Details

analyze440.0ms (6.6%)

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)

sample41.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	28×	body	4096	valid
9.0ms	192×	body	128	valid
5.0ms	22×	body	2048	valid
3.0ms	256×	pre	128	true
2.0ms	11×	body	1024	valid
0.0ms	3×	body	512	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

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

40.1b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.1%)

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)))
0.2b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite103.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

40.0b

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)
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)

series528.0ms (7.9%)

Error

0.5b

Counts

4 → 53

Calls

4 calls:

158.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
129.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
103.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
81.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 2407 to 2109 computations (12.4% saved)

simplify40.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5111	1818

prune113.0ms (1.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	100	9	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	9	110

Error

0.5b

Counts

110 → 9

Compiler

Compiled 2205 to 1164 computations (47.2% saved)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 0.5b
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

prune12.0ms (0.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	8	8
Picked	1	1
Done	0	0
Total	9	9

Error

0.5b

Counts

9 → 9

Compiler

Compiled 157 to 128 computations (18.5% saved)

localize13.0ms (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))
0.4b	(*.f64 (sqrt.f64 im) (sqrt.f64 2))

rewrite205.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

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:

10.0ms	(.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))
3.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 2828 to 2228 computations (21.2% saved)

series176.0ms (2.6%)

Error

0.5b

Counts

4 → 15

Calls

4 calls:

92.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
34.0ms	(*.f64 re (sqrt.f64 2))
23.0ms	(*.f64 (sqrt.f64 im) (sqrt.f64 2))
13.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 918 to 816 computations (11.1% saved)

simplify89.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4891	1398
1	4891	1398

prune188.0ms (2.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	124	3	127
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	125	11	136

Error

0.5b

Counts

136 → 11

Compiler

Compiled 3120 to 2457 computations (21.3% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 re (sqrt.f64 2))
0.4b	(*.f64 (sqrt.f64 2) (sqrt.f64 im))
0.4b	(*.f64 (sqrt.f64 2) (sqrt.f64 im))
0.5b	(.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im))) (sqrt.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 im))))

rewrite321.0ms (4.8%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

79×	`pow1_binary64_480`
64×	`sqrt-pow1_binary64_437`
45×	`pow-prod-down_binary64_490`
41×	`add-sqr-sqrt_binary64_441`
30×	`pow1/2_binary64_499`
28×	`sqrt-prod_binary64_435`
22×	`associate-r_binary64_359`
19×	`add-cube-cbrt_binary64_454` `-un-lft-identity_binary64_419` `associate-l*_binary64_360`
14×	`pow-prod-up_binary64_489`
12×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
11×	`unswap-sqr_binary64_387`
8×	`pow-sqr_binary64_392`
4×	`prod-exp_binary64_468` `add-log-exp_binary64_458` `cbrt-unprod_binary64_452` `swap-sqr_binary64_386` `*-commutative_binary64_350`
3×	`sqrt-unprod_binary64_439`
1×	`pow2_binary64_500` `pow-plus_binary64_482` `rem-square-sqrt_binary64_431`

Counts

4 → 139

Calls

4 calls:

14.0ms	(.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im))) (sqrt.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 im))))
7.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 im))
7.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 im))
5.0ms	(*.f64 re (sqrt.f64 2))

Compiler

Compiled 4410 to 3464 computations (21.5% saved)

series135.0ms (2%)

Error

0.5b

Counts

4 → 12

Calls

4 calls:

36.0ms	(*.f64 re (sqrt.f64 2))
30.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 im))
27.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 im))
25.0ms	(.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (sqrt.f64 im))) (sqrt.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 im))))

Compiler

Compiled 978 to 868 computations (11.2% saved)

simplify64.0ms (1%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5972	1285

prune284.0ms (4.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	151	11	162

Error

0.5b

Counts

162 → 11

Compiler

Compiled 4186 to 3305 computations (21% saved)

regimes1.5s (21.9%)

Accuracy

Total 14.5b remaining (97%)

Threshold costs 0b (0%)

Compiler

Compiled 9548 to 7021 computations (26.5% saved)

bsearch97.0ms (1.5%)

Steps

Iters	Range		Point
10	1.4647811070724324e-12	0.13444283782341124	1.5402852044913168e-10
10	-5.0927032170888586e-40	-3.9040706960312294e-50	-3.939109501128109e-50
9	-1.829309496693132e+17	-149930839836.53296	-1.8009108557666285e+17
3	-1.3043035310648537e+102	-9.984192410750776e+101	-1.0117735354501902e+102

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	70	126
1	70	126

end0.0ms (0%)

sample2.3s (34.3%)

Algorithm

1×

intervals

Results

280.0ms	6072×	body	128	valid
164.0ms	535×	body	4096	valid
142.0ms	627×	body	2048	valid
102.0ms	8000×	pre	128	true
79.0ms	407×	body	1024	valid
32.0ms	246×	body	512	valid
10.0ms	113×	body	256	valid

Compiler

Compiled 1284 to 960 computations (25.2% saved)

Details

analyze440.0ms (6.6%)

sample41.0ms (0.6%)

simplify24.0ms (0.4%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite103.0ms (1.5%)

series528.0ms (7.9%)

simplify40.0ms (0.6%)

prune113.0ms (1.7%)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.1%)

prune12.0ms (0.2%)

localize13.0ms (0.2%)

rewrite205.0ms (3.1%)

series176.0ms (2.6%)

simplify89.0ms (1.3%)

prune188.0ms (2.8%)

localize18.0ms (0.3%)

rewrite321.0ms (4.8%)

series135.0ms (2%)

simplify64.0ms (1%)

prune284.0ms (4.3%)

regimes1.5s (21.9%)

bsearch97.0ms (1.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.3s (34.3%)

Profiling