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

Percentage Accurate: 88.8% → 99.8%

Time: 16.1s

Alternatives: 16

Speedup: 1.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 90.9%

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

   1. sub-neg 90.9%

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

   2. +-commutative 90.9%

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

   3. associate-+l+ 90.9%

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

   4. fma-define 90.9%

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

   5. sub-neg 90.9%

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

   6. metadata-eval 90.9%

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

   7. sub-neg 90.9%

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

   8. log1p-define 99.8%

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

   9. fma-define 99.9%

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

   10. sub-neg 99.9%

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

   11. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 90.9%

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

   1. +-commutative 90.9%

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

   2. fma-define 90.9%

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

   3. sub-neg 90.9%

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

   4. metadata-eval 90.9%

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

   5. sub-neg 90.9%

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

   6. log1p-define 99.8%

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

   7. sub-neg 99.8%

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

   8. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 3: 99.6% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.9%

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

3. Taylor expanded in y around 0 99.6%

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

4. Final simplification 99.6%

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

Alternative 4: 99.4% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.9%

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

3. Taylor expanded in y around 0 99.6%

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

4. Taylor expanded in z around inf 99.6%

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

5. Final simplification 99.6%

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

Alternative 5: 99.5% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.9%

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

3. Taylor expanded in y around 0 99.6%

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

4. Final simplification 99.6%

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

Alternative 6: 99.4% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.9%

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

3. Taylor expanded in y around 0 99.6%

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

4. Final simplification 99.6%

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

Alternative 7: 77.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6200000000000 \lor \neg \left(t \leq 1.95 \cdot 10^{+18}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot \left(y \cdot -0.3333333333333333 - 0.5\right)\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(-1 + x\right) \cdot \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6200000000000.0) (not (<= t 1.95e+18)))
   (- (* y (* z (+ -1.0 (* y (- (* y -0.3333333333333333) 0.5))))) t)
   (* (+ -1.0 x) (log y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6200000000000.0) || !(t <= 1.95e+18)) {
		tmp = (y * (z * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5))))) - t;
	} else {
		tmp = (-1.0 + x) * log(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 <= (-6200000000000.0d0)) .or. (.not. (t <= 1.95d+18))) then
        tmp = (y * (z * ((-1.0d0) + (y * ((y * (-0.3333333333333333d0)) - 0.5d0))))) - t
    else
        tmp = ((-1.0d0) + x) * log(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6200000000000.0) || !(t <= 1.95e+18)) {
		tmp = (y * (z * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5))))) - t;
	} else {
		tmp = (-1.0 + x) * Math.log(y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6200000000000.0) or not (t <= 1.95e+18):
		tmp = (y * (z * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5))))) - t
	else:
		tmp = (-1.0 + x) * math.log(y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6200000000000.0) || !(t <= 1.95e+18))
		tmp = Float64(Float64(y * Float64(z * Float64(-1.0 + Float64(y * Float64(Float64(y * -0.3333333333333333) - 0.5))))) - t);
	else
		tmp = Float64(Float64(-1.0 + x) * log(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6200000000000.0) || ~((t <= 1.95e+18)))
		tmp = (y * (z * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5))))) - t;
	else
		tmp = (-1.0 + x) * log(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6200000000000.0], N[Not[LessEqual[t, 1.95e+18]], $MachinePrecision]], N[(N[(y * N[(z * N[(-1.0 + N[(y * N[(N[(y * -0.3333333333333333), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(-1.0 + x), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.2e12 or 1.95e18 < t

   1. Initial program 92.1%

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

   3. Taylor expanded in y around 0 99.9%

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

   4. Taylor expanded in z around inf 99.9%

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

   5. Taylor expanded in z around inf 99.9%

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + y \cdot \left(\color{blue}{-1 \cdot z} + y \cdot \left(z \cdot \left(-0.3333333333333333 \cdot y - 0.5\right)\right)\right)\right) - t \]
   6. Step-by-step derivation

