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

Percentage Accurate: 89.5% → 99.8%

Time: 22.1s

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: 89.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

   1. +-commutative 87.9%

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

   2. fma-def 87.9%

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

   3. sub-neg 87.9%

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

   4. metadata-eval 87.9%

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

   5. sub-neg 87.9%

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

   6. log1p-def 99.9%

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

   7. sub-neg 99.9%

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

   8. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 99.6% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

3. Taylor expanded in z around inf 87.6%

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

   1. *-commutative 87.6%

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

   2. sub-neg 87.6%

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

   3. mul-1-neg 87.6%

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

   4. log1p-def 99.5%

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

   5. mul-1-neg 99.5%

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

5. Simplified 99.5%

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

6. Taylor expanded in x around 0 87.6%

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

   1. mul-1-neg 87.6%

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

   2. log-rec 87.6%

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

   3. associate-+r+ 87.6%

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

   4. +-commutative 87.6%

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

   5. log-rec 87.6%

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

   6. sub-neg 87.6%

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

   7. *-lft-identity 87.6%

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

   8. distribute-rgt-out-- 87.6%

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

   9. +-commutative 87.6%

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

   10. associate--l+ 87.6%

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

   11. fma-def 87.6%

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

   12. sub-neg 87.6%

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

   13. log1p-def 99.5%

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

8. Simplified 99.5%

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

9. Final simplification 99.5%

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

Alternative 3: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

public static double code(double x, double y, double z, double t) {
	return ((z * Math.log1p(-y)) + ((-1.0 + x) * Math.log(y))) - t;
}

Python

def code(x, y, z, t):
	return ((z * math.log1p(-y)) + ((-1.0 + x) * math.log(y))) - t

