Details

analyze503.0ms (9.6%)

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)

sample23.0ms (0.4%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
1.0ms	15×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify411.0ms (7.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (248.0ms)

Iter	Nodes	Cost
0	5127	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

Merged error: 24.9b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.2b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
24.4b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1783` `*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794`
9×	`times-frac_binary64_1768`
7×	`add-log-exp_binary64_1798`
5×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
3×	`associate-/r_binary64_1708` `associate-/l_binary64_1709` `pow1_binary64_1820`
2×	`associate-/r/_binary64_1710` `flip3--_binary64_1766` `associate-/l/_binary64_1711` `flip3-+_binary64_1765` `flip-+_binary64_1736` `flip--_binary64_1737`
1×	`frac-2neg_binary64_1773` `diff-log_binary64_1851` `div-sub_binary64_1767` `clear-num_binary64_1761` `div-inv_binary64_1759` `+-commutative_binary64_1694` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `sub-neg_binary64_1755` `sum-log_binary64_1850`

Counts

3 → 54

Calls

3 calls:

12.0ms	(/.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 y.re y.re) (.f64 y.im y.im))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series335.0ms (6.4%)

Counts

3 → 9

Calls

3 calls:

199.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
97.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
39.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

simplify74.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5716	1814

prune99.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	53	10	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	10	64

Merged error: 24.0b

Counts

64 → 10

Compiler

Compiled 1721 to 736 computations (57.2% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
18.7b	(/.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))))
28.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.0b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite46.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_1762`
28×	`sqrt-prod_binary64_1777`
25×	`add-sqr-sqrt_binary64_1783`
24×	`times-frac_binary64_1768`
23×	`add-cube-cbrt_binary64_1794`
10×	`distribute-lft-out_binary64_1715` `unpow-prod-down_binary64_1838`
8×	`associate-/r*_binary64_1708`
6×	`add-log-exp_binary64_1798` `add-cbrt-cube_binary64_1795` `sqrt-div_binary64_1778` `add-exp-log_binary64_1797` `pow1_binary64_1820`
3×	`flip3-+_binary64_1765` `flip-+_binary64_1736` `associate-/l*_binary64_1709`
2×	`associate-/r/_binary64_1710` `flip3--_binary64_1766` `rem-sqrt-square_binary64_1775` `associate-/l/_binary64_1711` `flip--_binary64_1737` `sqrt-pow1_binary64_1779` `pow1/2_binary64_1839`
1×	`frac-2neg_binary64_1773` `diff-log_binary64_1851` `div-sub_binary64_1767` `clear-num_binary64_1761` `div-inv_binary64_1759` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `sub-neg_binary64_1755`

Counts

4 → 95

Calls

4 calls:

15.0ms	(/.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))))
11.0ms	(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))

series422.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

251.0ms	(/.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))))
75.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
50.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
46.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify66.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5185	3239

prune156.0ms (3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	106	11	117

Merged error: 21.8b

Counts

117 → 11

Compiler

Compiled 3760 to 1598 computations (57.5% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
18.7b	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
28.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.0b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite45.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_1762`
28×	`sqrt-prod_binary64_1777`
25×	`add-sqr-sqrt_binary64_1783`
24×	`times-frac_binary64_1768`
23×	`add-cube-cbrt_binary64_1794`
10×	`distribute-lft-out_binary64_1715` `unpow-prod-down_binary64_1838`
8×	`associate-/l*_binary64_1709`
6×	`add-log-exp_binary64_1798` `add-cbrt-cube_binary64_1795` `sqrt-div_binary64_1778` `add-exp-log_binary64_1797` `pow1_binary64_1820`
3×	`flip3-+_binary64_1765` `associate-/r*_binary64_1708` `flip-+_binary64_1736`
2×	`associate-/r/_binary64_1710` `flip3--_binary64_1766` `rem-sqrt-square_binary64_1775` `associate-/l/_binary64_1711` `flip--_binary64_1737` `sqrt-pow1_binary64_1779` `pow1/2_binary64_1839`
1×	`frac-2neg_binary64_1773` `diff-log_binary64_1851` `clear-num_binary64_1761` `div-inv_binary64_1759` `cbrt-undiv_binary64_1793` `div-exp_binary64_1810` `sub-neg_binary64_1755`

