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

Percentage Accurate: 89.0% → 99.6%

Time: 15.1s

Alternatives: 15

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: 89.0% 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: 99.6% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 86.9%

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

   1. fma-define 86.9%

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

   2. sub-neg 86.9%

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

   3. metadata-eval 86.9%

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

   4. sub-neg 86.9%

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

   5. metadata-eval 86.9%

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

   6. sub-neg 86.9%

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

   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. Taylor expanded in z around inf 99.8%

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

Alternative 2: 97.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + -1 \leq -1 \cdot 10^{+38} \lor \neg \left(x + -1 \leq -0.5\right):\\ \;\;\;\;\left(x \cdot \log y - y \cdot z\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-\log y\right) - y \cdot z\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (+ x -1.0) -1e+38) (not (<= (+ x -1.0) -0.5)))
   (- (- (* x (log y)) (* y z)) t)
   (- (- (- (log y)) (* y z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x + -1.0) <= -1e+38) || !((x + -1.0) <= -0.5)) {
		tmp = ((x * log(y)) - (y * z)) - t;
	} else {
		tmp = (-log(y) - (y * z)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x + (-1.0d0)) <= (-1d+38)) .or. (.not. ((x + (-1.0d0)) <= (-0.5d0)))) then
        tmp = ((x * log(y)) - (y * z)) - t
    else
        tmp = (-log(y) - (y * z)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x + -1.0) <= -1e+38) || !((x + -1.0) <= -0.5)) {
		tmp = ((x * Math.log(y)) - (y * z)) - t;
	} else {
		tmp = (-Math.log(y) - (y * z)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x + -1.0) <= -1e+38) or not ((x + -1.0) <= -0.5):
		tmp = ((x * math.log(y)) - (y * z)) - t
	else:
		tmp = (-math.log(y) - (y * z)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x + -1.0) <= -1e+38) || !(Float64(x + -1.0) <= -0.5))
		tmp = Float64(Float64(Float64(x * log(y)) - Float64(y * z)) - t);
	else
		tmp = Float64(Float64(Float64(-log(y)) - Float64(y * z)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x + -1.0) <= -1e+38) || ~(((x + -1.0) <= -0.5)))
		tmp = ((x * log(y)) - (y * z)) - t;
	else
		tmp = (-log(y) - (y * z)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x + -1.0), $MachinePrecision], -1e+38], N[Not[LessEqual[N[(x + -1.0), $MachinePrecision], -0.5]], $MachinePrecision]], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[((-N[Log[y], $MachinePrecision]) - N[(y * z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 x #s(literal 1 binary64)) < -9.99999999999999977e37 or -0.5 < (-.f64 x #s(literal 1 binary64))

   1. Initial program 91.8%

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

      1. fma-define 91.8%

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

      2. sub-neg 91.8%

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

      3. metadata-eval 91.8%

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

      4. sub-neg 91.8%

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

      5. metadata-eval 91.8%

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

      6. sub-neg 91.8%

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

      7. log1p-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in y around 0 99.1%

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

      1. +-commutative 99.1%

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

      2. sub-neg 99.1%

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

      3. metadata-eval 99.1%

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

      4. *-commutative 99.1%

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

      5. mul-1-neg 99.1%

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

      6. unsub-neg 99.1%

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

      7. *-commutative 99.1%

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

      8. +-commutative 99.1%

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

   8. Simplified 99.1%

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

   9. Taylor expanded in x around inf 98.7%

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

       1. *-commutative 98.7%

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

   11. Simplified 98.7%

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

   if -9.99999999999999977e37 < (-.f64 x #s(literal 1 binary64)) < -0.5

   1. Initial program 82.8%

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

      1. fma-define 82.8%

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

      2. sub-neg 82.8%

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

      3. metadata-eval 82.8%

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

      4. sub-neg 82.8%

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

      5. metadata-eval 82.8%

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

      6. sub-neg 82.8%

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

      7. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

   6. Taylor expanded in y around 0 99.7%

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

      1. +-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. *-commutative 99.7%

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

      5. mul-1-neg 99.7%

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

      6. unsub-neg 99.7%

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

      7. *-commutative 99.7%

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

      8. +-commutative 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in x around 0 98.4%