Julia

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

3. Taylor expanded in z around inf 87.6%

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

   1. *-commutative 87.6%

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

   2. sub-neg 87.6%

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

   3. mul-1-neg 87.6%

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

   4. log1p-def 99.5%

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

   5. mul-1-neg 99.5%

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

5. Simplified 99.5%

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

6. Final simplification 99.5%

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

Alternative 4: 99.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

   1. *-commutative 87.9%

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

   2. sub-neg 87.9%

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

   3. metadata-eval 87.9%

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

   4. distribute-lft-in 87.9%

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

4. Applied egg-rr 87.9%

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

   1. distribute-lft-out 87.9%

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

   2. metadata-eval 87.9%

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

   3. sub-neg 87.9%

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

   4. add-sqr-sqrt 20.7%

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

   5. associate-*r* 20.7%

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

   6. sub-neg 20.7%

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

   7. metadata-eval 20.7%

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

   8. sub-neg 20.7%

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

   9. metadata-eval 20.7%

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

6. Applied egg-rr 20.7%

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

7. Taylor expanded in y around 0 98.9%

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

   1. +-commutative 98.9%

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

   2. sub-neg 98.9%

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

   3. metadata-eval 98.9%

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

   4. +-commutative 98.9%

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

   5. mul-1-neg 98.9%

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

   6. unsub-neg 98.9%

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

   7. +-commutative 98.9%

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

   8. sub-neg 98.9%

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

   9. metadata-eval 98.9%

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

   10. +-commutative 98.9%

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

9. Simplified 98.9%

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

10. Taylor expanded in y around 0 98.9%

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

    1. fma-def 99.0%

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

    2. sub-neg 99.0%

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

    3. metadata-eval 99.0%

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

12. Simplified 99.0%

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

13. Final simplification 99.0%

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

Alternative 5: 85.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-\log y\right) - t\\ t_2 := x \cdot \log y - t\\ \mathbf{if}\;x \leq -37000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-257}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-275}:\\ \;\;\;\;y \cdot \left(1 - z\right) - t\\ \mathbf{elif}\;x \leq 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (- (log y)) t)) (t_2 (- (* x (log y)) t)))
   (if (<= x -37000000000.0)
     t_2
     (if (<= x -5.5e-257)
       t_1
       (if (<= x 2.4e-275) (- (* y (- 1.0 z)) t) (if (<= x 1e-31) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -log(y) - t;
	double t_2 = (x * log(y)) - t;
	double tmp;
	if (x <= -37000000000.0) {
		tmp = t_2;
	} else if (x <= -5.5e-257) {
		tmp = t_1;
	} else if (x <= 2.4e-275) {
		tmp = (y * (1.0 - z)) - t;
	} else if (x <= 1e-31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -log(y) - t
    t_2 = (x * log(y)) - t
    if (x <= (-37000000000.0d0)) then
        tmp = t_2
    else if (x <= (-5.5d-257)) then
        tmp = t_1
    else if (x <= 2.4d-275) then
        tmp = (y * (1.0d0 - z)) - t
    else if (x <= 1d-31) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -Math.log(y) - t;
	double t_2 = (x * Math.log(y)) - t;
	double tmp;
	if (x <= -37000000000.0) {
		tmp = t_2;
	} else if (x <= -5.5e-257) {
		tmp = t_1;
	} else if (x <= 2.4e-275) {
		tmp = (y * (1.0 - z)) - t;
	} else if (x <= 1e-31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -math.log(y) - t
	t_2 = (x * math.log(y)) - t
	tmp = 0
	if x <= -37000000000.0:
		tmp = t_2
	elif x <= -5.5e-257:
		tmp = t_1
	elif x <= 2.4e-275:
		tmp = (y * (1.0 - z)) - t
	elif x <= 1e-31:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-log(y)) - t)
	t_2 = Float64(Float64(x * log(y)) - t)
	tmp = 0.0
	if (x <= -37000000000.0)
		tmp = t_2;
	elseif (x <= -5.5e-257)
		tmp = t_1;
	elseif (x <= 2.4e-275)
		tmp = Float64(Float64(y * Float64(1.0 - z)) - t);
	elseif (x <= 1e-31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -log(y) - t;
	t_2 = (x * log(y)) - t;
	tmp = 0.0;
	if (x <= -37000000000.0)
		tmp = t_2;
	elseif (x <= -5.5e-257)
		tmp = t_1;
	elseif (x <= 2.4e-275)
		tmp = (y * (1.0 - z)) - t;
	elseif (x <= 1e-31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-N[Log[y], $MachinePrecision]) - t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]}, If[LessEqual[x, -37000000000.0], t$95$2, If[LessEqual[x, -5.5e-257], t$95$1, If[LessEqual[x, 2.4e-275], N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], If[LessEqual[x, 1e-31], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7e10 or 1e-31 < x

   1. Initial program 93.6%

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

   3. Taylor expanded in z around inf 93.6%

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

      1. *-commutative 93.6%

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

      2. sub-neg 93.6%

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

      3. mul-1-neg 93.6%

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

      4. log1p-def 99.7%

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

      5. mul-1-neg 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in x around inf 92.8%

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

      1. *-commutative 92.8%

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

   8. Simplified 92.8%

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

   if -3.7e10 < x < -5.50000000000000025e-257 or 2.39999999999999991e-275 < x < 1e-31

   1. Initial program 86.6%

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

      1. +-commutative 86.6%

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

      2. fma-def 86.6%

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

      3. sub-neg 86.6%

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

      4. metadata-eval 86.6%

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

      5. sub-neg 86.6%

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

      6. log1p-def 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 84.5%

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

      1. fma-neg 84.5%

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

      2. sub-neg 84.5%

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

      3. metadata-eval 84.5%

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

      4. +-commutative 84.5%

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

   7. Simplified 84.5%

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

   8. Taylor expanded in x around 0 83.8%

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

      1. mul-1-neg 83.8%

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

   10. Simplified 83.8%

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

   if -5.50000000000000025e-257 < x < 2.39999999999999991e-275

   1. Initial program 48.5%

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

      1. *-commutative 48.5%

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

      2. sub-neg 48.5%

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

      3. metadata-eval 48.5%

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

      4. distribute-lft-in 48.5%

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

   4. Applied egg-rr 48.5%

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

      1. distribute-lft-out 48.5%

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

      2. metadata-eval 48.5%

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

      3. sub-neg 48.5%

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

      4. add-sqr-sqrt 0.0%

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

      5. associate-*r* 0.0%

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

      6. sub-neg 0.0%

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

      7. metadata-eval 0.0%

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

      8. sub-neg 0.0%

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

      9. metadata-eval 0.0%

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

   6. Applied egg-rr 0.0%

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

   7. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

      4. +-commutative 100.0%

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

      5. mul-1-neg 100.0%

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

      6. unsub-neg 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. +-commutative 100.0%

