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

Percentage Accurate: 84.5% → 99.8%

Time: 13.8s

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: 84.5% 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, 0.7× 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 83.1%

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

   1. +-commutative 83.1%

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

   2. fma-def 83.1%

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

   3. sub-neg 83.1%

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

   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 2: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 83.1%

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

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. associate-+r+ 99.5%

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

   2. associate-*r* 99.5%

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

   3. associate-*r* 99.5%

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

   4. distribute-rgt-out 99.5%

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

   5. mul-1-neg 99.5%

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

   6. unsub-neg 99.5%

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

   7. *-commutative 99.5%

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

   8. unpow2 99.5%

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

   9. associate-*l* 99.5%

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

4. Simplified 99.5%

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

5. Taylor expanded in z around 0 99.5%

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

   1. sub-neg 99.5%

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

   2. +-commutative 99.5%

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

   3. associate-+r+ 99.5%

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

   4. +-commutative 99.5%

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

   5. sub-neg 99.5%

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

   6. *-commutative 99.5%

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

   7. *-commutative 99.5%

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

   8. fma-neg 99.5%

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

   9. unpow2 99.5%

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

   10. +-commutative 99.5%

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

   11. fma-def 99.5%

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

   12. unpow2 99.5%

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

   13. fma-neg 99.5%

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

   14. *-commutative 99.5%

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

   15. unpow2 99.5%

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

   16. *-commutative 99.5%

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

7. Simplified 99.5%

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

8. Final simplification 99.5%

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

Alternative 3: 99.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.1%

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

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. associate-+r+ 99.5%

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

   2. associate-*r* 99.5%

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

   3. associate-*r* 99.5%

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

   4. distribute-rgt-out 99.5%

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

   5. mul-1-neg 99.5%

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

   6. unsub-neg 99.5%

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

   7. *-commutative 99.5%

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

   8. unpow2 99.5%

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

   9. associate-*l* 99.5%

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

4. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 4: 72.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-76} \lor \neg \left(x \leq 1.2 \cdot 10^{-7} \lor \neg \left(x \leq 7.6 \cdot 10^{+56}\right) \land x \leq 1.5 \cdot 10^{+154}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.65e-76)
         (not (or (<= x 1.2e-7) (and (not (<= x 7.6e+56)) (<= x 1.5e+154)))))
   (* x (log y))
   (- (* z (- y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.65e-76) || !((x <= 1.2e-7) || (!(x <= 7.6e+56) && (x <= 1.5e+154)))) {
		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 <= (-1.65d-76)) .or. (.not. (x <= 1.2d-7) .or. (.not. (x <= 7.6d+56)) .and. (x <= 1.5d+154))) 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 <= -1.65e-76) || !((x <= 1.2e-7) || (!(x <= 7.6e+56) && (x <= 1.5e+154)))) {
		tmp = x * Math.log(y);
	} else {
		tmp = (z * -y) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.65e-76) or not ((x <= 1.2e-7) or (not (x <= 7.6e+56) and (x <= 1.5e+154))):
		tmp = x * math.log(y)
	else:
		tmp = (z * -y) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.65e-76) || !((x <= 1.2e-7) || (!(x <= 7.6e+56) && (x <= 1.5e+154))))
		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 <= -1.65e-76) || ~(((x <= 1.2e-7) || (~((x <= 7.6e+56)) && (x <= 1.5e+154)))))
		tmp = x * log(y);
	else
		tmp = (z * -y) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.65e-76], N[Not[Or[LessEqual[x, 1.2e-7], And[N[Not[LessEqual[x, 7.6e+56]], $MachinePrecision], LessEqual[x, 1.5e+154]]]], $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 < -1.64999999999999992e-76 or 1.19999999999999989e-7 < x < 7.59999999999999991e56 or 1.50000000000000013e154 < x

