log y\right)} - t \]

   7. sub-neg 99.5%

      \[\leadsto \mathsf{fma}\left(-y, \color{blue}{z + \left(-1\right)}, \left(x + -1\right) \cdot \log y\right) - t \]

   8. metadata-eval 99.5%

      \[\leadsto \mathsf{fma}\left(-y, z + \color{blue}{-1}, \left(x + -1\right) \cdot \log y\right) - t \]

   9. +-commutative 99.5%

      \[\leadsto \mathsf{fma}\left(-y, \color{blue}{-1 + z}, \left(x + -1\right) \cdot \log y\right) - t \]

   10. *-commutative 99.5%

       \[\leadsto \mathsf{fma}\left(-y, -1 + z, \color{blue}{\log y \cdot \left(x + -1\right)}\right) - t \]

   11. +-commutative 99.5%

       \[\leadsto \mathsf{fma}\left(-y, -1 + z, \log y \cdot \color{blue}{\left(-1 + x\right)}\right) - t \]

6. Simplified 99.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-y, -1 + z, \log y \cdot \left(-1 + x\right)\right)} - t \]

7. Taylor expanded in z around inf 87.4%

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

   1. +-commutative 87.4%

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

   2. mul-1-neg 87.4%

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

   3. unsub-neg 87.4%

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

   4. +-commutative 87.4%

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

   5. associate-/l* 87.3%

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

   6. fma-define 87.3%

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

   7. sub-neg 87.3%

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

   8. metadata-eval 87.3%

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

9. Simplified 87.3%

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

10. Taylor expanded in y around inf 44.7%

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

11. Final simplification 44.7%

    \[\leadsto z \cdot \left(\frac{y}{z} - y\right) - t \]
12. Add Preprocessing

Alternative 14: 45.9% accurate, 35.8× speedup

Math

\[\begin{array}{l} \\ \left(-t\right) - z \cdot y \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- (- t) (* z y)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[((-t) - N[(z * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 88.6%

   \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
2. Add Preprocessing

3. Taylor expanded in y around 0 99.5%

   \[\leadsto \left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \color{blue}{\left(y \cdot \left(-0.5 \cdot y - 1\right)\right)}\right) - t \]

4. Taylor expanded in z around inf 44.5%

   \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(-0.5 \cdot y - 1\right)\right)} - t \]

5. Taylor expanded in y around 0 44.5%

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

   1. associate-*r* 44.5%

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

   2. mul-1-neg 44.5%

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

7. Simplified 44.5%

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

8. Final simplification 44.5%

   \[\leadsto \left(-t\right) - z \cdot y \]
9. Add Preprocessing

Alternative 15: 35.4% accurate, 107.5× speedup

Math

\[\begin{array}{l} \\ -t \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- t))

C

double code(double x, double y, double z, double t) {
	return -t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = -t
end function

Java

public static double code(double x, double y, double z, double t) {
	return -t;
}

Python

def code(x, y, z, t):
	return -t

Julia

function code(x, y, z, t)
	return Float64(-t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = -t;
end

Wolfram

code[x_, y_, z_, t_] := (-t)

Derivation

1. Initial program 88.6%

   \[\left(\left(x - 1\right) \cdot \log y + \left(z - 1\right) \cdot \log \left(1 - y\right)\right) - t \]
2. Add Preprocessing

3. Taylor expanded in t around inf 33.6%

   \[\leadsto \color{blue}{-1 \cdot t} \]
4. Step-by-step derivation

   1. mul-1-neg 33.6%

      \[\leadsto \color{blue}{-t} \]

5. Simplified 33.6%

   \[\leadsto \color{blue}{-t} \]

6. Final simplification 33.6%

   \[\leadsto -t \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024077 
(FPCore (x y z t)
  :name "Statistics.Distribution.Beta:$cdensity from math-functions-0.1.5.2"
  :precision binary64
  (- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t))