Details

analyze753.0ms (7.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	338	46
1	338	46
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
25%	25%	50%	2
25%	25%	50%	3
31.2%	18.7%	50%	4
31.2%	18.7%	50%	5
34.3%	15.6%	50%	6
34.3%	15.6%	50%	7
35.9%	14%	50%	8
35.9%	14%	50%	9
36.7%	13.3%	50%	10
36.7%	13.3%	50%	11
37.1%	12.9%	50%	12
37.1%	12.9%	50%	13
37.3%	12.7%	50%	14

Compiler

Compiled 18 to 14 computations (22.2% saved)

sample57.0ms (0.6%)

Algorithm

1×

intervals

Results

15.0ms	194×	body	128	valid
9.0ms	18×	body	4096	valid
7.0ms	18×	body	2048	valid
6.0ms	18×	body	1024	valid
5.0ms	256×	pre	128	true
2.0ms	7×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 33 to 28 computations (15.2% saved)

simplify40.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	249	23
1	249	23

prune5.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

36.7b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize18.0ms (0.2%)

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)))
0.6b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite72.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_441`
8×	`*-un-lft-identity_binary64_419` `add-log-exp_binary64_458` `pow1_binary64_480`
6×	`add-cube-cbrt_binary64_454`
5×	`sqrt-prod_binary64_435`
4×	`sqrt-div_binary64_436` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`sqrt-pow1_binary64_437` `cancel-sign-sub-inv_binary64_385`
2×	`flip3-+_binary64_422` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `flip3--_binary64_423` `associate-*r/_binary64_361` `flip-+_binary64_393` `flip--_binary64_394`
1×	`pow-prod-down_binary64_490` `sub-neg_binary64_412` `sum-log_binary64_510` `distribute-lft-out--_binary64_371` `diff-log_binary64_511` `rem-sqrt-square_binary64_432` `+-commutative_binary64_349`

Counts

4 → 56

Calls

4 calls:

20.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
17.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
9.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
7.0ms	(+.f64 (.f64 re re) (.f64 im im))

series561.0ms (5.6%)

Counts

4 → 42

Calls

4 calls:

160.0ms	(+.f64 (.f64 re re) (.f64 im im))
147.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
130.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
123.0ms	(sqrt.f64 (.f64 2 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))

Compiler

Compiled 1051 to 976 computations (7.1% saved)

simplify119.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5067	1402

prune182.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	6	99

Error

0.8b

Counts

99 → 6

Compiler

Compiled 1800 to 863 computations (52.1% saved)

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(sqrt.f64 (*.f64 2 (-.f64 im re)))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64_480`
2×	`sqrt-div_binary64_436` `associate-*r/_binary64_361` `sqrt-pow1_binary64_437`
1×	`*-un-lft-identity_binary64_419` `pow-prod-down_binary64_490` `add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `pow1/2_binary64_499` `add-sqr-sqrt_binary64_441` `flip3--_binary64_423` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `flip--_binary64_394` `sqrt-prod_binary64_435`

Counts

1 → 13

Calls

1 calls:

8.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

series89.0ms (0.9%)

Counts

1 → 7

Calls

1 calls:

88.0ms

(sqrt.f64 (*.f64 2 (-.f64 im re)))

Compiler

Compiled 198 to 189 computations (4.5% saved)

simplify159.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 0 (146.0ms)

Iter	Nodes	Cost
0	4981	216
1	4981	216

prune37.0ms (0.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	18	2	20
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	19	7	26

Error

0.8b

Counts

26 → 7

Compiler

Compiled 316 to 240 computations (24.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 im re)))) (cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
0.5b	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
0.5b	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
0.5b	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))

rewrite86.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`cbrt-prod_binary64_450`
23×	`add-sqr-sqrt_binary64_441`
20×	`associate-*r/_binary64_361`
18×	`sqrt-div_binary64_436` `cbrt-div_binary64_451`
15×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
11×	`pow1_binary64_480`
9×	`pow1/3_binary64_501` `flip3--_binary64_423` `flip--_binary64_394`
7×	`associate-r_binary64_359` `swap-sqr_binary64_386` `associate-l_binary64_360` `sqrt-prod_binary64_435`
6×	`add-exp-log_binary64_457`
4×	`add-log-exp_binary64_458` `unswap-sqr_binary64_387` `frac-times_binary64_429` `add-cbrt-cube_binary64_455`
2×	`associate-*l/_binary64_362` `pow-prod-down_binary64_490` `pow-sqr_binary64_392` `pow-prod-up_binary64_489`
1×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `pow-plus_binary64_482` `*-commutative_binary64_350` `pow2_binary64_500`

Counts

4 → 93

Calls

4 calls:

18.0ms	(.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 im re)))) (cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
13.0ms	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
10.0ms	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
10.0ms	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))

series700.0ms (7%)

Counts

4 → 25

Calls

4 calls:

