Average Error: 0.1 → 0.1
Time: 27.0s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(z + \left(y + x\right)\right) - \left(z \cdot \log \left(\sqrt[3]{t}\right) + \left(z \cdot \log \left(\sqrt[3]{t}\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)\right)\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(z + \left(y + x\right)\right) - \left(z \cdot \log \left(\sqrt[3]{t}\right) + \left(z \cdot \log \left(\sqrt[3]{t}\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)\right)\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r14510473 = x;
        double r14510474 = y;
        double r14510475 = r14510473 + r14510474;
        double r14510476 = z;
        double r14510477 = r14510475 + r14510476;
        double r14510478 = t;
        double r14510479 = log(r14510478);
        double r14510480 = r14510476 * r14510479;
        double r14510481 = r14510477 - r14510480;
        double r14510482 = a;
        double r14510483 = 0.5;
        double r14510484 = r14510482 - r14510483;
        double r14510485 = b;
        double r14510486 = r14510484 * r14510485;
        double r14510487 = r14510481 + r14510486;
        return r14510487;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r14510488 = z;
        double r14510489 = y;
        double r14510490 = x;
        double r14510491 = r14510489 + r14510490;
        double r14510492 = r14510488 + r14510491;
        double r14510493 = t;
        double r14510494 = cbrt(r14510493);
        double r14510495 = log(r14510494);
        double r14510496 = r14510488 * r14510495;
        double r14510497 = r14510496 + r14510496;
        double r14510498 = r14510496 + r14510497;
        double r14510499 = r14510492 - r14510498;
        double r14510500 = a;
        double r14510501 = 0.5;
        double r14510502 = r14510500 - r14510501;
        double r14510503 = b;
        double r14510504 = r14510502 * r14510503;
        double r14510505 = r14510499 + r14510504;
        return r14510505;
}

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
Target0.3
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. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"

  :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)))