Details

analyze798.0ms (5.5%)

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
3.1%	96.8%	0.1%	6
15.6%	81.2%	3.2%	7
23.4%	72.6%	4%	8
32.4%	56.2%	11.4%	9
36.3%	51.7%	12%	10
40.7%	42.9%	16.4%	11
42.6%	40.3%	17.1%	12
44.5%	36%	19.4%	13
45.5%	34.5%	20%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample185.0ms (1.3%)

Algorithm

1×

intervals

Results

87.0ms	55×	body	2048	valid
59.0ms	94×	body	1024	valid
8.0ms	33×	body	512	valid
6.0ms	9×	body	1024	invalid
4.0ms	22×	body	256	valid
4.0ms	51×	body	128	valid
3.0ms	1×	body	4096	valid
2.0ms	5×	body	512	invalid
2.0ms	17×	body	128	invalid
2.0ms	6×	body	256	invalid
0.0ms	9×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify220.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4939	22
1	4939	22

prune6.0ms (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: 50.3b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
1.9b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
5.5b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
9.2b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite195.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

584×	`times-frac_binary64_3181`
486×	`add-sqr-sqrt_binary64_3197`
367×	`*-un-lft-identity_binary64_3175`
225×	`add-cube-cbrt_binary64_3210`
174×	`associate-r_binary64_3115`
168×	`difference-of-squares_binary64_3144`
88×	`unpow-prod-down_binary64_3254`
85×	`sqr-pow_binary64_3147`
84×	`difference-of-sqr-1_binary64_3145`
29×	`div-inv_binary64_3172`
28×	`distribute-lft-out--_binary64_3127`
19×	`add-exp-log_binary64_3213`
18×	`add-cbrt-cube_binary64_3211`
13×	`associate-/l_binary64_3120` `associate-/r_binary64_3119`
7×	`pow1_binary64_3236`
6×	`cbrt-undiv_binary64_3209` `div-exp_binary64_3226` `add-log-exp_binary64_3214`
3×	`prod-exp_binary64_3224` `pow-unpow_binary64_3252` `cbrt-unprod_binary64_3208` `associate-l_binary64_3116` `unswap-sqr_binary64_3143` `cancel-sign-sub-inv_binary64_3141`
2×	`flip--_binary64_3150` `flip3--_binary64_3179` `associate-/l/_binary64_3122` `associate-/r/_binary64_3121`
1×	`associate-r/_binary64_3117` `div-sub_binary64_3180` `pow-exp_binary64_3243` `diff-log_binary64_3267` `-commutative_binary64_3106` `distribute-lft-out_binary64_3126` `pow-prod-down_binary64_3246` `clear-num_binary64_3174` `frac-2neg_binary64_3186` `pow-pow_binary64_3247` `sub-neg_binary64_3168` `pow-to-exp_binary64_3244`

Counts

4 → 451

Calls

4 calls:

69.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
23.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
13.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
8.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

series1.8s (12.6%)

Counts

4 → 12

Calls

4 calls:

615.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
555.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
357.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
300.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify147.0ms (1%)

Algorithm

1×	egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5117	14771

prune1.2s (8.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	455	8	463
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	456	8	464

Merged error: 18.6b

Counts

464 → 8

Compiler

Compiled 22544 to 13180 computations (41.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
0.1b	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
0.3b	(*.f64 1/6 i)
14.8b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

rewrite68.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64_3181`
97×	`add-sqr-sqrt_binary64_3197`
85×	`*-un-lft-identity_binary64_3175` `add-cube-cbrt_binary64_3210`
50×	`associate-r_binary64_3115`
25×	`add-cbrt-cube_binary64_3211` `add-exp-log_binary64_3213`
13×	`associate-/r*_binary64_3119` `pow1_binary64_3236`
9×	`div-inv_binary64_3172`
7×	`prod-exp_binary64_3224` `cbrt-unprod_binary64_3208` `associate-l_binary64_3116`
6×	`cbrt-undiv_binary64_3209` `div-exp_binary64_3226`
5×	`pow-prod-down_binary64_3246` `unswap-sqr_binary64_3143`
4×	`add-log-exp_binary64_3214`
3×	`associate-r/_binary64_3117` `-commutative_binary64_3106` `associate-/l*_binary64_3120`
2×	`flip-+_binary64_3149` `flip3-+_binary64_3178` `associate-/l/_binary64_3122` `associate-/r/_binary64_3121`
1×	`clear-num_binary64_3174` `frac-2neg_binary64_3186` `distribute-lft-in_binary64_3124` `distribute-rgt-in_binary64_3125`

Counts

4 → 179

Calls

4 calls:

23.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
10.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
9.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
4.0ms	(*.f64 1/6 i)

series301.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

96.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
94.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
90.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
21.0ms	(*.f64 1/6 i)

simplify108.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4928	5462
1	4928	5462

prune1.9s (13.4%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	179	12	191
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	180	19	199

