Average Error: 6.7 → 2.4
Time: 1.4s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -1.42353461194104736 \cdot 10^{-171}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 0.0:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le 3.02269632815386811 \cdot 10^{162}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -1.42353461194104736 \cdot 10^{-171}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le 0.0:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;x \cdot y \le 3.02269632815386811 \cdot 10^{162}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\

\end{array}
double f(double x, double y, double z) {
        double r649353 = x;
        double r649354 = y;
        double r649355 = r649353 * r649354;
        double r649356 = z;
        double r649357 = r649355 / r649356;
        return r649357;
}
↓
double f(double x, double y, double z) {
        double r649358 = x;
        double r649359 = y;
        double r649360 = r649358 * r649359;
        double r649361 = -1.4235346119410474e-171;
        bool r649362 = r649360 <= r649361;
        double r649363 = z;
        double r649364 = r649360 / r649363;
        double r649365 = 0.0;
        bool r649366 = r649360 <= r649365;
        double r649367 = r649359 / r649363;
        double r649368 = r649358 * r649367;
        double r649369 = 3.022696328153868e+162;
        bool r649370 = r649360 <= r649369;
        double r649371 = 1.0;
        double r649372 = r649363 / r649358;
        double r649373 = r649372 / r649359;
        double r649374 = r649371 / r649373;
        double r649375 = r649370 ? r649364 : r649374;
        double r649376 = r649366 ? r649368 : r649375;
        double r649377 = r649362 ? r649364 : r649376;
        return r649377;
}

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

Original6.7
Target6.3
Herbie2.4
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -1.4235346119410474e-171 or 0.0 < (* x y) < 3.022696328153868e+162

    1. Initial program 3.0

      \[\frac{x \cdot y}{z}\]

    if -1.4235346119410474e-171 < (* x y) < 0.0

    1. Initial program 13.0

      \[\frac{x \cdot y}{z}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity13.0

      \[\leadsto \frac{x \cdot y}{\color{blue}{1 \cdot z}}\]

    4. Applied times-frac0.5

      \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y}{z}}\]

    5. Simplified0.5

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

    if 3.022696328153868e+162 < (* x y)

    1. Initial program 20.1

      \[\frac{x \cdot y}{z}\]
    2. Using strategy rm

    3. Applied clear-num20.1

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x \cdot y}}}\]
    4. Using strategy rm

    5. Applied associate-/r*2.5

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{z}{x}}{y}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -1.42353461194104736 \cdot 10^{-171}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 0.0:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \le 3.02269632815386811 \cdot 10^{162}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020020 
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -4.262230790519429e-138) (/ (* x y) z) (if (< z 1.7042130660650472e-164) (/ x (/ z y)) (* (/ x z) y)))

  (/ (* x y) z))