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

Percentage Accurate: 85.6% → 99.8%

Time: 16.5s

Alternatives: 12

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: 85.6% 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 83.0%

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

   1. +-commutative 83.0%

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

   2. associate--l+ 83.0%

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

   3. fma-define 83.0%

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

   4. sub-neg 83.0%

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

   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: 99.6% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.0%

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

3. Taylor expanded in y around 0 99.8%

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

4. Final simplification 99.8%

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

Alternative 3: 90.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \log y\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{-99} \lor \neg \left(t \leq 6.2 \cdot 10^{-59}\right):\\ \;\;\;\;t\_1 - t\\ \mathbf{else}:\\ \;\;\;\;t\_1 - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (log y))))
   (if (or (<= t -5.5e-99) (not (<= t 6.2e-59))) (- t_1 t) (- t_1 (* z y)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * log(y);
	double tmp;
	if ((t <= -5.5e-99) || !(t <= 6.2e-59)) {
		tmp = t_1 - t;
	} else {
		tmp = t_1 - (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) :: t_1
    real(8) :: tmp
    t_1 = x * log(y)
    if ((t <= (-5.5d-99)) .or. (.not. (t <= 6.2d-59))) then
        tmp = t_1 - t
    else
        tmp = t_1 - (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x * Math.log(y);
	double tmp;
	if ((t <= -5.5e-99) || !(t <= 6.2e-59)) {
		tmp = t_1 - t;
	} else {
		tmp = t_1 - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * math.log(y)
	tmp = 0
	if (t <= -5.5e-99) or not (t <= 6.2e-59):
		tmp = t_1 - t
	else:
		tmp = t_1 - (z * y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * log(y))
	tmp = 0.0
	if ((t <= -5.5e-99) || !(t <= 6.2e-59))
		tmp = Float64(t_1 - t);
	else
		tmp = Float64(t_1 - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * log(y);
	tmp = 0.0;
	if ((t <= -5.5e-99) || ~((t <= 6.2e-59)))
		tmp = t_1 - t;
	else
		tmp = t_1 - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -5.5e-99], N[Not[LessEqual[t, 6.2e-59]], $MachinePrecision]], N[(t$95$1 - t), $MachinePrecision], N[(t$95$1 - N[(z * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.49999999999999991e-99 or 6.19999999999999998e-59 < t

   1. Initial program 92.9%

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

   3. Taylor expanded in y around 0 99.8%

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

   4. Taylor expanded in x around inf 92.1%

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

   if -5.49999999999999991e-99 < t < 6.19999999999999998e-59

   1. Initial program 70.1%

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

      1. +-commutative 70.1%

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

      2. associate--l+ 70.1%

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

      3. fma-define 70.1%

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

      4. sub-neg 70.1%

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

      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 74.3%

      \[\leadsto \mathsf{fma}\left(z, \mathsf{log1p}\left(-y\right), \color{blue}{t \cdot \left(\frac{x \cdot \log y}{t} - 1\right)}\right) \]
   6. Step-by-step derivation

