Average Error: 5.9 → 3.2
Time: 3.1s
Precision: binary64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.54695433870281 \cdot 10^{-225} \lor \neg \left(x \cdot y \leq 5.1871952156872 \cdot 10^{-320}\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \leq -3.54695433870281 \cdot 10^{-225} \lor \neg \left(x \cdot y \leq 5.1871952156872 \cdot 10^{-320}\right):\\
\;\;\;\;\frac{x \cdot y}{z}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x y) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= (* x y) -3.54695433870281e-225)
         (not (<= (* x y) 5.1871952156872e-320)))
   (/ (* x y) z)
   (* x (/ y z))))
double code(double x, double y, double z) {
	return (x * y) / z;
}
↓
double code(double x, double y, double z) {
	double tmp;
	if (((x * y) <= -3.54695433870281e-225) || !((x * y) <= 5.1871952156872e-320)) {
		tmp = (x * y) / z;
	} else {
		tmp = x * (y / z);
	}
	return tmp;
}

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

Original5.9
Target6.1
Herbie3.2
\[\begin{array}{l} \mathbf{if}\;z < -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z < 1.7042130660650472 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (*.f64 x y) < -3.54695433870280997e-225 or 5.1872e-320 < (*.f64 x y)

    1. Initial program 3.9

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

    if -3.54695433870280997e-225 < (*.f64 x y) < 5.1872e-320

    1. Initial program 14.4

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

    3. Applied *-un-lft-identity_binary64_1746914.4

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

    4. Applied times-frac_binary64_174750.2

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

    5. Simplified0.2

      \[\leadsto \color{blue}{x} \cdot \frac{y}{z}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.54695433870281 \cdot 10^{-225} \lor \neg \left(x \cdot y \leq 5.1871952156872 \cdot 10^{-320}\right):\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2021042 
(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))