Statistics.Distribution.Beta:$cdensity from math-functions-0.1.5.2

Percentage Accurate: 88.9% → 99.8%

Time: 16.1s

Alternatives: 19

Speedup: 1.9×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (((x - 1.0) * log(y)) + ((z - 1.0) * 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 - 1.0d0) * log(y)) + ((z - 1.0d0) * log((1.0d0 - y)))) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (((x - 1.0) * log(y)) + ((z - 1.0) * 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 - 1.0d0) * log(y)) + ((z - 1.0d0) * log((1.0d0 - y)))) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \left(-1 + x\right) \cdot \log y\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (fma (+ z -1.0) (log1p (- y)) (* (+ -1.0 x) (log y))) t))

C

double code(double x, double y, double z, double t) {
	return fma((z + -1.0), log1p(-y), ((-1.0 + x) * log(y))) - t;
}

Julia

function code(x, y, z, t)
	return Float64(fma(Float64(z + -1.0), log1p(Float64(-y)), Float64(Float64(-1.0 + x) * log(y))) - t)
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(z + -1.0), $MachinePrecision] * N[Log[1 + (-y)], $MachinePrecision] + N[(N[(-1.0 + x), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 89.9%

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

   1. +-commutative 89.9%

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

   2. fma-define 89.9%

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

   3. sub-neg 89.9%

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

   4. metadata-eval 89.9%

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

   5. sub-neg 89.9%

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

   6. log1p-define 99.8%

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

   7. sub-neg 99.8%

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

   8. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(z + -1, \mathsf{log1p}\left(-y\right), \left(-1 + x\right) \cdot \log y\right) - t \]
6. Add Preprocessing

Alternative 2: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(-1 + x, \log y, \left(z + -1\right) \cdot \mathsf{log1p}\left(-y\right)\right) - t \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (fma (+ -1.0 x) (log y) (* (+ z -1.0) (log1p (- y)))) t))

C

double code(double x, double y, double z, double t) {
	return fma((-1.0 + x), log(y), ((z + -1.0) * log1p(-y))) - t;
}

Julia

function code(x, y, z, t)
	return Float64(fma(Float64(-1.0 + x), log(y), Float64(Float64(z + -1.0) * log1p(Float64(-y)))) - t)
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(-1.0 + x), $MachinePrecision] * N[Log[y], $MachinePrecision] + N[(N[(z + -1.0), $MachinePrecision] * N[Log[1 + (-y)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]

Derivation

1. Initial program 89.9%

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

   1. fma-define 89.9%

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

   2. sub-neg 89.9%

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

   3. metadata-eval 89.9%

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

   4. sub-neg 89.9%

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

   5. metadata-eval 89.9%

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

   6. sub-neg 89.9%

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

   7. log1p-define 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(-1 + x, \log y, \left(z + -1\right) \cdot \mathsf{log1p}\left(-y\right)\right) - t \]
6. Add Preprocessing

Alternative 3: 99.6% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((((-1.0d0) + x) * log(y)) + ((z + (-1.0d0)) * (y * ((-1.0d0) + (y * ((y * ((y * (-0.25d0)) - 0.3333333333333333d0)) - 0.5d0)))))) - t
end function

Java

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

Python

def code(x, y, z, t):
	return (((-1.0 + x) * math.log(y)) + ((z + -1.0) * (y * (-1.0 + (y * ((y * ((y * -0.25) - 0.3333333333333333)) - 0.5)))))) - t

Julia

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

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((-1.0 + x) * log(y)) + ((z + -1.0) * (y * (-1.0 + (y * ((y * ((y * -0.25) - 0.3333333333333333)) - 0.5)))))) - t;
end

Wolfram

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

Derivation

1. Initial program 89.9%

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

3. Taylor expanded in y around 0 99.1%

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

4. Final simplification 99.1%

   \[\leadsto \left(\left(-1 + x\right) \cdot \log y + \left(z + -1\right) \cdot \left(y \cdot \left(-1 + y \cdot \left(y \cdot \left(y \cdot -0.25 - 0.3333333333333333\right) - 0.5\right)\right)\right)\right) - t \]
5. Add Preprocessing

