Details

analyze251.0ms (4.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample69.0ms (1.2%)

Algorithm

1×

intervals

Results

32.0ms	78×	body	1024	valid
11.0ms	35×	body	2048	valid
10.0ms	49×	body	512	valid
3.0ms	78×	body	128	valid
1.0ms	13×	body	256	valid
1.0ms	3×	body	4096	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify95.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

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

Error

51.3b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.7b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.7b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
13.0b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite76.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

51.0b

Rules

9×	`*-un-lft-identity_binary64_5193`
6×	`add-sqr-sqrt_binary64_5215`
5×	`pow1_binary64_5254` `add-log-exp_binary64_5232` `add-cube-cbrt_binary64_5228`
4×	`add-exp-log_binary64_5231` `log-prod_binary64_5279`
3×	`add-cbrt-cube_binary64_5229` `flip3-+_binary64_5196` `flip-+_binary64_5167` `sqrt-prod_binary64_5209`
2×	`sqrt-div_binary64_5210` `log-div_binary64_5280` `distribute-lft-out_binary64_5144`
1×	`pow1/2_binary64_5273` `sqrt-pow1_binary64_5211` `rem-sqrt-square_binary64_5206` `log-pow_binary64_5282` `rem-log-exp_binary64_5234` `sum-log_binary64_5284` `+-commutative_binary64_5123`

Counts

3 → 42

Calls

3 calls:

7.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
6.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Compiler

Compiled 766 to 464 computations (39.4% saved)

series207.0ms (3.7%)

Error

Counts

3 → 27

Calls

3 calls:

84.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
51.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
42.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Compiler

Compiled 781 to 670 computations (14.2% saved)

simplify67.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5255	990

prune69.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	4	70

Error

Counts

70 → 4

Compiler

Compiled 928 to 612 computations (34.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 3/40 (pow.f64 x 5))
0.3b	(*.f64 (pow.f64 x 3) 1/6)
16.3b	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 3/40 (pow.f64 x 5)))

rewrite106.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

22×	`add-sqr-sqrt_binary64_5215`
15×	`associate-l_binary64_5134`
13×	`add-exp-log_binary64_5231`
10×	`add-cube-cbrt_binary64_5228` `-un-lft-identity_binary64_5193` `associate-r*_binary64_5133`
8×	`add-log-exp_binary64_5232` `unpow-prod-down_binary64_5272`
7×	`add-cbrt-cube_binary64_5229` `unswap-sqr_binary64_5161`
6×	`prod-exp_binary64_5242`
4×	`cube-prod_binary64_5221` `sqr-pow_binary64_5165`
3×	`pow1_binary64_5254`
2×	`sum-log_binary64_5284` `associate-+l+_binary64_5126` `pow-to-exp_binary64_5262` `pow-exp_binary64_5261` `cbrt-unprod_binary64_5226` `*-commutative_binary64_5124`
1×	`diff-log_binary64_5285` `flip3-+_binary64_5196` `flip-+_binary64_5167` `associate-+l-_binary64_5128` `sub-neg_binary64_5186` `cancel-sign-sub-inv_binary64_5159` `+-commutative_binary64_5123` `unpow3_binary64_5259` `cube-mult_binary64_5223`

Counts

3 → 71

Calls

3 calls:

6.0ms	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 3/40 (pow.f64 x 5)))
6.0ms	(*.f64 (pow.f64 x 3) 1/6)
6.0ms	(*.f64 3/40 (pow.f64 x 5))

Compiler

Compiled 1437 to 1128 computations (21.5% saved)

series129.0ms (2.3%)

Error

Counts

3 → 11

Calls

3 calls:

45.0ms	(+.f64 (-.f64 x (.f64 (pow.f64 x 3) 1/6)) (.f64 3/40 (pow.f64 x 5)))
42.0ms	(*.f64 3/40 (pow.f64 x 5))
35.0ms	(*.f64 (pow.f64 x 3) 1/6)

Compiler

Compiled 331 to 275 computations (16.9% saved)

simplify69.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5095	1020

prune86.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	82	4	86

Error

Counts

86 → 4

Compiler

Compiled 1463 to 1134 computations (22.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (+.f64 x (/.f64 1/2 x)))
0.0b	(+.f64 x (/.f64 1/2 x))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

9×	`add-log-exp_binary64_5232` `*-un-lft-identity_binary64_5193`
4×	`sum-log_binary64_5284` `distribute-lft-out_binary64_5144`
2×	`pow1_binary64_5254` `add-exp-log_binary64_5231` `add-cbrt-cube_binary64_5229` `add-cube-cbrt_binary64_5228` `add-sqr-sqrt_binary64_5215` `flip3-+_binary64_5196` `flip-+_binary64_5167` `+-commutative_binary64_5123`
1×	`associate-+r+_binary64_5125`

Counts

2 → 27

Calls

2 calls:

9.0ms	(+.f64 x (+.f64 x (/.f64 1/2 x)))
6.0ms	(+.f64 x (/.f64 1/2 x))

