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

Percentage Accurate: 97.2% → 99.1%

Time: 16.9s

Alternatives: 9

Speedup: 1.8×

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: 97.2% 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: 99.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.1 \cdot 10^{-47}:\\ \;\;\;\;\left(x \cdot \log y - \log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x + -1, \log y, \mathsf{log1p}\left(-y\right) \cdot \left(-1 + z\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.1e-47)
   (- (- (* x (log y)) (log y)) t)
   (- (fma (+ x -1.0) (log y) (* (log1p (- y)) (+ -1.0 z))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.1e-47) {
		tmp = ((x * log(y)) - log(y)) - t;
	} else {
		tmp = fma((x + -1.0), log(y), (log1p(-y) * (-1.0 + z))) - t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.1e-47)
		tmp = Float64(Float64(Float64(x * log(y)) - log(y)) - t);
	else
		tmp = Float64(fma(Float64(x + -1.0), log(y), Float64(log1p(Float64(-y)) * Float64(-1.0 + z))) - t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.1e-47], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[(x + -1.0), $MachinePrecision] * N[Log[y], $MachinePrecision] + N[(N[Log[1 + (-y)], $MachinePrecision] * N[(-1.0 + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.10000000000000009e-47

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 99.8%

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

   4. Taylor expanded in x around inf 99.8%

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

      1. +-commutative 99.8%

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

      2. mul-1-neg 99.8%

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

      3. unsub-neg 99.8%

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

   6. Applied egg-rr 99.8%

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

   if 1.10000000000000009e-47 < y

   1. Initial program 77.8%

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

      1. fma-def 77.8%

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

      2. sub-neg 77.8%

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

      3. metadata-eval 77.8%

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

      4. sub-neg 77.8%

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

      5. metadata-eval 77.8%

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

      6. sub-neg 77.8%

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

      7. log1p-def 94.8%

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

   3. Simplified 94.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x + -1, \log y, \left(z + -1\right) \cdot \mathsf{log1p}\left(-y\right)\right) - t} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.1 \cdot 10^{-47}:\\ \;\;\;\;\left(x \cdot \log y - \log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x + -1, \log y, \mathsf{log1p}\left(-y\right) \cdot \left(-1 + z\right)\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.1 \cdot 10^{-47}:\\ \;\;\;\;\left(x \cdot \log y - \log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log y \cdot \left(x + -1\right) - y \cdot \left(-1 + z\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.1e-47)
   (- (- (* x (log y)) (log y)) t)
   (- (- (* (log y) (+ x -1.0)) (* y (+ -1.0 z))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.1e-47) {
		tmp = ((x * log(y)) - log(y)) - t;
	} else {
		tmp = ((log(y) * (x + -1.0)) - (y * (-1.0 + z))) - 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 (y <= 1.1d-47) then
        tmp = ((x * log(y)) - log(y)) - t
    else
        tmp = ((log(y) * (x + (-1.0d0))) - (y * ((-1.0d0) + z))) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.1e-47) {
		tmp = ((x * Math.log(y)) - Math.log(y)) - t;
	} else {
		tmp = ((Math.log(y) * (x + -1.0)) - (y * (-1.0 + z))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.1e-47:
		tmp = ((x * math.log(y)) - math.log(y)) - t
	else:
		tmp = ((math.log(y) * (x + -1.0)) - (y * (-1.0 + z))) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.1e-47)
		tmp = Float64(Float64(Float64(x * log(y)) - log(y)) - t);
	else
		tmp = Float64(Float64(Float64(log(y) * Float64(x + -1.0)) - Float64(y * Float64(-1.0 + z))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.1e-47)
		tmp = ((x * log(y)) - log(y)) - t;
	else
		tmp = ((log(y) * (x + -1.0)) - (y * (-1.0 + z))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.1e-47], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[(N[Log[y], $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision] - N[(y * N[(-1.0 + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.10000000000000009e-47

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 99.8%

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

   4. Taylor expanded in x around inf 99.8%

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

      1. +-commutative 99.8%

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

      2. mul-1-neg 99.8%

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

      3. unsub-neg 99.8%

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

   6. Applied egg-rr 99.8%

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

   if 1.10000000000000009e-47 < y

   1. Initial program 77.8%

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

   3. Taylor expanded in y around 0 91.4%

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

      1. +-commutative 91.4%

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

      2. sub-neg 91.4%

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

      3. metadata-eval 91.4%

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

      4. fma-def 91.4%

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

      5. mul-1-neg 91.4%

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

      6. fma-neg 91.4%

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

      7. +-commutative 91.4%

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

      8. sub-neg 91.4%

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

      9. metadata-eval 91.4%

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

      10. +-commutative 91.4%

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

   5. Simplified 91.4%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.1 \cdot 10^{-47}:\\ \;\;\;\;\left(x \cdot \log y - \log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log y \cdot \left(x + -1\right) - y \cdot \left(-1 + z\right)\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \log y \cdot \left(x + -1\right)\\ \mathbf{if}\;y \leq 5 \cdot 10^{-48}:\\ \;\;\;\;t\_1 - t\\ \mathbf{else}:\\ \;\;\;\;\left(t\_1 - y \cdot \left(-1 + z\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (log y) (+ x -1.0))))
   (if (<= y 5e-48) (- t_1 t) (- (- t_1 (* y (+ -1.0 z))) t))))

