Average Error: 13.0 → 0.0

Time: 1.3s

Precision: 64

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

↓

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

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

↓

y \cdot \left(x - z\right)

double code(double x, double y, double z) {
	return ((((x * y) - (y * y)) + (y * y)) - (y * z));
}

↓

double code(double x, double y, double z) {
	return (y * (x - z));
}

Error

The X axis uses an exponential scale — Bits error versus `x`

Try it out

In
Out

Enter valid numbers for all inputs

Target

Original	13.0
Target	0.0
Herbie	0.0

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

Derivation

Initial program 13.0
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
Simplified0.0
\[\leadsto \color{blue}{y \cdot \left(x - z\right)}\]
Final simplification0.0
\[\leadsto y \cdot \left(x - z\right)\]

Reproduce

herbie shell --seed 2020091 
(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)))