Average Error: 0.0 → 0.0

Time: 12.3s

Precision: 64

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

↓

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

a \cdot a - b \cdot b

↓

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

double f(double a, double b) {
        double r9941 = a;
        double r9942 = r9941 * r9941;
        double r9943 = b;
        double r9944 = r9943 * r9943;
        double r9945 = r9942 - r9944;
        return r9945;
}

↓

double f(double a, double b) {
        double r9946 = a;
        double r9947 = b;
        double r9948 = r9946 - r9947;
        double r9949 = r9946 + r9947;
        double r9950 = r9948 * r9949;
        return r9950;
}

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
\[a \cdot a - b \cdot b\]
Simplified0.0
\[\leadsto \color{blue}{\left(a - b\right) \cdot \left(a + b\right)}\]
Final simplification0.0
\[\leadsto \left(a - b\right) \cdot \left(a + b\right)\]

Reproduce

herbie shell --seed 2019315 
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

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

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