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

       1. mul-1-neg 98.4%

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

       2. *-commutative 98.4%

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

   11. Simplified 98.4%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + -1 \leq -1 \cdot 10^{+38} \lor \neg \left(x + -1 \leq -0.5\right):\\ \;\;\;\;\left(x \cdot \log y - y \cdot z\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-\log y\right) - y \cdot z\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.6% accurate, 1.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return ((log(y) * (x + -1.0)) + ((-1.0 + z) * (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 = ((log(y) * (x + (-1.0d0))) + (((-1.0d0) + z) * (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 ((Math.log(y) * (x + -1.0)) + ((-1.0 + z) * (y * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5)))))) - t;
}

Python

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[Log[y], $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 + z), $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 86.9%

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

3. Taylor expanded in y around 0 99.8%

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

4. Final simplification 99.8%

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

Alternative 4: 95.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + -1 \leq -1 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{elif}\;x + -1 \leq -0.99999995:\\ \;\;\;\;\left(\left(-\log y\right) - y \cdot z\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(x + -1\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ x -1.0) -1e+38)
   (- (* x (log y)) t)
   (if (<= (+ x -1.0) -0.99999995)
     (- (- (- (log y)) (* y z)) t)
     (- (* (log y) (+ x -1.0)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + -1.0) <= -1e+38) {
		tmp = (x * log(y)) - t;
	} else if ((x + -1.0) <= -0.99999995) {
		tmp = (-log(y) - (y * z)) - t;
	} else {
		tmp = (log(y) * (x + -1.0)) - 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 + (-1.0d0)) <= (-1d+38)) then
        tmp = (x * log(y)) - t
    else if ((x + (-1.0d0)) <= (-0.99999995d0)) then
        tmp = (-log(y) - (y * z)) - t
    else
        tmp = (log(y) * (x + (-1.0d0))) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x + -1.0) <= -1e+38) {
		tmp = (x * Math.log(y)) - t;
	} else if ((x + -1.0) <= -0.99999995) {
		tmp = (-Math.log(y) - (y * z)) - t;
	} else {
		tmp = (Math.log(y) * (x + -1.0)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x + -1.0) <= -1e+38:
		tmp = (x * math.log(y)) - t
	elif (x + -1.0) <= -0.99999995:
		tmp = (-math.log(y) - (y * z)) - t
	else:
		tmp = (math.log(y) * (x + -1.0)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x + -1.0) <= -1e+38)
		tmp = Float64(Float64(x * log(y)) - t);
	elseif (Float64(x + -1.0) <= -0.99999995)
		tmp = Float64(Float64(Float64(-log(y)) - Float64(y * z)) - t);
	else
		tmp = Float64(Float64(log(y) * Float64(x + -1.0)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x + -1.0) <= -1e+38)
		tmp = (x * log(y)) - t;
	elseif ((x + -1.0) <= -0.99999995)
		tmp = (-log(y) - (y * z)) - t;
	else
		tmp = (log(y) * (x + -1.0)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x + -1.0), $MachinePrecision], -1e+38], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[N[(x + -1.0), $MachinePrecision], -0.99999995], N[(N[((-N[Log[y], $MachinePrecision]) - N[(y * z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[Log[y], $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 x #s(literal 1 binary64)) < -9.99999999999999977e37

   1. Initial program 92.9%

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

      1. fma-define 92.9%

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

      2. sub-neg 92.9%

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

      3. metadata-eval 92.9%

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

      4. sub-neg 92.9%

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

      5. metadata-eval 92.9%

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

      6. sub-neg 92.9%

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

      7. log1p-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in y around 0 98.9%

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

      1. +-commutative 98.9%

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

      2. sub-neg 98.9%

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

      3. metadata-eval 98.9%

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

      4. *-commutative 98.9%

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

      5. mul-1-neg 98.9%

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

      6. unsub-neg 98.9%

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

      7. *-commutative 98.9%

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

      8. +-commutative 98.9%

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

   8. Simplified 98.9%

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

   9. Taylor expanded in z around inf 71.9%

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

       1. sub-neg 71.9%

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

       2. metadata-eval 71.9%

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

       3. +-commutative 71.9%

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

       4. associate-*r/ 71.8%

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

   11. Simplified 71.8%

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

   12. Taylor expanded in x around inf 91.6%

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

   if -9.99999999999999977e37 < (-.f64 x #s(literal 1 binary64)) < -0.999999949999999971