Counts

4 → 94

Calls

4 calls:

15.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
5.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))

series321.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

152.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
81.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
45.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
42.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify82.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4964	3259
1	4964	3259

prune162.0ms (3.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	106	11	117

Merged error: 21.8b

Counts

117 → 11

Compiler

Compiled 3945 to 1803 computations (54.3% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.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)))))
18.7b	(/.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))))
28.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.0b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite107.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

107×	`*-un-lft-identity_binary64_1762`
101×	`add-sqr-sqrt_binary64_1783`
94×	`times-frac_binary64_1768`
71×	`sqrt-prod_binary64_1777`
53×	`add-cube-cbrt_binary64_1794`
30×	`associate-l_binary64_1705` `associate-r_binary64_1704`
28×	`add-exp-log_binary64_1797`
24×	`distribute-lft-out_binary64_1715` `unpow-prod-down_binary64_1838`
18×	`add-cbrt-cube_binary64_1795`
15×	`unswap-sqr_binary64_1730`
10×	`sqrt-div_binary64_1778`
9×	`div-exp_binary64_1810`
8×	`prod-exp_binary64_1808` `associate-/r*_binary64_1708` `pow1_binary64_1820`
6×	`associate-/r/_binary64_1710`
5×	`flip3-+_binary64_1765` `flip-+_binary64_1736` `cbrt-undiv_binary64_1793`
4×	`add-log-exp_binary64_1798` `cbrt-unprod_binary64_1792`
3×	`div-inv_binary64_1759` `associate-/l*_binary64_1709`
2×	`rem-sqrt-square_binary64_1775` `associate-/l/_binary64_1711` `sqrt-pow1_binary64_1779` `1-exp_binary64_1803` `rec-exp_binary64_1809` `pow1/2_binary64_1839`
1×	`flip3--_binary64_1766` `frac-2neg_binary64_1773` `frac-times_binary64_1772` `div-sub_binary64_1767` `pow-prod-down_binary64_1830` `clear-num_binary64_1761` `associate-l/_binary64_1707` `associate-r/_binary64_1706` `flip--_binary64_1737` `*-commutative_binary64_1695`

Counts

4 → 185

Calls

4 calls:

48.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.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)))))
15.0ms	(/.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))))
9.0ms	(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)))

series604.0ms (11.5%)

Counts

4 → 12

Calls

4 calls:

273.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.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)))))
245.0ms	(/.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))))
44.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
42.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify117.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5441	7497

prune546.0ms (10.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	195	2	197
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	195	13	208

Merged error: 21.8b

Counts

208 → 13

Compiler

Compiled 6824 to 3923 computations (42.5% saved)

regimes115.0ms (2.2%)

Compiler: Compiled 1068 to 868 computations (18.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	51
1	53	51

end0.0ms (0%)

sample908.0ms (17.4%)

Algorithm

1×

intervals

Results

347.0ms	8000×	body	128	valid
20.0ms	479×	body	128	invalid

Compiler

Compiled 308 to 246 computations (20.1% saved)

Details

analyze503.0ms (9.6%)

sample23.0ms (0.4%)

simplify411.0ms (7.9%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite25.0ms (0.5%)

series335.0ms (6.4%)

simplify74.0ms (1.4%)

prune99.0ms (1.9%)

localize17.0ms (0.3%)

rewrite46.0ms (0.9%)

series422.0ms (8.1%)

simplify66.0ms (1.3%)

prune156.0ms (3%)

localize19.0ms (0.4%)

rewrite45.0ms (0.9%)

series321.0ms (6.1%)

simplify82.0ms (1.6%)

prune162.0ms (3.1%)

localize14.0ms (0.3%)

rewrite107.0ms (2%)

series604.0ms (11.5%)

simplify117.0ms (2.2%)

prune546.0ms (10.4%)

regimes115.0ms (2.2%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample908.0ms (17.4%)

Profiling