Average Error: 6.0 → 0.5
Time: 11.2s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -1.871003352164139 \cdot 10^{+282}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -9.609520285206618 \cdot 10^{-248}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 1.7178429536978092 \cdot 10^{-196}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;x \cdot y \le 3.3882771524409995 \cdot 10^{+143}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -1.871003352164139 \cdot 10^{+282}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;x \cdot y \le -9.609520285206618 \cdot 10^{-248}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;x \cdot y \le 1.7178429536978092 \cdot 10^{-196}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;x \cdot y \le 3.3882771524409995 \cdot 10^{+143}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
double f(double x, double y, double z) {
        double r37637397 = x;
        double r37637398 = y;
        double r37637399 = r37637397 * r37637398;
        double r37637400 = z;
        double r37637401 = r37637399 / r37637400;
        return r37637401;
}
↓
double f(double x, double y, double z) {
        double r37637402 = x;
        double r37637403 = y;
        double r37637404 = r37637402 * r37637403;
        double r37637405 = -1.871003352164139e+282;
        bool r37637406 = r37637404 <= r37637405;
        double r37637407 = z;
        double r37637408 = r37637407 / r37637403;
        double r37637409 = r37637402 / r37637408;
        double r37637410 = -9.609520285206618e-248;
        bool r37637411 = r37637404 <= r37637410;
        double r37637412 = r37637404 / r37637407;
        double r37637413 = 1.7178429536978092e-196;
        bool r37637414 = r37637404 <= r37637413;
        double r37637415 = r37637403 / r37637407;
        double r37637416 = r37637415 * r37637402;
        double r37637417 = 3.3882771524409995e+143;
        bool r37637418 = r37637404 <= r37637417;
        double r37637419 = r37637418 ? r37637412 : r37637416;
        double r37637420 = r37637414 ? r37637416 : r37637419;
        double r37637421 = r37637411 ? r37637412 : r37637420;
        double r37637422 = r37637406 ? r37637409 : r37637421;
        return r37637422;
}

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

Original6.0
Target6.1
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.7042130660650472 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -1.871003352164139e+282

    1. Initial program 51.5

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

    3. Applied associate-/l*0.3

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

    if -1.871003352164139e+282 < (* x y) < -9.609520285206618e-248 or 1.7178429536978092e-196 < (* x y) < 3.3882771524409995e+143

    1. Initial program 0.2

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

    if -9.609520285206618e-248 < (* x y) < 1.7178429536978092e-196 or 3.3882771524409995e+143 < (* x y)

    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-frac1.0

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

    5. Simplified1.0

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -1.871003352164139 \cdot 10^{+282}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;x \cdot y \le -9.609520285206618 \cdot 10^{-248}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;x \cdot y \le 1.7178429536978092 \cdot 10^{-196}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;x \cdot y \le 3.3882771524409995 \cdot 10^{+143}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(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))