Average Error: 0.0 → 0.0

Time: 5.5s

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 r54180 = a;
        double r54181 = r54180 * r54180;
        double r54182 = b;
        double r54183 = r54182 * r54182;
        double r54184 = r54181 - r54183;
        return r54184;
}

↓

double f(double a, double b) {
        double r54185 = a;
        double r54186 = r54185 * r54185;
        double r54187 = b;
        double r54188 = r54187 * r54187;
        double r54189 = r54186 - r54188;
        return r54189;
}

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 2019195 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"

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

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