Details

analyze418.0ms (4.6%)

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

Symmetry

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample32.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	201×	body	128	valid
6.0ms	21×	body	4096	valid
2.0ms	10×	body	2048	valid
2.0ms	10×	body	1024	valid
1.0ms	11×	body	512	valid
0.0ms	3×	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

38.6b

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))
0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.9b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite95.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

38.4b

Rules

8×	`pow1_binary64_2526` `add-log-exp_binary64_2504`
7×	`*-un-lft-identity_binary64_2465`
6×	`add-sqr-sqrt_binary64_2487`
5×	`add-cube-cbrt_binary64_2500`
4×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `flip3-+_binary64_2468` `sqrt-div_binary64_2482` `flip-+_binary64_2439` `sqrt-prod_binary64_2481`
3×	`sqrt-pow1_binary64_2483`
2×	`pow1/2_binary64_2545` `sum-log_binary64_2556` `+-commutative_binary64_2395` `associate-*r/_binary64_2407`
1×	`rem-sqrt-square_binary64_2478` `distribute-lft-out_binary64_2416` `pow-prod-down_binary64_2536`

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	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
7.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 1296 to 455 computations (64.9% saved)

series469.0ms (5.1%)

Error

5.7b

Counts

4 → 57

Calls

4 calls:

125.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
112.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
89.0ms	(+.f64 (.f64 re re) (.f64 im im))
83.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))

Compiler

Compiled 2314 to 2001 computations (13.5% saved)

simplify83.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5183	1713

prune106.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	102	7	109

Error

5.4b

Counts

109 → 7

Compiler

Compiled 2037 to 1065 computations (47.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
1.1b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.6b	(sqrt.f64 (.f64 2 (.f64 im im)))
31.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite172.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

5.4b

Rules

51×	`add-sqr-sqrt_binary64_2487`
50×	`sqrt-prod_binary64_2481`
38×	`*-un-lft-identity_binary64_2465`
36×	`times-frac_binary64_2471`
26×	`add-cube-cbrt_binary64_2500`
12×	`difference-of-squares_binary64_2434`
11×	`pow1_binary64_2526`
9×	`associate-/r*_binary64_2409`
6×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `distribute-lft-out--_binary64_2417`
4×	`sqrt-pow1_binary64_2483` `sqrt-div_binary64_2482` `associate-/l*_binary64_2410`
3×	`pow-prod-down_binary64_2536` `cancel-sign-sub-inv_binary64_2431`
2×	`pow1/2_binary64_2545` `flip3--_binary64_2469` `flip--_binary64_2440` `associate-/r/_binary64_2411`
1×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `sub-neg_binary64_2458` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `sqrt-undiv_binary64_2486` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `div-inv_binary64_2462`

Counts

4 → 108

Calls

4 calls:

17.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (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)
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)

series427.0ms (4.7%)

Error

2.0b

Counts

4 → 46

Calls

4 calls:

123.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
121.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
104.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))

Compiler

Compiled 2367 to 1855 computations (21.6% saved)

simplify114.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4937	4143
1	4937	4143

prune173.0ms (1.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	148	6	154
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	150	11	161

Error

1.9b

Counts

161 → 11

Compiler

Compiled 4389 to 1755 computations (60% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (fabs.f64 im) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.4b	(.f64 (sqrt.f64 2) (/.f64 (fabs.f64 im) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))))
1.1b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite216.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

1.9b

Rules

91×	`add-sqr-sqrt_binary64_2487`
61×	`sqrt-prod_binary64_2481`
58×	`*-un-lft-identity_binary64_2465` `times-frac_binary64_2471`
42×	`add-cube-cbrt_binary64_2500`
33×	`associate-r_binary64_2405`
16×	`difference-of-squares_binary64_2434`
11×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
9×	`associate-/r*_binary64_2409`
8×	`distribute-lft-out--_binary64_2417`
7×	`pow1_binary64_2526`
6×	`add-log-exp_binary64_2504` `sqrt-div_binary64_2482` `unswap-sqr_binary64_2433` `associate-l_binary64_2406`
4×	`associate-/r/_binary64_2411`
3×	`flip3--_binary64_2469` `flip--_binary64_2440` `cancel-sign-sub-inv_binary64_2431` `associate-/l*_binary64_2410`
2×	`div-exp_binary64_2516` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `cbrt-undiv_binary64_2499` `div-inv_binary64_2462`
1×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `flip3-+_binary64_2468` `flip-+_binary64_2439` `rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `sub-neg_binary64_2458` `pow-prod-down_binary64_2536` `associate-r/_binary64_2407` `-commutative_binary64_2396` `frac-2neg_binary64_2476` `clear-num_binary64_2464`

Counts

4 → 144

Calls

4 calls:

