Average Error: 0.0 → 0.0
Time: 3.9s
Precision: binary64
\[[x, y]=\mathsf{sort}([x, y])\]
\[\left(x + y\right) \cdot \left(z + 1\right)\]
↓
\[x + \left(y + \left(y + x\right) \cdot z\right)\]
\left(x + y\right) \cdot \left(z + 1\right)
↓
x + \left(y + \left(y + x\right) \cdot z\right)
(FPCore (x y z) :precision binary64 (* (+ x y) (+ z 1.0)))
↓
(FPCore (x y z) :precision binary64 (+ x (+ y (* (+ y x) z))))
double code(double x, double y, double z) {
	return (x + y) * (z + 1.0);
}
↓
double code(double x, double y, double z) {
	return x + (y + ((y + x) * 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

Derivation

  1. Initial program 0.0

    \[\left(x + y\right) \cdot \left(z + 1\right)\]
  2. Using strategy rm

  3. Applied distribute-rgt-in_binary64_13920.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  7. Applied associate-+r+_binary64_13740.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2021043 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1.0)))