Compiler

Compiled 408 to 272 computations (33.3% saved)

series96.0ms (1.7%)

Error

Counts

2 → 12

Calls

2 calls:

50.0ms	(+.f64 x (+.f64 x (/.f64 1/2 x)))
40.0ms	(+.f64 x (/.f64 1/2 x))

Compiler

Compiled 232 to 186 computations (19.8% saved)

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4933	402
1	4933	402

prune26.0ms (0.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	39	4	43

Error

Counts

43 → 4

Compiler

Compiled 457 to 303 computations (33.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1/16 (pow.f64 x 5))
0.4b	(/.f64 1/8 (pow.f64 x 3))
12.6b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
20.8b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite399.0ms (7.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

75×	`*-un-lft-identity_binary64_5193`
73×	`add-sqr-sqrt_binary64_5215` `times-frac_binary64_5199`
47×	`add-cube-cbrt_binary64_5228`
26×	`unpow-prod-down_binary64_5272`
19×	`associate-/r*_binary64_5137`
15×	`add-exp-log_binary64_5231`
14×	`cube-prod_binary64_5221`
11×	`log-prod_binary64_5279`
10×	`difference-of-squares_binary64_5162` `sqr-pow_binary64_5165`
9×	`add-log-exp_binary64_5232`
8×	`add-cbrt-cube_binary64_5229`
6×	`frac-sub_binary64_5202` `distribute-lft-out_binary64_5144` `distribute-lft-out--_binary64_5145` `div-exp_binary64_5244` `associate-/l*_binary64_5138`
5×	`pow1_binary64_5254` `cancel-sign-sub-inv_binary64_5159` `log-div_binary64_5280`
4×	`unpow3_binary64_5259` `cube-mult_binary64_5223`
2×	`diff-log_binary64_5285` `frac-add_binary64_5201` `flip3-+_binary64_5196` `flip-+_binary64_5167` `flip3--_binary64_5197` `flip--_binary64_5168` `pow-to-exp_binary64_5262` `pow-exp_binary64_5261` `cbrt-undiv_binary64_5227` `frac-2neg_binary64_5204` `clear-num_binary64_5192` `div-inv_binary64_5190`
1×	`sum-log_binary64_5284` `sub-neg_binary64_5186` `associate--r+_binary64_5129` `log-pow_binary64_5282` `rem-log-exp_binary64_5234`

Counts

4 → 164

Calls

4 calls:

44.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
37.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
5.0ms	(/.f64 1/8 (pow.f64 x 3))
5.0ms	(/.f64 1/16 (pow.f64 x 5))

Compiler

Compiled 4463 to 3632 computations (18.6% saved)

series237.0ms (4.2%)

Error

Counts

4 → 18

Calls

4 calls:

87.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
54.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
44.0ms	(/.f64 1/16 (pow.f64 x 5))
37.0ms	(/.f64 1/8 (pow.f64 x 3))

Compiler

Compiled 697 to 616 computations (11.6% saved)

simplify87.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5168	3684

prune280.0ms (5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	182	4	186

Error

Counts

186 → 4

Compiler

Compiled 4162 to 3313 computations (20.4% saved)

regimes243.0ms (4.3%)

Accuracy

Total 0.2b remaining (89.1%)

Threshold costs 0.2b (89.1%)

Compiler

Compiled 2038 to 1528 computations (25% saved)

bsearch43.0ms (0.8%)

Steps

Iters	Range		Point
10	4.95529031966384e-09	7999.917181353579	1.0402498559041
9	-1185.429642085118	-0.0015571097848107946	-1.0512841589287099

Compiler

Compiled 1 to 1 computations (0% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	169	76
1	169	76

end0.0ms (0%)

sample2.8s (50.3%)

Algorithm

1×

intervals

Results

875.0ms	2507×	body	1024	valid
448.0ms	1247×	body	512	valid
380.0ms	1230×	body	2048	valid
106.0ms	2347×	body	128	valid
68.0ms	625×	body	256	valid
19.0ms	44×	body	4096	valid

Compiler

Compiled 680 to 516 computations (24.1% saved)

Details

analyze251.0ms (4.5%)

sample69.0ms (1.2%)

simplify95.0ms (1.7%)

prune3.0ms (0%)

localize6.0ms (0.1%)

rewrite76.0ms (1.3%)

series207.0ms (3.7%)

simplify67.0ms (1.2%)

prune69.0ms (1.2%)

localize8.0ms (0.1%)

rewrite106.0ms (1.9%)

series129.0ms (2.3%)

simplify69.0ms (1.2%)

prune86.0ms (1.5%)

localize5.0ms (0.1%)

rewrite39.0ms (0.7%)

series96.0ms (1.7%)

simplify74.0ms (1.3%)

prune26.0ms (0.5%)

localize11.0ms (0.2%)

rewrite399.0ms (7.1%)

series237.0ms (4.2%)

simplify87.0ms (1.6%)

prune280.0ms (5%)

regimes243.0ms (4.3%)

bsearch43.0ms (0.8%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.8s (50.3%)

Profiling