Details

analyze325.0ms (4.7%)

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)

sample29.0ms (0.4%)

Algorithm

1×

intervals

Results

8.0ms	185×	body	128	valid
5.0ms	25×	body	2048	valid
4.0ms	16×	body	4096	valid
3.0ms	15×	body	1024	valid
1.0ms	9×	body	256	valid
1.0ms	6×	body	512	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify100.0ms (1.5%)

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%)

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: 41.6b

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	(+.f64 (.f64 re re) (.f64 im im))
0.2b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
1.1b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`pow1_binary64_2185` `add-log-exp_binary64_2163`
7×	`*-un-lft-identity_binary64_2124`
6×	`add-sqr-sqrt_binary64_2146`
5×	`add-cube-cbrt_binary64_2159`
4×	`sqrt-prod_binary64_2140` `sqrt-div_binary64_2141` `flip3-+_binary64_2127` `flip-+_binary64_2098` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`sqrt-pow1_binary64_2142`
2×	`sum-log_binary64_2215` `+-commutative_binary64_2054` `pow1/2_binary64_2204` `associate-*r/_binary64_2066`
1×	`pow-prod-down_binary64_2195` `distribute-lft-out_binary64_2075` `rem-sqrt-square_binary64_2137`

Counts

4 → 51

Calls

4 calls:

9.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
7.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series331.0ms (4.8%)

Counts

4 → 46

Calls

4 calls:

101.0ms	(+.f64 (.f64 re re) (.f64 im im))
90.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
80.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
60.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))

Compiler

Compiled 1141 to 1059 computations (7.2% saved)

simplify51.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5035	1463

prune107.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	88	9	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	9	98

Merged error: 17.8b

Counts

98 → 9

Compiler

Compiled 1854 to 978 computations (47.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
27.6b	(sqrt.f64 (.f64 (.f64 im im) 2))
30.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64_2146`
50×	`sqrt-prod_binary64_2140`
38×	`*-un-lft-identity_binary64_2124`
36×	`times-frac_binary64_2130`
26×	`add-cube-cbrt_binary64_2159`
12×	`difference-of-squares_binary64_2093`
11×	`pow1_binary64_2185`
9×	`associate-/r*_binary64_2068`
6×	`distribute-lft-out--_binary64_2076` `add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
4×	`sqrt-pow1_binary64_2142` `associate-/l*_binary64_2069` `sqrt-div_binary64_2141`
3×	`pow-prod-down_binary64_2195` `cancel-sign-sub-inv_binary64_2090`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/r/_binary64_2070` `pow1/2_binary64_2204`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `sqrt-undiv_binary64_2145` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `sub-neg_binary64_2117` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 108

Calls

4 calls:

15.0ms	(/.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)))
4.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))

series325.0ms (4.7%)

Counts

4 → 44

Calls

4 calls:

129.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
94.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
73.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
28.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))

Compiler

Compiled 1366 to 1155 computations (15.4% saved)

simplify60.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5126	4141

prune177.0ms (2.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	147	5	152
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	151	10	161

Merged error: 13.8b

Counts

161 → 10

Compiler

Compiled 4403 to 1774 computations (59.7% saved)

localize16.0ms (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 re re) (*.f64 im im))) re))))
0.4b	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite78.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`sqrt-prod_binary64_2140`
143×	`add-sqr-sqrt_binary64_2146`
112×	`times-frac_binary64_2130`
100×	`*-un-lft-identity_binary64_2124`
72×	`add-cube-cbrt_binary64_2159`
60×	`associate-r_binary64_2064`
28×	`difference-of-squares_binary64_2093`
14×	`distribute-lft-out--_binary64_2076`
11×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
9×	`associate-/r*_binary64_2068`
7×	`pow1_binary64_2185`
6×	`associate-/l*_binary64_2069` `sqrt-div_binary64_2141` `add-log-exp_binary64_2163`
5×	`unswap-sqr_binary64_2092`
4×	`associate-/r/_binary64_2070`
3×	`flip--_binary64_2099` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090` `associate-l_binary64_2065`
2×	`cbrt-undiv_binary64_2158` `prod-exp_binary64_2173` `div-inv_binary64_2121` `div-exp_binary64_2175` `cbrt-unprod_binary64_2157`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `-commutative_binary64_2055` `sqrt-undiv_binary64_2145` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `associate-r/_binary64_2066` `flip3-+_binary64_2127` `flip-+_binary64_2098` `frac-2neg_binary64_2135`

Counts

4 → 198

Calls

4 calls:

26.0ms	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))))
13.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series413.0ms (6%)

