Average Error: 9.6 → 2.5
Time: 4.1s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{y} \]
↓
\[\frac{x}{\frac{y}{y - z}} \]
\frac{x \cdot \left(y - z\right)}{y}
↓
\frac{x}{\frac{y}{y - z}}

(FPCore (x y z) :precision binary64 (/ (* x (- y z)) y))
↓
(FPCore (x y z) :precision binary64 (/ x (/ y (- y z))))
double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}
↓
double code(double x, double y, double z) {
	return x / (y / (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

Original9.6
Target2.6
Herbie2.5
\[\begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \]

Derivation

  1. Initial program 9.6

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

  2. Applied associate-/l*_binary642.5

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

  3. Applied *-un-lft-identity_binary642.5

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

  4. Applied associate-/r*_binary642.5

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

  5. Final simplification2.5

    \[\leadsto \frac{x}{\frac{y}{y - z}} \]

Reproduce

herbie shell --seed 2022068 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

  (/ (* x (- y z)) y))