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

Percentage Accurate: 85.5% → 99.8%

Time: 15.9s

Alternatives: 8

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: 85.5% 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, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.8%

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

   1. +-commutative 85.8%

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

   2. associate--l+ 85.8%

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

   3. fma-def 85.8%

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

   4. sub-neg 85.8%

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

   5. log1p-def 99.8%

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

   6. fma-neg 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 99.8% accurate, 0.7× speedup

Math

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

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 85.8%

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

   1. +-commutative 85.8%

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

   2. associate--l+ 85.8%

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

   3. fma-def 85.8%

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

   4. sub-neg 85.8%

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

   5. log1p-def 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 3: 87.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+169} \lor \neg \left(z \leq 4.8 \cdot 10^{+156}\right):\\ \;\;\;\;\left(-t\right) - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7e+169) (not (<= z 4.8e+156)))
   (- (- t) (* z y))
   (- (* x (log y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7e+169) || !(z <= 4.8e+156)) {
		tmp = -t - (z * y);
	} 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 <= (-7d+169)) .or. (.not. (z <= 4.8d+156))) then
        tmp = -t - (z * y)
    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 <= -7e+169) || !(z <= 4.8e+156)) {
		tmp = -t - (z * y);
	} else {
		tmp = (x * Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7e+169) or not (z <= 4.8e+156):
		tmp = -t - (z * y)
	else:
		tmp = (x * math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7e+169) || !(z <= 4.8e+156))
		tmp = Float64(Float64(-t) - Float64(z * y));
	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 <= -7e+169) || ~((z <= 4.8e+156)))
		tmp = -t - (z * y);
	else
		tmp = (x * log(y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7e+169], N[Not[LessEqual[z, 4.8e+156]], $MachinePrecision]], N[((-t) - N[(z * y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.00000000000000038e169 or 4.8000000000000002e156 < z

   1. Initial program 47.3%

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

      1. flip3-- 47.2%

         \[\leadsto \left(x \cdot \log y + z \cdot \log \color{blue}{\left(\frac{{1}^{3} - {y}^{3}}{1 \cdot 1 + \left(y \cdot y + 1 \cdot y\right)}\right)}\right) - t \]

      2. log-div 47.2%

         \[\leadsto \left(x \cdot \log y + z \cdot \color{blue}{\left(\log \left({1}^{3} - {y}^{3}\right) - \log \left(1 \cdot 1 + \left(y \cdot y + 1 \cdot y\right)\right)\right)}\right) - t \]

      3. metadata-eval 47.2%

         \[\leadsto \left(x \cdot \log y + z \cdot \left(\log \left(\color{blue}{1} - {y}^{3}\right) - \log \left(1 \cdot 1 + \left(y \cdot y + 1 \cdot y\right)\right)\right)\right) - t \]

      4. pow3 47.2%

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

      5. sub-neg 47.2%

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

      6. distribute-rgt-neg-out 47.2%

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

      7. add-sqr-sqrt 0.0%

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

      8. sqrt-unprod 47.2%

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

      9. sqr-neg 47.2%

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

      10. sqrt-unprod 47.2%

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

      11. add-sqr-sqrt 47.2%

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

      12. log1p-udef 47.2%

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

      13. pow3 47.2%

          \[\leadsto \left(x \cdot \log y + z \cdot \left(\mathsf{log1p}\left(\color{blue}{{y}^{3}}\right) - \log \left(1 \cdot 1 + \left(y \cdot y + 1 \cdot y\right)\right)\right)\right) - t \]

      14. metadata-eval 47.2%

          \[\leadsto \left(x \cdot \log y + z \cdot \left(\mathsf{log1p}\left({y}^{3}\right) - \log \left(\color{blue}{1} + \left(y \cdot y + 1 \cdot y\right)\right)\right)\right) - t \]

