Average Error: 12.3 → 3.1
Time: 2.2s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[x \cdot \frac{y - z}{y}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
x \cdot \frac{y - z}{y}
double code(double x, double y, double z) {
	return ((x * (y - z)) / y);
}
↓
double code(double x, double y, double z) {
	return (x * ((y - z) / y));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original12.3
Target3.0
Herbie3.1
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Initial program 12.3

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

  3. Applied *-un-lft-identity12.3

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

  4. Applied times-frac3.1

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

  5. Simplified3.1

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

  6. Final simplification3.1

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

Reproduce

herbie shell --seed 2020106 
(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))