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

   9. Simplified 100.0%

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

   10. Taylor expanded in y around inf 78.0%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -37000000000:\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-257}:\\ \;\;\;\;\left(-\log y\right) - t\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-275}:\\ \;\;\;\;y \cdot \left(1 - z\right) - t\\ \mathbf{elif}\;x \leq 10^{-31}:\\ \;\;\;\;\left(-\log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log y - t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -37000000000 \lor \neg \left(x \leq 4.6 \cdot 10^{-35}\right):\\ \;\;\;\;\left(x \cdot \log y - z \cdot y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z \cdot y\right) - \log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -37000000000.0) (not (<= x 4.6e-35)))
   (- (- (* x (log y)) (* z y)) t)
   (- (- (- (* z y)) (log y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -37000000000.0) || !(x <= 4.6e-35)) {
		tmp = ((x * log(y)) - (z * y)) - t;
	} else {
		tmp = (-(z * y) - log(y)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-37000000000.0d0)) .or. (.not. (x <= 4.6d-35))) then
        tmp = ((x * log(y)) - (z * y)) - t
    else
        tmp = (-(z * y) - log(y)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -37000000000.0) || !(x <= 4.6e-35)) {
		tmp = ((x * Math.log(y)) - (z * y)) - t;
	} else {
		tmp = (-(z * y) - Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -37000000000.0) or not (x <= 4.6e-35):
		tmp = ((x * math.log(y)) - (z * y)) - t
	else:
		tmp = (-(z * y) - math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -37000000000.0) || !(x <= 4.6e-35))
		tmp = Float64(Float64(Float64(x * log(y)) - Float64(z * y)) - t);
	else
		tmp = Float64(Float64(Float64(-Float64(z * y)) - log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -37000000000.0) || ~((x <= 4.6e-35)))
		tmp = ((x * log(y)) - (z * y)) - t;
	else
		tmp = (-(z * y) - log(y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -37000000000.0], N[Not[LessEqual[x, 4.6e-35]], $MachinePrecision]], N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[((-N[(z * y), $MachinePrecision]) - N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7e10 or 4.5999999999999998e-35 < x

   1. Initial program 93.0%

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

   3. Taylor expanded in z around inf 93.0%

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

      1. *-commutative 93.0%

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

      2. sub-neg 93.0%

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

      3. mul-1-neg 93.0%

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

      4. log1p-def 99.7%

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

      5. mul-1-neg 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around 0 99.3%

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

      1. mul-1-neg 99.3%

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

      2. *-commutative 99.3%

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

      3. distribute-rgt-neg-in 99.3%

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

   8. Simplified 99.3%

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

   9. Taylor expanded in x around inf 99.1%

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

       1. *-commutative 99.1%

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

   11. Simplified 99.1%

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

       1. distribute-rgt-neg-out 99.1%

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

       2. unsub-neg 99.1%

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

   13. Applied egg-rr 99.1%

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

   if -3.7e10 < x < 4.5999999999999998e-35

   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. Add Preprocessing

   3. Taylor expanded in z around inf 82.1%

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

      1. *-commutative 82.1%

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

      2. sub-neg 82.1%

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

      3. mul-1-neg 82.1%

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

      4. log1p-def 99.3%

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

      5. mul-1-neg 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in y around 0 98.5%

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

      1. mul-1-neg 98.5%

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

      2. *-commutative 98.5%

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

      3. distribute-rgt-neg-in 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in x around 0 97.9%

