Average Error: 11.4 → 3.1
Time: 12.7s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.0429105902147922 \cdot 10^{+45}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{elif}\;z \le 9.854646036103107 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;z \le 3.474551814140681 \cdot 10^{+180}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.0429105902147922 \cdot 10^{+45}:\\
\;\;\;\;x - \frac{x \cdot z}{y}\\

\mathbf{elif}\;z \le 9.854646036103107 \cdot 10^{+107}:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{elif}\;z \le 3.474551814140681 \cdot 10^{+180}:\\
\;\;\;\;x - \frac{x \cdot z}{y}\\

\mathbf{else}:\\
\;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\

\end{array}
double f(double x, double y, double z) {
        double r24149227 = x;
        double r24149228 = y;
        double r24149229 = z;
        double r24149230 = r24149228 - r24149229;
        double r24149231 = r24149227 * r24149230;
        double r24149232 = r24149231 / r24149228;
        return r24149232;
}
↓
double f(double x, double y, double z) {
        double r24149233 = z;
        double r24149234 = -2.0429105902147922e+45;
        bool r24149235 = r24149233 <= r24149234;
        double r24149236 = x;
        double r24149237 = r24149236 * r24149233;
        double r24149238 = y;
        double r24149239 = r24149237 / r24149238;
        double r24149240 = r24149236 - r24149239;
        double r24149241 = 9.854646036103107e+107;
        bool r24149242 = r24149233 <= r24149241;
        double r24149243 = r24149238 - r24149233;
        double r24149244 = r24149238 / r24149243;
        double r24149245 = r24149236 / r24149244;
        double r24149246 = 3.474551814140681e+180;
        bool r24149247 = r24149233 <= r24149246;
        double r24149248 = r24149236 / r24149238;
        double r24149249 = r24149243 * r24149248;
        double r24149250 = r24149247 ? r24149240 : r24149249;
        double r24149251 = r24149242 ? r24149245 : r24149250;
        double r24149252 = r24149235 ? r24149240 : r24149251;
        return r24149252;
}

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

Original11.4
Target3.1
Herbie3.1
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -2.0429105902147922e+45 or 9.854646036103107e+107 < z < 3.474551814140681e+180

    1. Initial program 10.3

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

    3. Applied associate-/l*8.4

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

    4. Taylor expanded around 0 8.2

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

    if -2.0429105902147922e+45 < z < 9.854646036103107e+107

    1. Initial program 11.6

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

    3. Applied associate-/l*0.5

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

    if 3.474551814140681e+180 < z

    1. Initial program 12.2

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

    3. Applied associate-/l*12.7

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{y - z}}}\]
    4. Using strategy rm

    5. Applied associate-/r/12.6

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

  4. Final simplification3.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.0429105902147922 \cdot 10^{+45}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{elif}\;z \le 9.854646036103107 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;z \le 3.474551814140681 \cdot 10^{+180}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"

  :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))