Average Error: 12.7 → 3.3
Time: 8.8s
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 r571168 = x;
        double r571169 = y;
        double r571170 = z;
        double r571171 = r571169 - r571170;
        double r571172 = r571168 * r571171;
        double r571173 = r571172 / r571169;
        return r571173;
}
↓
double f(double x, double y, double z) {
        double r571174 = x;
        double r571175 = y;
        double r571176 = z;
        double r571177 = r571175 - r571176;
        double r571178 = r571177 / r571175;
        double r571179 = r571174 * r571178;
        return r571179;
}

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

Original12.7
Target3.0
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 3 regimes

  2. if (/ (* x (- y z)) y) < -2.524820331362256e+277

    1. Initial program 52.5

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

    3. Applied associate-/l*3.0

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

    if -2.524820331362256e+277 < (/ (* x (- y z)) y) < -3.3534311254178616e+42 or 8.006142339531644e+61 < (/ (* x (- y z)) y) < 2.568234767735741e+261

    1. Initial program 0.2

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

    if -3.3534311254178616e+42 < (/ (* x (- y z)) y) < 8.006142339531644e+61 or 2.568234767735741e+261 < (/ (* x (- y z)) y)

    1. Initial program 12.6

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

    3. Applied *-un-lft-identity12.6

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

    4. Applied times-frac0.9

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

    5. Simplified0.9

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

  4. Final simplification3.3

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

Reproduce

herbie shell --seed 2019291 
(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))