Details

analyze515.0ms (7.3%)

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)

sample20.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	18×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify101.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	30
1	18	30

prune2.0ms (0%)

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

26.7b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.4b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
26.2b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
9×	`times-frac_binary64_1448`
7×	`add-log-exp_binary64_1481`
5×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
4×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
3×	`associate-/r_binary64_1386` `associate-/l_binary64_1387` `pow1_binary64_1503`
2×	`sum-log_binary64_1533` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `+-commutative_binary64_1372`
1×	`cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `div-exp_binary64_1493`

Counts

3 → 53

Calls

3 calls:

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

series512.0ms (7.3%)

Counts

3 → 60

Calls

3 calls:

287.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
142.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
82.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

Compiler

Compiled 1290 to 1074 computations (16.7% saved)

simplify104.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	5051	2576

prune129.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	104	9	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	9	114

Error

2.5b

Counts

114 → 9

Compiler

Compiled 2285 to 854 computations (62.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
15.1b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
29.6b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
29.6b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite45.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_1442`
30×	`sqrt-prod_binary64_1458`
25×	`add-sqr-sqrt_binary64_1464`
24×	`times-frac_binary64_1448`
23×	`add-cube-cbrt_binary64_1477`
12×	`distribute-lft-out_binary64_1393` `unpow-prod-down_binary64_1521`
8×	`associate-/r*_binary64_1386`
6×	`add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `pow1_binary64_1503`
5×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
3×	`associate-/l*_binary64_1387`
2×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `pow1/2_binary64_1522`
1×	`cbrt-undiv_binary64_1476` `sum-log_binary64_1533` `div-inv_binary64_1439` `clear-num_binary64_1441` `+-commutative_binary64_1372` `frac-2neg_binary64_1453` `div-exp_binary64_1493`

Counts

4 → 96

Calls

4 calls:

13.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im 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)))
7.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series836.0ms (11.9%)

Counts

4 → 91

Calls

4 calls:

414.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
163.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
132.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
126.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 3708 to 3148 computations (15.1% saved)

simplify87.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4990	4766
1	4990	4766

prune315.0ms (4.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	187	9	196

Error

2.5b

Counts

196 → 9

Compiler

Compiled 6067 to 3645 computations (39.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.4b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.7b	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
25.7b	(.f64 (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))

rewrite53.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`*-un-lft-identity_binary64_1442`
32×	`times-frac_binary64_1448`
31×	`add-sqr-sqrt_binary64_1464`
24×	`add-cube-cbrt_binary64_1477`
21×	`associate-r_binary64_1382`
17×	`add-exp-log_binary64_1480`
16×	`distribute-lft-out_binary64_1393` `unpow-prod-down_binary64_1521`
11×	`add-cbrt-cube_binary64_1478`
8×	`add-log-exp_binary64_1481`
7×	`pow1_binary64_1503`
6×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
5×	`associate-/r*_binary64_1386`
4×	`associate-/r/_binary64_1388` `prod-exp_binary64_1491` `div-exp_binary64_1493`
3×	`associate-/l_binary64_1387` `associate-l*_binary64_1383` `unswap-sqr_binary64_1410`
2×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `sum-log_binary64_1533` `div-inv_binary64_1439` `1-exp_binary64_1486` `+-commutative_binary64_1372` `rec-exp_binary64_1492` `frac-times_binary64_1452` `associate-*l/_binary64_1385`
1×	`associate-r/_binary64_1384` `inv-pow_binary64_1527` `clear-num_binary64_1441` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `pow-flip_binary64_1516` `frac-2neg_binary64_1453` `un-div-inv_binary64_1440`

Counts

4 → 113

Calls

4 calls:

18.0ms	(.f64 (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
11.0ms	(+.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.re y.re) (.f64 x.im y.im))

series543.0ms (7.7%)

Counts

4 → 66

Calls

4 calls:

