Details

analyze51.0ms (1.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
50%	50%	0.1%	5
62.4%	37.5%	0.1%	6
74.9%	25%	0.1%	7
81.2%	18.7%	0.1%	8
87.4%	12.5%	0.1%	9
90.5%	9.4%	0.1%	10
93.7%	6.2%	0.1%	11
95.2%	4.7%	0.1%	12
96.8%	3.1%	0.1%	13
97.6%	2.3%	0.1%	14

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample24.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify182.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	133	16
1	133	16

prune3.0ms (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 22 to 18 computations (18.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (*.f64 x y) 2)
0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
7.4b	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))

rewrite40.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64_8679`
28×	`times-frac_binary64_8685`
27×	`add-sqr-sqrt_binary64_8701`
22×	`add-cube-cbrt_binary64_8714`
18×	`cancel-sign-sub-inv_binary64_8645`
10×	`add-cbrt-cube_binary64_8715` `add-exp-log_binary64_8717`
7×	`associate-/r*_binary64_8623` `distribute-lft-out_binary64_8630`
5×	`add-log-exp_binary64_8718`
4×	`associate-/l*_binary64_8624` `associate-/r/_binary64_8625`
3×	`cbrt-undiv_binary64_8713` `div-exp_binary64_8730` `pow1_binary64_8740` `div-inv_binary64_8676`
2×	`frac-2neg_binary64_8690` `difference-of-squares_binary64_8648` `clear-num_binary64_8678` `flip-+_binary64_8653` `flip3-+_binary64_8682`
1×	`distribute-lft-out--_binary64_8631` `prod-exp_binary64_8728` `sub-neg_binary64_8672` `flip3--_binary64_8683` `cbrt-unprod_binary64_8712` `diff-log_binary64_8771` `flip--_binary64_8654`

Counts

3 → 86

Calls

3 calls:

14.0ms	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
13.0ms	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))
5.0ms	(/.f64 (*.f64 x y) 2)

series211.0ms (4.7%)

Counts

3 → 9

Calls

3 calls:

121.0ms	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))
60.0ms	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
30.0ms	(/.f64 (*.f64 x y) 2)

simplify74.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4975	1705
1	4975	1705

prune210.0ms (4.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	91	4	95
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	91	5	96

Merged error: 0b

Counts

96 → 5

Compiler

Compiled 3405 to 2265 computations (33.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)))
0.0b	(/.f64 (*.f64 y x) 2)
0.1b	(/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y))
7.3b	(/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)

rewrite81.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

201×	`times-frac_binary64_8685`
160×	`*-un-lft-identity_binary64_8679`
119×	`add-sqr-sqrt_binary64_8701`
105×	`add-cube-cbrt_binary64_8714`
53×	`cancel-sign-sub-inv_binary64_8645`
25×	`distribute-lft-out_binary64_8630`
22×	`associate-/r*_binary64_8623` `add-exp-log_binary64_8717`
16×	`add-cbrt-cube_binary64_8715`
12×	`div-inv_binary64_8676`
10×	`div-exp_binary64_8730`
8×	`associate-/l*_binary64_8624`
6×	`cbrt-undiv_binary64_8713` `add-log-exp_binary64_8718`
5×	`difference-of-squares_binary64_8648` `pow1_binary64_8740`
3×	`frac-2neg_binary64_8690` `clear-num_binary64_8678`
2×	`1-exp_binary64_8723` `distribute-lft-out--_binary64_8631` `associate-/r/_binary64_8625` `rec-exp_binary64_8729` `associate-/l/_binary64_8626`
1×	`pow-flip_binary64_8753` `prod-exp_binary64_8728` `sub-neg_binary64_8672` `flip3--_binary64_8683` `cbrt-unprod_binary64_8712` `diff-log_binary64_8771` `inv-pow_binary64_8764` `flip-+_binary64_8653` `flip--_binary64_8654` `flip3-+_binary64_8682`

Counts

4 → 213

Calls

4 calls:

26.0ms	(-.f64 x (/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)))
11.0ms	(/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y))
8.0ms	(/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)
5.0ms	(/.f64 (*.f64 y x) 2)

series282.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

120.0ms	(/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y))
69.0ms	(/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)
59.0ms	(-.f64 x (/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)))
34.0ms	(/.f64 (*.f64 y x) 2)

simplify106.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5007	5088

prune232.0ms (5.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	225	0	225
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	225	5	230

Merged error: 0b

Counts

230 → 5

Compiler

Compiled 4537 to 2760 computations (39.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 x (sqrt.f64 2)) (/.f64 y (sqrt.f64 2)))
0.4b	(/.f64 x (sqrt.f64 2))
0.5b	(/.f64 y (sqrt.f64 2))
7.4b	(/.f64 y (+.f64 1 (*.f64 (/.f64 x (sqrt.f64 2)) (/.f64 y (sqrt.f64 2)))))

rewrite63.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`add-sqr-sqrt_binary64_8701`
93×	`times-frac_binary64_8685`
68×	`add-cube-cbrt_binary64_8714` `*-un-lft-identity_binary64_8679`
48×	`sqrt-prod_binary64_8695`
22×	`associate-l_binary64_8620` `add-cbrt-cube_binary64_8715` `add-exp-log_binary64_8717` `associate-r_binary64_8619`
15×	`associate-/r*_binary64_8623`
9×	`unswap-sqr_binary64_8647` `associate-/l*_binary64_8624`
7×	`cbrt-undiv_binary64_8713` `div-exp_binary64_8730`
6×	`pow1_binary64_8740`
5×	`div-inv_binary64_8676`
4×	`prod-exp_binary64_8728` `cbrt-unprod_binary64_8712` `add-log-exp_binary64_8718`
3×	`frac-2neg_binary64_8690` `clear-num_binary64_8678`
2×	`associate-/r/_binary64_8625`
1×	`pow-prod-down_binary64_8750` `-commutative_binary64_8610` `associate-r/_binary64_8621` `frac-times_binary64_8689` `associate-*l/_binary64_8622` `flip-+_binary64_8653` `flip3-+_binary64_8682`