   1. Initial program 92.3%

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

   2. Taylor expanded in y around 0 99.0%

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

      1. associate-+r+ 99.0%

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

      2. associate-*r* 99.0%

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

      3. associate-*r* 99.0%

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

      4. distribute-rgt-out 99.0%

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

      5. mul-1-neg 99.0%

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

      6. unsub-neg 99.0%

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

      7. *-commutative 99.0%

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

      8. unpow2 99.0%

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

      9. associate-*l* 99.0%

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

   4. Simplified 99.0%

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

   5. Taylor expanded in x around inf 72.5%

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

   if -1.64999999999999992e-76 < x < 1.19999999999999989e-7 or 7.59999999999999991e56 < x < 1.50000000000000013e154

   1. Initial program 77.0%

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

   2. Taylor expanded in y around 0 99.5%

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

      1. +-commutative 99.5%

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

      2. *-commutative 99.5%

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

      3. mul-1-neg 99.5%

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

      4. unsub-neg 99.5%

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

      5. *-commutative 99.5%

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

   4. Simplified 99.5%

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

      1. *-commutative 99.5%

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

      2. add-sqr-sqrt 37.7%

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

      3. unpow2 37.7%

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

      4. add-cbrt-cube 34.4%

         \[\leadsto \left(\color{blue}{\sqrt[3]{\left({\left(\sqrt{x \cdot \log y}\right)}^{2} \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}\right) \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}}} - y \cdot z\right) - t \]

      5. pow-prod-down 34.4%

         \[\leadsto \left(\sqrt[3]{\color{blue}{{\left(\sqrt{x \cdot \log y} \cdot \sqrt{x \cdot \log y}\right)}^{2}} \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}} - y \cdot z\right) - t \]

      6. add-sqr-sqrt 34.4%

         \[\leadsto \left(\sqrt[3]{{\color{blue}{\left(x \cdot \log y\right)}}^{2} \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}} - y \cdot z\right) - t \]

      7. unpow2 34.4%

         \[\leadsto \left(\sqrt[3]{\color{blue}{\left(\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right)\right)} \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}} - y \cdot z\right) - t \]

      8. unpow2 34.4%

         \[\leadsto \left(\sqrt[3]{\left(\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right)\right) \cdot \color{blue}{\left(\sqrt{x \cdot \log y} \cdot \sqrt{x \cdot \log y}\right)}} - y \cdot z\right) - t \]

      9. add-sqr-sqrt 80.8%

         \[\leadsto \left(\sqrt[3]{\left(\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right)\right) \cdot \color{blue}{\left(x \cdot \log y\right)}} - y \cdot z\right) - t \]

      10. pow3 80.8%

          \[\leadsto \left(\sqrt[3]{\color{blue}{{\left(x \cdot \log y\right)}^{3}}} - y \cdot z\right) - t \]

      11. *-commutative 80.8%

          \[\leadsto \left(\sqrt[3]{{\color{blue}{\left(\log y \cdot x\right)}}^{3}} - y \cdot z\right) - t \]

   6. Applied egg-rr 80.8%

      \[\leadsto \left(\color{blue}{\sqrt[3]{{\left(\log y \cdot x\right)}^{3}}} - y \cdot z\right) - t \]

   7. Taylor expanded in y around inf 81.0%

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

      1. mul-1-neg 81.0%

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

      2. distribute-rgt-neg-in 81.0%

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

   9. Simplified 81.0%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-76} \lor \neg \left(x \leq 1.2 \cdot 10^{-7} \lor \neg \left(x \leq 7.6 \cdot 10^{+56}\right) \land x \leq 1.5 \cdot 10^{+154}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right) - t\\ \end{array} \]

Alternative 5: 86.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+240} \lor \neg \left(z \leq 1.15 \cdot 10^{+133}\right):\\ \;\;\;\;z \cdot \mathsf{log1p}\left(-y\right) - t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1e+240) (not (<= z 1.15e+133)))
   (- (* z (log1p (- y))) t)
   (- (* x (log y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e+240) || !(z <= 1.15e+133)) {
		tmp = (z * log1p(-y)) - t;
	} else {
		tmp = (x * log(y)) - t;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e+240) || !(z <= 1.15e+133)) {
		tmp = (z * Math.log1p(-y)) - t;
	} else {
		tmp = (x * Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1e+240) or not (z <= 1.15e+133):
		tmp = (z * math.log1p(-y)) - t
	else:
		tmp = (x * math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1e+240) || !(z <= 1.15e+133))
		tmp = Float64(Float64(z * log1p(Float64(-y))) - t);
	else
		tmp = Float64(Float64(x * log(y)) - t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1e+240], N[Not[LessEqual[z, 1.15e+133]], $MachinePrecision]], N[(N[(z * N[Log[1 + (-y)], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000001e240 or 1.14999999999999995e133 < z

