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

Percentage Accurate: 85.3% → 99.8%

Time: 13.7s

Alternatives: 9

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: 85.3% 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

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

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

Wolfram

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

Derivation

1. Initial program 87.1%

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

   1. +-commutative 87.1%

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

   2. associate--l+ 87.1%

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

   3. fma-define 87.1%

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

   4. sub-neg 87.1%

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

   5. log1p-define 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 89.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-131} \lor \neg \left(x \leq 3 \cdot 10^{-110}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot \left(z \cdot -0.5 + \left(z \cdot y\right) \cdot -0.3333333333333333\right) - z\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.5e-131) (not (<= x 3e-110)))
   (- (* x (log y)) t)
   (- (* y (- (* y (+ (* z -0.5) (* (* z y) -0.3333333333333333))) z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.5e-131) || !(x <= 3e-110)) {
		tmp = (x * log(y)) - t;
	} else {
		tmp = (y * ((y * ((z * -0.5) + ((z * y) * -0.3333333333333333))) - z)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.5d-131)) .or. (.not. (x <= 3d-110))) then
        tmp = (x * log(y)) - t
    else
        tmp = (y * ((y * ((z * (-0.5d0)) + ((z * y) * (-0.3333333333333333d0)))) - z)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.5e-131) || !(x <= 3e-110)) {
		tmp = (x * Math.log(y)) - t;
	} else {
		tmp = (y * ((y * ((z * -0.5) + ((z * y) * -0.3333333333333333))) - z)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.5e-131) or not (x <= 3e-110):
		tmp = (x * math.log(y)) - t
	else:
		tmp = (y * ((y * ((z * -0.5) + ((z * y) * -0.3333333333333333))) - z)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.5e-131) || !(x <= 3e-110))
		tmp = Float64(Float64(x * log(y)) - t);
	else
		tmp = Float64(Float64(y * Float64(Float64(y * Float64(Float64(z * -0.5) + Float64(Float64(z * y) * -0.3333333333333333))) - z)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.5e-131) || ~((x <= 3e-110)))
		tmp = (x * log(y)) - t;
	else
		tmp = (y * ((y * ((z * -0.5) + ((z * y) * -0.3333333333333333))) - z)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.5e-131], N[Not[LessEqual[x, 3e-110]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(y * N[(N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.49999999999999998e-131 or 2.99999999999999986e-110 < x

