Average Error: 2.0 → 1.1
Time: 38.9s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{x}{\frac{\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \sqrt[3]{\sqrt[3]{y}}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{x}{\frac{\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \sqrt[3]{\sqrt[3]{y}}}{\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}}}
double f(double x, double y, double z, double t, double a, double b) {
        double r31653192 = x;
        double r31653193 = y;
        double r31653194 = z;
        double r31653195 = log(r31653194);
        double r31653196 = r31653193 * r31653195;
        double r31653197 = t;
        double r31653198 = 1.0;
        double r31653199 = r31653197 - r31653198;
        double r31653200 = a;
        double r31653201 = log(r31653200);
        double r31653202 = r31653199 * r31653201;
        double r31653203 = r31653196 + r31653202;
        double r31653204 = b;
        double r31653205 = r31653203 - r31653204;
        double r31653206 = exp(r31653205);
        double r31653207 = r31653192 * r31653206;
        double r31653208 = r31653207 / r31653193;
        return r31653208;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r31653209 = y;
        double r31653210 = z;
        double r31653211 = log(r31653210);
        double r31653212 = r31653209 * r31653211;
        double r31653213 = t;
        double r31653214 = 1.0;
        double r31653215 = r31653213 - r31653214;
        double r31653216 = a;
        double r31653217 = log(r31653216);
        double r31653218 = r31653215 * r31653217;
        double r31653219 = r31653212 + r31653218;
        double r31653220 = b;
        double r31653221 = r31653219 - r31653220;
        double r31653222 = exp(r31653221);
        double r31653223 = cbrt(r31653222);
        double r31653224 = r31653223 * r31653223;
        double r31653225 = cbrt(r31653209);
        double r31653226 = r31653225 * r31653225;
        double r31653227 = r31653224 / r31653226;
        double r31653228 = x;
        double r31653229 = cbrt(r31653225);
        double r31653230 = r31653229 * r31653229;
        double r31653231 = r31653230 * r31653229;
        double r31653232 = r31653231 / r31653223;
        double r31653233 = r31653228 / r31653232;
        double r31653234 = r31653227 * r31653233;
        return r31653234;
}

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
Target10.8
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;t \lt -0.8845848504127471478852839936735108494759:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.228837407310493290424346923828125:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

  1. Initial program 2.0

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

  3. Applied associate-/l*1.9

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

  5. Applied add-cube-cbrt1.9

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

  6. Applied add-cube-cbrt1.9

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

  7. Applied times-frac1.9

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

  8. Applied *-un-lft-identity1.9

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

  9. Applied times-frac1.1

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

  10. Simplified1.1

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

  12. Applied add-cube-cbrt1.1

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

  13. Final simplification1.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"

  :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))