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

Percentage Accurate: 85.1% → 99.6%

Time: 13.8s

Alternatives: 9

Speedup: 1.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% 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: 99.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \log y + \left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.25, y, -0.3333333333333333\right), y, -0.5\right), y, -1\right) \cdot z\right) \cdot y\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (-
  (+
   (* x (log y))
   (* (* (fma (fma (fma -0.25 y -0.3333333333333333) y -0.5) y -1.0) z) y))
  t))

C

double code(double x, double y, double z, double t) {
	return ((x * log(y)) + ((fma(fma(fma(-0.25, y, -0.3333333333333333), y, -0.5), y, -1.0) * z) * y)) - t;
}

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x * log(y)) + Float64(Float64(fma(fma(fma(-0.25, y, -0.3333333333333333), y, -0.5), y, -1.0) * z) * y)) - t)
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(-0.25 * y + -0.3333333333333333), $MachinePrecision] * y + -0.5), $MachinePrecision] * y + -1.0), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 86.0%

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

3. Taylor expanded in y around 0

   \[\leadsto \left(x \cdot \log y + \color{blue}{y \cdot \left(-1 \cdot z + y \cdot \left(\frac{-1}{2} \cdot z + y \cdot \left(\frac{-1}{3} \cdot z + \frac{-1}{4} \cdot \left(y \cdot z\right)\right)\right)\right)}\right) - t \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(x \cdot \log y + \color{blue}{\left(-1 \cdot z + y \cdot \left(\frac{-1}{2} \cdot z + y \cdot \left(\frac{-1}{3} \cdot z + \frac{-1}{4} \cdot \left(y \cdot z\right)\right)\right)\right) \cdot y}\right) - t \]

   2. lower-*.f64 N/A

      \[\leadsto \left(x \cdot \log y + \color{blue}{\left(-1 \cdot z + y \cdot \left(\frac{-1}{2} \cdot z + y \cdot \left(\frac{-1}{3} \cdot z + \frac{-1}{4} \cdot \left(y \cdot z\right)\right)\right)\right) \cdot y}\right) - t \]

5. Applied rewrites 99.8%

   \[\leadsto \left(x \cdot \log y + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.25, y, -0.3333333333333333\right) \cdot z, y, -0.5 \cdot z\right), y, -z\right) \cdot y}\right) - t \]

6. Taylor expanded in z around 0

   \[\leadsto \left(x \cdot \log y + \left(z \cdot \left(y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right) - 1\right)\right) \cdot y\right) - t \]
7. Step-by-step derivation

8. Applied rewrites 99.8%

   \[\leadsto \left(x \cdot \log y + \left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.25, y, -0.3333333333333333\right), y, -0.5\right), y, -1\right) \cdot z\right) \cdot y\right) - t \]
9. Add Preprocessing

Alternative 2: 99.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\log y, x, \left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.25, y, -0.3333333333333333\right), y, -0.5\right), y, -1\right) \cdot z\right) \cdot y - t\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (fma
  (log y)
  x
  (-
   (* (* (fma (fma (fma -0.25 y -0.3333333333333333) y -0.5) y -1.0) z) y)
   t)))

C

double code(double x, double y, double z, double t) {
	return fma(log(y), x, (((fma(fma(fma(-0.25, y, -0.3333333333333333), y, -0.5), y, -1.0) * z) * y) - t));
}

Julia

function code(x, y, z, t)
	return fma(log(y), x, Float64(Float64(Float64(fma(fma(fma(-0.25, y, -0.3333333333333333), y, -0.5), y, -1.0) * z) * y) - t))
end

Wolfram

code[x_, y_, z_, t_] := N[(N[Log[y], $MachinePrecision] * x + N[(N[(N[(N[(N[(N[(-0.25 * y + -0.3333333333333333), $MachinePrecision] * y + -0.5), $MachinePrecision] * y + -1.0), $MachinePrecision] * z), $MachinePrecision] * y), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.0%

