Average Error: 1.9 → 2.0
Time: 38.0s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[\frac{\left(x \cdot {\left(\sqrt{e}\right)}^{\left(\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b\right)}\right) \cdot {\left(\sqrt{e}\right)}^{\left(\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b\right)}}{y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
\frac{\left(x \cdot {\left(\sqrt{e}\right)}^{\left(\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b\right)}\right) \cdot {\left(\sqrt{e}\right)}^{\left(\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b\right)}}{y}
double f(double x, double y, double z, double t, double a, double b) {
        double r72167 = x;
        double r72168 = y;
        double r72169 = z;
        double r72170 = log(r72169);
        double r72171 = r72168 * r72170;
        double r72172 = t;
        double r72173 = 1.0;
        double r72174 = r72172 - r72173;
        double r72175 = a;
        double r72176 = log(r72175);
        double r72177 = r72174 * r72176;
        double r72178 = r72171 + r72177;
        double r72179 = b;
        double r72180 = r72178 - r72179;
        double r72181 = exp(r72180);
        double r72182 = r72167 * r72181;
        double r72183 = r72182 / r72168;
        return r72183;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r72184 = x;
        double r72185 = exp(1.0);
        double r72186 = sqrt(r72185);
        double r72187 = y;
        double r72188 = z;
        double r72189 = log(r72188);
        double r72190 = r72187 * r72189;
        double r72191 = t;
        double r72192 = 1.0;
        double r72193 = r72191 - r72192;
        double r72194 = a;
        double r72195 = log(r72194);
        double r72196 = r72193 * r72195;
        double r72197 = r72190 + r72196;
        double r72198 = b;
        double r72199 = r72197 - r72198;
        double r72200 = pow(r72186, r72199);
        double r72201 = r72184 * r72200;
        double r72202 = r72201 * r72200;
        double r72203 = r72202 / r72187;
        return r72203;
}

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 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 *-un-lft-identity1.9

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

  4. Applied exp-prod2.0

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

  5. Simplified2.0

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

  7. Applied add-sqr-sqrt2.2

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

  8. Applied unpow-prod-down2.0

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

  9. Applied associate-*r*2.0

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

  10. Final simplification2.0

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

Reproduce

herbie shell --seed 2019322 
(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))