Details

analyze49.0ms (1.3%)

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)

sample15.0ms (0.4%)

Algorithm

1×

intervals

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify164.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	133	16
1	133	16

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: 0.0b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (*.f64 x y) 2)
0.0b	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
0.0b	(+.f64 1 (/.f64 (*.f64 x y) 2))
6.7b	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))

rewrite36.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64_5469`
20×	`add-sqr-sqrt_binary64_5490`
16×	`times-frac_binary64_5475`
15×	`add-cube-cbrt_binary64_5501`
11×	`add-exp-log_binary64_5504` `add-cbrt-cube_binary64_5502`
8×	`add-log-exp_binary64_5505`
7×	`associate-/r*_binary64_5415`
5×	`distribute-lft-out_binary64_5422`
4×	`associate-/l*_binary64_5416` `pow1_binary64_5527`
3×	`cbrt-undiv_binary64_5500` `div-exp_binary64_5517`
2×	`clear-num_binary64_5468` `flip-+_binary64_5443` `difference-of-squares_binary64_5438` `div-inv_binary64_5466` `associate-/r/_binary64_5417` `frac-2neg_binary64_5480` `flip3-+_binary64_5472`
1×	`+-commutative_binary64_5401` `sub-neg_binary64_5462` `sum-log_binary64_5557` `flip3--_binary64_5473` `cbrt-unprod_binary64_5499` `diff-log_binary64_5558` `flip--_binary64_5444` `distribute-lft-out--_binary64_5423` `prod-exp_binary64_5515`

Counts

4 → 80

Calls

4 calls:

12.0ms	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
7.0ms	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))
5.0ms	(+.f64 1 (/.f64 (*.f64 x y) 2))
5.0ms	(/.f64 (*.f64 x y) 2)

series243.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2)))
52.0ms	(-.f64 x (/.f64 y (+.f64 1 (/.f64 (*.f64 x y) 2))))
48.0ms	(+.f64 1 (/.f64 (*.f64 x y) 2))
29.0ms	(/.f64 (*.f64 x y) 2)

simplify95.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4882	1606
1	4882	1606

prune92.0ms (2.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	89	3	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	3	93

Merged error: 0b

Counts

93 → 3

Compiler

Compiled 1638 to 982 computations (40% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (*.f64 y x) 2)
0.0b	(+.f64 1 (/.f64 (*.f64 y x) 2))
0.4b	(/.f64 1 (+.f64 1 (/.f64 (*.f64 y x) 2)))
6.3b	(.f64 y (/.f64 1 (+.f64 1 (/.f64 (.f64 y x) 2))))

rewrite40.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64_5469`
31×	`add-sqr-sqrt_binary64_5490`
29×	`times-frac_binary64_5475`
24×	`add-cube-cbrt_binary64_5501`
22×	`add-exp-log_binary64_5504`
18×	`associate-r_binary64_5411`
16×	`add-cbrt-cube_binary64_5502`
8×	`distribute-lft-out_binary64_5422`
7×	`associate-/r*_binary64_5415` `pow1_binary64_5527`
6×	`div-exp_binary64_5517` `add-log-exp_binary64_5505`
5×	`prod-exp_binary64_5515`
4×	`cbrt-undiv_binary64_5500` `associate-/l*_binary64_5416` `associate-/r/_binary64_5417`
3×	`flip-+_binary64_5443` `cbrt-unprod_binary64_5499` `div-inv_binary64_5466` `unswap-sqr_binary64_5437` `associate-l_binary64_5412` `flip3-+_binary64_5472`
2×	`rec-exp_binary64_5516` `clear-num_binary64_5468` `1-exp_binary64_5510` `frac-2neg_binary64_5480`
1×	`+-commutative_binary64_5401` `pow-prod-down_binary64_5537` `sum-log_binary64_5557` `inv-pow_binary64_5551` `associate-r/_binary64_5413` `un-div-inv_binary64_5467` `pow-flip_binary64_5540` `-commutative_binary64_5402`

Counts

4 → 111

Calls

4 calls:

13.0ms	(.f64 y (/.f64 1 (+.f64 1 (/.f64 (.f64 y x) 2))))
8.0ms	(/.f64 1 (+.f64 1 (/.f64 (*.f64 y x) 2)))
6.0ms	(+.f64 1 (/.f64 (*.f64 y x) 2))
5.0ms	(/.f64 (*.f64 y x) 2)

series276.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

119.0ms	(.f64 y (/.f64 1 (+.f64 1 (/.f64 (.f64 y x) 2))))
81.0ms	(/.f64 1 (+.f64 1 (/.f64 (*.f64 y x) 2)))
45.0ms	(+.f64 1 (/.f64 (*.f64 y x) 2))
30.0ms	(/.f64 (*.f64 y x) 2)

simplify74.0ms (2%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4905	1908
1	4905	1908

prune122.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	123	3	126

Merged error: 0b

Counts

126 → 3

Compiler

Compiled 2350 to 1533 computations (34.8% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (*.f64 y x) 2)
0.0b	(+.f64 1 (/.f64 (*.f64 y x) 2))
0.1b	(/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y))
6.6b	(/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)

