Average Error: 0.1 → 0.1
Time: 20.5s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\left(x \cdot \log y - y\right) - z\right) + \log \left(\sqrt{t}\right)\right) + \log \left(\sqrt{t}\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\left(x \cdot \log y - y\right) - z\right) + \log \left(\sqrt{t}\right)\right) + \log \left(\sqrt{t}\right)
double f(double x, double y, double z, double t) {
        double r7461308 = x;
        double r7461309 = y;
        double r7461310 = log(r7461309);
        double r7461311 = r7461308 * r7461310;
        double r7461312 = r7461311 - r7461309;
        double r7461313 = z;
        double r7461314 = r7461312 - r7461313;
        double r7461315 = t;
        double r7461316 = log(r7461315);
        double r7461317 = r7461314 + r7461316;
        return r7461317;
}
↓
double f(double x, double y, double z, double t) {
        double r7461318 = x;
        double r7461319 = y;
        double r7461320 = log(r7461319);
        double r7461321 = r7461318 * r7461320;
        double r7461322 = r7461321 - r7461319;
        double r7461323 = z;
        double r7461324 = r7461322 - r7461323;
        double r7461325 = t;
        double r7461326 = sqrt(r7461325);
        double r7461327 = log(r7461326);
        double r7461328 = r7461324 + r7461327;
        double r7461329 = r7461328 + r7461327;
        return r7461329;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Results

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Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.1

    \[\leadsto \left(\left(x \cdot \log y - y\right) - z\right) + \log \color{blue}{\left(\sqrt{t} \cdot \sqrt{t}\right)}\]

  4. Applied log-prod0.1

    \[\leadsto \left(\left(x \cdot \log y - y\right) - z\right) + \color{blue}{\left(\log \left(\sqrt{t}\right) + \log \left(\sqrt{t}\right)\right)}\]

  5. Applied associate-+r+0.1

    \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y - y\right) - z\right) + \log \left(\sqrt{t}\right)\right) + \log \left(\sqrt{t}\right)}\]

  6. Final simplification0.1

    \[\leadsto \left(\left(\left(x \cdot \log y - y\right) - z\right) + \log \left(\sqrt{t}\right)\right) + \log \left(\sqrt{t}\right)\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))