189.0ms	(.f64 (cbrt.f64 (sqrt.f64 (.f64 2 (-.f64 im re)))) (cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re)))))
174.0ms	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
170.0ms	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))
166.0ms	(cbrt.f64 (sqrt.f64 (*.f64 2 (-.f64 im re))))

Compiler

Compiled 1741 to 1520 computations (12.7% saved)

simplify176.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (131.0ms)

Iter	Nodes	Cost
0	4910	2093
1	4910	2093

prune301.0ms (3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	117	8	125

Error

0.8b

Counts

125 → 8

Compiler

Compiled 3483 to 2276 computations (34.7% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1 im))
0.2b	(.f64 1/2 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2)))))
0.3b	(.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2))
0.5b	(.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 re (*.f64 (sqrt.f64 (/.f64 1 im)) -1/2))))

rewrite75.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_441`
18×	`pow1_binary64_480`
17×	`*-un-lft-identity_binary64_419` `sqrt-prod_binary64_435`
16×	`add-cube-cbrt_binary64_454` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
12×	`associate-l_binary64_360`
11×	`times-frac_binary64_425`
7×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-*r/_binary64_361`
5×	`distribute-rgt-in_binary64_369` `associate-r_binary64_359` `distribute-lft-in_binary64_368`
4×	`add-log-exp_binary64_458`
3×	`*-commutative_binary64_350` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`
2×	`flip3-+_binary64_422` `sqrt-div_binary64_436` `unswap-sqr_binary64_387` `flip-+_binary64_393`
1×	`associate-*l/_binary64_362` `inv-pow_binary64_504` `pow1/2_binary64_499` `div-inv_binary64_416` `pow-flip_binary64_493`

Counts

4 → 97

Calls

4 calls:

18.0ms	(.f64 1/2 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2)))))
16.0ms	(.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 re (*.f64 (sqrt.f64 (/.f64 1 im)) -1/2))))
16.0ms	(.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2))
6.0ms	(sqrt.f64 (/.f64 1 im))

series759.0ms (7.6%)

Counts

4 → 27

Calls

4 calls:

309.0ms	(.f64 1/2 (.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2)))))
272.0ms	(.f64 (sqrt.f64 2) (+.f64 (sqrt.f64 im) (.f64 re (*.f64 (sqrt.f64 (/.f64 1 im)) -1/2))))
148.0ms	(.f64 re (.f64 (sqrt.f64 (/.f64 1 im)) -1/2))
29.0ms	(sqrt.f64 (/.f64 1 im))

Compiler

Compiled 828 to 779 computations (5.9% saved)

simplify148.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4941	2204
1	4941	2204

prune253.0ms (2.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	123	9	132

Error

0.8b

Counts

132 → 9

Compiler

Compiled 2471 to 1873 computations (24.2% saved)

regimes1.5s (15.4%)

Accuracy

Total 14.6b remaining (96.5%)

Threshold costs 0b (0%)

Compiler

Compiled 5960 to 4754 computations (20.2% saved)

bsearch315.0ms (3.1%)

Steps

Iters	Range		Point
8	5.623647634104349e+83	1.8240241623419972e+86	8.779002270216535e+85
8	6.752240335602407e+35	1.9363184661672255e+40	6.943865471115237e+35
8	0.08678436482584874	1333.913386118954	608.4785949488302
8	8.793283140772164e-80	2.341372171497423e-75	8.108748112900304e-79
7	-1.5899387838377837e-125	-1.6452302653905082e-127	-1.6689021186793083e-127
9	-2.209567462296527e-76	-2.686296341015629e-81	-1.297043385487507e-77
5	-1.275857687576327e+22	-4.377846363716704e+21	-4.4330676814994195e+21

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	91	185
1	91	185

end0.0ms (0%)

sample3.5s (35%)

Algorithm

1×

intervals

Results

572.0ms	6088×	body	128	valid
309.0ms	664×	body	2048	valid
303.0ms	506×	body	4096	valid
199.0ms	8000×	pre	128	true
146.0ms	400×	body	1024	valid
67.0ms	237×	body	512	valid
19.0ms	105×	body	256	valid

Compiler

Compiled 882 to 700 computations (20.6% saved)

Details

analyze753.0ms (7.5%)

sample57.0ms (0.6%)

simplify40.0ms (0.4%)

prune5.0ms (0%)

localize18.0ms (0.2%)

rewrite72.0ms (0.7%)

series561.0ms (5.6%)

simplify119.0ms (1.2%)

prune182.0ms (1.8%)

localize10.0ms (0.1%)

rewrite11.0ms (0.1%)

series89.0ms (0.9%)

simplify159.0ms (1.6%)

prune37.0ms (0.4%)

localize18.0ms (0.2%)

rewrite86.0ms (0.9%)

series700.0ms (7%)

simplify176.0ms (1.8%)

prune301.0ms (3%)

localize24.0ms (0.2%)

rewrite75.0ms (0.7%)

series759.0ms (7.6%)

simplify148.0ms (1.5%)

prune253.0ms (2.5%)

regimes1.5s (15.4%)

bsearch315.0ms (3.1%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample3.5s (35%)

Profiling