Average Error: 0.1 → 0.1
Time: 30.0s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(x + z\right) + \left(y - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right) - \log \left(\sqrt[3]{t}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(x + z\right) + \left(y - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right) - \log \left(\sqrt[3]{t}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r292467 = x;
        double r292468 = y;
        double r292469 = r292467 + r292468;
        double r292470 = z;
        double r292471 = r292469 + r292470;
        double r292472 = t;
        double r292473 = log(r292472);
        double r292474 = r292470 * r292473;
        double r292475 = r292471 - r292474;
        double r292476 = a;
        double r292477 = 0.5;
        double r292478 = r292476 - r292477;
        double r292479 = b;
        double r292480 = r292478 * r292479;
        double r292481 = r292475 + r292480;
        return r292481;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r292482 = x;
        double r292483 = z;
        double r292484 = r292482 + r292483;
        double r292485 = y;
        double r292486 = 2.0;
        double r292487 = t;
        double r292488 = cbrt(r292487);
        double r292489 = log(r292488);
        double r292490 = r292486 * r292489;
        double r292491 = r292490 * r292483;
        double r292492 = r292485 - r292491;
        double r292493 = r292484 + r292492;
        double r292494 = r292489 * r292483;
        double r292495 = r292493 - r292494;
        double r292496 = a;
        double r292497 = 0.5;
        double r292498 = r292496 - r292497;
        double r292499 = b;
        double r292500 = r292498 * r292499;
        double r292501 = r292495 + r292500;
        return r292501;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.4
Herbie0.1
\[\left(\left(x + y\right) + \frac{\left(1 - {\left(\log t\right)}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b\]

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \log \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}\right) + \left(a - 0.5\right) \cdot b\]

  4. Applied log-prod0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - z \cdot \color{blue}{\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right)}\right) + \left(a - 0.5\right) \cdot b\]

  5. Applied distribute-rgt-in0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \color{blue}{\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot z + \log \left(\sqrt[3]{t}\right) \cdot z\right)}\right) + \left(a - 0.5\right) \cdot b\]

  6. Applied associate--r+0.1

    \[\leadsto \color{blue}{\left(\left(\left(\left(x + y\right) + z\right) - \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot z\right) - \log \left(\sqrt[3]{t}\right) \cdot z\right)} + \left(a - 0.5\right) \cdot b\]

  7. Simplified0.1

    \[\leadsto \left(\color{blue}{\left(\left(x + z\right) + \left(y - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right)} - \log \left(\sqrt[3]{t}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b\]

  8. Final simplification0.1

    \[\leadsto \left(\left(\left(x + z\right) + \left(y - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right) - \log \left(\sqrt[3]{t}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b\]

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1 (pow (log t) 2)) z) (+ 1 (log t)))) (* (- a 0.5) b))

  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))