   1. Initial program 82.7%

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

      1. fma-define 82.7%

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

      2. sub-neg 82.7%

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

      3. metadata-eval 82.7%

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

      4. sub-neg 82.7%

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

      5. metadata-eval 82.7%

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

      6. sub-neg 82.7%

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

      7. log1p-define 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

   6. Taylor expanded in y around 0 99.7%

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

      1. +-commutative 99.7%

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

      2. sub-neg 99.7%

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

      3. metadata-eval 99.7%

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

      4. *-commutative 99.7%

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

      5. mul-1-neg 99.7%

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

      6. unsub-neg 99.7%

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

      7. *-commutative 99.7%

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

      8. +-commutative 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in x around 0 98.8%

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

       1. mul-1-neg 98.8%

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

       2. *-commutative 98.8%

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

   11. Simplified 98.8%

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

   if -0.999999949999999971 < (-.f64 x #s(literal 1 binary64))

   1. Initial program 90.8%

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

      1. fma-define 90.8%

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

      2. sub-neg 90.8%

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

      3. metadata-eval 90.8%

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

      4. sub-neg 90.8%

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

      5. metadata-eval 90.8%

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

      6. sub-neg 90.8%

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

      7. log1p-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 90.0%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + -1 \leq -1 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{elif}\;x + -1 \leq -0.99999995:\\ \;\;\;\;\left(\left(-\log y\right) - y \cdot z\right) - t\\ \mathbf{else}:\\ \;\;\;\;\log y \cdot \left(x + -1\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.9%

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

3. Taylor expanded in y around 0 99.8%

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

4. Final simplification 99.8%

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

Alternative 6: 89.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+206}:\\ \;\;\;\;\left(-t\right) - y \cdot z\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+163}:\\ \;\;\;\;\log y \cdot \left(x + -1\right) - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.2e+206)
   (- (- t) (* y z))
   (if (<= z 2e+163)
     (- (* (log y) (+ x -1.0)) t)
     (- (* y (* z (+ -1.0 (* y -0.5)))) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.2e+206) {
		tmp = -t - (y * z);
	} else if (z <= 2e+163) {
		tmp = (log(y) * (x + -1.0)) - t;
	} else {
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-7.2d+206)) then
        tmp = -t - (y * z)
    else if (z <= 2d+163) then
        tmp = (log(y) * (x + (-1.0d0))) - t
    else
        tmp = (y * (z * ((-1.0d0) + (y * (-0.5d0))))) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.2e+206) {
		tmp = -t - (y * z);
	} else if (z <= 2e+163) {
		tmp = (Math.log(y) * (x + -1.0)) - t;
	} else {
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -7.2e+206:
		tmp = -t - (y * z)
	elif z <= 2e+163:
		tmp = (math.log(y) * (x + -1.0)) - t
	else:
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.2e+206)
		tmp = Float64(Float64(-t) - Float64(y * z));
	elseif (z <= 2e+163)
		tmp = Float64(Float64(log(y) * Float64(x + -1.0)) - t);
	else
		tmp = Float64(Float64(y * Float64(z * Float64(-1.0 + Float64(y * -0.5)))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.2e+206)
		tmp = -t - (y * z);
	elseif (z <= 2e+163)
		tmp = (log(y) * (x + -1.0)) - t;
	else
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -7.2e+206], N[((-t) - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+163], N[(N[(N[Log[y], $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(y * N[(z * N[(-1.0 + N[(y * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.20000000000000057e206

   1. Initial program 53.7%

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

      1. fma-define 53.7%

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

      2. sub-neg 53.7%

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

      3. metadata-eval 53.7%

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

      4. sub-neg 53.7%

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

      5. metadata-eval 53.7%

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

      6. sub-neg 53.7%

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

      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. Taylor expanded in z around inf 99.8%

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

   6. Taylor expanded in y around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. sub-neg 99.8%

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

      3. metadata-eval 99.8%

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

      4. *-commutative 99.8%

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

      5. mul-1-neg 99.8%

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

      6. unsub-neg 99.8%

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

      7. *-commutative 99.8%

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

      8. +-commutative 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in y around inf 71.7%

