Details

analyze476.0ms (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)

sample41.0ms (0.8%)

Algorithm

1×

intervals

Results

8.0ms	186×	body	128	valid
6.0ms	16×	body	1024	valid
5.0ms	20×	body	4096	valid
4.0ms	20×	body	2048	valid
3.0ms	256×	pre	128	true
1.0ms	6×	body	512	valid
1.0ms	8×	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 (18.0ms)

Iter	Nodes	Cost
0	249	23
1	249	23

prune3.0ms (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

38.1b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
1.2b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
27.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite81.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

37.8b

Rules

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

Counts

3 → 43

Calls

3 calls:

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

Compiler

Compiled 1070 to 382 computations (64.3% saved)

series408.0ms (7.7%)

Error

9.3b

Counts

3 → 41

Calls

3 calls:

137.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
115.0ms	(+.f64 (.f64 re re) (.f64 im im))
108.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 1572 to 1355 computations (13.8% saved)

simplify67.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5126	1305

prune95.0ms (1.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	5	85

Error

9.3b

Counts

85 → 5

Compiler

Compiled 1636 to 834 computations (49% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

9.3b

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)

series77.0ms (1.4%)

Error

9.3b

Counts

1 → 7

Calls

1 calls:

72.0ms

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

Compiler

Compiled 253 to 237 computations (6.3% saved)

simplify99.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4981	216
1	4981	216

prune21.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	19	6	25

Error

9.3b

Counts

25 → 6

Compiler

Compiled 282 to 213 computations (24.5% saved)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

9.3b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 9.3b
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

6 alts after pruning (4 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	1	1
Total	6	6

Error

9.3b

Counts

6 → 6

Compiler

Compiled 55 to 48 computations (12.7% 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))
0.3b	(.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))))

rewrite153.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

9.3b

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)

series507.0ms (9.5%)

Error

9.3b

Counts

4 → 27

Calls

4 calls:

224.0ms	(.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 re (*.f64 (sqrt.f64 (/.f64 1 im)) -1/2))))
140.0ms	(+.f64 (sqrt.f64 im) (.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2)))
105.0ms	(.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2))
16.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 1145 to 1011 computations (11.7% saved)

simplify72.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5194	1755

prune137.0ms (2.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	111	6	117

Error

9.3b

Counts

117 → 6

Compiler

Compiled 2193 to 1652 computations (24.7% saved)

regimes1.0s (18.9%)

Accuracy

Total 11.9b remaining (61.6%)

Threshold costs 0b (0%)

Compiler

Compiled 5882 to 4370 computations (25.7% saved)

bsearch136.0ms (2.6%)

Steps

Iters	Range		Point
10	4.287751348134154e+104	4.7958669913300463e+114	4.7556426971851874e+114
8	5.337080377840801e-20	2.5690159893717516e-17	5.384102014280888e-20
10	-5.4547353343632275e-126	-1.247263795516534e-138	-1.2610372716287457e-138
6	-94471064006.93654	-6374625483.463396	-92382353356.81528

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	148	162
1	148	162

end0.0ms (0%)

sample1.8s (34.7%)

Algorithm

1×

intervals

Results

277.0ms	6100×	body	128	valid
153.0ms	533×	body	4096	valid
146.0ms	613×	body	2048	valid
100.0ms	8000×	pre	128	true
69.0ms	408×	body	1024	valid
29.0ms	230×	body	512	valid
10.0ms	116×	body	256	valid

Compiler

Compiled 877 to 651 computations (25.8% saved)

Details

analyze476.0ms (9%)

sample41.0ms (0.8%)

simplify24.0ms (0.4%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite81.0ms (1.5%)

series408.0ms (7.7%)

simplify67.0ms (1.3%)

prune95.0ms (1.8%)

localize6.0ms (0.1%)

rewrite18.0ms (0.3%)

series77.0ms (1.4%)

simplify99.0ms (1.9%)

prune21.0ms (0.4%)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.1%)

prune5.0ms (0.1%)

localize12.0ms (0.2%)

rewrite153.0ms (2.9%)

series507.0ms (9.5%)

simplify72.0ms (1.3%)

prune137.0ms (2.6%)

regimes1.0s (18.9%)

bsearch136.0ms (2.6%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.8s (34.7%)

Profiling