Average Error: 2.0 → 0.5
Time: 17.6s
Precision: binary64
\[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\]
↓
\[x \cdot {e}^{\left(y \cdot \left(\log z - t\right) - a \cdot \left(z + b\right)\right)}\]
x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}
↓
x \cdot {e}^{\left(y \cdot \left(\log z - t\right) - a \cdot \left(z + b\right)\right)}
(FPCore (x y z t a b)
 :precision binary64
 (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))
↓
(FPCore (x y z t a b)
 :precision binary64
 (* x (pow E (- (* y (- (log z) t)) (* a (+ z b))))))
double code(double x, double y, double z, double t, double a, double b) {
	return x * exp((y * (log(z) - t)) + (a * (log(1.0 - z) - b)));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	return x * pow(((double) M_E), ((y * (log(z) - t)) - (a * (z + b))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 2.0

    \[x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\log \left(1 - z\right) - b\right)}\]

  2. Taylor expanded around 0 0.5

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

  3. Simplified0.5

    \[\leadsto x \cdot e^{y \cdot \left(\log z - t\right) + a \cdot \left(\color{blue}{\left(-z\right)} - b\right)}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity_binary64_17830.5

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

  6. Applied exp-prod_binary64_18350.5

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

  7. Simplified0.5

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

  8. Final simplification0.5

    \[\leadsto x \cdot {e}^{\left(y \cdot \left(\log z - t\right) - a \cdot \left(z + b\right)\right)}\]

Reproduce

herbie shell --seed 2021098 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, B"
  :precision binary64
  (* x (exp (+ (* y (- (log z) t)) (* a (- (log (- 1.0 z)) b))))))