Details

analyze1.9s (15.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5006	504
0	4	4
1	4	4

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)

sample144.0ms (1.2%)

Algorithm

1×

intervals

Results

51.0ms	85×	body	1024	invalid
34.0ms	238×	body	128	valid
14.0ms	33×	body	512	invalid
5.0ms	15×	body	256	invalid
5.0ms	7×	body	1024	valid
2.0ms	16×	body	128	invalid
2.0ms	3×	body	2048	invalid
2.0ms	4×	body	512	valid
1.0ms	6×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune14.0ms (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

36.8b

Counts

2 → 1

Compiler

Compiled 73 to 38 computations (47.9% saved)

localize41.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
32.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
32.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.2b	(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)))

rewrite123.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

36.7b

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:

8.0ms	(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)))
4.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.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 2594 to 353 computations (86.4% saved)

series743.0ms (6%)

Error

22.1b

Counts

4 → 51

Calls

4 calls:

296.0ms	(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)))
168.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
100.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
82.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 5292 to 2678 computations (49.4% saved)

simplify90.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5151	2028

prune183.0ms (1.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	102	5	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	5	108

Error

22.1b

Counts

108 → 5

Compiler

Compiled 4452 to 1158 computations (74% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
1.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
19.3b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
32.3b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite93.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

22.1b

Rules

14×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
9×	`add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-l*_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-r_binary64`
4×	`add-log-exp_binary64`
3×	`sqrt-prod_binary64` `log-pow_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`
1×	`flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64`

Counts

4 → 61

Calls

4 calls:

5.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
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)
1.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 1998 to 384 computations (80.8% saved)

series899.0ms (7.2%)

Error

4.4b

Counts

4 → 54

Calls

4 calls:

399.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 x.re x.re) (*.f64 x.im x.im)))) y.re)
172.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
165.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
95.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 3976 to 2290 computations (42.4% saved)

simplify80.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5039	2019

prune166.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	112	8	120

Error

4.4b

Counts

120 → 8

Compiler

Compiled 3485 to 1166 computations (66.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (log.f64 (neg.f64 x.im)) y.re)
0.2b	(*.f64 y.re (atan2.f64 x.im x.re))
1.9b	(*.f64 (atan2.f64 x.im x.re) y.im)
19.3b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

rewrite100.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

4.4b

Rules

16×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-l*_binary64`
9×	`associate-r_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`log-pow_binary64`

Counts

4 → 62

Calls

4 calls:

8.0ms	(*.f64 (log.f64 (neg.f64 x.im)) y.re)
7.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
7.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
3.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 1541 to 323 computations (79% saved)

series564.0ms (4.5%)

Error

4.4b

Counts

4 → 34

Calls

4 calls:

223.0ms	(*.f64 (log.f64 (neg.f64 x.im)) y.re)
146.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
79.0ms	(*.f64 y.re (atan2.f64 x.im x.re))
76.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 1969 to 1034 computations (47.5% saved)

simplify90.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4883	1176
1	4883	1176

prune104.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	96	8	104

Error

4.4b

Counts

104 → 8

Compiler

Compiled 2320 to 440 computations (81% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.1b	(cbrt.f64 (atan2.f64 x.im x.re))
4.1b	(cbrt.f64 (atan2.f64 x.im x.re))
4.1b	(cbrt.f64 (atan2.f64 x.im x.re))
19.3b	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

rewrite77.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

4.4b

Rules

9×	`cbrt-prod_binary64`
7×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
4×	`pow1_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64`

Counts

4 → 40

Calls

4 calls:

2.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))
2.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
2.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
2.0ms	(cbrt.f64 (atan2.f64 x.im x.re))

Compiler

Compiled 1435 to 247 computations (82.8% saved)

series767.0ms (6.2%)

Error

4.4b

Counts

4 → 28

Calls

4 calls:

216.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
201.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
176.0ms	(cbrt.f64 (atan2.f64 x.im x.re))
142.0ms	(cos.f64 (*.f64 y.re (atan2.f64 x.im x.re)))

Compiler

Compiled 2567 to 1183 computations (53.9% saved)

simplify89.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4910	768
1	4910	768

prune73.0ms (0.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	68	8	76

Error

4.4b

Counts

76 → 8

Compiler

Compiled 2220 to 253 computations (88.6% saved)

regimes830.0ms (6.7%)

Accuracy

Total 6.1b remaining (64.3%)

Threshold costs 0b (0%)

Compiler

Compiled 5157 to 2910 computations (43.6% saved)

bsearch252.0ms (2%)

Steps

Iters	Range		Point
10	-2.0900747234974714e-303	2.790433275347491e-300	4.3354624121682e-310
8	-2.2018441581627254e-65	-9.670250962732699e-70	-1.0023614876036504e-65
6	-2493285051684366.5	-319741171256093.3	-326275111805596.6

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	184	239
1	184	239

end0.0ms (0%)

sample4.8s (38.8%)

Algorithm

1×

intervals

Results

1.4s	2387×	body	1024	invalid
996.0ms	7580×	body	128	valid
400.0ms	979×	body	512	invalid
119.0ms	415×	body	256	invalid
115.0ms	189×	body	1024	valid
75.0ms	556×	body	128	invalid
58.0ms	138×	body	512	valid
31.0ms	34×	body	2048	invalid
21.0ms	81×	body	256	valid
11.0ms	12×	body	2048	valid

Compiler

Compiled 1174 to 640 computations (45.5% saved)

Details

analyze1.9s (15.6%)

sample144.0ms (1.2%)

simplify83.0ms (0.7%)

prune14.0ms (0.1%)

localize41.0ms (0.3%)

rewrite123.0ms (1%)

series743.0ms (6%)

simplify90.0ms (0.7%)

prune183.0ms (1.5%)

localize29.0ms (0.2%)

rewrite93.0ms (0.7%)

series899.0ms (7.2%)

simplify80.0ms (0.6%)

prune166.0ms (1.3%)

localize16.0ms (0.1%)

rewrite100.0ms (0.8%)

series564.0ms (4.5%)

simplify90.0ms (0.7%)

prune104.0ms (0.8%)

localize18.0ms (0.1%)

rewrite77.0ms (0.6%)

series767.0ms (6.2%)

simplify89.0ms (0.7%)

prune73.0ms (0.6%)

regimes830.0ms (6.7%)

bsearch252.0ms (2%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample4.8s (38.8%)

Profiling