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

       1. mul-1-neg 97.9%

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

       2. unsub-neg 97.9%

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

       3. mul-1-neg 97.9%

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

   11. Simplified 97.9%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -37000000000 \lor \neg \left(x \leq 4.6 \cdot 10^{-35}\right):\\ \;\;\;\;\left(x \cdot \log y - z \cdot y\right) - t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z \cdot y\right) - \log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-15} \lor \neg \left(x \leq 1.8 \cdot 10^{-22}\right):\\ \;\;\;\;\left(-1 + x\right) \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z \cdot y\right) - \log y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -9.5e-15) (not (<= x 1.8e-22)))
   (- (* (+ -1.0 x) (log y)) t)
   (- (- (- (* z y)) (log y)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9.5e-15) || !(x <= 1.8e-22)) {
		tmp = ((-1.0 + x) * log(y)) - t;
	} else {
		tmp = (-(z * y) - log(y)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-9.5d-15)) .or. (.not. (x <= 1.8d-22))) then
        tmp = (((-1.0d0) + x) * log(y)) - t
    else
        tmp = (-(z * y) - log(y)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -9.5e-15) || !(x <= 1.8e-22)) {
		tmp = ((-1.0 + x) * Math.log(y)) - t;
	} else {
		tmp = (-(z * y) - Math.log(y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -9.5e-15) or not (x <= 1.8e-22):
		tmp = ((-1.0 + x) * math.log(y)) - t
	else:
		tmp = (-(z * y) - math.log(y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -9.5e-15) || !(x <= 1.8e-22))
		tmp = Float64(Float64(Float64(-1.0 + x) * log(y)) - t);
	else
		tmp = Float64(Float64(Float64(-Float64(z * y)) - log(y)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -9.5e-15) || ~((x <= 1.8e-22)))
		tmp = ((-1.0 + x) * log(y)) - t;
	else
		tmp = (-(z * y) - log(y)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -9.5e-15], N[Not[LessEqual[x, 1.8e-22]], $MachinePrecision]], N[(N[(N[(-1.0 + x), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[((-N[(z * y), $MachinePrecision]) - N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5000000000000005e-15 or 1.7999999999999999e-22 < x

   1. Initial program 95.3%

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

      1. +-commutative 95.3%

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

      2. fma-def 95.3%

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

      3. sub-neg 95.3%

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

      4. metadata-eval 95.3%

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

      5. sub-neg 95.3%

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

      6. log1p-def 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 y around 0 94.7%

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

   if -9.5000000000000005e-15 < x < 1.7999999999999999e-22

   1. Initial program 80.2%

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

   3. Taylor expanded in z around inf 79.5%

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

      1. *-commutative 79.5%

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

      2. sub-neg 79.5%

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

      3. mul-1-neg 79.5%

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

      4. log1p-def 99.3%

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

      5. mul-1-neg 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in y around 0 98.5%

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

      1. mul-1-neg 98.5%

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

      2. *-commutative 98.5%

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

      3. distribute-rgt-neg-in 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in x around 0 98.5%

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

       1. mul-1-neg 98.5%

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

       2. unsub-neg 98.5%

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

       3. mul-1-neg 98.5%

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

   11. Simplified 98.5%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-15} \lor \neg \left(x \leq 1.8 \cdot 10^{-22}\right):\\ \;\;\;\;\left(-1 + x\right) \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z \cdot y\right) - \log y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -38000000000 \lor \neg \left(t \leq 0.00092\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;t + \left(-1 + x\right) \cdot \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -38000000000.0) (not (<= t 0.00092)))
   (- (* x (log y)) t)
   (+ t (* (+ -1.0 x) (log y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -38000000000.0) || !(t <= 0.00092)) {
		tmp = (x * log(y)) - t;
	} else {
		tmp = t + ((-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 <= (-38000000000.0d0)) .or. (.not. (t <= 0.00092d0))) then
        tmp = (x * log(y)) - t
    else
        tmp = t + (((-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 <= -38000000000.0) || !(t <= 0.00092)) {
		tmp = (x * Math.log(y)) - t;
	} else {
		tmp = t + ((-1.0 + x) * Math.log(y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -38000000000.0) or not (t <= 0.00092):
		tmp = (x * math.log(y)) - t
	else:
		tmp = t + ((-1.0 + x) * math.log(y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -38000000000.0) || !(t <= 0.00092))
		tmp = Float64(Float64(x * log(y)) - t);
	else
		tmp = Float64(t + 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 <= -38000000000.0) || ~((t <= 0.00092)))
		tmp = (x * log(y)) - t;
	else
		tmp = t + ((-1.0 + x) * log(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -38000000000.0], N[Not[LessEqual[t, 0.00092]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(t + N[(N[(-1.0 + x), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.8e10 or 9.2000000000000003e-4 < 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. Add Preprocessing

