Average Error: 2.0 → 0.3
Time: 29.5s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -8.9526966727005439 \cdot 10^{73} \lor \neg \left(x \le 1.54253563263351339 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{1}{a}\right)}^{1} \cdot \frac{\frac{1}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{\frac{y}{x}}\\ \end{array}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -8.9526966727005439 \cdot 10^{73} \lor \neg \left(x \le 1.54253563263351339 \cdot 10^{-62}\right):\\
\;\;\;\;\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}\\

\mathbf{else}:\\
\;\;\;\;{\left(\frac{1}{a}\right)}^{1} \cdot \frac{\frac{1}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{\frac{y}{x}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r642105 = x;
        double r642106 = y;
        double r642107 = z;
        double r642108 = log(r642107);
        double r642109 = r642106 * r642108;
        double r642110 = t;
        double r642111 = 1.0;
        double r642112 = r642110 - r642111;
        double r642113 = a;
        double r642114 = log(r642113);
        double r642115 = r642112 * r642114;
        double r642116 = r642109 + r642115;
        double r642117 = b;
        double r642118 = r642116 - r642117;
        double r642119 = exp(r642118);
        double r642120 = r642105 * r642119;
        double r642121 = r642120 / r642106;
        return r642121;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r642122 = x;
        double r642123 = -8.952696672700544e+73;
        bool r642124 = r642122 <= r642123;
        double r642125 = 1.5425356326335134e-62;
        bool r642126 = r642122 <= r642125;
        double r642127 = !r642126;
        bool r642128 = r642124 || r642127;
        double r642129 = 1.0;
        double r642130 = a;
        double r642131 = r642129 / r642130;
        double r642132 = 1.0;
        double r642133 = pow(r642131, r642132);
        double r642134 = y;
        double r642135 = z;
        double r642136 = r642129 / r642135;
        double r642137 = log(r642136);
        double r642138 = r642134 * r642137;
        double r642139 = log(r642131);
        double r642140 = t;
        double r642141 = r642139 * r642140;
        double r642142 = b;
        double r642143 = r642141 + r642142;
        double r642144 = r642138 + r642143;
        double r642145 = exp(r642144);
        double r642146 = r642133 / r642145;
        double r642147 = r642122 * r642146;
        double r642148 = r642147 / r642134;
        double r642149 = r642129 / r642145;
        double r642150 = r642134 / r642122;
        double r642151 = r642149 / r642150;
        double r642152 = r642133 * r642151;
        double r642153 = r642128 ? r642148 : r642152;
        return r642153;
}

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
Target10.9
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;t \lt -0.88458485041274715:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{elif}\;t \lt 852031.22883740731:\\ \;\;\;\;\frac{\frac{x}{y} \cdot {a}^{\left(t - 1\right)}}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t - 1\right)}}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -8.952696672700544e+73 or 1.5425356326335134e-62 < x

    1. Initial program 0.9

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

    2. Taylor expanded around inf 0.9

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

    3. Simplified0.2

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

    if -8.952696672700544e+73 < x < 1.5425356326335134e-62

    1. Initial program 3.0

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

    2. Taylor expanded around inf 3.0

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

    3. Simplified0.4

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

    5. Applied *-un-lft-identity0.4

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

    6. Applied *-un-lft-identity0.4

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

    7. Applied times-frac0.4

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

    8. Applied div-inv0.4

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

    9. Applied times-frac0.4

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

    10. Simplified0.4

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -8.9526966727005439 \cdot 10^{73} \lor \neg \left(x \le 1.54253563263351339 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x \cdot \frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{y}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{1}{a}\right)}^{1} \cdot \frac{\frac{1}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}{\frac{y}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020057 
(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)) y)) (- (+ b 1) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1) (log a))) b))) y))