Details

analyze537.0ms (11%)

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 (0.4%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	10×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify297.0ms (6.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	5232	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: 26.1b

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))
0.8b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
25.7b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_2165` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
9×	`times-frac_binary64_2149`
7×	`add-log-exp_binary64_2182`
5×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
3×	`pow1_binary64_2204` `associate-/r_binary64_2087` `associate-/l_binary64_2088`
2×	`flip--_binary64_2118` `associate-/r/_binary64_2089` `flip3--_binary64_2147` `flip3-+_binary64_2146` `flip-+_binary64_2117` `associate-/l/_binary64_2090`
1×	`cbrt-undiv_binary64_2177` `+-commutative_binary64_2073` `diff-log_binary64_2235` `clear-num_binary64_2142` `sub-neg_binary64_2136` `div-inv_binary64_2140` `sum-log_binary64_2234` `cancel-sign-sub-inv_binary64_2109` `div-exp_binary64_2194` `frac-2neg_binary64_2154` `div-sub_binary64_2148`

Counts

3 → 55

Calls

3 calls:

10.0ms	(/.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))

series323.0ms (6.6%)

Counts

3 → 9

Calls

3 calls:

198.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
86.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
39.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

simplify95.0ms (2%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4981	1822
1	4981	1822

prune391.0ms (8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	53	11	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	11	65

Merged error: 25.1b

Counts

65 → 11

Compiler

Compiled 7919 to 5060 computations (36.1% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
14.5b	(/.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))))
29.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
29.8b	(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_2143`
28×	`sqrt-prod_binary64_2159`
25×	`add-sqr-sqrt_binary64_2165`
24×	`times-frac_binary64_2149`
23×	`add-cube-cbrt_binary64_2178`
10×	`unpow-prod-down_binary64_2222` `distribute-lft-out_binary64_2094`
8×	`associate-/r*_binary64_2087`
6×	`sqrt-div_binary64_2160` `pow1_binary64_2204` `add-log-exp_binary64_2182` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
3×	`associate-/l*_binary64_2088` `flip3-+_binary64_2146` `flip-+_binary64_2117`
2×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `flip--_binary64_2118` `associate-/r/_binary64_2089` `flip3--_binary64_2147` `sqrt-pow1_binary64_2161` `associate-/l/_binary64_2090`
1×	`cbrt-undiv_binary64_2177` `diff-log_binary64_2235` `clear-num_binary64_2142` `sub-neg_binary64_2136` `div-inv_binary64_2140` `cancel-sign-sub-inv_binary64_2109` `div-exp_binary64_2194` `frac-2neg_binary64_2154` `div-sub_binary64_2148`

Counts

4 → 96

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))))
9.0ms	(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))

series420.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

244.0ms	(/.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))))
80.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
49.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
47.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify90.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5542	3247

prune274.0ms (5.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	109	10	119

Merged error: 23.6b

Counts

119 → 10

Compiler

Compiled 6075 to 3392 computations (44.2% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
25.7b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (*.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
29.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
29.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite57.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`sqrt-div_binary64_2160` `*-un-lft-identity_binary64_2143`
10×	`add-sqr-sqrt_binary64_2165` `sqrt-prod_binary64_2159`
9×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
8×	`associate-/r/_binary64_2089` `add-cube-cbrt_binary64_2178` `flip3-+_binary64_2146` `flip-+_binary64_2117`
6×	`pow1_binary64_2204` `add-log-exp_binary64_2182`
4×	`unpow-prod-down_binary64_2222` `frac-times_binary64_2153` `distribute-lft-out_binary64_2094`
3×	`associate-/l*_binary64_2088` `times-frac_binary64_2149`
2×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `cbrt-undiv_binary64_2177` `flip--_binary64_2118` `flip3--_binary64_2147` `associate-l/_binary64_2086` `associate-r/_binary64_2085` `sqrt-pow1_binary64_2161` `div-exp_binary64_2194` `associate-/l/_binary64_2090`
1×	`diff-log_binary64_2235` `clear-num_binary64_2142` `associate-/r*_binary64_2087` `sub-neg_binary64_2136` `div-inv_binary64_2140` `cbrt-unprod_binary64_2176` `prod-exp_binary64_2192` `cancel-sign-sub-inv_binary64_2109` `frac-2neg_binary64_2154` `div-sub_binary64_2148`

Counts

4 → 78

Calls

4 calls:

27.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (*.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (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)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series376.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

206.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (*.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
82.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
48.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
41.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify78.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4955	2130
1	4955	2130

prune125.0ms (2.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	90	10	100

Merged error: 23.6b

Counts

100 → 10

Compiler

Compiled 2750 to 1601 computations (41.8% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
14.5b	(/.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))))
29.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
29.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite50.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_2143`
30×	`sqrt-prod_binary64_2159`
25×	`add-sqr-sqrt_binary64_2165`
24×	`times-frac_binary64_2149`
23×	`add-cube-cbrt_binary64_2178`
12×	`unpow-prod-down_binary64_2222` `distribute-lft-out_binary64_2094`
8×	`associate-/r*_binary64_2087`
6×	`sqrt-div_binary64_2160` `pow1_binary64_2204` `add-log-exp_binary64_2182` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
3×	`associate-/l*_binary64_2088` `flip3-+_binary64_2146` `flip-+_binary64_2117`
2×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `flip--_binary64_2118` `associate-/r/_binary64_2089` `flip3--_binary64_2147` `sqrt-pow1_binary64_2161` `associate-/l/_binary64_2090`
1×	`cbrt-undiv_binary64_2177` `diff-log_binary64_2235` `clear-num_binary64_2142` `sub-neg_binary64_2136` `div-inv_binary64_2140` `cancel-sign-sub-inv_binary64_2109` `div-exp_binary64_2194` `frac-2neg_binary64_2154` `div-sub_binary64_2148`

Counts

4 → 98

Calls

4 calls:

16.0ms	(/.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)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series426.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

255.0ms	(/.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))))
87.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
42.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
41.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify82.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5398	3277

prune178.0ms (3.7%)

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

Merged error: 23.6b

Counts

120 → 10

Compiler

Compiled 4032 to 2412 computations (40.2% saved)

regimes90.0ms (1.8%)

Compiler: Compiled 772 to 648 computations (16.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	48
1	51	48

end0.0ms (0%)

sample823.0ms (16.9%)

Algorithm

1×

intervals

Results

352.0ms	8000×	body	128	valid
20.0ms	470×	body	128	invalid

Compiler

Compiled 232 to 189 computations (18.5% saved)

Details

analyze537.0ms (11%)

sample21.0ms (0.4%)

simplify297.0ms (6.1%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite23.0ms (0.5%)

series323.0ms (6.6%)

simplify95.0ms (2%)

prune391.0ms (8%)

localize18.0ms (0.4%)

rewrite45.0ms (0.9%)

series420.0ms (8.6%)

simplify90.0ms (1.9%)

prune274.0ms (5.6%)

localize14.0ms (0.3%)

rewrite57.0ms (1.2%)

series376.0ms (7.7%)

simplify78.0ms (1.6%)

prune125.0ms (2.6%)

localize18.0ms (0.4%)

rewrite50.0ms (1%)

series426.0ms (8.7%)

simplify82.0ms (1.7%)

prune178.0ms (3.7%)

regimes90.0ms (1.8%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample823.0ms (16.9%)

Profiling