Average Error: 17.8 → 0.0
Time: 1.3s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r455480 = x;
        double r455481 = y;
        double r455482 = r455480 * r455481;
        double r455483 = z;
        double r455484 = r455481 * r455483;
        double r455485 = r455482 - r455484;
        double r455486 = r455481 * r455481;
        double r455487 = r455485 - r455486;
        double r455488 = r455487 + r455486;
        return r455488;
}
↓
double f(double x, double y, double z) {
        double r455489 = y;
        double r455490 = x;
        double r455491 = z;
        double r455492 = r455490 - r455491;
        double r455493 = r455489 * r455492;
        return r455493;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

Enter valid numbers for all inputs

Target

Original17.8
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.8

    \[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(x - z\right)}\]

  3. Final simplification0.0

    \[\leadsto y \cdot \left(x - z\right)\]

Reproduce

herbie shell --seed 2020064 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (* (- x z) y)

  (+ (- (- (* x y) (* y z)) (* y y)) (* y y)))