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

       1. mul-1-neg 71.7%

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

       2. distribute-lft-neg-out 71.7%

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

       3. *-commutative 71.7%

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

   11. Simplified 71.7%

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

   if -7.20000000000000057e206 < z < 1.9999999999999999e163

   1. Initial program 97.2%

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

      1. fma-define 97.2%

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

      2. sub-neg 97.2%

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

      3. metadata-eval 97.2%

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

      4. sub-neg 97.2%

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

      5. metadata-eval 97.2%

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

      6. sub-neg 97.2%

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

      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. Taylor expanded in y around 0 96.7%

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

   if 1.9999999999999999e163 < z

   1. Initial program 46.0%

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

   3. Taylor expanded in y around 0 99.3%

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

      1. add-cbrt-cube 76.8%

         \[\leadsto \left(\color{blue}{\sqrt[3]{\left(\left(\left(x - 1\right) \cdot \log y\right) \cdot \left(\left(x - 1\right) \cdot \log y\right)\right) \cdot \left(\left(x - 1\right) \cdot \log y\right)}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

      2. pow3 76.8%

         \[\leadsto \left(\sqrt[3]{\color{blue}{{\left(\left(x - 1\right) \cdot \log y\right)}^{3}}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

      3. sub-neg 76.8%

         \[\leadsto \left(\sqrt[3]{{\left(\color{blue}{\left(x + \left(-1\right)\right)} \cdot \log y\right)}^{3}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

      4. metadata-eval 76.8%

         \[\leadsto \left(\sqrt[3]{{\left(\left(x + \color{blue}{-1}\right) \cdot \log y\right)}^{3}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

      5. *-commutative 76.8%

         \[\leadsto \left(\sqrt[3]{{\color{blue}{\left(\log y \cdot \left(x + -1\right)\right)}}^{3}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

   5. Applied egg-rr 76.8%

      \[\leadsto \left(\color{blue}{\sqrt[3]{{\left(\log y \cdot \left(x + -1\right)\right)}^{3}}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

   6. Taylor expanded in z around inf 80.4%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+206}:\\ \;\;\;\;\left(-t\right) - y \cdot z\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+163}:\\ \;\;\;\;\log y \cdot \left(x + -1\right) - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.15 \cdot 10^{+37} \lor \neg \left(x \leq 175\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.15e+37) (not (<= x 175.0)))
   (- (* x (log y)) t)
   (- (* y (* z (+ -1.0 (* y -0.5)))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.15e+37) || !(x <= 175.0)) {
		tmp = (x * log(y)) - t;
	} else {
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - 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 <= (-3.15d+37)) .or. (.not. (x <= 175.0d0))) then
        tmp = (x * log(y)) - t
    else
        tmp = (y * (z * ((-1.0d0) + (y * (-0.5d0))))) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.15e+37) || !(x <= 175.0)) {
		tmp = (x * Math.log(y)) - t;
	} else {
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.15e+37) or not (x <= 175.0):
		tmp = (x * math.log(y)) - t
	else:
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.15e+37) || !(x <= 175.0))
		tmp = Float64(Float64(x * log(y)) - t);
	else
		tmp = Float64(Float64(y * Float64(z * Float64(-1.0 + Float64(y * -0.5)))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.15e+37) || ~((x <= 175.0)))
		tmp = (x * log(y)) - t;
	else
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.15e+37], N[Not[LessEqual[x, 175.0]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(y * N[(z * N[(-1.0 + N[(y * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.14999999999999992e37 or 175 < x

   1. Initial program 91.8%

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

      1. fma-define 91.8%

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

      2. sub-neg 91.8%

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

      3. metadata-eval 91.8%

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

      4. sub-neg 91.8%

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

      5. metadata-eval 91.8%

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

      6. sub-neg 91.8%

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

      7. log1p-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in y around 0 99.1%