      1. mul-1-neg 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 77.3%

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

   if -6.2e12 < t < 1.95e18

   1. Initial program 89.7%

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

      1. +-commutative 89.7%

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

      2. fma-define 89.7%

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

      3. sub-neg 89.7%

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

      4. metadata-eval 89.7%

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

      5. sub-neg 89.7%

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

      6. log1p-define 99.8%

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

      7. sub-neg 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 88.1%

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

      1. fmm-def 88.1%

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

      2. sub-neg 88.1%

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

      3. metadata-eval 88.1%

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

      4. +-commutative 88.1%

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

   7. Simplified 88.1%

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

   8. Taylor expanded in t around 0 87.2%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6200000000000 \lor \neg \left(t \leq 1.95 \cdot 10^{+18}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot \left(y \cdot -0.3333333333333333 - 0.5\right)\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(-1 + x\right) \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+112} \lor \neg \left(x \leq 8 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) - \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2e+112) (not (<= x 8e+28))) (* x (log y)) (- (- t) (log y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2e+112) || !(x <= 8e+28)) {
		tmp = x * log(y);
	} else {
		tmp = -t - log(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-2d+112)) .or. (.not. (x <= 8d+28))) then
        tmp = x * log(y)
    else
        tmp = -t - log(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2e+112) || !(x <= 8e+28)) {
		tmp = x * Math.log(y);
	} else {
		tmp = -t - Math.log(y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2e+112) or not (x <= 8e+28):
		tmp = x * math.log(y)
	else:
		tmp = -t - math.log(y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2e+112) || !(x <= 8e+28))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(-t) - log(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2e+112) || ~((x <= 8e+28)))
		tmp = x * log(y);
	else
		tmp = -t - log(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2e+112], N[Not[LessEqual[x, 8e+28]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[((-t) - N[Log[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9999999999999999e112 or 7.99999999999999967e28 < x

   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. +-commutative 96.6%

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

      2. fma-define 96.6%

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

      3. sub-neg 96.6%

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

      4. metadata-eval 96.6%

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

      5. sub-neg 96.6%

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

      6. log1p-define 99.7%

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

      7. sub-neg 99.7%

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

      8. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around -inf 96.6%

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

      1. associate-*r* 96.6%

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

      2. distribute-lft-out 96.6%

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

      3. associate-*r* 96.6%

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

      4. *-commutative 96.6%

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

      5. neg-mul-1 96.6%

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

      6. distribute-lft-neg-in 96.6%

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

      7. metadata-eval 96.6%

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

      8. *-lft-identity 96.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in x around inf 77.4%

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

   if -1.9999999999999999e112 < x < 7.99999999999999967e28

   1. Initial program 86.5%

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

      1. +-commutative 86.5%

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

      2. fma-define 86.5%

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

      3. sub-neg 86.5%

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

      4. metadata-eval 86.5%

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

      5. sub-neg 86.5%

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

      6. log1p-define 100.0%

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

      7. sub-neg 100.0%

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

      8. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 84.9%

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

      1. fmm-def 84.9%

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

      2. sub-neg 84.9%

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

      3. metadata-eval 84.9%

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

      4. +-commutative 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in x around 0 78.3%

