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

Percentage Accurate: 90.0% → 99.8%

Time: 18.6s

Alternatives: 14

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: 90.0% 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 87.2%

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

   1. +-commutative 87.2%

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

   2. associate--l+ 87.2%

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

   3. fma-def 87.2%

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

   4. sub-neg 87.2%

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

   5. metadata-eval 87.2%

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

   6. sub-neg 87.2%

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

   7. log1p-def 99.8%

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

   8. fma-neg 99.9%

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

   9. sub-neg 99.9%

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

   10. 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. Final simplification 99.9%

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

Alternative 2: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 87.2%

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

   1. sub-neg 87.2%

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

   2. +-commutative 87.2%

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

   3. associate-+l+ 87.2%

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

   4. fma-def 87.2%

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

   5. sub-neg 87.2%

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

   6. metadata-eval 87.2%

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

   7. sub-neg 87.2%

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

   8. log1p-def 99.8%

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

   9. sub-neg 99.8%

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

   10. sub-neg 99.8%

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

   11. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 3: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x, double y, double z, double t) {
	return ((z * Math.log1p(-y)) + (Math.log(y) * (-1.0 + x))) - t;
}

Python

def code(x, y, z, t):
	return ((z * math.log1p(-y)) + (math.log(y) * (-1.0 + x))) - t

Julia

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

Wolfram

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

Derivation

1. Initial program 87.2%

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

2. Taylor expanded in z around inf 86.6%

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

   1. *-commutative 86.6%

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

   2. sub-neg 86.6%

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

   3. mul-1-neg 86.6%

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

   4. log1p-def 99.2%

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

   5. mul-1-neg 99.2%

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

4. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 4: 96.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-1 + x \leq -100 \lor \neg \left(-1 + x \leq 5000000\right):\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-\log y\right) - \left(z + -1\right) \cdot y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (+ -1.0 x) -100.0) (not (<= (+ -1.0 x) 5000000.0)))
   (- (* (log y) (+ -1.0 x)) t)
   (- (- (- (log y)) (* (+ z -1.0) y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((-1.0 + x) <= -100.0) || !((-1.0 + x) <= 5000000.0)) {
		tmp = (log(y) * (-1.0 + x)) - t;
	} else {
		tmp = (-log(y) - ((z + -1.0) * 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) <= (-100.0d0)) .or. (.not. (((-1.0d0) + x) <= 5000000.0d0))) then
        tmp = (log(y) * ((-1.0d0) + x)) - t
    else
        tmp = (-log(y) - ((z + (-1.0d0)) * 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) <= -100.0) || !((-1.0 + x) <= 5000000.0)) {
		tmp = (Math.log(y) * (-1.0 + x)) - t;
	} else {
		tmp = (-Math.log(y) - ((z + -1.0) * y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((-1.0 + x) <= -100.0) or not ((-1.0 + x) <= 5000000.0):
		tmp = (math.log(y) * (-1.0 + x)) - t
	else:
		tmp = (-math.log(y) - ((z + -1.0) * y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(-1.0 + x) <= -100.0) || !(Float64(-1.0 + x) <= 5000000.0))
		tmp = Float64(Float64(log(y) * Float64(-1.0 + x)) - t);
	else
		tmp = Float64(Float64(Float64(-log(y)) - Float64(Float64(z + -1.0) * y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((-1.0 + x) <= -100.0) || ~(((-1.0 + x) <= 5000000.0)))
		tmp = (log(y) * (-1.0 + x)) - t;
	else
		tmp = (-log(y) - ((z + -1.0) * y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(-1.0 + x), $MachinePrecision], -100.0], N[Not[LessEqual[N[(-1.0 + x), $MachinePrecision], 5000000.0]], $MachinePrecision]], N[(N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[((-N[Log[y], $MachinePrecision]) - N[(N[(z + -1.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 x 1) < -100 or 5e6 < (-.f64 x 1)

