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

Percentage Accurate: 85.0% → 99.8%

Time: 13.9s

Alternatives: 11

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: 85.0% 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 86.0%

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

   1. +-commutative 86.0%

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

   2. associate--l+ 86.0%

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

   3. +-commutative 86.0%

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

   4. associate-+l- 86.0%

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

   5. fma-neg 86.0%

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

   6. sub0-neg 86.0%

      \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{0 - \left(t - z \cdot \log \left(1 - y\right)\right)}\right) \]

   7. associate-+l- 86.0%

      \[\leadsto \mathsf{fma}\left(x, \log y, \color{blue}{\left(0 - t\right) + z \cdot \log \left(1 - y\right)}\right) \]

   8. neg-sub0 86.0%

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

   9. +-commutative 86.0%

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

   10. fma-def 86.0%

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

   11. sub-neg 86.0%

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

   12. 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 86.0%

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

   1. +-commutative 86.0%

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

   2. fma-def 86.0%

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

   3. sub-neg 86.0%

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

   4. log1p-def 99.8%

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

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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.0%

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

2. Taylor expanded in y around 0 99.5%

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

   1. expm1-log1p-u 94.0%

      \[\leadsto \left(-0.5 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({y}^{2} \cdot z\right)\right)} + \left(-1 \cdot \left(y \cdot z\right) + \log y \cdot x\right)\right) - t \]

   2. expm1-udef 94.0%

      \[\leadsto \left(-0.5 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left({y}^{2} \cdot z\right)} - 1\right)} + \left(-1 \cdot \left(y \cdot z\right) + \log y \cdot x\right)\right) - t \]

   3. *-commutative 94.0%

      \[\leadsto \left(-0.5 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{z \cdot {y}^{2}}\right)} - 1\right) + \left(-1 \cdot \left(y \cdot z\right) + \log y \cdot x\right)\right) - t \]

   4. unpow2 94.0%

      \[\leadsto \left(-0.5 \cdot \left(e^{\mathsf{log1p}\left(z \cdot \color{blue}{\left(y \cdot y\right)}\right)} - 1\right) + \left(-1 \cdot \left(y \cdot z\right) + \log y \cdot x\right)\right) - t \]

   5. associate-*r* 94.0%

      \[\leadsto \left(-0.5 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(z \cdot y\right) \cdot y}\right)} - 1\right) + \left(-1 \cdot \left(y \cdot z\right) + \log y \cdot x\right)\right) - t \]

   6. *-commutative 94.0%

      \[\leadsto \left(-0.5 \cdot \left(e^{\mathsf{log1p}\left(\color{blue}{\left(y \cdot z\right)} \cdot y\right)} - 1\right) + \left(-1 \cdot \left(y \cdot z\right) + \log y \cdot x\right)\right) - t \]

4. Applied egg-rr 94.0%

   \[\leadsto \left(-0.5 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\left(y \cdot z\right) \cdot y\right)} - 1\right)} + \left(-1 \cdot \left(y \cdot z\right) + \log y \cdot x\right)\right) - t \]
5. Step-by-step derivation

   1. expm1-def 94.0%

      \[\leadsto \left(-0.5 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(y \cdot z\right) \cdot y\right)\right)} + \left(-1 \cdot \left(y \cdot z\right) + \log y \cdot x\right)\right) - t \]

