Details

analyze325.0ms (4.9%)

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)

sample32.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	183×	body	128	valid
6.0ms	22×	body	4096	valid
6.0ms	27×	body	2048	valid
2.0ms	11×	body	1024	valid
1.0ms	10×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify172.0ms (2.6%)

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%)

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: 40.7b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.0b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
0.0b	(+.f64 (.f64 re re) (.f64 im im))
30.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_2472` `pow1_binary64_2494`
7×	`*-un-lft-identity_binary64_2436`
6×	`add-sqr-sqrt_binary64_2457`
5×	`add-cube-cbrt_binary64_2468`
4×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469` `sqrt-prod_binary64_2451` `sqrt-div_binary64_2452`
3×	`sqrt-pow1_binary64_2453`
2×	`pow1/2_binary64_2513` `associate-*r/_binary64_2380` `sum-log_binary64_2524` `+-commutative_binary64_2368`
1×	`distribute-lft-out_binary64_2389` `pow-prod-down_binary64_2504` `rem-sqrt-square_binary64_2449`

Counts

4 → 51

Calls

4 calls:

9.0ms	(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)))
5.0ms	(+.f64 (.f64 re re) (.f64 im im))

series355.0ms (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)))
57.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
51.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
37.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify56.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5113	1040

prune82.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	56	7	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	8	64

Merged error: 18.3b

Counts

64 → 8

Compiler

Compiled 1331 to 616 computations (53.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.6b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.2b	(sqrt.f64 (.f64 (.f64 im im) 2))

rewrite46.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64_2457` `sqrt-prod_binary64_2451`
37×	`*-un-lft-identity_binary64_2436`
36×	`times-frac_binary64_2442`
25×	`add-cube-cbrt_binary64_2468`
12×	`difference-of-squares_binary64_2405`
11×	`pow1_binary64_2494`
9×	`associate-/r*_binary64_2382`
6×	`distribute-lft-out--_binary64_2390` `add-log-exp_binary64_2472` `add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
4×	`associate-/l*_binary64_2383` `sqrt-div_binary64_2452` `sqrt-pow1_binary64_2453`
3×	`pow-prod-down_binary64_2504`
2×	`associate-/r/_binary64_2384` `pow1/2_binary64_2513` `flip3--_binary64_2440` `flip--_binary64_2411`
1×	`flip3-+_binary64_2439` `cbrt-undiv_binary64_2467` `flip-+_binary64_2410` `div-inv_binary64_2433` `diff-log_binary64_2525` `div-exp_binary64_2484` `sqrt-undiv_binary64_2456` `clear-num_binary64_2435` `rem-sqrt-square_binary64_2449` `frac-2neg_binary64_2447` `sub-neg_binary64_2429`

Counts

4 → 105

Calls

4 calls:

16.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.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)))
5.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))

series330.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

183.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
59.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
44.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))
44.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify111.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4923	3604
1	4923	3604

prune151.0ms (2.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	111	6	117
Fresh	3	3	6
Picked	1	0	1
Done	1	0	1
Total	116	9	125

Merged error: 10.3b

Counts

125 → 9

Compiler

Compiled 3647 to 1330 computations (63.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
0.3b	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
0.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
30.6b	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

rewrite86.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`sqrt-prod_binary64_2451`
142×	`add-sqr-sqrt_binary64_2457`
112×	`times-frac_binary64_2442`
99×	`*-un-lft-identity_binary64_2436`
71×	`add-cube-cbrt_binary64_2468`
60×	`associate-r_binary64_2378`
28×	`difference-of-squares_binary64_2405`
14×	`distribute-lft-out--_binary64_2390`
11×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
9×	`associate-/r*_binary64_2382`
7×	`pow1_binary64_2494`
6×	`associate-/l*_binary64_2383` `add-log-exp_binary64_2472` `sqrt-div_binary64_2452`
5×	`unswap-sqr_binary64_2404`
4×	`associate-/r/_binary64_2384`
3×	`flip3--_binary64_2440` `associate-l_binary64_2379` `flip--_binary64_2411`
2×	`prod-exp_binary64_2482` `cbrt-undiv_binary64_2467` `div-inv_binary64_2433` `div-exp_binary64_2484` `cbrt-unprod_binary64_2466`
1×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `-commutative_binary64_2369` `diff-log_binary64_2525` `pow-prod-down_binary64_2504` `pow1/2_binary64_2513` `associate-r/_binary64_2380` `sqrt-undiv_binary64_2456` `clear-num_binary64_2435` `rem-sqrt-square_binary64_2449` `frac-2neg_binary64_2447` `sqrt-pow1_binary64_2453` `sub-neg_binary64_2429`

