Average Error: 0.0 → 0.0
Time: 1.3s
Precision: 64
\[x \cdot y + z \cdot \left(1 - y\right)\]
↓
\[\mathsf{fma}\left(z, 1 - y, x \cdot y\right)\]
x \cdot y + z \cdot \left(1 - y\right)
↓
\mathsf{fma}\left(z, 1 - y, x \cdot y\right)
double code(double x, double y, double z) {
	return ((double) (((double) (x * y)) + ((double) (z * ((double) (1.0 - y))))));
}
↓
double code(double x, double y, double z) {
	return ((double) fma(z, ((double) (1.0 - y)), ((double) (x * y))));
}

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

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. Using strategy rm

  3. Applied sub-neg0.0

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

  4. Applied distribute-rgt-in0.0

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

  5. Applied associate-+r+0.0

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

  6. Simplified0.0

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

  7. Taylor expanded around 0 0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020114 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
  :precision binary64

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

  (+ (* x y) (* z (- 1 y))))