   2. expm1-log1p 99.5%

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

   3. *-commutative 99.5%

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

6. Simplified 99.5%

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

7. Taylor expanded in y around inf 99.5%

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

   1. +-commutative 99.5%

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

   2. mul-1-neg 99.5%

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

   3. unsub-neg 99.5%

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

   4. mul-1-neg 99.5%

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

   5. distribute-lft-neg-in 99.5%

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

   6. log-rec 99.5%

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

   7. remove-double-neg 99.5%

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

9. Simplified 99.5%

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

10. Final simplification 99.5%

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

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 86.0%

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

2. Taylor expanded in y around 0 99.5%

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

   1. *-commutative 99.5%

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

   2. associate-+r+ 99.5%

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

   3. +-commutative 99.5%

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

   4. *-commutative 99.5%

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

   5. associate-*r* 99.5%

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

   6. associate-*r* 99.5%

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

   7. distribute-rgt-out 99.5%

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

   8. mul-1-neg 99.5%

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

   9. unsub-neg 99.5%

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

   10. unpow2 99.5%

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

   11. associate-*r* 99.5%

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

4. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 5: 90.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-91} \lor \neg \left(x \leq 2.7 \cdot 10^{-111}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{log1p}\left(-y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.02e-91) (not (<= x 2.7e-111)))
   (- (* x (log y)) t)
   (- (* z (log1p (- y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.02e-91) || !(x <= 2.7e-111)) {
		tmp = (x * log(y)) - t;
	} else {
		tmp = (z * log1p(-y)) - t;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.02e-91) || !(x <= 2.7e-111)) {
		tmp = (x * Math.log(y)) - t;
	} else {
		tmp = (z * Math.log1p(-y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.02e-91) or not (x <= 2.7e-111):
		tmp = (x * math.log(y)) - t
	else:
		tmp = (z * math.log1p(-y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.02e-91) || !(x <= 2.7e-111))
		tmp = Float64(Float64(x * log(y)) - t);
	else
		tmp = Float64(Float64(z * log1p(Float64(-y))) - t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.02e-91], N[Not[LessEqual[x, 2.7e-111]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(z * N[Log[1 + (-y)], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.01999999999999994e-91 or 2.69999999999999989e-111 < x

   1. Initial program 91.2%

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

   2. Taylor expanded in y around 0 90.9%

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

   if -1.01999999999999994e-91 < x < 2.69999999999999989e-111

   1. Initial program 76.3%

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

   2. Taylor expanded in x around 0 72.2%

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

      1. sub-neg 72.2%

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

      2. mul-1-neg 72.2%

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

      3. log1p-def 95.9%

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

      4. mul-1-neg 95.9%

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

   4. Simplified 95.9%

      \[\leadsto \color{blue}{z \cdot \mathsf{log1p}\left(-y\right) - t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-91} \lor \neg \left(x \leq 2.7 \cdot 10^{-111}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{log1p}\left(-y\right) - t\\ \end{array} \]

Alternative 6: 90.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-94} \lor \neg \left(x \leq 2.1 \cdot 10^{-114}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -7.2e-94) (not (<= x 2.1e-114)))
   (- (* x (log y)) t)
   (- (* z (- y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -7.2e-94) || !(x <= 2.1e-114)) {
		tmp = (x * log(y)) - t;
	} else {
		tmp = (z * -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 <= (-7.2d-94)) .or. (.not. (x <= 2.1d-114))) then
        tmp = (x * log(y)) - t
    else
        tmp = (z * -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 <= -7.2e-94) || !(x <= 2.1e-114)) {
		tmp = (x * Math.log(y)) - t;
	} else {
		tmp = (z * -y) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -7.2e-94) or not (x <= 2.1e-114):
		tmp = (x * math.log(y)) - t
	else:
		tmp = (z * -y) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -7.2e-94) || !(x <= 2.1e-114))
		tmp = Float64(Float64(x * log(y)) - t);
	else
		tmp = Float64(Float64(z * Float64(-y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -7.2e-94) || ~((x <= 2.1e-114)))
		tmp = (x * log(y)) - t;
	else
		tmp = (z * -y) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -7.2e-94], N[Not[LessEqual[x, 2.1e-114]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(z * (-y)), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.2e-94 or 2.09999999999999993e-114 < x

   1. Initial program 91.2%

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

   2. Taylor expanded in y around 0 90.9%

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

   if -7.2e-94 < x < 2.09999999999999993e-114

   1. Initial program 76.3%

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

   2. Taylor expanded in x around 0 72.2%

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

      1. sub-neg 72.2%

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

      2. mul-1-neg 72.2%

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

      3. log1p-def 95.9%

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

      4. mul-1-neg 95.9%

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

   4. Simplified 95.9%

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

   5. Taylor expanded in y around 0 94.6%

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

      1. associate-*r* 94.6%

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

      2. mul-1-neg 94.6%

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

   7. Simplified 94.6%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-94} \lor \neg \left(x \leq 2.1 \cdot 10^{-114}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right) - t\\ \end{array} \]