      15. log1p-udef 99.9%

          \[\leadsto \left(x \cdot \log y + z \cdot \left(\mathsf{log1p}\left({y}^{3}\right) - \color{blue}{\mathsf{log1p}\left(y \cdot y + 1 \cdot y\right)}\right)\right) - t \]

      16. *-un-lft-identity 99.9%

          \[\leadsto \left(x \cdot \log y + z \cdot \left(\mathsf{log1p}\left({y}^{3}\right) - \mathsf{log1p}\left(y \cdot y + \color{blue}{y}\right)\right)\right) - t \]

      17. fma-def 99.9%

          \[\leadsto \left(x \cdot \log y + z \cdot \left(\mathsf{log1p}\left({y}^{3}\right) - \mathsf{log1p}\left(\color{blue}{\mathsf{fma}\left(y, y, y\right)}\right)\right)\right) - t \]

   4. Applied egg-rr 99.9%

      \[\leadsto \left(x \cdot \log y + z \cdot \color{blue}{\left(\mathsf{log1p}\left({y}^{3}\right) - \mathsf{log1p}\left(\mathsf{fma}\left(y, y, y\right)\right)\right)}\right) - t \]

   5. Taylor expanded in y around 0 99.9%

      \[\leadsto \left(x \cdot \log y + z \cdot \left(\color{blue}{{y}^{3}} - \mathsf{log1p}\left(\mathsf{fma}\left(y, y, y\right)\right)\right)\right) - t \]

   6. Taylor expanded in x around 0 34.9%

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

      1. log1p-def 87.3%

         \[\leadsto z \cdot \left({y}^{3} - \color{blue}{\mathsf{log1p}\left(y + {y}^{2}\right)}\right) - t \]

      2. +-commutative 87.3%

         \[\leadsto z \cdot \left({y}^{3} - \mathsf{log1p}\left(\color{blue}{{y}^{2} + y}\right)\right) - t \]

      3. unpow2 87.3%

         \[\leadsto z \cdot \left({y}^{3} - \mathsf{log1p}\left(\color{blue}{y \cdot y} + y\right)\right) - t \]

      4. fma-udef 87.3%

         \[\leadsto z \cdot \left({y}^{3} - \mathsf{log1p}\left(\color{blue}{\mathsf{fma}\left(y, y, y\right)}\right)\right) - t \]

   8. Simplified 87.3%

      \[\leadsto \color{blue}{z \cdot \left({y}^{3} - \mathsf{log1p}\left(\mathsf{fma}\left(y, y, y\right)\right)\right)} - t \]

   9. Taylor expanded in y around 0 86.6%

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

       1. mul-1-neg 86.6%

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

   11. Simplified 86.6%

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

   if -7.00000000000000038e169 < z < 4.8000000000000002e156

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0 95.8%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+169} \lor \neg \left(z \leq 4.8 \cdot 10^{+156}\right):\\ \;\;\;\;\left(-t\right) - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+56} \lor \neg \left(x \leq 4.8 \cdot 10^{+41}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.2e+56) (not (<= x 4.8e+41)))
   (* x (log y))
   (- (- t) (* z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.2e+56) || !(x <= 4.8e+41)) {
		tmp = x * log(y);
	} else {
		tmp = -t - (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 ((x <= (-5.2d+56)) .or. (.not. (x <= 4.8d+41))) then
        tmp = x * log(y)
    else
        tmp = -t - (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.2e+56) || !(x <= 4.8e+41)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -t - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.2e+56) or not (x <= 4.8e+41):
		tmp = x * math.log(y)
	else:
		tmp = -t - (z * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.2e+56) || !(x <= 4.8e+41))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(-t) - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.2e+56) || ~((x <= 4.8e+41)))
		tmp = x * log(y);
	else
		tmp = -t - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.2e+56], N[Not[LessEqual[x, 4.8e+41]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-t) - N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.20000000000000022e56 or 4.8000000000000003e41 < x

   1. Initial program 97.4%

      \[\left(x \cdot \log y + z \cdot \log \left(1 - y\right)\right) - t \]
   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 x around inf 79.6%