Alternative 4: 94.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-1 + x \leq -1.000001 \lor \neg \left(-1 + x \leq 2 \cdot 10^{+32}\right):\\ \;\;\;\;\left(-1 + x\right) \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(1 - z\right) - \log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (+ -1.0 x) -1.000001) (not (<= (+ -1.0 x) 2e+32)))
   (- (* (+ -1.0 x) (log y)) t)
   (- (- (* y (- 1.0 z)) (log y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((-1.0 + x) <= -1.000001) || !((-1.0 + x) <= 2e+32)) {
		tmp = ((-1.0 + x) * log(y)) - t;
	} else {
		tmp = ((y * (1.0 - z)) - 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 ((((-1.0d0) + x) <= (-1.000001d0)) .or. (.not. (((-1.0d0) + x) <= 2d+32))) then
        tmp = (((-1.0d0) + x) * log(y)) - t
    else
        tmp = ((y * (1.0d0 - z)) - 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 (((-1.0 + x) <= -1.000001) || !((-1.0 + x) <= 2e+32)) {
		tmp = ((-1.0 + x) * Math.log(y)) - t;
	} else {
		tmp = ((y * (1.0 - z)) - Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((-1.0 + x) <= -1.000001) or not ((-1.0 + x) <= 2e+32):
		tmp = ((-1.0 + x) * math.log(y)) - t
	else:
		tmp = ((y * (1.0 - z)) - math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(-1.0 + x) <= -1.000001) || !(Float64(-1.0 + x) <= 2e+32))
		tmp = Float64(Float64(Float64(-1.0 + x) * log(y)) - t);
	else
		tmp = Float64(Float64(Float64(y * Float64(1.0 - z)) - log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((-1.0 + x) <= -1.000001) || ~(((-1.0 + x) <= 2e+32)))
		tmp = ((-1.0 + x) * log(y)) - t;
	else
		tmp = ((y * (1.0 - z)) - log(y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(-1.0 + x), $MachinePrecision], -1.000001], N[Not[LessEqual[N[(-1.0 + x), $MachinePrecision], 2e+32]], $MachinePrecision]], N[(N[(N[(-1.0 + x), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 x #s(literal 1 binary64)) < -1.00000099999999992 or 2.00000000000000011e32 < (-.f64 x #s(literal 1 binary64))

   1. Initial program 93.7%

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

   3. Taylor expanded in y around 0 93.6%

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

   if -1.00000099999999992 < (-.f64 x #s(literal 1 binary64)) < 2.00000000000000011e32

   1. Initial program 85.9%

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

   3. Taylor expanded in y around 0 98.1%

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

      1. associate--l+ 98.1%

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

      2. associate-*r* 98.1%

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

      3. mul-1-neg 98.1%

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

      4. fma-neg 98.1%

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

      5. sub-neg 98.1%

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

      6. metadata-eval 98.1%

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

      7. fma-define 98.1%

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

      8. *-commutative 98.1%

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

      9. fma-define 98.1%

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

      10. sub-neg 98.1%

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

      11. metadata-eval 98.1%

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

      12. +-commutative 98.1%

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

      13. sub-neg 98.1%

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

      14. *-commutative 98.1%

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

      15. +-commutative 98.1%

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

   5. Simplified 98.1%

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

   6. Taylor expanded in x around 0 97.2%

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

      1. +-commutative 97.2%

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

      2. mul-1-neg 97.2%

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

      3. unsub-neg 97.2%

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

      4. mul-1-neg 97.2%

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

      5. sub-neg 97.2%

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

      6. metadata-eval 97.2%

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

      7. distribute-rgt-neg-in 97.2%

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

      8. +-commutative 97.2%

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

      9. distribute-neg-in 97.2%

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

      10. metadata-eval 97.2%

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

   8. Simplified 97.2%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-1 + x \leq -1.000001 \lor \neg \left(-1 + x \leq 2 \cdot 10^{+32}\right):\\ \;\;\;\;\left(-1 + x\right) \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(1 - z\right) - \log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.6% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.9%

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

3. Taylor expanded in y around 0 99.0%

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

4. Final simplification 99.0%

   \[\leadsto \left(\left(-1 + x\right) \cdot \log y + \left(z + -1\right) \cdot \left(y \cdot \left(-1 + y \cdot \left(y \cdot -0.3333333333333333 - 0.5\right)\right)\right)\right) - t \]
5. Add Preprocessing

