Details

analyze503.0ms (9.3%)

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)

sample53.0ms (1%)

Algorithm

1×

intervals

Results

19.0ms	188×	body	128	valid
9.0ms	22×	body	2048	valid
8.0ms	17×	body	4096	valid
4.0ms	12×	body	1024	valid
3.0ms	13×	body	512	valid
1.0ms	4×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify108.0ms (2%)

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

Error

43.9b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.1b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
32.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64_1101`
4×	`add-sqr-sqrt_binary64_1123` `add-log-exp_binary64_1140`
3×	`pow1_binary64_1162` `sqrt-prod_binary64_1117` `add-cube-cbrt_binary64_1136`
2×	`add-exp-log_binary64_1139` `flip3-+_binary64_1104` `add-cbrt-cube_binary64_1137` `sqrt-div_binary64_1118` `flip-+_binary64_1075`
1×	`rem-sqrt-square_binary64_1114` `distribute-lft-out_binary64_1052` `sum-log_binary64_1192` `sqrt-pow1_binary64_1119` `+-commutative_binary64_1031` `pow1/2_binary64_1181`

Counts

2 → 27

Calls

2 calls:

10.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series81.0ms (1.5%)

Counts

2 → 6

Calls

2 calls:

56.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
25.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify106.0ms (2%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4893	497
1	4893	497

prune72.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	25	8	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	8	34

Error

16.4b

Counts

34 → 8

Compiler

Compiled 766 to 369 computations (51.8% saved)

localize11.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64_1162`
2×	`sqrt-pow1_binary64_1119` `associate-*r/_binary64_1043` `sqrt-div_binary64_1118`
1×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `flip3-+_binary64_1104` `sqrt-prod_binary64_1117` `add-cube-cbrt_binary64_1136` `add-cbrt-cube_binary64_1137` `pow-prod-down_binary64_1172` `flip-+_binary64_1075` `pow1/2_binary64_1181`

Counts

1 → 13

Calls

1 calls:

9.0ms

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

series48.0ms (0.9%)

Counts

1 → 3

Calls

1 calls:

48.0ms

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

simplify64.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4969	248
1	4969	248

prune27.0ms (0.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	15	9	24

Error

16.4b

Counts

24 → 9

Compiler

Compiled 372 to 257 computations (30.9% saved)

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 im re))
0.3b	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 im re)))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_1123`
15×	`sqrt-prod_binary64_1117`
11×	`*-un-lft-identity_binary64_1101`
7×	`pow1_binary64_1162` `add-cube-cbrt_binary64_1136` `associate-r_binary64_1041`
6×	`associate-l_binary64_1042`
4×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `sqrt-div_binary64_1118` `unswap-sqr_binary64_1069`
3×	`sqrt-pow1_binary64_1119` `pow-prod-down_binary64_1172` `pow1/2_binary64_1181`
2×	`add-log-exp_binary64_1140` `distribute-lft-out_binary64_1052` `flip3-+_binary64_1104` `associate-*r/_binary64_1043` `flip-+_binary64_1075`
1×	`*-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `sqrt-unprod_binary64_1121`

Counts

2 → 49

Calls

2 calls:

18.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 im re)))
6.0ms	(sqrt.f64 (+.f64 im re))

series83.0ms (1.5%)

Counts

2 → 6

Calls

2 calls:

57.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 im re)))
26.0ms	(sqrt.f64 (+.f64 im re))

simplify82.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5154	803

prune67.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	55	9	64

Error

16.4b

Counts

64 → 9

Compiler

Compiled 993 to 606 computations (39% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 im re)))
0.3b	(cbrt.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 im re))))
0.3b	(cbrt.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 im re))))
0.3b	(cbrt.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 im re))))

rewrite47.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_1123`
11×	`sqrt-prod_binary64_1117`
10×	`*-un-lft-identity_binary64_1101`
8×	`pow1_binary64_1162` `associate-*r/_binary64_1043` `add-cube-cbrt_binary64_1136` `sqrt-div_binary64_1118`
7×	`associate-r_binary64_1041`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `associate-l_binary64_1042` `cbrt-div_binary64_1133`
4×	`add-log-exp_binary64_1140` `flip3-+_binary64_1104` `flip-+_binary64_1075` `unswap-sqr_binary64_1069`
3×	`pow1/3_binary64_1183` `pow-prod-down_binary64_1172` `cbrt-prod_binary64_1132`
2×	`sqrt-pow1_binary64_1119` `pow1/2_binary64_1181`
1×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `distribute-lft-out_binary64_1052` `sqrt-unprod_binary64_1121`

Counts

4 → 66

Calls

4 calls:

12.0ms	(cbrt.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 im re))))
9.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 im re)))
9.0ms	(cbrt.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 im re))))
9.0ms	(cbrt.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 im re))))

series773.0ms (14.3%)

Counts

4 → 12

Calls

4 calls:

277.0ms	(cbrt.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 im re))))
224.0ms	(cbrt.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 im re))))
207.0ms	(cbrt.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 im re))))
64.0ms	(*.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 im re)))

simplify91.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5024	1480

prune167.0ms (3.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	78	9	87

Error

16.4b

Counts

87 → 9

Compiler

Compiled 2753 to 1656 computations (39.8% saved)

regimes824.0ms (15.3%)

Accuracy

Total 11.2b remaining (39.3%)

Threshold costs 0b (0%)

Compiler

Compiled 3277 to 2301 computations (29.8% saved)

bsearch96.0ms (1.8%)

Steps

Iters	Range		Point
8	7.320783634518993e-33	4.3312833680972396e-30	4.274677831505091e-30
7	5.88283336347013e-180	3.019304358802458e-178	1.568426616406061e-179
8	-2.1161687990177889e-168	-4.525842011655338e-171	-4.885823738028584e-171

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	57	94
1	57	94

end0.0ms (0%)

sample2.0s (36.8%)

Algorithm

1×

intervals

Results

434.0ms	6065×	body	128	valid
256.0ms	566×	body	4096	valid
226.0ms	630×	body	2048	valid
107.0ms	396×	body	1024	valid
49.0ms	230×	body	512	valid
15.0ms	113×	body	256	valid

Compiler

Compiled 506 to 347 computations (31.4% saved)

Details

analyze503.0ms (9.3%)

sample53.0ms (1%)

simplify108.0ms (2%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

rewrite18.0ms (0.3%)

series81.0ms (1.5%)

simplify106.0ms (2%)

prune72.0ms (1.3%)

localize11.0ms (0.2%)

rewrite10.0ms (0.2%)

series48.0ms (0.9%)

simplify64.0ms (1.2%)

prune27.0ms (0.5%)

localize13.0ms (0.2%)

rewrite30.0ms (0.6%)

series83.0ms (1.5%)

simplify82.0ms (1.5%)

prune67.0ms (1.2%)

localize16.0ms (0.3%)

rewrite47.0ms (0.9%)

series773.0ms (14.3%)

simplify91.0ms (1.7%)

prune167.0ms (3.1%)

regimes824.0ms (15.3%)

bsearch96.0ms (1.8%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.0s (36.8%)

Profiling