Average Error: 0.1 → 0.1
Time: 19.2s
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 r102271 = x;
        double r102272 = y;
        double r102273 = log(r102272);
        double r102274 = r102271 * r102273;
        double r102275 = r102274 - r102272;
        double r102276 = z;
        double r102277 = r102275 - r102276;
        double r102278 = t;
        double r102279 = log(r102278);
        double r102280 = r102277 + r102279;
        return r102280;
}
↓
double f(double x, double y, double z, double t) {
        double r102281 = x;
        double r102282 = y;
        double r102283 = log(r102282);
        double r102284 = r102281 * r102283;
        double r102285 = r102284 - r102282;
        double r102286 = z;
        double r102287 = r102285 - r102286;
        double r102288 = t;
        double r102289 = sqrt(r102288);
        double r102290 = log(r102289);
        double r102291 = r102287 + r102290;
        double r102292 = r102291 + r102290;
        return r102292;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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 2019209 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))