Details

analyze1.1s (10.7%)

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
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample227.0ms (2.2%)

Algorithm

1×

intervals

Results

49.0ms	89×	body	1024	valid
47.0ms	53×	body	1024	nan
38.0ms	55×	body	2048	valid
19.0ms	37×	body	512	nan
16.0ms	88×	body	128	overflowed
14.0ms	39×	body	512	valid
6.0ms	12×	body	512	invalid
6.0ms	7×	body	1024	invalid
5.0ms	52×	body	128	valid
4.0ms	21×	body	256	valid
3.0ms	10×	body	256	invalid
2.0ms	8×	body	256	nan
2.0ms	25×	body	128	nan
1.0ms	8×	body	128	invalid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify216.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4814	19
1	4814	19

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: 33.6b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(pow.f64 x (/.f64 1 n))
3.5b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_101`
19×	`*-un-lft-identity_binary64_79`
16×	`unpow-prod-down_binary64_158`
13×	`pow-unpow_binary64_156`
12×	`add-cube-cbrt_binary64_114`
9×	`times-frac_binary64_85` `difference-of-squares_binary64_48`
8×	`sqr-pow_binary64_51`
7×	`cancel-sign-sub-inv_binary64_45`
4×	`add-log-exp_binary64_118`
3×	`add-exp-log_binary64_117` `distribute-lft-out--_binary64_31` `pow1_binary64_140`
2×	`add-cbrt-cube_binary64_115`
1×	`pow-exp_binary64_147` `pow-to-exp_binary64_148` `pow-pow_binary64_151` `div-inv_binary64_76` `flip--_binary64_54` `diff-log_binary64_171` `flip3--_binary64_83` `sub-neg_binary64_72` `distribute-lft-out_binary64_30`

Counts

2 → 57

Calls

2 calls:

12.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
4.0ms	(pow.f64 x (/.f64 1 n))

series353.0ms (3.4%)

Counts

2 → 6

Calls

2 calls:

263.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
90.0ms	(pow.f64 x (/.f64 1 n))

simplify50.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5116	1288

prune158.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	59	4	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	4	64

Merged error: 24.4b

Counts

64 → 4

Compiler

Compiled 2769 to 2047 computations (26.1% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.3b	(/.f64 (log.f64 x) n)
3.5b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_101`
14×	`*-un-lft-identity_binary64_79`
12×	`times-frac_binary64_85` `add-cube-cbrt_binary64_114`
6×	`pow1_binary64_140`
4×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `associate-/l*_binary64_24` `add-log-exp_binary64_118` `log-pow_binary64_168`
3×	`associate-/r*_binary64_23` `difference-of-squares_binary64_48` `cancel-sign-sub-inv_binary64_45`
1×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `distribute-lft-out--_binary64_31` `sqr-pow_binary64_51` `div-inv_binary64_76` `flip--_binary64_54` `unpow-prod-down_binary64_158` `diff-log_binary64_171` `clear-num_binary64_78` `flip3--_binary64_83` `sub-neg_binary64_72` `frac-2neg_binary64_90`

Counts

2 → 49

Calls

2 calls:

11.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))
4.0ms	(/.f64 (log.f64 x) n)

series329.0ms (3.2%)

Counts

2 → 6

Calls

2 calls:

271.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (exp.f64 (/.f64 (log.f64 x) n)))
57.0ms	(/.f64 (log.f64 x) n)

simplify61.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	6415	986

prune61.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	55	4	59

Merged error: 24.4b

Counts

59 → 4

Compiler

Compiled 1275 to 703 computations (44.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 1/2 (.f64 x (.f64 x n)))
0.9b	(/.f64 1 (*.f64 x n))
5.0b	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
7.3b	(.f64 x (.f64 n n))

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log_binary64_117`
23×	`add-cbrt-cube_binary64_115`
16×	`*-un-lft-identity_binary64_79`
14×	`add-sqr-sqrt_binary64_101`
12×	`pow1_binary64_140`
11×	`times-frac_binary64_85` `add-cube-cbrt_binary64_114`
9×	`prod-exp_binary64_128`
7×	`div-exp_binary64_130` `cbrt-unprod_binary64_112` `cancel-sign-sub-inv_binary64_45`
6×	`associate-/l*_binary64_24` `add-log-exp_binary64_118`
5×	`cbrt-undiv_binary64_113`
4×	`div-inv_binary64_76` `pow-prod-down_binary64_150`
3×	`associate-l_binary64_20` `distribute-lft-out--_binary64_31`
2×	`associate-/r*_binary64_23` `1-exp_binary64_123` `rec-exp_binary64_129` `clear-num_binary64_78` `frac-2neg_binary64_90` `pow-flip_binary64_153`
1×	`flip--_binary64_54` `frac-sub_binary64_88` `unswap-sqr_binary64_47` `inv-pow_binary64_164` `-commutative_binary64_10` `difference-of-squares_binary64_48` `diff-log_binary64_171` `flip3--_binary64_83` `sub-neg_binary64_72` `associate-r*_binary64_19`

Counts

4 → 93

Calls

4 calls:

