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

Average Error: 0.1 → 0.1

Time: 25.9s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b) {
        double r13350573 = x;
        double r13350574 = y;
        double r13350575 = r13350573 + r13350574;
        double r13350576 = z;
        double r13350577 = r13350575 + r13350576;
        double r13350578 = t;
        double r13350579 = log(r13350578);
        double r13350580 = r13350576 * r13350579;
        double r13350581 = r13350577 - r13350580;
        double r13350582 = a;
        double r13350583 = 0.5;
        double r13350584 = r13350582 - r13350583;
        double r13350585 = b;
        double r13350586 = r13350584 * r13350585;
        double r13350587 = r13350581 + r13350586;
        return r13350587;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r13350588 = a;
        double r13350589 = 0.5;
        double r13350590 = r13350588 - r13350589;
        double r13350591 = b;
        double r13350592 = r13350590 * r13350591;
        double r13350593 = z;
        double r13350594 = y;
        double r13350595 = x;
        double r13350596 = r13350594 + r13350595;
        double r13350597 = r13350593 + r13350596;
        double r13350598 = t;
        double r13350599 = log(r13350598);
        double r13350600 = r13350593 * r13350599;
        double r13350601 = r13350597 - r13350600;
        double r13350602 = r13350592 + r13350601;
        return r13350602;
}

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. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(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)))