Average Error: 1.9 → 1.9
Time: 1.9m
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\sqrt[3]{\sqrt[3]{\frac{e^{\left(\left(t - 1\right) \cdot \log a + \log z \cdot y\right) - b} \cdot x}{y}} \cdot \left(\sqrt[3]{\frac{e^{\left(\left(t - 1\right) \cdot \log a + \log z \cdot y\right) - b} \cdot x}{y}} \cdot \sqrt[3]{\frac{e^{\left(\left(t - 1\right) \cdot \log a + \log z \cdot y\right) - b} \cdot x}{y}}\right)} \cdot \left(\sqrt[3]{\frac{e^{\left(\left(t - 1\right) \cdot \log a + \log z \cdot y\right) - b} \cdot x}{y}} \cdot \sqrt[3]{\sqrt[3]{\frac{e^{\left(\left(t - 1\right) \cdot \log a + \log z \cdot y\right) - b} \cdot x}{y}} \cdot \left(\sqrt[3]{\frac{e^{\left(\left(t - 1\right) \cdot \log a + \log z \cdot y\right) - b} \cdot x}{y}} \cdot \sqrt[3]{\frac{e^{\left(\left(t - 1\right) \cdot \log a + \log z \cdot y\right) - b} \cdot x}{y}}\right)}\right)\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\sqrt[3]{\sqrt[3]{\frac{e^{\left(\left(t - 1\right) \cdot \log a + \log z \cdot y\right) - b} \cdot x}{y}} \cdot \left(\sqrt[3]{\frac{e^{\left(\left(t - 1\right) \cdot \log a + \log z \cdot y\right) - b} \cdot x}{y}} \cdot \sqrt[3]{\frac{e^{\left(\left(t - 1\right) \cdot \log a + \log z \cdot y\right) - b} \cdot x}{y}}\right)} \cdot \left(\sqrt[3]{\frac{e^{\left(\left(t - 1\right) \cdot \log a + \log z \cdot y\right) - b} \cdot x}{y}} \cdot \sqrt[3]{\sqrt[3]{\frac{e^{\left(\left(t - 1\right) \cdot \log a + \log z \cdot y\right) - b} \cdot x}{y}} \cdot \left(\sqrt[3]{\frac{e^{\left(\left(t - 1\right) \cdot \log a + \log z \cdot y\right) - b} \cdot x}{y}} \cdot \sqrt[3]{\frac{e^{\left(\left(t - 1\right) \cdot \log a + \log z \cdot y\right) - b} \cdot x}{y}}\right)}\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r22331149 = x;
        double r22331150 = y;
        double r22331151 = z;
        double r22331152 = log(r22331151);
        double r22331153 = r22331150 * r22331152;
        double r22331154 = t;
        double r22331155 = 1.0;
        double r22331156 = r22331154 - r22331155;
        double r22331157 = a;
        double r22331158 = log(r22331157);
        double r22331159 = r22331156 * r22331158;
        double r22331160 = r22331153 + r22331159;
        double r22331161 = b;
        double r22331162 = r22331160 - r22331161;
        double r22331163 = exp(r22331162);
        double r22331164 = r22331149 * r22331163;
        double r22331165 = r22331164 / r22331150;
        return r22331165;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r22331166 = t;
        double r22331167 = 1.0;
        double r22331168 = r22331166 - r22331167;
        double r22331169 = a;
        double r22331170 = log(r22331169);
        double r22331171 = r22331168 * r22331170;
        double r22331172 = z;
        double r22331173 = log(r22331172);
        double r22331174 = y;
        double r22331175 = r22331173 * r22331174;
        double r22331176 = r22331171 + r22331175;
        double r22331177 = b;
        double r22331178 = r22331176 - r22331177;
        double r22331179 = exp(r22331178);
        double r22331180 = x;
        double r22331181 = r22331179 * r22331180;
        double r22331182 = r22331181 / r22331174;
        double r22331183 = cbrt(r22331182);
        double r22331184 = r22331183 * r22331183;
        double r22331185 = r22331183 * r22331184;
        double r22331186 = cbrt(r22331185);
        double r22331187 = r22331183 * r22331186;
        double r22331188 = r22331186 * r22331187;
        return r22331188;
}

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
Target10.8
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;t \lt -0.8845848504127471478852839936735108494759:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.228837407310493290424346923828125:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

  1. Initial program 1.9

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

  3. Applied add-cube-cbrt1.9

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

  5. Applied add-cube-cbrt1.9

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

  7. Applied add-cube-cbrt1.9

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

  8. Final simplification1.9

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

Reproduce

herbie shell --seed 2019200 
(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))