      1. *-commutative 74.3%

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

      2. associate-/l* 74.3%

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

      3. fma-neg 74.3%

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

      4. metadata-eval 74.3%

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

   7. Simplified 74.3%

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

   8. Taylor expanded in y around 0 73.6%

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

   9. Taylor expanded in x around inf 99.0%

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

       1. mul-1-neg 99.0%

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

       2. unsub-neg 99.0%

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

   11. Simplified 99.0%

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

   12. Taylor expanded in t around 0 90.5%

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

       1. mul-1-neg 90.5%

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

       2. distribute-rgt-neg-out 90.5%

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

       3. +-commutative 90.5%

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

       4. distribute-rgt-neg-out 90.5%

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

       5. unsub-neg 90.5%

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

   14. Simplified 90.5%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-99} \lor \neg \left(t \leq 6.2 \cdot 10^{-59}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-25} \lor \neg \left(x \leq 3.8 \cdot 10^{-142}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-0.5 \cdot \left(z \cdot y\right) - z\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.7e-25) (not (<= x 3.8e-142)))
   (- (* x (log y)) t)
   (- (* y (- (* -0.5 (* z y)) z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.7e-25) || !(x <= 3.8e-142)) {
		tmp = (x * log(y)) - t;
	} else {
		tmp = (y * ((-0.5 * (z * y)) - 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 <= (-1.7d-25)) .or. (.not. (x <= 3.8d-142))) then
        tmp = (x * log(y)) - t
    else
        tmp = (y * (((-0.5d0) * (z * y)) - 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 <= -1.7e-25) || !(x <= 3.8e-142)) {
		tmp = (x * Math.log(y)) - t;
	} else {
		tmp = (y * ((-0.5 * (z * y)) - z)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.7e-25) or not (x <= 3.8e-142):
		tmp = (x * math.log(y)) - t
	else:
		tmp = (y * ((-0.5 * (z * y)) - z)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.7e-25) || !(x <= 3.8e-142))
		tmp = Float64(Float64(x * log(y)) - t);
	else
		tmp = Float64(Float64(y * Float64(Float64(-0.5 * Float64(z * y)) - z)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.7e-25) || ~((x <= 3.8e-142)))
		tmp = (x * log(y)) - t;
	else
		tmp = (y * ((-0.5 * (z * y)) - z)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.7e-25], N[Not[LessEqual[x, 3.8e-142]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(y * N[(N[(-0.5 * N[(z * y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.70000000000000001e-25 or 3.79999999999999972e-142 < x

   1. Initial program 91.3%

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

   3. Taylor expanded in y around 0 99.7%

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

   4. Taylor expanded in x around inf 90.2%

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

   if -1.70000000000000001e-25 < x < 3.79999999999999972e-142

   1. Initial program 70.4%

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

   3. Taylor expanded in x around 0 62.0%

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

      1. sub-neg 62.0%

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

      2. log1p-define 89.9%

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

   5. Simplified 89.9%

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

   6. Taylor expanded in y around 0 90.0%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-25} \lor \neg \left(x \leq 3.8 \cdot 10^{-142}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-0.5 \cdot \left(z \cdot y\right) - z\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return ((x * log(y)) + (z * (y * (-1.0 + (y * -0.5))))) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x * log(y)) + (z * (y * ((-1.0d0) + (y * (-0.5d0)))))) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.0%

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

3. Taylor expanded in y around 0 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \left(x \cdot \log y + z \cdot \left(y \cdot \left(-1 + y \cdot -0.5\right)\right)\right) - t \]
5. Add Preprocessing

Alternative 6: 99.2% 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 83.0%

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

3. Taylor expanded in y around 0 99.2%

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

   1. +-commutative 99.2%

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

   2. mul-1-neg 99.2%

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

   3. unsub-neg 99.2%

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

5. Simplified 99.2%

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

6. Final simplification 99.2%

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

Alternative 7: 56.8% accurate, 14.1× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.0%

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

3. Taylor expanded in x around 0 41.5%

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

   1. sub-neg 41.5%

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

   2. log1p-define 57.7%

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

5. Simplified 57.7%

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

6. Taylor expanded in y around 0 57.7%

   \[\leadsto \color{blue}{y \cdot \left(-1 \cdot z + y \cdot \left(-0.5 \cdot z + y \cdot \left(-0.3333333333333333 \cdot z + -0.25 \cdot \left(y \cdot z\right)\right)\right)\right)} - t \]

7. Taylor expanded in y around 0 57.7%

   \[\leadsto \color{blue}{y \cdot \left(-1 \cdot z + y \cdot \left(-0.5 \cdot z + -0.3333333333333333 \cdot \left(y \cdot z\right)\right)\right)} - t \]
8. Step-by-step derivation

