Details

analyze432.0ms (6.9%)

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 (0.7%)

Algorithm

1×

intervals

Results

11.0ms	182×	body	128	valid
7.0ms	24×	body	4096	valid
5.0ms	22×	body	2048	valid
3.0ms	256×	pre	128	true
2.0ms	14×	body	1024	valid
1.0ms	9×	body	512	valid
0.0ms	5×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify24.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

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

40.0b

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	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
1.0b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite90.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

39.8b

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` `pow-prod-down_binary64_490` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

4 → 56

Calls

4 calls:

9.0ms	(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	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 1418 to 497 computations (65% saved)

series466.0ms (7.4%)

Error

0.7b

Counts

4 → 52

Calls

4 calls:

121.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
111.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
91.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
90.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 2200 to 1922 computations (12.6% saved)

simplify61.0ms (1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5224	1703

prune107.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	102	7	109

Error

0.7b

Counts

109 → 7

Compiler

Compiled 2045 to 1034 computations (49.4% saved)

localize4.0ms (0.1%)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 0.7b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune5.0ms (0.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	1	1
Total	7	7

Error

0.7b

Counts

7 → 7

Compiler

Compiled 72 to 65 computations (9.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 1/2 (.f64 (*.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im))))
0.3b	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
0.4b	(*.f64 (sqrt.f64 im) (sqrt.f64 2))
0.4b	(*.f64 re (sqrt.f64 2))

rewrite197.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

32×	`add-sqr-sqrt_binary64_441`
29×	`associate-r_binary64_359`
27×	`sqrt-prod_binary64_435`
24×	`pow1_binary64_480`
22×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
20×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
13×	`pow-prod-down_binary64_490` `associate-l_binary64_360`
11×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
9×	`times-frac_binary64_425`
6×	`unswap-sqr_binary64_387`
4×	`add-log-exp_binary64_458` `*-commutative_binary64_350`
3×	`associate-*r/_binary64_361`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `sqrt-div_binary64_436`
1×	`sqrt-unprod_binary64_439` `div-inv_binary64_416`

Counts

4 → 106

Calls

4 calls:

12.0ms	(.f64 1/2 (.f64 (*.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im))))
11.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
7.0ms	(*.f64 (sqrt.f64 im) (sqrt.f64 2))
5.0ms	(*.f64 re (sqrt.f64 2))

Compiler

Compiled 2732 to 2168 computations (20.6% saved)

series283.0ms (4.5%)

Error

0.7b

Counts

4 → 18

Calls

4 calls:

113.0ms	(.f64 1/2 (.f64 (*.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im))))
95.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
35.0ms	(*.f64 re (sqrt.f64 2))
23.0ms	(*.f64 (sqrt.f64 im) (sqrt.f64 2))

Compiler

Compiled 1106 to 984 computations (11% saved)

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5356	1609

prune169.0ms (2.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	120	4	124
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	121	10	131

Error

0.7b

Counts

131 → 10

Compiler

Compiled 2968 to 2361 computations (20.5% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 im) (cbrt.f64 im))
0.6b	(cbrt.f64 im)
0.6b	(cbrt.f64 im)
0.6b	(cbrt.f64 im)

rewrite128.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

25×	`cbrt-prod_binary64_450`
23×	`add-sqr-sqrt_binary64_441`
15×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
11×	`pow1_binary64_480`
9×	`pow1/3_binary64_501`
6×	`add-exp-log_binary64_457` `swap-sqr_binary64_386` `associate-l_binary64_360` `associate-r_binary64_359`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `unswap-sqr_binary64_387`
2×	`pow-prod-down_binary64_490` `pow-prod-up_binary64_489` `pow-sqr_binary64_392`
1×	`pow2_binary64_500` `pow-plus_binary64_482` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `*-commutative_binary64_350`

Counts

4 → 73

Calls

4 calls:

7.0ms	(*.f64 (cbrt.f64 im) (cbrt.f64 im))
1.0ms	(cbrt.f64 im)
1.0ms	(cbrt.f64 im)
1.0ms	(cbrt.f64 im)

Compiler

Compiled 2327 to 1398 computations (39.9% saved)

series352.0ms (5.6%)

Error

0.7b

Counts

4 → 12

Calls

4 calls:

94.0ms	(*.f64 (cbrt.f64 im) (cbrt.f64 im))
86.0ms	(cbrt.f64 im)
80.0ms	(cbrt.f64 im)
74.0ms	(cbrt.f64 im)

Compiler

Compiled 1059 to 888 computations (16.1% saved)

simplify78.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4873	548
1	4873	548

prune121.0ms (1.9%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	83	12	95

Error

0.7b

Counts

95 → 12

Compiler

Compiled 2508 to 1645 computations (34.4% saved)

regimes1.2s (18.8%)

Accuracy

Total 15.5b remaining (97.4%)

Threshold costs 0b (0%)

Compiler

Compiled 9786 to 7798 computations (20.3% saved)

bsearch52.0ms (0.8%)

Steps

Iters	Range		Point
9	1.4152359761785702e-53	2.783886984951941e-48	2.3450661578035385e-51
7	-3.639159310753773e+145	-7.135840477720308e+143	-7.221635243629302e+143

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	49	58
1	49	58

end0.0ms (0%)

sample2.3s (37.5%)

Algorithm

1×

intervals

Results

295.0ms	6079×	body	128	valid
157.0ms	640×	body	2048	valid
153.0ms	528×	body	4096	valid
100.0ms	8000×	pre	128	true
70.0ms	395×	body	1024	valid
32.0ms	241×	body	512	valid
10.0ms	117×	body	256	valid

Compiler

Compiled 1359 to 1092 computations (19.6% saved)

Details

analyze432.0ms (6.9%)

sample43.0ms (0.7%)

simplify24.0ms (0.4%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite90.0ms (1.4%)

series466.0ms (7.4%)

simplify61.0ms (1%)

prune107.0ms (1.7%)

localize4.0ms (0.1%)

rewrite1.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.1%)

prune5.0ms (0.1%)

localize12.0ms (0.2%)

rewrite197.0ms (3.1%)

series283.0ms (4.5%)

simplify73.0ms (1.2%)

prune169.0ms (2.7%)

localize20.0ms (0.3%)

rewrite128.0ms (2%)

series352.0ms (5.6%)

simplify78.0ms (1.2%)

prune121.0ms (1.9%)

regimes1.2s (18.8%)

bsearch52.0ms (0.8%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.3s (37.5%)

Profiling