Average Error: 0.0 → 0.0
Time: 4.4s
Precision: binary64
Cost: 448
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[z + x \cdot \left(y + 0.5\right)\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
z + x \cdot \left(y + 0.5\right)
(FPCore (x y z) :precision binary64 (+ (+ (/ x 2.0) (* y x)) z))
↓
(FPCore (x y z) :precision binary64 (+ z (* x (+ y 0.5))))
double code(double x, double y, double z) {
	return ((x / 2.0) + (y * x)) + z;
}
↓
double code(double x, double y, double z) {
	return z + (x * (y + 0.5));
}

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

Alternatives

Alternative 1
Error12.0
Cost1604
\[\begin{array}{l} \mathbf{if}\;y \leq -1134533.0004973644:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{elif}\;y \leq 3423479.55969982:\\ \;\;\;\;z + x \cdot 0.5\\ \mathbf{elif}\;y \leq 3.967091293867695 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{elif}\;y \leq 2.3076460644555176 \cdot 10^{+247}:\\ \;\;\;\;z + x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array}\]
Alternative 2
Error14.7
Cost962
\[\begin{array}{l} \mathbf{if}\;z \leq -6.002232716397476 \cdot 10^{+75}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.2605158133931097 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \left(y + 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array}\]
Alternative 3
Error29.8
Cost785
\[\begin{array}{l} \mathbf{if}\;y \leq -5.130097724137686 \cdot 10^{+22} \lor \neg \left(y \leq 117606286.04561709 \lor \neg \left(y \leq 9.175209039785383 \cdot 10^{+197}\right) \land y \leq 4.027074399529589 \cdot 10^{+247}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array}\]
Alternative 4
Error34.7
Cost64
\[z\]
Alternative 5
Error61.9
Cost64
\[-1\]
Alternative 6
Error61.9
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

    \[\left(\frac{x}{2} + y \cdot x\right) + z\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{x \cdot y + \left(z + 0.5 \cdot x\right)}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{z + x \cdot \left(y + 0.5\right)}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{z + x \cdot \left(y + 0.5\right)}\]

  5. Final simplification0.0

    \[\leadsto z + x \cdot \left(y + 0.5\right)\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2.0) (* y x)) z))