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

Average Error: 0.1 → 0.1

Time: 20.7s

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 r19511248 = x;
        double r19511249 = y;
        double r19511250 = r19511248 + r19511249;
        double r19511251 = z;
        double r19511252 = r19511250 + r19511251;
        double r19511253 = t;
        double r19511254 = log(r19511253);
        double r19511255 = r19511251 * r19511254;
        double r19511256 = r19511252 - r19511255;
        double r19511257 = a;
        double r19511258 = 0.5;
        double r19511259 = r19511257 - r19511258;
        double r19511260 = b;
        double r19511261 = r19511259 * r19511260;
        double r19511262 = r19511256 + r19511261;
        return r19511262;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r19511263 = a;
        double r19511264 = 0.5;
        double r19511265 = r19511263 - r19511264;
        double r19511266 = b;
        double r19511267 = r19511265 * r19511266;
        double r19511268 = z;
        double r19511269 = y;
        double r19511270 = x;
        double r19511271 = r19511269 + r19511270;
        double r19511272 = r19511268 + r19511271;
        double r19511273 = t;
        double r19511274 = log(r19511273);
        double r19511275 = r19511268 * r19511274;
        double r19511276 = r19511272 - r19511275;
        double r19511277 = r19511267 + r19511276;
        return r19511277;
}

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 
(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)))