Details

analyze543.0ms (8.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	338	46
1	338	46
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

Compiler

Compiled 18 to 14 computations (22.2% saved)

sample43.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	193×	body	128	valid
7.0ms	22×	body	4096	valid
4.0ms	15×	body	2048	valid
4.0ms	256×	pre	128	true
2.0ms	14×	body	1024	valid
1.0ms	9×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify32.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	249	23
1	249	23

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

Error

39.1b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite101.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

39.0b

Rules

10×	`add-sqr-sqrt_binary64_441`
7×	`pow1_binary64_480` `*-un-lft-identity_binary64_419`
5×	`add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `sqrt-prod_binary64_435`
4×	`sqrt-div_binary64_436`
3×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `sqrt-pow1_binary64_437` `cancel-sign-sub-inv_binary64_385`
2×	`pow1/2_binary64_499` `flip3--_binary64_423` `flip--_binary64_394` `difference-of-squares_binary64_388` `associate-*r/_binary64_361`
1×	`flip3-+_binary64_422` `flip-+_binary64_393` `rem-sqrt-square_binary64_432` `diff-log_binary64_511` `sub-neg_binary64_412` `distribute-lft-out--_binary64_371` `pow-prod-down_binary64_490`

Counts

3 → 45

Calls

3 calls:

14.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 1152 to 396 computations (65.6% saved)

series429.0ms (6.4%)

Error

0.4b

Counts

3 → 42

Calls

3 calls:

142.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
138.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
101.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))

Compiler

Compiled 1771 to 1525 computations (13.9% saved)

simplify154.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (125.0ms)

Iter	Nodes	Cost
0	4916	1522
1	4916	1522

prune130.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	80	7	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	7	88

Error

0.4b

Counts

88 → 7

Compiler

Compiled 1735 to 913 computations (47.4% saved)

localize5.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 0.4b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune7.0ms (0.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	0	0
Total	7	7

Error

0.4b

Counts

7 → 7

Compiler

Compiled 91 to 81 computations (11% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1 im))
0.3b	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
0.4b	(*.f64 re (sqrt.f64 2))
0.5b	(*.f64 (sqrt.f64 im) (sqrt.f64 2))

rewrite217.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

42×	`add-sqr-sqrt_binary64_441`
40×	`sqrt-prod_binary64_435`
28×	`associate-r_binary64_359`
27×	`*-un-lft-identity_binary64_419`
26×	`add-cube-cbrt_binary64_454`
20×	`times-frac_binary64_425`
17×	`pow1_binary64_480`
13×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
10×	`associate-l_binary64_360`
7×	`pow-prod-down_binary64_490`
6×	`unswap-sqr_binary64_387`
5×	`sqrt-pow1_binary64_437` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
4×	`add-log-exp_binary64_458`
3×	`pow1/2_binary64_499` `*-commutative_binary64_350` `rem-sqrt-square_binary64_432`
2×	`sqrt-div_binary64_436` `div-inv_binary64_416`
1×	`sqrt-unprod_binary64_439` `associate-*r/_binary64_361` `inv-pow_binary64_504` `pow-flip_binary64_493`

Counts

4 → 112

Calls

4 calls:

11.0ms	(*.f64 (sqrt.f64 im) (sqrt.f64 2))
10.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
6.0ms	(sqrt.f64 (/.f64 1 im))
5.0ms	(*.f64 re (sqrt.f64 2))

Compiler

Compiled 2828 to 2228 computations (21.2% saved)

series204.0ms (3%)

Error

0.4b

Counts

4 → 15

Calls

4 calls:

