Average Error: 6.4 → 1.0
Time: 1.9s
Precision: binary64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{z} \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \leq -2.884898688967562 \cdot 10^{-241} \lor \neg \left(\frac{x \cdot y}{z} \leq 0\right) \land \frac{x \cdot y}{z} \leq 1.09577377537907 \cdot 10^{+301}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot y}{z} \leq -\infty:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;\frac{x \cdot y}{z} \leq -2.884898688967562 \cdot 10^{-241} \lor \neg \left(\frac{x \cdot y}{z} \leq 0\right) \land \frac{x \cdot y}{z} \leq 1.09577377537907 \cdot 10^{+301}:\\
\;\;\;\;\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) z) (- INFINITY))
   (* x (/ y z))
   (if (or (<= (/ (* x y) z) -2.884898688967562e-241)
           (and (not (<= (/ (* x y) z) 0.0))
                (<= (/ (* x y) z) 1.09577377537907e+301)))
     (/ (* 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) / z) <= -((double) INFINITY)) {
		tmp = x * (y / z);
	} else if ((((x * y) / z) <= -2.884898688967562e-241) || (!(((x * y) / z) <= 0.0) && (((x * y) / z) <= 1.09577377537907e+301))) {
		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

Original6.4
Target6.3
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;z < -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z < 1.7042130660650472 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/.f64 (*.f64 x y) z) < -inf.0

    1. Initial program 64.0

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

    3. Applied *-un-lft-identity_binary64_1883364.0

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

    4. Applied times-frac_binary64_188390.2

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

    5. Simplified0.2

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

    if -inf.0 < (/.f64 (*.f64 x y) z) < -2.88489868896756189e-241 or 0.0 < (/.f64 (*.f64 x y) z) < 1.09577377537907007e301

    1. Initial program 0.5

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

    if -2.88489868896756189e-241 < (/.f64 (*.f64 x y) z) < 0.0 or 1.09577377537907007e301 < (/.f64 (*.f64 x y) z)

    1. Initial program 14.7

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

    3. Applied associate-/l*_binary64_187782.2

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{z} \leq -\infty:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{z} \leq -2.884898688967562 \cdot 10^{-241} \lor \neg \left(\frac{x \cdot y}{z} \leq 0\right) \land \frac{x \cdot y}{z} \leq 1.09577377537907 \cdot 10^{+301}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020355 
(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))