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

Percentage Accurate: 85.5% → 99.8%

Time: 18.2s

Alternatives: 10

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, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 89.2%

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

   1. +-commutative 89.2%

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

   2. fma-def 89.2%

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

   3. sub-neg 89.2%

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

   4. log1p-def 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 89.2%

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

2. Taylor expanded in y around 0 99.1%

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

   1. fma-def 99.1%

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

   2. unpow2 99.1%

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

4. Simplified 99.1%

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

5. Final simplification 99.1%

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

Alternative 3: 88.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-237} \lor \neg \left(x \leq 1.24 \cdot 10^{-141}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(y \cdot -0.5\right) - y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.6e-237) (not (<= x 1.24e-141)))
   (- (* x (log y)) t)
   (- (* z (- (* y (* y -0.5)) y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.6e-237) || !(x <= 1.24e-141)) {
		tmp = (x * log(y)) - t;
	} else {
		tmp = (z * ((y * (y * -0.5)) - y)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.6d-237)) .or. (.not. (x <= 1.24d-141))) then
        tmp = (x * log(y)) - t
    else
        tmp = (z * ((y * (y * (-0.5d0))) - y)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.6e-237) || !(x <= 1.24e-141)) {
		tmp = (x * Math.log(y)) - t;
	} else {
		tmp = (z * ((y * (y * -0.5)) - y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.6e-237) or not (x <= 1.24e-141):
		tmp = (x * math.log(y)) - t
	else:
		tmp = (z * ((y * (y * -0.5)) - y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.6e-237) || !(x <= 1.24e-141))
		tmp = Float64(Float64(x * log(y)) - t);
	else
		tmp = Float64(Float64(z * Float64(Float64(y * Float64(y * -0.5)) - y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.6e-237) || ~((x <= 1.24e-141)))
		tmp = (x * log(y)) - t;
	else
		tmp = (z * ((y * (y * -0.5)) - y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.6e-237], N[Not[LessEqual[x, 1.24e-141]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(z * N[(N[(y * N[(y * -0.5), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e-237 or 1.24e-141 < x

   1. Initial program 94.4%

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

      1. +-commutative 94.4%

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

      2. fma-def 94.4%

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

      3. sub-neg 94.4%

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

      4. log1p-def 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 92.5%

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

   if -1.6e-237 < x < 1.24e-141

   1. Initial program 68.2%

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

   2. Taylor expanded in y around 0 100.0%

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

      1. fma-def 100.0%

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

      2. unpow2 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. neg-mul-1 100.0%

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

      3. associate-*l* 100.0%

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

      4. distribute-rgt-in 100.0%

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

      5. +-commutative 100.0%

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

      6. unsub-neg 100.0%

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

      7. unpow2 100.0%

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

      8. associate-*r* 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-237} \lor \neg \left(x \leq 1.24 \cdot 10^{-141}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(y \cdot -0.5\right) - y\right) - t\\ \end{array} \]

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 89.2%

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

2. Taylor expanded in y around 0 98.6%

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

   1. log-pow 44.0%

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

   2. +-commutative 44.0%

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

   3. mul-1-neg 44.0%

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

   4. unsub-neg 44.0%

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

   5. log-pow 98.6%

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

4. Simplified 98.6%

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

5. Final simplification 98.6%

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

Alternative 5: 77.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+60} \lor \neg \left(x \leq 1.02 \cdot 10^{+83}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right) - \left(t + z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.9e+60) (not (<= x 1.02e+83)))
   (* x (log y))
   (- (* -0.5 (* z (* y y))) (+ t (* z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.9e+60) || !(x <= 1.02e+83)) {
		tmp = x * log(y);
	} else {
		tmp = (-0.5 * (z * (y * y))) - (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 <= (-1.9d+60)) .or. (.not. (x <= 1.02d+83))) then
        tmp = x * log(y)
    else
        tmp = ((-0.5d0) * (z * (y * y))) - (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 <= -1.9e+60) || !(x <= 1.02e+83)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (-0.5 * (z * (y * y))) - (t + (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.9e+60) or not (x <= 1.02e+83):
		tmp = x * math.log(y)
	else:
		tmp = (-0.5 * (z * (y * y))) - (t + (z * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.9e+60) || !(x <= 1.02e+83))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(-0.5 * Float64(z * Float64(y * y))) - Float64(t + Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.9e+60) || ~((x <= 1.02e+83)))
		tmp = x * log(y);
	else
		tmp = (-0.5 * (z * (y * y))) - (t + (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.9e+60], N[Not[LessEqual[x, 1.02e+83]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(-0.5 * N[(z * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.90000000000000005e60 or 1.0200000000000001e83 < x

