Average Error: 8.7 → 0.2
Time: 8.7s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.632921685862537 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1.0}}\\ \mathbf{elif}\;x \le 2472351452.7513905:\\ \;\;\;\;\frac{\left(\left(y - z\right) + 1.0\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1.0}}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -3.632921685862537 \cdot 10^{-81}:\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1.0}}\\

\mathbf{elif}\;x \le 2472351452.7513905:\\
\;\;\;\;\frac{\left(\left(y - z\right) + 1.0\right) \cdot x}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1.0}}\\

\end{array}
double f(double x, double y, double z) {
        double r12365406 = x;
        double r12365407 = y;
        double r12365408 = z;
        double r12365409 = r12365407 - r12365408;
        double r12365410 = 1.0;
        double r12365411 = r12365409 + r12365410;
        double r12365412 = r12365406 * r12365411;
        double r12365413 = r12365412 / r12365408;
        return r12365413;
}
↓
double f(double x, double y, double z) {
        double r12365414 = x;
        double r12365415 = -3.632921685862537e-81;
        bool r12365416 = r12365414 <= r12365415;
        double r12365417 = z;
        double r12365418 = y;
        double r12365419 = r12365418 - r12365417;
        double r12365420 = 1.0;
        double r12365421 = r12365419 + r12365420;
        double r12365422 = r12365417 / r12365421;
        double r12365423 = r12365414 / r12365422;
        double r12365424 = 2472351452.7513905;
        bool r12365425 = r12365414 <= r12365424;
        double r12365426 = r12365421 * r12365414;
        double r12365427 = r12365426 / r12365417;
        double r12365428 = r12365425 ? r12365427 : r12365423;
        double r12365429 = r12365416 ? r12365423 : r12365428;
        return r12365429;
}

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

Original8.7
Target0.5
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \lt -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1.0\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -3.632921685862537e-81 or 2472351452.7513905 < x

    1. Initial program 19.4

      \[\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*0.3

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(y - z\right) + 1.0}}}\]

    if -3.632921685862537e-81 < x < 2472351452.7513905

    1. Initial program 0.2

      \[\frac{x \cdot \left(\left(y - z\right) + 1.0\right)}{z}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.632921685862537 \cdot 10^{-81}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1.0}}\\ \mathbf{elif}\;x \le 2472351452.7513905:\\ \;\;\;\;\frac{\left(\left(y - z\right) + 1.0\right) \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1.0}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1.0)) z))