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

      1. neg-mul-1 78.3%

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

   10. Simplified 78.3%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+112} \lor \neg \left(x \leq 8 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) - \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 88.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+195}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot \left(y \cdot -0.3333333333333333 - 0.5\right)\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(-1 + x\right) \cdot \log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.1e+195)
   (- (* y (* z (+ -1.0 (* y (- (* y -0.3333333333333333) 0.5))))) t)
   (- (+ y (* (+ -1.0 x) (log y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e+195) {
		tmp = (y * (z * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5))))) - t;
	} else {
		tmp = (y + ((-1.0 + x) * log(y))) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.1d+195)) then
        tmp = (y * (z * ((-1.0d0) + (y * ((y * (-0.3333333333333333d0)) - 0.5d0))))) - t
    else
        tmp = (y + (((-1.0d0) + x) * log(y))) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e+195) {
		tmp = (y * (z * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5))))) - t;
	} else {
		tmp = (y + ((-1.0 + x) * Math.log(y))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.1e+195:
		tmp = (y * (z * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5))))) - t
	else:
		tmp = (y + ((-1.0 + x) * math.log(y))) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.1e+195)
		tmp = Float64(Float64(y * Float64(z * Float64(-1.0 + Float64(y * Float64(Float64(y * -0.3333333333333333) - 0.5))))) - t);
	else
		tmp = Float64(Float64(y + Float64(Float64(-1.0 + x) * log(y))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.1e+195)
		tmp = (y * (z * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5))))) - t;
	else
		tmp = (y + ((-1.0 + x) * log(y))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.1e+195], N[(N[(y * N[(z * N[(-1.0 + N[(y * N[(N[(y * -0.3333333333333333), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(y + N[(N[(-1.0 + x), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e195

   1. Initial program 54.3%

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

   3. Taylor expanded in y around 0 99.9%

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

   4. Taylor expanded in z around inf 99.9%

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

   5. Taylor expanded in z around inf 99.9%

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + y \cdot \left(\color{blue}{-1 \cdot z} + y \cdot \left(z \cdot \left(-0.3333333333333333 \cdot y - 0.5\right)\right)\right)\right) - t \]
   6. Step-by-step derivation

      1. mul-1-neg 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 72.5%

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

   if -1.1e195 < z

   1. Initial program 95.0%

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

   3. Taylor expanded in y around 0 99.6%

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

   4. Taylor expanded in z around inf 99.6%

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

   5. Taylor expanded in z around 0 94.4%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+195}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot \left(y \cdot -0.3333333333333333 - 0.5\right)\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(y + \left(-1 + x\right) \cdot \log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+112} \lor \neg \left(x \leq 1.02 \cdot 10^{+38}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot \left(y \cdot -0.3333333333333333 - 0.5\right)\right)\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -2.8e+112) (not (<= x 1.02e+38)))
   (* x (log y))
   (- (* y (* z (+ -1.0 (* y (- (* y -0.3333333333333333) 0.5))))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -2.8e+112) || !(x <= 1.02e+38)) {
		tmp = x * log(y);
	} else {
		tmp = (y * (z * (-1.0 + (y * ((y * -0.3333333333333333) - 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 <= (-2.8d+112)) .or. (.not. (x <= 1.02d+38))) then
        tmp = x * log(y)
    else
        tmp = (y * (z * ((-1.0d0) + (y * ((y * (-0.3333333333333333d0)) - 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 <= -2.8e+112) || !(x <= 1.02e+38)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (y * (z * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5))))) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -2.8e+112) or not (x <= 1.02e+38):
		tmp = x * math.log(y)
	else:
		tmp = (y * (z * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5))))) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -2.8e+112) || !(x <= 1.02e+38))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(y * Float64(z * Float64(-1.0 + Float64(y * Float64(Float64(y * -0.3333333333333333) - 0.5))))) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -2.8e+112) || ~((x <= 1.02e+38)))
		tmp = x * log(y);
	else
		tmp = (y * (z * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5))))) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -2.8e+112], N[Not[LessEqual[x, 1.02e+38]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(z * N[(-1.0 + N[(y * N[(N[(y * -0.3333333333333333), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8000000000000001e112 or 1.02000000000000006e38 < x

