Details

analyze818.0ms (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)

sample189.0ms (1.2%)

Algorithm

1×

intervals

Results

91.0ms	53×	body	2048	valid
53.0ms	85×	body	1024	valid
12.0ms	38×	body	512	valid
5.0ms	62×	body	128	valid
4.0ms	6×	body	1024	invalid
4.0ms	1×	body	4096	valid
3.0ms	17×	body	256	valid
2.0ms	5×	body	512	invalid
1.0ms	7×	body	256	invalid
1.0ms	1×	body	2048	invalid
1.0ms	12×	body	128	invalid
1.0ms	12×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify188.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4966	22
1	4966	22

prune3.0ms (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: 48.9b

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)))
1.6b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
6.1b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
10.9b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite181.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

584×	`times-frac_binary64_2779`
485×	`add-sqr-sqrt_binary64_2794`
366×	`*-un-lft-identity_binary64_2773`
224×	`add-cube-cbrt_binary64_2805`
174×	`associate-r_binary64_2715`
168×	`difference-of-squares_binary64_2742`
88×	`unpow-prod-down_binary64_2849`
85×	`sqr-pow_binary64_2745`
84×	`difference-of-sqr-1_binary64_2743`
29×	`div-inv_binary64_2770`
28×	`distribute-lft-out--_binary64_2727`
19×	`add-exp-log_binary64_2808`
18×	`add-cbrt-cube_binary64_2806`
13×	`associate-/r_binary64_2719` `associate-/l_binary64_2720`
7×	`pow1_binary64_2831`
6×	`cbrt-undiv_binary64_2804` `div-exp_binary64_2821` `add-log-exp_binary64_2809`
3×	`cbrt-unprod_binary64_2803` `unswap-sqr_binary64_2741` `pow-unpow_binary64_2847` `associate-l_binary64_2716` `prod-exp_binary64_2819`
2×	`associate-/r/_binary64_2721` `associate-/l/_binary64_2722` `flip3--_binary64_2777` `flip--_binary64_2748`
1×	`pow-exp_binary64_2838` `div-sub_binary64_2778` `frac-2neg_binary64_2784` `pow-prod-down_binary64_2841` `pow-to-exp_binary64_2839` `diff-log_binary64_2862` `sub-neg_binary64_2766` `distribute-lft-out_binary64_2726` `-commutative_binary64_2706` `clear-num_binary64_2772` `associate-r/_binary64_2717` `pow-pow_binary64_2842`

Counts

4 → 448

Calls

4 calls:

63.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
22.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
12.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
8.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

series1.8s (11.2%)

Counts

4 → 12

Calls

4 calls:

607.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
569.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
352.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
309.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify152.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

460 → 460

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5097	14768

prune819.0ms (5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	448	12	460
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	449	12	461

Merged error: 19.9b

Counts

461 → 12

Compiler

Compiled 14072 to 7415 computations (47.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
0.1b	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
0.3b	(*.f64 1/6 i)
17.7b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

rewrite65.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64_2779`
97×	`add-sqr-sqrt_binary64_2794`
85×	`add-cube-cbrt_binary64_2805` `*-un-lft-identity_binary64_2773`
50×	`associate-r_binary64_2715`
25×	`add-exp-log_binary64_2808` `add-cbrt-cube_binary64_2806`
13×	`pow1_binary64_2831` `associate-/r*_binary64_2719`
9×	`div-inv_binary64_2770`
7×	`cbrt-unprod_binary64_2803` `associate-l_binary64_2716` `prod-exp_binary64_2819`
6×	`cbrt-undiv_binary64_2804` `div-exp_binary64_2821`
5×	`pow-prod-down_binary64_2841` `unswap-sqr_binary64_2741`
4×	`add-log-exp_binary64_2809`
3×	`-commutative_binary64_2706` `associate-r/_binary64_2717` `associate-/l*_binary64_2720`
2×	`associate-/r/_binary64_2721` `associate-/l/_binary64_2722` `flip3-+_binary64_2776` `flip-+_binary64_2747`
1×	`frac-2neg_binary64_2784` `distribute-rgt-in_binary64_2725` `distribute-lft-in_binary64_2724` `clear-num_binary64_2772`

Counts

4 → 179

Calls

4 calls:

18.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
9.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
8.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
4.0ms	(*.f64 1/6 i)

series313.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

102.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
101.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
89.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
21.0ms	(*.f64 1/6 i)

simplify81.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5624	5462

prune313.0ms (1.9%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	177	14	191
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	178	25	203

Merged error: 8.7b

Counts

203 → 25

Compiler

Compiled 6061 to 3359 computations (44.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 100 (.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i) n))
0.3b	(*.f64 i 1/6)
2.7b	(.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) i) n)
3.9b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i)

rewrite38.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_2794`
23×	`add-cube-cbrt_binary64_2805` `*-un-lft-identity_binary64_2773`
22×	`add-exp-log_binary64_2808` `add-cbrt-cube_binary64_2806`
19×	`times-frac_binary64_2779` `associate-l_binary64_2716`
13×	`pow1_binary64_2831`
8×	`cbrt-unprod_binary64_2803` `prod-exp_binary64_2819`
7×	`associate-r_binary64_2715`
5×	`pow-prod-down_binary64_2841`
4×	`add-log-exp_binary64_2809`
3×	`cbrt-undiv_binary64_2804` `unswap-sqr_binary64_2741` `div-exp_binary64_2821` `associate-/r_binary64_2719` `-commutative_binary64_2706` `associate-/l*_binary64_2720`
2×	`associate-/l/_binary64_2722` `div-inv_binary64_2770` `associate-*l/_binary64_2718`
1×	`frac-2neg_binary64_2784` `flip3-+_binary64_2776` `clear-num_binary64_2772` `associate-*r/_binary64_2717` `flip-+_binary64_2747`