Counts

4 → 49

Calls

4 calls:

133.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
117.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
93.0ms	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))))
70.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))

Compiler

Compiled 1624 to 1422 computations (12.4% saved)

simplify106.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4951	6904
1	4951	6904

prune317.0ms (4.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	238	9	247
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	240	17	257

Merged error: 13.5b

Counts

257 → 17

Compiler

Compiled 7477 to 2927 computations (60.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (fabs.f64 im) (sqrt.f64 (/.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))))
0.3b	(sqrt.f64 (/.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite55.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-sqr-sqrt_binary64_2146`
60×	`sqrt-prod_binary64_2140`
42×	`*-un-lft-identity_binary64_2124`
38×	`times-frac_binary64_2130`
28×	`add-cube-cbrt_binary64_2159`
27×	`associate-r_binary64_2064`
14×	`difference-of-squares_binary64_2093`
8×	`pow1_binary64_2185`
7×	`distribute-lft-out--_binary64_2076`
6×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
4×	`associate-/r/_binary64_2070` `sqrt-div_binary64_2141`
3×	`flip--_binary64_2099` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090` `unswap-sqr_binary64_2092` `rem-sqrt-square_binary64_2137` `associate-l_binary64_2065`
2×	`sqrt-pow1_binary64_2142` `pow1/2_binary64_2204` `div-inv_binary64_2121`
1×	`pow-prod-down_binary64_2195` `-commutative_binary64_2055` `diff-log_binary64_2216` `prod-exp_binary64_2173` `sub-neg_binary64_2117` `associate-r/_binary64_2066` `flip3-+_binary64_2127` `flip-+_binary64_2098` `cbrt-unprod_binary64_2157`

Counts

4 → 113

Calls

4 calls:

19.0ms	(.f64 (fabs.f64 im) (sqrt.f64 (/.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))))
11.0ms	(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)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series410.0ms (6%)

Counts

4 → 51

Calls

4 calls:

128.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
122.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
92.0ms	(.f64 (fabs.f64 im) (sqrt.f64 (/.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))))
67.0ms	(sqrt.f64 (/.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))

Compiler

Compiled 1608 to 1401 computations (12.9% saved)

simplify92.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5121	3780

prune173.0ms (2.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	156	8	164
Fresh	8	8	16
Picked	1	0	1
Done	0	0	0
Total	165	16	181

Merged error: 13.5b

Counts

181 → 16

Compiler

Compiled 4140 to 1751 computations (57.7% saved)

regimes1.4s (20%)

Compiler: Compiled 11335 to 7853 computations (30.7% saved)

bsearch81.0ms (1.2%)

Steps

Iters	Range	Point
9	3.609398986536744e+49	6.818993930479115e+54	6.503475815263617e+54
4	2.5312990710315855e-305	4.754669852777982e-305	2.5976900549837345e-305
10	-2.6679564635887278e+163	-3.767463776000618e+153	-1.3365884841721249e+154

Iters

Range

Point

3.609398986536744e+49

6.818993930479115e+54

6.503475815263617e+54

2.5312990710315855e-305

4.754669852777982e-305

2.5976900549837345e-305

-2.6679564635887278e+163

-3.767463776000618e+153

-1.3365884841721249e+154

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	59	95
1	59	95

end0.0ms (0%)

sample2.1s (31.1%)

Algorithm

1×

intervals

Results

287.0ms	6114×	body	128	valid
142.0ms	508×	body	4096	valid
137.0ms	635×	body	2048	valid
70.0ms	396×	body	1024	valid
27.0ms	215×	body	512	valid
11.0ms	132×	body	256	valid

Compiler

Compiled 1607 to 1116 computations (30.6% saved)

Details

analyze325.0ms (4.7%)

sample29.0ms (0.4%)

simplify100.0ms (1.5%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite28.0ms (0.4%)

series331.0ms (4.8%)

simplify51.0ms (0.7%)

prune107.0ms (1.6%)

localize12.0ms (0.2%)

rewrite43.0ms (0.6%)

series325.0ms (4.7%)

simplify60.0ms (0.9%)

prune177.0ms (2.6%)

localize16.0ms (0.2%)

rewrite78.0ms (1.1%)

series413.0ms (6%)

simplify106.0ms (1.5%)

prune317.0ms (4.6%)

localize12.0ms (0.2%)

rewrite55.0ms (0.8%)

series410.0ms (6%)

simplify92.0ms (1.3%)

prune173.0ms (2.5%)

regimes1.4s (20%)

bsearch81.0ms (1.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.1s (31.1%)

Profiling