   1. Initial program 94.3%

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

   2. Taylor expanded in y around 0 93.8%

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

   if -100 < (-.f64 x 1) < 5e6

   1. Initial program 79.9%

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

      1. sub-neg 79.9%

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

      2. metadata-eval 79.9%

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

      3. flip-+ 79.9%

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

      4. associate-*l/ 79.9%

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

      5. metadata-eval 79.9%

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

      6. fma-neg 79.9%

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

      7. metadata-eval 79.9%

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

      8. sub-neg 79.9%

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

      9. metadata-eval 79.9%

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

      10. +-commutative 79.9%

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

   3. Applied egg-rr 79.9%

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

   4. Taylor expanded in y around 0 98.2%

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

      1. mul-1-neg 98.2%

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

   6. Simplified 98.2%

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

   7. Taylor expanded in x around 0 97.8%

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

      1. mul-1-neg 97.8%

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

      2. sub-neg 97.8%

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

      3. metadata-eval 97.8%

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

      4. unsub-neg 97.8%

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

      5. mul-1-neg 97.8%

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

      6. +-commutative 97.8%

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

   9. Simplified 97.8%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-1 + x \leq -100 \lor \neg \left(-1 + x \leq 5000000\right):\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-\log y\right) - \left(z + -1\right) \cdot y\right) - t\\ \end{array} \]

Alternative 5: 96.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-1 + x \leq -100:\\ \;\;\;\;\left(-t\right) - \left(-1 + x\right) \cdot \log \left(\frac{1}{y}\right)\\ \mathbf{elif}\;-1 + x \leq 5000000:\\ \;\;\;\;\left(\left(-\log y\right) - \left(z + -1\right) \cdot y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ -1.0 x) -100.0)
   (- (- t) (* (+ -1.0 x) (log (/ 1.0 y))))
   (if (<= (+ -1.0 x) 5000000.0)
     (- (- (- (log y)) (* (+ z -1.0) y)) t)
     (- (* (log y) (+ -1.0 x)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((-1.0 + x) <= -100.0) {
		tmp = -t - ((-1.0 + x) * log((1.0 / y)));
	} else if ((-1.0 + x) <= 5000000.0) {
		tmp = (-log(y) - ((z + -1.0) * y)) - t;
	} else {
		tmp = (log(y) * (-1.0 + x)) - 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) <= (-100.0d0)) then
        tmp = -t - (((-1.0d0) + x) * log((1.0d0 / y)))
    else if (((-1.0d0) + x) <= 5000000.0d0) then
        tmp = (-log(y) - ((z + (-1.0d0)) * y)) - t
    else
        tmp = (log(y) * ((-1.0d0) + x)) - 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) <= -100.0) {
		tmp = -t - ((-1.0 + x) * Math.log((1.0 / y)));
	} else if ((-1.0 + x) <= 5000000.0) {
		tmp = (-Math.log(y) - ((z + -1.0) * y)) - t;
	} else {
		tmp = (Math.log(y) * (-1.0 + x)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (-1.0 + x) <= -100.0:
		tmp = -t - ((-1.0 + x) * math.log((1.0 / y)))
	elif (-1.0 + x) <= 5000000.0:
		tmp = (-math.log(y) - ((z + -1.0) * y)) - t
	else:
		tmp = (math.log(y) * (-1.0 + x)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(-1.0 + x) <= -100.0)
		tmp = Float64(Float64(-t) - Float64(Float64(-1.0 + x) * log(Float64(1.0 / y))));
	elseif (Float64(-1.0 + x) <= 5000000.0)
		tmp = Float64(Float64(Float64(-log(y)) - Float64(Float64(z + -1.0) * y)) - t);
	else
		tmp = Float64(Float64(log(y) * Float64(-1.0 + x)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((-1.0 + x) <= -100.0)
		tmp = -t - ((-1.0 + x) * log((1.0 / y)));
	elseif ((-1.0 + x) <= 5000000.0)
		tmp = (-log(y) - ((z + -1.0) * y)) - t;
	else
		tmp = (log(y) * (-1.0 + x)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(-1.0 + x), $MachinePrecision], -100.0], N[((-t) - N[(N[(-1.0 + x), $MachinePrecision] * N[Log[N[(1.0 / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(-1.0 + x), $MachinePrecision], 5000000.0], N[(N[((-N[Log[y], $MachinePrecision]) - N[(N[(z + -1.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 x 1) < -100