C

double code(double x, double y, double z, double t) {
	double t_1 = log(y) * (x + -1.0);
	double tmp;
	if (y <= 5e-48) {
		tmp = t_1 - t;
	} else {
		tmp = (t_1 - (y * (-1.0 + z))) - 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 = log(y) * (x + (-1.0d0))
    if (y <= 5d-48) then
        tmp = t_1 - t
    else
        tmp = (t_1 - (y * ((-1.0d0) + z))) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = Math.log(y) * (x + -1.0);
	double tmp;
	if (y <= 5e-48) {
		tmp = t_1 - t;
	} else {
		tmp = (t_1 - (y * (-1.0 + z))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = math.log(y) * (x + -1.0)
	tmp = 0
	if y <= 5e-48:
		tmp = t_1 - t
	else:
		tmp = (t_1 - (y * (-1.0 + z))) - t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(log(y) * Float64(x + -1.0))
	tmp = 0.0
	if (y <= 5e-48)
		tmp = Float64(t_1 - t);
	else
		tmp = Float64(Float64(t_1 - Float64(y * Float64(-1.0 + z))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = log(y) * (x + -1.0);
	tmp = 0.0;
	if (y <= 5e-48)
		tmp = t_1 - t;
	else
		tmp = (t_1 - (y * (-1.0 + z))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Log[y], $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 5e-48], N[(t$95$1 - t), $MachinePrecision], N[(N[(t$95$1 - N[(y * N[(-1.0 + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 4.9999999999999999e-48

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 99.8%

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

   if 4.9999999999999999e-48 < y

   1. Initial program 77.8%

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

   3. Taylor expanded in y around 0 91.4%

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

      1. +-commutative 91.4%

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

      2. sub-neg 91.4%

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

      3. metadata-eval 91.4%

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

      4. fma-def 91.4%

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

      5. mul-1-neg 91.4%

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

      6. fma-neg 91.4%

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

      7. +-commutative 91.4%

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

      8. sub-neg 91.4%

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

      9. metadata-eval 91.4%

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

      10. +-commutative 91.4%

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

   5. Simplified 91.4%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{-48}:\\ \;\;\;\;\log y \cdot \left(x + -1\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\log y \cdot \left(x + -1\right) - y \cdot \left(-1 + z\right)\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1000 \lor \neg \left(x \leq 5.8 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\left(-\log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1000.0) (not (<= x 5.8e-8)))
   (- (* x (log y)) t)
   (- (- (log y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1000.0) || !(x <= 5.8e-8)) {
		tmp = (x * log(y)) - t;
	} 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 ((x <= (-1000.0d0)) .or. (.not. (x <= 5.8d-8))) then
        tmp = (x * log(y)) - t
    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 ((x <= -1000.0) || !(x <= 5.8e-8)) {
		tmp = (x * Math.log(y)) - t;
	} else {
		tmp = -Math.log(y) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1000.0) or not (x <= 5.8e-8):
		tmp = (x * math.log(y)) - t
	else:
		tmp = -math.log(y) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1000.0) || !(x <= 5.8e-8))
		tmp = Float64(Float64(x * log(y)) - t);
	else
		tmp = Float64(Float64(-log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1000.0) || ~((x <= 5.8e-8)))
		tmp = (x * log(y)) - t;
	else
		tmp = -log(y) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1000.0], N[Not[LessEqual[x, 5.8e-8]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[((-N[Log[y], $MachinePrecision]) - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1e3 or 5.8000000000000003e-8 < x

