Average Error: 0.0 → 0.0

Time: 4.8s

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 r64784 = a;
        double r64785 = r64784 * r64784;
        double r64786 = b;
        double r64787 = r64786 * r64786;
        double r64788 = r64785 - r64787;
        return r64788;
}

↓

double f(double a, double b) {
        double r64789 = a;
        double r64790 = r64789 * r64789;
        double r64791 = b;
        double r64792 = r64791 * r64791;
        double r64793 = r64790 - r64792;
        return r64793;
}

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 2019196 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"

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

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