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

↓

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

\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 r728254 = x;
        double r728255 = y;
        double r728256 = r728254 * r728255;
        double r728257 = z;
        double r728258 = r728256 / r728257;
        return r728258;
}

↓

double f(double x, double y, double z) {
        double r728259 = x;
        double r728260 = y;
        double r728261 = r728259 * r728260;
        double r728262 = -1.4235346119410474e-171;
        bool r728263 = r728261 <= r728262;
        double r728264 = z;
        double r728265 = r728261 / r728264;
        double r728266 = 0.0;
        bool r728267 = r728261 <= r728266;
        double r728268 = r728260 / r728264;
        double r728269 = r728259 * r728268;
        double r728270 = 3.022696328153868e+162;
        bool r728271 = r728261 <= r728270;
        double r728272 = 1.0;
        double r728273 = r728264 / r728259;
        double r728274 = r728273 / r728260;
        double r728275 = r728272 / r728274;
        double r728276 = r728271 ? r728265 : r728275;
        double r728277 = r728267 ? r728269 : r728276;
        double r728278 = r728263 ? r728265 : r728277;
        return r728278;
}

Original	6.7
Target	6.3
Herbie	2.4

Derivation

Split input into 3 regimes
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
  \[\leadsto \frac{1}{\color{blue}{\frac{\frac{z}{x}}{y}}}\]
Recombined 3 regimes into one program.
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 +o rules:numerics
(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))

Error

Try it out

Target

Derivation

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

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

`if 3.022696328153868e+162 < (* x y)`

Reproduce

In
Out