Details

analyze66.0ms (1.7%)

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
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
59.3%	40.6%	0.1%	6
76.5%	23.4%	0.1%	7
82%	18%	0.1%	8
87.8%	12.1%	0.1%	9
90.7%	9.2%	0.1%	10
93.8%	6.1%	0.1%	11
95.3%	4.6%	0.1%	12
96.8%	3.1%	0.1%	13
97.6%	2.3%	0.1%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample20.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 15 to 13 computations (13.3% saved)

simplify301.0ms (8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (119.0ms)

Iter	Nodes	Cost
0	782	10
1	782	10

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: 0.0b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64_21561`
22×	`add-sqr-sqrt_binary64_21583`
20×	`times-frac_binary64_21567`
12×	`add-cube-cbrt_binary64_21596`
6×	`distribute-lft-out_binary64_21512`
5×	`associate-/l*_binary64_21506` `difference-of-squares_binary64_21530` `distribute-lft-out--_binary64_21513`
4×	`associate-/r*_binary64_21505`
3×	`add-exp-log_binary64_21599` `add-cbrt-cube_binary64_21597`
2×	`associate-/l/_binary64_21508` `associate-/r/_binary64_21507`
1×	`cbrt-undiv_binary64_21595` `div-exp_binary64_21612` `flip3--_binary64_21565` `div-sub_binary64_21566` `frac-2neg_binary64_21572` `flip-+_binary64_21535` `flip3-+_binary64_21564` `add-log-exp_binary64_21600` `div-inv_binary64_21558` `clear-num_binary64_21560` `pow1_binary64_21622` `flip--_binary64_21536`

Counts

1 → 46

Calls

1 calls:

17.0ms

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

series73.0ms (1.9%)

Counts

1 → 3

Calls

1 calls:

72.0ms

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

simplify91.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5176	810

prune70.0ms (1.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	45	4	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	4	50

Merged error: 0b

Counts

50 → 4

Compiler

Compiled 712 to 161 computations (77.4% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite81.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64_21561`
52×	`times-frac_binary64_21567`
43×	`add-sqr-sqrt_binary64_21583`
31×	`add-cube-cbrt_binary64_21596`
18×	`cancel-sign-sub-inv_binary64_21527`
15×	`distribute-lft-out_binary64_21512`
10×	`associate-/r/_binary64_21507`
8×	`associate-/r*_binary64_21505`
7×	`add-exp-log_binary64_21599` `distribute-lft-out--_binary64_21513` `add-cbrt-cube_binary64_21597`
6×	`associate-/l*_binary64_21506`
5×	`flip-+_binary64_21535` `flip3-+_binary64_21564` `add-log-exp_binary64_21600` `div-inv_binary64_21558`
4×	`difference-of-squares_binary64_21530`
3×	`distribute-rgt-out--_binary64_21515` `pow1_binary64_21622`
2×	`cbrt-undiv_binary64_21595` `div-exp_binary64_21612` `frac-2neg_binary64_21572` `clear-num_binary64_21560`
1×	`flip3--_binary64_21565` `diff-log_binary64_21653` `sub-neg_binary64_21554` `frac-sub_binary64_21570` `sub-div_binary64_21568` `flip--_binary64_21536`

Counts

3 → 111

Calls

3 calls:

48.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
9.0ms	(/.f64 x (+.f64 x y))
9.0ms	(/.f64 y (+.f64 x y))

series188.0ms (5%)

Counts

3 → 9

Calls

3 calls:

92.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
51.0ms	(/.f64 y (+.f64 x y))
45.0ms	(/.f64 x (+.f64 x y))

simplify164.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	4921	1617
1	4921	1617

prune133.0ms (3.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	120	4	124

Merged error: 0b

Counts

124 → 4

Compiler

Compiled 1927 to 357 computations (81.5% saved)

localize16.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(exp.f64 (/.f64 (-.f64 x y) (+.f64 x y)))
0.0b	(log.f64 (exp.f64 (/.f64 (-.f64 x y) (+.f64 x y))))
0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

rewrite78.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`*-un-lft-identity_binary64_21561`
61×	`add-sqr-sqrt_binary64_21583`
60×	`times-frac_binary64_21567`
52×	`exp-prod_binary64_21613`
35×	`add-cube-cbrt_binary64_21596`
27×	`log-pow_binary64_21650`
16×	`distribute-lft-out_binary64_21512`
13×	`difference-of-squares_binary64_21530` `distribute-lft-out--_binary64_21513`
6×	`associate-/r/_binary64_21507`
5×	`associate-/l*_binary64_21506` `add-exp-log_binary64_21599` `add-cbrt-cube_binary64_21597`
4×	`add-log-exp_binary64_21600` `associate-/r*_binary64_21505` `pow1_binary64_21622`
3×	`div-sub_binary64_21566` `log-prod_binary64_21647` `flip-+_binary64_21535` `flip3-+_binary64_21564` `div-inv_binary64_21558`
2×	`associate-/l/_binary64_21508` `exp-diff_binary64_21609`
1×	`cbrt-undiv_binary64_21595` `log-div_binary64_21648` `div-exp_binary64_21612` `flip3--_binary64_21565` `rem-log-exp_binary64_21602` `frac-2neg_binary64_21572` `clear-num_binary64_21560` `rem-exp-log_binary64_21601` `flip--_binary64_21536`

