Average Error: 12.5 → 3.3
Time: 6.9s
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 f(double x, double y, double z) {
        double r585228 = x;
        double r585229 = y;
        double r585230 = z;
        double r585231 = r585229 - r585230;
        double r585232 = r585228 * r585231;
        double r585233 = r585232 / r585229;
        return r585233;
}
↓
double f(double x, double y, double z) {
        double r585234 = x;
        double r585235 = y;
        double r585236 = z;
        double r585237 = r585235 - r585236;
        double r585238 = r585237 / r585235;
        double r585239 = r585234 * r585238;
        return r585239;
}

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

Original12.5
Target2.9
Herbie3.3
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739024383612783691266533098 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.693976601382852594702773997610248441465 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -3.389527714480622e-184 or 1.0512835017445004e-148 < y

    1. Initial program 12.8

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

    3. Applied *-un-lft-identity12.8

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

    4. Applied times-frac1.6

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

    5. Simplified1.6

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

    if -3.389527714480622e-184 < y < 1.0512835017445004e-148

    1. Initial program 10.8

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

    3. Applied associate-/l*11.2

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

    4. Taylor expanded around 0 7.1

      \[\leadsto \color{blue}{x - \frac{x \cdot z}{y}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.3

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

Reproduce

herbie shell --seed 2019298 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e104) (- x (/ (* z x) y)) (if (< z 1.69397660138285259e213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

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