Details

sample48.0ms

Algorithm

intervals

Results

12.0ms	281×	body	80	valid
11.0ms	270×	body	80	nan

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	4
1	14	4
2	14	4

prune5.0ms

Filtered

1 candidates to 0 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: 13.7b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.8b	(* c0 (sqrt (/ A (* V l))))
5.0b	(/ A (* V l))
10.8b	(sqrt (/ A (* V l)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-sqr-sqrt`
112×	`times-frac`
83×	`sqrt-prod`
82×	`add-cube-cbrt` `*-un-lft-identity`
79×	`associate-r`
39×	`associate-l`
36×	`sqrt-div` `associate-/r*`
18×	`associate-*r/` `unswap-sqr`
13×	`*-commutative`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
6×	`pow1`
3×	`expm1-log1p-u` `rem-sqrt-square` `frac-2neg` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`sqrt-pow1` `pow1/2` `pow-prod-down`

Counts

3 → 220

Calls

3 calls:

19.0ms	(* c0 (sqrt (/ A (* V l))))
8.0ms	(/ A (* V l))
11.0ms	(sqrt (/ A (* V l)))

series115.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(* c0 (sqrt (/ A (* V l))))
23.0ms	(/ A (* V l))
42.0ms	(sqrt (/ A (* V l)))

simplify69.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	530	1282
1	1933	1239
2	5001	1224

prune455.0ms

Filtered

229 candidates to 177 candidates (22.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	212	17	229
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	213	17	230

Merged error: 1.2b

Counts

230 → 17

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt A)
0.8b	(* c0 (* (fabs (/ (cbrt A) (cbrt V))) (sqrt (/ (cbrt A) (* (cbrt V) l)))))
1.2b	(/ (cbrt A) (* (cbrt V) l))
4.0b	(sqrt (/ (cbrt A) (* (cbrt V) l)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

360×	`add-sqr-sqrt`
306×	`times-frac`
285×	`associate-r`
255×	`cbrt-prod`
214×	`sqrt-prod`
197×	`add-cube-cbrt` `*-un-lft-identity`
132×	`associate-l`
79×	`unswap-sqr`
50×	`sqrt-div` `associate-*r/`
48×	`associate-/r*`
23×	`*-commutative`
20×	`add-cbrt-cube`
18×	`associate-/l*`
14×	`add-exp-log`
10×	`pow1`
7×	`rem-sqrt-square` `cbrt-unprod`
6×	`cbrt-undiv`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num` `div-inv`
2×	`div-exp`
1×	`sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 466

Calls

4 calls:

1.0ms	(cbrt A)
62.0ms	(* c0 (* (fabs (/ (cbrt A) (cbrt V))) (sqrt (/ (cbrt A) (* (cbrt V) l)))))
10.0ms	(/ (cbrt A) (* (cbrt V) l))
17.0ms	(sqrt (/ (cbrt A) (* (cbrt V) l)))

series644.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt A)
168.0ms	(* c0 (* (fabs (/ (cbrt A) (cbrt V))) (sqrt (/ (cbrt A) (* (cbrt V) l)))))
101.0ms	(/ (cbrt A) (* (cbrt V) l))
192.0ms	(sqrt (/ (cbrt A) (* (cbrt V) l)))

simplify94.0ms

Algorithm

egg-herbie

Counts

478 → 478

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1562	5258
1	5002	5153

prune1.8s

Filtered

478 candidates to 407 candidates (14.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	470	8	478
Fresh	7	9	16
Picked	1	0	1
Done	0	0	0
Total	478	17	495

Merged error: 0.0b

Counts

495 → 17

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (cbrt A) (cbrt A)))
0.8b	(* c0 (* (fabs (/ (cbrt A) (cbrt V))) (* (sqrt (/ (cbrt (* (cbrt A) (cbrt A))) (* (cbrt (cbrt V)) (cbrt (cbrt V))))) (sqrt (/ (cbrt (cbrt A)) (* (cbrt (cbrt V)) l))))))
0.8b	(/ (cbrt (cbrt A)) (* (cbrt (cbrt V)) l))
0.9b	(sqrt (/ (cbrt (cbrt A)) (* (cbrt (cbrt V)) l)))

rewrite7.7s

Algorithm

rewrite-expression-head

Rules

46659×	`add-sqr-sqrt`
38235×	`cbrt-prod`
24364×	`unswap-sqr`
13872×	`sqrt-prod`
13554×	`times-frac`
10767×	`associate-r`
4980×	`associate-*r/`
4874×	`sqrt-div`
3537×	`swap-sqr`
3196×	`associate-l`
2893×	`associate-/r*`
2512×	`add-cube-cbrt` `*-un-lft-identity`
2368×	`frac-times`
1683×	`associate-/l*`
1295×	`*-commutative`
110×	`frac-2neg` `clear-num`
74×	`associate-*l/`
24×	`add-cbrt-cube`
18×	`add-exp-log`
14×	`pow1`
13×	`rem-sqrt-square`
10×	`cbrt-unprod`
7×	`prod-exp`
6×	`cbrt-undiv` `pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`div-exp`
1×	`sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 10826

Calls

4 calls:

