Details

analyze319.0ms (8.5%)

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)

sample29.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	191×	body	128	valid
5.0ms	19×	body	4096	valid
4.0ms	19×	body	2048	valid
3.0ms	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)

simplify171.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune3.0ms (0.1%)

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: 41.3b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.3b	(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)
31.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1_binary64_2157`
6×	`*-un-lft-identity_binary64_2099`
5×	`add-sqr-sqrt_binary64_2120` `add-log-exp_binary64_2135`
4×	`add-cube-cbrt_binary64_2131` `sqrt-div_binary64_2115` `sqrt-prod_binary64_2114`
3×	`flip3-+_binary64_2102` `add-cbrt-cube_binary64_2132` `sqrt-pow1_binary64_2116` `flip-+_binary64_2073` `add-exp-log_binary64_2134`
2×	`associate-*r/_binary64_2043` `pow1/2_binary64_2176`
1×	`distribute-lft-out_binary64_2052` `sum-log_binary64_2187` `rem-sqrt-square_binary64_2112` `+-commutative_binary64_2031` `pow-prod-down_binary64_2167`

Counts

3 → 40

Calls

3 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)))

series338.0ms (9%)

Counts

3 → 9

Calls

3 calls:

230.0ms	(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)
52.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify65.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5404	847

prune77.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	41	8	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	8	50

Merged error: 16.1b

Counts

50 → 8

Compiler

Compiled 1122 to 508 computations (54.7% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.7b	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
31.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite30.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_2120`
9×	`*-un-lft-identity_binary64_2099` `sqrt-prod_binary64_2114`
7×	`add-cube-cbrt_binary64_2131` `pow1_binary64_2157`
6×	`add-log-exp_binary64_2135` `sqrt-div_binary64_2115`
4×	`flip3-+_binary64_2102` `add-cbrt-cube_binary64_2132` `flip-+_binary64_2073` `add-exp-log_binary64_2134`
3×	`rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `sqrt-pow1_binary64_2116`
1×	`distribute-lft-out_binary64_2052` `sum-log_binary64_2187` `+-commutative_binary64_2031`

Counts

4 → 57

Calls

4 calls:

7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
6.0ms	(+.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 (4.8%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
44.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
42.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
40.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify66.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4943	999
1	4943	999

prune95.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	69	8	77

Merged error: 16.1b

Counts

77 → 8

Compiler

Compiled 3166 to 756 computations (76.1% saved)

localize13.0ms (0.3%)

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)))))
9.3b	(+.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)
31.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite63.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`sqrt-prod_binary64_2114`
50×	`add-sqr-sqrt_binary64_2120`
34×	`sqrt-pow1_binary64_2116`
29×	`pow1_binary64_2157`
28×	`sqrt-div_binary64_2115`
18×	`add-cube-cbrt_binary64_2131` `*-un-lft-identity_binary64_2099` `pow1/2_binary64_2176`
15×	`swap-sqr_binary64_2066`
9×	`associate-l_binary64_2042` `flip3-+_binary64_2102` `unswap-sqr_binary64_2067` `associate-r_binary64_2041` `pow-prod-up_binary64_2166` `flip-+_binary64_2073`
6×	`add-cbrt-cube_binary64_2132` `add-log-exp_binary64_2135` `add-exp-log_binary64_2134`
5×	`pow-prod-down_binary64_2167` `pow-sqr_binary64_2072`
4×	`frac-times_binary64_2109`
2×	`associate-r/_binary64_2043` `associate-l/_binary64_2044` `rem-sqrt-square_binary64_2112`
1×	`sqrt-unprod_binary64_2118` `rem-square-sqrt_binary64_2111` `*-commutative_binary64_2032` `sum-log_binary64_2187` `prod-exp_binary64_2145` `pow2_binary64_2177` `pow-plus_binary64_2159` `+-commutative_binary64_2031` `cbrt-unprod_binary64_2129`

Counts

4 → 124

Calls

4 calls:

