Average Error: 0.1 → 0.1
Time: 19.2s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(z + \left(\left(x + y\right) - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right) - z \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(z + \left(\left(x + y\right) - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right) - z \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r639519 = x;
        double r639520 = y;
        double r639521 = r639519 + r639520;
        double r639522 = z;
        double r639523 = r639521 + r639522;
        double r639524 = t;
        double r639525 = log(r639524);
        double r639526 = r639522 * r639525;
        double r639527 = r639523 - r639526;
        double r639528 = a;
        double r639529 = 0.5;
        double r639530 = r639528 - r639529;
        double r639531 = b;
        double r639532 = r639530 * r639531;
        double r639533 = r639527 + r639532;
        return r639533;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r639534 = z;
        double r639535 = x;
        double r639536 = y;
        double r639537 = r639535 + r639536;
        double r639538 = 2.0;
        double r639539 = t;
        double r639540 = cbrt(r639539);
        double r639541 = log(r639540);
        double r639542 = r639538 * r639541;
        double r639543 = r639542 * r639534;
        double r639544 = r639537 - r639543;
        double r639545 = r639534 + r639544;
        double r639546 = r639534 * r639541;
        double r639547 = r639545 - r639546;
        double r639548 = a;
        double r639549 = 0.5;
        double r639550 = r639548 - r639549;
        double r639551 = b;
        double r639552 = r639550 * r639551;
        double r639553 = r639547 + r639552;
        return r639553;
}

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 pow10.1

    \[\leadsto \color{blue}{{\left(\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\right)}^{1}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.1

    \[\leadsto {\left(\left(\left(\left(x + y\right) + z\right) - z \cdot \log \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}\right) + \left(a - 0.5\right) \cdot b\right)}^{1}\]

  6. Applied log-prod0.1

    \[\leadsto {\left(\left(\left(\left(x + y\right) + z\right) - z \cdot \color{blue}{\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right)}\right) + \left(a - 0.5\right) \cdot b\right)}^{1}\]

  7. Applied distribute-lft-in0.1

    \[\leadsto {\left(\left(\left(\left(x + y\right) + z\right) - \color{blue}{\left(z \cdot \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)}\right) + \left(a - 0.5\right) \cdot b\right)}^{1}\]

  8. Applied associate--r+0.1

    \[\leadsto {\left(\color{blue}{\left(\left(\left(\left(x + y\right) + z\right) - z \cdot \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) - z \cdot \log \left(\sqrt[3]{t}\right)\right)} + \left(a - 0.5\right) \cdot b\right)}^{1}\]

  9. Simplified0.1

    \[\leadsto {\left(\left(\color{blue}{\left(z + \left(\left(x + y\right) - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right)} - z \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot b\right)}^{1}\]

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 
(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)))