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

3. Taylor expanded in y around 0

   \[\leadsto \left(x \cdot \log y + \color{blue}{y \cdot \left(-1 \cdot z + y \cdot \left(\frac{-1}{2} \cdot z + y \cdot \left(\frac{-1}{3} \cdot z + \frac{-1}{4} \cdot \left(y \cdot z\right)\right)\right)\right)}\right) - t \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(x \cdot \log y + \color{blue}{\left(-1 \cdot z + y \cdot \left(\frac{-1}{2} \cdot z + y \cdot \left(\frac{-1}{3} \cdot z + \frac{-1}{4} \cdot \left(y \cdot z\right)\right)\right)\right) \cdot y}\right) - t \]

   2. lower-*.f64 N/A

      \[\leadsto \left(x \cdot \log y + \color{blue}{\left(-1 \cdot z + y \cdot \left(\frac{-1}{2} \cdot z + y \cdot \left(\frac{-1}{3} \cdot z + \frac{-1}{4} \cdot \left(y \cdot z\right)\right)\right)\right) \cdot y}\right) - t \]

5. Applied rewrites 99.8%

   \[\leadsto \left(x \cdot \log y + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.25, y, -0.3333333333333333\right) \cdot z, y, -0.5 \cdot z\right), y, -z\right) \cdot y}\right) - t \]

6. Taylor expanded in z around 0

   \[\leadsto \left(x \cdot \log y + \left(z \cdot \left(y \cdot \left(y \cdot \left(\frac{-1}{4} \cdot y - \frac{1}{3}\right) - \frac{1}{2}\right) - 1\right)\right) \cdot y\right) - t \]
7. Step-by-step derivation

8. Applied rewrites 99.8%

   \[\leadsto \left(x \cdot \log y + \left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.25, y, -0.3333333333333333\right), y, -0.5\right), y, -1\right) \cdot z\right) \cdot y\right) - t \]
9. Step-by-step derivation

   1. lift--.f64 N/A

      \[\leadsto \color{blue}{\left(x \cdot \log y + \left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{4}, y, \frac{-1}{3}\right), y, \frac{-1}{2}\right), y, -1\right) \cdot z\right) \cdot y\right) - t} \]

   2. lift-+.f64 N/A

      \[\leadsto \color{blue}{\left(x \cdot \log y + \left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{4}, y, \frac{-1}{3}\right), y, \frac{-1}{2}\right), y, -1\right) \cdot z\right) \cdot y\right)} - t \]

   3. associate--l+ N/A

      \[\leadsto \color{blue}{x \cdot \log y + \left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{4}, y, \frac{-1}{3}\right), y, \frac{-1}{2}\right), y, -1\right) \cdot z\right) \cdot y - t\right)} \]

   4. lift-*.f64 N/A

      \[\leadsto \color{blue}{x \cdot \log y} + \left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{4}, y, \frac{-1}{3}\right), y, \frac{-1}{2}\right), y, -1\right) \cdot z\right) \cdot y - t\right) \]

   5. *-commutative N/A

      \[\leadsto \color{blue}{\log y \cdot x} + \left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{4}, y, \frac{-1}{3}\right), y, \frac{-1}{2}\right), y, -1\right) \cdot z\right) \cdot y - t\right) \]

   6. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{-1}{4}, y, \frac{-1}{3}\right), y, \frac{-1}{2}\right), y, -1\right) \cdot z\right) \cdot y - t\right)} \]

10. Applied rewrites 99.8%

    \[\leadsto \color{blue}{\mathsf{fma}\left(\log y, x, \left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.25, y, -0.3333333333333333\right), y, -0.5\right), y, -1\right) \cdot z\right) \cdot y - t\right)} \]
11. Add Preprocessing

Alternative 3: 89.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{-122} \lor \neg \left(t \leq 3.2 \cdot 10^{-112}\right):\\ \;\;\;\;\log y \cdot x - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \left(-z\right) \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9.4e-122) (not (<= t 3.2e-112)))
   (- (* (log y) x) t)
   (fma (log y) x (* (- z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9.4e-122) || !(t <= 3.2e-112)) {
		tmp = (log(y) * x) - t;
	} else {
		tmp = fma(log(y), x, (-z * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -9.4e-122) || !(t <= 3.2e-112))
		tmp = Float64(Float64(log(y) * x) - t);
	else
		tmp = fma(log(y), x, Float64(Float64(-z) * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -9.4e-122], N[Not[LessEqual[t, 3.2e-112]], $MachinePrecision]], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - t), $MachinePrecision], N[(N[Log[y], $MachinePrecision] * x + N[((-z) * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.3999999999999999e-122 or 3.19999999999999993e-112 < t