Counts

4 → 100

Calls

4 calls:

9.0ms	(.f64 100 (.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i) n))
8.0ms	(.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) i) n)
6.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i)
4.0ms	(*.f64 i 1/6)

series244.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) i) n)
85.0ms	(.f64 100 (.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i) n))
44.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i)
23.0ms	(*.f64 i 1/6)

simplify93.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4902	2477
1	4902	2477

prune160.0ms (1%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	1	23	24
Picked	1	0	1
Done	0	0	0
Total	112	25	137

Merged error: 8.7b

Counts

137 → 25

Compiler

Compiled 3328 to 2098 computations (37% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.1b	(exp.f64 (log.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i)))
2.7b	(.f64 (exp.f64 (log.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) i))) n)
3.9b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i)
13.3b	(log.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i))

rewrite45.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64_2794`
41×	`log-prod_binary64_2856`
37×	`times-frac_binary64_2779`
36×	`add-cube-cbrt_binary64_2805` `*-un-lft-identity_binary64_2773`
28×	`exp-sum_binary64_2816`
16×	`associate-l_binary64_2716`
10×	`add-exp-log_binary64_2808`
8×	`pow1_binary64_2831` `add-cbrt-cube_binary64_2806`
4×	`exp-prod_binary64_2822` `div-inv_binary64_2770` `add-log-exp_binary64_2809`
3×	`log-div_binary64_2857` `unswap-sqr_binary64_2741` `associate-/r_binary64_2719` `associate-r_binary64_2715` `associate-/l_binary64_2720`
2×	`rem-log-exp_binary64_2811` `associate-/l/_binary64_2722` `exp-diff_binary64_2818` `div-exp_binary64_2821` `log-pow_binary64_2859`
1×	`cbrt-unprod_binary64_2803` `cbrt-undiv_binary64_2804` `frac-2neg_binary64_2784` `pow-prod-down_binary64_2841` `flip3-+_binary64_2776` `-commutative_binary64_2706` `clear-num_binary64_2772` `prod-exp_binary64_2819` `rem-exp-log_binary64_2810` `flip-+_binary64_2747` `associate-l/_binary64_2718`

Counts

4 → 113

Calls

4 calls:

15.0ms	(.f64 (exp.f64 (log.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) i))) n)
6.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i)
6.0ms	(exp.f64 (log.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i)))
5.0ms	(log.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i))

series372.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

173.0ms	(.f64 (exp.f64 (log.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 i 1/6)))) i))) n)
85.0ms	(exp.f64 (log.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i)))
68.0ms	(log.f64 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i))
46.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 i 1/6)))) i)

simplify100.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4987	3453
1	4987	3453

prune318.0ms (1.9%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	117	8	125
Fresh	8	16	24
Picked	1	0	1
Done	0	0	0
Total	126	24	150

Merged error: 8.7b

Counts

150 → 24

Compiler

Compiled 3531 to 2232 computations (36.8% saved)

regimes1.6s (9.8%)

Compiler: Compiled 15437 to 10576 computations (31.5% saved)

bsearch169.0ms (1%)

Steps

Iters	Range		Point
8	1.8505735226168966e+139	4.1227880209909884e+142	5.8779358902733686e+141
4	9.43466207479006	17.72397208122039	9.666765948721938
8	-175.01868109941555	-0.02022013763224878	-0.056267999484461595

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	53	89
1	53	89

end0.0ms (0%)

sample8.3s (50.4%)

Algorithm

1×

intervals

Results

2.8s	1774×	body	2048	valid
1.6s	2672×	body	1024	valid
331.0ms	1147×	body	512	valid
132.0ms	1850×	body	128	valid
119.0ms	40×	body	4096	valid
107.0ms	177×	body	1024	invalid
86.0ms	517×	body	256	valid
78.0ms	206×	body	512	invalid
46.0ms	459×	body	128	invalid
34.0ms	156×	body	256	invalid
23.0ms	14×	body	2048	invalid
14.0ms	297×	body	128	nan

Compiler

Compiled 3904 to 2669 computations (31.6% saved)

Details

analyze818.0ms (5%)

sample189.0ms (1.2%)

simplify188.0ms (1.1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

rewrite181.0ms (1.1%)

series1.8s (11.2%)

simplify152.0ms (0.9%)

prune819.0ms (5%)

localize12.0ms (0.1%)

rewrite65.0ms (0.4%)

series313.0ms (1.9%)

simplify81.0ms (0.5%)

prune313.0ms (1.9%)

localize13.0ms (0.1%)

rewrite38.0ms (0.2%)

series244.0ms (1.5%)

simplify93.0ms (0.6%)

prune160.0ms (1%)

localize14.0ms (0.1%)

rewrite45.0ms (0.3%)

series372.0ms (2.3%)

simplify100.0ms (0.6%)

prune318.0ms (1.9%)

regimes1.6s (9.8%)

bsearch169.0ms (1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample8.3s (50.4%)

Profiling