Details

analyze2.4s (14.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
1.6%	98.3%	0.1%	8
2.3%	97.5%	0.1%	9
7.4%	90.9%	1.7%	10
9.2%	87.4%	3.5%	11
11.7%	83.5%	4.8%	12
15.2%	76%	8.8%	13
16.4%	72%	11.6%	14

sample131.0ms (0.8%)

Algorithm

1×

intervals

Results

52.0ms	59×	body	1280	valid
28.0ms	50×	body	640	valid
15.0ms	116×	body	80	valid
8.0ms	21×	body	320	valid
6.0ms	47×	body	80	invalid
3.0ms	6×	body	640	invalid
3.0ms	10×	body	160	valid
1.0ms	2×	body	320	invalid
0.0ms	1×	body	160	invalid

simplify24.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5086	25

prune15.0ms (0.1%)

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: 28.1b

Counts

2 → 2

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))))
5.3b	(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l))
7.4b	(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l)
23.0b	(* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))

rewrite98.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

170×	`add-exp-log`
106×	`prod-exp`
74×	`add-cbrt-cube`
40×	`cbrt-unprod`
37×	`associate-*r/`
30×	`div-exp`
22×	`associate-l`
14×	`add-sqr-sqrt`
12×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `add-cube-cbrt` `*-un-lft-identity` `distribute-lft-in` `pow-exp`
11×	`pow1`
10×	`associate-/r/`
9×	`tan-quot`
6×	`frac-times` `flip3-+` `times-frac` `flip-+`
5×	`associate-r` `associate-*l/`
4×	`pow-prod-down` `add-log-exp`
3×	`unpow-prod-down` `-commutative` `associate-/l`
2×	`div-inv`
1×	`frac-2neg` `clear-num` `associate-/r*` `unswap-sqr` `sqr-pow`

Counts

4 → 152

Calls

4 calls:

25.0ms	(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l))
23.0ms	(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l)
23.0ms	(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))))
20.0ms	(* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))

series520.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l)
119.0ms	(/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))))))
117.0ms	(* l (* (/ 2.0 (* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))) l))
101.0ms	(* (pow t 3.0) (* (sin k) (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))))))

simplify52.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5068	3715

prune466.0ms (2.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	154	10	164
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	155	11	166

Merged error: 20.2b

Counts

166 → 11

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.4b	(* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))
5.3b	(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l))
7.4b	(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l)
17.6b	(* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))

rewrite124.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

551×	`add-exp-log`
424×	`prod-exp`
85×	`add-cbrt-cube`
74×	`pow-exp`
66×	`div-exp`
52×	`cbrt-unprod`
50×	`pow-to-exp`
27×	`associate-*r/`
21×	`associate-l`
20×	`associate-*l/`
15×	`associate-r`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
10×	`cbrt-undiv`
9×	`tan-quot`
7×	`unpow-prod-down`
6×	`frac-times` `flip3-+` `flip-+`
5×	`associate-/r/`
4×	`pow-prod-down` `*-commutative` `add-log-exp`
3×	`cbrt-prod` `times-frac`
2×	`sqr-pow`
1×	`div-inv` `unswap-sqr`

Counts

4 → 210

Calls

4 calls:

35.0ms	(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l))
30.0ms	(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l)
26.0ms	(* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))
18.0ms	(* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))

series523.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

205.0ms	(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l)
126.0ms	(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))) l))
113.0ms	(* (pow (* (cbrt t) (cbrt t)) 3.0) (* (sin k) (* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))))
78.0ms	(* (* (tan k) (+ 1.0 (+ 1.0 (pow (/ k t) 2.0)))) (pow (cbrt t) 3.0))

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5033	6560

prune741.0ms (4.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	214	8	222
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	218	15	233

Merged error: 17.2b

Counts

233 → 15

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.3b	(* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))
5.3b	(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l))
7.2b	(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))
7.4b	(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l)

rewrite187.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

1830×	`add-exp-log`
1542×	`prod-exp`
314×	`pow-exp`
183×	`pow-to-exp`
178×	`div-exp`
112×	`add-cbrt-cube`
73×	`cbrt-unprod`
32×	`associate-*l/`
27×	`associate-*r/`
21×	`associate-l`
12×	`cbrt-undiv` `add-sqr-sqrt`
11×	`pow1`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
9×	`tan-quot`
6×	`frac-times` `flip3-+` `flip-+`
5×	`associate-/r/`
4×	`pow-prod-down` `*-commutative` `add-log-exp`
3×	`times-frac`
2×	`unpow-prod-down` `sqr-pow`
1×	`div-inv` `unswap-sqr`