   1. Initial program 92.1%

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

   3. Taylor expanded in y around 0

      \[\leadsto \left(x \cdot \log y + \color{blue}{y \cdot \left(-1 \cdot z + y \cdot \left(\frac{-1}{2} \cdot z + y \cdot \left(\frac{-1}{3} \cdot z + \frac{-1}{4} \cdot \left(y \cdot z\right)\right)\right)\right)}\right) - t \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(x \cdot \log y + \color{blue}{\left(-1 \cdot z + y \cdot \left(\frac{-1}{2} \cdot z + y \cdot \left(\frac{-1}{3} \cdot z + \frac{-1}{4} \cdot \left(y \cdot z\right)\right)\right)\right) \cdot y}\right) - t \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \log y + \color{blue}{\left(-1 \cdot z + y \cdot \left(\frac{-1}{2} \cdot z + y \cdot \left(\frac{-1}{3} \cdot z + \frac{-1}{4} \cdot \left(y \cdot z\right)\right)\right)\right) \cdot y}\right) - t \]

   5. Applied rewrites 99.9%

      \[\leadsto \left(x \cdot \log y + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.25, y, -0.3333333333333333\right) \cdot z, y, -0.5 \cdot z\right), y, -z\right) \cdot y}\right) - t \]

   6. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-log.f64 90.6

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

   8. Applied rewrites 90.6%

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

   if -9.3999999999999999e-122 < t < 3.19999999999999993e-112

   1. Initial program 74.2%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. remove-double-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. neg-mul-1 N/A

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

      8. mul-1-neg N/A

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

      9. log-rec N/A

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

      10. associate--l- N/A

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

      11. lower--.f64 N/A

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

   5. Applied rewrites 99.1%

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

   6. Taylor expanded in t around 0

      \[\leadsto x \cdot \log y - \color{blue}{y \cdot z} \]
   7. Step-by-step derivation

   8. Applied rewrites 94.7%

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

   10. Applied rewrites 94.7%

       \[\leadsto \mathsf{fma}\left(\log y, x, \left(-z\right) \cdot y\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{-122} \lor \neg \left(t \leq 3.2 \cdot 10^{-112}\right):\\ \;\;\;\;\log y \cdot x - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\log y, x, \left(-z\right) \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-80} \lor \neg \left(x \leq 2.7 \cdot 10^{-92}\right):\\ \;\;\;\;\log y \cdot x - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{log1p}\left(-y\right) \cdot z - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.1e-80) (not (<= x 2.7e-92)))
   (- (* (log y) x) t)
   (- (* (log1p (- y)) z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.1e-80) || !(x <= 2.7e-92)) {
		tmp = (log(y) * x) - t;
	} else {
		tmp = (log1p(-y) * z) - t;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.1e-80) || !(x <= 2.7e-92)) {
		tmp = (Math.log(y) * x) - t;
	} else {
		tmp = (Math.log1p(-y) * z) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.1e-80) or not (x <= 2.7e-92):
		tmp = (math.log(y) * x) - t
	else:
		tmp = (math.log1p(-y) * z) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.1e-80) || !(x <= 2.7e-92))
		tmp = Float64(Float64(log(y) * x) - t);
	else
		tmp = Float64(Float64(log1p(Float64(-y)) * z) - t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.1e-80], N[Not[LessEqual[x, 2.7e-92]], $MachinePrecision]], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[Log[1 + (-y)], $MachinePrecision] * z), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.10000000000000016e-80 or 2.69999999999999995e-92 < x