   1. Initial program 91.7%

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

   2. Taylor expanded in y around 0 90.6%

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

   3. Taylor expanded in y around inf 90.6%

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

   if -100 < (-.f64 x 1) < 5e6

   1. Initial program 79.9%

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

      1. sub-neg 79.9%

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

      2. metadata-eval 79.9%

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

      3. flip-+ 79.9%

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

      4. associate-*l/ 79.9%

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

      5. metadata-eval 79.9%

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

      6. fma-neg 79.9%

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

      7. metadata-eval 79.9%

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

      8. sub-neg 79.9%

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

      9. metadata-eval 79.9%

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

      10. +-commutative 79.9%

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

   3. Applied egg-rr 79.9%

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

   4. Taylor expanded in y around 0 98.2%

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

      1. mul-1-neg 98.2%

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

   6. Simplified 98.2%

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

   7. Taylor expanded in x around 0 97.8%

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

      1. mul-1-neg 97.8%

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

      2. sub-neg 97.8%

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

      3. metadata-eval 97.8%

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

      4. unsub-neg 97.8%

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

      5. mul-1-neg 97.8%

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

      6. +-commutative 97.8%

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

   9. Simplified 97.8%

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

   if 5e6 < (-.f64 x 1)

   1. Initial program 96.9%

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

   2. Taylor expanded in y around 0 96.9%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-1 + x \leq -100:\\ \;\;\;\;\left(-t\right) - \left(-1 + x\right) \cdot \log \left(\frac{1}{y}\right)\\ \mathbf{elif}\;-1 + x \leq 5000000:\\ \;\;\;\;\left(\left(-\log y\right) - \left(z + -1\right) \cdot y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right) - t\\ \end{array} \]

Alternative 6: 75.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-1 + x \leq -3.5 \cdot 10^{+24} \lor \neg \left(-1 + x \leq 1.35 \cdot 10^{+122}\right):\\ \;\;\;\;\log y \cdot \left(-1 + x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) - \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (+ -1.0 x) -3.5e+24) (not (<= (+ -1.0 x) 1.35e+122)))
   (* (log y) (+ -1.0 x))
   (- (- t) (log y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((-1.0 + x) <= -3.5e+24) || !((-1.0 + x) <= 1.35e+122)) {
		tmp = log(y) * (-1.0 + x);
	} 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 ((((-1.0d0) + x) <= (-3.5d+24)) .or. (.not. (((-1.0d0) + x) <= 1.35d+122))) then
        tmp = log(y) * ((-1.0d0) + x)
    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 (((-1.0 + x) <= -3.5e+24) || !((-1.0 + x) <= 1.35e+122)) {
		tmp = Math.log(y) * (-1.0 + x);
	} else {
		tmp = -t - Math.log(y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((-1.0 + x) <= -3.5e+24) or not ((-1.0 + x) <= 1.35e+122):
		tmp = math.log(y) * (-1.0 + x)
	else:
		tmp = -t - math.log(y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(-1.0 + x) <= -3.5e+24) || !(Float64(-1.0 + x) <= 1.35e+122))
		tmp = Float64(log(y) * Float64(-1.0 + x));
	else
		tmp = Float64(Float64(-t) - log(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((-1.0 + x) <= -3.5e+24) || ~(((-1.0 + x) <= 1.35e+122)))
		tmp = log(y) * (-1.0 + x);
	else
		tmp = -t - log(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(-1.0 + x), $MachinePrecision], -3.5e+24], N[Not[LessEqual[N[(-1.0 + x), $MachinePrecision], 1.35e+122]], $MachinePrecision]], N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision], N[((-t) - N[Log[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 x 1) < -3.5000000000000002e24 or 1.3499999999999999e122 < (-.f64 x 1)

   1. Initial program 94.8%

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

   2. Taylor expanded in y around 0 94.1%

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

   3. Taylor expanded in t around 0 79.4%

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

   if -3.5000000000000002e24 < (-.f64 x 1) < 1.3499999999999999e122

   1. Initial program 82.4%

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

   2. Taylor expanded in y around 0 80.1%

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

   3. Taylor expanded in x around 0 72.5%

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

      1. mul-1-neg 72.5%

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

   5. Simplified 72.5%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-1 + x \leq -3.5 \cdot 10^{+24} \lor \neg \left(-1 + x \leq 1.35 \cdot 10^{+122}\right):\\ \;\;\;\;\log y \cdot \left(-1 + x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) - \log y\\ \end{array} \]

