Average Error: 1.9 → 2.0
Time: 9.9s
Precision: binary64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \le -1.18253629801421881 \cdot 10^{41} \lor \neg \left(\left(t - 1\right) \cdot \log a \le -620.375444517756591\right):\\ \;\;\;\;\frac{x \cdot e^{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left({z}^{y} \cdot \frac{{\left(\sqrt{a}\right)}^{\left(t - 1\right)} \cdot \frac{{\left(\sqrt{a}\right)}^{\left(t - 1\right)}}{e^{b}}}{y}\right)\\ \end{array}\]
\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 \le -1.18253629801421881 \cdot 10^{41} \lor \neg \left(\left(t - 1\right) \cdot \log a \le -620.375444517756591\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({z}^{y} \cdot \frac{{\left(\sqrt{a}\right)}^{\left(t - 1\right)} \cdot \frac{{\left(\sqrt{a}\right)}^{\left(t - 1\right)}}{e^{b}}}{y}\right)\\

\end{array}
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((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 VAR;
	if (((((double) (((double) (t - 1.0)) * ((double) log(a)))) <= -1.1825362980142188e+41) || !(((double) (((double) (t - 1.0)) * ((double) log(a)))) <= -620.3754445177566))) {
		VAR = ((double) (((double) (x * ((double) exp(((double) (((double) (((double) (((double) (t - 1.0)) * ((double) log(a)))) + ((double) (y * ((double) log(z)))))) - b)))))) / y));
	} else {
		VAR = ((double) (x * ((double) (((double) pow(z, y)) * ((double) (((double) (((double) pow(((double) sqrt(a)), ((double) (t - 1.0)))) * ((double) (((double) pow(((double) sqrt(a)), ((double) (t - 1.0)))) / ((double) exp(b)))))) / y))))));
	}
	return VAR;
}

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

Original1.9
Target11.0
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;t \lt -0.88458485041274715:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.22883740731:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (- t 1.0) (log a)) < -1.18253629801421881e41 or -620.375444517756591 < (* (- t 1.0) (log a))

    1. Initial program 1.7

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

    if -1.18253629801421881e41 < (* (- t 1.0) (log a)) < -620.375444517756591

    1. Initial program 4.1

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

    2. Simplified5.6

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t - 1\right)}}{e^{b}}}{y}\right)}\]
    3. Using strategy rm

    4. Applied *-un-lft-identity5.6

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

    5. Applied add-sqr-sqrt5.6

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

    6. Applied unpow-prod-down5.6

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

    7. Applied times-frac5.6

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

    8. Simplified5.6

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \le -1.18253629801421881 \cdot 10^{41} \lor \neg \left(\left(t - 1\right) \cdot \log a \le -620.375444517756591\right):\\ \;\;\;\;\frac{x \cdot e^{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left({z}^{y} \cdot \frac{{\left(\sqrt{a}\right)}^{\left(t - 1\right)} \cdot \frac{{\left(\sqrt{a}\right)}^{\left(t - 1\right)}}{e^{b}}}{y}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020181 
(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))