Average Error: 0.0 → 0.0
Time: 3.7s
Precision: binary64
\[x + y \cdot \left(z - x\right)\]
↓
\[\left(z \cdot y + x\right) - y \cdot x\]
x + y \cdot \left(z - x\right)
↓
\left(z \cdot y + x\right) - y \cdot x
(FPCore (x y z) :precision binary64 (+ x (* y (- z x))))
↓
(FPCore (x y z) :precision binary64 (- (+ (* z y) x) (* y x)))
double code(double x, double y, double z) {
	return x + (y * (z - x));
}
↓
double code(double x, double y, double z) {
	return ((z * y) + x) - (y * x);
}

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

Derivation

  1. Initial program 0.0

    \[x + y \cdot \left(z - x\right)\]
  2. Using strategy rm

  3. Applied sub-neg_binary64_710.0

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

  4. Applied distribute-rgt-in_binary64_280.0

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

  5. Applied associate-+r+_binary64_100.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2021176 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))