rewrite44.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

111×	`times-frac_binary64_5475`
98×	`*-un-lft-identity_binary64_5469`
64×	`add-cube-cbrt_binary64_5501` `add-sqr-sqrt_binary64_5490`
22×	`associate-/r*_binary64_5415` `add-exp-log_binary64_5504`
17×	`distribute-lft-out_binary64_5422`
16×	`add-cbrt-cube_binary64_5502`
10×	`div-exp_binary64_5517`
8×	`associate-/l*_binary64_5416`
7×	`div-inv_binary64_5466`
6×	`cbrt-undiv_binary64_5500` `add-log-exp_binary64_5505`
5×	`pow1_binary64_5527`
3×	`clear-num_binary64_5468` `frac-2neg_binary64_5480`
2×	`associate-/l/_binary64_5418` `rec-exp_binary64_5516` `flip-+_binary64_5443` `1-exp_binary64_5510` `flip3-+_binary64_5472`
1×	`+-commutative_binary64_5401` `sum-log_binary64_5557` `cbrt-unprod_binary64_5499` `inv-pow_binary64_5551` `associate-/r/_binary64_5417` `pow-flip_binary64_5540` `prod-exp_binary64_5515`

Counts

4 → 154

Calls

4 calls:

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 1 (/.f64 (*.f64 y x) 2))
5.0ms	(/.f64 (*.f64 y x) 2)

series252.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

115.0ms	(/.f64 1 (/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y))
63.0ms	(/.f64 (+.f64 1 (/.f64 (*.f64 y x) 2)) y)
43.0ms	(+.f64 1 (/.f64 (*.f64 y x) 2))
30.0ms	(/.f64 (*.f64 y x) 2)

simplify92.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4924	3436
1	4924	3436

prune173.0ms (4.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	166	3	169

Merged error: 0b

Counts

169 → 3

Compiler

Compiled 3393 to 2119 computations (37.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 y)
0.5b	(cbrt.f64 y)
2.1b	(/.f64 (cbrt.f64 y) (+.f64 1 (/.f64 (*.f64 y x) 2)))
4.6b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (+.f64 1 (/.f64 (*.f64 y x) 2))))

rewrite46.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`*-un-lft-identity_binary64_5469`
50×	`times-frac_binary64_5475`
43×	`add-sqr-sqrt_binary64_5490`
38×	`add-cube-cbrt_binary64_5501`
34×	`cbrt-prod_binary64_5497`
30×	`associate-r_binary64_5411`
18×	`add-exp-log_binary64_5504`
13×	`distribute-lft-out_binary64_5422`
11×	`add-cbrt-cube_binary64_5502`
9×	`pow1_binary64_5527`
6×	`cbrt-unprod_binary64_5499` `associate-/l*_binary64_5416` `prod-exp_binary64_5515`
4×	`associate-/r*_binary64_5415` `associate-/r/_binary64_5417` `add-log-exp_binary64_5505`
3×	`pow-prod-down_binary64_5537` `cbrt-undiv_binary64_5500` `div-exp_binary64_5517` `unswap-sqr_binary64_5437`
2×	`flip-+_binary64_5443` `pow1/3_binary64_5548` `div-inv_binary64_5466` `flip3-+_binary64_5472`
1×	`clear-num_binary64_5468` `associate-r/_binary64_5413` `frac-2neg_binary64_5480` `-commutative_binary64_5402` `associate-l_binary64_5412`

Counts

4 → 123

Calls

4 calls:

22.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (+.f64 1 (/.f64 (*.f64 y x) 2))))
8.0ms	(/.f64 (cbrt.f64 y) (+.f64 1 (/.f64 (*.f64 y x) 2)))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)

series825.0ms (22.1%)

Counts

4 → 12

Calls

4 calls:

341.0ms	(/.f64 (cbrt.f64 y) (+.f64 1 (/.f64 (*.f64 y x) 2)))
173.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (+.f64 1 (/.f64 (*.f64 y x) 2))))
162.0ms	(cbrt.f64 y)
149.0ms	(cbrt.f64 y)

simplify104.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4869	2663
1	4869	2663

prune147.0ms (3.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	135	3	138

Merged error: 0b

Counts

138 → 3

Compiler

Compiled 3340 to 1685 computations (49.6% saved)

regimes88.0ms (2.4%)

Compiler: Compiled 749 to 587 computations (21.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	16
1	29	16

end0.0ms (0%)

sample707.0ms (18.9%)

Algorithm

1×

intervals

Results

269.0ms	7999×	body	128	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 264 to 208 computations (21.2% saved)

Details

analyze49.0ms (1.3%)

sample15.0ms (0.4%)

simplify164.0ms (4.4%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite36.0ms (1%)

series243.0ms (6.5%)

simplify95.0ms (2.5%)

prune92.0ms (2.5%)

localize11.0ms (0.3%)

rewrite40.0ms (1.1%)

series276.0ms (7.4%)

simplify74.0ms (2%)

prune122.0ms (3.3%)

localize11.0ms (0.3%)

rewrite44.0ms (1.2%)

series252.0ms (6.8%)

simplify92.0ms (2.5%)

prune173.0ms (4.6%)

localize12.0ms (0.3%)

rewrite46.0ms (1.2%)

series825.0ms (22.1%)

simplify104.0ms (2.8%)

prune147.0ms (3.9%)

regimes88.0ms (2.4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample707.0ms (18.9%)

Profiling