Details

analyze614.0ms (7%)

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)

sample73.0ms (0.8%)

Algorithm

1×

intervals

Results

16.0ms	21×	body	4096	valid
15.0ms	185×	body	128	valid
9.0ms	21×	body	2048	valid
5.0ms	256×	pre	128	true
5.0ms	15×	body	1024	valid
2.0ms	9×	body	512	valid
1.0ms	5×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify190.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	249	23
1	249	23

prune5.0ms (0.1%)

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

38.9b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize21.0ms (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))
0.4b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite180.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

38.7b

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:

23.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
15.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
8.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 1418 to 497 computations (65% saved)

series715.0ms (8.2%)

Error

0.3b

Counts

4 → 46

Calls

4 calls:

190.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
173.0ms	(+.f64 (.f64 re re) (.f64 im im))
145.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
129.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 1842 to 1624 computations (11.8% saved)

simplify145.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	5185	1535

prune177.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	94	8	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	8	103

Error

0.3b

Counts

103 → 8

Compiler

Compiled 1924 to 956 computations (50.3% saved)

localize8.0ms (0.1%)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series1.0ms (0%)

Error: 0.3b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	0	0

prune14.0ms (0.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	0	0
Total	8	8

Error

0.3b

Counts

8 → 8

Compiler

Compiled 99 to 87 computations (12.1% saved)

localize14.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite57.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

13×	`add-sqr-sqrt_binary64_441`
10×	`sqrt-prod_binary64_435`
6×	`associate-l_binary64_360` `associate-r_binary64_359`
5×	`pow1_binary64_480` `add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
4×	`unswap-sqr_binary64_387`
3×	`pow-prod-down_binary64_490` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437`
1×	`prod-exp_binary64_468` `add-log-exp_binary64_458` `cbrt-unprod_binary64_452` `sqrt-unprod_binary64_439` `*-commutative_binary64_350`

Counts

1 → 30

Calls

1 calls:

13.0ms

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

Compiler

Compiled 377 to 277 computations (26.5% saved)

series40.0ms (0.5%)

Error

0.3b

Counts

1 → 3

Calls

1 calls:

36.0ms

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

Compiler

Compiled 89 to 92 computations (-3.4% saved)

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5215	353

prune56.0ms (0.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	33	8	41

Error

0.3b

Counts

41 → 8

Compiler

Compiled 460 to 352 computations (23.5% saved)

localize25.0ms (0.3%)

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))

rewrite330.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

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:

20.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
13.0ms	(*.f64 (sqrt.f64 im) (sqrt.f64 2))
10.0ms	(*.f64 re (sqrt.f64 2))
6.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 2828 to 2228 computations (21.2% saved)

series328.0ms (3.8%)

Error

0.3b

Counts

4 → 15

Calls

4 calls:

174.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
60.0ms	(*.f64 re (sqrt.f64 2))
39.0ms	(*.f64 (sqrt.f64 im) (sqrt.f64 2))
27.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 918 to 816 computations (11.1% saved)

simplify159.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	4891	1398
1	4891	1398

prune291.0ms (3.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	0	5	5
Picked	0	1	1
Done	1	1	2
Total	126	9	135

Error

0.3b

Counts

135 → 9

Compiler

Compiled 2907 to 2281 computations (21.5% saved)

regimes1.7s (18.9%)

Accuracy

Total 13.5b remaining (96.9%)

Threshold costs 0b (0%)

Compiler

Compiled 6428 to 4946 computations (23.1% saved)

bsearch81.0ms (0.9%)

Steps

Iters	Range		Point
5	6.5624062316180195e-24	1.5258529668938478e-23	8.321275884393451e-24
1	-4.964051115194031e-125	-4.56389440634415e-125	-4.634337825695654e-125
10	-1.9411504243177815e+33	-1.481415629574978e+23	-9.288187725469977e+32

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	70	99
1	70	99

end0.0ms (0%)

sample3.5s (39.6%)

Algorithm

1×

intervals

Results

508.0ms	6065×	body	128	valid
295.0ms	547×	body	4096	valid
252.0ms	595×	body	2048	valid
174.0ms	8000×	pre	128	true
143.0ms	406×	body	1024	valid
68.0ms	258×	body	512	valid
21.0ms	129×	body	256	valid

Compiler

Compiled 894 to 695 computations (22.3% saved)

Details

analyze614.0ms (7%)

sample73.0ms (0.8%)

simplify190.0ms (2.2%)

prune5.0ms (0.1%)

localize21.0ms (0.2%)

rewrite180.0ms (2.1%)

series715.0ms (8.2%)

simplify145.0ms (1.7%)

prune177.0ms (2%)

localize8.0ms (0.1%)

rewrite1.0ms (0%)

series1.0ms (0%)

simplify12.0ms (0.1%)

prune14.0ms (0.2%)

localize14.0ms (0.2%)

rewrite57.0ms (0.7%)

series40.0ms (0.5%)

simplify90.0ms (1%)

prune56.0ms (0.6%)

localize25.0ms (0.3%)

rewrite330.0ms (3.8%)

series328.0ms (3.8%)

simplify159.0ms (1.8%)

prune291.0ms (3.3%)

regimes1.7s (18.9%)

bsearch81.0ms (0.9%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample3.5s (39.6%)

Profiling