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

   if -5.20000000000000022e56 < x < 4.8000000000000003e41

   1. Initial program 78.6%

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

      1. flip3-- 78.6%

         \[\leadsto \left(x \cdot \log y + z \cdot \log \color{blue}{\left(\frac{{1}^{3} - {y}^{3}}{1 \cdot 1 + \left(y \cdot y + 1 \cdot y\right)}\right)}\right) - t \]

      2. log-div 78.6%

         \[\leadsto \left(x \cdot \log y + z \cdot \color{blue}{\left(\log \left({1}^{3} - {y}^{3}\right) - \log \left(1 \cdot 1 + \left(y \cdot y + 1 \cdot y\right)\right)\right)}\right) - t \]

      3. metadata-eval 78.6%

         \[\leadsto \left(x \cdot \log y + z \cdot \left(\log \left(\color{blue}{1} - {y}^{3}\right) - \log \left(1 \cdot 1 + \left(y \cdot y + 1 \cdot y\right)\right)\right)\right) - t \]

      4. pow3 78.6%

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

      5. sub-neg 78.6%

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

      6. distribute-rgt-neg-out 78.6%

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

      7. add-sqr-sqrt 0.0%

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

      8. sqrt-unprod 78.4%

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

      9. sqr-neg 78.4%

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

      10. sqrt-unprod 78.4%

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

      11. add-sqr-sqrt 78.4%

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

      12. log1p-udef 78.4%

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

      13. pow3 78.4%

          \[\leadsto \left(x \cdot \log y + z \cdot \left(\mathsf{log1p}\left(\color{blue}{{y}^{3}}\right) - \log \left(1 \cdot 1 + \left(y \cdot y + 1 \cdot y\right)\right)\right)\right) - t \]

      14. metadata-eval 78.4%

          \[\leadsto \left(x \cdot \log y + z \cdot \left(\mathsf{log1p}\left({y}^{3}\right) - \log \left(\color{blue}{1} + \left(y \cdot y + 1 \cdot y\right)\right)\right)\right) - t \]

      15. log1p-udef 99.7%

          \[\leadsto \left(x \cdot \log y + z \cdot \left(\mathsf{log1p}\left({y}^{3}\right) - \color{blue}{\mathsf{log1p}\left(y \cdot y + 1 \cdot y\right)}\right)\right) - t \]

      16. *-un-lft-identity 99.7%

          \[\leadsto \left(x \cdot \log y + z \cdot \left(\mathsf{log1p}\left({y}^{3}\right) - \mathsf{log1p}\left(y \cdot y + \color{blue}{y}\right)\right)\right) - t \]

      17. fma-def 99.7%

          \[\leadsto \left(x \cdot \log y + z \cdot \left(\mathsf{log1p}\left({y}^{3}\right) - \mathsf{log1p}\left(\color{blue}{\mathsf{fma}\left(y, y, y\right)}\right)\right)\right) - t \]

   4. Applied egg-rr 99.7%

      \[\leadsto \left(x \cdot \log y + z \cdot \color{blue}{\left(\mathsf{log1p}\left({y}^{3}\right) - \mathsf{log1p}\left(\mathsf{fma}\left(y, y, y\right)\right)\right)}\right) - t \]

   5. Taylor expanded in y around 0 99.7%

      \[\leadsto \left(x \cdot \log y + z \cdot \left(\color{blue}{{y}^{3}} - \mathsf{log1p}\left(\mathsf{fma}\left(y, y, y\right)\right)\right)\right) - t \]

   6. Taylor expanded in x around 0 64.6%

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

      1. log1p-def 85.4%

         \[\leadsto z \cdot \left({y}^{3} - \color{blue}{\mathsf{log1p}\left(y + {y}^{2}\right)}\right) - t \]

      2. +-commutative 85.4%

         \[\leadsto z \cdot \left({y}^{3} - \mathsf{log1p}\left(\color{blue}{{y}^{2} + y}\right)\right) - t \]