21.0ms	(.f64 (sqrt.f64 2) (/.f64 (fabs.f64 im) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))))
11.0ms	(/.f64 (fabs.f64 im) (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)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 4875 to 1272 computations (73.9% saved)

series596.0ms (6.5%)

Error

0.3b

Counts

4 → 53

Calls

4 calls:

171.0ms	(.f64 (sqrt.f64 2) (/.f64 (fabs.f64 im) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))))
141.0ms	(/.f64 (fabs.f64 im) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
130.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
95.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)

Compiler

Compiled 3164 to 2525 computations (20.2% saved)

simplify89.0ms (1%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4960	5302
1	4960	5302

prune218.0ms (2.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	194	3	197
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	198	10	208

Error

0.3b

Counts

208 → 10

Compiler

Compiled 5624 to 1967 computations (65% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (fabs.f64 im)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
0.6b	(*.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 im)))
1.1b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite213.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

93×	`sqrt-prod_binary64_2481`
85×	`add-sqr-sqrt_binary64_2487`
60×	`*-un-lft-identity_binary64_2465`
54×	`times-frac_binary64_2471`
44×	`add-cube-cbrt_binary64_2500`
16×	`difference-of-squares_binary64_2434`
9×	`pow1_binary64_2526` `associate-/r*_binary64_2409`
8×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `distribute-lft-out--_binary64_2417`
6×	`add-log-exp_binary64_2504` `associate-l_binary64_2406` `associate-r_binary64_2405` `associate-/l*_binary64_2410`
4×	`sqrt-div_binary64_2482` `unswap-sqr_binary64_2433`
3×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `cancel-sign-sub-inv_binary64_2431` `pow-prod-down_binary64_2536`
2×	`flip3--_binary64_2469` `flip--_binary64_2440` `associate-/r/_binary64_2411`
1×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `sub-neg_binary64_2458` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `sqrt-unprod_binary64_2485` `*-commutative_binary64_2396` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `sqrt-undiv_binary64_2486` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `div-inv_binary64_2462`

Counts

4 → 146

Calls

4 calls:

12.0ms	(/.f64 (sqrt.f64 (fabs.f64 im)) (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)
7.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 5435 to 1425 computations (73.8% saved)

series467.0ms (5.1%)

Error

0.3b

Counts

4 → 47

Calls

4 calls:

146.0ms	(/.f64 (sqrt.f64 (fabs.f64 im)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
130.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
95.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
42.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (fabs.f64 im)))

Compiler

Compiled 3134 to 2217 computations (29.3% saved)

simplify88.0ms (1%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4960	5222
1	4960	5222

prune223.0ms (2.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	193	10	203

Error

0.3b

Counts

203 → 10

Compiler

Compiled 6211 to 1938 computations (68.8% saved)

regimes2.0s (22.3%)

Accuracy

Total 22.0b remaining (98.5%)

Threshold costs 0b (0%)

Compiler

Compiled 14302 to 10061 computations (29.7% saved)

bsearch191.0ms (2.1%)

Steps

Iters	Range		Point
9	1.9503851609011364e+147	2.0699616931792827e+152	8.928679478924893e+147
7	2.037479440022981e+105	2.7420626548785586e+107	3.369741936920371e+105
9	3.1831374233514505e-08	0.10158509873603133	0.00038145371029701177
10	1.3652804699665224e-178	1.0153924785300751e-165	8.227571145686253e-166
10	-3.908092480963717e-156	-5.463266627909851e-167	-6.515755502939793e-159
11	-7.939322113124722e+123	-3.2144898536041683e+103	-8.689735234224661e+115

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	134	220
1	134	220

Removed

()

end0.0ms (0%)

sample2.6s (28.9%)

Algorithm

1×

intervals

Results

307.0ms	6098×	body	128	valid
151.0ms	510×	body	4096	valid
150.0ms	646×	body	2048	valid
69.0ms	377×	body	1024	valid
37.0ms	251×	body	512	valid
11.0ms	118×	body	256	valid

Compiler

Compiled 2039 to 1426 computations (30.1% saved)

Details

analyze418.0ms (4.6%)

sample32.0ms (0.3%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite95.0ms (1%)

series469.0ms (5.1%)

simplify83.0ms (0.9%)

prune106.0ms (1.2%)

localize12.0ms (0.1%)

rewrite172.0ms (1.9%)

series427.0ms (4.7%)

simplify114.0ms (1.3%)

prune173.0ms (1.9%)

localize16.0ms (0.2%)

rewrite216.0ms (2.4%)

series596.0ms (6.5%)

simplify89.0ms (1%)

prune218.0ms (2.4%)

localize17.0ms (0.2%)

rewrite213.0ms (2.3%)

series467.0ms (5.1%)

simplify88.0ms (1%)

prune223.0ms (2.4%)

regimes2.0s (22.3%)

bsearch191.0ms (2.1%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.6s (28.9%)

Profiling