neg log

Average Error: 0.0 → 0.0

Time: 2.7s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[-\log \left(\frac{1}{x} - 1\right)\]

↓

\[-\log \left(\frac{1}{x} - 1\right)\]

C

double f(double x) {
        double r4571 = 1.0;
        double r4572 = x;
        double r4573 = r4571 / r4572;
        double r4574 = r4573 - r4571;
        double r4575 = log(r4574);
        double r4576 = -r4575;
        return r4576;
}

↓

double f(double x) {
        double r4577 = 1.0;
        double r4578 = x;
        double r4579 = r4577 / r4578;
        double r4580 = r4579 - r4577;
        double r4581 = log(r4580);
        double r4582 = -r4581;
        return r4582;
}

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[-\log \left(\frac{1}{x} - 1\right)\]

2. Final simplification 0.0

   \[\leadsto -\log \left(\frac{1}{x} - 1\right)\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))