      3. unpow2 85.4%

         \[\leadsto z \cdot \left({y}^{3} - \mathsf{log1p}\left(\color{blue}{y \cdot y} + y\right)\right) - t \]

      4. fma-udef 85.4%

         \[\leadsto z \cdot \left({y}^{3} - \mathsf{log1p}\left(\color{blue}{\mathsf{fma}\left(y, y, y\right)}\right)\right) - t \]

   8. Simplified 85.4%

      \[\leadsto \color{blue}{z \cdot \left({y}^{3} - \mathsf{log1p}\left(\mathsf{fma}\left(y, y, y\right)\right)\right)} - t \]

   9. Taylor expanded in y around 0 85.3%

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

       1. mul-1-neg 85.3%

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

   11. Simplified 85.3%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+56} \lor \neg \left(x \leq 4.8 \cdot 10^{+41}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) - z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 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 85.8%

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

3. Taylor expanded in y around 0 99.4%

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

   1. +-commutative 99.4%

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

   2. mul-1-neg 99.4%

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

   3. unsub-neg 99.4%

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

5. Simplified 99.4%

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

6. Final simplification 99.4%

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

Alternative 6: 48.0% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-153} \lor \neg \left(t \leq 3.6 \cdot 10^{-98}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.2e-153) (not (<= t 3.6e-98))) (- t) (* z (- y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.2e-153) || !(t <= 3.6e-98)) {
		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 <= (-8.2d-153)) .or. (.not. (t <= 3.6d-98))) 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 <= -8.2e-153) || !(t <= 3.6e-98)) {
		tmp = -t;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.2e-153) or not (t <= 3.6e-98):
		tmp = -t
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.2e-153) || !(t <= 3.6e-98))
		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 <= -8.2e-153) || ~((t <= 3.6e-98)))
		tmp = -t;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.2e-153], N[Not[LessEqual[t, 3.6e-98]], $MachinePrecision]], (-t), N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.2e-153 or 3.6000000000000002e-98 < t

   1. Initial program 93.6%

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

   3. Taylor expanded in t around inf 62.3%

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

      1. mul-1-neg 62.3%

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

   5. Simplified 62.3%

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

   if -8.2e-153 < t < 3.6000000000000002e-98

   1. Initial program 67.6%

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

   3. Taylor expanded in z around inf 4.6%

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

      1. sub-neg 4.6%

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

      2. mul-1-neg 4.6%

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

      3. log1p-def 36.0%

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

      4. mul-1-neg 36.0%

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

   5. Simplified 36.0%

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

   6. Taylor expanded in y around 0 35.3%

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

      1. associate-*r* 35.3%

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

      2. mul-1-neg 35.3%

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

   8. Simplified 35.3%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-153} \lor \neg \left(t \leq 3.6 \cdot 10^{-98}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.0% 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 85.8%

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

   1. flip3-- 85.7%

      \[\leadsto \left(x \cdot \log y + z \cdot \log \color{blue}{\left(\frac{{1}^{3} - {y}^{3}}{1 \cdot 1 + \left(y \cdot y + 1 \cdot y\right)}\right)}\right) - t \]

   2. log-div 85.7%

      \[\leadsto \left(x \cdot \log y + z \cdot \color{blue}{\left(\log \left({1}^{3} - {y}^{3}\right) - \log \left(1 \cdot 1 + \left(y \cdot y + 1 \cdot y\right)\right)\right)}\right) - t \]

   3. metadata-eval 85.7%

      \[\leadsto \left(x \cdot \log y + z \cdot \left(\log \left(\color{blue}{1} - {y}^{3}\right) - \log \left(1 \cdot 1 + \left(y \cdot y + 1 \cdot y\right)\right)\right)\right) - t \]