   1. Initial program 90.2%

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

   3. Taylor expanded in y around 0

      \[\leadsto \left(x \cdot \log y + \color{blue}{y \cdot \left(-1 \cdot z + y \cdot \left(\frac{-1}{2} \cdot z + y \cdot \left(\frac{-1}{3} \cdot z + \frac{-1}{4} \cdot \left(y \cdot z\right)\right)\right)\right)}\right) - t \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(x \cdot \log y + \color{blue}{\left(-1 \cdot z + y \cdot \left(\frac{-1}{2} \cdot z + y \cdot \left(\frac{-1}{3} \cdot z + \frac{-1}{4} \cdot \left(y \cdot z\right)\right)\right)\right) \cdot y}\right) - t \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \log y + \color{blue}{\left(-1 \cdot z + y \cdot \left(\frac{-1}{2} \cdot z + y \cdot \left(\frac{-1}{3} \cdot z + \frac{-1}{4} \cdot \left(y \cdot z\right)\right)\right)\right) \cdot y}\right) - t \]

   5. Applied rewrites 99.8%

      \[\leadsto \left(x \cdot \log y + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.25, y, -0.3333333333333333\right) \cdot z, y, -0.5 \cdot z\right), y, -z\right) \cdot y}\right) - t \]

   6. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-log.f64 89.4

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

   8. Applied rewrites 89.4%

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

   if -3.10000000000000016e-80 < x < 2.69999999999999995e-92

   1. Initial program 77.4%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. lower-log1p.f64 N/A

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

      5. lower-neg.f64 92.3

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

   5. Applied rewrites 92.3%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(-y\right) \cdot z} - t \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-80} \lor \neg \left(x \leq 2.7 \cdot 10^{-92}\right):\\ \;\;\;\;\log y \cdot x - t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{log1p}\left(-y\right) \cdot z - t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-80} \lor \neg \left(x \leq 2.7 \cdot 10^{-92}\right):\\ \;\;\;\;\log y \cdot x - t\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(z, y, t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.1e-80) (not (<= x 2.7e-92)))
   (- (* (log y) x) t)
   (- (fma z y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.1e-80) || !(x <= 2.7e-92)) {
		tmp = (log(y) * x) - t;
	} else {
		tmp = -fma(z, y, t);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.1e-80) || !(x <= 2.7e-92))
		tmp = Float64(Float64(log(y) * x) - t);
	else
		tmp = Float64(-fma(z, y, t));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.1e-80], N[Not[LessEqual[x, 2.7e-92]], $MachinePrecision]], N[(N[(N[Log[y], $MachinePrecision] * x), $MachinePrecision] - t), $MachinePrecision], (-N[(z * y + t), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if x < -3.10000000000000016e-80 or 2.69999999999999995e-92 < x

   1. Initial program 90.2%

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

   3. Taylor expanded in y around 0

      \[\leadsto \left(x \cdot \log y + \color{blue}{y \cdot \left(-1 \cdot z + y \cdot \left(\frac{-1}{2} \cdot z + y \cdot \left(\frac{-1}{3} \cdot z + \frac{-1}{4} \cdot \left(y \cdot z\right)\right)\right)\right)}\right) - t \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(x \cdot \log y + \color{blue}{\left(-1 \cdot z + y \cdot \left(\frac{-1}{2} \cdot z + y \cdot \left(\frac{-1}{3} \cdot z + \frac{-1}{4} \cdot \left(y \cdot z\right)\right)\right)\right) \cdot y}\right) - t \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x \cdot \log y + \color{blue}{\left(-1 \cdot z + y \cdot \left(\frac{-1}{2} \cdot z + y \cdot \left(\frac{-1}{3} \cdot z + \frac{-1}{4} \cdot \left(y \cdot z\right)\right)\right)\right) \cdot y}\right) - t \]

   5. Applied rewrites 99.8%

      \[\leadsto \left(x \cdot \log y + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(-0.25, y, -0.3333333333333333\right) \cdot z, y, -0.5 \cdot z\right), y, -z\right) \cdot y}\right) - t \]

   6. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-log.f64 89.4

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

   8. Applied rewrites 89.4%

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

   if -3.10000000000000016e-80 < x < 2.69999999999999995e-92

   1. Initial program 77.4%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. remove-double-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. neg-mul-1 N/A

