Average Error: 12.1 → 3.0
Time: 2.8s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\frac{x}{\frac{y}{y - z}}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\frac{x}{\frac{y}{y - z}}
double f(double x, double y, double z) {
        double r800591 = x;
        double r800592 = y;
        double r800593 = z;
        double r800594 = r800592 - r800593;
        double r800595 = r800591 * r800594;
        double r800596 = r800595 / r800592;
        return r800596;
}
↓
double f(double x, double y, double z) {
        double r800597 = x;
        double r800598 = y;
        double r800599 = z;
        double r800600 = r800598 - r800599;
        double r800601 = r800598 / r800600;
        double r800602 = r800597 / r800601;
        return r800602;
}

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

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

Derivation

  1. Initial program 12.1

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

  3. Applied associate-/l*3.0

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

  4. Final simplification3.0

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

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(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))