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. fma-define 97.5%

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

      3. sub-neg 97.5%

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

      4. metadata-eval 97.5%

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

      5. sub-neg 97.5%

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

      6. log1p-define 99.7%

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

      7. sub-neg 99.7%

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

      8. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around -inf 97.5%

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

      1. associate-*r* 97.5%

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

      2. distribute-lft-out 97.5%

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

      3. associate-*r* 97.5%

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

      4. *-commutative 97.5%

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

      5. neg-mul-1 97.5%

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

      6. distribute-lft-neg-in 97.5%

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

      7. metadata-eval 97.5%

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

      8. *-lft-identity 97.5%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in x around inf 78.1%

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

   if -2.8000000000000001e112 < x < 1.02000000000000006e38

   1. Initial program 85.9%

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

   3. Taylor expanded in y around 0 99.6%

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

   4. Taylor expanded in z around inf 99.6%

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

   5. Taylor expanded in z around inf 99.5%

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + y \cdot \left(\color{blue}{-1 \cdot z} + y \cdot \left(z \cdot \left(-0.3333333333333333 \cdot y - 0.5\right)\right)\right)\right) - t \]
   6. Step-by-step derivation

      1. mul-1-neg 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in z around inf 61.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(y \cdot \left(-0.3333333333333333 \cdot y - 0.5\right) - 1\right)\right)} - t \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+112} \lor \neg \left(x \leq 1.02 \cdot 10^{+38}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot \left(y \cdot -0.3333333333333333 - 0.5\right)\right)\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.0% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.9%

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

   1. add-cbrt-cube 90.6%

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

   2. pow3 90.6%

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

4. Applied egg-rr 90.6%

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

5. Taylor expanded in y around 0 99.2%

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

   1. +-commutative 99.2%

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

   2. sub-neg 99.2%

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

   3. metadata-eval 99.2%

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

   4. +-commutative 99.2%

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

   5. mul-1-neg 99.2%

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

   6. sub-neg 99.2%

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

   7. metadata-eval 99.2%

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

   8. distribute-rgt-neg-out 99.2%

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

   9. distribute-neg-in 99.2%

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

   10. mul-1-neg 99.2%

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

   11. metadata-eval 99.2%

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

   12. +-commutative 99.2%

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

   13. mul-1-neg 99.2%

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

   14. unsub-neg 99.2%

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

7. Simplified 99.2%

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

8. Final simplification 99.2%

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

Alternative 12: 88.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+194}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot \left(y \cdot -0.3333333333333333 - 0.5\right)\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(-1 + x\right) \cdot \log y - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.5e+194)
   (- (* y (* z (+ -1.0 (* y (- (* y -0.3333333333333333) 0.5))))) t)
   (- (* (+ -1.0 x) (log y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.5e+194) {
		tmp = (y * (z * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5))))) - t;
	} else {
		tmp = ((-1.0 + x) * log(y)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-9.5d+194)) then
        tmp = (y * (z * ((-1.0d0) + (y * ((y * (-0.3333333333333333d0)) - 0.5d0))))) - t
    else
        tmp = (((-1.0d0) + x) * log(y)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.5e+194) {
		tmp = (y * (z * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5))))) - t;
	} else {
		tmp = ((-1.0 + x) * Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.5e+194:
		tmp = (y * (z * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5))))) - t
	else:
		tmp = ((-1.0 + x) * math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.5e+194)
		tmp = Float64(Float64(y * Float64(z * Float64(-1.0 + Float64(y * Float64(Float64(y * -0.3333333333333333) - 0.5))))) - t);
	else
		tmp = Float64(Float64(Float64(-1.0 + x) * log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.5e+194)
		tmp = (y * (z * (-1.0 + (y * ((y * -0.3333333333333333) - 0.5))))) - t;
	else
		tmp = ((-1.0 + x) * log(y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.5e+194], N[(N[(y * N[(z * N[(-1.0 + N[(y * N[(N[(y * -0.3333333333333333), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(N[(-1.0 + x), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5e194