   3. Taylor expanded in z around inf 94.2%

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

      1. *-commutative 94.2%

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

      2. sub-neg 94.2%

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

      3. mul-1-neg 94.2%

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

      4. log1p-def 99.9%

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

      5. mul-1-neg 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in x around inf 92.0%

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

      1. *-commutative 92.0%

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

   8. Simplified 92.0%

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

   if -3.8e10 < t < 9.2000000000000003e-4

   1. Initial program 82.6%

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

      1. +-commutative 82.6%

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

      2. fma-def 82.6%

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

      3. sub-neg 82.6%

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

      4. metadata-eval 82.6%

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

      5. sub-neg 82.6%

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

      6. log1p-def 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 81.1%

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

      1. fma-neg 81.1%

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

      2. sub-neg 81.1%

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

      3. metadata-eval 81.1%

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

      4. +-commutative 81.1%

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

   7. Simplified 81.1%

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

      1. fma-udef 81.1%

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

      2. +-commutative 81.1%

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

      3. metadata-eval 81.1%

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

      4. sub-neg 81.1%

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

      5. *-commutative 81.1%

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

      6. sub-neg 81.1%

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

      7. metadata-eval 81.1%

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

      8. add-sqr-sqrt 43.7%

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

      9. sqrt-unprod 80.9%

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

      10. sqr-neg 80.9%

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

      11. sqrt-unprod 37.2%

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

      12. add-sqr-sqrt 80.1%

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

   9. Applied egg-rr 80.1%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -38000000000 \lor \neg \left(t \leq 0.00092\right):\\ \;\;\;\;x \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;t + \left(-1 + x\right) \cdot \log y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+143}:\\ \;\;\;\;\left(-z \cdot y\right) - t\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+85}:\\ \;\;\;\;\left(-\log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.55e+143)
   (- (- (* z y)) t)
   (if (<= z 6.2e+85) (- (- (log y)) t) (- (* y (- 1.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.55e+143) {
		tmp = -(z * y) - t;
	} else if (z <= 6.2e+85) {
		tmp = -log(y) - t;
	} else {
		tmp = (y * (1.0 - z)) - t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.55d+143)) then
        tmp = -(z * y) - t
    else if (z <= 6.2d+85) then
        tmp = -log(y) - t
    else
        tmp = (y * (1.0d0 - z)) - t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.55e+143) {
		tmp = -(z * y) - t;
	} else if (z <= 6.2e+85) {
		tmp = -Math.log(y) - t;
	} else {
		tmp = (y * (1.0 - z)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.55e+143:
		tmp = -(z * y) - t
	elif z <= 6.2e+85:
		tmp = -math.log(y) - t
	else:
		tmp = (y * (1.0 - z)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.55e+143)
		tmp = Float64(Float64(-Float64(z * y)) - t);
	elseif (z <= 6.2e+85)
		tmp = Float64(Float64(-log(y)) - t);
	else
		tmp = Float64(Float64(y * Float64(1.0 - z)) - t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.55e+143)
		tmp = -(z * y) - t;
	elseif (z <= 6.2e+85)
		tmp = -log(y) - t;
	else
		tmp = (y * (1.0 - z)) - t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.55e+143], N[((-N[(z * y), $MachinePrecision]) - t), $MachinePrecision], If[LessEqual[z, 6.2e+85], N[((-N[Log[y], $MachinePrecision]) - t), $MachinePrecision], N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.55000000000000019e143