Alternative 7: 99.2% accurate, 1.9× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return ((log(y) * (-1.0 + x)) - ((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 = ((log(y) * ((-1.0d0) + x)) - ((z + (-1.0d0)) * y)) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.2%

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

   1. sub-neg 87.2%

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

   2. metadata-eval 87.2%

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

   3. flip-+ 64.5%

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

   4. associate-*l/ 64.4%

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

   5. metadata-eval 64.4%

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

   6. fma-neg 64.4%

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

   7. metadata-eval 64.4%

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

   8. sub-neg 64.4%

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

   9. metadata-eval 64.4%

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

   10. +-commutative 64.4%

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

3. Applied egg-rr 64.4%

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

4. Taylor expanded in y around 0 76.1%

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

   1. mul-1-neg 76.1%

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

6. Simplified 76.1%

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

7. Taylor expanded in x around 0 98.8%

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

   1. +-commutative 98.8%

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

   2. mul-1-neg 98.8%

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

   3. sub-neg 98.8%

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

   4. metadata-eval 98.8%

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

   5. unsub-neg 98.8%

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

   6. associate--l+ 98.8%

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

   7. distribute-rgt-out 98.8%

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

   8. +-commutative 98.8%

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

9. Simplified 98.8%

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

10. Final simplification 98.8%

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

Alternative 8: 87.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7200000000 \lor \neg \left(t \leq 4.1 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -7200000000.0) (not (<= t 4.1e-16)))
   (- (* x (log y)) t)
   (* (log y) (+ -1.0 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7200000000.0) || !(t <= 4.1e-16)) {
		tmp = (x * log(y)) - t;
	} else {
		tmp = log(y) * (-1.0 + x);
	}
	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 <= (-7200000000.0d0)) .or. (.not. (t <= 4.1d-16))) then
        tmp = (x * log(y)) - t
    else
        tmp = log(y) * ((-1.0d0) + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7200000000.0) || !(t <= 4.1e-16)) {
		tmp = (x * Math.log(y)) - t;
	} else {
		tmp = Math.log(y) * (-1.0 + x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -7200000000.0) or not (t <= 4.1e-16):
		tmp = (x * math.log(y)) - t
	else:
		tmp = math.log(y) * (-1.0 + x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -7200000000.0) || !(t <= 4.1e-16))
		tmp = Float64(Float64(x * log(y)) - t);
	else
		tmp = Float64(log(y) * Float64(-1.0 + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -7200000000.0) || ~((t <= 4.1e-16)))
		tmp = (x * log(y)) - t;
	else
		tmp = log(y) * (-1.0 + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -7200000000.0], N[Not[LessEqual[t, 4.1e-16]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * N[(-1.0 + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.2e9 or 4.10000000000000006e-16 < t

   1. Initial program 92.3%

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

   2. Taylor expanded in y around 0 91.6%

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

   3. Taylor expanded in x around inf 91.5%

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

   if -7.2e9 < t < 4.10000000000000006e-16

   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. Taylor expanded in y around 0 79.5%

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

   3. Taylor expanded in t around 0 79.1%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7200000000 \lor \neg \left(t \leq 4.1 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(-1 + x\right)\\ \end{array} \]

Alternative 9: 89.1% accurate, 2.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (y + (log(y) * (-1.0 + x))) - 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 = (y + (log(y) * ((-1.0d0) + x))) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.2%

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

2. Taylor expanded in z around 0 86.2%

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

   1. +-commutative 86.2%

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

   2. sub-neg 86.2%

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

   3. metadata-eval 86.2%

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

   4. fma-def 86.2%

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

   5. mul-1-neg 86.2%

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

   6. fma-neg 86.2%

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

   7. +-commutative 86.2%

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

   8. sub-neg 86.2%

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

   9. mul-1-neg 86.2%

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

   10. log1p-def 86.2%

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

   11. mul-1-neg 86.2%

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

4. Simplified 86.2%

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

5. Taylor expanded in y around 0 85.8%

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

6. Final simplification 85.8%

   \[\leadsto \left(y + \log y \cdot \left(-1 + x\right)\right) - t \]