Alternative 6: 99.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.9%

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

3. Taylor expanded in y around 0 99.0%

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

4. Final simplification 99.0%

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

Alternative 7: 86.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\left(y - \log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.1) (not (<= x 1.0)))
   (- (* x (log y)) t)
   (- (- y (log y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.1) || !(x <= 1.0)) {
		tmp = (x * log(y)) - t;
	} else {
		tmp = (y - 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 ((x <= (-1.1d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = (x * log(y)) - t
    else
        tmp = (y - 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 ((x <= -1.1) || !(x <= 1.0)) {
		tmp = (x * Math.log(y)) - t;
	} else {
		tmp = (y - Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.1) or not (x <= 1.0):
		tmp = (x * math.log(y)) - t
	else:
		tmp = (y - math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.1) || !(x <= 1.0))
		tmp = Float64(Float64(x * log(y)) - t);
	else
		tmp = Float64(Float64(y - log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.1) || ~((x <= 1.0)))
		tmp = (x * log(y)) - t;
	else
		tmp = (y - log(y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.1], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(y - N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1000000000000001 or 1 < x

   1. Initial program 93.1%

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

   3. Taylor expanded in y around 0 99.7%

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

   4. Taylor expanded in x around inf 93.0%

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

      1. *-commutative 93.0%

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

   6. Simplified 93.0%

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

   if -1.1000000000000001 < x < 1

   1. Initial program 86.4%

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

   3. Taylor expanded in y around 0 98.1%

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

      1. associate--l+ 98.1%

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

      2. associate-*r* 98.1%

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

      3. mul-1-neg 98.1%

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

      4. fma-neg 98.1%

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

      5. sub-neg 98.1%

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

      6. metadata-eval 98.1%

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

      7. fma-define 98.1%

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

      8. *-commutative 98.1%

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

      9. fma-define 98.1%

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

      10. sub-neg 98.1%

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

      11. metadata-eval 98.1%

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

      12. +-commutative 98.1%

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

      13. sub-neg 98.1%

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

      14. *-commutative 98.1%

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

      15. +-commutative 98.1%

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

   5. Simplified 98.1%

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

   6. Taylor expanded in z around 0 84.3%

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

   7. Taylor expanded in x around 0 82.7%

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

      1. neg-mul-1 82.7%

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

      2. unsub-neg 82.7%

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

   9. Simplified 82.7%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\left(y - \log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+30} \lor \neg \left(x \leq 2.7 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.4e+30) (not (<= x 2.7e+34)))
   (- (* x (log y)) t)
   (- (* y (- 1.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.4e+30) || !(x <= 2.7e+34)) {
		tmp = (x * log(y)) - t;
	} else {
		tmp = (y * (1.0 - z)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-5.4d+30)) .or. (.not. (x <= 2.7d+34))) then
        tmp = (x * log(y)) - t
    else
        tmp = (y * (1.0d0 - z)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.4e+30) || !(x <= 2.7e+34)) {
		tmp = (x * Math.log(y)) - t;
	} else {
		tmp = (y * (1.0 - z)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.4e+30) or not (x <= 2.7e+34):
		tmp = (x * math.log(y)) - t
	else:
		tmp = (y * (1.0 - z)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.4e+30) || !(x <= 2.7e+34))
		tmp = Float64(Float64(x * log(y)) - t);
	else
		tmp = Float64(Float64(y * Float64(1.0 - z)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.4e+30) || ~((x <= 2.7e+34)))
		tmp = (x * log(y)) - t;
	else
		tmp = (y * (1.0 - z)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.4e+30], N[Not[LessEqual[x, 2.7e+34]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.3999999999999997e30 or 2.7e34 < x

