Details

analyze836.0ms (5.4%)

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)

sample193.0ms (1.3%)

Algorithm

1×

intervals

Results

93.0ms	53×	body	2048	valid
54.0ms	85×	body	1024	valid
13.0ms	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)

simplify215.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4939	22
1	4939	22

prune2.0ms (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))

rewrite179.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

584×	`times-frac_binary64_2837`
486×	`add-sqr-sqrt_binary64_2853`
367×	`*-un-lft-identity_binary64_2831`
225×	`add-cube-cbrt_binary64_2866`
174×	`associate-r_binary64_2771`
168×	`difference-of-squares_binary64_2800`
88×	`unpow-prod-down_binary64_2910`
85×	`sqr-pow_binary64_2803`
84×	`difference-of-sqr-1_binary64_2801`
29×	`div-inv_binary64_2828`
28×	`distribute-lft-out--_binary64_2783`
19×	`add-exp-log_binary64_2869`
18×	`add-cbrt-cube_binary64_2867`
13×	`associate-/l_binary64_2776` `associate-/r_binary64_2775`
7×	`pow1_binary64_2892`
6×	`add-log-exp_binary64_2870` `cbrt-undiv_binary64_2865` `div-exp_binary64_2882`
3×	`cbrt-unprod_binary64_2864` `pow-unpow_binary64_2908` `unswap-sqr_binary64_2799` `prod-exp_binary64_2880` `cancel-sign-sub-inv_binary64_2797` `associate-l_binary64_2772`
2×	`associate-/l/_binary64_2778` `flip3--_binary64_2835` `flip--_binary64_2806` `associate-/r/_binary64_2777`
1×	`frac-2neg_binary64_2842` `pow-prod-down_binary64_2902` `pow-exp_binary64_2899` `pow-pow_binary64_2903` `-commutative_binary64_2762` `distribute-lft-out_binary64_2782` `diff-log_binary64_2923` `sub-neg_binary64_2824` `pow-to-exp_binary64_2900` `clear-num_binary64_2830` `div-sub_binary64_2836` `associate-r/_binary64_2773`

Counts

4 → 451

Calls

4 calls:

64.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
26.0ms	(/.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%)

Counts

4 → 12

Calls

4 calls:

622.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
571.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
355.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
301.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify155.0ms (1%)

Algorithm

1×	egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5117	14771

prune1.5s (10%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	451	12	463
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	452	12	464

Merged error: 19.9b

Counts

464 → 12

Compiler

Compiled 26610 to 15792 computations (40.7% saved)

localize13.0ms (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))

rewrite63.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64_2837`
97×	`add-sqr-sqrt_binary64_2853`
85×	`add-cube-cbrt_binary64_2866` `*-un-lft-identity_binary64_2831`
50×	`associate-r_binary64_2771`
25×	`add-cbrt-cube_binary64_2867` `add-exp-log_binary64_2869`
13×	`pow1_binary64_2892` `associate-/r*_binary64_2775`
9×	`div-inv_binary64_2828`
7×	`cbrt-unprod_binary64_2864` `prod-exp_binary64_2880` `associate-l_binary64_2772`
6×	`cbrt-undiv_binary64_2865` `div-exp_binary64_2882`
5×	`pow-prod-down_binary64_2902` `unswap-sqr_binary64_2799`
4×	`add-log-exp_binary64_2870`
3×	`-commutative_binary64_2762` `associate-/l_binary64_2776` `associate-*r/_binary64_2773`
2×	`associate-/l/_binary64_2778` `flip3-+_binary64_2834` `flip-+_binary64_2805` `associate-/r/_binary64_2777`
1×	`frac-2neg_binary64_2842` `clear-num_binary64_2830` `distribute-lft-in_binary64_2780` `distribute-rgt-in_binary64_2781`

Counts

4 → 179

Calls

4 calls:

19.0ms	(.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))
9.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
4.0ms	(*.f64 1/6 i)

series286.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

90.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
90.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
83.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
23.0ms	(*.f64 1/6 i)

simplify109.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4928	5462
1	4928	5462

prune1.8s (12%)