Alternative 10: 52.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7200000000:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-5}:\\ \;\;\;\;-\log y\\ \mathbf{else}:\\ \;\;\;\;\log y - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -7200000000.0) (- t) (if (<= t 3.4e-5) (- (log y)) (- (log y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7200000000.0) {
		tmp = -t;
	} else if (t <= 3.4e-5) {
		tmp = -log(y);
	} else {
		tmp = 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 (t <= (-7200000000.0d0)) then
        tmp = -t
    else if (t <= 3.4d-5) then
        tmp = -log(y)
    else
        tmp = 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 (t <= -7200000000.0) {
		tmp = -t;
	} else if (t <= 3.4e-5) {
		tmp = -Math.log(y);
	} else {
		tmp = Math.log(y) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -7200000000.0:
		tmp = -t
	elif t <= 3.4e-5:
		tmp = -math.log(y)
	else:
		tmp = math.log(y) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -7200000000.0)
		tmp = Float64(-t);
	elseif (t <= 3.4e-5)
		tmp = Float64(-log(y));
	else
		tmp = Float64(log(y) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -7200000000.0)
		tmp = -t;
	elseif (t <= 3.4e-5)
		tmp = -log(y);
	else
		tmp = log(y) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -7200000000.0], (-t), If[LessEqual[t, 3.4e-5], (-N[Log[y], $MachinePrecision]), N[(N[Log[y], $MachinePrecision] - t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.2e9

   1. Initial program 95.4%

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

   2. Taylor expanded in t around inf 75.8%

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

      1. mul-1-neg 75.8%

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

   4. Simplified 75.8%

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

   if -7.2e9 < t < 3.4e-5

   1. Initial program 82.4%

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

   2. Taylor expanded in y around 0 79.8%

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

   3. Taylor expanded in x around 0 33.8%

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

      1. mul-1-neg 33.8%

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

   5. Simplified 33.8%

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

   6. Taylor expanded in t around 0 33.4%

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

      1. mul-1-neg 33.4%

         \[\leadsto \color{blue}{-\log y} \]

   8. Simplified 33.4%

      \[\leadsto \color{blue}{-\log y} \]

   if 3.4e-5 < t

   1. Initial program 89.0%

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

   2. Taylor expanded in z around 0 88.0%

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

      1. +-commutative 88.0%

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

      2. sub-neg 88.0%

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

      3. metadata-eval 88.0%

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

      4. fma-def 88.0%

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

      5. mul-1-neg 88.0%

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

      6. fma-neg 88.0%

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

      7. +-commutative 88.0%

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

      8. sub-neg 88.0%

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

      9. mul-1-neg 88.0%

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

      10. log1p-def 88.0%

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

      11. mul-1-neg 88.0%

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

   4. Simplified 88.0%

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

   5. Taylor expanded in x around 0 61.9%

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

      1. neg-mul-1 61.9%

         \[\leadsto \left(\color{blue}{\left(-\log y\right)} - \mathsf{log1p}\left(-y\right)\right) - t \]

   7. Simplified 61.9%

      \[\leadsto \left(\color{blue}{\left(-\log y\right)} - \mathsf{log1p}\left(-y\right)\right) - t \]
   8. Step-by-step derivation

      1. log1p-expm1-u 61.9%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\left(-\log y\right) - \mathsf{log1p}\left(-y\right)\right)\right)} - t \]

      2. expm1-udef 61.9%

         \[\leadsto \mathsf{log1p}\left(\color{blue}{e^{\left(-\log y\right) - \mathsf{log1p}\left(-y\right)} - 1}\right) - t \]

      3. exp-diff 61.9%

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

      4. add-sqr-sqrt 61.9%

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

      5. sqrt-unprod 61.9%

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

      6. sqr-neg 61.9%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 10.6%

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

      9. add-exp-log 10.6%

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

      10. log1p-udef 10.6%

          \[\leadsto \mathsf{log1p}\left(\frac{y}{e^{\color{blue}{\log \left(1 + \left(-y\right)\right)}}} - 1\right) - t \]

      11. rem-exp-log 10.6%

          \[\leadsto \mathsf{log1p}\left(\frac{y}{\color{blue}{1 + \left(-y\right)}} - 1\right) - t \]

      12. add-sqr-sqrt 0.0%

          \[\leadsto \mathsf{log1p}\left(\frac{y}{1 + \color{blue}{\sqrt{-y} \cdot \sqrt{-y}}} - 1\right) - t \]

