Details

analyze783.0ms (19.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	316	98
1	316	98
0	4	4
1	4	4

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
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
12.5%	87.3%	0.2%	10
25%	74.9%	0.2%	11
31.2%	63.9%	4.9%	12
39%	50.9%	10.1%	13
44.8%	44.4%	10.7%	14

Compiler

Compiled 8 to 8 computations (0% saved)

sample20.0ms (0.5%)

Algorithm

1×

intervals

Results

6.0ms	256×	body	128	valid
1.0ms	51×	body	128	invalid

Compiler

Compiled 15 to 19 computations (-26.7% saved)

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	160	14
1	160	14

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

0.0b

Counts

2 → 1

Compiler

Compiled 14 to 14 computations (0% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_799`
1×	`diff-log_binary64_852` `*-un-lft-identity_binary64_760` `add-exp-log_binary64_798` `cancel-sign-sub-inv_binary64_726` `add-cube-cbrt_binary64_795` `add-cbrt-cube_binary64_796` `pow1_binary64_821` `sub-neg_binary64_753` `flip--_binary64_735` `add-sqr-sqrt_binary64_782` `flip3--_binary64_764`

Counts

1 → 12

Calls

1 calls:

4.0ms

(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

series39.0ms (1%)

Counts

1 → 3

Calls

1 calls:

39.0ms

(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

simplify73.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4948	294
1	4948	294

prune11.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	13	2	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	3	16

Error

0.0b

Counts

16 → 3

Compiler

Compiled 226 to 59 computations (73.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (cbrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
1.9b	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
1.9b	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
1.9b	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_791`
23×	`add-sqr-sqrt_binary64_782`
18×	`cbrt-div_binary64_792`
15×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
11×	`pow1_binary64_821`
9×	`pow1/3_binary64_842` `flip--_binary64_735` `flip3--_binary64_764`
6×	`add-exp-log_binary64_798` `swap-sqr_binary64_727` `associate-r_binary64_700` `associate-l_binary64_701`
4×	`unswap-sqr_binary64_728` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `frac-times_binary64_770`
2×	`associate-l/_binary64_703` `pow-sqr_binary64_733` `associate-r/_binary64_702` `pow-prod-up_binary64_830` `pow-prod-down_binary64_831`
1×	`pow2_binary64_841` `prod-exp_binary64_809` `pow-plus_binary64_823` `cbrt-unprod_binary64_793` `*-commutative_binary64_691`

Counts

4 → 87

Calls

4 calls:

12.0ms	(.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (cbrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
4.0ms	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
4.0ms	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
3.0ms	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

series592.0ms (15%)

Counts

4 → 12

Calls

4 calls:

170.0ms	(.f64 (cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (cbrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
145.0ms	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
140.0ms	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
137.0ms	(cbrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

simplify84.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4949	2776
1	4949	2776

prune94.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	99	3	102

Error

0.0b

Counts

102 → 3

Compiler

Compiled 3222 to 548 computations (83% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.3b	(.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (sqrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
1.5b	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
1.5b	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_782`
24×	`sqrt-prod_binary64_776`
21×	`pow1_binary64_821`
16×	`sqrt-div_binary64_777`
14×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
10×	`sqrt-pow1_binary64_778` `pow1/2_binary64_840`
9×	`flip--_binary64_735` `flip3--_binary64_764`
8×	`swap-sqr_binary64_727`
6×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `associate-r_binary64_700` `associate-l_binary64_701`
5×	`pow-prod-up_binary64_830`
4×	`unswap-sqr_binary64_728` `rem-sqrt-square_binary64_773` `frac-times_binary64_770`
3×	`pow-sqr_binary64_733` `pow-prod-down_binary64_831`
2×	`associate-l/_binary64_703` `associate-r/_binary64_702`
1×	`pow2_binary64_841` `diff-log_binary64_852` `prod-exp_binary64_809` `cancel-sign-sub-inv_binary64_726` `rem-square-sqrt_binary64_772` `pow-plus_binary64_823` `sqr-abs_binary64_775` `sqrt-unprod_binary64_780` `cbrt-unprod_binary64_793` `sub-neg_binary64_753` `*-commutative_binary64_691`

