Average Error: 0.1 → 0.1
Time: 23.0s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\log t + \left(\left(\left(x \cdot \log \left({y}^{\frac{1}{3}}\right) - y\right) + \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x\right) - z\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\log t + \left(\left(\left(x \cdot \log \left({y}^{\frac{1}{3}}\right) - y\right) + \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x\right) - z\right)
double f(double x, double y, double z, double t) {
        double r4566484 = x;
        double r4566485 = y;
        double r4566486 = log(r4566485);
        double r4566487 = r4566484 * r4566486;
        double r4566488 = r4566487 - r4566485;
        double r4566489 = z;
        double r4566490 = r4566488 - r4566489;
        double r4566491 = t;
        double r4566492 = log(r4566491);
        double r4566493 = r4566490 + r4566492;
        return r4566493;
}
↓
double f(double x, double y, double z, double t) {
        double r4566494 = t;
        double r4566495 = log(r4566494);
        double r4566496 = x;
        double r4566497 = y;
        double r4566498 = 0.3333333333333333;
        double r4566499 = pow(r4566497, r4566498);
        double r4566500 = log(r4566499);
        double r4566501 = r4566496 * r4566500;
        double r4566502 = r4566501 - r4566497;
        double r4566503 = cbrt(r4566497);
        double r4566504 = r4566503 * r4566503;
        double r4566505 = log(r4566504);
        double r4566506 = r4566505 * r4566496;
        double r4566507 = r4566502 + r4566506;
        double r4566508 = z;
        double r4566509 = r4566507 - r4566508;
        double r4566510 = r4566495 + r4566509;
        return r4566510;
}

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-rgt-in0.1

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

  6. Applied associate--l+0.1

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

  8. Applied pow1/30.1

    \[\leadsto \left(\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\log \color{blue}{\left({y}^{\frac{1}{3}}\right)} \cdot x - y\right)\right) - z\right) + \log t\]

  9. Final simplification0.1

    \[\leadsto \log t + \left(\left(\left(x \cdot \log \left({y}^{\frac{1}{3}}\right) - y\right) + \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x\right) - z\right)\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))