Expression 4, p15

Average Error: 0.0 → 0.0

Time: 6.5s

Precision: 64

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

\[5 \le a \le 10 \land 0.0 \le b \le 10^{-3}\]

Math

\[\left(a + b\right) \cdot \left(a + b\right)\]

↓

\[a \cdot \left(a + b\right) + \left(a + b\right) \cdot b\]

C

double f(double a, double b) {
        double r102430 = a;
        double r102431 = b;
        double r102432 = r102430 + r102431;
        double r102433 = r102432 * r102432;
        return r102433;
}

↓

double f(double a, double b) {
        double r102434 = a;
        double r102435 = b;
        double r102436 = r102434 + r102435;
        double r102437 = r102434 * r102436;
        double r102438 = r102436 * r102435;
        double r102439 = r102437 + r102438;
        return r102439;
}

Error

Bits error versus a

Bits error versus b

Target

Original	0.0
Target	0.0
Herbie	0.0

\[\left(\left(b \cdot a + b \cdot b\right) + b \cdot a\right) + a \cdot a\]

Derivation

1. Initial program 0.0

   \[\left(a + b\right) \cdot \left(a + b\right)\]
2. Using strategy rm

3. Applied distribute-lft-in 0.0

   \[\leadsto \color{blue}{\left(a + b\right) \cdot a + \left(a + b\right) \cdot b}\]

4. Simplified 0.0

   \[\leadsto \color{blue}{a \cdot \left(a + b\right)} + \left(a + b\right) \cdot b\]

5. Final simplification 0.0

   \[\leadsto a \cdot \left(a + b\right) + \left(a + b\right) \cdot b\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (a b)
  :name "Expression 4, p15"
  :precision binary64
  :pre (and (<= 5 a 10) (<= 0.0 b 0.001))

  :herbie-target
  (+ (+ (+ (* b a) (* b b)) (* b a)) (* a a))

  (* (+ a b) (+ a b)))