   1. Initial program 41.9%

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

   2. Taylor expanded in x around 0 30.2%

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

      1. sub-neg 30.2%

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

      2. mul-1-neg 30.2%

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

      3. log1p-def 85.8%

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

      4. mul-1-neg 85.8%

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

   4. Simplified 85.8%

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

   if -1.00000000000000001e240 < z < 1.14999999999999995e133

   1. Initial program 93.4%

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

      1. +-commutative 93.4%

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

      2. fma-def 93.4%

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

      3. sub-neg 93.4%

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

      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 z around 0 92.9%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+240} \lor \neg \left(z \leq 1.15 \cdot 10^{+133}\right):\\ \;\;\;\;z \cdot \mathsf{log1p}\left(-y\right) - t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - t\\ \end{array} \]

Alternative 6: 85.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+121}:\\ \;\;\;\;t_1 - z \cdot y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+132}:\\ \;\;\;\;t_1 - t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{log1p}\left(-y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (<= z -3.4e+121)
     (- t_1 (* z y))
     (if (<= z 4.2e+132) (- t_1 t) (- (* z (log1p (- y))) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if (z <= -3.4e+121) {
		tmp = t_1 - (z * y);
	} else if (z <= 4.2e+132) {
		tmp = t_1 - t;
	} else {
		tmp = (z * log1p(-y)) - t;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double tmp;
	if (z <= -3.4e+121) {
		tmp = t_1 - (z * y);
	} else if (z <= 4.2e+132) {
		tmp = t_1 - t;
	} else {
		tmp = (z * Math.log1p(-y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if z <= -3.4e+121:
		tmp = t_1 - (z * y)
	elif z <= 4.2e+132:
		tmp = t_1 - t
	else:
		tmp = (z * math.log1p(-y)) - t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if (z <= -3.4e+121)
		tmp = Float64(t_1 - Float64(z * y));
	elseif (z <= 4.2e+132)
		tmp = Float64(t_1 - t);
	else
		tmp = Float64(Float64(z * log1p(Float64(-y))) - t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+121], N[(t$95$1 - N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+132], N[(t$95$1 - t), $MachinePrecision], N[(N[(z * N[Log[1 + (-y)], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4000000000000001e121

   1. Initial program 60.3%

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

   2. Taylor expanded in y around 0 97.6%

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

      1. +-commutative 97.6%

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

      2. *-commutative 97.6%

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

      3. mul-1-neg 97.6%

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

      4. unsub-neg 97.6%

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

      5. *-commutative 97.6%

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

   4. Simplified 97.6%

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

   5. Taylor expanded in t around 0 75.7%

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

   if -3.4000000000000001e121 < z < 4.19999999999999987e132

   1. Initial program 96.7%

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

      1. +-commutative 96.7%

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

      2. fma-def 96.7%

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

      3. sub-neg 96.7%

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

      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 z around 0 96.7%

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

   if 4.19999999999999987e132 < z

   1. Initial program 41.8%

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

   2. Taylor expanded in x around 0 31.2%

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

      1. sub-neg 31.2%

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

      2. mul-1-neg 31.2%

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

      3. log1p-def 86.4%

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

      4. mul-1-neg 86.4%

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

   4. Simplified 86.4%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+121}:\\ \;\;\;\;x \cdot \log y - z \cdot y\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+132}:\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{log1p}\left(-y\right) - t\\ \end{array} \]