Counts

4 → 391

Calls

4 calls:

40.0ms	(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l))
40.0ms	(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l)
29.0ms	(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))
26.0ms	(* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))

series507.0ms (3%)

Counts

4 → 12

Calls

4 calls:

203.0ms	(* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l)
126.0ms	(* l (* (/ 2.0 (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))) l))
108.0ms	(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))))
69.0ms	(* (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))

simplify142.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

403 → 403

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5022	14013

prune1.7s (10.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	398	5	403
Fresh	4	10	14
Picked	0	1	1
Done	0	0	0
Total	402	16	418

Merged error: 13.1b

Counts

418 → 16

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.3b	(* l (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ (sqrt 2.0) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))))
5.5b	(* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ (sqrt 2.0) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))))))))
5.5b	(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))
7.1b	(* l (/ (sqrt 2.0) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))

rewrite210.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

2324×	`add-exp-log`
1682×	`prod-exp`
491×	`div-exp`
300×	`pow-exp`
215×	`add-cbrt-cube`
174×	`pow-to-exp`
133×	`cbrt-unprod`
45×	`associate-l`
39×	`cbrt-undiv`
36×	`times-frac`
34×	`associate-*r/`
29×	`add-sqr-sqrt`
27×	`add-cube-cbrt` `*-un-lft-identity`
20×	`pow1`
18×	`associate-r` `sqrt-prod`
12×	`associate-*l/`
10×	`pow-prod-down`
7×	`unpow-prod-down` `sqr-pow`
6×	`tan-quot` `frac-times`
5×	`associate-/r/`
4×	`flip3-+` `*-commutative` `flip-+` `add-log-exp`
2×	`div-inv`
1×	`unswap-sqr`

Counts

4 → 474

Calls

4 calls:

48.0ms	(* l (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ (sqrt 2.0) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))))
39.0ms	(* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ (sqrt 2.0) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))))))))
33.0ms	(* l (/ (sqrt 2.0) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))
25.0ms	(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))

series595.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

206.0ms	(* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ (sqrt 2.0) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0))))))))
147.0ms	(* l (/ (sqrt 2.0) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))
134.0ms	(* l (* (/ (sqrt 2.0) (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (* l (/ (sqrt 2.0) (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))))))
107.0ms	(* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (sin k) (* (tan k) (* (+ 1.0 (+ 1.0 (pow (/ k t) 2.0))) (pow (cbrt t) 3.0)))))

simplify148.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

486 → 486

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5032	19557

prune2.5s (14.6%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	477	9	486
Fresh	3	11	14
Picked	1	0	1
Done	0	1	1
Total	481	21	502

Merged error: 12.5b

Counts

502 → 21

regimes1.2s (7.4%)

Accuracy

Total 4.8b remaining (27.3%)

Threshold costs 0b (0%)

bsearch215.0ms (1.3%)

Steps

Iters	Range		Point
9	9.76169172432333e+15	2.860343770148502e+22	9.836929728792166e+18
9	8.303996350574105e-300	4.5840800093673676e-294	8.415250548228389e-300

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	90	186
1	90	186

end0.0ms (0%)

sample4.0s (24%)

Algorithm

1×

intervals

Results

1.7s	2034×	body	1280	valid
907.0ms	1621×	body	640	valid
432.0ms	3276×	body	80	valid
294.0ms	724×	body	320	valid
178.0ms	1332×	body	80	invalid
93.0ms	345×	body	160	valid
76.0ms	130×	body	640	invalid
50.0ms	119×	body	320	invalid
24.0ms	88×	body	160	invalid
17.0ms	18×	body	1280	invalid

Details

analyze2.4s (14.5%)

sample131.0ms (0.8%)

simplify24.0ms (0.1%)

prune15.0ms (0.1%)

localize26.0ms (0.2%)

rewrite98.0ms (0.6%)

series520.0ms (3.1%)

simplify52.0ms (0.3%)

prune466.0ms (2.8%)

localize32.0ms (0.2%)

rewrite124.0ms (0.7%)

series523.0ms (3.1%)

simplify82.0ms (0.5%)

prune741.0ms (4.4%)

localize35.0ms (0.2%)

rewrite187.0ms (1.1%)

series507.0ms (3%)

simplify142.0ms (0.8%)

prune1.7s (10.2%)

localize39.0ms (0.2%)

rewrite210.0ms (1.2%)

series595.0ms (3.5%)

simplify148.0ms (0.9%)

prune2.5s (14.6%)

regimes1.2s (7.4%)

bsearch215.0ms (1.3%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.0s (24%)

Profiling