Average Error: 5.8 → 1.9
Time: 4.1s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -2.7695334225662796 \cdot 10^{-244}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \le 1.8204694772158963 \cdot 10^{-280}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;x \cdot y \le 1.0368740468265092 \cdot 10^{+191}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -2.7695334225662796 \cdot 10^{-244}:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\

\mathbf{elif}\;x \cdot y \le 1.8204694772158963 \cdot 10^{-280}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;x \cdot y \le 1.0368740468265092 \cdot 10^{+191}:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\

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

\end{array}
double f(double x, double y, double z) {
        double r12590448 = x;
        double r12590449 = y;
        double r12590450 = r12590448 * r12590449;
        double r12590451 = z;
        double r12590452 = r12590450 / r12590451;
        return r12590452;
}
↓
double f(double x, double y, double z) {
        double r12590453 = x;
        double r12590454 = y;
        double r12590455 = r12590453 * r12590454;
        double r12590456 = -2.7695334225662796e-244;
        bool r12590457 = r12590455 <= r12590456;
        double r12590458 = 1.0;
        double r12590459 = z;
        double r12590460 = r12590459 / r12590455;
        double r12590461 = r12590458 / r12590460;
        double r12590462 = 1.8204694772158963e-280;
        bool r12590463 = r12590455 <= r12590462;
        double r12590464 = r12590454 / r12590459;
        double r12590465 = r12590464 * r12590453;
        double r12590466 = 1.0368740468265092e+191;
        bool r12590467 = r12590455 <= r12590466;
        double r12590468 = r12590459 / r12590454;
        double r12590469 = r12590453 / r12590468;
        double r12590470 = r12590467 ? r12590461 : r12590469;
        double r12590471 = r12590463 ? r12590465 : r12590470;
        double r12590472 = r12590457 ? r12590461 : r12590471;
        return r12590472;
}

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

Original5.8
Target6.0
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.7042130660650472 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -2.7695334225662796e-244 or 1.8204694772158963e-280 < (* x y) < 1.0368740468265092e+191

    1. Initial program 2.0

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

    3. Applied clear-num2.4

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

    if -2.7695334225662796e-244 < (* x y) < 1.8204694772158963e-280

    1. Initial program 14.4

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

    3. Applied *-un-lft-identity14.4

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

    if 1.0368740468265092e+191 < (* x y)

    1. Initial program 23.0

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

    3. Applied associate-/l*1.2

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -2.7695334225662796 \cdot 10^{-244}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;x \cdot y \le 1.8204694772158963 \cdot 10^{-280}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;x \cdot y \le 1.0368740468265092 \cdot 10^{+191}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"

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

  (/ (* x y) z))