   1. Initial program 94.3%

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

   3. Taylor expanded in y around 0 99.7%

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

   4. Taylor expanded in x around inf 94.2%

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

      1. *-commutative 94.2%

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

   6. Simplified 94.2%

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

   if -5.3999999999999997e30 < x < 2.7e34

   1. Initial program 85.9%

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

   3. Taylor expanded in y around 0 98.2%

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

      1. +-commutative 98.2%

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

      2. sub-neg 98.2%

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

      3. metadata-eval 98.2%

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

      4. fma-define 98.3%

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

      5. mul-1-neg 98.3%

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

      6. fma-neg 98.2%

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

      7. +-commutative 98.2%

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

      8. sub-neg 98.2%

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

      9. metadata-eval 98.2%

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

      10. +-commutative 98.2%

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

   5. Simplified 98.2%

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

   6. Taylor expanded in y around inf 64.6%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+30} \lor \neg \left(x \leq 2.7 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 7 \cdot 10^{+277}:\\ \;\;\;\;\left(y + \left(-1 + x\right) \cdot \log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \left(z + \frac{\log y}{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 7e+277)
   (- (+ y (* (+ -1.0 x) (log y))) t)
   (* y (- 1.0 (+ z (/ (log y) y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 7e+277) {
		tmp = (y + ((-1.0 + x) * log(y))) - t;
	} else {
		tmp = y * (1.0 - (z + (log(y) / 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 (z <= 7d+277) then
        tmp = (y + (((-1.0d0) + x) * log(y))) - t
    else
        tmp = y * (1.0d0 - (z + (log(y) / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 7e+277) {
		tmp = (y + ((-1.0 + x) * Math.log(y))) - t;
	} else {
		tmp = y * (1.0 - (z + (Math.log(y) / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 7e+277:
		tmp = (y + ((-1.0 + x) * math.log(y))) - t
	else:
		tmp = y * (1.0 - (z + (math.log(y) / y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 7e+277)
		tmp = Float64(Float64(y + Float64(Float64(-1.0 + x) * log(y))) - t);
	else
		tmp = Float64(y * Float64(1.0 - Float64(z + Float64(log(y) / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 7e+277)
		tmp = (y + ((-1.0 + x) * log(y))) - t;
	else
		tmp = y * (1.0 - (z + (log(y) / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 7e+277], N[(N[(y + N[(N[(-1.0 + x), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(y * N[(1.0 - N[(z + N[(N[Log[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 7.0000000000000002e277

   1. Initial program 91.6%

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

   3. Taylor expanded in y around 0 98.9%

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

      1. associate--l+ 98.9%

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

      2. associate-*r* 98.9%

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

      3. mul-1-neg 98.9%

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

      4. fma-neg 98.9%

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

      5. sub-neg 98.9%

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

      6. metadata-eval 98.9%

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

      7. fma-define 98.9%

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

      8. *-commutative 98.9%

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

      9. fma-define 98.9%

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

      10. sub-neg 98.9%

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

      11. metadata-eval 98.9%

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

      12. +-commutative 98.9%

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

      13. sub-neg 98.9%

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

      14. *-commutative 98.9%

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

      15. +-commutative 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in z around 0 90.6%

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

   if 7.0000000000000002e277 < z

   1. Initial program 17.3%

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

   3. Taylor expanded in y around 0 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r* 99.7%

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

      3. mul-1-neg 99.7%

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

      4. fma-neg 99.7%

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

      5. sub-neg 99.7%

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

      6. metadata-eval 99.7%

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

      7. fma-define 99.7%

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

      8. *-commutative 99.7%

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

      9. fma-define 99.7%

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

      10. sub-neg 99.7%

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

      11. metadata-eval 99.7%

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

      12. +-commutative 99.7%

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

      13. sub-neg 99.7%

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

      14. *-commutative 99.7%

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

      15. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around inf 100.0%

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

   7. Taylor expanded in t around 0 100.0%

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

      1. distribute-lft-out 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-*r/ 99.7%

