Average Error: 10.2 → 0.2
Time: 4.0s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -9.33691623494502822 \cdot 10^{51} \lor \neg \left(z \le 3.0566564905939977 \cdot 10^{-28}\right):\\ \;\;\;\;x \cdot \frac{1}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -9.33691623494502822 \cdot 10^{51} \lor \neg \left(z \le 3.0566564905939977 \cdot 10^{-28}\right):\\
\;\;\;\;x \cdot \frac{1}{\frac{z}{\left(y - z\right) + 1}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)\\

\end{array}
double f(double x, double y, double z) {
        double r728247 = x;
        double r728248 = y;
        double r728249 = z;
        double r728250 = r728248 - r728249;
        double r728251 = 1.0;
        double r728252 = r728250 + r728251;
        double r728253 = r728247 * r728252;
        double r728254 = r728253 / r728249;
        return r728254;
}
↓
double f(double x, double y, double z) {
        double r728255 = z;
        double r728256 = -9.336916234945028e+51;
        bool r728257 = r728255 <= r728256;
        double r728258 = 3.0566564905939977e-28;
        bool r728259 = r728255 <= r728258;
        double r728260 = !r728259;
        bool r728261 = r728257 || r728260;
        double r728262 = x;
        double r728263 = 1.0;
        double r728264 = y;
        double r728265 = r728264 - r728255;
        double r728266 = 1.0;
        double r728267 = r728265 + r728266;
        double r728268 = r728255 / r728267;
        double r728269 = r728263 / r728268;
        double r728270 = r728262 * r728269;
        double r728271 = r728262 / r728255;
        double r728272 = r728271 * r728267;
        double r728273 = r728261 ? r728270 : r728272;
        return r728273;
}

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

Original10.2
Target0.4
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \lt -2.7148310671343599 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.87410881643954616 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -9.336916234945028e+51 or 3.0566564905939977e-28 < z

    1. Initial program 17.1

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*0.1

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(y - z\right) + 1}}}\]
    4. Using strategy rm

    5. Applied div-inv0.1

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

    if -9.336916234945028e+51 < z < 3.0566564905939977e-28

    1. Initial program 0.4

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*7.5

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(y - z\right) + 1}}}\]
    4. Using strategy rm

    5. Applied associate-/r/0.4

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -9.33691623494502822 \cdot 10^{51} \lor \neg \left(z \le 3.0566564905939977 \cdot 10^{-28}\right):\\ \;\;\;\;x \cdot \frac{1}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020021 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1)) z))