   1. Initial program 58.9%

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

   3. Taylor expanded in z around inf 58.9%

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

      1. *-commutative 58.9%

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

      2. sub-neg 58.9%

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

      3. mul-1-neg 58.9%

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

      4. log1p-def 99.8%

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

      5. mul-1-neg 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 97.8%

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

      1. mul-1-neg 97.8%

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

      2. *-commutative 97.8%

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

      3. distribute-rgt-neg-in 97.8%

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

   8. Simplified 97.8%

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

   9. Taylor expanded in y around inf 60.0%

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

       1. mul-1-neg 60.0%

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

       2. *-commutative 60.0%

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

       3. distribute-rgt-neg-in 60.0%

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

   11. Simplified 60.0%

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

   if -2.55000000000000019e143 < z < 6.20000000000000023e85

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      2. fma-def 98.0%

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

      3. sub-neg 98.0%

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

      4. metadata-eval 98.0%

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

      5. sub-neg 98.0%

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

      6. log1p-def 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 97.5%

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

      1. fma-neg 97.5%

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

      2. sub-neg 97.5%

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

      3. metadata-eval 97.5%

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

      4. +-commutative 97.5%

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

   7. Simplified 97.5%

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

   8. Taylor expanded in x around 0 61.0%

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

      1. mul-1-neg 61.0%

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

   10. Simplified 61.0%

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

   if 6.20000000000000023e85 < z

   1. Initial program 70.3%

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

      1. *-commutative 70.3%

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

      2. sub-neg 70.3%

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

      3. metadata-eval 70.3%

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

      4. distribute-lft-in 70.3%

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

   4. Applied egg-rr 70.3%

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

      1. distribute-lft-out 70.3%

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

      2. metadata-eval 70.3%

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

      3. sub-neg 70.3%

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

      4. add-sqr-sqrt 25.4%

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

      5. associate-*r* 25.4%

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

      6. sub-neg 25.4%

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

      7. metadata-eval 25.4%

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

      8. sub-neg 25.4%

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

      9. metadata-eval 25.4%

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

   6. Applied egg-rr 25.4%

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

   7. Taylor expanded in y around 0 98.0%

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

      1. +-commutative 98.0%

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

      2. sub-neg 98.0%

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

      3. metadata-eval 98.0%

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

      4. +-commutative 98.0%

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

      5. mul-1-neg 98.0%

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

      6. unsub-neg 98.0%

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

      7. +-commutative 98.0%

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

      8. sub-neg 98.0%

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

      9. metadata-eval 98.0%

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

      10. +-commutative 98.0%

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

   9. Simplified 98.0%

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

   10. Taylor expanded in y around inf 57.2%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+143}:\\ \;\;\;\;\left(-z \cdot y\right) - t\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+85}:\\ \;\;\;\;\left(-\log y\right) - t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - z\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.1% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

   1. *-commutative 87.9%

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

   2. sub-neg 87.9%

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

   3. metadata-eval 87.9%

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

   4. distribute-lft-in 87.9%

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

4. Applied egg-rr 87.9%

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

   1. distribute-lft-out 87.9%

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

   2. metadata-eval 87.9%

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

   3. sub-neg 87.9%

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

   4. add-sqr-sqrt 20.7%

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

   5. associate-*r* 20.7%

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

   6. sub-neg 20.7%

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

   7. metadata-eval 20.7%

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

   8. sub-neg 20.7%

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

   9. metadata-eval 20.7%

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

6. Applied egg-rr 20.7%

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

7. Taylor expanded in y around 0 98.9%

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

   1. +-commutative 98.9%

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

   2. sub-neg 98.9%

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

   3. metadata-eval 98.9%

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

   4. +-commutative 98.9%

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

   5. mul-1-neg 98.9%

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

   6. unsub-neg 98.9%

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

   7. +-commutative 98.9%

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

   8. sub-neg 98.9%

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

   9. metadata-eval 98.9%

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

   10. +-commutative 98.9%

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

9. Simplified 98.9%

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

10. Final simplification 98.9%

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

Alternative 11: 88.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.95 \cdot 10^{+170}:\\ \;\;\;\;\left(-1 + x\right) \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{log1p}\left(-y\right) - t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z 2.95e+170) (- (* (+ -1.0 x) (log y)) t) (- (* z (log1p (- y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 2.95e+170) {
		tmp = ((-1.0 + x) * log(y)) - t;
	} else {
		tmp = (z * log1p(-y)) - t;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 2.95e+170) {
		tmp = ((-1.0 + x) * Math.log(y)) - t;
	} else {
		tmp = (z * Math.log1p(-y)) - t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= 2.95e+170:
		tmp = ((-1.0 + x) * math.log(y)) - t
	else:
		tmp = (z * math.log1p(-y)) - t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= 2.95e+170)
		tmp = Float64(Float64(Float64(-1.0 + x) * log(y)) - t);
	else
		tmp = Float64(Float64(z * log1p(Float64(-y))) - t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, 2.95e+170], N[(N[(N[(-1.0 + x), $MachinePrecision] * N[Log[y], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision], N[(N[(z * N[Log[1 + (-y)], $MachinePrecision]), $MachinePrecision] - t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.9499999999999997e170