   4. pow3 85.7%

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

   5. sub-neg 85.7%

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

   6. distribute-rgt-neg-out 85.7%

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

   7. add-sqr-sqrt 0.0%

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

   8. sqrt-unprod 85.7%

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

   9. sqr-neg 85.7%

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

   10. sqrt-unprod 85.7%

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

   11. add-sqr-sqrt 85.7%

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

   12. log1p-udef 85.6%

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

   13. pow3 85.6%

       \[\leadsto \left(x \cdot \log y + z \cdot \left(\mathsf{log1p}\left(\color{blue}{{y}^{3}}\right) - \log \left(1 \cdot 1 + \left(y \cdot y + 1 \cdot y\right)\right)\right)\right) - t \]

   14. metadata-eval 85.6%

       \[\leadsto \left(x \cdot \log y + z \cdot \left(\mathsf{log1p}\left({y}^{3}\right) - \log \left(\color{blue}{1} + \left(y \cdot y + 1 \cdot y\right)\right)\right)\right) - t \]

   15. log1p-udef 99.6%

       \[\leadsto \left(x \cdot \log y + z \cdot \left(\mathsf{log1p}\left({y}^{3}\right) - \color{blue}{\mathsf{log1p}\left(y \cdot y + 1 \cdot y\right)}\right)\right) - t \]

   16. *-un-lft-identity 99.6%

       \[\leadsto \left(x \cdot \log y + z \cdot \left(\mathsf{log1p}\left({y}^{3}\right) - \mathsf{log1p}\left(y \cdot y + \color{blue}{y}\right)\right)\right) - t \]

   17. fma-def 99.6%

       \[\leadsto \left(x \cdot \log y + z \cdot \left(\mathsf{log1p}\left({y}^{3}\right) - \mathsf{log1p}\left(\color{blue}{\mathsf{fma}\left(y, y, y\right)}\right)\right)\right) - t \]

4. Applied egg-rr 99.6%

   \[\leadsto \left(x \cdot \log y + z \cdot \color{blue}{\left(\mathsf{log1p}\left({y}^{3}\right) - \mathsf{log1p}\left(\mathsf{fma}\left(y, y, y\right)\right)\right)}\right) - t \]

5. Taylor expanded in y around 0 99.6%

   \[\leadsto \left(x \cdot \log y + z \cdot \left(\color{blue}{{y}^{3}} - \mathsf{log1p}\left(\mathsf{fma}\left(y, y, y\right)\right)\right)\right) - t \]

6. Taylor expanded in x around 0 46.8%

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

   1. log1p-def 60.6%

      \[\leadsto z \cdot \left({y}^{3} - \color{blue}{\mathsf{log1p}\left(y + {y}^{2}\right)}\right) - t \]

   2. +-commutative 60.6%

      \[\leadsto z \cdot \left({y}^{3} - \mathsf{log1p}\left(\color{blue}{{y}^{2} + y}\right)\right) - t \]

   3. unpow2 60.6%

      \[\leadsto z \cdot \left({y}^{3} - \mathsf{log1p}\left(\color{blue}{y \cdot y} + y\right)\right) - t \]

   4. fma-udef 60.6%

      \[\leadsto z \cdot \left({y}^{3} - \mathsf{log1p}\left(\color{blue}{\mathsf{fma}\left(y, y, y\right)}\right)\right) - t \]

8. Simplified 60.6%

   \[\leadsto \color{blue}{z \cdot \left({y}^{3} - \mathsf{log1p}\left(\mathsf{fma}\left(y, y, y\right)\right)\right)} - t \]

9. Taylor expanded in y around 0 60.4%

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

    1. mul-1-neg 60.4%

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

11. Simplified 60.4%

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

12. Final simplification 60.4%

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

Alternative 8: 42.8% 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 85.8%

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

3. Taylor expanded in t around inf 46.3%

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

   1. mul-1-neg 46.3%

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

5. Simplified 46.3%

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

6. Final simplification 46.3%

   \[\leadsto -t \]
7. 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 2024020 
(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))