Average Error: 13.0 → 3.4
Time: 2.5s
Precision: binary64
\[\frac{x \cdot \left(y + z\right)}{z}\]
↓
\[x \cdot \frac{y + z}{z}\]
\frac{x \cdot \left(y + z\right)}{z}
↓
x \cdot \frac{y + z}{z}
(FPCore (x y z) :precision binary64 (/ (* x (+ y z)) z))
↓
(FPCore (x y z) :precision binary64 (* x (/ (+ y z) z)))
double code(double x, double y, double z) {
	return (x * (y + z)) / z;
}
↓
double code(double x, double y, double z) {
	return x * ((y + z) / 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

Original13.0
Target3.1
Herbie3.4
\[\frac{x}{\frac{z}{y + z}}\]

Derivation

  1. Initial program 13.0

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

  3. Applied *-un-lft-identity_binary64_1187213.0

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

  4. Applied times-frac_binary64_118783.4

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y + z}{z}}\]

  5. Simplified3.4

    \[\leadsto \color{blue}{x} \cdot \frac{y + z}{z}\]

  6. Final simplification3.4

    \[\leadsto x \cdot \frac{y + z}{z}\]

Reproduce

herbie shell --seed 2020292 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (/ x (/ z (+ y z)))

  (/ (* x (+ y z)) z))