7.0ms	(cbrt (* (cbrt A) (cbrt A)))
4.7s	(* c0 (* (fabs (/ (cbrt A) (cbrt V))) (* (sqrt (/ (cbrt (* (cbrt A) (cbrt A))) (* (cbrt (cbrt V)) (cbrt (cbrt V))))) (sqrt (/ (cbrt (cbrt A)) (* (cbrt (cbrt V)) l))))))
13.0ms	(/ (cbrt (cbrt A)) (* (cbrt (cbrt V)) l))
26.0ms	(sqrt (/ (cbrt (cbrt A)) (* (cbrt (cbrt V)) l)))

series743.0ms

Counts

4 → 12

Calls

4 calls:

269.0ms	(cbrt (* (cbrt A) (cbrt A)))
198.0ms	(* c0 (* (fabs (/ (cbrt A) (cbrt V))) (* (sqrt (/ (cbrt (* (cbrt A) (cbrt A))) (* (cbrt (cbrt V)) (cbrt (cbrt V))))) (sqrt (/ (cbrt (cbrt A)) (* (cbrt (cbrt V)) l))))))
99.0ms	(/ (cbrt (cbrt A)) (* (cbrt (cbrt V)) l))
176.0ms	(sqrt (/ (cbrt (cbrt A)) (* (cbrt (cbrt V)) l)))

simplify3.1s

Algorithm

egg-herbie

Counts

10838 → 10838

Iterations

Useful iterations: 0 (287.0ms)

Iter	Nodes	Cost
0	16733	356283

prune47.5s

Filtered

10838 candidates to 6698 candidates (38.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	10835	3	10838
Fresh	4	12	16
Picked	1	0	1
Done	0	0	0
Total	10840	15	10855

Merged error: 0.0b

Counts

10855 → 15

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (cbrt A) (cbrt A)))
0.7b	(cbrt (* (cbrt (cbrt A)) (cbrt (cbrt A))))
0.8b	(* c0 (* (fabs (/ (cbrt A) (cbrt V))) (* (sqrt (/ (cbrt (* (cbrt A) (cbrt A))) (* (cbrt (cbrt V)) (cbrt (cbrt V))))) (sqrt (* (/ (cbrt (* (cbrt (cbrt A)) (cbrt (cbrt A)))) (* (cbrt (cbrt V)) 1)) (/ (cbrt (cbrt (cbrt A))) l))))))
0.9b	(sqrt (* (/ (cbrt (* (cbrt (cbrt A)) (cbrt (cbrt A)))) (* (cbrt (cbrt V)) 1)) (/ (cbrt (cbrt (cbrt A))) l)))

rewrite4.0m

Algorithm

rewrite-expression-head

Rules

2463410×	`add-sqr-sqrt`
2345356×	`cbrt-prod`
1437110×	`unswap-sqr`
722984×	`times-frac`
519433×	`sqrt-prod`
304814×	`associate-r`
205366×	`associate-*r/`
202574×	`sqrt-div`
202292×	`*-un-lft-identity`
195660×	`frac-times`
184461×	`swap-sqr`
168894×	`associate-/l*`
104791×	`associate-/r*`
87460×	`add-cube-cbrt`
64392×	`*-commutative`
51269×	`associate-l`
8267×	`clear-num`
8191×	`frac-2neg`
5394×	`associate-*l/`
566×	`rem-sqrt-square`
152×	`un-div-inv`
16×	`pow1`
13×	`add-exp-log` `add-cbrt-cube`
7×	`pow-prod-down`
6×	`prod-exp` `cbrt-unprod`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow1/3`
1×	`pow1/2`

Counts

4 → 366422

Calls

4 calls:

7.0ms	(cbrt (* (cbrt A) (cbrt A)))
10.0ms	(cbrt (* (cbrt (cbrt A)) (cbrt (cbrt A))))
1.5m	(* c0 (* (fabs (/ (cbrt A) (cbrt V))) (* (sqrt (/ (cbrt (* (cbrt A) (cbrt A))) (* (cbrt (cbrt V)) (cbrt (cbrt V))))) (sqrt (* (/ (cbrt (* (cbrt (cbrt A)) (cbrt (cbrt A)))) (* (cbrt (cbrt V)) 1)) (/ (cbrt (cbrt (cbrt A))) l))))))
727.0ms	(sqrt (* (/ (cbrt (* (cbrt (cbrt A)) (cbrt (cbrt A)))) (* (cbrt (cbrt V)) 1)) (/ (cbrt (cbrt (cbrt A))) l)))

series918.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(cbrt (* (cbrt A) (cbrt A)))
269.0ms	(cbrt (* (cbrt (cbrt A)) (cbrt (cbrt A))))
189.0ms	(* c0 (* (fabs (/ (cbrt A) (cbrt V))) (* (sqrt (/ (cbrt (* (cbrt A) (cbrt A))) (* (cbrt (cbrt V)) (cbrt (cbrt V))))) (sqrt (* (/ (cbrt (* (cbrt (cbrt A)) (cbrt (cbrt A)))) (* (cbrt (cbrt V)) 1)) (/ (cbrt (cbrt (cbrt A))) l))))))
182.0ms	(sqrt (* (/ (cbrt (* (cbrt (cbrt A)) (cbrt (cbrt A)))) (* (cbrt (cbrt V)) 1)) (/ (cbrt (cbrt (cbrt A))) l)))

simplify3.1m

Algorithm

egg-herbie

Counts

366434 → 366434

Iterations

Useful iterations: 0 (12.5s)

Iter	Nodes	Cost
0	421141	17721694

prune1.8m

Filtered: 366434 candidates to 179945 candidates (50.9%)