Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, B

Percentage Accurate: 84.9% → 99.8%

Time: 13.2s

Alternatives: 10

Speedup: 1.9×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 87.6%

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

   1. associate--l+ 87.6%

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

   2. fma-def 87.6%

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

   3. fma-neg 87.6%

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

   4. sub-neg 87.6%

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

   5. log1p-def 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 87.6%

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

   1. +-commutative 87.6%

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

   2. fma-def 87.6%

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

   3. sub-neg 87.6%

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

   4. log1p-def 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 3: 99.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return ((x * log(y)) - ((y * z) + (z * (y * (y * 0.5))))) - 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 * log(y)) - ((y * z) + (z * (y * (y * 0.5d0))))) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.6%

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

2. Taylor expanded in y around 0 99.6%

   \[\leadsto \left(x \cdot \log y + \color{blue}{\left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot \left({y}^{2} \cdot z\right)\right)}\right) - t \]
3. Step-by-step derivation

   1. fma-def 99.6%

      \[\leadsto \left(x \cdot \log y + \color{blue}{\mathsf{fma}\left(-1, y \cdot z, -0.5 \cdot \left({y}^{2} \cdot z\right)\right)}\right) - t \]

   2. unpow2 99.6%

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

4. Simplified 99.6%

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

5. Taylor expanded in z around -inf 99.6%

   \[\leadsto \color{blue}{\left(-1 \cdot \left(z \cdot \left(y + 0.5 \cdot {y}^{2}\right)\right) + x \cdot \log y\right)} - t \]
6. Step-by-step derivation

   1. +-commutative 99.6%

      \[\leadsto \color{blue}{\left(x \cdot \log y + -1 \cdot \left(z \cdot \left(y + 0.5 \cdot {y}^{2}\right)\right)\right)} - t \]

   2. mul-1-neg 99.6%

      \[\leadsto \left(x \cdot \log y + \color{blue}{\left(-z \cdot \left(y + 0.5 \cdot {y}^{2}\right)\right)}\right) - t \]

   3. unsub-neg 99.6%

      \[\leadsto \color{blue}{\left(x \cdot \log y - z \cdot \left(y + 0.5 \cdot {y}^{2}\right)\right)} - t \]

   4. *-commutative 99.6%

      \[\leadsto \left(x \cdot \log y - z \cdot \left(y + \color{blue}{{y}^{2} \cdot 0.5}\right)\right) - t \]

   5. unpow2 99.6%

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

7. Simplified 99.6%

   \[\leadsto \color{blue}{\left(x \cdot \log y - z \cdot \left(y + \left(y \cdot y\right) \cdot 0.5\right)\right)} - t \]
8. Step-by-step derivation

   1. distribute-rgt-in 99.6%

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

   2. *-commutative 99.6%

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

   3. associate-*l* 99.6%

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

9. Applied egg-rr 99.6%

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

10. Final simplification 99.6%

    \[\leadsto \left(x \cdot \log y - \left(y \cdot z + z \cdot \left(y \cdot \left(y \cdot 0.5\right)\right)\right)\right) - t \]

Alternative 4: 99.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return ((x * log(y)) + (z * ((y * (y * -0.5)) - 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 * log(y)) + (z * ((y * (y * (-0.5d0))) - y))) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.6%

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

2. Taylor expanded in y around 0 99.6%

   \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot z\right) + \left(-0.5 \cdot \left({y}^{2} \cdot z\right) + x \cdot \log y\right)\right)} - t \]
3. Step-by-step derivation

   1. log-pow 42.0%

      \[\leadsto \left(-1 \cdot \left(y \cdot z\right) + \left(-0.5 \cdot \left({y}^{2} \cdot z\right) + \color{blue}{\log \left({y}^{x}\right)}\right)\right) - t \]

   2. associate-+r+ 42.0%

      \[\leadsto \color{blue}{\left(\left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot \left({y}^{2} \cdot z\right)\right) + \log \left({y}^{x}\right)\right)} - t \]

   3. associate-*r* 42.0%

      \[\leadsto \left(\left(\color{blue}{\left(-1 \cdot y\right) \cdot z} + -0.5 \cdot \left({y}^{2} \cdot z\right)\right) + \log \left({y}^{x}\right)\right) - t \]

   4. associate-*r* 42.0%

      \[\leadsto \left(\left(\left(-1 \cdot y\right) \cdot z + \color{blue}{\left(-0.5 \cdot {y}^{2}\right) \cdot z}\right) + \log \left({y}^{x}\right)\right) - t \]

   5. distribute-rgt-out 42.0%

      \[\leadsto \left(\color{blue}{z \cdot \left(-1 \cdot y + -0.5 \cdot {y}^{2}\right)} + \log \left({y}^{x}\right)\right) - t \]