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

      1. +-commutative 99.1%

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

      2. sub-neg 99.1%

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

      3. metadata-eval 99.1%

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

      4. *-commutative 99.1%

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

      5. mul-1-neg 99.1%

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

      6. unsub-neg 99.1%

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

      7. *-commutative 99.1%

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

      8. +-commutative 99.1%

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

   8. Simplified 99.1%

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

   9. Taylor expanded in z around inf 75.4%

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

       1. sub-neg 75.4%

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

       2. metadata-eval 75.4%

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

       3. +-commutative 75.4%

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

       4. associate-*r/ 75.4%

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

   11. Simplified 75.4%

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

   12. Taylor expanded in x around inf 90.3%

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

   if -3.14999999999999992e37 < x < 175

   1. Initial program 82.8%

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

   3. Taylor expanded in y around 0 100.0%

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

      1. add-cbrt-cube 99.8%

         \[\leadsto \left(\color{blue}{\sqrt[3]{\left(\left(\left(x - 1\right) \cdot \log y\right) \cdot \left(\left(x - 1\right) \cdot \log y\right)\right) \cdot \left(\left(x - 1\right) \cdot \log y\right)}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

      2. pow3 99.8%

         \[\leadsto \left(\sqrt[3]{\color{blue}{{\left(\left(x - 1\right) \cdot \log y\right)}^{3}}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

      3. sub-neg 99.8%

         \[\leadsto \left(\sqrt[3]{{\left(\color{blue}{\left(x + \left(-1\right)\right)} \cdot \log y\right)}^{3}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

      4. metadata-eval 99.8%

         \[\leadsto \left(\sqrt[3]{{\left(\left(x + \color{blue}{-1}\right) \cdot \log y\right)}^{3}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

      5. *-commutative 99.8%

         \[\leadsto \left(\sqrt[3]{{\color{blue}{\left(\log y \cdot \left(x + -1\right)\right)}}^{3}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

   5. Applied egg-rr 99.8%

      \[\leadsto \left(\color{blue}{\sqrt[3]{{\left(\log y \cdot \left(x + -1\right)\right)}^{3}}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

   6. Taylor expanded in z around inf 65.3%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.15 \cdot 10^{+37} \lor \neg \left(x \leq 175\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.04 \cdot 10^{+83} \lor \neg \left(x \leq 6.5 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.04e+83) (not (<= x 6.5e+33)))
   (* x (log y))
   (- (* y (* z (+ -1.0 (* y -0.5)))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.04e+83) || !(x <= 6.5e+33)) {
		tmp = x * log(y);
	} else {
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - 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 <= (-1.04d+83)) .or. (.not. (x <= 6.5d+33))) then
        tmp = x * log(y)
    else
        tmp = (y * (z * ((-1.0d0) + (y * (-0.5d0))))) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.04e+83) || !(x <= 6.5e+33)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.04e+83) or not (x <= 6.5e+33):
		tmp = x * math.log(y)
	else:
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.04e+83) || !(x <= 6.5e+33))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(y * Float64(z * Float64(-1.0 + Float64(y * -0.5)))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.04e+83) || ~((x <= 6.5e+33)))
		tmp = x * log(y);
	else
		tmp = (y * (z * (-1.0 + (y * -0.5)))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.04e+83], N[Not[LessEqual[x, 6.5e+33]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(z * N[(-1.0 + N[(y * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.0399999999999999e83 or 6.49999999999999993e33 < x

   1. Initial program 93.2%

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

      1. fma-define 93.2%

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

      2. sub-neg 93.2%

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

      3. metadata-eval 93.2%

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

      4. sub-neg 93.2%

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

      5. metadata-eval 93.2%

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

      6. sub-neg 93.2%

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

      7. log1p-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 99.6%

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

   6. Taylor expanded in x around inf 81.2%

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

      1. *-commutative 81.2%

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

   8. Simplified 81.2%

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

   if -1.0399999999999999e83 < x < 6.49999999999999993e33

   1. Initial program 82.9%

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

   3. Taylor expanded in y around 0 99.9%

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

      1. add-cbrt-cube 99.7%

         \[\leadsto \left(\color{blue}{\sqrt[3]{\left(\left(\left(x - 1\right) \cdot \log y\right) \cdot \left(\left(x - 1\right) \cdot \log y\right)\right) \cdot \left(\left(x - 1\right) \cdot \log y\right)}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

      2. pow3 99.7%

         \[\leadsto \left(\sqrt[3]{\color{blue}{{\left(\left(x - 1\right) \cdot \log y\right)}^{3}}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

      3. sub-neg 99.7%

         \[\leadsto \left(\sqrt[3]{{\left(\color{blue}{\left(x + \left(-1\right)\right)} \cdot \log y\right)}^{3}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

