Details

analyze1.4s (12.9%)

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
49%	50.8%	0.2%	13
50.1%	49.7%	0.2%	14

Compiler

Compiled 38 to 20 computations (47.4% saved)

sample140.0ms (1.3%)

Algorithm

1×

intervals

Results

53.0ms	98×	body	1024	invalid
30.0ms	248×	body	128	valid
15.0ms	41×	body	512	invalid
10.0ms	11×	body	2048	invalid
6.0ms	16×	body	128	invalid
3.0ms	12×	body	256	invalid
1.0ms	3×	body	512	valid
1.0ms	4×	body	256	valid
1.0ms	1×	body	1024	valid

Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify160.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4944	72
1	4944	72

prune15.0ms (0.1%)

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

30.0b

Counts

2 → 2

Compiler

Compiled 109 to 57 computations (47.7% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
26.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
26.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.1b	(sin.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)))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

8.0ms	(sin.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)

series671.0ms (6%)

Counts

4 → 57

Calls

4 calls:

348.0ms	(sin.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)))
142.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
109.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
72.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 3896 to 2563 computations (34.2% saved)

simplify78.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5072	2329

prune174.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	107	6	113
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	108	7	115

Error

17.8b

Counts

115 → 7

Compiler

Compiled 4880 to 1353 computations (72.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(*.f64 (atan2.f64 x.im x.re) y.re)
1.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
17.4b	(sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
26.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_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)
3.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)
1.0ms	(sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re))

series397.0ms (3.5%)

Counts

4 → 48

Calls

4 calls:

137.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
125.0ms	(sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
68.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)
67.0ms	(*.f64 (atan2.f64 x.im x.re) y.re)

Compiler

Compiled 2230 to 1566 computations (29.8% saved)

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4942	1603
1	4942	1603

prune118.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	104	9	113

Error

7.9b

Counts

113 → 9

Compiler

Compiled 3344 to 864 computations (74.2% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.6b	(*.f64 (atan2.f64 x.im x.re) y.im)
17.4b	(sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
25.0b	(cbrt.f64 (pow.f64 (sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re)) 3))
26.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`cbrt-prod_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r_binary64` `associate-l_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `rem-cbrt-cube_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `flip-+_binary64` `unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

4 → 61

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)
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re)) 3))
2.0ms	(sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re))

series490.0ms (4.4%)

Counts

4 → 51

Calls

4 calls:

145.0ms	(sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
137.0ms	(cbrt.f64 (pow.f64 (sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re)) 3))
134.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
74.0ms	(*.f64 (atan2.f64 x.im x.re) y.im)

Compiler

Compiled 2534 to 1830 computations (27.8% saved)

simplify61.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5079	1983

prune139.0ms (1.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	110	11	121

Error

7.9b

Counts

121 → 11

Compiler

Compiled 3931 to 1239 computations (68.5% saved)

localize35.0ms (0.3%)

Local error

Found 4 expressions with local error:

26.6b	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))
33.1b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
33.1b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
33.1b	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`sin-sum_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 39

Calls

4 calls:

7.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
7.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
6.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) 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)))

series1.2s (11%)

Counts

4 → 66

Calls

4 calls:

354.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
354.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
344.0ms	(sin.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (.f64 (atan2.f64 x.im x.re) y.re)))
179.0ms	(sqrt.f64 (+.f64 (.f64 x.re x.re) (.f64 x.im x.im)))

Compiler

Compiled 9504 to 6261 computations (34.1% saved)

simplify80.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5169	3360

prune358.0ms (3.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	104	12	116

Error

7.9b

Counts

116 → 12

Compiler

Compiled 8618 to 4285 computations (50.3% saved)

regimes687.0ms (6.1%)

Accuracy

Total 9.7b remaining (47.5%)

Threshold costs 0b (0%)

Compiler

Compiled 7137 to 4795 computations (32.8% saved)

bsearch163.0ms (1.4%)

Steps

Iters	Range		Point
9	5.777036210315481e+66	1.2363277129503212e+73	1.3647098970719681e+69
7	-5.029776341151594e-10	-3.141024685448495e-12	-4.508803433959976e-10

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	87	162
1	87	162

end0.0ms (0%)

sample4.6s (40.5%)

Algorithm

1×

intervals

Results

1.3s	2484×	body	1024	invalid
871.0ms	7587×	body	128	valid
325.0ms	898×	body	512	invalid
165.0ms	194×	body	2048	invalid
91.0ms	173×	body	1024	valid
83.0ms	348×	body	256	invalid
57.0ms	484×	body	128	invalid
47.0ms	130×	body	512	valid
23.0ms	96×	body	256	valid
11.0ms	14×	body	2048	valid

Compiler

Compiled 1531 to 1006 computations (34.3% saved)

Details

analyze1.4s (12.9%)

sample140.0ms (1.3%)

simplify160.0ms (1.4%)

prune15.0ms (0.1%)

localize22.0ms (0.2%)

rewrite27.0ms (0.2%)

series671.0ms (6%)

simplify78.0ms (0.7%)

prune174.0ms (1.6%)

localize18.0ms (0.2%)

rewrite18.0ms (0.2%)

series397.0ms (3.5%)

simplify66.0ms (0.6%)

prune118.0ms (1.1%)

localize21.0ms (0.2%)

rewrite19.0ms (0.2%)

series490.0ms (4.4%)

simplify61.0ms (0.5%)

prune139.0ms (1.2%)

localize35.0ms (0.3%)

rewrite31.0ms (0.3%)

series1.2s (11%)

simplify80.0ms (0.7%)

prune358.0ms (3.2%)

regimes687.0ms (6.1%)

bsearch163.0ms (1.4%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.6s (40.5%)

Profiling