Details

analyze337.0ms (5.6%)

Algorithm

1×

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)

sample42.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	186×	body	128	valid
8.0ms	22×	body	2048	valid
5.0ms	19×	body	4096	valid
3.0ms	256×	pre	128	true
3.0ms	14×	body	1024	valid
1.0ms	11×	body	512	valid
0.0ms	4×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify107.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	249	23
1	249	23

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

41.8b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.7b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite102.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

41.6b

Rules

11×	`add-sqr-sqrt_binary64_441`
8×	`pow1_binary64_480` `add-log-exp_binary64_458` `*-un-lft-identity_binary64_419`
6×	`add-cube-cbrt_binary64_454`
5×	`sqrt-prod_binary64_435`
4×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `sqrt-div_binary64_436`
3×	`sqrt-pow1_binary64_437` `cancel-sign-sub-inv_binary64_385`
2×	`pow1/2_binary64_499` `flip3-+_binary64_422` `flip-+_binary64_393` `flip3--_binary64_423` `flip--_binary64_394` `difference-of-squares_binary64_388` `associate-*r/_binary64_361`
1×	`rem-sqrt-square_binary64_432` `diff-log_binary64_511` `sub-neg_binary64_412` `distribute-lft-out--_binary64_371` `sum-log_binary64_510` `+-commutative_binary64_349` `pow-prod-down_binary64_490`

Counts

4 → 56

Calls

4 calls:

12.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
9.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 1418 to 497 computations (65% saved)

series412.0ms (6.8%)

Error

0.2b

Counts

4 → 49

Calls

4 calls:

97.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
93.0ms	(+.f64 (.f64 re re) (.f64 im im))
91.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
83.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))

Compiler

Compiled 1946 to 1702 computations (12.5% saved)

simplify78.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5162	1574

prune99.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	99	6	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	7	106

Error

0.2b

Counts

106 → 7

Compiler

Compiled 1951 to 956 computations (51% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

4×	`pow1_binary64_480`
2×	`sqrt-pow1_binary64_437` `associate-*r/_binary64_361` `sqrt-div_binary64_436`
1×	`pow1/2_binary64_499` `add-log-exp_binary64_458` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `pow-prod-down_binary64_490` `flip3--_binary64_423` `flip--_binary64_394` `sqrt-prod_binary64_435` `*-un-lft-identity_binary64_419`

Counts

1 → 13

Calls

1 calls:

5.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

Compiler

Compiled 187 to 126 computations (32.6% saved)

series54.0ms (0.9%)

Error

0.2b

Counts

1 → 7

Calls

1 calls:

50.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

Compiler

Compiled 253 to 237 computations (6.3% saved)

simplify99.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4981	216
1	4981	216

prune22.0ms (0.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	19	8	27

Error

0.2b

Counts

27 → 8

Compiler

Compiled 310 to 234 computations (24.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 im) (.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2)))
0.1b	(sqrt.f64 (/.f64 1 im))
0.2b	(.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2))
0.4b	(.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 re (*.f64 (sqrt.f64 (/.f64 1 im)) -1/2))))

rewrite137.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

23×	`add-sqr-sqrt_binary64_441`
17×	`sqrt-prod_binary64_435`
16×	`*-un-lft-identity_binary64_419`
15×	`add-cube-cbrt_binary64_454`
13×	`pow1_binary64_480`
11×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `times-frac_binary64_425`
9×	`associate-l_binary64_360`
6×	`add-log-exp_binary64_458`
4×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-r_binary64_359`
3×	`associate-*r/_binary64_361` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`
2×	`unswap-sqr_binary64_387` `flip3-+_binary64_422` `flip-+_binary64_393` `*-commutative_binary64_350` `sqrt-div_binary64_436`
1×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `associate-*l/_binary64_362` `pow1/2_binary64_499` `inv-pow_binary64_504` `pow-flip_binary64_493` `div-inv_binary64_416` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

4 → 84

Calls

4 calls:

9.0ms	(.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2))
8.0ms	(.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 re (*.f64 (sqrt.f64 (/.f64 1 im)) -1/2))))
4.0ms	(+.f64 (sqrt.f64 im) (.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2)))
3.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 2078 to 1570 computations (24.4% saved)

series372.0ms (6.2%)

