Details

sample75.0ms

Algorithm

intervals

Results

15.0ms	306×	body	80	nan
9.0ms	159×	body	80	valid
7.0ms	24×	body	1280	valid
5.0ms	26×	body	640	valid
4.0ms	27×	body	320	valid
4.0ms	16×	body	1280	nan
3.0ms	17×	body	640	nan
2.0ms	20×	body	160	valid
1.0ms	8×	body	320	nan
1.0ms	11×	body	160	nan

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	18	27
1	41	26
2	94	26
3	218	26
4	436	26
5	824	26
6	1335	26
7	2447	26
done	5000	26

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.5b	(* (sqrt 2.0) t)
12.4b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.7b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`times-frac` `associate-l` `associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 90

Calls

4 calls:

25.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
5.0ms	(* (sqrt 2.0) t)
18.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
23.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.8s

Counts

4 → 12

Calls

4 calls:

431.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
39.0ms	(* (sqrt 2.0) t)
209.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.1s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify604.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (152.0ms)

Iter	Nodes	Cost
0	179	2660
1	455	2371
2	1907	2177
done	5000	2177

prune386.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.0b

localize19.0ms

Local error

Found 4 expressions with local error:

3.6b	(fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
5.9b	(/ (pow l 2) x)
9.7b	(/ (pow t 2) x)
27.0b	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 127

Calls

4 calls:

0.0ms	(fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
4.0ms	(/ (pow l 2) x)
4.0ms	(/ (pow t 2) x)
1.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

series367.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
23.0ms	(/ (pow l 2) x)
18.0ms	(/ (pow t 2) x)
262.0ms	(sqrt (fma 2.0 (* t t) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify109.0ms

Iterations

Useful iterations: 1 (45.0ms)

Iter	Nodes	Cost
0	218	1816
1	382	1665