Counts

4 → 100

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (sqrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
4.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
4.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
4.0ms	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series259.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
86.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
46.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im))) (sqrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im))))
38.0ms	(-.f64 (.f64 x.re y.re) (.f64 x.im y.im))

simplify65.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4953	2577
1	4953	2577

prune80.0ms (2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	111	4	115

Error

0.0b

Counts

115 → 4

Compiler

Compiled 2353 to 431 computations (81.7% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))) (pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im)))) 3))
0.4b	(pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))) 3)
1.5b	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
1.5b	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

rewrite52.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`sqrt-prod_binary64_776`
70×	`add-sqr-sqrt_binary64_782`
32×	`sqrt-div_binary64_777`
27×	`cube-prod_binary64_788` `unpow-prod-down_binary64_839`
24×	`unswap-sqr_binary64_728` `associate-r_binary64_700`
23×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
10×	`add-exp-log_binary64_798` `pow1_binary64_821`
9×	`associate-l_binary64_701` `flip--_binary64_735` `flip3--_binary64_764`
8×	`cube-div_binary64_789`
7×	`add-cbrt-cube_binary64_796`
6×	`sqrt-pow1_binary64_778`
5×	`sqr-pow_binary64_732` `pow-pow_binary64_832`
4×	`add-log-exp_binary64_799` `frac-times_binary64_770` `pow1/2_binary64_840`
3×	`prod-exp_binary64_809` `pow-unpow_binary64_837`
2×	`cube-mult_binary64_790` `rem-sqrt-square_binary64_773` `associate-l/_binary64_703` `unpow3_binary64_826` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `associate-r/_binary64_702`
1×	`rem-cube-cbrt_binary64_783` `cbrt-unprod_binary64_793` `pow-prod-up_binary64_830` `sqrt-pow2_binary64_779` `*-commutative_binary64_691`

Counts

4 → 150

Calls

4 calls:

20.0ms	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))) (pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im)))) 3))
7.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))) 3)
4.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
4.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

series560.0ms (14.2%)

Counts

4 → 12

Calls

4 calls:

340.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))) 3)
91.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
86.0ms	(sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
44.0ms	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (.f64 x.im y.im)))) (pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 x.re y.re) (*.f64 x.im y.im)))) 3))

simplify94.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5047	4550

prune145.0ms (3.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	162	4	166

Error

Counts

166 → 4

Compiler

Compiled 4150 to 856 computations (79.4% saved)

regimes138.0ms (3.5%)

Accuracy

Total 0.0b remaining (40.4%)

Threshold costs 0.0b (40.4%)

Compiler

Compiled 1203 to 808 computations (32.8% saved)

bsearch0.0ms (0%)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	14
1	38	14

Compiler

Compiled 28 to 28 computations (0% saved)

end0.0ms (0%)

sample730.0ms (18.5%)

Algorithm

1×

intervals

Results

217.0ms	8000×	body	128	valid
38.0ms	1354×	body	128	invalid

Compiler

Compiled 182 to 125 computations (31.3% saved)

Details

analyze783.0ms (19.8%)

sample20.0ms (0.5%)

simplify13.0ms (0.3%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite5.0ms (0.1%)

series39.0ms (1%)

simplify73.0ms (1.8%)

prune11.0ms (0.3%)

localize9.0ms (0.2%)

rewrite32.0ms (0.8%)

series592.0ms (15%)

simplify84.0ms (2.1%)

prune94.0ms (2.4%)

localize8.0ms (0.2%)

rewrite33.0ms (0.8%)

series259.0ms (6.6%)

simplify65.0ms (1.6%)

prune80.0ms (2%)

localize12.0ms (0.3%)

rewrite52.0ms (1.3%)

series560.0ms (14.2%)

simplify94.0ms (2.4%)

prune145.0ms (3.7%)

regimes138.0ms (3.5%)

bsearch0.0ms (0%)

simplify8.0ms (0.2%)

end0.0ms (0%)

sample730.0ms (18.5%)

Profiling