Average Error: 18.0 → 0.0
Time: 22.7s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[\left(-z\right) \cdot y + y \cdot x\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
\left(-z\right) \cdot y + y \cdot x
double f(double x, double y, double z) {
        double r18491124 = x;
        double r18491125 = y;
        double r18491126 = r18491124 * r18491125;
        double r18491127 = r18491125 * r18491125;
        double r18491128 = r18491126 + r18491127;
        double r18491129 = z;
        double r18491130 = r18491125 * r18491129;
        double r18491131 = r18491128 - r18491130;
        double r18491132 = r18491131 - r18491127;
        return r18491132;
}
↓
double f(double x, double y, double z) {
        double r18491133 = z;
        double r18491134 = -r18491133;
        double r18491135 = y;
        double r18491136 = r18491134 * r18491135;
        double r18491137 = x;
        double r18491138 = r18491135 * r18491137;
        double r18491139 = r18491136 + r18491138;
        return r18491139;
}

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

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

Derivation

  1. Initial program 18.0

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

  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

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"

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

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