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

      7. log-rec 99.7%

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

      8. mul-1-neg 99.7%

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

      9. +-commutative 99.7%

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

      10. +-commutative 99.7%

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

   9. Simplified 99.7%

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

   10. Taylor expanded in x around 0 87.2%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7 \cdot 10^{+277}:\\ \;\;\;\;\left(y + \left(-1 + x\right) \cdot \log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \left(z + \frac{\log y}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 88.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 7.5 \cdot 10^{+275}:\\ \;\;\;\;\left(-1 + x\right) \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \left(z + \frac{\log y}{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 7.5e+275)
   (- (* (+ -1.0 x) (log y)) t)
   (* y (- 1.0 (+ z (/ (log y) y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 7.5e+275) {
		tmp = ((-1.0 + x) * log(y)) - t;
	} else {
		tmp = y * (1.0 - (z + (log(y) / 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 (z <= 7.5d+275) then
        tmp = (((-1.0d0) + x) * log(y)) - t
    else
        tmp = y * (1.0d0 - (z + (log(y) / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 7.5e+275) {
		tmp = ((-1.0 + x) * Math.log(y)) - t;
	} else {
		tmp = y * (1.0 - (z + (Math.log(y) / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 7.5e+275:
		tmp = ((-1.0 + x) * math.log(y)) - t
	else:
		tmp = y * (1.0 - (z + (math.log(y) / y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 7.5e+275)
		tmp = Float64(Float64(Float64(-1.0 + x) * log(y)) - t);
	else
		tmp = Float64(y * Float64(1.0 - Float64(z + Float64(log(y) / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 7.5e+275)
		tmp = ((-1.0 + x) * log(y)) - t;
	else
		tmp = y * (1.0 - (z + (log(y) / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 7.5e+275], N[(N[(N[(-1.0 + x), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(y * N[(1.0 - N[(z + N[(N[Log[y], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 7.49999999999999978e275

   1. Initial program 91.6%

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

   3. Taylor expanded in y around 0 90.5%

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

   if 7.49999999999999978e275 < z

   1. Initial program 17.3%

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

   3. Taylor expanded in y around 0 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r* 99.7%

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

      3. mul-1-neg 99.7%

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

      4. fma-neg 99.7%

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

      5. sub-neg 99.7%

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

      6. metadata-eval 99.7%

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

      7. fma-define 99.7%

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

      8. *-commutative 99.7%

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

      9. fma-define 99.7%

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

      10. sub-neg 99.7%

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

      11. metadata-eval 99.7%

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

      12. +-commutative 99.7%

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

      13. sub-neg 99.7%

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

      14. *-commutative 99.7%

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

      15. +-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around inf 100.0%

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

   7. Taylor expanded in t around 0 100.0%

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

      1. distribute-lft-out 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-*r/ 99.7%

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

      7. log-rec 99.7%

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

      8. mul-1-neg 99.7%

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

      9. +-commutative 99.7%

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

      10. +-commutative 99.7%

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

   9. Simplified 99.7%

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

   10. Taylor expanded in x around 0 87.2%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7.5 \cdot 10^{+275}:\\ \;\;\;\;\left(-1 + x\right) \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - \left(z + \frac{\log y}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.1% accurate, 1.9× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (((-1.0 + x) * log(y)) - ((z + -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 = ((((-1.0d0) + x) * log(y)) - ((z + (-1.0d0)) * y)) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.9%

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

3. Taylor expanded in y around 0 98.9%

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

   1. +-commutative 98.9%

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

   2. sub-neg 98.9%

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

   3. metadata-eval 98.9%

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

   4. fma-define 98.9%

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

   5. mul-1-neg 98.9%

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

   6. fma-neg 98.9%

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

   7. +-commutative 98.9%

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

   8. sub-neg 98.9%

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

   9. metadata-eval 98.9%

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

   10. +-commutative 98.9%

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

5. Simplified 98.9%

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

6. Final simplification 98.9%

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

Alternative 12: 88.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5.1 \cdot 10^{+177}:\\ \;\;\;\;\left(-1 + x\right) \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{log1p}\left(-y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 5.1e+177) (- (* (+ -1.0 x) (log y)) t) (- (* z (log1p (- y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 5.1e+177) {
		tmp = ((-1.0 + x) * log(y)) - t;
	} else {
		tmp = (z * log1p(-y)) - t;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 5.1e+177) {
		tmp = ((-1.0 + x) * Math.log(y)) - t;
	} else {
		tmp = (z * Math.log1p(-y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 5.1e+177:
		tmp = ((-1.0 + x) * math.log(y)) - t
	else:
		tmp = (z * math.log1p(-y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 5.1e+177)
		tmp = Float64(Float64(Float64(-1.0 + x) * log(y)) - t);
	else
		tmp = Float64(Float64(z * log1p(Float64(-y))) - t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 5.1e+177], N[(N[(N[(-1.0 + x), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(z * N[Log[1 + (-y)], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.1000000000000004e177

   1. Initial program 93.9%

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

   3. Taylor expanded in y around 0 93.2%

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

   if 5.1000000000000004e177 < z

   1. Initial program 52.6%

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

   3. Taylor expanded in z around inf 19.2%

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

      1. *-commutative 19.2%

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

      2. sub-neg 19.2%

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

      3. log1p-define 65.1%

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

   5. Simplified 65.1%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5.1 \cdot 10^{+177}:\\ \;\;\;\;\left(-1 + x\right) \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{log1p}\left(-y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 98.9% accurate, 1.9× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (((-1.0 + 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 = ((((-1.0d0) + x) * log(y)) - (z * y)) - t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.9%

