Average Error: 0.1 → 0.1
Time: 26.0s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\log t + \left(\left(\left(\log \left(\sqrt{y}\right) \cdot x + \log \left(\sqrt{y}\right) \cdot x\right) - y\right) - z\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\log t + \left(\left(\left(\log \left(\sqrt{y}\right) \cdot x + \log \left(\sqrt{y}\right) \cdot x\right) - y\right) - z\right)
double f(double x, double y, double z, double t) {
        double r3545563 = x;
        double r3545564 = y;
        double r3545565 = log(r3545564);
        double r3545566 = r3545563 * r3545565;
        double r3545567 = r3545566 - r3545564;
        double r3545568 = z;
        double r3545569 = r3545567 - r3545568;
        double r3545570 = t;
        double r3545571 = log(r3545570);
        double r3545572 = r3545569 + r3545571;
        return r3545572;
}
↓
double f(double x, double y, double z, double t) {
        double r3545573 = t;
        double r3545574 = log(r3545573);
        double r3545575 = y;
        double r3545576 = sqrt(r3545575);
        double r3545577 = log(r3545576);
        double r3545578 = x;
        double r3545579 = r3545577 * r3545578;
        double r3545580 = r3545579 + r3545579;
        double r3545581 = r3545580 - r3545575;
        double r3545582 = z;
        double r3545583 = r3545581 - r3545582;
        double r3545584 = r3545574 + r3545583;
        return r3545584;
}

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

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

  4. Applied log-prod0.1

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

  5. Applied distribute-rgt-in0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))