   6. +-commutative 42.0%

      \[\leadsto \left(z \cdot \color{blue}{\left(-0.5 \cdot {y}^{2} + -1 \cdot y\right)} + \log \left({y}^{x}\right)\right) - t \]

   7. mul-1-neg 42.0%

      \[\leadsto \left(z \cdot \left(-0.5 \cdot {y}^{2} + \color{blue}{\left(-y\right)}\right) + \log \left({y}^{x}\right)\right) - t \]

   8. unsub-neg 42.0%

      \[\leadsto \left(z \cdot \color{blue}{\left(-0.5 \cdot {y}^{2} - y\right)} + \log \left({y}^{x}\right)\right) - t \]

   9. unpow2 42.0%

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

   10. associate-*r* 42.0%

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

   11. log-pow 99.6%

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

4. Simplified 99.6%

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

5. Final simplification 99.6%

   \[\leadsto \left(x \cdot \log y + z \cdot \left(y \cdot \left(y \cdot -0.5\right) - y\right)\right) - t \]

Alternative 5: 90.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-113} \lor \neg \left(x \leq 3.4 \cdot 10^{-119}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-0.5 \cdot \left(y \cdot y\right) - y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.5e-113) (not (<= x 3.4e-119)))
   (- (* x (log y)) t)
   (- (* z (- (* -0.5 (* y y)) y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.5e-113) || !(x <= 3.4e-119)) {
		tmp = (x * log(y)) - t;
	} else {
		tmp = (z * ((-0.5 * (y * y)) - 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 <= (-4.5d-113)) .or. (.not. (x <= 3.4d-119))) then
        tmp = (x * log(y)) - t
    else
        tmp = (z * (((-0.5d0) * (y * y)) - 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 <= -4.5e-113) || !(x <= 3.4e-119)) {
		tmp = (x * Math.log(y)) - t;
	} else {
		tmp = (z * ((-0.5 * (y * y)) - y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.5e-113) or not (x <= 3.4e-119):
		tmp = (x * math.log(y)) - t
	else:
		tmp = (z * ((-0.5 * (y * y)) - y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.5e-113) || !(x <= 3.4e-119))
		tmp = Float64(Float64(x * log(y)) - t);
	else
		tmp = Float64(Float64(z * Float64(Float64(-0.5 * Float64(y * y)) - y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.5e-113) || ~((x <= 3.4e-119)))
		tmp = (x * log(y)) - t;
	else
		tmp = (z * ((-0.5 * (y * y)) - y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.5e-113], N[Not[LessEqual[x, 3.4e-119]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(z * N[(N[(-0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5000000000000001e-113 or 3.40000000000000024e-119 < x

   1. Initial program 92.0%

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

      1. +-commutative 92.0%

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

      2. fma-def 92.0%

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

      3. sub-neg 92.0%

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

      4. log1p-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 91.3%

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

   if -4.5000000000000001e-113 < x < 3.40000000000000024e-119

   1. Initial program 76.2%

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

   2. Taylor expanded in y around 0 100.0%

      \[\leadsto \left(x \cdot \log y + \color{blue}{\left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot \left({y}^{2} \cdot z\right)\right)}\right) - t \]
   3. Step-by-step derivation

      1. fma-def 100.0%

         \[\leadsto \left(x \cdot \log y + \color{blue}{\mathsf{fma}\left(-1, y \cdot z, -0.5 \cdot \left({y}^{2} \cdot z\right)\right)}\right) - t \]

      2. unpow2 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 94.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot \left({y}^{2} \cdot z\right)\right)} - t \]
   6. Step-by-step derivation

      1. associate-*r* 94.6%

         \[\leadsto \left(\color{blue}{\left(-1 \cdot y\right) \cdot z} + -0.5 \cdot \left({y}^{2} \cdot z\right)\right) - t \]

      2. neg-mul-1 94.6%

         \[\leadsto \left(\color{blue}{\left(-y\right)} \cdot z + -0.5 \cdot \left({y}^{2} \cdot z\right)\right) - t \]

      3. associate-*r* 94.6%

         \[\leadsto \left(\left(-y\right) \cdot z + \color{blue}{\left(-0.5 \cdot {y}^{2}\right) \cdot z}\right) - t \]

      4. distribute-rgt-in 94.6%

         \[\leadsto \color{blue}{z \cdot \left(\left(-y\right) + -0.5 \cdot {y}^{2}\right)} - t \]

      5. +-commutative 94.6%

         \[\leadsto z \cdot \color{blue}{\left(-0.5 \cdot {y}^{2} + \left(-y\right)\right)} - t \]