99.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
43.0ms	(*.f64 re (sqrt.f64 2))
30.0ms	(*.f64 (sqrt.f64 im) (sqrt.f64 2))
16.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 918 to 816 computations (11.1% saved)

simplify122.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	4891	1398
1	4891	1398

prune195.0ms (2.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	127	7	134

Error

0.4b

Counts

134 → 7

Compiler

Compiled 3000 to 2364 computations (21.2% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
0.4b	(*.f64 re (sqrt.f64 2))
0.5b	(*.f64 (sqrt.f64 2) (sqrt.f64 im))
4.9b	(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 im))))

rewrite252.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

32×	`add-sqr-sqrt_binary64_441`
28×	`associate-r_binary64_359`
27×	`sqrt-prod_binary64_435`
20×	`pow1_binary64_480` `add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
13×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
10×	`pow-prod-down_binary64_490` `associate-l_binary64_360`
9×	`times-frac_binary64_425`
7×	`exp-prod_binary64_471`
6×	`unswap-sqr_binary64_387`
5×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
4×	`pow1/2_binary64_499` `log-pow_binary64_508` `sqrt-pow1_binary64_437` `add-log-exp_binary64_458`
3×	`*-commutative_binary64_350`
1×	`log-prod_binary64_505` `exp-sum_binary64_465` `rem-exp-log_binary64_459` `sqrt-unprod_binary64_439` `sqrt-div_binary64_436` `associate-*r/_binary64_361` `div-inv_binary64_416`

Counts

4 → 100

Calls

4 calls:

11.0ms	(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 im))))
10.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
7.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 im))
5.0ms	(*.f64 re (sqrt.f64 2))

Compiler

Compiled 2725 to 2196 computations (19.4% saved)

series225.0ms (3.4%)

Error

0.4b

Counts

4 → 15

Calls

4 calls:

109.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
38.0ms	(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 im))))
38.0ms	(*.f64 re (sqrt.f64 2))
23.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 im))

Compiler

Compiled 1039 to 939 computations (9.6% saved)

simplify105.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5157	1285

prune193.0ms (2.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	115	7	122

Error

0.4b

Counts

122 → 7

Compiler

Compiled 2838 to 2289 computations (19.3% saved)

regimes1.2s (17.5%)

Accuracy

Total 13.7b remaining (97.5%)

Threshold costs 0b (0%)

Compiler

Compiled 6591 to 4855 computations (26.3% saved)

bsearch185.0ms (2.8%)

Steps

Iters	Range		Point
5	1.4997115579960871e+91	4.4169498983791226e+91	2.6425163668929388e+91
10	2.18280916713774e+20	7.390727970954304e+35	5.594187968714849e+35
8	4.962169800219719e-24	2.4511412872876517e-20	8.443019886679552e-21
8	-3.3893284954853406e-130	-7.828998547410895e-133	-1.704786349615486e-131
9	-2.1582259929573573e+123	-4.908557165745598e+114	-3.695071676918518e+120

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	84	122
1	84	122

end0.0ms (0%)

sample2.3s (34.8%)

Algorithm

1×

intervals

Results

364.0ms	6105×	body	128	valid
184.0ms	513×	body	4096	valid
181.0ms	636×	body	2048	valid
128.0ms	8000×	pre	128	true
86.0ms	396×	body	1024	valid
36.0ms	222×	body	512	valid
14.0ms	128×	body	256	valid

Compiler

Compiled 887 to 670 computations (24.5% saved)

Details

analyze543.0ms (8.1%)

sample43.0ms (0.6%)

simplify32.0ms (0.5%)

prune2.0ms (0%)

localize13.0ms (0.2%)

rewrite101.0ms (1.5%)

series429.0ms (6.4%)

simplify154.0ms (2.3%)

prune130.0ms (1.9%)

localize5.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.1%)

prune7.0ms (0.1%)

localize16.0ms (0.2%)

rewrite217.0ms (3.2%)

series204.0ms (3%)

simplify122.0ms (1.8%)

prune195.0ms (2.9%)

localize28.0ms (0.4%)

rewrite252.0ms (3.8%)

series225.0ms (3.4%)

simplify105.0ms (1.6%)

prune193.0ms (2.9%)

regimes1.2s (17.5%)

bsearch185.0ms (2.8%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.3s (34.8%)

Profiling