Alternative 7: 86.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+238} \lor \neg \left(z \leq 2.2 \cdot 10^{+132}\right):\\ \;\;\;\;z \cdot \left(-y\right) - t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.2e+238) (not (<= z 2.2e+132)))
   (- (* z (- y)) t)
   (- (* x (log y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.2e+238) || !(z <= 2.2e+132)) {
		tmp = (z * -y) - t;
	} else {
		tmp = (x * log(y)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-8.2d+238)) .or. (.not. (z <= 2.2d+132))) then
        tmp = (z * -y) - t
    else
        tmp = (x * log(y)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.2e+238) || !(z <= 2.2e+132)) {
		tmp = (z * -y) - t;
	} else {
		tmp = (x * Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.2e+238) or not (z <= 2.2e+132):
		tmp = (z * -y) - t
	else:
		tmp = (x * math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.2e+238) || !(z <= 2.2e+132))
		tmp = Float64(Float64(z * Float64(-y)) - t);
	else
		tmp = Float64(Float64(x * log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.2e+238) || ~((z <= 2.2e+132)))
		tmp = (z * -y) - t;
	else
		tmp = (x * log(y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.2e+238], N[Not[LessEqual[z, 2.2e+132]], $MachinePrecision]], N[(N[(z * (-y)), $MachinePrecision] - t), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.1999999999999998e238 or 2.19999999999999989e132 < z

   1. Initial program 41.9%

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

   2. Taylor expanded in y around 0 98.5%

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

      1. +-commutative 98.5%

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

      2. *-commutative 98.5%

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

      3. mul-1-neg 98.5%

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

      4. unsub-neg 98.5%

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

      5. *-commutative 98.5%

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

   4. Simplified 98.5%

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

      1. *-commutative 98.5%

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

      2. add-sqr-sqrt 50.7%

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

      3. unpow2 50.7%

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

      4. add-cbrt-cube 33.6%

         \[\leadsto \left(\color{blue}{\sqrt[3]{\left({\left(\sqrt{x \cdot \log y}\right)}^{2} \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}\right) \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}}} - y \cdot z\right) - t \]

      5. pow-prod-down 33.6%

         \[\leadsto \left(\sqrt[3]{\color{blue}{{\left(\sqrt{x \cdot \log y} \cdot \sqrt{x \cdot \log y}\right)}^{2}} \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}} - y \cdot z\right) - t \]

      6. add-sqr-sqrt 33.6%

         \[\leadsto \left(\sqrt[3]{{\color{blue}{\left(x \cdot \log y\right)}}^{2} \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}} - y \cdot z\right) - t \]

      7. unpow2 33.6%

         \[\leadsto \left(\sqrt[3]{\color{blue}{\left(\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right)\right)} \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}} - y \cdot z\right) - t \]

      8. unpow2 33.6%

         \[\leadsto \left(\sqrt[3]{\left(\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right)\right) \cdot \color{blue}{\left(\sqrt{x \cdot \log y} \cdot \sqrt{x \cdot \log y}\right)}} - y \cdot z\right) - t \]

      9. add-sqr-sqrt 69.4%

         \[\leadsto \left(\sqrt[3]{\left(\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right)\right) \cdot \color{blue}{\left(x \cdot \log y\right)}} - y \cdot z\right) - t \]

      10. pow3 69.4%

          \[\leadsto \left(\sqrt[3]{\color{blue}{{\left(x \cdot \log y\right)}^{3}}} - y \cdot z\right) - t \]

      11. *-commutative 69.4%

          \[\leadsto \left(\sqrt[3]{{\color{blue}{\left(\log y \cdot x\right)}}^{3}} - y \cdot z\right) - t \]

   6. Applied egg-rr 69.4%

      \[\leadsto \left(\color{blue}{\sqrt[3]{{\left(\log y \cdot x\right)}^{3}}} - y \cdot z\right) - t \]

   7. Taylor expanded in y around inf 85.0%

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

      1. mul-1-neg 85.0%

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

      2. distribute-rgt-neg-in 85.0%

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

   9. Simplified 85.0%

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

   if -8.1999999999999998e238 < z < 2.19999999999999989e132

   1. Initial program 93.4%

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

      1. +-commutative 93.4%

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

      2. fma-def 93.4%

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

      3. sub-neg 93.4%

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

      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 z around 0 92.9%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+238} \lor \neg \left(z \leq 2.2 \cdot 10^{+132}\right):\\ \;\;\;\;z \cdot \left(-y\right) - t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - t\\ \end{array} \]

