Details

sample46.0ms

Algorithm

intervals

Results

20.0ms	92×	body	1280	valid
6.0ms	130×	body	80	valid
4.0ms	23×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	5×	body	160	valid

simplify51.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	258
1	19	258
2	24	258
3	28	258
4	30	258
done	30	258

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
2.1b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
4×	`pow1`
3×	`associate-/r` `associate-/l`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `flip3--` `diff-log` `div-exp` `flip-+` `div-inv` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

0.0ms	(hypot 1.0 x)
9.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
4.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series159.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(hypot 1.0 x)
51.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
9.0ms	(/ 1.0 (hypot 1.0 x))
96.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify3.0s

Counts

72 → 72

Iterations

Useful iterations: 2 (242.0ms)

Iter	Nodes	Cost
0	101	17916
1	220	16821
2	650	16495
3	2621	16495
done	5000	16495

prune336.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
0.1b	(exp (log (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
2.1b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `log-prod` `exp-sum`
4×	`exp-prod`
3×	`associate-/r` `associate-/l`
2×	`log-div` `flip3--` `exp-diff` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `log-pow` `flip-+` `div-inv` `distribute-lft-out` `rem-exp-log`

Counts

4 → 72

Calls

4 calls:

17.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
6.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(exp (log (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
5.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
14.0ms	(/ 1.0 (hypot 1.0 x))
113.0ms	(exp (log (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
111.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify141.0ms

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	134	28406