Average Error: 18.1 → 0.0
Time: 1.2s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[y \cdot x + y \cdot \left(-z\right)\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
y \cdot x + y \cdot \left(-z\right)
double f(double x, double y, double z) {
        double r548560 = x;
        double r548561 = y;
        double r548562 = r548560 * r548561;
        double r548563 = r548561 * r548561;
        double r548564 = r548562 + r548563;
        double r548565 = z;
        double r548566 = r548561 * r548565;
        double r548567 = r548564 - r548566;
        double r548568 = r548567 - r548563;
        return r548568;
}
↓
double f(double x, double y, double z) {
        double r548569 = y;
        double r548570 = x;
        double r548571 = r548569 * r548570;
        double r548572 = z;
        double r548573 = -r548572;
        double r548574 = r548569 * r548573;
        double r548575 = r548571 + r548574;
        return r548575;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original18.1
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 18.1

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

  2. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(x - z\right)}\]
  3. Using strategy rm

  4. Applied sub-neg0.0

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

  5. Applied distribute-lft-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020049 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"
  :precision binary64

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

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