Average Error: 0.1 → 0.1
Time: 24.4s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(z + \left(y + x\right)\right) - \left(z \cdot \log \left(\sqrt[3]{t}\right) + \left(\log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right) + \left(a - 0.5\right) \cdot b\]
\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(\log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r20259436 = x;
        double r20259437 = y;
        double r20259438 = r20259436 + r20259437;
        double r20259439 = z;
        double r20259440 = r20259438 + r20259439;
        double r20259441 = t;
        double r20259442 = log(r20259441);
        double r20259443 = r20259439 * r20259442;
        double r20259444 = r20259440 - r20259443;
        double r20259445 = a;
        double r20259446 = 0.5;
        double r20259447 = r20259445 - r20259446;
        double r20259448 = b;
        double r20259449 = r20259447 * r20259448;
        double r20259450 = r20259444 + r20259449;
        return r20259450;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r20259451 = z;
        double r20259452 = y;
        double r20259453 = x;
        double r20259454 = r20259452 + r20259453;
        double r20259455 = r20259451 + r20259454;
        double r20259456 = t;
        double r20259457 = cbrt(r20259456);
        double r20259458 = log(r20259457);
        double r20259459 = r20259451 * r20259458;
        double r20259460 = r20259458 + r20259458;
        double r20259461 = r20259460 * r20259451;
        double r20259462 = r20259459 + r20259461;
        double r20259463 = r20259455 - r20259462;
        double r20259464 = a;
        double r20259465 = 0.5;
        double r20259466 = r20259464 - r20259465;
        double r20259467 = b;
        double r20259468 = r20259466 * r20259467;
        double r20259469 = r20259463 + r20259468;
        return r20259469;
}

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

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(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)))