   1. +-commutative 57.7%

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

   2. mul-1-neg 57.7%

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

   3. unsub-neg 57.7%

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

   4. associate-*r* 57.7%

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

   5. distribute-rgt-out 57.7%

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

   6. *-commutative 57.7%

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

9. Simplified 57.7%

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

10. Final simplification 57.7%

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

Alternative 8: 48.1% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.9 \cdot 10^{-109} \lor \neg \left(t \leq 3.5 \cdot 10^{-58}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.9e-109) (not (<= t 3.5e-58))) (- t) (* z (- y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.9e-109) || !(t <= 3.5e-58)) {
		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 <= (-5.9d-109)) .or. (.not. (t <= 3.5d-58))) 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 <= -5.9e-109) || !(t <= 3.5e-58)) {
		tmp = -t;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.9e-109) or not (t <= 3.5e-58):
		tmp = -t
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.9e-109) || !(t <= 3.5e-58))
		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 <= -5.9e-109) || ~((t <= 3.5e-58)))
		tmp = -t;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.9e-109], N[Not[LessEqual[t, 3.5e-58]], $MachinePrecision]], (-t), N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.90000000000000021e-109 or 3.4999999999999999e-58 < t

   1. Initial program 93.0%

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

   3. Taylor expanded in x around 0 62.5%

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

      1. sub-neg 62.5%

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

      2. log1p-define 69.4%

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

   5. Simplified 69.4%

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

   6. Taylor expanded in z around 0 61.6%

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

      1. neg-mul-1 61.6%

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

   8. Simplified 61.6%

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

   if -5.90000000000000021e-109 < t < 3.4999999999999999e-58

   1. Initial program 69.5%

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

   3. Taylor expanded in x around 0 13.1%

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

      1. sub-neg 13.1%

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

      2. log1p-define 41.8%

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

   5. Simplified 41.8%

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

   6. Taylor expanded in y around 0 41.1%

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

      1. mul-1-neg 41.1%

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

      2. distribute-rgt-neg-out 41.1%

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

   8. Simplified 41.1%

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

   9. Taylor expanded in y around inf 33.0%

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

       1. associate-*r* 33.0%

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

       2. mul-1-neg 33.0%

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

   11. Simplified 33.0%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.9 \cdot 10^{-109} \lor \neg \left(t \leq 3.5 \cdot 10^{-58}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 56.7% accurate, 19.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (y * (z * (-1.0 + (y * -0.5)))) - t;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (y * (z * ((-1.0d0) + (y * (-0.5d0))))) - t
end function

Java

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

Python

def code(x, y, z, t):
	return (y * (z * (-1.0 + (y * -0.5)))) - t

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.0%

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

3. Taylor expanded in x around 0 41.5%

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

   1. sub-neg 41.5%

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

   2. log1p-define 57.7%

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

5. Simplified 57.7%

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

6. Taylor expanded in y around 0 57.7%

   \[\leadsto \color{blue}{y \cdot \left(-1 \cdot z + y \cdot \left(-0.5 \cdot z + y \cdot \left(-0.3333333333333333 \cdot z + -0.25 \cdot \left(y \cdot z\right)\right)\right)\right)} - t \]

7. Taylor expanded in y around 0 57.7%

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

   1. +-commutative 57.7%

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

   2. associate-*r* 57.7%

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

   3. distribute-rgt-out 57.6%

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

   4. *-commutative 57.6%

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

9. Simplified 57.6%

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

10. Final simplification 57.6%

    \[\leadsto y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t \]
11. Add Preprocessing

Alternative 10: 56.7% accurate, 19.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.0%

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

3. Taylor expanded in x around 0 41.5%

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

   1. sub-neg 41.5%

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

   2. log1p-define 57.7%

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

5. Simplified 57.7%

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

6. Taylor expanded in y around 0 57.7%

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

7. Final simplification 57.7%

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

Alternative 11: 56.3% 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 83.0%

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

3. Taylor expanded in x around 0 41.5%

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

   1. sub-neg 41.5%

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

   2. log1p-define 57.7%

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

5. Simplified 57.7%

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

6. Taylor expanded in y around 0 57.0%

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

   1. mul-1-neg 57.0%

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

   2. distribute-rgt-neg-out 57.0%

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

8. Simplified 57.0%

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

9. Final simplification 57.0%

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

Alternative 12: 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 83.0%

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

3. Taylor expanded in x around 0 41.5%

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

   1. sub-neg 41.5%

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

   2. log1p-define 57.7%

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

5. Simplified 57.7%

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

6. Taylor expanded in z around 0 40.3%

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

   1. neg-mul-1 40.3%

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

8. Simplified 40.3%

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

9. Final simplification 40.3%

   \[\leadsto -t \]
10. 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 2024066 
(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))