Details

sample116.0ms

Algorithm

intervals

Results

43.0ms	63×	body	1280	valid
26.0ms	52×	body	640	valid
20.0ms	195×	body	80	valid
8.0ms	25×	body	320	valid
2.0ms	10×	body	160	valid

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (29.0ms)

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

prune12.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 31.0b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

3.0b	(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
3.2b	(* (pow t 3.0) (sin k))
5.6b	(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
23.7b	(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite506.0ms

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:

23.0ms	(/ (/ 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)))
195.0ms	(* (/ (/ 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:

336.0ms	(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
173.0ms	(* (pow t 3.0) (sin k))
73.0ms	(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
897.0ms	(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

simplify506.0ms

Algorithm

egg-herbie

Counts

2664 → 2664

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5001	46792

prune7.7s

Filtered

2664 candidates to 1568 candidates (58.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	2646	18	2664
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	2648	18	2666

Merged error: 17.5b

Counts

2666 → 18

localize32.0ms

Local error

Found 4 expressions with local error:

2.8b	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
4.1b	(* (/ (tan k) (/ (cbrt 2.0) (* (pow (cbrt t) 3.0) (sin k)))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))
8.1b	(* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) 3.0)) l)
15.1b	(/ (* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) 3.0)) l) (* (/ (tan k) (/ (cbrt 2.0) (* (pow (cbrt t) 3.0) (sin k)))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)))

rewrite2.3m

Algorithm

rewrite-expression-head

Rules

1743263×	`times-frac`
1271422×	`add-sqr-sqrt`
1182250×	`associate-l`
788981×	`cbrt-prod`
629497×	`*-un-lft-identity`
629495×	`add-cube-cbrt`
547644×	`unpow-prod-down`
311456×	`unswap-sqr`
237891×	`associate-r`
188980×	`swap-sqr`
57716×	`sqr-pow`
57617×	`*-commutative`
30922×	`associate-/r/`
25056×	`associate-/r*`
7638×	`associate-/l*`
5264×	`div-inv`
2574×	`frac-times`
1265×	`clear-num`
1263×	`frac-2neg`
1021×	`add-exp-log`
648×	`add-cbrt-cube`
507×	`div-exp`
408×	`associate-*l/` `prod-exp`
354×	`cbrt-undiv`
268×	`cbrt-unprod`
81×	`associate-/l/`
78×	`pow-exp`
50×	`pow-to-exp`
20×	`tan-quot`
18×	`associate-*r/`
8×	`pow1`
4×	`expm1-log1p-u` `un-div-inv` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down`

Counts

4 → 466450

Calls

4 calls:

3.0ms	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
178.0ms	(* (/ (tan k) (/ (cbrt 2.0) (* (pow (cbrt t) 3.0) (sin k)))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))
162.0ms	(* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) 3.0)) l)
12.2s	(/ (* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) 3.0)) l) (* (/ (tan k) (/ (cbrt 2.0) (* (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:

121.0ms	(/ (fma 2 1.0 (pow (/ k t) 2.0)) l)
679.0ms	(* (/ (tan k) (/ (cbrt 2.0) (* (pow (cbrt t) 3.0) (sin k)))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l))
329.0ms	(* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) 3.0)) l)
789.0ms	(/ (* (/ (* (cbrt 2.0) (cbrt 2.0)) (pow (* (cbrt t) (cbrt t)) 3.0)) l) (* (/ (tan k) (/ (cbrt 2.0) (* (pow (cbrt t) 3.0) (sin k)))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)))

simplify6.2m

Algorithm

egg-herbie

Counts

466462 → 466462

Iterations

Useful iterations: 0 (24.1s)

Iter	Nodes	Cost
0	389330	21881483

prune1.3m

Filtered: 466462 candidates to 294735 candidates (63.2%)