18.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
17.0ms	(+.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)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series195.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(+.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)
51.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
42.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
41.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify79.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4990	2259
1	4990	2259

prune140.0ms (3.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	136	8	144

Merged error: 16.1b

Counts

144 → 8

Compiler

Compiled 3604 to 1277 computations (64.6% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.8b	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) 3)
12.2b	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) 3)) re)
31.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite50.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`sqrt-prod_binary64_2114`
17×	`add-sqr-sqrt_binary64_2120`
15×	`add-cube-cbrt_binary64_2131` `*-un-lft-identity_binary64_2099`
12×	`unpow-prod-down_binary64_2175` `cube-prod_binary64_2124`
11×	`sqrt-pow1_binary64_2116`
10×	`pow1_binary64_2157` `sqrt-div_binary64_2115`
7×	`pow-pow_binary64_2168`
6×	`add-log-exp_binary64_2135`
5×	`add-cbrt-cube_binary64_2132` `pow1/2_binary64_2176` `add-exp-log_binary64_2134`
4×	`flip3-+_binary64_2102` `flip-+_binary64_2073`
3×	`pow-unpow_binary64_2173`
2×	`cube-div_binary64_2125` `rem-sqrt-square_binary64_2112`
1×	`sqr-pow_binary64_2071` `sqrt-pow2_binary64_2117` `pow-exp_binary64_2164` `rem-cube-cbrt_binary64_2121` `pow-to-exp_binary64_2165` `sum-log_binary64_2187` `unpow3_binary64_2162` `+-commutative_binary64_2031` `cube-mult_binary64_2126`

Counts

4 → 91

Calls

4 calls:

20.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) 3)) re)
9.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) 3)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series337.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

187.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) 3)
63.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) 3)) re)
47.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
40.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify53.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5007	1958

prune121.0ms (3.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	103	8	111

Merged error: 16.1b

Counts

111 → 8

Compiler

Compiled 3474 to 1192 computations (65.7% saved)

regimes142.0ms (3.8%)

Compiler: Compiled 624 to 388 computations (37.8% saved)

bsearch55.0ms (1.5%)

Steps

Iters	Range	Point
7	5.857620486384966e+127	2.4643783387014438e+129	1.0946873832682728e+128
4	8.721242409093886e-44	1.5237069649932555e-43	8.82691264352238e-44
11	-1.969542763962399e-265	-2.6838291301680593e-298	-3.868203887880326e-293

Iters

Range

Point

5.857620486384966e+127

2.4643783387014438e+129

1.0946873832682728e+128

8.721242409093886e-44

1.5237069649932555e-43

8.82691264352238e-44

-1.969542763962399e-265

-2.6838291301680593e-298

-3.868203887880326e-293

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	114
1	60	114

end0.0ms (0%)

sample1.1s (28.5%)

Algorithm

1×

intervals

Results

291.0ms	6100×	body	128	valid
147.0ms	651×	body	2048	valid
144.0ms	510×	body	4096	valid
77.0ms	414×	body	1024	valid
28.0ms	212×	body	512	valid
10.0ms	113×	body	256	valid

Compiler

Compiled 283 to 175 computations (38.2% saved)

Details

analyze319.0ms (8.5%)

sample29.0ms (0.8%)

simplify171.0ms (4.6%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

rewrite25.0ms (0.7%)

series338.0ms (9%)

simplify65.0ms (1.7%)

prune77.0ms (2%)

localize15.0ms (0.4%)

rewrite30.0ms (0.8%)

series180.0ms (4.8%)

simplify66.0ms (1.7%)

prune95.0ms (2.5%)

localize13.0ms (0.3%)

rewrite63.0ms (1.7%)

series195.0ms (5.2%)

simplify79.0ms (2.1%)

prune140.0ms (3.7%)

localize16.0ms (0.4%)

rewrite50.0ms (1.3%)

series337.0ms (8.9%)

simplify53.0ms (1.4%)

prune121.0ms (3.2%)

regimes142.0ms (3.8%)

bsearch55.0ms (1.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (28.5%)

Profiling