Details

sample120.0ms

Algorithm

intervals

Results

41.0ms	62×	body	1280	valid
33.0ms	63×	body	640	valid
18.0ms	187×	body	80	valid
9.0ms	26×	body	320	valid
2.0ms	10×	body	160	valid

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	48	13
1	161	13
2	944	13
3	5002	12

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 34.3b

Counts

2 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

2.2b	(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
2.4b	(* (pow t 3.0) (sin k))
5.3b	(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
29.3b	(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite503.0ms

Algorithm

rewrite-expression-head

Rules

2755×	`associate-/l*`
2677×	`add-sqr-sqrt`
2088×	`times-frac`
1848×	`frac-times`
1764×	`*-un-lft-identity`
1762×	`add-cube-cbrt`
1245×	`associate-l`
753×	`associate-/r*`
670×	`associate-r`
552×	`associate-/l/`
489×	`unswap-sqr`
450×	`unpow-prod-down`
294×	`swap-sqr`
228×	`sqr-pow`
214×	`*-commutative`
137×	`clear-num`
136×	`frac-2neg`
117×	`add-exp-log`
88×	`associate-*l/`
74×	`add-cbrt-cube`
50×	`div-exp`
40×	`prod-exp`
33×	`div-inv`
30×	`cbrt-undiv`
22×	`cbrt-unprod`
21×	`associate-*r/`
8×	`pow1`
5×	`pow-to-exp` `pow-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`un-div-inv`
2×	`tan-quot` `pow-prod-down` `associate-/r/`

Counts

4 → 2652

Calls

4 calls:

22.0ms	(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
6.0ms	(* (pow t 3.0) (sin k))
8.0ms	(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
179.0ms	(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

series1.5s

Counts

4 → 12

Calls

4 calls:

342.0ms	(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
184.0ms	(* (pow t 3.0) (sin k))
69.0ms	(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
889.0ms	(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

simplify536.0ms

Algorithm

egg-herbie

Counts

2664 → 2664

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5001	46792

prune7.6s

Filtered

2664 candidates to 1568 candidates (41.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	2649	15	2664
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	2651	15	2666

Merged error: 20.8b

Counts

2666 → 15

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
6.7b	(* (* (tan k) (* (pow (cbrt t) 3.0) (sin k))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))
8.2b	(* (/ 2.0 (pow (* (cbrt t) (cbrt t)) 3.0)) l)
15.2b	(/ (* (/ 2.0 (pow (* (cbrt t) (cbrt t)) 3.0)) l) (* (* (tan k) (* (pow (cbrt t) 3.0) (sin k))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

18137×	`add-sqr-sqrt`
16367×	`times-frac`
13429×	`associate-l`
7750×	`unpow-prod-down`
7001×	`unswap-sqr`
6115×	`*-un-lft-identity`
6113×	`add-cube-cbrt`
5941×	`associate-r`
4483×	`cbrt-prod`
1352×	`swap-sqr`
865×	`sqr-pow`
694×	`*-commutative`
450×	`add-exp-log`
240×	`prod-exp`
188×	`div-inv`
150×	`div-exp`
142×	`associate-/r*`
140×	`add-cbrt-cube` `associate-/l*`
96×	`associate-*l/`
64×	`cbrt-unprod`
42×	`cbrt-undiv`
38×	`pow-exp`
37×	`associate-/l/`
26×	`pow-to-exp`
21×	`associate-/r/`
20×	`tan-quot`
18×	`frac-times` `associate-*r/`
15×	`pow1`
10×	`clear-num`
8×	`frac-2neg`
7×	`pow-prod-down`
4×	`expm1-log1p-u` `un-div-inv` `log1p-expm1-u` `add-log-exp`

Counts

4 → 8250

Calls

4 calls:

3.0ms	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
33.0ms	(* (* (tan k) (* (pow (cbrt t) 3.0) (sin k))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))
29.0ms	(* (/ 2.0 (pow (* (cbrt t) (cbrt t)) 3.0)) l)
239.0ms	(/ (* (/ 2.0 (pow (* (cbrt t) (cbrt t)) 3.0)) l) (* (* (tan k) (* (pow (cbrt t) 3.0) (sin k))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)))

series1.9s

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
532.0ms	(* (* (tan k) (* (pow (cbrt t) 3.0) (sin k))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))
239.0ms	(* (/ 2.0 (pow (* (cbrt t) (cbrt t)) 3.0)) l)
966.0ms	(/ (* (/ 2.0 (pow (* (cbrt t) (cbrt t)) 3.0)) l) (* (* (tan k) (* (pow (cbrt t) 3.0) (sin k))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)))

simplify2.6s

Algorithm

egg-herbie

Counts

8262 → 8262

Iterations

Useful iterations: 0 (155.0ms)

Iter	Nodes	Cost
0	10775	281881

prune44.7s

Filtered

8262 candidates to 6484 candidates (21.5%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	8237	25	8262
Fresh	9	5	14
Picked	1	0	1
Done	0	0	0
Total	8247	30	8277

Merged error: 12.4b

Counts

8277 → 30

localize39.0ms

Local error

Found 4 expressions with local error:

1.2b	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
4.9b	(* (/ (/ (sqrt 2.0) (pow (sqrt (* (cbrt t) (cbrt t))) 3.0)) (* (cbrt (tan k)) (cbrt (tan k)))) (/ (* (/ (sqrt 2.0) (pow (sqrt (* (cbrt t) (cbrt t))) 3.0)) l) (* (* (cbrt (tan k)) (* (pow (cbrt t) 3.0) (sin k))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))))
5.4b	(* (* (cbrt (tan k)) (* (pow (cbrt t) 3.0) (sin k))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))
7.4b	(/ (* (/ (sqrt 2.0) (pow (sqrt (* (cbrt t) (cbrt t))) 3.0)) l) (* (* (cbrt (tan k)) (* (pow (cbrt t) 3.0) (sin k))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)))

rewrite9.0m

Algorithm

rewrite-expression-head

Calls

2 calls:

32.0ms

(* (* (cbrt (tan k)) (* (pow (cbrt t) 3.0) (sin k))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))

528.0ms

(/ (* (/ (sqrt 2.0) (pow (sqrt (* (cbrt t) (cbrt t))) 3.0)) l) (* (* (cbrt (tan k)) (* (pow (cbrt t) 3.0) (sin k))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)))