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 38137 to 25223 computations (33.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
0.1b	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
0.3b	(*.f64 i 1/6)
2.7b	(.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_2853`
15×	`pow1_binary64_2892` `add-cbrt-cube_binary64_2867` `add-exp-log_binary64_2869`
12×	`associate-l_binary64_2772`
11×	`add-cube-cbrt_binary64_2866` `*-un-lft-identity_binary64_2831`
10×	`associate-r_binary64_2771`
8×	`associate-*r/_binary64_2773`
6×	`pow-prod-down_binary64_2902` `cbrt-unprod_binary64_2864` `prod-exp_binary64_2880` `distribute-lft-in_binary64_2780` `distribute-rgt-in_binary64_2781`
4×	`add-log-exp_binary64_2870` `*-commutative_binary64_2762`
3×	`flip3-+_binary64_2834` `unswap-sqr_binary64_2799` `flip-+_binary64_2805`

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)

series268.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
81.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))
71.0ms	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
21.0ms	(*.f64 i 1/6)

simplify53.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4963	1381
1	4963	1381

prune349.0ms (2.3%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	2	22	24
Picked	1	0	1
Done	0	0	0
Total	97	26	123

Merged error: 8.7b

Counts

123 → 26

Compiler

Compiled 6750 to 4813 computations (28.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 i)
0.6b	(cbrt.f64 i)
0.6b	(cbrt.f64 i)
2.7b	(.f64 n (.f64 i (+.f64 1/2 (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (*.f64 1/6 (cbrt.f64 i))))))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64_2892` `add-cbrt-cube_binary64_2867` `add-exp-log_binary64_2869` `cbrt-prod_binary64_2862`
8×	`add-cube-cbrt_binary64_2866` `add-sqr-sqrt_binary64_2853` `*-un-lft-identity_binary64_2831`
4×	`add-log-exp_binary64_2870` `associate-*r/_binary64_2773` `distribute-lft-in_binary64_2780` `distribute-rgt-in_binary64_2781`
3×	`pow-prod-down_binary64_2902` `cbrt-unprod_binary64_2864` `pow1/3_binary64_2913` `prod-exp_binary64_2880` `associate-l_binary64_2772`
1×	`flip3-+_binary64_2834` `-commutative_binary64_2762` `associate-r*_binary64_2771` `flip-+_binary64_2805`

Counts

4 → 57

Calls

4 calls:

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

series567.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt.f64 i)
145.0ms	(cbrt.f64 i)
144.0ms	(cbrt.f64 i)
133.0ms	(.f64 n (.f64 i (+.f64 1/2 (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (*.f64 1/6 (cbrt.f64 i))))))

simplify58.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4977	652
1	4977	652

prune101.0ms (0.7%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	25	25
Picked	1	0	1
Done	0	0	0
Total	69	26	95

Merged error: 8.7b

Counts

95 → 26

Compiler

Compiled 2106 to 1298 computations (38.4% saved)

regimes275.0ms (1.8%)

Compiler: Compiled 1863 to 1341 computations (28% saved)

bsearch161.0ms (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	91
1	53	91

end0.0ms (0%)

sample6.2s (40.2%)

Algorithm

1×

intervals

Results

2.8s	1774×	body	2048	valid
1.6s	2672×	body	1024	valid
331.0ms	1147×	body	512	valid
141.0ms	1850×	body	128	valid
118.0ms	40×	body	4096	valid
107.0ms	177×	body	1024	invalid
87.0ms	517×	body	256	valid
79.0ms	206×	body	512	invalid
44.0ms	459×	body	128	invalid
35.0ms	156×	body	256	invalid
22.0ms	14×	body	2048	invalid
14.0ms	297×	body	128	nan

Compiler

Compiled 707 to 500 computations (29.3% saved)

Details

analyze836.0ms (5.4%)

sample193.0ms (1.3%)

simplify215.0ms (1.4%)

prune2.0ms (0%)

localize9.0ms (0.1%)

rewrite179.0ms (1.2%)

series1.8s (12%)

simplify155.0ms (1%)

prune1.5s (10%)

localize13.0ms (0.1%)

rewrite63.0ms (0.4%)

series286.0ms (1.9%)

simplify109.0ms (0.7%)

prune1.8s (12%)

localize9.0ms (0.1%)

rewrite32.0ms (0.2%)

series268.0ms (1.7%)

simplify53.0ms (0.3%)

prune349.0ms (2.3%)

localize13.0ms (0.1%)

rewrite17.0ms (0.1%)

series567.0ms (3.7%)

simplify58.0ms (0.4%)

prune101.0ms (0.7%)

regimes275.0ms (1.8%)

bsearch161.0ms (1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.2s (40.2%)

Profiling