Details

analyze26.0ms (0.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	0.1%	2
50%	50%	0.1%	3
74.9%	25%	0.1%	4
74.9%	25%	0.1%	5
87.4%	12.5%	0.1%	6
87.4%	12.5%	0.1%	7
93.7%	6.2%	0.1%	8
93.7%	6.2%	0.1%	9
96.8%	3.1%	0.1%	10
96.8%	3.1%	0.1%	11
98.3%	1.6%	0.1%	12
98.3%	1.6%	0.1%	13
99.1%	0.8%	0.1%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample13.0ms (0.3%)

Algorithm

1×

intervals

Results

6.0ms	248×	body	128	valid
1.0ms	5×	body	2048	valid
0.0ms	2×	body	512	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 17 to 17 computations (0% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	55	12
1	55	12

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

Merged error: 0.1b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
1×	`flip3-+_binary64` `pow1_binary64` `distribute-lft-out_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

1 → 12

Calls

1 calls:

7.0ms

(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

series41.0ms (0.9%)

Counts

1 → 3

Calls

1 calls:

41.0ms

(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5380	259

prune21.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	11	4	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	11	5	16

Merged error: 0.0b

Counts

16 → 5

Compiler

Compiled 311 to 163 computations (47.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))) (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
0.5b	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
0.5b	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
0.5b	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))

rewrite54.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`cbrt-prod_binary64`
35×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`cbrt-div_binary64`
15×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`flip3-+_binary64` `swap-sqr_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `flip-+_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 95

Calls

4 calls:

20.0ms	(*.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))) (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
8.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
7.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
7.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))

series862.0ms (19.8%)

Counts

4 → 12

Calls

4 calls:

255.0ms	(*.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))) (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
212.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
200.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
194.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))

simplify65.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4991	3142
1	4991	3142

prune398.0ms (9.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	105	7	112

Merged error: 0.0b

Counts

112 → 7

Compiler

Compiled 4223 to 2245 computations (46.8% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
0.5b	(cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
0.5b	(cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
1.0b	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))) 5)

rewrite46.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`cbrt-prod_binary64`
21×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
10×	`cbrt-div_binary64` `unpow-prod-down_binary64`
5×	`pow1_binary64` `add-exp-log_binary64`
4×	`add-log-exp_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `flip-+_binary64`
2×	`pow-pow_binary64`
1×	`pow-to-exp_binary64` `sqr-pow_binary64` `pow-exp_binary64`

Counts

4 → 73

Calls

4 calls:

11.0ms	(cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
10.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))) 5)
8.0ms	(cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
7.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))

series1.2s (27.6%)

Counts

4 → 12

Calls

4 calls:

586.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))) 5)
210.0ms	(cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
204.0ms	(cbrt.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
199.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))

simplify73.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4949	2621
1	4949	2621

prune170.0ms (3.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	85	7	92

Merged error: 0.0b

Counts

92 → 7

Compiler

Compiled 3905 to 2260 computations (42.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
0.0b	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
0.0b	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
0.4b	(*.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))) (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))

rewrite53.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64` `sqrt-prod_binary64`
28×	`add-sqr-sqrt_binary64`
21×	`pow1_binary64`
16×	`sqrt-div_binary64`
14×	`add-cube-cbrt_binary64`
11×	`swap-sqr_binary64`
10×	`pow1/2_binary64` `sqrt-pow1_binary64`
9×	`flip3-+_binary64` `distribute-lft-out_binary64` `flip-+_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-up_binary64`
4×	`unswap-sqr_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`associate-r/_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 106

Calls

4 calls:

20.0ms	(*.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))) (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
7.0ms	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
7.0ms	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
7.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

series349.0ms (8%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
120.0ms	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
45.0ms	(*.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))) (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
45.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

simplify84.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5801	2483

prune122.0ms (2.8%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	117	8	125

Merged error: 0b

Counts

125 → 8

Compiler

Compiled 2718 to 1372 computations (49.5% saved)

regimes69.0ms (1.6%)

Compiler: Compiled 653 to 430 computations (34.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	12
1	19	12

end0.0ms (0%)

sample565.0ms (13%)

Algorithm

1×

intervals

Results

199.0ms	7702×	body	128	valid
10.0ms	86×	body	2048	valid
9.0ms	105×	body	1024	valid
5.0ms	72×	body	512	valid
2.0ms	35×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 228 to 153 computations (32.9% saved)

Details

analyze26.0ms (0.6%)

sample13.0ms (0.3%)

simplify11.0ms (0.2%)

prune2.0ms (0.1%)

localize6.0ms (0.1%)

rewrite8.0ms (0.2%)

series41.0ms (0.9%)

simplify71.0ms (1.6%)

prune21.0ms (0.5%)

localize10.0ms (0.2%)

rewrite54.0ms (1.3%)

series862.0ms (19.8%)

simplify65.0ms (1.5%)

prune398.0ms (9.2%)

localize13.0ms (0.3%)

rewrite46.0ms (1.1%)

series1.2s (27.6%)

simplify73.0ms (1.7%)

prune170.0ms (3.9%)

localize8.0ms (0.2%)

rewrite53.0ms (1.2%)

series349.0ms (8%)

simplify84.0ms (1.9%)

prune122.0ms (2.8%)

regimes69.0ms (1.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample565.0ms (13%)

Profiling