      4. metadata-eval 99.7%

         \[\leadsto \left(\sqrt[3]{{\left(\left(x + \color{blue}{-1}\right) \cdot \log y\right)}^{3}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

      5. *-commutative 99.7%

         \[\leadsto \left(\sqrt[3]{{\color{blue}{\left(\log y \cdot \left(x + -1\right)\right)}}^{3}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

   5. Applied egg-rr 99.7%

      \[\leadsto \left(\color{blue}{\sqrt[3]{{\left(\log y \cdot \left(x + -1\right)\right)}^{3}}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

   6. Taylor expanded in z around inf 65.5%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.04 \cdot 10^{+83} \lor \neg \left(x \leq 6.5 \cdot 10^{+33}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot -0.5\right)\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.1% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.9%

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

   1. fma-define 86.9%

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

   2. sub-neg 86.9%

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

   3. metadata-eval 86.9%

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

   4. sub-neg 86.9%

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

   5. metadata-eval 86.9%

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

   6. sub-neg 86.9%

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

   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. Taylor expanded in z around inf 99.8%

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

6. Taylor expanded in y around 0 99.4%

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

   1. +-commutative 99.4%

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

   2. sub-neg 99.4%

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

   3. metadata-eval 99.4%

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

   4. *-commutative 99.4%

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

   5. mul-1-neg 99.4%

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

   6. unsub-neg 99.4%

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

   7. *-commutative 99.4%

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

   8. +-commutative 99.4%

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

8. Simplified 99.4%

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

9. Final simplification 99.4%

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

Alternative 10: 42.5% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+44}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 80000000000:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;-1 + \left(1 - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6.5e+44)
   (- t)
   (if (<= t 80000000000.0) (* z (- y)) (+ -1.0 (- 1.0 t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.5e+44) {
		tmp = -t;
	} else if (t <= 80000000000.0) {
		tmp = z * -y;
	} else {
		tmp = -1.0 + (1.0 - t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-6.5d+44)) then
        tmp = -t
    else if (t <= 80000000000.0d0) then
        tmp = z * -y
    else
        tmp = (-1.0d0) + (1.0d0 - t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.5e+44) {
		tmp = -t;
	} else if (t <= 80000000000.0) {
		tmp = z * -y;
	} else {
		tmp = -1.0 + (1.0 - t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6.5e+44:
		tmp = -t
	elif t <= 80000000000.0:
		tmp = z * -y
	else:
		tmp = -1.0 + (1.0 - t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6.5e+44)
		tmp = Float64(-t);
	elseif (t <= 80000000000.0)
		tmp = Float64(z * Float64(-y));
	else
		tmp = Float64(-1.0 + Float64(1.0 - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6.5e+44)
		tmp = -t;
	elseif (t <= 80000000000.0)
		tmp = z * -y;
	else
		tmp = -1.0 + (1.0 - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6.5e+44], (-t), If[LessEqual[t, 80000000000.0], N[(z * (-y)), $MachinePrecision], N[(-1.0 + N[(1.0 - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.50000000000000018e44

   1. Initial program 96.6%

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

      1. fma-define 96.6%

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

      2. sub-neg 96.6%

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

      3. metadata-eval 96.6%

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

      4. sub-neg 96.6%

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

      5. metadata-eval 96.6%

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

      6. sub-neg 96.6%

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

      7. log1p-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 76.7%

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

      1. mul-1-neg 76.7%

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

   7. Simplified 76.7%

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

   if -6.50000000000000018e44 < t < 8e10

   1. Initial program 80.3%

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

      1. fma-define 80.3%

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

      2. sub-neg 80.3%

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

      3. metadata-eval 80.3%

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

      4. sub-neg 80.3%

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

      5. metadata-eval 80.3%

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

      6. sub-neg 80.3%

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

      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. Taylor expanded in z around inf 99.8%