      6. unsub-neg 94.6%

         \[\leadsto z \cdot \color{blue}{\left(-0.5 \cdot {y}^{2} - y\right)} - t \]

      7. *-commutative 94.6%

         \[\leadsto z \cdot \left(\color{blue}{{y}^{2} \cdot -0.5} - y\right) - t \]

      8. unpow2 94.6%

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

   7. Simplified 94.6%

      \[\leadsto \color{blue}{z \cdot \left(\left(y \cdot y\right) \cdot -0.5 - y\right)} - t \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-113} \lor \neg \left(x \leq 3.4 \cdot 10^{-119}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-0.5 \cdot \left(y \cdot y\right) - y\right) - t\\ \end{array} \]

Alternative 6: 99.1% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.6%

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

2. Taylor expanded in y around 0 99.2%

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

   1. log-pow 41.7%

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

   2. +-commutative 41.7%

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

   3. mul-1-neg 41.7%

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

   4. unsub-neg 41.7%

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

   5. log-pow 99.2%

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

4. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 7: 57.9% accurate, 19.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

public static double code(double x, double y, double z, double t) {
	return (z * ((-0.5 * (y * y)) - y)) - t;
}

Python

def code(x, y, z, t):
	return (z * ((-0.5 * (y * y)) - y)) - t

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.6%

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

2. Taylor expanded in y around 0 99.6%

   \[\leadsto \left(x \cdot \log y + \color{blue}{\left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot \left({y}^{2} \cdot z\right)\right)}\right) - t \]
3. Step-by-step derivation

   1. fma-def 99.6%

      \[\leadsto \left(x \cdot \log y + \color{blue}{\mathsf{fma}\left(-1, y \cdot z, -0.5 \cdot \left({y}^{2} \cdot z\right)\right)}\right) - t \]

   2. unpow2 99.6%

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

4. Simplified 99.6%

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

5. Taylor expanded in x around 0 55.5%

   \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot z\right) + -0.5 \cdot \left({y}^{2} \cdot z\right)\right)} - t \]
6. Step-by-step derivation

   1. associate-*r* 55.5%

      \[\leadsto \left(\color{blue}{\left(-1 \cdot y\right) \cdot z} + -0.5 \cdot \left({y}^{2} \cdot z\right)\right) - t \]

   2. neg-mul-1 55.5%

      \[\leadsto \left(\color{blue}{\left(-y\right)} \cdot z + -0.5 \cdot \left({y}^{2} \cdot z\right)\right) - t \]

   3. associate-*r* 55.5%

      \[\leadsto \left(\left(-y\right) \cdot z + \color{blue}{\left(-0.5 \cdot {y}^{2}\right) \cdot z}\right) - t \]

   4. distribute-rgt-in 55.5%

      \[\leadsto \color{blue}{z \cdot \left(\left(-y\right) + -0.5 \cdot {y}^{2}\right)} - t \]

   5. +-commutative 55.5%

      \[\leadsto z \cdot \color{blue}{\left(-0.5 \cdot {y}^{2} + \left(-y\right)\right)} - t \]

   6. unsub-neg 55.5%

      \[\leadsto z \cdot \color{blue}{\left(-0.5 \cdot {y}^{2} - y\right)} - t \]

   7. *-commutative 55.5%

      \[\leadsto z \cdot \left(\color{blue}{{y}^{2} \cdot -0.5} - y\right) - t \]

   8. unpow2 55.5%

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

7. Simplified 55.5%

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

8. Final simplification 55.5%

   \[\leadsto z \cdot \left(-0.5 \cdot \left(y \cdot y\right) - y\right) - t \]

Alternative 8: 48.8% accurate, 26.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-45}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-132}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6.5e-45) (- t) (if (<= t 6.2e-132) (* z (- y)) (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.5e-45) {
		tmp = -t;
	} else if (t <= 6.2e-132) {
		tmp = z * -y;
	} else {
		tmp = -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 <= (-6.5d-45)) then
        tmp = -t
    else if (t <= 6.2d-132) then
        tmp = z * -y
    else
        tmp = -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.5e-45) {
		tmp = -t;
	} else if (t <= 6.2e-132) {
		tmp = z * -y;
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6.5e-45:
		tmp = -t
	elif t <= 6.2e-132:
		tmp = z * -y
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6.5e-45)
		tmp = Float64(-t);
	elseif (t <= 6.2e-132)
		tmp = Float64(z * Float64(-y));
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6.5e-45)
		tmp = -t;
	elseif (t <= 6.2e-132)
		tmp = z * -y;
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6.5e-45], (-t), If[LessEqual[t, 6.2e-132], N[(z * (-y)), $MachinePrecision], (-t)]]

