Average Error: 2.0 → 1.7
Time: 16.1s
Precision: binary64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq -693.8935985720383 \lor \neg \left(\left(t - 1\right) \cdot \log a \leq -308.7479833632883\right):\\ \;\;\;\;\frac{x \cdot e^{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{{a}^{\left(t - 1\right)}}{e^{b}} \cdot \frac{{z}^{y}}{y}\right)\\ \end{array}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\begin{array}{l}
\mathbf{if}\;\left(t - 1\right) \cdot \log a \leq -693.8935985720383 \lor \neg \left(\left(t - 1\right) \cdot \log a \leq -308.7479833632883\right):\\
\;\;\;\;\frac{x \cdot e^{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right) - b}}{y}\\

\mathbf{else}:\\
\;\;\;\;x \cdot \left(\frac{{a}^{\left(t - 1\right)}}{e^{b}} \cdot \frac{{z}^{y}}{y}\right)\\

\end{array}
(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))
↓
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (* (- t 1.0) (log a)) -693.8935985720383)
         (not (<= (* (- t 1.0) (log a)) -308.7479833632883)))
   (/ (* x (exp (- (+ (* (- t 1.0) (log a)) (* y (log z))) b))) y)
   (* x (* (/ (pow a (- t 1.0)) (exp b)) (/ (pow z y) y)))))
double code(double x, double y, double z, double t, double a, double b) {
	return (((double) (x * ((double) exp(((double) (((double) (((double) (y * ((double) log(z)))) + ((double) (((double) (t - 1.0)) * ((double) log(a)))))) - b)))))) / y);
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((((double) (((double) (t - 1.0)) * ((double) log(a)))) <= -693.8935985720383) || !(((double) (((double) (t - 1.0)) * ((double) log(a)))) <= -308.7479833632883))) {
		tmp = (((double) (x * ((double) exp(((double) (((double) (((double) (((double) (t - 1.0)) * ((double) log(a)))) + ((double) (y * ((double) log(z)))))) - b)))))) / y);
	} else {
		tmp = ((double) (x * ((double) ((((double) pow(a, ((double) (t - 1.0)))) / ((double) exp(b))) * (((double) pow(z, y)) / y)))));
	}
	return tmp;
}

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

Target

Original2.0
Target11.5
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (- t 1.0) (log a)) < -693.893598572038286 or -308.74798336328831 < (* (- t 1.0) (log a))

    1. Initial program Error: 0.9 bits

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

    if -693.893598572038286 < (* (- t 1.0) (log a)) < -308.74798336328831

    1. Initial program Error: 7.9 bits

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

    2. SimplifiedError: 5.9 bits

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

  4. Final simplificationError: 1.7 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \leq -693.8935985720383 \lor \neg \left(\left(t - 1\right) \cdot \log a \leq -308.7479833632883\right):\\ \;\;\;\;\frac{x \cdot e^{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{{a}^{\left(t - 1\right)}}{e^{b}} \cdot \frac{{z}^{y}}{y}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020203 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))