Details

analyze562.0ms (13.1%)

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
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample21.0ms (0.5%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify215.0ms (5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (119.0ms)

Iter	Nodes	Cost
0	5232	30

prune2.0ms (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

26.8b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.6b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
26.3b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
9×	`times-frac_binary64_1107`
4×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
3×	`associate-/l_binary64_1046` `associate-/r_binary64_1045`
2×	`pow1_binary64_1162` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047`
1×	`diff-log_binary64_1193` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `clear-num_binary64_1100` `flip3-+_binary64_1104` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075` `cancel-sign-sub-inv_binary64_1067` `div-sub_binary64_1106`

Counts

2 → 44

Calls

2 calls:

9.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series147.0ms (3.4%)

Counts

2 → 6

Calls

2 calls:

107.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
40.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

simplify70.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	6255	1595

prune79.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	42	8	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	8	51

Error

25.9b

Counts

51 → 8

Compiler

Compiled 1366 to 564 computations (58.7% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
17.7b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
28.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.8b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite38.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_1101`
28×	`sqrt-prod_binary64_1117`
25×	`add-sqr-sqrt_binary64_1123`
24×	`times-frac_binary64_1107`
23×	`add-cube-cbrt_binary64_1136`
10×	`unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052`
8×	`associate-/r*_binary64_1045`
6×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137` `sqrt-div_binary64_1118`
3×	`flip3-+_binary64_1104` `associate-/l*_binary64_1046` `flip-+_binary64_1075`
2×	`rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047` `pow1/2_binary64_1181`
1×	`diff-log_binary64_1193` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `clear-num_binary64_1100` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cancel-sign-sub-inv_binary64_1067` `div-sub_binary64_1106`

Counts

4 → 96

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series213.0ms (5%)

Counts

4 → 12

Calls

4 calls:

124.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
39.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
25.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
25.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify92.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5542	3247

prune162.0ms (3.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	106	10	116

Error

22.8b

Counts

116 → 10

Compiler

Compiled 3704 to 1563 computations (57.8% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
17.8b	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
28.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.8b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite49.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64_1101`
36×	`add-sqr-sqrt_binary64_1123`
30×	`associate-r_binary64_1041`
28×	`times-frac_binary64_1107`
25×	`sqrt-prod_binary64_1117`
22×	`add-cube-cbrt_binary64_1136`
13×	`add-exp-log_binary64_1139`
9×	`add-cbrt-cube_binary64_1137`
8×	`unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052` `pow1_binary64_1162`
6×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118`
5×	`unswap-sqr_binary64_1069`
4×	`prod-exp_binary64_1150`
3×	`flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `flip-+_binary64_1075` `associate-l_binary64_1042`
2×	`rem-sqrt-square_binary64_1114` `cbrt-unprod_binary64_1134` `frac-times_binary64_1111` `sqrt-pow1_binary64_1119` `associate-/r/_binary64_1047` `div-exp_binary64_1152` `associate-*l/_binary64_1044` `pow1/2_binary64_1181`
1×	`diff-log_binary64_1193` `-commutative_binary64_1032` `1-exp_binary64_1145` `sub-neg_binary64_1094` `associate-r/_binary64_1043` `div-inv_binary64_1098` `rec-exp_binary64_1151` `pow-prod-down_binary64_1172` `cbrt-undiv_binary64_1135` `cancel-sign-sub-inv_binary64_1067` `un-div-inv_binary64_1099`

Counts

4 → 103

Calls

4 calls:

22.0ms	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series229.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
43.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
27.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
25.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify83.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5290	2922

prune162.0ms (3.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	115	10	125

Error

22.8b

Counts

125 → 10

Compiler

Compiled 3970 to 1861 computations (53.1% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.4b	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
0.6b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
25.9b	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))

rewrite41.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_1101`
32×	`times-frac_binary64_1107`
30×	`add-sqr-sqrt_binary64_1123`
23×	`add-cube-cbrt_binary64_1136`
21×	`associate-r_binary64_1041`
16×	`add-exp-log_binary64_1139`
14×	`unpow-prod-down_binary64_1180` `distribute-lft-out_binary64_1052`
10×	`add-cbrt-cube_binary64_1137`
6×	`pow1_binary64_1162`
5×	`add-log-exp_binary64_1140` `associate-/r*_binary64_1045`
4×	`prod-exp_binary64_1150` `associate-/r/_binary64_1047` `div-exp_binary64_1152`
3×	`flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l_binary64_1046` `associate-l*_binary64_1042` `unswap-sqr_binary64_1069`
2×	`1-exp_binary64_1145` `cbrt-unprod_binary64_1134` `frac-times_binary64_1111` `flip3-+_binary64_1104` `div-inv_binary64_1098` `rec-exp_binary64_1151` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075` `associate-*l/_binary64_1044`
1×	`inv-pow_binary64_1186` `diff-log_binary64_1193` `-commutative_binary64_1032` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `clear-num_binary64_1100` `associate-r/_binary64_1043` `pow-prod-down_binary64_1172` `cancel-sign-sub-inv_binary64_1067` `pow-flip_binary64_1175` `un-div-inv_binary64_1099`

Counts

3 → 101

Calls

3 calls:

19.0ms	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
9.0ms	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series163.0ms (3.8%)

Counts

3 → 9

Calls

3 calls:

97.0ms	(.f64 (-.f64 (.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
43.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
22.0ms	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify77.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5664	2638

prune113.0ms (2.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	110	10	120

Error

22.8b

Counts

120 → 10

Compiler

Compiled 2542 to 1358 computations (46.6% saved)

regimes344.0ms (8%)

Accuracy

Total 2.7b remaining (10.5%)

Threshold costs 0b (0%)

Compiler

Compiled 4224 to 3097 computations (26.7% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	105
1	64	105

end0.0ms (0%)

sample1.3s (31.4%)

Algorithm

1×

intervals

Results

339.0ms	8000×	body	128	valid
18.0ms	443×	body	128	invalid

Compiler

Compiled 898 to 642 computations (28.5% saved)

Details

analyze562.0ms (13.1%)

sample21.0ms (0.5%)

simplify215.0ms (5%)

prune2.0ms (0.1%)

localize10.0ms (0.2%)

rewrite16.0ms (0.4%)

series147.0ms (3.4%)

simplify70.0ms (1.6%)

prune79.0ms (1.8%)

localize17.0ms (0.4%)

rewrite38.0ms (0.9%)

series213.0ms (5%)

simplify92.0ms (2.2%)

prune162.0ms (3.8%)

localize22.0ms (0.5%)

rewrite49.0ms (1.2%)

series229.0ms (5.3%)

simplify83.0ms (1.9%)

prune162.0ms (3.8%)

localize11.0ms (0.3%)

rewrite41.0ms (1%)

series163.0ms (3.8%)

simplify77.0ms (1.8%)

prune113.0ms (2.6%)

regimes344.0ms (8%)

bsearch2.0ms (0.1%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.3s (31.4%)

Profiling