Details

analyze412.0ms (4.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	46
1	34	46
0	2	2
1	2	2

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 (0.3%)

Algorithm

1×

intervals

Results

9.0ms	191×	body	128	valid
6.0ms	28×	body	2048	valid
4.0ms	13×	body	4096	valid
2.0ms	11×	body	1024	valid
1.0ms	6×	body	512	valid
1.0ms	7×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify7.0ms (0.1%)

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

Error

39.8b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize13.0ms (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 (.f64 re re) (.f64 im im))
0.5b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite89.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

39.6b

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×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `flip3-+_binary64_2127` `sqrt-div_binary64_2141` `flip-+_binary64_2098` `sqrt-prod_binary64_2140`
3×	`sqrt-pow1_binary64_2142`
2×	`pow1/2_binary64_2204` `sum-log_binary64_2215` `+-commutative_binary64_2054` `associate-*r/_binary64_2066`
1×	`rem-sqrt-square_binary64_2137` `distribute-lft-out_binary64_2075` `pow-prod-down_binary64_2195`

Counts

4 → 51

Calls

4 calls:

8.0ms	(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	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 1296 to 455 computations (64.9% saved)

series380.0ms (4.1%)

Error

8.3b

Counts

4 → 50

Calls

4 calls:

92.0ms	(+.f64 (.f64 re re) (.f64 im im))
87.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
82.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
70.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)

Compiler

Compiled 1893 to 1646 computations (13% saved)

simplify73.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5055	1519

prune100.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	93	8	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	8	102

Error

8.0b

Counts

102 → 8

Compiler

Compiled 1891 to 971 computations (48.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (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)
29.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.3b	(sqrt.f64 (.f64 2 (.f64 im im)))

rewrite169.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

8.0b

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×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `distribute-lft-out--_binary64_2076`
4×	`sqrt-pow1_binary64_2142` `sqrt-div_binary64_2141` `associate-/l*_binary64_2069`
3×	`pow-prod-down_binary64_2195` `cancel-sign-sub-inv_binary64_2090`
2×	`pow1/2_binary64_2204` `flip3--_binary64_2128` `flip--_binary64_2099` `associate-/r/_binary64_2070`
1×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `rem-sqrt-square_binary64_2137` `diff-log_binary64_2216` `sub-neg_binary64_2117` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `sqrt-undiv_binary64_2145` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121`

Counts

4 → 108

Calls

4 calls:

14.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
10.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 3656 to 1176 computations (67.8% saved)

series367.0ms (4%)

Error

2.6b

Counts

4 → 44

Calls

4 calls:

100.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
99.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
92.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
33.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))

Compiler

Compiled 2212 to 1731 computations (21.7% saved)

simplify81.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4955	4086
1	4955	4086

prune175.0ms (1.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	145	7	152
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	146	14	160

Error

2.5b

Counts

160 → 14

Compiler

Compiled 4388 to 1763 computations (59.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im))
0.4b	(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im)))
0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite527.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Error

2.5b

Rules

402×	`times-frac_binary64_2130`
305×	`add-sqr-sqrt_binary64_2146`
275×	`sqrt-prod_binary64_2140`
252×	`*-un-lft-identity_binary64_2124`
200×	`add-cube-cbrt_binary64_2159`
52×	`difference-of-squares_binary64_2093`
34×	`associate-/r*_binary64_2068`
26×	`distribute-lft-out--_binary64_2076`
15×	`associate-/l*_binary64_2069`
11×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
9×	`div-inv_binary64_2121`
6×	`add-log-exp_binary64_2163`
5×	`pow1_binary64_2185`
4×	`sqrt-div_binary64_2141` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158`
3×	`cancel-sign-sub-inv_binary64_2090`
2×	`flip3--_binary64_2128` `flip--_binary64_2099` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `associate-/l/_binary64_2071`
1×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `flip3-+_binary64_2127` `flip-+_binary64_2098` `rem-sqrt-square_binary64_2137` `diff-log_binary64_2216` `sub-neg_binary64_2117` `associate-/r/_binary64_2070`

Counts

4 → 323

Calls

4 calls:

20.0ms	(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im)))
11.0ms	(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 12437 to 3554 computations (71.4% saved)

series494.0ms (5.4%)

Error

0.6b

Counts

4 → 52

Calls

4 calls:

132.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
119.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
97.0ms	(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im))
91.0ms	(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im)))

Compiler

Compiled 2724 to 2179 computations (20% saved)

simplify175.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

375 → 375

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5003	15677

prune501.0ms (5.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	370	5	375
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	377	12	389

