Average Error: 2.0 → 3.7
Time: 12.6s
Precision: binary64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \leq -7.112241749727716 \cdot 10^{-59} \lor \neg \left(t \leq -9.466108571856053 \cdot 10^{-300}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{y}{{z}^{y}}} \cdot \frac{\sqrt[3]{x}}{\frac{e^{b}}{{a}^{\left(t - 1\right)}}}\\ \end{array}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\begin{array}{l}
\mathbf{if}\;t \leq -7.112241749727716 \cdot 10^{-59} \lor \neg \left(t \leq -9.466108571856053 \cdot 10^{-300}\right):\\
\;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\

\mathbf{else}:\\
\;\;\;\;\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{y}{{z}^{y}}} \cdot \frac{\sqrt[3]{x}}{\frac{e^{b}}{{a}^{\left(t - 1\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 -7.112241749727716e-59) (not (<= t -9.466108571856053e-300)))
   (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y)
   (*
    (/ (* (cbrt x) (cbrt x)) (/ y (pow z y)))
    (/ (cbrt x) (/ (exp b) (pow a (- t 1.0)))))))
double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp(((y * log(z)) + ((t - 1.0) * log(a))) - b)) / y;
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.112241749727716e-59) || !(t <= -9.466108571856053e-300)) {
		tmp = (x * exp(((y * log(z)) + ((t - 1.0) * log(a))) - b)) / y;
	} else {
		tmp = ((cbrt(x) * cbrt(x)) / (y / pow(z, y))) * (cbrt(x) / (exp(b) / pow(a, (t - 1.0))));
	}
	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
Target11.4
Herbie3.7
\[\begin{array}{l} \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -7.11224174972771598e-59 or -9.4661085718560529e-300 < t

    1. Initial program 1.5

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

    if -7.11224174972771598e-59 < t < -9.4661085718560529e-300

    1. Initial program 4.3

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

    3. Applied associate-/l*_binary64_79364.0

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

    4. Simplified9.0

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

    6. Applied add-cube-cbrt_binary64_80269.3

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

    7. Applied times-frac_binary64_799712.3

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

  4. Final simplification3.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.112241749727716 \cdot 10^{-59} \lor \neg \left(t \leq -9.466108571856053 \cdot 10^{-300}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{y}{{z}^{y}}} \cdot \frac{\sqrt[3]{x}}{\frac{e^{b}}{{a}^{\left(t - 1\right)}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020280 
(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))