Derivation

1. Split input into 2 regimes

2. if t < -6.4999999999999995e-45 or 6.20000000000000016e-132 < t

   1. Initial program 91.9%

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

      1. +-commutative 91.9%

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

      2. fma-def 91.9%

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

      3. sub-neg 91.9%

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

      4. log1p-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around inf 61.8%

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

      1. mul-1-neg 61.8%

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

   6. Simplified 61.8%

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

   if -6.4999999999999995e-45 < t < 6.20000000000000016e-132

   1. Initial program 79.2%

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

   2. Taylor expanded in y around 0 97.9%

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

      1. log-pow 28.4%

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

      2. +-commutative 28.4%

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

      3. mul-1-neg 28.4%

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

      4. unsub-neg 28.4%

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

      5. log-pow 97.9%

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

   4. Simplified 97.9%

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

   5. Taylor expanded in x around 0 26.9%

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

      1. associate-*r* 26.9%

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

      2. neg-mul-1 26.9%

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

      3. *-commutative 26.9%

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

   7. Simplified 26.9%

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

   8. Taylor expanded in z around inf 22.6%

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

      1. associate-*r* 22.6%

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

      2. neg-mul-1 22.6%

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

      3. *-commutative 22.6%

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

   10. Simplified 22.6%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-45}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-132}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]

Alternative 9: 57.5% accurate, 35.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.6%

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

2. Taylor expanded in y around 0 99.2%

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

   1. log-pow 41.7%

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

   2. +-commutative 41.7%

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

   3. mul-1-neg 41.7%

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

   4. unsub-neg 41.7%

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

   5. log-pow 99.2%

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

4. Simplified 99.2%

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

5. Taylor expanded in x around 0 55.2%

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

   1. associate-*r* 55.2%

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

   2. neg-mul-1 55.2%

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

   3. *-commutative 55.2%

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

7. Simplified 55.2%

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

8. Final simplification 55.2%

   \[\leadsto z \cdot \left(-y\right) - t \]

Alternative 10: 42.6% accurate, 105.5× 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 87.6%

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

   1. +-commutative 87.6%

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

   2. fma-def 87.6%

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

   3. sub-neg 87.6%

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

   4. log1p-def 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in t around inf 43.1%

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

   1. mul-1-neg 43.1%

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

6. Simplified 43.1%

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

7. Final simplification 43.1%

   \[\leadsto -t \]

Developer target: 99.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \left(-z\right) \cdot \left(\left(0.5 \cdot \left(y \cdot y\right) + y\right) + \frac{0.3333333333333333}{1 \cdot \left(1 \cdot 1\right)} \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) - \left(t - x \cdot \log y\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (-
  (*
   (- z)
   (+
    (+ (* 0.5 (* y y)) y)
    (* (/ 0.3333333333333333 (* 1.0 (* 1.0 1.0))) (* y (* y y)))))
  (- t (* x (log y)))))

C

double code(double x, double y, double z, double t) {
	return (-z * (((0.5 * (y * y)) + y) + ((0.3333333333333333 / (1.0 * (1.0 * 1.0))) * (y * (y * y))))) - (t - (x * 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 = (-z * (((0.5d0 * (y * y)) + y) + ((0.3333333333333333d0 / (1.0d0 * (1.0d0 * 1.0d0))) * (y * (y * y))))) - (t - (x * log(y)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (-z * (((0.5 * (y * y)) + y) + ((0.3333333333333333 / (1.0 * (1.0 * 1.0))) * (y * (y * y))))) - (t - (x * Math.log(y)));
}

Python

def code(x, y, z, t):
	return (-z * (((0.5 * (y * y)) + y) + ((0.3333333333333333 / (1.0 * (1.0 * 1.0))) * (y * (y * y))))) - (t - (x * math.log(y)))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(-z) * Float64(Float64(Float64(0.5 * Float64(y * y)) + y) + Float64(Float64(0.3333333333333333 / Float64(1.0 * Float64(1.0 * 1.0))) * Float64(y * Float64(y * y))))) - Float64(t - Float64(x * log(y))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (-z * (((0.5 * (y * y)) + y) + ((0.3333333333333333 / (1.0 * (1.0 * 1.0))) * (y * (y * y))))) - (t - (x * log(y)));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[((-z) * N[(N[(N[(0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] + N[(N[(0.3333333333333333 / N[(1.0 * N[(1.0 * 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t - N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023290 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (- (* (- z) (+ (+ (* 0.5 (* y y)) y) (* (/ 0.3333333333333333 (* 1.0 (* 1.0 1.0))) (* y (* y y))))) (- t (* x (log y))))

  (- (+ (* x (log y)) (* z (log (- 1.0 y)))) t))