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

Average Error: 0.1 → 0.1

Time: 30.0s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b) {
        double r225967 = x;
        double r225968 = y;
        double r225969 = r225967 + r225968;
        double r225970 = z;
        double r225971 = r225969 + r225970;
        double r225972 = t;
        double r225973 = log(r225972);
        double r225974 = r225970 * r225973;
        double r225975 = r225971 - r225974;
        double r225976 = a;
        double r225977 = 0.5;
        double r225978 = r225976 - r225977;
        double r225979 = b;
        double r225980 = r225978 * r225979;
        double r225981 = r225975 + r225980;
        return r225981;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r225982 = x;
        double r225983 = y;
        double r225984 = r225982 + r225983;
        double r225985 = z;
        double r225986 = r225984 + r225985;
        double r225987 = t;
        double r225988 = log(r225987);
        double r225989 = r225985 * r225988;
        double r225990 = r225986 - r225989;
        double r225991 = a;
        double r225992 = 0.5;
        double r225993 = r225991 - r225992;
        double r225994 = b;
        double r225995 = r225993 * r225994;
        double r225996 = r225990 + r225995;
        return r225996;
}

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

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

Reproduce

herbie shell --seed 2019304 +o rules:numerics
(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)))