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

3. Taylor expanded in y around 0 98.9%

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

   1. +-commutative 98.9%

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

   2. sub-neg 98.9%

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

   3. metadata-eval 98.9%

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

   4. fma-define 98.9%

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

   5. mul-1-neg 98.9%

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

   6. fma-neg 98.9%

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

   7. +-commutative 98.9%

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

   8. sub-neg 98.9%

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

   9. metadata-eval 98.9%

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

   10. +-commutative 98.9%

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

5. Simplified 98.9%

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

6. Taylor expanded in z around inf 98.9%

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

7. Final simplification 98.9%

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

Alternative 14: 43.2% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -37000 \lor \neg \left(t \leq 2.65 \cdot 10^{+16}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -37000.0) (not (<= t 2.65e+16))) (- t) (* y (- 1.0 z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -37000.0) || !(t <= 2.65e+16)) {
		tmp = -t;
	} else {
		tmp = y * (1.0 - z);
	}
	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 <= (-37000.0d0)) .or. (.not. (t <= 2.65d+16))) then
        tmp = -t
    else
        tmp = y * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -37000.0) || !(t <= 2.65e+16)) {
		tmp = -t;
	} else {
		tmp = y * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -37000.0) or not (t <= 2.65e+16):
		tmp = -t
	else:
		tmp = y * (1.0 - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -37000.0) || !(t <= 2.65e+16))
		tmp = Float64(-t);
	else
		tmp = Float64(y * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -37000.0) || ~((t <= 2.65e+16)))
		tmp = -t;
	else
		tmp = y * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -37000.0], N[Not[LessEqual[t, 2.65e+16]], $MachinePrecision]], (-t), N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -37000 or 2.65e16 < t

   1. Initial program 94.7%

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

   3. Taylor expanded in t around inf 73.6%

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

      1. neg-mul-1 73.6%

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

   5. Simplified 73.6%

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

   if -37000 < t < 2.65e16

   1. Initial program 85.3%

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

   3. Taylor expanded in y around 0 98.0%

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

      1. associate--l+ 98.0%

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

      2. associate-*r* 98.0%

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

      3. mul-1-neg 98.0%

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

      4. fma-neg 98.0%

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

      5. sub-neg 98.0%

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

      6. metadata-eval 98.0%

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

      7. fma-define 98.0%

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

      8. *-commutative 98.0%

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

      9. fma-define 98.0%

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

      10. sub-neg 98.0%

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

      11. metadata-eval 98.0%

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

      12. +-commutative 98.0%

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

      13. sub-neg 98.0%

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

      14. *-commutative 98.0%

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

      15. +-commutative 98.0%

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

   5. Simplified 98.0%

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

   6. Taylor expanded in y around inf 68.5%

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

   7. Taylor expanded in y around inf 17.2%

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

      1. mul-1-neg 17.2%

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

      2. distribute-rgt-neg-in 17.2%

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

      3. sub-neg 17.2%

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

      4. metadata-eval 17.2%

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

      5. +-commutative 17.2%

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

      6. distribute-neg-in 17.2%

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

      7. metadata-eval 17.2%

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

      8. unsub-neg 17.2%

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

   9. Simplified 17.2%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -37000 \lor \neg \left(t \leq 2.65 \cdot 10^{+16}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.9% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -246 \lor \neg \left(t \leq 2.5 \cdot 10^{+16}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -246.0) (not (<= t 2.5e+16))) (- t) (* y (- z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -246.0) || !(t <= 2.5e+16)) {
		tmp = -t;
	} else {
		tmp = y * -z;
	}
	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 <= (-246.0d0)) .or. (.not. (t <= 2.5d+16))) then
        tmp = -t
    else
        tmp = y * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -246.0) || !(t <= 2.5e+16)) {
		tmp = -t;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -246.0) or not (t <= 2.5e+16):
		tmp = -t
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -246.0) || !(t <= 2.5e+16))
		tmp = Float64(-t);
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -246.0) || ~((t <= 2.5e+16)))
		tmp = -t;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -246.0], N[Not[LessEqual[t, 2.5e+16]], $MachinePrecision]], (-t), N[(y * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -246 or 2.5e16 < t

