Details

analyze337.0ms (8.8%)

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)

sample38.0ms (1%)

Algorithm

1×

intervals

Results

9.0ms	192×	body	80	valid
9.0ms	32×	body	2560	valid
4.0ms	19×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	8×	body	5120	valid
1.0ms	3×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify51.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	250	23
1	250	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

Merged error: 40.0b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize11.0ms (0.3%)

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)))
0.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite34.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64` `pow1_binary64`
7×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`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 → 57

Calls

4 calls:

10.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
10.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
6.0ms	(+.f64 (.f64 re re) (.f64 im im))

series357.0ms (9.3%)

Counts

4 → 12

Calls

4 calls:

197.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
63.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
58.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
38.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify148.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	4954	1196
1	4954	1196

prune90.0ms (2.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	63	6	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	6	70

Merged error: 9.9b

Counts

70 → 6

Compiler

Compiled 1458 to 651 computations (55.3% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite6.0ms (0.2%)

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` `insert-posit16` `flip--_binary64` `sqrt-prod_binary64`

Counts

1 → 14

Calls

1 calls:

6.0ms

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

series108.0ms (2.8%)

Counts

1 → 3

Calls

1 calls:

108.0ms

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

simplify141.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	4962	266
1	4962	266

prune21.0ms (0.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	15	2	17
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	15	8	23

Merged error: 9.9b

Counts

23 → 8

Compiler

Compiled 342 to 245 computations (28.4% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (-.f64 im re))
0.4b	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
17×	`sqrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
8×	`associate-r_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`associate-l_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `sqrt-div_binary64`
3×	`pow-prod-down_binary64` `pow1/2_binary64` `sqrt-pow1_binary64`
2×	`add-log-exp_binary64` `flip3--_binary64` `associate-*r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `insert-posit16` `flip--_binary64`
1×	`cbrt-unprod_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

2 → 53

Calls

2 calls:

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

series180.0ms (4.7%)

Counts

2 → 6

Calls

2 calls:

121.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 im re)))
59.0ms	(sqrt.f64 (-.f64 im re))

simplify209.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (185.0ms)

Iter	Nodes	Cost
0	4935	859
1	4935	859

prune55.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	59	8	67

Merged error: 9.9b

Counts

67 → 8

Compiler

Compiled 990 to 604 computations (39% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(log.f64 (sqrt.f64 (-.f64 im re)))
0.0b	(sqrt.f64 (-.f64 im re))
0.4b	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
3.5b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))

rewrite38.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
28×	`log-prod_binary64` `sqrt-prod_binary64`
23×	`*-un-lft-identity_binary64`
20×	`exp-sum_binary64`
15×	`add-cube-cbrt_binary64`
11×	`pow1_binary64` `associate-r_binary64`
8×	`sqrt-div_binary64`
6×	`log-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64` `unswap-sqr_binary64` `log-div_binary64` `exp-prod_binary64`
4×	`add-log-exp_binary64` `flip3--_binary64` `exp-diff_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `insert-posit16` `flip--_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64`
2×	`associate-*r/_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 102

Calls

4 calls:

15.0ms	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
9.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))
5.0ms	(log.f64 (sqrt.f64 (-.f64 im re)))
4.0ms	(sqrt.f64 (-.f64 im re))

series315.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(*.f64 (sqrt.f64 2) (exp.f64 (log.f64 (sqrt.f64 (-.f64 im re)))))
77.0ms	(log.f64 (sqrt.f64 (-.f64 im re)))
70.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 im re))))
58.0ms	(sqrt.f64 (-.f64 im re))

simplify81.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5119	1647

prune99.0ms (2.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	114	8	122

Merged error: 9.9b

Counts

122 → 8

Compiler

Compiled 1874 to 1041 computations (44.5% saved)

regimes130.0ms (3.4%)

Compiler: Compiled 422 to 342 computations (19% saved)

bsearch67.0ms (1.7%)

Steps

Iters	Range		Point
5	2.598882232530773e+24	8.291699899693349e+24	2.6608325349767907e+24
9	-6.332404097599858e-57	-8.127927816624858e-62	-1.381537308339346e-60
9	-1.4804299246070387e+154	-5.002539079463111e+145	-5.413770018556036e+145

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	63	114
1	63	114

end0.0ms (0%)

sample1.3s (33.2%)

Algorithm

1×

intervals

Results

288.0ms	5999×	body	80	valid
195.0ms	689×	body	2560	valid
116.0ms	8000×	pre	80	true
113.0ms	500×	body	1280	valid
93.0ms	281×	body	5120	valid
53.0ms	295×	body	640	valid
20.0ms	153×	body	320	valid
7.0ms	83×	body	160	valid

Compiler

Compiled 202 to 149 computations (26.2% saved)

Details

analyze337.0ms (8.8%)

sample38.0ms (1%)

simplify51.0ms (1.3%)

prune3.0ms (0.1%)

localize11.0ms (0.3%)

rewrite34.0ms (0.9%)

series357.0ms (9.3%)

simplify148.0ms (3.9%)

prune90.0ms (2.3%)

localize6.0ms (0.2%)

rewrite6.0ms (0.2%)

series108.0ms (2.8%)

simplify141.0ms (3.7%)

prune21.0ms (0.5%)

localize7.0ms (0.2%)

rewrite17.0ms (0.4%)

series180.0ms (4.7%)

simplify209.0ms (5.4%)

prune55.0ms (1.4%)

localize11.0ms (0.3%)

rewrite38.0ms (1%)

series315.0ms (8.2%)

simplify81.0ms (2.1%)

prune99.0ms (2.6%)

regimes130.0ms (3.4%)

bsearch67.0ms (1.7%)

simplify7.0ms (0.2%)

end0.0ms (0%)

sample1.3s (33.2%)

Profiling