      13. sqrt-unprod 10.6%

          \[\leadsto \mathsf{log1p}\left(\frac{y}{1 + \color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}} - 1\right) - t \]

      14. sqr-neg 10.6%

          \[\leadsto \mathsf{log1p}\left(\frac{y}{1 + \sqrt{\color{blue}{y \cdot y}}} - 1\right) - t \]

      15. sqrt-unprod 10.6%

          \[\leadsto \mathsf{log1p}\left(\frac{y}{1 + \color{blue}{\sqrt{y} \cdot \sqrt{y}}} - 1\right) - t \]

      16. add-sqr-sqrt 10.6%

          \[\leadsto \mathsf{log1p}\left(\frac{y}{1 + \color{blue}{y}} - 1\right) - t \]

   9. Applied egg-rr 10.6%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(\frac{y}{1 + y} - 1\right)} - t \]

   10. Taylor expanded in y around 0 62.0%

       \[\leadsto \color{blue}{\log y} - t \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7200000000:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-5}:\\ \;\;\;\;-\log y\\ \mathbf{else}:\\ \;\;\;\;\log y - t\\ \end{array} \]

Alternative 11: 88.9% accurate, 2.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (log(y) * (-1.0 + x)) - 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 = (log(y) * ((-1.0d0) + x)) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.2%

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

2. Taylor expanded in y around 0 85.5%

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

3. Final simplification 85.5%

   \[\leadsto \log y \cdot \left(-1 + x\right) - t \]

Alternative 12: 52.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7200000000 \lor \neg \left(t \leq 3.4 \cdot 10^{-5}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;-\log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -7200000000.0) (not (<= t 3.4e-5))) (- t) (- (log y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7200000000.0) || !(t <= 3.4e-5)) {
		tmp = -t;
	} else {
		tmp = -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 ((t <= (-7200000000.0d0)) .or. (.not. (t <= 3.4d-5))) then
        tmp = -t
    else
        tmp = -log(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7200000000.0) || !(t <= 3.4e-5)) {
		tmp = -t;
	} else {
		tmp = -Math.log(y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -7200000000.0) or not (t <= 3.4e-5):
		tmp = -t
	else:
		tmp = -math.log(y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -7200000000.0) || !(t <= 3.4e-5))
		tmp = Float64(-t);
	else
		tmp = Float64(-log(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -7200000000.0) || ~((t <= 3.4e-5)))
		tmp = -t;
	else
		tmp = -log(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -7200000000.0], N[Not[LessEqual[t, 3.4e-5]], $MachinePrecision]], (-t), (-N[Log[y], $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if t < -7.2e9 or 3.4e-5 < t

   1. Initial program 92.1%

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

   2. Taylor expanded in t around inf 68.7%

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

      1. mul-1-neg 68.7%

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

   4. Simplified 68.7%

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

   if -7.2e9 < t < 3.4e-5

   1. Initial program 82.4%

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

   2. Taylor expanded in y around 0 79.8%

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

   3. Taylor expanded in x around 0 33.8%

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

      1. mul-1-neg 33.8%

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

   5. Simplified 33.8%

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

   6. Taylor expanded in t around 0 33.4%

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

      1. mul-1-neg 33.4%

         \[\leadsto \color{blue}{-\log y} \]

   8. Simplified 33.4%

      \[\leadsto \color{blue}{-\log y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7200000000 \lor \neg \left(t \leq 3.4 \cdot 10^{-5}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;-\log y\\ \end{array} \]

Alternative 13: 53.3% accurate, 2.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return -t - log(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 - log(y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.2%

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

2. Taylor expanded in y around 0 85.5%

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

3. Taylor expanded in x around 0 51.0%

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

   1. mul-1-neg 51.0%

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

5. Simplified 51.0%

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

6. Final simplification 51.0%

   \[\leadsto \left(-t\right) - \log y \]

Alternative 14: 35.7% 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 87.2%

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

2. Taylor expanded in t around inf 35.4%

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

   1. mul-1-neg 35.4%

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

4. Simplified 35.4%

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

5. Final simplification 35.4%

   \[\leadsto -t \]

Reproduce

herbie shell --seed 2023312 
(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))