Average Error: 0.0 → 0.0
Time: 14.4s
Precision: 64
\[x \cdot y + z \cdot \left(1 - y\right)\]
↓
\[\mathsf{fma}\left(y, x - z, 1 \cdot z\right)\]
x \cdot y + z \cdot \left(1 - y\right)
↓
\mathsf{fma}\left(y, x - z, 1 \cdot z\right)
double f(double x, double y, double z) {
        double r27564142 = x;
        double r27564143 = y;
        double r27564144 = r27564142 * r27564143;
        double r27564145 = z;
        double r27564146 = 1.0;
        double r27564147 = r27564146 - r27564143;
        double r27564148 = r27564145 * r27564147;
        double r27564149 = r27564144 + r27564148;
        return r27564149;
}
↓
double f(double x, double y, double z) {
        double r27564150 = y;
        double r27564151 = x;
        double r27564152 = z;
        double r27564153 = r27564151 - r27564152;
        double r27564154 = 1.0;
        double r27564155 = r27564154 * r27564152;
        double r27564156 = fma(r27564150, r27564153, r27564155);
        return r27564156;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.0
Target0.0
Herbie0.0
\[z - \left(z - x\right) \cdot y\]

Derivation

  1. Initial program 0.0

    \[x \cdot y + z \cdot \left(1 - y\right)\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(1 \cdot z + x \cdot y\right) - z \cdot y}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, x - z, 1 \cdot z\right)}\]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, x - z, 1 \cdot z\right)\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"

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

  (+ (* x y) (* z (- 1.0 y))))