Details

analyze331.0ms (4.8%)

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)

sample37.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	185×	body	128	valid
5.0ms	23×	body	2048	valid
4.0ms	14×	body	4096	valid
3.0ms	256×	pre	128	true
3.0ms	20×	body	1024	valid
1.0ms	6×	body	512	valid
1.0ms	8×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	156	23
1	156	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

Merged error: 40.8b

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))
0.2b	(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)
30.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64`
6×	`add-cube-cbrt_binary64`
5×	`sqrt-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-*r/_binary64` `difference-of-squares_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 56

Calls

4 calls:

10.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(+.f64 (.f64 re re) (.f64 im im))

series360.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

209.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
62.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
53.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
36.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify62.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5370	1125

prune242.0ms (3.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	8	69

Merged error: 9.8b

Counts

69 → 8

Compiler

Compiled 4161 to 2512 computations (39.6% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64`
2×	`associate-*r/_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1/2_binary64` `flip3--_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `flip--_binary64` `sqrt-prod_binary64`

Counts

1 → 13

Calls

1 calls:

5.0ms

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

series105.0ms (1.5%)

Counts

1 → 3

Calls

1 calls:

104.0ms

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

simplify49.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5019	253

prune40.0ms (0.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	14	2	16
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	14	10	24

Merged error: 9.8b

Counts

24 → 10

Compiler

Compiled 667 to 478 computations (28.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
0.4b	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
0.4b	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
0.4b	(.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 im re)))) (cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
20×	`associate-*r/_binary64`
18×	`cbrt-div_binary64` `sqrt-div_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`flip3--_binary64` `pow1/3_binary64` `flip--_binary64`
7×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `associate-*l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 93

Calls

4 calls:

11.0ms	(.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 im re)))) (cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
6.0ms	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
6.0ms	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
6.0ms	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))

series1.7s (25.1%)

Counts

4 → 12

Calls

4 calls:

449.0ms	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
434.0ms	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
434.0ms	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
407.0ms	(.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 im re)))) (cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))

simplify77.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4871	2117
1	4871	2117

prune207.0ms (3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	105	10	115

Merged error: 9.8b

Counts

115 → 10

Compiler

Compiled 3871 to 2573 computations (33.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (exp.f64 (.f64 2 (log.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 im re)))))
0.4b	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
0.4b	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
3.0b	(exp.f64 (.f64 2 (log.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 im re)))))))

rewrite44.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64` `cbrt-prod_binary64`
36×	`log-prod_binary64` `exp-sum_binary64`
18×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
17×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
10×	`unswap-sqr_binary64`
8×	`associate-*r/_binary64`
7×	`associate-r_binary64` `sqrt-prod_binary64`
6×	`cbrt-div_binary64` `add-log-exp_binary64` `pow1_binary64` `sqrt-div_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`pow1/3_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `rem-exp-log_binary64` `prod-exp_binary64` `exp-to-pow_binary64` `exp-prod_binary64` `*-commutative_binary64`

Counts

4 → 99

Calls

4 calls:

15.0ms	(.f64 (exp.f64 (.f64 2 (log.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 im re)))))
6.0ms	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
6.0ms	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
5.0ms	(exp.f64 (.f64 2 (log.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 im re)))))))

series1.6s (23.7%)

Counts

4 → 12

Calls

4 calls:

647.0ms	(exp.f64 (.f64 2 (log.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 im re)))))))
446.0ms	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
422.0ms	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
112.0ms	(.f64 (exp.f64 (.f64 2 (log.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 im re))))))) (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 im re)))))

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5492	2381

prune182.0ms (2.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	111	10	121

Merged error: 9.8b

Counts

121 → 10

Compiler

Compiled 3430 to 2467 computations (28.1% saved)

regimes349.0ms (5.1%)

Compiler: Compiled 1649 to 1278 computations (22.5% saved)

bsearch2.0ms (0%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	116
1	49	116

end0.0ms (0%)

sample1.2s (17.8%)

Algorithm

1×

intervals

Results

281.0ms	6057×	body	128	valid
153.0ms	532×	body	4096	valid
140.0ms	616×	body	2048	valid
114.0ms	8000×	pre	128	true
84.0ms	451×	body	1024	valid
28.0ms	212×	body	512	valid
12.0ms	132×	body	256	valid

Compiler

Compiled 263 to 184 computations (30% saved)

Details

analyze331.0ms (4.8%)

sample37.0ms (0.5%)

simplify15.0ms (0.2%)

prune3.0ms (0%)

localize10.0ms (0.2%)

rewrite35.0ms (0.5%)

series360.0ms (5.3%)

simplify62.0ms (0.9%)

prune242.0ms (3.5%)

localize6.0ms (0.1%)

rewrite6.0ms (0.1%)

series105.0ms (1.5%)

simplify49.0ms (0.7%)

prune40.0ms (0.6%)

localize10.0ms (0.1%)

rewrite41.0ms (0.6%)

series1.7s (25.1%)

simplify77.0ms (1.1%)

prune207.0ms (3%)

localize12.0ms (0.2%)

rewrite44.0ms (0.6%)

series1.6s (23.7%)

simplify64.0ms (0.9%)

prune182.0ms (2.7%)

regimes349.0ms (5.1%)

bsearch2.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.2s (17.8%)

Profiling