Details

sample98.0ms

Algorithm

intervals

Results

45.0ms	728×	body	80	nan
19.0ms	256×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	12	13
2	16	13
3	18	13
done	18	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.0b	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.0b	(/ (sqrt (- 1.0 (* x x))) x)
0.0b	(sqrt (- 1.0 (* x x)))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
42×	`times-frac`
39×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
20×	`sqrt-prod`
13×	`fma-def`
8×	`log-prod` `distribute-lft-out`
7×	`add-exp-log` `associate-/l*`
6×	`pow1` `add-cbrt-cube` `div-inv` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`log-div` `associate-/r*`
2×	`distribute-rgt-out` `flip3--` `flip3-+` `frac-add` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `clear-num` `sum-log` `log-pow`

Counts

4 → 119

Calls

4 calls:

45.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
77.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
21.0ms	(/ (sqrt (- 1.0 (* x x))) x)
9.0ms	(sqrt (- 1.0 (* x x)))

series745.0ms

Counts

4 → 12

Calls

4 calls:

381.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
135.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
148.0ms	(/ (sqrt (- 1.0 (* x x))) x)
80.0ms	(sqrt (- 1.0 (* x x)))

simplify2.0s

Counts

131 → 131

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	239	2032
1	570	1884
2	2436	1770
done	5001	1753

prune601.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (- 1.0 (* x x))))
0.3b	(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
0.3b	(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
0.5b	(* (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)) (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)))

rewrite314.0ms

Algorithm

rewrite-expression-head

Rules

950×	`sqrt-prod`
671×	`add-sqr-sqrt`
580×	`times-frac`
284×	`add-cube-cbrt` `*-un-lft-identity`
132×	`swap-sqr`
64×	`associate-r` `associate-l`
49×	`unswap-sqr`
43×	`difference-of-squares`
20×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
13×	`pow1`
12×	`sqrt-div` `associate-/r*`
6×	`cbrt-undiv` `sqrt-undiv` `div-exp` `div-inv`
4×	`expm1-log1p-u` `sqrt-pow1` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `frac-2neg` `pow1/2` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `pow-prod-down` `associate-l/` `rem-square-sqrt` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 547

Calls

4 calls:

14.0ms	(sqrt (sqrt (- 1.0 (* x x))))
40.0ms	(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
21.0ms	(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
164.0ms	(* (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)) (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)))

series856.0ms

Counts

4 → 12

Calls

4 calls:

319.0ms	(sqrt (sqrt (- 1.0 (* x x))))
191.0ms	(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
151.0ms	(/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x))
194.0ms	(* (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)) (/ (sqrt (sqrt (- 1.0 (* x x)))) (sqrt x)))

simplify823.0ms

Counts

559 → 559

Iterations

Useful iterations: done (783.0ms)

Iter	Nodes	Cost
0	431	17192
1	1419	15720
done	5000	15143

prune1.7s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	26
1	13	26
done	13	26

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.9s	24032×	body	80	nan
1.2s	8000×	body	80	valid