Average Error: 0.1 → 0.1
Time: 20.9s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[x - \left(\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot z + \left(z \cdot \log \left(\sqrt[3]{t}\right) + \left(0.5 - a\right) \cdot b\right)\right) - \left(z + y\right)\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
x - \left(\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot z + \left(z \cdot \log \left(\sqrt[3]{t}\right) + \left(0.5 - a\right) \cdot b\right)\right) - \left(z + y\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r313565 = x;
        double r313566 = y;
        double r313567 = r313565 + r313566;
        double r313568 = z;
        double r313569 = r313567 + r313568;
        double r313570 = t;
        double r313571 = log(r313570);
        double r313572 = r313568 * r313571;
        double r313573 = r313569 - r313572;
        double r313574 = a;
        double r313575 = 0.5;
        double r313576 = r313574 - r313575;
        double r313577 = b;
        double r313578 = r313576 * r313577;
        double r313579 = r313573 + r313578;
        return r313579;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r313580 = x;
        double r313581 = t;
        double r313582 = cbrt(r313581);
        double r313583 = r313582 * r313582;
        double r313584 = log(r313583);
        double r313585 = z;
        double r313586 = r313584 * r313585;
        double r313587 = log(r313582);
        double r313588 = r313585 * r313587;
        double r313589 = 0.5;
        double r313590 = a;
        double r313591 = r313589 - r313590;
        double r313592 = b;
        double r313593 = r313591 * r313592;
        double r313594 = r313588 + r313593;
        double r313595 = r313586 + r313594;
        double r313596 = y;
        double r313597 = r313585 + r313596;
        double r313598 = r313595 - r313597;
        double r313599 = r313580 - r313598;
        return r313599;
}

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. 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. Applied associate-+l+0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 
(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)))