289.0ms	(.f64 (+.f64 (.f64 x.re y.re) (*.f64 x.im y.im)) (/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
142.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
79.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
33.0ms	(/.f64 1 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 1602 to 1434 computations (10.5% saved)

simplify92.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5161	3642

prune176.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	180	8	188

Error

2.5b

Counts

188 → 8

Compiler

Compiled 3743 to 1987 computations (46.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
25.7b	(.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))))
29.6b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
29.6b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite67.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`add-exp-log_binary64_1480`
33×	`prod-exp_binary64_1491`
22×	`add-cbrt-cube_binary64_1478`
16×	`div-exp_binary64_1493`
15×	`*-un-lft-identity_binary64_1442`
11×	`frac-times_binary64_1452` `pow1_binary64_1503`
10×	`add-sqr-sqrt_binary64_1464` `sqrt-prod_binary64_1458`
9×	`cbrt-unprod_binary64_1475`
8×	`1-exp_binary64_1486` `rec-exp_binary64_1492` `flip3-+_binary64_1445` `flip-+_binary64_1416`
7×	`associate-*r/_binary64_1384` `add-cube-cbrt_binary64_1477`
6×	`add-log-exp_binary64_1481`
5×	`associate-*l/_binary64_1385`
4×	`cbrt-undiv_binary64_1476` `sqrt-div_binary64_1459` `distribute-lft-out_binary64_1393` `unpow-prod-down_binary64_1521`
3×	`associate-l_binary64_1383` `pow-prod-down_binary64_1513` `un-div-inv_binary64_1440`
2×	`sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `pow1/2_binary64_1522`
1×	`associate-r_binary64_1382` `sum-log_binary64_1533` `+-commutative_binary64_1372` `*-commutative_binary64_1373` `unswap-sqr_binary64_1410`

Counts

4 → 96

Calls

4 calls:

35.0ms	(.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.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)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series686.0ms (9.8%)

Counts

4 → 84

Calls

4 calls:

271.0ms	(.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))))
147.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
137.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
131.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 3264 to 2790 computations (14.5% saved)

simplify118.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4963	4120
1	4963	4120

prune249.0ms (3.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	178	2	180
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	181	7	188

Error

2.5b

Counts

188 → 7

Compiler

Compiled 4874 to 2869 computations (41.1% saved)

regimes831.0ms (11.8%)

Accuracy

Total 10.4b remaining (69%)

Threshold costs 0b (0%)

Compiler

Compiled 4593 to 3494 computations (23.9% saved)

bsearch79.0ms (1.1%)

Steps

Iters	Range		Point
6	2.6620654795435365e+26	3.1376670427465036e+27	3.0690585850140043e+27
8	5.824580220351484e-148	8.190990157080617e-144	6.598497970238571e-145
9	-5.031768708408147e-73	-9.26288554196244e-81	-5.164382113824996e-80
10	-4.2244150222226545e+116	-2.438288904484117e+106	-1.2232339396640187e+115

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	49	154
1	49	154

end0.0ms (0%)

sample1.4s (19.9%)

Algorithm

1×

intervals

Results

337.0ms	8000×	body	128	valid
19.0ms	476×	body	128	invalid

Compiler

Compiled 1008 to 747 computations (25.9% saved)

Details

analyze515.0ms (7.3%)

sample20.0ms (0.3%)

simplify101.0ms (1.4%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite21.0ms (0.3%)

series512.0ms (7.3%)

simplify104.0ms (1.5%)

prune129.0ms (1.8%)

localize14.0ms (0.2%)

rewrite45.0ms (0.6%)

series836.0ms (11.9%)

simplify87.0ms (1.2%)

prune315.0ms (4.5%)

localize12.0ms (0.2%)

rewrite53.0ms (0.8%)

series543.0ms (7.7%)

simplify92.0ms (1.3%)

prune176.0ms (2.5%)

localize17.0ms (0.2%)

rewrite67.0ms (0.9%)

series686.0ms (9.8%)

simplify118.0ms (1.7%)

prune249.0ms (3.5%)

regimes831.0ms (11.8%)

bsearch79.0ms (1.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.4s (19.9%)

Profiling