   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. +-commutative 91.8%

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

      2. fma-def 91.8%

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

      3. sub-neg 91.8%

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

      4. metadata-eval 91.8%

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

      5. sub-neg 91.8%

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

      6. log1p-def 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 91.0%

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

   if 2.9499999999999997e170 < z

   1. Initial program 56.1%

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

   3. Taylor expanded in z around inf 56.1%

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

      1. *-commutative 56.1%

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

      2. sub-neg 56.1%

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

      3. mul-1-neg 56.1%

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

      4. log1p-def 99.9%

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

      5. mul-1-neg 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in z around inf 28.6%

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

      1. sub-neg 28.6%

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

      2. log1p-def 70.1%

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

   8. Simplified 70.1%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.95 \cdot 10^{+170}:\\ \;\;\;\;\left(-1 + x\right) \cdot \log y - t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \mathsf{log1p}\left(-y\right) - t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.0% 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 87.9%

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

3. Taylor expanded in z around inf 87.6%

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

   1. *-commutative 87.6%

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

   2. sub-neg 87.6%

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

   3. mul-1-neg 87.6%

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

   4. log1p-def 99.5%

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

   5. mul-1-neg 99.5%

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

5. Simplified 99.5%

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

6. Taylor expanded in y around 0 98.9%

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

   1. mul-1-neg 98.9%

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

   2. *-commutative 98.9%

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

   3. distribute-rgt-neg-in 98.9%

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

8. Simplified 98.9%

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

9. Final simplification 98.9%

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

Alternative 13: 46.3% accurate, 30.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

   1. *-commutative 87.9%

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

   2. sub-neg 87.9%

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

   3. metadata-eval 87.9%

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

   4. distribute-lft-in 87.9%

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

4. Applied egg-rr 87.9%

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

   1. distribute-lft-out 87.9%

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

   2. metadata-eval 87.9%

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

   3. sub-neg 87.9%

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

   4. add-sqr-sqrt 20.7%

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

   5. associate-*r* 20.7%

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

   6. sub-neg 20.7%

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

   7. metadata-eval 20.7%

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

   8. sub-neg 20.7%

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

   9. metadata-eval 20.7%

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

6. Applied egg-rr 20.7%

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

7. Taylor expanded in y around 0 98.9%

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

   1. +-commutative 98.9%

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

   2. sub-neg 98.9%

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

   3. metadata-eval 98.9%

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

   4. +-commutative 98.9%

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

   5. mul-1-neg 98.9%

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

   6. unsub-neg 98.9%

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

   7. +-commutative 98.9%

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

   8. sub-neg 98.9%

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

   9. metadata-eval 98.9%

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

   10. +-commutative 98.9%

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

9. Simplified 98.9%

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

10. Taylor expanded in y around inf 43.5%

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

11. Final simplification 43.5%

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

Alternative 14: 46.1% accurate, 35.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.9%

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

3. Taylor expanded in z around inf 87.6%

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

   1. *-commutative 87.6%

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

   2. sub-neg 87.6%

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

   3. mul-1-neg 87.6%

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

   4. log1p-def 99.5%

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

   5. mul-1-neg 99.5%

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

5. Simplified 99.5%

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

6. Taylor expanded in y around 0 98.9%

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

   1. mul-1-neg 98.9%

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

   2. *-commutative 98.9%

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

   3. distribute-rgt-neg-in 98.9%

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

8. Simplified 98.9%

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

9. Taylor expanded in y around inf 43.3%

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

    1. mul-1-neg 43.3%

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

    2. *-commutative 43.3%

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

    3. distribute-rgt-neg-in 43.3%

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

11. Simplified 43.3%

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

12. Final simplification 43.3%

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

Alternative 15: 35.9% 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 87.9%

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

   1. +-commutative 87.9%

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

   2. fma-def 87.9%

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

   3. sub-neg 87.9%

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

   4. metadata-eval 87.9%

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

   5. sub-neg 87.9%

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

   6. log1p-def 99.9%

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

   7. sub-neg 99.9%

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

   8. metadata-eval 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in t around inf 32.1%

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

   1. neg-mul-1 32.1%

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

7. Simplified 32.1%

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

8. Final simplification 32.1%

   \[\leadsto -t \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024026 
(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))