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

      8. mul-1-neg N/A

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

      9. log-rec N/A

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

      10. associate--l- N/A

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

      11. lower--.f64 N/A

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

   5. Applied rewrites 98.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 90.9%

      \[\leadsto -\mathsf{fma}\left(z, y, t\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-80} \lor \neg \left(x \leq 2.7 \cdot 10^{-92}\right):\\ \;\;\;\;\log y \cdot x - t\\ \mathbf{else}:\\ \;\;\;\;-\mathsf{fma}\left(z, y, t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.1% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 86.0%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. mul-1-neg N/A

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

   3. unsub-neg N/A

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

   4. remove-double-neg N/A

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

   5. mul-1-neg N/A

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

   6. distribute-rgt-neg-in N/A

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

   7. neg-mul-1 N/A

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

   8. mul-1-neg N/A

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

   9. log-rec N/A

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

   10. associate--l- N/A

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

   11. lower--.f64 N/A

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

5. Applied rewrites 99.0%

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

Alternative 7: 48.5% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-85} \lor \neg \left(t \leq 6.5 \cdot 10^{-114}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;-z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.4e-85) (not (<= t 6.5e-114))) (- t) (- (* z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.4e-85) || !(t <= 6.5e-114)) {
		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 <= (-3.4d-85)) .or. (.not. (t <= 6.5d-114))) 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 <= -3.4e-85) || !(t <= 6.5e-114)) {
		tmp = -t;
	} else {
		tmp = -(z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.4e-85) or not (t <= 6.5e-114):
		tmp = -t
	else:
		tmp = -(z * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.4e-85) || !(t <= 6.5e-114))
		tmp = Float64(-t);
	else
		tmp = Float64(-Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.4e-85) || ~((t <= 6.5e-114)))
		tmp = -t;
	else
		tmp = -(z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.4e-85], N[Not[LessEqual[t, 6.5e-114]], $MachinePrecision]], (-t), (-N[(z * y), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if t < -3.4e-85 or 6.4999999999999998e-114 < t

   1. Initial program 92.5%

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

   3. Taylor expanded in t around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(t\right)} \]

      2. lower-neg.f64 62.4

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

   5. Applied rewrites 62.4%

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

   if -3.4e-85 < t < 6.4999999999999998e-114

   1. Initial program 74.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. mul-1-neg N/A

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

      3. unsub-neg N/A

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

      4. remove-double-neg N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. neg-mul-1 N/A

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

      8. mul-1-neg N/A

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

      9. log-rec N/A

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

      10. associate--l- N/A

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

      11. lower--.f64 N/A

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

   5. Applied rewrites 99.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 34.0%

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

   9. Taylor expanded in y around inf

      \[\leadsto -y \cdot z \]
   10. Step-by-step derivation

   11. Applied rewrites 29.4%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-85} \lor \neg \left(t \leq 6.5 \cdot 10^{-114}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;-z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.3% accurate, 24.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 86.0%

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

3. Taylor expanded in y around 0

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

   1. +-commutative N/A

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

   2. mul-1-neg N/A

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

   3. unsub-neg N/A

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

   4. remove-double-neg N/A

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

   5. mul-1-neg N/A

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

   6. distribute-rgt-neg-in N/A

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

   7. neg-mul-1 N/A

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

   8. mul-1-neg N/A

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

   9. log-rec N/A

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

   10. associate--l- N/A

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

   11. lower--.f64 N/A

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

5. Applied rewrites 99.0%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 57.6%

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

Alternative 9: 42.7% accurate, 73.3× 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 86.0%

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

3. Taylor expanded in t around inf

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

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(t\right)} \]

   2. lower-neg.f64 43.1

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

5. Applied rewrites 43.1%

   \[\leadsto \color{blue}{-t} \]
6. Add Preprocessing

Developer Target 1: 99.6% accurate, 1.3× 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 2024318 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, B"
  :precision binary64

  :alt
  (! :herbie-platform default (- (* (- z) (+ (+ (* 1/2 (* y y)) y) (* (/ 1/3 (* 1 (* 1 1))) (* y (* y y))))) (- t (* x (log y)))))

  (- (+ (* x (log y)) (* z (log (- 1.0 y)))) t))