Average Error: 0.1 → 0.1
Time: 12.5s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + x \cdot \log \left(\sqrt[3]{y}\right)\right) - y\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + x \cdot \log \left(\sqrt[3]{y}\right)\right) - y\right) - z\right) + \log t
double f(double x, double y, double z, double t) {
        double r100377 = x;
        double r100378 = y;
        double r100379 = log(r100378);
        double r100380 = r100377 * r100379;
        double r100381 = r100380 - r100378;
        double r100382 = z;
        double r100383 = r100381 - r100382;
        double r100384 = t;
        double r100385 = log(r100384);
        double r100386 = r100383 + r100385;
        return r100386;
}
↓
double f(double x, double y, double z, double t) {
        double r100387 = 2.0;
        double r100388 = y;
        double r100389 = cbrt(r100388);
        double r100390 = log(r100389);
        double r100391 = r100387 * r100390;
        double r100392 = x;
        double r100393 = r100391 * r100392;
        double r100394 = r100392 * r100390;
        double r100395 = r100393 + r100394;
        double r100396 = r100395 - r100388;
        double r100397 = z;
        double r100398 = r100396 - r100397;
        double r100399 = t;
        double r100400 = log(r100399);
        double r100401 = r100398 + r100400;
        return r100401;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

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-cube-cbrt0.1

    \[\leadsto \left(\left(x \cdot \log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} - y\right) - z\right) + \log t\]

  4. Applied log-prod0.1

    \[\leadsto \left(\left(x \cdot \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)} - y\right) - z\right) + \log t\]

  5. Applied distribute-lft-in0.1

    \[\leadsto \left(\left(\color{blue}{\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right)} - y\right) - z\right) + \log t\]

  6. Simplified0.1

    \[\leadsto \left(\left(\left(\color{blue}{\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x} + x \cdot \log \left(\sqrt[3]{y}\right)\right) - y\right) - z\right) + \log t\]

  7. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + x \cdot \log \left(\sqrt[3]{y}\right)\right) - y\right) - z\right) + \log t\]

Reproduce

herbie shell --seed 2020042 
(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)))