Error

0.2b

Counts

4 → 27

Calls

4 calls:

148.0ms	(.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 re (*.f64 (sqrt.f64 (/.f64 1 im)) -1/2))))
113.0ms	(+.f64 (sqrt.f64 im) (.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2)))
78.0ms	(.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2))
14.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 1145 to 1011 computations (11.7% saved)

simplify74.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5194	1755

prune122.0ms (2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	111	8	119

Error

0.2b

Counts

119 → 8

Compiler

Compiled 2266 to 1713 computations (24.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
5.6b	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))))
22.9b	(/.f64 (.f64 im im) (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
31.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite102.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

13×	`*-un-lft-identity_binary64_419`
9×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
8×	`pow1_binary64_480` `add-sqr-sqrt_binary64_441`
7×	`add-cube-cbrt_binary64_454`
6×	`add-log-exp_binary64_458`
4×	`sqrt-prod_binary64_435` `times-frac_binary64_425` `associate-/r*_binary64_363`
3×	`sqrt-pow1_binary64_437` `flip3-+_binary64_422` `sqrt-div_binary64_436` `flip-+_binary64_393` `distribute-lft-out_binary64_370`
2×	`pow1/2_binary64_499` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/r/_binary64_365`
1×	`rem-sqrt-square_binary64_432` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416` `associate-/l_binary64_364` `pow-prod-down_binary64_490` `associate-r/_binary64_361` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

4 → 64

Calls

4 calls:

10.0ms	(/.f64 (.f64 im im) (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
10.0ms	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))))
6.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 1913 to 565 computations (70.5% saved)

series487.0ms (8.1%)

Error

0.2b

Counts

4 → 57

Calls

4 calls:

139.0ms	(/.f64 (.f64 im im) (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
101.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
99.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
99.0ms	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))))

Compiler

Compiled 2627 to 2113 computations (19.6% saved)

simplify81.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4952	2127
1	4952	2127

prune110.0ms (1.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	0	4	4
Picked	1	0	1
Done	0	3	3
Total	120	9	129

Error

0.2b

Counts

129 → 9

Compiler

Compiled 2601 to 1107 computations (57.4% saved)

regimes1.1s (18.1%)

Accuracy

Total 15.3b remaining (97.5%)

Threshold costs 0b (0%)

Compiler

Compiled 7753 to 4942 computations (36.3% saved)

bsearch116.0ms (1.9%)

Steps

Iters	Range		Point
7	1.3459667694089648e+98	7.092236650746964e+99	1.361057747206771e+98
6	6.235912845756696e+65	4.456080298790509e+66	2.6036362270967298e+66
9	2.7064583641662356e-27	4.127804430701887e-18	1.1861914428536724e-19
11	-7.740689633500964e+115	-5.191951034682716e+92	-5.26708834568496e+92

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	81
1	63	81

end0.0ms (0%)

sample1.9s (31.9%)

Algorithm

1×

intervals

Results

296.0ms	6085×	body	128	valid
158.0ms	644×	body	2048	valid
152.0ms	517×	body	4096	valid
108.0ms	8000×	pre	128	true
74.0ms	392×	body	1024	valid
33.0ms	243×	body	512	valid
11.0ms	119×	body	256	valid

Compiler

Compiled 1031 to 672 computations (34.8% saved)

Details

analyze337.0ms (5.6%)

sample42.0ms (0.7%)

simplify107.0ms (1.8%)

prune3.0ms (0%)

localize10.0ms (0.2%)

rewrite102.0ms (1.7%)

series412.0ms (6.8%)

simplify78.0ms (1.3%)

prune99.0ms (1.6%)

localize8.0ms (0.1%)

rewrite16.0ms (0.3%)

series54.0ms (0.9%)

simplify99.0ms (1.6%)

prune22.0ms (0.4%)

localize12.0ms (0.2%)

rewrite137.0ms (2.3%)

series372.0ms (6.2%)

simplify74.0ms (1.2%)

prune122.0ms (2%)

localize13.0ms (0.2%)

rewrite102.0ms (1.7%)

series487.0ms (8.1%)

simplify81.0ms (1.3%)

prune110.0ms (1.8%)

regimes1.1s (18.1%)

bsearch116.0ms (1.9%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.9s (31.9%)

Profiling