   1. Initial program 94.7%

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

   3. Taylor expanded in t around inf 73.6%

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

      1. neg-mul-1 73.6%

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

   5. Simplified 73.6%

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

   if -246 < t < 2.5e16

   1. Initial program 85.3%

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

   3. Taylor expanded in y around 0 98.0%

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

      1. associate--l+ 98.0%

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

      2. associate-*r* 98.0%

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

      3. mul-1-neg 98.0%

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

      4. fma-neg 98.0%

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

      5. sub-neg 98.0%

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

      6. metadata-eval 98.0%

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

      7. fma-define 98.0%

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

      8. *-commutative 98.0%

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

      9. fma-define 98.0%

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

      10. sub-neg 98.0%

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

      11. metadata-eval 98.0%

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

      12. +-commutative 98.0%

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

      13. sub-neg 98.0%

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

      14. *-commutative 98.0%

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

      15. +-commutative 98.0%

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

   5. Simplified 98.0%

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

   6. Taylor expanded in z around inf 16.6%

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

      1. associate-*r* 16.6%

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

      2. neg-mul-1 16.6%

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

   8. Simplified 16.6%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -246 \lor \neg \left(t \leq 2.5 \cdot 10^{+16}\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 46.3% accurate, 30.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 89.9%

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

3. Taylor expanded in y around 0 98.9%

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

   1. +-commutative 98.9%

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

   2. sub-neg 98.9%

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

   3. metadata-eval 98.9%

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

   4. fma-define 98.9%

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

   5. mul-1-neg 98.9%

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

   6. fma-neg 98.9%

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

   7. +-commutative 98.9%

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

   8. sub-neg 98.9%

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

   9. metadata-eval 98.9%

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

   10. +-commutative 98.9%

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

5. Simplified 98.9%

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

6. Taylor expanded in y around inf 47.4%

   \[\leadsto \color{blue}{y \cdot \left(1 - z\right)} - t \]
7. Add Preprocessing

Alternative 17: 46.1% accurate, 35.8× 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 89.9%

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

3. Taylor expanded in y around 0 98.9%

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

   1. +-commutative 98.9%

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

   2. sub-neg 98.9%

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

   3. metadata-eval 98.9%

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

   4. fma-define 98.9%

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

   5. mul-1-neg 98.9%

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

   6. fma-neg 98.9%

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

   7. +-commutative 98.9%

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

   8. sub-neg 98.9%

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

   9. metadata-eval 98.9%

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

   10. +-commutative 98.9%

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

5. Simplified 98.9%

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

6. Taylor expanded in z around inf 47.2%

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

   1. mul-1-neg 47.2%

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

   2. distribute-rgt-neg-in 47.2%

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

8. Simplified 47.2%

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

9. Final simplification 47.2%

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

Alternative 18: 35.3% accurate, 107.5× 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 89.9%

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

3. Taylor expanded in t around inf 37.4%

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

   1. neg-mul-1 37.4%

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

5. Simplified 37.4%

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

Alternative 19: 2.9% accurate, 215.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 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 = y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := y

Derivation

1. Initial program 89.9%

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

3. Taylor expanded in y around 0 98.9%

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

   1. associate--l+ 98.9%

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

   2. associate-*r* 98.9%

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

   3. mul-1-neg 98.9%

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

   4. fma-neg 98.9%

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

   5. sub-neg 98.9%

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

   6. metadata-eval 98.9%

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

   7. fma-define 98.9%

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

   8. *-commutative 98.9%

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

   9. fma-define 98.9%

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

   10. sub-neg 98.9%

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

   11. metadata-eval 98.9%

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

   12. +-commutative 98.9%

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

   13. sub-neg 98.9%

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

   14. *-commutative 98.9%

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

   15. +-commutative 98.9%

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

5. Simplified 98.9%

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

6. Taylor expanded in z around 0 88.8%

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

7. Taylor expanded in y around inf 2.9%

   \[\leadsto \color{blue}{y} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024100 
(FPCore (x y z t)
  :name "Statistics.Distribution.Beta:$cdensity from math-functions-0.1.5.2"
  :precision binary64
  (- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t))