Average Error: 0.1 → 0.1
Time: 23.7s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[x - \left(\left(\left(\log \left({t}^{\frac{1}{3}}\right) \cdot z + \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right) + b \cdot \left(0.5 - a\right)\right) - \left(y + z\right)\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
x - \left(\left(\left(\log \left({t}^{\frac{1}{3}}\right) \cdot z + \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right) + b \cdot \left(0.5 - a\right)\right) - \left(y + z\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r304536 = x;
        double r304537 = y;
        double r304538 = r304536 + r304537;
        double r304539 = z;
        double r304540 = r304538 + r304539;
        double r304541 = t;
        double r304542 = log(r304541);
        double r304543 = r304539 * r304542;
        double r304544 = r304540 - r304543;
        double r304545 = a;
        double r304546 = 0.5;
        double r304547 = r304545 - r304546;
        double r304548 = b;
        double r304549 = r304547 * r304548;
        double r304550 = r304544 + r304549;
        return r304550;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r304551 = x;
        double r304552 = t;
        double r304553 = 0.3333333333333333;
        double r304554 = pow(r304552, r304553);
        double r304555 = log(r304554);
        double r304556 = z;
        double r304557 = r304555 * r304556;
        double r304558 = 2.0;
        double r304559 = cbrt(r304552);
        double r304560 = log(r304559);
        double r304561 = r304558 * r304560;
        double r304562 = r304561 * r304556;
        double r304563 = r304557 + r304562;
        double r304564 = b;
        double r304565 = 0.5;
        double r304566 = a;
        double r304567 = r304565 - r304566;
        double r304568 = r304564 * r304567;
        double r304569 = r304563 + r304568;
        double r304570 = y;
        double r304571 = r304570 + r304556;
        double r304572 = r304569 - r304571;
        double r304573 = r304551 - r304572;
        return r304573;
}

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. Simplified0.1

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

  4. Applied add-cube-cbrt0.1

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

  5. Applied log-prod0.1

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

  6. Applied distribute-lft-in0.1

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

  7. Simplified0.1

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

  9. Applied pow1/30.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t)))) (* (- a 0.5) b))

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