Merged error: 9.2b

Counts

199 → 19

Compiler

Compiled 36842 to 24205 computations (34.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
0.0b	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
0.3b	(*.f64 i 1/6)
2.6b	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_3197`
15×	`add-cbrt-cube_binary64_3211` `add-exp-log_binary64_3213` `pow1_binary64_3236`
12×	`associate-l_binary64_3116`
11×	`*-un-lft-identity_binary64_3175` `add-cube-cbrt_binary64_3210`
10×	`associate-r_binary64_3115`
8×	`associate-*r/_binary64_3117`
6×	`prod-exp_binary64_3224` `pow-prod-down_binary64_3246` `cbrt-unprod_binary64_3208` `distribute-lft-in_binary64_3124` `distribute-rgt-in_binary64_3125`
4×	`*-commutative_binary64_3106` `add-log-exp_binary64_3214`
3×	`flip-+_binary64_3149` `flip3-+_binary64_3178` `unswap-sqr_binary64_3143`

Counts

4 → 86

Calls

4 calls:

8.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))
6.0ms	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
6.0ms	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
4.0ms	(*.f64 i 1/6)

series267.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

93.0ms	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
83.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))
70.0ms	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
20.0ms	(*.f64 i 1/6)

simplify53.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4963	1381
1	4963	1381

prune297.0ms (2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	2	16	18
Picked	1	0	1
Done	0	0	0
Total	98	19	117

Merged error: 9.2b

Counts

117 → 19

Compiler

Compiled 6028 to 4319 computations (28.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 1/6)
1.0b	(cbrt.f64 1/6)
1.0b	(cbrt.f64 1/6)
2.6b	(.f64 n (.f64 i (+.f64 1/2 (.f64 (.f64 i (*.f64 (cbrt.f64 1/6) (cbrt.f64 1/6))) (cbrt.f64 1/6)))))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64_3206` `add-cbrt-cube_binary64_3211` `add-exp-log_binary64_3213` `pow1_binary64_3236`
8×	`*-un-lft-identity_binary64_3175` `add-cube-cbrt_binary64_3210` `add-sqr-sqrt_binary64_3197`
4×	`associate-*r/_binary64_3117` `distribute-lft-in_binary64_3124` `distribute-rgt-in_binary64_3125` `add-log-exp_binary64_3214`
3×	`prod-exp_binary64_3224` `pow-prod-down_binary64_3246` `cbrt-unprod_binary64_3208` `pow1/3_binary64_3257` `associate-l_binary64_3116`
1×	`-commutative_binary64_3106` `flip-+_binary64_3149` `flip3-+_binary64_3178` `associate-r*_binary64_3115`

Counts

4 → 57

Calls

4 calls:

8.0ms	(.f64 n (.f64 i (+.f64 1/2 (.f64 (.f64 i (*.f64 (cbrt.f64 1/6) (cbrt.f64 1/6))) (cbrt.f64 1/6)))))
1.0ms	(cbrt.f64 1/6)
1.0ms	(cbrt.f64 1/6)
1.0ms	(cbrt.f64 1/6)

series158.0ms (1.1%)

Counts

4 → 6

Calls

4 calls:

158.0ms	(.f64 n (.f64 i (+.f64 1/2 (.f64 (.f64 i (*.f64 (cbrt.f64 1/6) (cbrt.f64 1/6))) (cbrt.f64 1/6)))))
0.0ms	(cbrt.f64 1/6)
0.0ms	(cbrt.f64 1/6)
0.0ms	(cbrt.f64 1/6)

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4968	637
1	4968	637

prune100.0ms (0.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	0	18	18
Picked	1	0	1
Done	0	0	0
Total	63	19	82

Merged error: 9.2b

Counts

82 → 19

Compiler

Compiled 1836 to 1432 computations (22% saved)

regimes224.0ms (1.5%)

Compiler: Compiled 1440 to 1054 computations (26.8% saved)

bsearch140.0ms (1%)

Steps

Iters	Range		Point
8	4.962814741263785e-08	0.00013568675421882443	0.00013295774325707314
9	-121.15849076930778	-1.7403074637660075e-05	-0.02786839728628234

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	63
1	40	63

end0.0ms (0%)

sample6.1s (41.8%)

Algorithm

1×

intervals

Results

2.8s	1774×	body	2048	valid
1.6s	2620×	body	1024	valid
338.0ms	1184×	body	512	valid
132.0ms	1843×	body	128	valid
102.0ms	33×	body	4096	valid
96.0ms	154×	body	1024	invalid
86.0ms	546×	body	256	valid
83.0ms	228×	body	512	invalid
51.0ms	530×	body	128	invalid
38.0ms	174×	body	256	invalid
15.0ms	331×	body	128	nan
14.0ms	10×	body	2048	invalid

Compiler

Compiled 553 to 402 computations (27.3% saved)

Details

analyze798.0ms (5.5%)

sample185.0ms (1.3%)

simplify220.0ms (1.5%)

prune6.0ms (0%)

localize9.0ms (0.1%)

rewrite195.0ms (1.3%)

series1.8s (12.6%)

simplify147.0ms (1%)

prune1.2s (8.5%)

localize11.0ms (0.1%)

rewrite68.0ms (0.5%)

series301.0ms (2.1%)

simplify108.0ms (0.7%)

prune1.9s (13.4%)

localize11.0ms (0.1%)

rewrite32.0ms (0.2%)

series267.0ms (1.8%)

simplify53.0ms (0.4%)

prune297.0ms (2%)

localize12.0ms (0.1%)

rewrite20.0ms (0.1%)

series158.0ms (1.1%)

simplify76.0ms (0.5%)

prune100.0ms (0.7%)

regimes224.0ms (1.5%)

bsearch140.0ms (1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.1s (41.8%)

Profiling