12.0ms	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
7.0ms	(/.f64 1/2 (.f64 x (.f64 x n)))
6.0ms	(.f64 x (.f64 n n))
5.0ms	(/.f64 1 (*.f64 x n))

series136.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(-.f64 (/.f64 1 (.f64 x n)) (/.f64 1/2 (.f64 x (*.f64 x n))))
45.0ms	(.f64 x (.f64 n n))
26.0ms	(/.f64 1/2 (.f64 x (.f64 x n)))
18.0ms	(/.f64 1 (*.f64 x n))

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4894	1299
1	4894	1299

prune206.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	100	5	105
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	101	8	109

Merged error: 23.5b

Counts

109 → 8

Compiler

Compiled 4817 to 2426 computations (49.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
0.7b	(/.f64 1/2 (.f64 x (.f64 x n)))
5.0b	(-.f64 (/.f64 (/.f64 1 x) n) (/.f64 1/2 (.f64 x (.f64 x n))))
7.3b	(.f64 x (.f64 n n))

rewrite63.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
24×	`add-sqr-sqrt_binary64_101`
16×	`times-frac_binary64_85`
15×	`*-un-lft-identity_binary64_79`
11×	`add-cube-cbrt_binary64_114` `pow1_binary64_140`
9×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128`
7×	`associate-/l*_binary64_24` `cancel-sign-sub-inv_binary64_45`
6×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `add-log-exp_binary64_118`
4×	`div-inv_binary64_76` `difference-of-squares_binary64_48`
3×	`associate-l_binary64_20` `pow-prod-down_binary64_150`
2×	`associate-/r*_binary64_23` `distribute-lft-out--_binary64_31` `clear-num_binary64_78` `log-pow_binary64_168` `frac-2neg_binary64_90`
1×	`flip--_binary64_54` `frac-sub_binary64_88` `unswap-sqr_binary64_47` `-commutative_binary64_10` `diff-log_binary64_171` `flip3--_binary64_83` `sub-neg_binary64_72` `associate-r*_binary64_19`

Counts

4 → 92

Calls

4 calls:

33.0ms	(-.f64 (/.f64 (/.f64 1 x) n) (/.f64 1/2 (.f64 x (.f64 x n))))
8.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
7.0ms	(/.f64 1/2 (.f64 x (.f64 x n)))
6.0ms	(.f64 x (.f64 n n))

series209.0ms (2%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(/.f64 (log.f64 x) (.f64 x (.f64 n n)))
50.0ms	(-.f64 (/.f64 (/.f64 1 x) n) (/.f64 1/2 (.f64 x (.f64 x n))))
47.0ms	(.f64 x (.f64 n n))
28.0ms	(/.f64 1/2 (.f64 x (.f64 x n)))

simplify61.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5321	1603

prune114.0ms (1.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	103	9	112

Merged error: 23.5b

Counts

112 → 9

Compiler

Compiled 2967 to 1200 computations (59.6% saved)

regimes74.0ms (0.7%)

Compiler: Compiled 468 to 344 computations (26.5% saved)

bsearch100.0ms (1%)

Steps

Iters	Range		Point
7	7868775.6119357115	244904629.29692948	28730378.808545448
6	-26147309677994544.0	-3239889307155958.5	-3292888712184467.5

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	62	67
1	62	67

end0.0ms (0%)

sample6.6s (63.9%)

Algorithm

1×

intervals

Results

1.4s	2686×	body	1024	valid
1.2s	1445×	body	1024	nan
1.2s	1717×	body	2048	valid
493.0ms	2555×	body	128	overflowed
429.0ms	1194×	body	512	valid
363.0ms	697×	body	512	nan
190.0ms	193×	body	1024	invalid
176.0ms	1788×	body	128	valid
136.0ms	262×	body	512	invalid
136.0ms	615×	body	256	valid
89.0ms	342×	body	256	nan
63.0ms	810×	body	128	nan
41.0ms	289×	body	128	invalid
40.0ms	146×	body	256	invalid
10.0ms	7×	body	2048	nan

Compiler

Compiled 290 to 212 computations (26.9% saved)

Details

analyze1.1s (10.7%)

sample227.0ms (2.2%)

simplify216.0ms (2.1%)

prune2.0ms (0%)

localize9.0ms (0.1%)

rewrite22.0ms (0.2%)

series353.0ms (3.4%)

simplify50.0ms (0.5%)

prune158.0ms (1.5%)

localize10.0ms (0.1%)

rewrite19.0ms (0.2%)

series329.0ms (3.2%)

simplify61.0ms (0.6%)

prune61.0ms (0.6%)

localize14.0ms (0.1%)

rewrite41.0ms (0.4%)

series136.0ms (1.3%)

simplify68.0ms (0.7%)

prune206.0ms (2%)

localize15.0ms (0.1%)

rewrite63.0ms (0.6%)

series209.0ms (2%)

simplify61.0ms (0.6%)

prune114.0ms (1.1%)

regimes74.0ms (0.7%)

bsearch100.0ms (1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.6s (63.9%)

Profiling