Average Error: 0.0 → 0.0
Time: 1.7s
Precision: binary64
\[x + y \cdot \left(z - x\right)\]
↓
\[\left(x + y \cdot z\right) - x \cdot y\]
x + y \cdot \left(z - x\right)
↓
\left(x + y \cdot z\right) - x \cdot y
(FPCore (x y z) :precision binary64 (+ x (* y (- z x))))
↓
(FPCore (x y z) :precision binary64 (- (+ x (* y z)) (* x y)))
double code(double x, double y, double z) {
	return ((double) (x + ((double) (y * ((double) (z - x))))));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (x + ((double) (y * z)))) - ((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

Derivation

  1. Initial program Error: 0.0 bits

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

  3. Applied sub-negError: 0.0 bits

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

  4. Applied distribute-lft-inError: 0.0 bits

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

  5. Applied associate-+r+Error: 0.0 bits

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

  6. Final simplificationError: 0.0 bits

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

Reproduce

herbie shell --seed 2020204 
(FPCore (x y z)
  :name "SynthBasics:oscSampleBasedAux from YampaSynth-0.2"
  :precision binary64
  (+ x (* y (- z x))))