Alternative 7: 90.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-92} \lor \neg \left(x \leq 2.7 \cdot 10^{-111}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, -t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.9e-92) (not (<= x 2.7e-111)))
   (- (* x (log y)) t)
   (fma (- y) z (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.9e-92) || !(x <= 2.7e-111)) {
		tmp = (x * log(y)) - t;
	} else {
		tmp = fma(-y, z, -t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.9e-92) || !(x <= 2.7e-111))
		tmp = Float64(Float64(x * log(y)) - t);
	else
		tmp = fma(Float64(-y), z, Float64(-t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.9e-92], N[Not[LessEqual[x, 2.7e-111]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[((-y) * z + (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9e-92 or 2.69999999999999989e-111 < x

   1. Initial program 91.2%

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

   2. Taylor expanded in y around 0 90.9%

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

   if -1.9e-92 < x < 2.69999999999999989e-111

   1. Initial program 76.3%

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

   2. Taylor expanded in x around 0 72.2%

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

      1. sub-neg 72.2%

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

      2. mul-1-neg 72.2%

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

      3. log1p-def 95.9%

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

      4. mul-1-neg 95.9%

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

   4. Simplified 95.9%

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

   5. Taylor expanded in y around 0 94.6%

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

      1. associate-*r* 94.6%

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

      2. mul-1-neg 94.6%

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

   7. Simplified 94.6%

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

      1. fma-neg 94.6%

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

   9. Applied egg-rr 94.6%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-92} \lor \neg \left(x \leq 2.7 \cdot 10^{-111}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, z, -t\right)\\ \end{array} \]

Alternative 8: 99.2% 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 86.0%

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

2. Taylor expanded in y around 0 99.3%

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

   1. +-commutative 99.3%

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

   2. fma-def 99.3%

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

   3. mul-1-neg 99.3%

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

   4. fma-neg 99.3%

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

4. Simplified 99.3%

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

5. Final simplification 99.3%

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

Alternative 9: 76.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+54} \lor \neg \left(x \leq 9.5 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.25e+54) (not (<= x 9.5e-33)))
   (* x (log y))
   (- (* z (- y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.25e+54) || !(x <= 9.5e-33)) {
		tmp = x * log(y);
	} else {
		tmp = (z * -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 <= (-1.25d+54)) .or. (.not. (x <= 9.5d-33))) then
        tmp = x * log(y)
    else
        tmp = (z * -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 <= -1.25e+54) || !(x <= 9.5e-33)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (z * -y) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.25e+54) or not (x <= 9.5e-33):
		tmp = x * math.log(y)
	else:
		tmp = (z * -y) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.25e+54) || !(x <= 9.5e-33))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(z * Float64(-y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.25e+54) || ~((x <= 9.5e-33)))
		tmp = x * log(y);
	else
		tmp = (z * -y) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.25e+54], N[Not[LessEqual[x, 9.5e-33]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(z * (-y)), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25000000000000001e54 or 9.50000000000000019e-33 < x

   1. Initial program 95.4%

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

   2. Taylor expanded in y around 0 99.7%

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

   3. Taylor expanded in x around inf 77.1%

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

   if -1.25000000000000001e54 < x < 9.50000000000000019e-33

   1. Initial program 77.6%

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

   2. Taylor expanded in x around 0 61.7%

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

      1. sub-neg 61.7%

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

      2. mul-1-neg 61.7%

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

      3. log1p-def 83.9%

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

      4. mul-1-neg 83.9%

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

   4. Simplified 83.9%

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

   5. Taylor expanded in y around 0 83.0%

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

      1. associate-*r* 83.0%

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

      2. mul-1-neg 83.0%

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

   7. Simplified 83.0%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+54} \lor \neg \left(x \leq 9.5 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right) - t\\ \end{array} \]

Alternative 10: 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 86.0%

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

2. Taylor expanded in x around 0 42.4%

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

   1. sub-neg 42.4%

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

   2. mul-1-neg 42.4%

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

   3. log1p-def 55.9%

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

   4. mul-1-neg 55.9%

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

4. Simplified 55.9%

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

5. Taylor expanded in y around 0 55.4%

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

   1. associate-*r* 55.4%

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

   2. mul-1-neg 55.4%

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

7. Simplified 55.4%

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

8. Final simplification 55.4%

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

Alternative 11: 42.7% 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 86.0%

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

2. Taylor expanded in t around inf 41.6%

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

   1. mul-1-neg 41.6%

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

4. Simplified 41.6%

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

5. Final simplification 41.6%

   \[\leadsto -t \]

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 2023230 
(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))