   1. Initial program 97.1%

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

   3. Taylor expanded in x around inf 95.6%

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

      1. *-commutative 95.6%

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

   5. Simplified 95.6%

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

   if -1e3 < x < 5.8000000000000003e-8

   1. Initial program 95.5%

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

   3. Taylor expanded in x around 0 95.5%

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

   4. Taylor expanded in x around inf 94.5%

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

   5. Taylor expanded in x around 0 94.2%

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

      1. mul-1-neg 94.2%

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

   7. Simplified 94.2%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1000 \lor \neg \left(x \leq 5.8 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\left(-\log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.75 \cdot 10^{-45}:\\ \;\;\;\;\left(-\log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.75e-45) (- (- (log y)) t) (- (* y (- 1.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.75e-45) {
		tmp = -log(y) - t;
	} else {
		tmp = (y * (1.0 - z)) - 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 (y <= 2.75d-45) then
        tmp = -log(y) - t
    else
        tmp = (y * (1.0d0 - z)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.75e-45) {
		tmp = -Math.log(y) - t;
	} else {
		tmp = (y * (1.0 - z)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 2.75e-45:
		tmp = -math.log(y) - t
	else:
		tmp = (y * (1.0 - z)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.75e-45)
		tmp = Float64(Float64(-log(y)) - t);
	else
		tmp = Float64(Float64(y * Float64(1.0 - z)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2.75e-45)
		tmp = -log(y) - t;
	else
		tmp = (y * (1.0 - z)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 2.75e-45], N[((-N[Log[y], $MachinePrecision]) - t), $MachinePrecision], N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.75000000000000015e-45

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 99.8%

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

   4. Taylor expanded in x around inf 99.8%

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

   5. Taylor expanded in x around 0 62.9%

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

      1. mul-1-neg 62.9%

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

   7. Simplified 62.9%

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

   if 2.75000000000000015e-45 < y

   1. Initial program 77.2%

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

   3. Taylor expanded in y around 0 91.1%

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

      1. +-commutative 91.1%

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

      2. sub-neg 91.1%

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

      3. metadata-eval 91.1%

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

      4. fma-def 91.1%

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

      5. mul-1-neg 91.1%

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

      6. fma-neg 91.1%

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

      7. +-commutative 91.1%

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

      8. sub-neg 91.1%

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

      9. metadata-eval 91.1%

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

      10. +-commutative 91.1%

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

   5. Simplified 91.1%

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

      1. *-commutative 91.1%

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

      2. +-commutative 91.1%

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

      3. flip-+ 72.4%

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

      4. associate-*l/ 72.4%

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

      5. metadata-eval 72.4%

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

      6. fma-neg 72.4%

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

      7. metadata-eval 72.4%

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

      8. sub-neg 72.4%

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

      9. metadata-eval 72.4%

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

   7. Applied egg-rr 72.4%

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

   8. Taylor expanded in y around inf 58.2%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.75 \cdot 10^{-45}:\\ \;\;\;\;\left(-\log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.0% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

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

3. Taylor expanded in y around 0 95.4%

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

4. Final simplification 95.4%

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

Alternative 7: 39.0% accurate, 30.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z, t):
	return (y * (1.0 - z)) - t

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

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

3. Taylor expanded in y around 0 90.3%

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

   1. +-commutative 90.3%

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

   2. sub-neg 90.3%

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

   3. metadata-eval 90.3%

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

   4. fma-def 90.3%

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

   5. mul-1-neg 90.3%

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

   6. fma-neg 90.3%

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

   7. +-commutative 90.3%

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

   8. sub-neg 90.3%

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

   9. metadata-eval 90.3%

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

   10. +-commutative 90.3%

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

5. Simplified 90.3%

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

   1. *-commutative 90.3%

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

   2. +-commutative 90.3%

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

   3. flip-+ 69.0%

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

   4. associate-*l/ 69.0%

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

   5. metadata-eval 69.0%

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

   6. fma-neg 69.0%

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

   7. metadata-eval 69.0%

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

   8. sub-neg 69.0%

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

   9. metadata-eval 69.0%

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

7. Applied egg-rr 69.0%

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

8. Taylor expanded in y around inf 43.7%

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

9. Final simplification 43.7%

   \[\leadsto y \cdot \left(1 - z\right) - t \]
10. Add Preprocessing

Alternative 8: 38.8% accurate, 35.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

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

3. Taylor expanded in y around 0 90.3%

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

   1. +-commutative 90.3%

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

   2. sub-neg 90.3%

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

   3. metadata-eval 90.3%

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

   4. fma-def 90.3%

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

   5. mul-1-neg 90.3%

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

   6. fma-neg 90.3%

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

   7. +-commutative 90.3%

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

   8. sub-neg 90.3%

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

   9. metadata-eval 90.3%

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

   10. +-commutative 90.3%

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

5. Simplified 90.3%

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

6. Taylor expanded in z around inf 43.6%

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

   1. associate-*r* 43.6%

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

   2. neg-mul-1 43.6%

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

8. Simplified 43.6%

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

9. Final simplification 43.6%

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

Alternative 9: 37.8% 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 96.3%

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

3. Taylor expanded in t around inf 42.3%

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

   1. neg-mul-1 42.3%

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

5. Simplified 42.3%

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

6. Final simplification 42.3%

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

Reproduce

herbie shell --seed 2024031 
(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))