Details

analyze409.0ms (6.4%)

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)

sample49.0ms (0.8%)

Algorithm

1×

intervals

Results

12.0ms	199×	body	128	valid
7.0ms	16×	body	2048	valid
6.0ms	21×	body	4096	valid
4.0ms	256×	pre	128	true
2.0ms	10×	body	1024	valid
1.0ms	6×	body	512	valid
0.0ms	4×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify123.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (20.0ms)

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

39.4b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize22.0ms (0.4%)

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)))
1.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite128.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

39.3b

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:

13.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
10.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
9.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 1418 to 497 computations (65% saved)

series448.0ms (7%)

Error

0.3b

Counts

4 → 45

Calls

4 calls:

109.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
99.0ms	(+.f64 (.f64 re re) (.f64 im im))
98.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
76.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 1736 to 1528 computations (12% saved)

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5066	1486

prune136.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	95	6	101
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	95	7	102

Error

0.3b

Counts

102 → 7

Compiler

Compiled 1865 to 906 computations (51.4% saved)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	0	0

prune11.0ms (0.2%)

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

0.3b

Counts

7 → 7

Compiler

Compiled 73 to 66 computations (9.6% saved)

localize24.0ms (0.4%)

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))

rewrite250.0ms (3.9%)

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:

11.0ms	(*.f64 (sqrt.f64 im) (sqrt.f64 2))
10.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
5.0ms	(*.f64 re (sqrt.f64 2))
3.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 2828 to 2228 computations (21.2% saved)

series221.0ms (3.5%)

Error

0.3b

Counts

4 → 15

Calls

4 calls:

118.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
40.0ms	(*.f64 re (sqrt.f64 2))
31.0ms	(*.f64 (sqrt.f64 im) (sqrt.f64 2))
17.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 918 to 816 computations (11.1% saved)

simplify103.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4891	1398
1	4891	1398

prune204.0ms (3.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	126	8	134

Error

0.3b

Counts

134 → 8

Compiler

Compiled 2985 to 2349 computations (21.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
0.4b	(.f64 (sqrt.f64 (sqrt.f64 im)) (.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 im))))
0.4b	(*.f64 re (sqrt.f64 2))
0.5b	(*.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 im)))

rewrite281.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

47×	`sqrt-prod_binary64_435`
39×	`add-sqr-sqrt_binary64_441`
32×	`associate-r_binary64_359`
23×	`pow1_binary64_480` `add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
19×	`associate-l_binary64_360`
18×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
14×	`pow-prod-down_binary64_490`
9×	`times-frac_binary64_425`
8×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `unswap-sqr_binary64_387`
5×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437`
4×	`add-log-exp_binary64_458` `*-commutative_binary64_350`
3×	`sqrt-unprod_binary64_439`
1×	`sqrt-div_binary64_436` `associate-*r/_binary64_361` `div-inv_binary64_416`

Counts

4 → 116

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 (sqrt.f64 im)) (.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 im))))
15.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
9.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 im)))
5.0ms	(*.f64 re (sqrt.f64 2))

Compiler

Compiled 3560 to 2386 computations (33% saved)

series308.0ms (4.8%)

Error

0.3b

Counts

4 → 15

Calls

4 calls:

129.0ms	(.f64 (.f64 re (sqrt.f64 2)) (sqrt.f64 (/.f64 1 im)))
74.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 im)))
55.0ms	(*.f64 re (sqrt.f64 2))
35.0ms	(.f64 (sqrt.f64 (sqrt.f64 im)) (.f64 (sqrt.f64 2) (sqrt.f64 (sqrt.f64 im))))

Compiler

Compiled 1096 to 900 computations (17.9% saved)

simplify105.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5186	1592

prune213.0ms (3.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	4	4
Picked	1	0	1
Done	0	3	3
Total	131	8	139

Error

0.3b

Counts

139 → 8

Compiler

Compiled 3574 to 2465 computations (31% saved)

regimes1.0s (15.9%)

Accuracy

Total 14.0b remaining (96.6%)

Threshold costs 0b (0%)

Compiler

Compiled 6344 to 4525 computations (28.7% saved)

bsearch88.0ms (1.4%)

Steps

Iters	Range		Point
10	5.016884420632471e-11	391.71007182887496	0.002430769351198334
9	-5.884081932497442e-77	-9.787020184875875e-84	-9.968109785951101e-84
7	-8.316110930659237e+122	-3.5419061742644057e+121	-2.7738602567774047e+122

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	99
1	70	99

end0.0ms (0%)

sample2.1s (33.6%)

Algorithm

1×

intervals

Results

333.0ms	6073×	body	128	valid
182.0ms	523×	body	4096	valid
178.0ms	639×	body	2048	valid
118.0ms	8000×	pre	128	true
85.0ms	402×	body	1024	valid
35.0ms	226×	body	512	valid
14.0ms	137×	body	256	valid

Compiler

Compiled 850 to 621 computations (26.9% saved)

Details

analyze409.0ms (6.4%)

sample49.0ms (0.8%)

simplify123.0ms (1.9%)

prune5.0ms (0.1%)

localize22.0ms (0.4%)

rewrite128.0ms (2%)

series448.0ms (7%)

simplify67.0ms (1%)

prune136.0ms (2.1%)

localize4.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.1%)

prune11.0ms (0.2%)

localize24.0ms (0.4%)

rewrite250.0ms (3.9%)

series221.0ms (3.5%)

simplify103.0ms (1.6%)

prune204.0ms (3.2%)

localize15.0ms (0.2%)

rewrite281.0ms (4.4%)

series308.0ms (4.8%)

simplify105.0ms (1.6%)

prune213.0ms (3.3%)

regimes1.0s (15.9%)

bsearch88.0ms (1.4%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.1s (33.6%)

Profiling