Alternative 8: 99.1% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.1%

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

2. Taylor expanded in y around 0 99.2%

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

   1. +-commutative 99.2%

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

   2. *-commutative 99.2%

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

   3. mul-1-neg 99.2%

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

   4. unsub-neg 99.2%

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

   5. *-commutative 99.2%

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

4. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 9: 48.7% accurate, 26.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-71}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-128}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -7.2e-71) (- t) (if (<= t 2.5e-128) (* z (- y)) (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -7.2e-71) {
		tmp = -t;
	} else if (t <= 2.5e-128) {
		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 <= (-7.2d-71)) then
        tmp = -t
    else if (t <= 2.5d-128) 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 <= -7.2e-71) {
		tmp = -t;
	} else if (t <= 2.5e-128) {
		tmp = z * -y;
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -7.2e-71:
		tmp = -t
	elif t <= 2.5e-128:
		tmp = z * -y
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -7.2e-71)
		tmp = Float64(-t);
	elseif (t <= 2.5e-128)
		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 <= -7.2e-71)
		tmp = -t;
	elseif (t <= 2.5e-128)
		tmp = z * -y;
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -7.2e-71], (-t), If[LessEqual[t, 2.5e-128], N[(z * (-y)), $MachinePrecision], (-t)]]

Derivation

1. Split input into 2 regimes

2. if t < -7.2e-71 or 2.5000000000000001e-128 < t

   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 99.8%

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

   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 61.6%

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

      1. neg-mul-1 61.6%

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

   6. Simplified 61.6%

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

   if -7.2e-71 < t < 2.5000000000000001e-128

   1. Initial program 67.8%

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

   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. *-commutative 99.3%

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

      3. mul-1-neg 99.3%

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

      4. unsub-neg 99.3%

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

      5. *-commutative 99.3%

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

   4. Simplified 99.3%

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

      1. *-commutative 99.3%

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

      2. add-sqr-sqrt 55.0%

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

      3. unpow2 55.0%

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

      4. add-cbrt-cube 36.5%

         \[\leadsto \left(\color{blue}{\sqrt[3]{\left({\left(\sqrt{x \cdot \log y}\right)}^{2} \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}\right) \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}}} - y \cdot z\right) - t \]

      5. pow-prod-down 36.5%

         \[\leadsto \left(\sqrt[3]{\color{blue}{{\left(\sqrt{x \cdot \log y} \cdot \sqrt{x \cdot \log y}\right)}^{2}} \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}} - y \cdot z\right) - t \]

      6. add-sqr-sqrt 36.6%

         \[\leadsto \left(\sqrt[3]{{\color{blue}{\left(x \cdot \log y\right)}}^{2} \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}} - y \cdot z\right) - t \]

      7. unpow2 36.6%

         \[\leadsto \left(\sqrt[3]{\color{blue}{\left(\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right)\right)} \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}} - y \cdot z\right) - t \]

      8. unpow2 36.6%

         \[\leadsto \left(\sqrt[3]{\left(\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right)\right) \cdot \color{blue}{\left(\sqrt{x \cdot \log y} \cdot \sqrt{x \cdot \log y}\right)}} - y \cdot z\right) - t \]

      9. add-sqr-sqrt 66.1%

         \[\leadsto \left(\sqrt[3]{\left(\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right)\right) \cdot \color{blue}{\left(x \cdot \log y\right)}} - y \cdot z\right) - t \]

      10. pow3 66.0%

          \[\leadsto \left(\sqrt[3]{\color{blue}{{\left(x \cdot \log y\right)}^{3}}} - y \cdot z\right) - t \]

      11. *-commutative 66.0%

          \[\leadsto \left(\sqrt[3]{{\color{blue}{\left(\log y \cdot x\right)}}^{3}} - y \cdot z\right) - t \]

