Average Error: 5.9 → 0.3
Time: 3.8s
Precision: binary64
\[[x, y]=\mathsf{sort}([x, y])\]
\[\frac{x \cdot y}{z} \]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.785360067185023 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \leq -5.736233703803795 \cdot 10^{-209} \lor \neg \left(x \cdot y \leq 3.44583644 \cdot 10^{-316}\right) \land x \cdot y \leq 7.836433327857973 \cdot 10^{+280}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \leq -3.785360067185023 \cdot 10^{+178}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;x \cdot y \leq -5.736233703803795 \cdot 10^{-209} \lor \neg \left(x \cdot y \leq 3.44583644 \cdot 10^{-316}\right) \land x \cdot y \leq 7.836433327857973 \cdot 10^{+280}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

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


\end{array}

(FPCore (x y z) :precision binary64 (/ (* x y) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= (* x y) -3.785360067185023e+178)
   (* x (/ y z))
   (if (or (<= (* x y) -5.736233703803795e-209)
           (and (not (<= (* x y) 3.44583644e-316))
                (<= (* x y) 7.836433327857973e+280)))
     (/ (* x y) z)
     (/ x (/ z y)))))
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) <= -3.785360067185023e+178) {
		tmp = x * (y / z);
	} else if (((x * y) <= -5.736233703803795e-209) || (!((x * y) <= 3.44583644e-316) && ((x * y) <= 7.836433327857973e+280))) {
		tmp = (x * y) / z;
	} else {
		tmp = x / (z / y);
	}
	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
Target6.2
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;z < -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z < 1.7042130660650472 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array} \]

Derivation

  1. Split input into 3 regimes

  2. if (*.f64 x y) < -3.7853600671850233e178

    1. Initial program 22.3

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

    2. Applied *-un-lft-identity_binary6422.3

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

    3. Applied times-frac_binary641.6

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

    if -3.7853600671850233e178 < (*.f64 x y) < -5.7362337038037949e-209 or 3.44583644e-316 < (*.f64 x y) < 7.8364333278579731e280

    1. Initial program 0.3

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

    if -5.7362337038037949e-209 < (*.f64 x y) < 3.44583644e-316 or 7.8364333278579731e280 < (*.f64 x y)

    1. Initial program 18.2

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

    2. Applied associate-/l*_binary640.2

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -3.785360067185023 \cdot 10^{+178}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \leq -5.736233703803795 \cdot 10^{-209} \lor \neg \left(x \cdot y \leq 3.44583644 \cdot 10^{-316}\right) \land x \cdot y \leq 7.836433327857973 \cdot 10^{+280}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array} \]

Reproduce

herbie shell --seed 2021329 
(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))