   1. Initial program 92.1%

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

      1. +-commutative 92.1%

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

      2. associate--l+ 92.1%

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

      3. fma-define 92.1%

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

      4. sub-neg 92.1%

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

      5. log1p-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 91.4%

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

   if -1.49999999999999998e-131 < x < 2.99999999999999986e-110

   1. Initial program 73.3%

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

      1. +-commutative 73.3%

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

      2. associate--l+ 73.3%

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

      3. fma-define 73.3%

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

      4. sub-neg 73.3%

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

      5. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 68.3%

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

      1. fma-neg 68.3%

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

      2. sub-neg 68.3%

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

      3. log1p-define 94.4%

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

   7. Simplified 94.4%

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

   8. Taylor expanded in y around 0 94.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot z + y \cdot \left(-0.5 \cdot z + -0.3333333333333333 \cdot \left(y \cdot z\right)\right)\right) - t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{-131} \lor \neg \left(x \leq 3 \cdot 10^{-110}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot \left(z \cdot -0.5 + \left(z \cdot y\right) \cdot -0.3333333333333333\right) - z\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+23}:\\ \;\;\;\;\left(-t\right) - z \cdot y\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot \left(z \cdot -0.5 + \left(z \cdot y\right) \cdot -0.3333333333333333\right) - z\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2e+23)
   (- (- t) (* z y))
   (if (<= t 5.4e+22)
     (* x (log y))
     (- (* y (- (* y (+ (* z -0.5) (* (* z y) -0.3333333333333333))) z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2e+23) {
		tmp = -t - (z * y);
	} else if (t <= 5.4e+22) {
		tmp = x * log(y);
	} else {
		tmp = (y * ((y * ((z * -0.5) + ((z * y) * -0.3333333333333333))) - z)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2d+23)) then
        tmp = -t - (z * y)
    else if (t <= 5.4d+22) then
        tmp = x * log(y)
    else
        tmp = (y * ((y * ((z * (-0.5d0)) + ((z * y) * (-0.3333333333333333d0)))) - z)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2e+23) {
		tmp = -t - (z * y);
	} else if (t <= 5.4e+22) {
		tmp = x * Math.log(y);
	} else {
		tmp = (y * ((y * ((z * -0.5) + ((z * y) * -0.3333333333333333))) - z)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2e+23:
		tmp = -t - (z * y)
	elif t <= 5.4e+22:
		tmp = x * math.log(y)
	else:
		tmp = (y * ((y * ((z * -0.5) + ((z * y) * -0.3333333333333333))) - z)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2e+23)
		tmp = Float64(Float64(-t) - Float64(z * y));
	elseif (t <= 5.4e+22)
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(y * Float64(Float64(y * Float64(Float64(z * -0.5) + Float64(Float64(z * y) * -0.3333333333333333))) - z)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2e+23)
		tmp = -t - (z * y);
	elseif (t <= 5.4e+22)
		tmp = x * log(y);
	else
		tmp = (y * ((y * ((z * -0.5) + ((z * y) * -0.3333333333333333))) - z)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2e+23], N[((-t) - N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e+22], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(y * N[(N[(z * -0.5), $MachinePrecision] + N[(N[(z * y), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9999999999999998e23

   1. Initial program 95.0%

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

      1. +-commutative 95.0%

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

      2. associate--l+ 95.0%

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

      3. fma-define 95.0%

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

      4. sub-neg 95.0%

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

      5. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 83.8%

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

      1. fma-neg 83.8%

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

      2. sub-neg 83.8%

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

      3. log1p-define 88.7%

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

   7. Simplified 88.7%

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

   8. Taylor expanded in y around 0 88.7%

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

      1. sub-neg 88.7%

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

      2. mul-1-neg 88.7%

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

      3. distribute-neg-out 88.7%

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

   10. Applied egg-rr 88.7%

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

   if -1.9999999999999998e23 < t < 5.4000000000000004e22

   1. Initial program 79.6%

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

   3. Taylor expanded in y around 0 99.1%

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

      1. +-commutative 99.1%

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

      2. mul-1-neg 99.1%

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

      3. unsub-neg 99.1%

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

   5. Simplified 99.1%

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

   6. Taylor expanded in x around inf 67.3%

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

   if 5.4000000000000004e22 < t

   1. Initial program 95.4%

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

      1. +-commutative 95.4%

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

      2. associate--l+ 95.4%

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

      3. fma-define 95.4%

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

      4. sub-neg 95.4%

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

      5. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 84.0%

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

      1. fma-neg 84.0%

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

      2. sub-neg 84.0%

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

      3. log1p-define 88.4%

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

   7. Simplified 88.4%

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

   8. Taylor expanded in y around 0 87.6%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot z + y \cdot \left(-0.5 \cdot z + -0.3333333333333333 \cdot \left(y \cdot z\right)\right)\right) - t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+23}:\\ \;\;\;\;\left(-t\right) - z \cdot y\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{+22}:\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(y \cdot \left(z \cdot -0.5 + \left(z \cdot y\right) \cdot -0.3333333333333333\right) - z\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 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 87.1%

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

3. Taylor expanded in y around 0 99.3%

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

   1. +-commutative 99.3%

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

   2. mul-1-neg 99.3%

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

   3. unsub-neg 99.3%

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

5. Simplified 99.3%

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

6. Final simplification 99.3%

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

Alternative 5: 57.2% accurate, 12.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (y * ((y * ((z * -0.5) + ((z * y) * -0.3333333333333333))) - z)) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (y * ((y * ((z * (-0.5d0)) + ((z * y) * (-0.3333333333333333d0)))) - z)) - t
end function

Java

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

Python

def code(x, y, z, t):
	return (y * ((y * ((z * -0.5) + ((z * y) * -0.3333333333333333))) - z)) - t

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.1%

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

   1. +-commutative 87.1%

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

   2. associate--l+ 87.1%

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

   3. fma-define 87.1%

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

   4. sub-neg 87.1%

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

   5. log1p-define 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in x around 0 47.2%