   1. Initial program 97.1%

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

      1. associate--l+ 97.1%

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

      2. fma-def 97.1%

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

      3. fma-neg 97.1%

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

      4. sub-neg 97.1%

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

      5. log1p-def 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 98.9%

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

      1. mul-1-neg 98.9%

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

      2. mul-1-neg 98.9%

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

      3. unsub-neg 98.9%

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

   6. Simplified 98.9%

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

   7. Taylor expanded in x around inf 77.8%

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

   if -1.90000000000000005e60 < x < 1.0200000000000001e83

   1. Initial program 84.1%

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

   2. Taylor expanded in x around 0 62.9%

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

      1. sub-neg 62.9%

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

      2. mul-1-neg 62.9%

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

      3. log1p-def 78.8%

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

      4. mul-1-neg 78.8%

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

   4. Simplified 78.8%

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

   5. Taylor expanded in y around 0 78.0%

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

      1. neg-mul-1 78.0%

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

      2. associate-+r+ 78.0%

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

      3. +-commutative 78.0%

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

      4. sub-neg 78.0%

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

      5. associate-*r* 78.0%

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

      6. neg-mul-1 78.0%

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

      7. *-commutative 78.0%

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

      8. *-commutative 78.0%

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

      9. unpow2 78.0%

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

   7. Simplified 78.0%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+60} \lor \neg \left(x \leq 1.02 \cdot 10^{+83}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(z \cdot \left(y \cdot y\right)\right) - \left(t + z \cdot y\right)\\ \end{array} \]

Alternative 6: 56.9% accurate, 16.2× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.2%

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

2. Taylor expanded in x around 0 46.1%

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

   1. sub-neg 46.1%

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

   2. mul-1-neg 46.1%

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

   3. log1p-def 56.6%

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

   4. mul-1-neg 56.6%

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

4. Simplified 56.6%

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

5. Taylor expanded in y around 0 55.9%

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

   1. neg-mul-1 55.9%

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

   2. associate-+r+ 55.9%

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

   3. +-commutative 55.9%

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

   4. sub-neg 55.9%

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

   5. associate-*r* 55.9%

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

   6. neg-mul-1 55.9%

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

   7. *-commutative 55.9%

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

   8. *-commutative 55.9%

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

   9. unpow2 55.9%

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

7. Simplified 55.9%

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

8. Final simplification 55.9%

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

Alternative 7: 56.9% accurate, 19.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.2%

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

2. Taylor expanded in y around 0 99.1%

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

   1. fma-def 99.1%

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

   2. unpow2 99.1%

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

4. Simplified 99.1%

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

5. Taylor expanded in x around 0 55.9%

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

   1. associate-*r* 55.9%

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

   2. neg-mul-1 55.9%

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

   3. associate-*l* 55.9%

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

   4. distribute-rgt-in 55.9%

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

   5. +-commutative 55.9%

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

   6. unsub-neg 55.9%

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

   7. unpow2 55.9%

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

   8. associate-*r* 55.9%

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

7. Simplified 55.9%

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

8. Final simplification 55.9%

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

Alternative 8: 47.3% accurate, 26.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -30:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-69}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -30.0) (- t) (if (<= t 1.35e-69) (* z (- y)) (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -30.0) {
		tmp = -t;
	} else if (t <= 1.35e-69) {
		tmp = z * -y;
	} else {
		tmp = -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-30.0d0)) then
        tmp = -t
    else if (t <= 1.35d-69) then
        tmp = z * -y
    else
        tmp = -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -30.0) {
		tmp = -t;
	} else if (t <= 1.35e-69) {
		tmp = z * -y;
	} else {
		tmp = -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -30.0:
		tmp = -t
	elif t <= 1.35e-69:
		tmp = z * -y
	else:
		tmp = -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -30.0)
		tmp = Float64(-t);
	elseif (t <= 1.35e-69)
		tmp = Float64(z * Float64(-y));
	else
		tmp = Float64(-t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -30.0)
		tmp = -t;
	elseif (t <= 1.35e-69)
		tmp = z * -y;
	else
		tmp = -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -30.0], (-t), If[LessEqual[t, 1.35e-69], N[(z * (-y)), $MachinePrecision], (-t)]]

