Details

analyze1.8s (14%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
9.4%	90.4%	0.2%	6
17.2%	82.7%	0.2%	7
19.5%	80.3%	0.2%	8
30.8%	69%	0.2%	9
35.5%	64.3%	0.2%	10
42.4%	57.4%	0.2%	11
47.1%	52.7%	0.2%	12
48.9%	50.8%	0.3%	13
50%	49.7%	0.4%	14

Compiler

Compiled 38 to 20 computations (47.4% saved)

sample153.0ms (1.2%)

Algorithm

1×

intervals

Results

45.0ms	59×	body	1024	invalid
41.0ms	240×	body	128	valid
17.0ms	31×	body	512	invalid
12.0ms	8×	body	1024	valid
4.0ms	14×	body	256	invalid
4.0ms	8×	body	512	valid
2.0ms	8×	body	128	invalid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify184.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune8.0ms (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

32.9b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize50.0ms (0.4%)

Local error

Found 4 expressions with local error:

2.3b	(*.f64 (atan2.f64 x.im x.re) y.im)
29.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
29.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
30.9b	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

rewrite131.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

32.9b

Rules

12×	`add-sqr-sqrt_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
3×	`associate-l_binary64` `associate-r_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`
1×	`cos-sum_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 56

Calls

4 calls:

15.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
8.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
8.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
7.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2594 to 353 computations (86.4% saved)

series783.0ms (6%)

Error

20.9b

Counts

4 → 50

Calls

4 calls:

327.0ms	(cos.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
162.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
136.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
84.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 5269 to 2666 computations (49.4% saved)

simplify102.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5075	2052

prune201.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	99	7	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	7	107

Error

20.9b

Counts

107 → 7

Compiler

Compiled 4544 to 1237 computations (72.8% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(*.f64 y.re (atan2.f64 x.im x.re))
2.3b	(*.f64 (atan2.f64 x.im x.re) y.im)
16.4b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
29.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite94.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

20.9b

Rules

14×	`add-sqr-sqrt_binary64`
9×	`pow1_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-l_binary64` `associate-r_binary64`
4×	`add-log-exp_binary64`
3×	`sqrt-prod_binary64`
2×	`sqrt-div_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`

Counts

4 → 58

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
4.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
2.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 1851 to 341 computations (81.6% saved)

series517.0ms (4%)

Error

4.1b

Counts

4 → 45

Calls

4 calls:

163.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
154.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
78.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
75.0ms	(*.f64 y.re (atan2.f64 x.im x.re))

Compiler

Compiled 3270 to 1723 computations (47.3% saved)

simplify100.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5145	1447

prune142.0ms (1.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	100	10	110

Error

4.1b

Counts

110 → 10

Compiler

Compiled 3209 to 837 computations (73.9% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im)))
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
2.3b	(*.f64 (atan2.f64 x.im x.re) y.im)
29.0b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite111.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

Rules

15×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
10×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
9×	`associate-l_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`add-log-exp_binary64`
6×	`associate-r_binary64`
3×	`sqrt-prod_binary64` `log-pow_binary64` `exp-prod_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64` `exp-sum_binary64` `rem-exp-log_binary64`
1×	`flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64` `exp-diff_binary64` `sub-neg_binary64` `cancel-sign-sub-inv_binary64` `diff-log_binary64`

Counts

4 → 69

Calls

4 calls:

5.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
5.0ms	(exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
4.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 1980 to 478 computations (75.9% saved)

series976.0ms (7.5%)

Error

4.1b

Counts

4 → 57

Calls

4 calls:

367.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
273.0ms	(exp.f64 (-.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))) y.re) (.f64 (atan2.f64 x.im x.re) y.im)))
183.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
83.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 3589 to 2597 computations (27.6% saved)

simplify94.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4967	2611
1	4967	2611

prune233.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	127	9	136

Error

4.1b

Counts

136 → 9

Compiler

Compiled 3229 to 1566 computations (51.5% saved)

localize20.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (pow.f64 x.re y.re) (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re))))
2.3b	(*.f64 y.im (atan2.f64 x.im x.re))

rewrite105.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

Rules

22×	`add-sqr-sqrt_binary64`
21×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
12×	`unpow-prod-down_binary64`
7×	`associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64` `sqr-pow_binary64`
3×	`associate-l_binary64` `associate-r_binary64` `div-exp_binary64` `associate-/r*_binary64`
2×	`add-log-exp_binary64`
1×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

2 → 63

Calls

2 calls:

11.0ms	(/.f64 (pow.f64 x.re y.re) (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re))))
8.0ms	(*.f64 y.im (atan2.f64 x.im x.re))

Compiler

Compiled 1369 to 388 computations (71.7% saved)

series564.0ms (4.3%)

Error

4.1b

Counts

2 → 25

Calls

2 calls:

464.0ms	(/.f64 (pow.f64 x.re y.re) (exp.f64 (*.f64 y.im (atan2.f64 x.im x.re))))
84.0ms	(*.f64 y.im (atan2.f64 x.im x.re))

Compiler

Compiled 1054 to 685 computations (35% saved)

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5080	2299

prune76.0ms (0.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	87	10	97

Error

4.1b

Counts

97 → 10

Compiler

Compiled 1651 to 429 computations (74% saved)

regimes878.0ms (6.7%)

Accuracy

Total 2.5b remaining (43.4%)

Threshold costs 0b (0%)

Compiler

Compiled 5892 to 3865 computations (34.4% saved)

bsearch226.0ms (1.7%)

Steps

Iters	Range		Point
10	0.09278592785433953	2.213554645757965e+16	44576286.08340377
5	-0.9332362811806418	-0.2747176610643982	-0.28162235605699076

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	65	84
1	65	84

end0.0ms (0%)

sample5.4s (41.1%)

Algorithm

1×

intervals

Results

1.5s	2418×	body	1024	invalid
1.1s	7615×	body	128	valid
432.0ms	1000×	body	512	invalid
120.0ms	442×	body	256	invalid
117.0ms	183×	body	1024	valid
76.0ms	519×	body	128	invalid
58.0ms	136×	body	512	valid
42.0ms	45×	body	2048	invalid
15.0ms	55×	body	256	valid
9.0ms	11×	body	2048	valid

Compiler

Compiled 1243 to 809 computations (34.9% saved)

Details

analyze1.8s (14%)

sample153.0ms (1.2%)

simplify184.0ms (1.4%)

prune8.0ms (0.1%)

localize50.0ms (0.4%)

rewrite131.0ms (1%)

series783.0ms (6%)

simplify102.0ms (0.8%)

prune201.0ms (1.5%)

localize27.0ms (0.2%)

rewrite94.0ms (0.7%)

series517.0ms (4%)

simplify100.0ms (0.8%)

prune142.0ms (1.1%)

localize19.0ms (0.1%)

rewrite111.0ms (0.9%)

series976.0ms (7.5%)

simplify94.0ms (0.7%)

prune233.0ms (1.8%)

localize20.0ms (0.2%)

rewrite105.0ms (0.8%)

series564.0ms (4.3%)

simplify68.0ms (0.5%)

prune76.0ms (0.6%)

regimes878.0ms (6.7%)

bsearch226.0ms (1.7%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.4s (41.1%)

Profiling