   6. Applied egg-rr 66.0%

      \[\leadsto \left(\color{blue}{\sqrt[3]{{\left(\log y \cdot x\right)}^{3}}} - y \cdot z\right) - t \]

   7. Taylor expanded in y around inf 99.3%

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

      1. distribute-lft-out 99.3%

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

      2. mul-1-neg 99.3%

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

      3. fma-def 99.3%

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

      4. log-rec 99.3%

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

      5. distribute-lft-neg-in 99.3%

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

      6. distribute-rgt-neg-in 99.3%

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

   9. Simplified 99.3%

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

   10. Taylor expanded in y around inf 35.0%

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

       1. mul-1-neg 35.0%

          \[\leadsto \color{blue}{-y \cdot z} \]

   12. Simplified 35.0%

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

4. Final simplification 51.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-71}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-128}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]

Alternative 10: 57.4% 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 83.1%

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

2. Taylor expanded in y around 0 99.2%

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

   1. +-commutative 99.2%

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

   2. *-commutative 99.2%

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

   3. mul-1-neg 99.2%

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

   4. unsub-neg 99.2%

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

   5. *-commutative 99.2%

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

4. Simplified 99.2%

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

   1. *-commutative 99.2%

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

   2. add-sqr-sqrt 48.6%

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

   3. unpow2 48.6%

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

   4. add-cbrt-cube 32.6%

      \[\leadsto \left(\color{blue}{\sqrt[3]{\left({\left(\sqrt{x \cdot \log y}\right)}^{2} \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}\right) \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}}} - y \cdot z\right) - t \]

   5. pow-prod-down 32.6%

      \[\leadsto \left(\sqrt[3]{\color{blue}{{\left(\sqrt{x \cdot \log y} \cdot \sqrt{x \cdot \log y}\right)}^{2}} \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}} - y \cdot z\right) - t \]

   6. add-sqr-sqrt 32.6%

      \[\leadsto \left(\sqrt[3]{{\color{blue}{\left(x \cdot \log y\right)}}^{2} \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}} - y \cdot z\right) - t \]

   7. unpow2 32.6%

      \[\leadsto \left(\sqrt[3]{\color{blue}{\left(\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right)\right)} \cdot {\left(\sqrt{x \cdot \log y}\right)}^{2}} - y \cdot z\right) - t \]

   8. unpow2 32.6%

      \[\leadsto \left(\sqrt[3]{\left(\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right)\right) \cdot \color{blue}{\left(\sqrt{x \cdot \log y} \cdot \sqrt{x \cdot \log y}\right)}} - y \cdot z\right) - t \]

   9. add-sqr-sqrt 64.7%

      \[\leadsto \left(\sqrt[3]{\left(\left(x \cdot \log y\right) \cdot \left(x \cdot \log y\right)\right) \cdot \color{blue}{\left(x \cdot \log y\right)}} - y \cdot z\right) - t \]

   10. pow3 64.7%

       \[\leadsto \left(\sqrt[3]{\color{blue}{{\left(x \cdot \log y\right)}^{3}}} - y \cdot z\right) - t \]

   11. *-commutative 64.7%

       \[\leadsto \left(\sqrt[3]{{\color{blue}{\left(\log y \cdot x\right)}}^{3}} - y \cdot z\right) - t \]

6. Applied egg-rr 64.7%

   \[\leadsto \left(\color{blue}{\sqrt[3]{{\left(\log y \cdot x\right)}^{3}}} - y \cdot z\right) - t \]

7. Taylor expanded in y around inf 59.1%

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

   1. mul-1-neg 59.1%

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

   2. distribute-rgt-neg-in 59.1%

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

9. Simplified 59.1%

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

10. Final simplification 59.1%

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

Alternative 11: 42.2% 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 83.1%

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

   1. +-commutative 83.1%

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

   2. fma-def 83.1%

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

   3. sub-neg 83.1%

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

   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 42.7%

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

   1. neg-mul-1 42.7%

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

6. Simplified 42.7%

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

7. Final simplification 42.7%

   \[\leadsto -t \]

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 2023196 
(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))