Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A

Average Error: 0.1 → 0.1

Time: 7.2s

Precision: 64

Math

\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]

↓

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

C

double f(double x, double y, double z, double t, double a, double b) {
        double r398564 = x;
        double r398565 = y;
        double r398566 = r398564 + r398565;
        double r398567 = z;
        double r398568 = r398566 + r398567;
        double r398569 = t;
        double r398570 = log(r398569);
        double r398571 = r398567 * r398570;
        double r398572 = r398568 - r398571;
        double r398573 = a;
        double r398574 = 0.5;
        double r398575 = r398573 - r398574;
        double r398576 = b;
        double r398577 = r398575 * r398576;
        double r398578 = r398572 + r398577;
        return r398578;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r398579 = x;
        double r398580 = y;
        double r398581 = r398579 + r398580;
        double r398582 = z;
        double r398583 = r398581 + r398582;
        double r398584 = 2.0;
        double r398585 = t;
        double r398586 = cbrt(r398585);
        double r398587 = log(r398586);
        double r398588 = r398584 * r398587;
        double r398589 = r398582 * r398588;
        double r398590 = r398582 * r398587;
        double r398591 = r398589 + r398590;
        double r398592 = r398583 - r398591;
        double r398593 = a;
        double r398594 = 0.5;
        double r398595 = r398593 - r398594;
        double r398596 = b;
        double r398597 = r398595 * r398596;
        double r398598 = r398592 + r398597;
        return r398598;
}

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

Target

Original	0.1
Target	0.4
Herbie	0.1

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

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-cbrt 0.1

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

4. Applied log-prod 0.1

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

5. Applied distribute-lft-in 0.1

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

6. Simplified 0.1

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

7. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020049 
(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)))