Derivation

1. Split input into 2 regimes

2. if t < -30 or 1.3499999999999999e-69 < t

   1. Initial program 95.9%

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

      1. +-commutative 95.9%

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

      2. fma-def 95.9%

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

      3. sub-neg 95.9%

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

      4. log1p-def 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around inf 71.9%

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

      1. mul-1-neg 71.9%

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

   6. Simplified 71.9%

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

   if -30 < t < 1.3499999999999999e-69

   1. Initial program 80.6%

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

      1. associate--l+ 80.6%

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

      2. fma-def 80.6%

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

      3. fma-neg 80.6%

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

      4. sub-neg 80.6%

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

      5. log1p-def 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 98.8%

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

      1. mul-1-neg 98.8%

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

      2. mul-1-neg 98.8%

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

      3. unsub-neg 98.8%

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

   6. Simplified 98.8%

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

   7. Taylor expanded in y around inf 22.2%

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

      1. associate-*r* 22.2%

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

      2. neg-mul-1 22.2%

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

      3. *-commutative 22.2%

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

   9. Simplified 22.2%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -30:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-69}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;-t\\ \end{array} \]

Alternative 9: 56.5% accurate, 35.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.2%

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

2. Taylor expanded in y around 0 98.6%

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

   1. log-pow 44.0%

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

   2. +-commutative 44.0%

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

   3. mul-1-neg 44.0%

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

   4. unsub-neg 44.0%

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

   5. log-pow 98.6%

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

4. Simplified 98.6%

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

5. Taylor expanded in x around 0 55.4%

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

   1. mul-1-neg 55.4%

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

   2. *-commutative 55.4%

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

   3. distribute-rgt-neg-in 55.4%

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

7. Simplified 55.4%

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

8. Final simplification 55.4%

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

Alternative 10: 42.4% 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 89.2%

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

   1. +-commutative 89.2%

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

   2. fma-def 89.2%

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

   3. sub-neg 89.2%

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

   4. log1p-def 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in t around inf 44.5%

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

   1. mul-1-neg 44.5%

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

6. Simplified 44.5%

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

7. Final simplification 44.5%

   \[\leadsto -t \]

Developer target: 99.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \left(-z\right) \cdot \left(\left(0.5 \cdot \left(y \cdot y\right) + y\right) + \frac{0.3333333333333333}{1 \cdot \left(1 \cdot 1\right)} \cdot \left(y \cdot \left(y \cdot y\right)\right)\right) - \left(t - x \cdot \log y\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (-
  (*
   (- z)
   (+
    (+ (* 0.5 (* y y)) y)
    (* (/ 0.3333333333333333 (* 1.0 (* 1.0 1.0))) (* y (* y y)))))
  (- t (* x (log y)))))

C

double code(double x, double y, double z, double t) {
	return (-z * (((0.5 * (y * y)) + y) + ((0.3333333333333333 / (1.0 * (1.0 * 1.0))) * (y * (y * y))))) - (t - (x * log(y)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (-z * (((0.5d0 * (y * y)) + y) + ((0.3333333333333333d0 / (1.0d0 * (1.0d0 * 1.0d0))) * (y * (y * y))))) - (t - (x * log(y)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (-z * (((0.5 * (y * y)) + y) + ((0.3333333333333333 / (1.0 * (1.0 * 1.0))) * (y * (y * y))))) - (t - (x * Math.log(y)));
}

Python

def code(x, y, z, t):
	return (-z * (((0.5 * (y * y)) + y) + ((0.3333333333333333 / (1.0 * (1.0 * 1.0))) * (y * (y * y))))) - (t - (x * math.log(y)))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(-z) * Float64(Float64(Float64(0.5 * Float64(y * y)) + y) + Float64(Float64(0.3333333333333333 / Float64(1.0 * Float64(1.0 * 1.0))) * Float64(y * Float64(y * y))))) - Float64(t - Float64(x * log(y))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (-z * (((0.5 * (y * y)) + y) + ((0.3333333333333333 / (1.0 * (1.0 * 1.0))) * (y * (y * y))))) - (t - (x * log(y)));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[((-z) * N[(N[(N[(0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision] + N[(N[(0.3333333333333333 / N[(1.0 * N[(1.0 * 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t - N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023279 
(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))