Error

0.6b

Counts

389 → 12

Compiler

Compiled 12461 to 3741 computations (70% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))) (.f64 (fabs.f64 im) (sqrt.f64 2)))
0.4b	(*.f64 (fabs.f64 im) (sqrt.f64 2))
0.8b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite189.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

46×	`add-sqr-sqrt_binary64_2146`
36×	`associate-l_binary64_2065`
33×	`*-un-lft-identity_binary64_2124`
29×	`sqrt-prod_binary64_2140`
28×	`add-exp-log_binary64_2162`
27×	`times-frac_binary64_2130`
25×	`add-cube-cbrt_binary64_2159`
18×	`add-cbrt-cube_binary64_2160`
13×	`prod-exp_binary64_2173`
12×	`pow1_binary64_2185`
8×	`difference-of-squares_binary64_2093`
7×	`cbrt-unprod_binary64_2157` `associate-r_binary64_2064`
6×	`add-log-exp_binary64_2163`
4×	`sqrt-div_binary64_2141` `distribute-lft-out--_binary64_2076` `pow-prod-down_binary64_2195` `div-exp_binary64_2175`
3×	`cancel-sign-sub-inv_binary64_2090`
2×	`flip3--_binary64_2128` `flip--_binary64_2099` `unswap-sqr_binary64_2092` `*-commutative_binary64_2055` `1-exp_binary64_2168` `rec-exp_binary64_2174` `cbrt-undiv_binary64_2158` `associate-/r/_binary64_2070`
1×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `flip3-+_binary64_2127` `flip-+_binary64_2098` `rem-sqrt-square_binary64_2137` `diff-log_binary64_2216` `sub-neg_binary64_2117` `associate-*l/_binary64_2067` `div-inv_binary64_2121`

Counts

4 → 111

Calls

4 calls:

19.0ms	(.f64 (/.f64 1 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))) (.f64 (fabs.f64 im) (sqrt.f64 2)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(*.f64 (fabs.f64 im) (sqrt.f64 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 3687 to 1458 computations (60.5% saved)

series432.0ms (4.7%)

Error

0.6b

Counts

4 → 47

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)
97.0ms	(.f64 (/.f64 1 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))) (.f64 (fabs.f64 im) (sqrt.f64 2)))
32.0ms	(*.f64 (fabs.f64 im) (sqrt.f64 2))

Compiler

Compiled 2615 to 2118 computations (19% saved)

simplify72.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4954	3187
1	4954	3187

prune174.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	158	12	170

Error

0.6b

Counts

170 → 12

Compiler

Compiled 4204 to 1885 computations (55.2% saved)

regimes1.9s (20.6%)

Accuracy

Total 17.0b remaining (98.2%)

Threshold costs 0b (0%)

Compiler

Compiled 14608 to 10568 computations (27.7% saved)

bsearch135.0ms (1.5%)

Steps

Iters	Range		Point
7	5.259203264941018e+110	1.4094586695849595e+112	5.743696651812785e+111
8	4.65476617352645e-175	1.720969112904427e-170	3.4795012242168694e-174
9	1.8930948830477231e-221	1.4622423311880276e-216	3.963621779117234e-220
7	3.375323810972806e-304	2.791786398599382e-302	4.071140785912515e-303
12	-1.734028799711284e+177	-1.725337140516371e+135	-8.962122735460895e+136

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	99	162
1	99	162

end0.0ms (0%)

sample2.7s (28.9%)

Algorithm

1×

intervals

Results

278.0ms	6017×	body	128	valid
154.0ms	525×	body	4096	valid
153.0ms	654×	body	2048	valid
74.0ms	427×	body	1024	valid
32.0ms	245×	body	512	valid
12.0ms	132×	body	256	valid

Compiler

Compiled 2127 to 1531 computations (28% saved)

Details

analyze412.0ms (4.5%)

sample32.0ms (0.3%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite89.0ms (1%)

series380.0ms (4.1%)

simplify73.0ms (0.8%)

prune100.0ms (1.1%)

localize13.0ms (0.1%)

rewrite169.0ms (1.8%)

series367.0ms (4%)

simplify81.0ms (0.9%)

prune175.0ms (1.9%)

localize14.0ms (0.2%)

rewrite527.0ms (5.7%)

series494.0ms (5.4%)

simplify175.0ms (1.9%)

prune501.0ms (5.4%)

localize14.0ms (0.2%)

rewrite189.0ms (2.1%)

series432.0ms (4.7%)

simplify72.0ms (0.8%)

prune174.0ms (1.9%)

regimes1.9s (20.6%)

bsearch135.0ms (1.5%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.7s (28.9%)

Profiling