Average Error: 0.1 → 0.1
Time: 33.2s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(x + \left(\left(z + y\right) - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right) - \log \left({t}^{\frac{1}{3}}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(x + \left(\left(z + y\right) - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right) - \log \left({t}^{\frac{1}{3}}\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 r404384 = x;
        double r404385 = y;
        double r404386 = r404384 + r404385;
        double r404387 = z;
        double r404388 = r404386 + r404387;
        double r404389 = t;
        double r404390 = log(r404389);
        double r404391 = r404387 * r404390;
        double r404392 = r404388 - r404391;
        double r404393 = a;
        double r404394 = 0.5;
        double r404395 = r404393 - r404394;
        double r404396 = b;
        double r404397 = r404395 * r404396;
        double r404398 = r404392 + r404397;
        return r404398;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r404399 = x;
        double r404400 = z;
        double r404401 = y;
        double r404402 = r404400 + r404401;
        double r404403 = 2.0;
        double r404404 = t;
        double r404405 = cbrt(r404404);
        double r404406 = log(r404405);
        double r404407 = r404403 * r404406;
        double r404408 = r404407 * r404400;
        double r404409 = r404402 - r404408;
        double r404410 = r404399 + r404409;
        double r404411 = 0.3333333333333333;
        double r404412 = pow(r404404, r404411);
        double r404413 = log(r404412);
        double r404414 = r404413 * r404400;
        double r404415 = r404410 - r404414;
        double r404416 = a;
        double r404417 = 0.5;
        double r404418 = r404416 - r404417;
        double r404419 = b;
        double r404420 = r404418 * r404419;
        double r404421 = r404415 + r404420;
        return r404421;
}

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. 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

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

  9. Applied pow1/30.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 
(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)))