Average Error: 1.9 → 1.3
Time: 16.5s
Precision: 64
\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
↓
\[{\left(\frac{1}{{a}^{1}}\right)}^{1} \cdot \frac{x}{e^{\log \left(\frac{1}{z}\right) \cdot y + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)} \cdot y}\]
\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}
↓
{\left(\frac{1}{{a}^{1}}\right)}^{1} \cdot \frac{x}{e^{\log \left(\frac{1}{z}\right) \cdot y + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)} \cdot y}
double f(double x, double y, double z, double t, double a, double b) {
        double r103322 = x;
        double r103323 = y;
        double r103324 = z;
        double r103325 = log(r103324);
        double r103326 = r103323 * r103325;
        double r103327 = t;
        double r103328 = 1.0;
        double r103329 = r103327 - r103328;
        double r103330 = a;
        double r103331 = log(r103330);
        double r103332 = r103329 * r103331;
        double r103333 = r103326 + r103332;
        double r103334 = b;
        double r103335 = r103333 - r103334;
        double r103336 = exp(r103335);
        double r103337 = r103322 * r103336;
        double r103338 = r103337 / r103323;
        return r103338;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r103339 = 1.0;
        double r103340 = a;
        double r103341 = 1.0;
        double r103342 = pow(r103340, r103341);
        double r103343 = r103339 / r103342;
        double r103344 = pow(r103343, r103341);
        double r103345 = x;
        double r103346 = z;
        double r103347 = r103339 / r103346;
        double r103348 = log(r103347);
        double r103349 = y;
        double r103350 = r103348 * r103349;
        double r103351 = r103339 / r103340;
        double r103352 = log(r103351);
        double r103353 = t;
        double r103354 = r103352 * r103353;
        double r103355 = b;
        double r103356 = r103354 + r103355;
        double r103357 = r103350 + r103356;
        double r103358 = exp(r103357);
        double r103359 = r103358 * r103349;
        double r103360 = r103345 / r103359;
        double r103361 = r103344 * r103360;
        return r103361;
}

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. Taylor expanded around inf 1.9

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

  3. Simplified1.1

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

  5. Applied associate-/l*1.3

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

  6. Taylor expanded around inf 1.3

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

  7. Final simplification1.3

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(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))