Details

analyze408.0ms (3.8%)

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)

sample39.0ms (0.4%)

Algorithm

1×

intervals

Results

13.0ms	207×	body	128	valid
6.0ms	18×	body	2048	valid
4.0ms	11×	body	4096	valid
3.0ms	13×	body	1024	valid
1.0ms	3×	body	512	valid
0.0ms	4×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify108.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune5.0ms (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)

localize17.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
2.0b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite97.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

38.4b

Rules

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

Counts

3 → 40

Calls

3 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	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 1030 to 354 computations (65.6% saved)

series341.0ms (3.2%)

Error

5.6b

Counts

3 → 37

Calls

3 calls:

127.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
87.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
83.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))

Compiler

Compiled 1405 to 1211 computations (13.8% saved)

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5013	1215

prune102.0ms (1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	71	6	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	6	78

Error

5.3b

Counts

78 → 6

Compiler

Compiled 1431 to 739 computations (48.4% saved)

localize17.0ms (0.2%)

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)))
0.4b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.8b	(sqrt.f64 (.f64 2 (.f64 im im)))
30.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite203.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

5.3b

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:

15.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
11.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
8.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 3656 to 1176 computations (67.8% saved)

series461.0ms (4.3%)

Error

1.6b

Counts

4 → 43

Calls

4 calls:

144.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
143.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
98.0ms	(/.f64 (sqrt.f64 (.f64 2 (.f64 im im))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
31.0ms	(sqrt.f64 (.f64 2 (.f64 im im)))

Compiler

Compiled 2126 to 1656 computations (22.1% saved)

simplify106.0ms (1%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4947	4034
1	4947	4034

prune197.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	146	5	151
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	147	10	157

Error

1.6b

Counts

157 → 10

Compiler

Compiled 4281 to 1677 computations (60.8% saved)

localize18.0ms (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))))
0.4b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
30.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite252.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

1.6b

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))))
15.0ms	(-.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)))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 4875 to 1272 computations (73.9% saved)

series583.0ms (5.5%)

Error

0.1b

Counts

4 → 51

Calls

4 calls:

150.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
145.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
118.0ms	(.f64 (sqrt.f64 2) (/.f64 (fabs.f64 im) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))))
112.0ms	(/.f64 (fabs.f64 im) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))

Compiler

Compiled 2654 to 2127 computations (19.9% saved)

simplify108.0ms (1%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4986	5055
1	4986	5055

prune269.0ms (2.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	192	3	195
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	195	10	205

Error

0.1b

Counts

205 → 10

Compiler

Compiled 5470 to 1854 computations (66.1% saved)

localize16.0ms (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 (+.f64 (.f64 re re) (.f64 im im))) re)
0.6b	(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im)))
30.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite621.0ms (5.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

402×	`times-frac_binary64_2471`
305×	`add-sqr-sqrt_binary64_2487`
275×	`sqrt-prod_binary64_2481`
252×	`*-un-lft-identity_binary64_2465`
200×	`add-cube-cbrt_binary64_2500`
52×	`difference-of-squares_binary64_2434`
34×	`associate-/r*_binary64_2409`
26×	`distribute-lft-out--_binary64_2417`
15×	`associate-/l*_binary64_2410`
11×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
9×	`div-inv_binary64_2462`
6×	`add-log-exp_binary64_2504`
5×	`pow1_binary64_2526`
4×	`sqrt-div_binary64_2482` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499`
3×	`cancel-sign-sub-inv_binary64_2431`
2×	`frac-2neg_binary64_2476` `clear-num_binary64_2464` `flip3--_binary64_2469` `flip--_binary64_2440` `associate-/l/_binary64_2412`
1×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `flip3-+_binary64_2468` `flip-+_binary64_2439` `rem-sqrt-square_binary64_2478` `associate-/r/_binary64_2411` `diff-log_binary64_2557` `sub-neg_binary64_2458`

Counts

4 → 323

Calls

4 calls:

22.0ms	(/.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)

series609.0ms (5.7%)

Error

0.1b

Counts

4 → 52

Calls

4 calls:

187.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
126.0ms	(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im)))
122.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
120.0ms	(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)) (fabs.f64 im))

Compiler

Compiled 2740 to 2199 computations (19.7% saved)

simplify195.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

375 → 375

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4988	15671
1	4988	15671

prune557.0ms (5.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	374	1	375
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	374	11	385

Error

0.1b

Counts

385 → 11

Compiler

Compiled 12272 to 3581 computations (70.8% saved)

regimes2.2s (20.3%)

Accuracy

Total 23.6b remaining (98.5%)

Threshold costs 0b (0%)

Compiler

Compiled 13654 to 9476 computations (30.6% saved)

bsearch107.0ms (1%)

Steps

Iters	Range		Point
8	9.74913098744252e-49	1.9515848507345425e-44	1.6694765103601103e-44
6	3.0921839565878166e-173	1.4175822570343806e-172	1.395509735790332e-172
10	-6.254818025880814e-284	-1.153505436316687e-299	-2.0685955733607066e-292
4	-7.32518311386275e-51	-3.795880253604541e-51	-4.986259634894712e-51

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	77	128
1	77	128

end0.0ms (0%)

sample3.0s (27.9%)

Algorithm

1×

intervals

Results

339.0ms	6094×	body	128	valid
177.0ms	652×	body	2048	valid
176.0ms	510×	body	4096	valid
86.0ms	407×	body	1024	valid
34.0ms	214×	body	512	valid
13.0ms	123×	body	256	valid

Compiler

Compiled 1877 to 1311 computations (30.2% saved)

Details

analyze408.0ms (3.8%)

sample39.0ms (0.4%)

simplify108.0ms (1%)

prune5.0ms (0%)

localize17.0ms (0.2%)

rewrite97.0ms (0.9%)

series341.0ms (3.2%)

simplify72.0ms (0.7%)

prune102.0ms (1%)

localize17.0ms (0.2%)

rewrite203.0ms (1.9%)

series461.0ms (4.3%)

simplify106.0ms (1%)

prune197.0ms (1.8%)

localize18.0ms (0.2%)

rewrite252.0ms (2.4%)

series583.0ms (5.5%)

simplify108.0ms (1%)

prune269.0ms (2.5%)

localize16.0ms (0.2%)

rewrite621.0ms (5.8%)

series609.0ms (5.7%)

simplify195.0ms (1.8%)

prune557.0ms (5.2%)

regimes2.2s (20.3%)

bsearch107.0ms (1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.0s (27.9%)

Profiling