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

   1. fma-neg 47.2%

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

   2. sub-neg 47.2%

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

   3. log1p-define 59.5%

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

7. Simplified 59.5%

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

8. Taylor expanded in y around 0 59.3%

   \[\leadsto \color{blue}{y \cdot \left(-1 \cdot z + y \cdot \left(-0.5 \cdot z + -0.3333333333333333 \cdot \left(y \cdot z\right)\right)\right) - t} \]

9. Final simplification 59.3%

   \[\leadsto y \cdot \left(y \cdot \left(z \cdot -0.5 + \left(z \cdot y\right) \cdot -0.3333333333333333\right) - z\right) - t \]
10. Add Preprocessing

Alternative 6: 47.6% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+25} \lor \neg \left(t \leq 4.5 \cdot 10^{-56}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.3e+25) (not (<= t 4.5e-56))) (- t) (* z (- y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.3e+25) || !(t <= 4.5e-56)) {
		tmp = -t;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.3d+25)) .or. (.not. (t <= 4.5d-56))) then
        tmp = -t
    else
        tmp = z * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.3e+25) || !(t <= 4.5e-56)) {
		tmp = -t;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.3e+25) or not (t <= 4.5e-56):
		tmp = -t
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.3e+25) || !(t <= 4.5e-56))
		tmp = Float64(-t);
	else
		tmp = Float64(z * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.3e+25) || ~((t <= 4.5e-56)))
		tmp = -t;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.3e+25], N[Not[LessEqual[t, 4.5e-56]], $MachinePrecision]], (-t), N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2999999999999998e25 or 4.5000000000000001e-56 < t

   1. Initial program 95.7%

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

      1. +-commutative 95.7%

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

      2. associate--l+ 95.7%

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

      3. fma-define 95.7%

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

      4. sub-neg 95.7%

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

      5. log1p-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 78.4%

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

      1. neg-mul-1 78.4%

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

   7. Simplified 78.4%

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

   if -2.2999999999999998e25 < t < 4.5000000000000001e-56

   1. Initial program 77.4%

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

   3. Taylor expanded in y around 0 99.1%

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

      1. +-commutative 99.1%

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

      2. mul-1-neg 99.1%

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

      3. unsub-neg 99.1%

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

   5. Simplified 99.1%

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

   6. Taylor expanded in y around inf 24.0%

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

      1. associate-*r* 24.0%

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

      2. mul-1-neg 24.0%

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

   8. Simplified 24.0%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+25} \lor \neg \left(t \leq 4.5 \cdot 10^{-56}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.1% accurate, 19.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.1%

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

   1. +-commutative 87.1%

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

   2. associate--l+ 87.1%

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

   3. fma-define 87.1%

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

   4. sub-neg 87.1%

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

   5. log1p-define 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in x around 0 47.2%

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

   1. fma-neg 47.2%

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

   2. sub-neg 47.2%

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

   3. log1p-define 59.5%

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

7. Simplified 59.5%

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

8. Taylor expanded in y around 0 59.3%

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

9. Final simplification 59.3%

   \[\leadsto y \cdot \left(\left(z \cdot y\right) \cdot -0.5 - z\right) - t \]
10. Add Preprocessing

Alternative 8: 56.8% accurate, 35.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.1%

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

   1. +-commutative 87.1%

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

   2. associate--l+ 87.1%

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

   3. fma-define 87.1%

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

   4. sub-neg 87.1%

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

   5. log1p-define 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in x around 0 47.2%

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

   1. fma-neg 47.2%

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

   2. sub-neg 47.2%

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

   3. log1p-define 59.5%

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

7. Simplified 59.5%

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

8. Taylor expanded in y around 0 59.0%

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

   1. sub-neg 59.0%

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

   2. mul-1-neg 59.0%

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

   3. distribute-neg-out 59.0%

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

10. Applied egg-rr 59.0%

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

11. Final simplification 59.0%

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

Alternative 9: 42.3% accurate, 105.5× speedup

Math

\[\begin{array}{l} \\ -t \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := (-t)

Derivation

1. Initial program 87.1%

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

   1. +-commutative 87.1%

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

   2. associate--l+ 87.1%

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

   3. fma-define 87.1%

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

   4. sub-neg 87.1%

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

   5. log1p-define 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in t around inf 46.4%

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

   1. neg-mul-1 46.4%

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

7. Simplified 46.4%

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

8. Final simplification 46.4%

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

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 2024071 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, B"
  :precision binary64

  :alt
  (- (* (- 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))