Average Error: 1.9 → 1.2
Time: 39.3s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt{e^{\log z \cdot y + \left(\left(t - 1.0\right) \cdot \log a - b\right)}}}} \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt{e^{\log z \cdot y + \left(\left(t - 1.0\right) \cdot \log a - b\right)}}}}}{\sqrt[3]{y}}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}
↓
\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt{e^{\log z \cdot y + \left(\left(t - 1.0\right) \cdot \log a - b\right)}}}} \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt{e^{\log z \cdot y + \left(\left(t - 1.0\right) \cdot \log a - b\right)}}}}}{\sqrt[3]{y}}
double f(double x, double y, double z, double t, double a, double b) {
        double r25897140 = x;
        double r25897141 = y;
        double r25897142 = z;
        double r25897143 = log(r25897142);
        double r25897144 = r25897141 * r25897143;
        double r25897145 = t;
        double r25897146 = 1.0;
        double r25897147 = r25897145 - r25897146;
        double r25897148 = a;
        double r25897149 = log(r25897148);
        double r25897150 = r25897147 * r25897149;
        double r25897151 = r25897144 + r25897150;
        double r25897152 = b;
        double r25897153 = r25897151 - r25897152;
        double r25897154 = exp(r25897153);
        double r25897155 = r25897140 * r25897154;
        double r25897156 = r25897155 / r25897141;
        return r25897156;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r25897157 = x;
        double r25897158 = cbrt(r25897157);
        double r25897159 = r25897158 * r25897158;
        double r25897160 = y;
        double r25897161 = cbrt(r25897160);
        double r25897162 = z;
        double r25897163 = log(r25897162);
        double r25897164 = r25897163 * r25897160;
        double r25897165 = t;
        double r25897166 = 1.0;
        double r25897167 = r25897165 - r25897166;
        double r25897168 = a;
        double r25897169 = log(r25897168);
        double r25897170 = r25897167 * r25897169;
        double r25897171 = b;
        double r25897172 = r25897170 - r25897171;
        double r25897173 = r25897164 + r25897172;
        double r25897174 = exp(r25897173);
        double r25897175 = sqrt(r25897174);
        double r25897176 = r25897161 / r25897175;
        double r25897177 = r25897159 / r25897176;
        double r25897178 = r25897158 / r25897176;
        double r25897179 = r25897177 * r25897178;
        double r25897180 = r25897179 / r25897161;
        return r25897180;
}

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
Target10.9
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;t \lt -0.8845848504127471:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1.0\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1.0\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1.0\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

  1. Initial program 1.9

    \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt2.0

    \[\leadsto \frac{x \cdot \color{blue}{\left(\sqrt{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}} \cdot \sqrt{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}\right)}}{y}\]

  4. Taylor expanded around inf 2.0

    \[\leadsto \frac{x \cdot \left(\sqrt{\color{blue}{e^{1.0 \cdot \log \left(\frac{1}{a}\right) - \left(\log \left(\frac{1}{z}\right) \cdot y + \left(b + t \cdot \log \left(\frac{1}{a}\right)\right)\right)}}} \cdot \sqrt{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}\right)}{y}\]

  5. Simplified1.9

    \[\leadsto \frac{x \cdot \left(\sqrt{\color{blue}{e^{\left(\log a \cdot t + \left(-b\right)\right) + \left(\log z \cdot y + \left(-1.0\right) \cdot \log a\right)}}} \cdot \sqrt{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}\right)}{y}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt2.0

    \[\leadsto \frac{x \cdot \left(\sqrt{e^{\left(\log a \cdot t + \left(-b\right)\right) + \left(\log z \cdot y + \left(-1.0\right) \cdot \log a\right)}} \cdot \sqrt{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}\right)}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}\]

  8. Applied associate-/r*2.0

    \[\leadsto \color{blue}{\frac{\frac{x \cdot \left(\sqrt{e^{\left(\log a \cdot t + \left(-b\right)\right) + \left(\log z \cdot y + \left(-1.0\right) \cdot \log a\right)}} \cdot \sqrt{e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}\right)}{\sqrt[3]{y} \cdot \sqrt[3]{y}}}{\sqrt[3]{y}}}\]

  9. Simplified1.8

    \[\leadsto \frac{\color{blue}{\frac{x}{\frac{\sqrt[3]{y}}{\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) - b\right) + y \cdot \log z}}} \cdot \frac{\sqrt[3]{y}}{\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) - b\right) + y \cdot \log z}}}}}}{\sqrt[3]{y}}\]
  10. Using strategy rm

  11. Applied add-cube-cbrt1.8

    \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\frac{\sqrt[3]{y}}{\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) - b\right) + y \cdot \log z}}} \cdot \frac{\sqrt[3]{y}}{\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) - b\right) + y \cdot \log z}}}}}{\sqrt[3]{y}}\]

  12. Applied times-frac1.2

    \[\leadsto \frac{\color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) - b\right) + y \cdot \log z}}}} \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt{e^{\left(\log a \cdot \left(t - 1.0\right) - b\right) + y \cdot \log z}}}}}}{\sqrt[3]{y}}\]

  13. Final simplification1.2

    \[\leadsto \frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt{e^{\log z \cdot y + \left(\left(t - 1.0\right) \cdot \log a - b\right)}}}} \cdot \frac{\sqrt[3]{x}}{\frac{\sqrt[3]{y}}{\sqrt{e^{\log z \cdot y + \left(\left(t - 1.0\right) \cdot \log a - b\right)}}}}}{\sqrt[3]{y}}\]

Reproduce

herbie shell --seed 2019162 
(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) (* 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) (* y (log z))))))

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