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

   6. Taylor expanded in z around inf 3.6%

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

      1. sub-neg 3.6%

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

      2. log1p-undefine 22.2%

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

   8. Simplified 22.2%

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

   9. Taylor expanded in y around 0 21.8%

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

       1. associate-*r* 21.8%

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

       2. neg-mul-1 21.8%

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

   11. Simplified 21.8%

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

   if 8e10 < t

   1. Initial program 94.2%

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

      1. fma-define 94.2%

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

      2. sub-neg 94.2%

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

      3. metadata-eval 94.2%

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

      4. sub-neg 94.2%

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

      5. metadata-eval 94.2%

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

      6. sub-neg 94.2%

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

      7. log1p-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 70.7%

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

      1. mul-1-neg 70.7%

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

   7. Simplified 70.7%

      \[\leadsto \color{blue}{-t} \]
   8. Step-by-step derivation

      1. expm1-log1p-u 0.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-t\right)\right)} \]

      2. expm1-undefine 0.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} - 1} \]

   9. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} - 1} \]
   10. Step-by-step derivation

       1. sub-neg 0.0%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} + \left(-1\right)} \]

       2. log1p-undefine 0.0%

          \[\leadsto e^{\color{blue}{\log \left(1 + \left(-t\right)\right)}} + \left(-1\right) \]

       3. rem-exp-log 70.7%

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

       4. unsub-neg 70.7%

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

       5. metadata-eval 70.7%

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

   11. Simplified 70.7%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+44}:\\ \;\;\;\;-t\\ \mathbf{elif}\;t \leq 80000000000:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;-1 + \left(1 - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.5% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+44} \lor \neg \left(t \leq 580000000000\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9.5e+44) (not (<= t 580000000000.0))) (- t) (* z (- y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9.5e+44) || !(t <= 580000000000.0)) {
		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 <= (-9.5d+44)) .or. (.not. (t <= 580000000000.0d0))) 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 <= -9.5e+44) || !(t <= 580000000000.0)) {
		tmp = -t;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -9.5e+44) or not (t <= 580000000000.0):
		tmp = -t
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -9.5e+44) || !(t <= 580000000000.0))
		tmp = Float64(-t);
	else
		tmp = Float64(z * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -9.5e+44) || ~((t <= 580000000000.0)))
		tmp = -t;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -9.5e+44], N[Not[LessEqual[t, 580000000000.0]], $MachinePrecision]], (-t), N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.5000000000000004e44 or 5.8e11 < t

   1. Initial program 95.4%

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

      1. fma-define 95.4%

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

      2. sub-neg 95.4%

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

      3. metadata-eval 95.4%

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

      4. sub-neg 95.4%

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

      5. metadata-eval 95.4%

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

      6. sub-neg 95.4%

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

      7. log1p-define 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 73.8%

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

      1. mul-1-neg 73.8%

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

   7. Simplified 73.8%

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

   if -9.5000000000000004e44 < t < 5.8e11

   1. Initial program 80.3%

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

      1. fma-define 80.3%

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

      2. sub-neg 80.3%

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

      3. metadata-eval 80.3%

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

      4. sub-neg 80.3%

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

      5. metadata-eval 80.3%

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

      6. sub-neg 80.3%

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

      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. Taylor expanded in z around inf 99.8%

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

   6. Taylor expanded in z around inf 3.6%

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

      1. sub-neg 3.6%

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

      2. log1p-undefine 22.2%

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

   8. Simplified 22.2%

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

   9. Taylor expanded in y around 0 21.8%

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

       1. associate-*r* 21.8%

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

       2. neg-mul-1 21.8%

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

   11. Simplified 21.8%

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

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+44} \lor \neg \left(t \leq 580000000000\right):\\ \;\;\;\;-t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 46.8% accurate, 19.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.9%

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

3. Taylor expanded in y around 0 99.8%

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

   1. add-cbrt-cube 70.8%

      \[\leadsto \left(\color{blue}{\sqrt[3]{\left(\left(\left(x - 1\right) \cdot \log y\right) \cdot \left(\left(x - 1\right) \cdot \log y\right)\right) \cdot \left(\left(x - 1\right) \cdot \log y\right)}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

   2. pow3 70.8%

      \[\leadsto \left(\sqrt[3]{\color{blue}{{\left(\left(x - 1\right) \cdot \log y\right)}^{3}}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

   3. sub-neg 70.8%

      \[\leadsto \left(\sqrt[3]{{\left(\color{blue}{\left(x + \left(-1\right)\right)} \cdot \log y\right)}^{3}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

