Average Error: 12.9 → 0.0
Time: 2.6s
Precision: binary64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[y \cdot x - y \cdot z\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
y \cdot x - y \cdot z
(FPCore (x y z)
 :precision binary64
 (- (+ (- (* x y) (* y y)) (* y y)) (* y z)))
↓
(FPCore (x y z) :precision binary64 (- (* y x) (* y z)))
double code(double x, double y, double z) {
	return ((double) (((double) (((double) (((double) (x * y)) - ((double) (y * y)))) + ((double) (y * y)))) - ((double) (y * z))));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (y * x)) - ((double) (y * z))));
}

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

Original12.9
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program Error: 12.9 bits

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

  2. SimplifiedError: 0.0 bits

    \[\leadsto \color{blue}{y \cdot \left(x - z\right)}\]
  3. Using strategy rm

  4. Applied sub-negError: 0.0 bits

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

  5. Applied distribute-lft-inError: 0.0 bits

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

  6. Final simplificationError: 0.0 bits

    \[\leadsto y \cdot x - y \cdot z\]

Reproduce

herbie shell --seed 2020205 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"
  :precision binary64

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

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