Counts

4 → 195

Calls

4 calls:

32.0ms	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
13.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

series460.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

205.0ms	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
160.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
54.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
41.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

simplify97.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4982	6416
1	4982	6416

prune253.0ms (3.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	203	4	207
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	207	9	216

Merged error: 2.9b

Counts

216 → 9

Compiler

Compiled 6581 to 2360 computations (64.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
0.3b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 im)) (/.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re))))
0.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
30.6b	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

rewrite106.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

308×	`sqrt-prod_binary64_2451`
182×	`add-sqr-sqrt_binary64_2457`
162×	`times-frac_binary64_2442`
141×	`*-un-lft-identity_binary64_2436`
101×	`add-cube-cbrt_binary64_2468`
87×	`associate-r_binary64_2378`
40×	`difference-of-squares_binary64_2405`
20×	`distribute-lft-out--_binary64_2390`
18×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
10×	`pow1_binary64_2494`
9×	`associate-/l_binary64_2383` `associate-/r_binary64_2382`
6×	`prod-exp_binary64_2482` `add-log-exp_binary64_2472` `cbrt-unprod_binary64_2466` `sqrt-div_binary64_2452`
4×	`associate-/r/_binary64_2384`
3×	`cbrt-undiv_binary64_2467` `pow-prod-down_binary64_2504` `div-exp_binary64_2484` `flip3--_binary64_2440` `flip--_binary64_2411`
2×	`div-inv_binary64_2433`
1×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `-commutative_binary64_2369` `diff-log_binary64_2525` `pow1/2_binary64_2513` `associate-r/_binary64_2380` `sqrt-undiv_binary64_2456` `clear-num_binary64_2435` `rem-sqrt-square_binary64_2449` `frac-2neg_binary64_2447` `associate-l_binary64_2379` `sqrt-pow1_binary64_2453` `sub-neg_binary64_2429`

Counts

4 → 250

Calls

4 calls:

36.0ms	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 im)) (/.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re))))
15.0ms	(/.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

series492.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(.f64 (.f64 (sqrt.f64 (sqrt.f64 2)) (fabs.f64 im)) (/.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re))))
193.0ms	(/.f64 (sqrt.f64 (sqrt.f64 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
53.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
48.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

simplify111.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5126	9216

prune440.0ms (6.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	259	3	262
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	261	10	271

Merged error: 2.8b

Counts

271 → 10

Compiler

Compiled 9515 to 4134 computations (56.6% saved)

regimes1.0s (15.3%)

Compiler: Compiled 7769 to 5532 computations (28.8% saved)

bsearch79.0ms (1.2%)

Steps

Iters	Range		Point
9	1.0607121626001116e+35	2.3420129584332703e+42	2.308796599986344e+42
8	9.548525832634255e-223	4.566231549918478e-219	1.0374630035315453e-222
7	-1.3794740741452004e-299	-3.1837278662513398e-301	-6.527935055640734e-301
5	-2.445867495953277e+136	-7.828159777283928e+135	-2.3838929425074713e+136

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	71	119
1	71	119

end0.0ms (0%)

sample1.8s (26.8%)

Algorithm

1×

intervals

Results

292.0ms	6019×	body	128	valid
169.0ms	583×	body	4096	valid
151.0ms	645×	body	2048	valid
74.0ms	413×	body	1024	valid
31.0ms	215×	body	512	valid
11.0ms	125×	body	256	valid

Compiler

Compiled 1127 to 794 computations (29.5% saved)

Details

analyze325.0ms (4.9%)

sample32.0ms (0.5%)

simplify172.0ms (2.6%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite31.0ms (0.5%)

series355.0ms (5.3%)

simplify56.0ms (0.8%)

prune82.0ms (1.2%)

localize15.0ms (0.2%)

rewrite46.0ms (0.7%)

series330.0ms (4.9%)

simplify111.0ms (1.7%)

prune151.0ms (2.3%)

localize13.0ms (0.2%)

rewrite86.0ms (1.3%)

series460.0ms (6.9%)

simplify97.0ms (1.5%)

prune253.0ms (3.8%)

localize15.0ms (0.2%)

rewrite106.0ms (1.6%)

series492.0ms (7.4%)

simplify111.0ms (1.7%)

prune440.0ms (6.6%)

regimes1.0s (15.3%)

bsearch79.0ms (1.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.8s (26.8%)

Profiling