   4. metadata-eval 70.8%

      \[\leadsto \left(\sqrt[3]{{\left(\left(x + \color{blue}{-1}\right) \cdot \log y\right)}^{3}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

   5. *-commutative 70.8%

      \[\leadsto \left(\sqrt[3]{{\color{blue}{\left(\log y \cdot \left(x + -1\right)\right)}}^{3}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

5. Applied egg-rr 70.8%

   \[\leadsto \left(\color{blue}{\sqrt[3]{{\left(\log y \cdot \left(x + -1\right)\right)}^{3}}} + y \cdot \left(-1 \cdot \left(z - 1\right) + -0.5 \cdot \left(y \cdot \left(z - 1\right)\right)\right)\right) - t \]

6. Taylor expanded in z around inf 47.8%

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

7. Final simplification 47.8%

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

Alternative 13: 46.6% accurate, 35.8× speedup

Math

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

FPCore

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

C

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

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 - (y * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.9%

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

   1. fma-define 86.9%

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

   2. sub-neg 86.9%

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

   3. metadata-eval 86.9%

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

   4. sub-neg 86.9%

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

   5. metadata-eval 86.9%

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

   6. sub-neg 86.9%

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

   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. Taylor expanded in z around inf 99.8%

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

6. Taylor expanded in y around 0 99.4%

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

   1. +-commutative 99.4%

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

   2. sub-neg 99.4%

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

   3. metadata-eval 99.4%

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

   4. *-commutative 99.4%

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

   5. mul-1-neg 99.4%

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

   6. unsub-neg 99.4%

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

   7. *-commutative 99.4%

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

   8. +-commutative 99.4%

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

8. Simplified 99.4%

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

9. Taylor expanded in y around inf 47.5%

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

    1. mul-1-neg 47.5%

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

    2. distribute-lft-neg-out 47.5%

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

    3. *-commutative 47.5%

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

11. Simplified 47.5%

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

12. Final simplification 47.5%

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

Alternative 14: 36.0% 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 86.9%

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

   1. fma-define 86.9%

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

   2. sub-neg 86.9%

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

   3. metadata-eval 86.9%

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

   4. sub-neg 86.9%

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

   5. metadata-eval 86.9%

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

   6. sub-neg 86.9%

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

   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. Taylor expanded in t around inf 34.4%

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

   1. mul-1-neg 34.4%

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

7. Simplified 34.4%

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

Alternative 15: 2.3% accurate, 215.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 0.0)

C

double code(double x, double y, double z, double t) {
	return 0.0;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 0.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return 0.0;
}

Python

def code(x, y, z, t):
	return 0.0

Julia

function code(x, y, z, t)
	return 0.0
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 0.0;
end

Wolfram

code[x_, y_, z_, t_] := 0.0

Derivation

1. Initial program 86.9%

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

   1. fma-define 86.9%

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

   2. sub-neg 86.9%

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

   3. metadata-eval 86.9%

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

   4. sub-neg 86.9%

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

   5. metadata-eval 86.9%

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

   6. sub-neg 86.9%

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

   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. Taylor expanded in t around inf 34.4%

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

   1. mul-1-neg 34.4%

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

7. Simplified 34.4%

   \[\leadsto \color{blue}{-t} \]
8. Step-by-step derivation

   1. expm1-log1p-u 17.4%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-t\right)\right)} \]

   2. expm1-undefine 17.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} - 1} \]

9. Applied egg-rr 17.2%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} - 1} \]
10. Step-by-step derivation

    1. sub-neg 17.2%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-t\right)} + \left(-1\right)} \]

    2. log1p-undefine 17.2%

       \[\leadsto e^{\color{blue}{\log \left(1 + \left(-t\right)\right)}} + \left(-1\right) \]

    3. rem-exp-log 34.3%

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

    4. unsub-neg 34.3%

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

    5. metadata-eval 34.3%

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

11. Simplified 34.3%

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

12. Taylor expanded in t around 0 2.3%

    \[\leadsto \color{blue}{1} + -1 \]
13. Step-by-step derivation

    1. metadata-eval 2.3%

       \[\leadsto \color{blue}{0} \]

14. Applied egg-rr 2.3%

    \[\leadsto \color{blue}{0} \]
15. Add Preprocessing

Reproduce

herbie shell --seed 2024165 
(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))