Average Error: 10.1 → 0.1
Time: 20.6s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le -6.579027488067199411550511935864463917316 \cdot 10^{210} \lor \neg \left(\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le 3.530201563568855701403158383753448655305 \cdot 10^{90}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z} - x\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le -6.579027488067199411550511935864463917316 \cdot 10^{210} \lor \neg \left(\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le 3.530201563568855701403158383753448655305 \cdot 10^{90}\right):\\
\;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\

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

\end{array}
double f(double x, double y, double z) {
        double r475381 = x;
        double r475382 = y;
        double r475383 = z;
        double r475384 = r475382 - r475383;
        double r475385 = 1.0;
        double r475386 = r475384 + r475385;
        double r475387 = r475381 * r475386;
        double r475388 = r475387 / r475383;
        return r475388;
}
↓
double f(double x, double y, double z) {
        double r475389 = x;
        double r475390 = y;
        double r475391 = z;
        double r475392 = r475390 - r475391;
        double r475393 = 1.0;
        double r475394 = r475392 + r475393;
        double r475395 = r475389 * r475394;
        double r475396 = r475395 / r475391;
        double r475397 = -6.579027488067199e+210;
        bool r475398 = r475396 <= r475397;
        double r475399 = 3.5302015635688557e+90;
        bool r475400 = r475396 <= r475399;
        double r475401 = !r475400;
        bool r475402 = r475398 || r475401;
        double r475403 = r475389 / r475391;
        double r475404 = r475390 + r475393;
        double r475405 = r475403 * r475404;
        double r475406 = r475405 - r475389;
        double r475407 = r475389 * r475404;
        double r475408 = r475407 / r475391;
        double r475409 = r475408 - r475389;
        double r475410 = r475402 ? r475406 : r475409;
        return r475410;
}

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

Original10.1
Target0.5
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;x \lt -2.714831067134359919650240696134672137284 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.874108816439546156869494499878029491333 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (+ (- y z) 1.0)) z) < -6.579027488067199e+210 or 3.5302015635688557e+90 < (/ (* x (+ (- y z) 1.0)) z)

    1. Initial program 27.9

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

    2. Taylor expanded around 0 10.4

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

    3. Simplified0.1

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

    if -6.579027488067199e+210 < (/ (* x (+ (- y z) 1.0)) z) < 3.5302015635688557e+90

    1. Initial program 0.1

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

    2. Taylor expanded around 0 0.1

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

    3. Simplified2.7

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

    4. Taylor expanded around 0 0.1

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

    5. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le -6.579027488067199411550511935864463917316 \cdot 10^{210} \lor \neg \left(\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le 3.530201563568855701403158383753448655305 \cdot 10^{90}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + 1\right)}{z} - x\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 +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))