Average Error: 2.0 → 1.3
Time: 15.6s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\left(x \cdot \sqrt{\frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}\right) \cdot \sqrt{\frac{{\left(\frac{1}{a}\right)}^{1}}{e^{y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)}}}}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{\left(x \cdot \sqrt{\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)}}}\right) \cdot \sqrt{\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}
double f(double x, double y, double z, double t, double a, double b) {
        double r91100 = x;
        double r91101 = y;
        double r91102 = z;
        double r91103 = log(r91102);
        double r91104 = r91101 * r91103;
        double r91105 = t;
        double r91106 = 1.0;
        double r91107 = r91105 - r91106;
        double r91108 = a;
        double r91109 = log(r91108);
        double r91110 = r91107 * r91109;
        double r91111 = r91104 + r91110;
        double r91112 = b;
        double r91113 = r91111 - r91112;
        double r91114 = exp(r91113);
        double r91115 = r91100 * r91114;
        double r91116 = r91115 / r91101;
        return r91116;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r91117 = x;
        double r91118 = 1.0;
        double r91119 = a;
        double r91120 = r91118 / r91119;
        double r91121 = 1.0;
        double r91122 = pow(r91120, r91121);
        double r91123 = y;
        double r91124 = z;
        double r91125 = r91118 / r91124;
        double r91126 = log(r91125);
        double r91127 = r91123 * r91126;
        double r91128 = log(r91120);
        double r91129 = t;
        double r91130 = r91128 * r91129;
        double r91131 = b;
        double r91132 = r91130 + r91131;
        double r91133 = r91127 + r91132;
        double r91134 = exp(r91133);
        double r91135 = r91122 / r91134;
        double r91136 = sqrt(r91135);
        double r91137 = r91117 * r91136;
        double r91138 = r91137 * r91136;
        double r91139 = r91138 / r91123;
        return r91139;
}

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

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. Taylor expanded around inf 2.0

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

  3. Simplified1.3

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

  5. Applied add-sqr-sqrt1.3

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

  6. Applied associate-*r*1.3

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

  7. Final simplification1.3

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

Reproduce

herbie shell --seed 2020081 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  :precision binary64
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1) (log a))) b))) y))