Average Error: 17.6 → 0.0
Time: 2.4s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r512119 = x;
        double r512120 = y;
        double r512121 = r512119 * r512120;
        double r512122 = r512120 * r512120;
        double r512123 = r512121 + r512122;
        double r512124 = z;
        double r512125 = r512120 * r512124;
        double r512126 = r512123 - r512125;
        double r512127 = r512126 - r512122;
        return r512127;
}
↓
double f(double x, double y, double z) {
        double r512128 = y;
        double r512129 = x;
        double r512130 = z;
        double r512131 = r512129 - r512130;
        double r512132 = r512128 * r512131;
        return r512132;
}

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

Original17.6
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.6

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020039 
(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)))