Counts

4 → 180

Calls

4 calls:

22.0ms	(*.f64 (/.f64 x (sqrt.f64 2)) (/.f64 y (sqrt.f64 2)))
6.0ms	(/.f64 y (+.f64 1 (*.f64 (/.f64 x (sqrt.f64 2)) (/.f64 y (sqrt.f64 2)))))
5.0ms	(/.f64 y (sqrt.f64 2))
5.0ms	(/.f64 x (sqrt.f64 2))

series621.0ms (13.8%)

Counts

4 → 12

Calls

4 calls:

337.0ms	(/.f64 y (+.f64 1 (*.f64 (/.f64 x (sqrt.f64 2)) (/.f64 y (sqrt.f64 2)))))
143.0ms	(*.f64 (/.f64 x (sqrt.f64 2)) (/.f64 y (sqrt.f64 2)))
71.0ms	(/.f64 x (sqrt.f64 2))
70.0ms	(/.f64 y (sqrt.f64 2))

simplify105.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4930	2862
1	4930	2862

prune240.0ms (5.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	192	5	197

Merged error: 0b

Counts

197 → 5

Compiler

Compiled 3978 to 2805 computations (29.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)
3.1b	(/.f64 (cbrt.f64 y) (+.f64 1 (/.f64 (*.f64 y x) 2)))
4.5b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (+.f64 1 (/.f64 (*.f64 y x) 2))))

rewrite51.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`*-un-lft-identity_binary64_8679`
50×	`times-frac_binary64_8685`
43×	`add-sqr-sqrt_binary64_8701`
38×	`add-cube-cbrt_binary64_8714`
34×	`cbrt-prod_binary64_8710`
30×	`associate-r_binary64_8619`
18×	`add-exp-log_binary64_8717`
13×	`distribute-lft-out_binary64_8630`
11×	`add-cbrt-cube_binary64_8715`
9×	`pow1_binary64_8740`
6×	`prod-exp_binary64_8728` `cbrt-unprod_binary64_8712` `associate-/l*_binary64_8624`
4×	`associate-/r*_binary64_8623` `associate-/r/_binary64_8625` `add-log-exp_binary64_8718`
3×	`cbrt-undiv_binary64_8713` `pow-prod-down_binary64_8750` `unswap-sqr_binary64_8647` `div-exp_binary64_8730`
2×	`div-inv_binary64_8676` `flip-+_binary64_8653` `pow1/3_binary64_8761` `flip3-+_binary64_8682`
1×	`frac-2neg_binary64_8690` `associate-l_binary64_8620` `-commutative_binary64_8610` `associate-r/_binary64_8621` `clear-num_binary64_8678`

Counts

4 → 123

Calls

4 calls:

25.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (+.f64 1 (/.f64 (*.f64 y x) 2))))
9.0ms	(/.f64 (cbrt.f64 y) (+.f64 1 (/.f64 (*.f64 y x) 2)))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)

series861.0ms (19.2%)

Counts

4 → 12

Calls

4 calls:

353.0ms	(/.f64 (cbrt.f64 y) (+.f64 1 (/.f64 (*.f64 y x) 2)))
182.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (+.f64 1 (/.f64 (*.f64 y x) 2))))
180.0ms	(cbrt.f64 y)
145.0ms	(cbrt.f64 y)

simplify106.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4911	2661
1	4911	2661

prune156.0ms (3.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	135	5	140

Merged error: 0b

Counts

140 → 5

Compiler

Compiled 3339 to 1684 computations (49.6% saved)

regimes200.0ms (4.5%)

Compiler: Compiled 266 to 209 computations (21.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	16
1	29	16

end0.0ms (0%)

sample548.0ms (12.2%)

Algorithm

1×

intervals

Results

281.0ms	7998×	body	128	valid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 103 to 82 computations (20.4% saved)

Details

analyze51.0ms (1.1%)

sample24.0ms (0.5%)

simplify182.0ms (4%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

rewrite40.0ms (0.9%)

series211.0ms (4.7%)

simplify74.0ms (1.6%)

prune210.0ms (4.7%)

localize9.0ms (0.2%)

rewrite81.0ms (1.8%)

series282.0ms (6.3%)

simplify106.0ms (2.3%)

prune232.0ms (5.2%)

localize10.0ms (0.2%)

rewrite63.0ms (1.4%)

series621.0ms (13.8%)

simplify105.0ms (2.3%)

prune240.0ms (5.3%)

localize13.0ms (0.3%)

rewrite51.0ms (1.1%)

series861.0ms (19.2%)

simplify106.0ms (2.4%)

prune156.0ms (3.5%)

regimes200.0ms (4.5%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample548.0ms (12.2%)

Profiling