   1. Initial program 54.3%

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

   3. Taylor expanded in y around 0 99.9%

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

   4. Taylor expanded in z around inf 99.9%

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

   5. Taylor expanded in z around inf 99.9%

      \[\leadsto \left(\left(x - 1\right) \cdot \log y + y \cdot \left(\color{blue}{-1 \cdot z} + y \cdot \left(z \cdot \left(-0.3333333333333333 \cdot y - 0.5\right)\right)\right)\right) - t \]
   6. Step-by-step derivation

      1. mul-1-neg 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 72.5%

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

   if -9.5e194 < z

   1. Initial program 95.0%

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

      1. +-commutative 95.0%

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

      2. fma-define 95.0%

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

      3. sub-neg 95.0%

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

      4. metadata-eval 95.0%

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

      5. sub-neg 95.0%

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

      6. log1p-define 99.8%

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

      7. sub-neg 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 94.3%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+194}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-1 + y \cdot \left(y \cdot -0.3333333333333333 - 0.5\right)\right)\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(-1 + x\right) \cdot \log y - t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 98.8% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.9%

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

3. Taylor expanded in y around 0 99.6%

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

4. Taylor expanded in z around inf 99.6%

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

5. Taylor expanded in z around inf 99.6%

   \[\leadsto \left(\left(x - 1\right) \cdot \log y + y \cdot \left(\color{blue}{-1 \cdot z} + y \cdot \left(z \cdot \left(-0.3333333333333333 \cdot y - 0.5\right)\right)\right)\right) - t \]
6. Step-by-step derivation

   1. mul-1-neg 99.6%

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

7. Simplified 99.6%

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

8. Taylor expanded in y around 0 99.1%

   \[\leadsto \color{blue}{\left(-1 \cdot \left(y \cdot z\right) + \log y \cdot \left(x - 1\right)\right)} - t \]
9. 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%

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

   5. mul-1-neg 99.1%

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

   6. unsub-neg 99.1%

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

   7. *-commutative 99.1%

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

10. Simplified 99.1%

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

11. Final simplification 99.1%

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

Alternative 14: 46.6% accurate, 14.3× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.9%

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

3. Taylor expanded in y around 0 99.6%

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

4. Taylor expanded in z around inf 99.6%

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

5. Taylor expanded in z around inf 99.6%

   \[\leadsto \left(\left(x - 1\right) \cdot \log y + y \cdot \left(\color{blue}{-1 \cdot z} + y \cdot \left(z \cdot \left(-0.3333333333333333 \cdot y - 0.5\right)\right)\right)\right) - t \]
6. Step-by-step derivation

   1. mul-1-neg 99.6%

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

7. Simplified 99.6%

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

8. Taylor expanded in z around inf 44.3%

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

9. Final simplification 44.3%

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

Alternative 15: 35.4% 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 90.9%

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

   1. +-commutative 90.9%

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

   2. fma-define 90.9%

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

   3. sub-neg 90.9%

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

   4. metadata-eval 90.9%

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

   5. sub-neg 90.9%

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

   6. log1p-define 99.8%

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

   7. sub-neg 99.8%

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

   8. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in t around inf 35.1%

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

   1. mul-1-neg 35.1%

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

7. Simplified 35.1%

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

Alternative 16: 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 90.9%

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

   1. +-commutative 90.9%

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

   2. fma-define 90.9%

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

   3. sub-neg 90.9%

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

   4. metadata-eval 90.9%

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

   5. sub-neg 90.9%

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

   6. log1p-define 99.8%

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

   7. sub-neg 99.8%

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

   8. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in t around inf 35.1%

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

   1. mul-1-neg 35.1%

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

7. Simplified 35.1%

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

   1. expm1-log1p-u 17.3%

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

   2. expm1-undefine 17.3%

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

9. Applied egg-rr 17.3%

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

    1. sub-neg 17.3%

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

    2. log1p-undefine 17.3%

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

    3. rem-exp-log 35.0%

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

    4. unsub-neg 35.0%

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

    5. metadata-eval 35.0%

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

11. Simplified 35.0%

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

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 2024157 
(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))