Counts

3 → 120

Calls

3 calls:

21.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 x y) (+.f64 x y))))
18.0ms	(exp.f64 (/.f64 (-.f64 x y) (+.f64 x y)))
17.0ms	(/.f64 (-.f64 x y) (+.f64 x y))

series283.0ms (7.5%)

Counts

3 → 9

Calls

3 calls:

112.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 x y) (+.f64 x y))))
92.0ms	(exp.f64 (/.f64 (-.f64 x y) (+.f64 x y)))
79.0ms	(/.f64 (-.f64 x y) (+.f64 x y))

simplify144.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4916	1811
1	4916	1811

prune147.0ms (3.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	129	4	133

Merged error: 0b

Counts

133 → 4

Compiler

Compiled 2016 to 402 computations (80.1% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 x y))
0.0b	(sqrt.f64 (-.f64 x y))
0.1b	(/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y))
0.1b	(*.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y)))

rewrite100.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`*-un-lft-identity_binary64_21561`
86×	`add-sqr-sqrt_binary64_21583`
68×	`times-frac_binary64_21567`
65×	`sqrt-prod_binary64_21577`
44×	`add-cube-cbrt_binary64_21596`
38×	`associate-r_binary64_21501`
17×	`distribute-lft-out_binary64_21512`
12×	`difference-of-squares_binary64_21530` `distribute-lft-out--_binary64_21513`
11×	`add-exp-log_binary64_21599` `add-cbrt-cube_binary64_21597`
10×	`sqrt-div_binary64_21578`
8×	`associate-/l_binary64_21506` `associate-l*_binary64_21502` `pow1_binary64_21622`
6×	`unswap-sqr_binary64_21529`
5×	`flip3--_binary64_21565` `flip--_binary64_21536`
4×	`associate-/r/_binary64_21507` `add-log-exp_binary64_21600` `associate-/r*_binary64_21505`
2×	`cbrt-undiv_binary64_21595` `cbrt-unprod_binary64_21594` `div-exp_binary64_21612` `associate-*l/_binary64_21504` `associate-/l/_binary64_21508` `frac-times_binary64_21571` `rem-sqrt-square_binary64_21574` `prod-exp_binary64_21610` `flip-+_binary64_21535` `sqrt-pow1_binary64_21579` `flip3-+_binary64_21564` `div-inv_binary64_21558` `pow1/2_binary64_21641`
1×	`frac-2neg_binary64_21572` `associate-r/_binary64_21503` `-commutative_binary64_21492` `clear-num_binary64_21560` `pow-prod-down_binary64_21632`

Counts

4 → 164

Calls

4 calls:

38.0ms	(*.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y)))
16.0ms	(/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y))
7.0ms	(sqrt.f64 (-.f64 x y))
7.0ms	(sqrt.f64 (-.f64 x y))

series287.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

86.0ms	(/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y))
83.0ms	(*.f64 (sqrt.f64 (-.f64 x y)) (/.f64 (sqrt.f64 (-.f64 x y)) (+.f64 x y)))
62.0ms	(sqrt.f64 (-.f64 x y))
56.0ms	(sqrt.f64 (-.f64 x y))

simplify167.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	5939	3210

prune208.0ms (5.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	176	4	180

Merged error: 0b

Counts

180 → 4

Compiler

Compiled 3486 to 554 computations (84.1% saved)

regimes126.0ms (3.3%)

Compiler: Compiled 535 to 318 computations (40.6% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	16
1	25	16

end0.0ms (0%)

sample964.0ms (25.6%)

Algorithm

1×

intervals

Results

354.0ms

8000×

body

128

valid

Compiler

Compiled 174 to 103 computations (40.8% saved)

Details

analyze66.0ms (1.7%)

sample20.0ms (0.5%)

simplify301.0ms (8%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

rewrite24.0ms (0.6%)

series73.0ms (1.9%)

simplify91.0ms (2.4%)

prune70.0ms (1.9%)

localize11.0ms (0.3%)

rewrite81.0ms (2.1%)

series188.0ms (5%)

simplify164.0ms (4.4%)

prune133.0ms (3.5%)

localize16.0ms (0.4%)

rewrite78.0ms (2.1%)

series283.0ms (7.5%)

simplify144.0ms (3.8%)

prune147.0ms (3.9%)

localize12.0ms (0.3%)

rewrite100.0ms (2.6%)

series287.0ms (7.6%)

simplify167.0ms (4.4%)

prune208.0ms (5.5%)

regimes126.0ms (3.3%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample964.0ms (25.6%)

Profiling