Average Error: 0.0 → 0.0

Time: 655.0ms

Precision: 64

\[a \cdot a - b \cdot b\]

↓

\[a \cdot a - b \cdot b\]

a \cdot a - b \cdot b

↓

a \cdot a - b \cdot b

double f(double a, double b) {
        double r77440 = a;
        double r77441 = r77440 * r77440;
        double r77442 = b;
        double r77443 = r77442 * r77442;
        double r77444 = r77441 - r77443;
        return r77444;
}

↓

double f(double a, double b) {
        double r77445 = a;
        double r77446 = r77445 * r77445;
        double r77447 = b;
        double r77448 = r77447 * r77447;
        double r77449 = r77446 - r77448;
        return r77449;
}

Error

The X axis uses an exponential scale — Bits error versus `a`

Try it out

In
Out

Enter valid numbers for all inputs

Target

Original	0.0
Target	0.0
Herbie	0.0

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

Derivation

Initial program 0.0
\[a \cdot a - b \cdot b\]
Final simplification0.0
\[\leadsto a \cdot a - b \cdot b\]

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

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

  (- (* a a) (* b b)))