Details

analyze323.0ms (6.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample30.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	188×	body	128	valid
5.0ms	23×	body	2048	valid
5.0ms	18×	body	4096	valid
2.0ms	14×	body	1024	valid
1.0ms	7×	body	512	valid
1.0ms	6×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify173.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 36.6b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.7b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
26.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1_binary64_3208`
6×	`*-un-lft-identity_binary64_3147`
5×	`add-sqr-sqrt_binary64_3169` `add-log-exp_binary64_3186`
4×	`add-cube-cbrt_binary64_3182` `sqrt-div_binary64_3164` `sqrt-prod_binary64_3163`
3×	`add-exp-log_binary64_3185` `flip-+_binary64_3121` `add-cbrt-cube_binary64_3183` `flip3-+_binary64_3150` `sqrt-pow1_binary64_3165`
2×	`pow1/2_binary64_3227` `associate-*r/_binary64_3089`
1×	`pow-prod-down_binary64_3218` `distribute-lft-out_binary64_3098` `rem-sqrt-square_binary64_3160` `+-commutative_binary64_3077` `sum-log_binary64_3238`

Counts

3 → 40

Calls

3 calls:

10.0ms	(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)))

series327.0ms (6.6%)

Counts

3 → 9

Calls

3 calls:

221.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
55.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
51.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify66.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5233	847

prune72.0ms (1.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	40	9	49
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	10	50

Merged error: 18.1b

Counts

50 → 10

Compiler

Compiled 1154 to 531 computations (54% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
10.4b	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
26.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
26.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite70.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`sqrt-prod_binary64_3163`
58×	`add-sqr-sqrt_binary64_3169`
34×	`sqrt-pow1_binary64_3165`
29×	`pow1_binary64_3208`
28×	`sqrt-div_binary64_3164`
18×	`*-un-lft-identity_binary64_3147` `pow1/2_binary64_3227` `add-cube-cbrt_binary64_3182`
15×	`swap-sqr_binary64_3114`
10×	`rem-sqrt-square_binary64_3160`
9×	`unswap-sqr_binary64_3115` `flip-+_binary64_3121` `associate-r_binary64_3087` `flip3-+_binary64_3150` `pow-prod-up_binary64_3217` `associate-l_binary64_3088`
6×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `add-log-exp_binary64_3186`
5×	`pow-prod-down_binary64_3218` `pow-sqr_binary64_3120`
4×	`frac-times_binary64_3157` `sqr-abs_binary64_3162`
2×	`associate-l/_binary64_3090` `associate-r/_binary64_3089`
1×	`*-commutative_binary64_3078` `sqrt-unprod_binary64_3167` `+-commutative_binary64_3077` `prod-exp_binary64_3196` `pow-plus_binary64_3210` `pow2_binary64_3228` `cbrt-unprod_binary64_3180` `rem-square-sqrt_binary64_3159` `sum-log_binary64_3238`

Counts

4 → 128

Calls

4 calls:

23.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
19.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series204.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
55.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
44.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
43.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify57.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5161	2274

prune150.0ms (3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	139	11	150

Merged error: 18.1b

Counts

150 → 11

Compiler

Compiled 3835 to 1353 computations (64.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
26.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
26.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
26.4b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_3169`
9×	`*-un-lft-identity_binary64_3147` `sqrt-prod_binary64_3163`
7×	`pow1_binary64_3208` `add-cube-cbrt_binary64_3182`
6×	`add-log-exp_binary64_3186` `sqrt-div_binary64_3164`
4×	`add-exp-log_binary64_3185` `flip-+_binary64_3121` `add-cbrt-cube_binary64_3183` `flip3-+_binary64_3150`
3×	`rem-sqrt-square_binary64_3160` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227`
1×	`distribute-lft-out_binary64_3098` `+-commutative_binary64_3077` `sum-log_binary64_3238`

Counts

4 → 57

Calls

4 calls:

7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
7.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series180.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
44.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
43.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
42.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify66.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5185	999

prune129.0ms (2.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	69	11	80

Merged error: 18.1b

Counts

80 → 11

Compiler

Compiled 3620 to 1394 computations (61.5% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
7.0b	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
27.3b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.3b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite38.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_3169`
10×	`*-un-lft-identity_binary64_3147` `add-cube-cbrt_binary64_3182` `cbrt-prod_binary64_3178`
9×	`associate-r_binary64_3087`
8×	`sqrt-prod_binary64_3163`
6×	`cbrt-div_binary64_3179` `add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `pow1_binary64_3208` `add-log-exp_binary64_3186`
4×	`flip-+_binary64_3121` `flip3-+_binary64_3150`
3×	`unswap-sqr_binary64_3115` `associate-l_binary64_3088`
2×	`pow1/3_binary64_3229` `sqrt-div_binary64_3164` `associate-*r/_binary64_3089`
1×	`*-commutative_binary64_3078` `pow-prod-down_binary64_3218` `+-commutative_binary64_3077` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `sum-log_binary64_3238`

Counts

4 → 65

Calls

4 calls:

11.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
10.0ms	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
5.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series625.0ms (12.6%)

Counts

4 → 12

Calls

4 calls:

193.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
171.0ms	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
137.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
124.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify62.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4885	2138
1	4885	2138

prune91.0ms (1.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	7	7
Picked	1	0	1
Done	1	2	3
Total	77	11	88

Merged error: 18.1b

Counts

88 → 11

Compiler

Compiled 2616 to 775 computations (70.4% saved)

regimes679.0ms (13.7%)

Compiler: Compiled 5112 to 3344 computations (34.6% saved)

bsearch2.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	128
1	53	128

end0.0ms (0%)

sample1.5s (30.1%)

Algorithm

1×

intervals

Results

291.0ms	6094×	body	128	valid
153.0ms	521×	body	4096	valid
143.0ms	632×	body	2048	valid
74.0ms	388×	body	1024	valid
32.0ms	241×	body	512	valid
13.0ms	124×	body	256	valid

Compiler

Compiled 739 to 459 computations (37.9% saved)

Details

analyze323.0ms (6.5%)

sample30.0ms (0.6%)

simplify173.0ms (3.5%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite26.0ms (0.5%)

series327.0ms (6.6%)

simplify66.0ms (1.3%)

prune72.0ms (1.5%)

localize12.0ms (0.2%)

rewrite70.0ms (1.4%)

series204.0ms (4.1%)

simplify57.0ms (1.2%)

prune150.0ms (3%)

localize15.0ms (0.3%)

rewrite31.0ms (0.6%)

series180.0ms (3.6%)

simplify66.0ms (1.3%)

prune129.0ms (2.6%)

localize16.0ms (0.3%)

rewrite38.0ms (0.8%)

series625.0ms (12.6%)

simplify62.0ms (1.2%)

prune91.0ms (1.8%)

regimes679.0ms (13.7%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.5s (30.1%)

Profiling