Average Error: 10.4 → 0.4
Time: 22.5s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.894138962339348575688367605867883657369 \cdot 10^{-104}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;x \le 5.333921896352304070857289463437993050447 \cdot 10^{-71}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.894138962339348575688367605867883657369 \cdot 10^{-104}:\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\

\mathbf{elif}\;x \le 5.333921896352304070857289463437993050447 \cdot 10^{-71}:\\
\;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r361546 = x;
        double r361547 = y;
        double r361548 = z;
        double r361549 = r361547 - r361548;
        double r361550 = 1.0;
        double r361551 = r361549 + r361550;
        double r361552 = r361546 * r361551;
        double r361553 = r361552 / r361548;
        return r361553;
}
↓
double f(double x, double y, double z) {
        double r361554 = x;
        double r361555 = -1.8941389623393486e-104;
        bool r361556 = r361554 <= r361555;
        double r361557 = z;
        double r361558 = y;
        double r361559 = r361558 - r361557;
        double r361560 = 1.0;
        double r361561 = r361559 + r361560;
        double r361562 = r361557 / r361561;
        double r361563 = r361554 / r361562;
        double r361564 = 5.333921896352304e-71;
        bool r361565 = r361554 <= r361564;
        double r361566 = r361554 * r361561;
        double r361567 = 1.0;
        double r361568 = r361567 / r361557;
        double r361569 = r361566 * r361568;
        double r361570 = r361554 / r361557;
        double r361571 = r361558 + r361560;
        double r361572 = r361570 * r361571;
        double r361573 = r361572 - r361554;
        double r361574 = r361565 ? r361569 : r361573;
        double r361575 = r361556 ? r361563 : r361574;
        return r361575;
}

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

Original10.4
Target0.4
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -1.8941389623393486e-104

    1. Initial program 17.3

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

    3. Applied associate-/l*0.9

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

    if -1.8941389623393486e-104 < x < 5.333921896352304e-71

    1. Initial program 0.2

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

    3. Applied div-inv0.3

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

    if 5.333921896352304e-71 < x

    1. Initial program 19.4

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

    2. Taylor expanded around 0 6.2

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

    3. Simplified0.1

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.894138962339348575688367605867883657369 \cdot 10^{-104}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;x \le 5.333921896352304070857289463437993050447 \cdot 10^{-71}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\ \end{array}\]

Reproduce

herbie shell --seed 2019322 +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))