Details

analyze42.0ms (0.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
25%	25%	50%	4
25%	25%	50%	5
31.2%	18.7%	50%	6
34.3%	15.6%	50%	7
39%	10.9%	50%	8
40.6%	8.6%	50.8%	9
42.9%	5.9%	51.2%	10
43.7%	4.5%	51.8%	11
44.9%	3%	52.1%	12
45.3%	2.3%	52.4%	13
45.9%	1.5%	52.6%	14

Compiler

Compiled 15 to 14 computations (6.7% saved)

sample19.0ms (0.3%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 29 to 29 computations (0% saved)

simplify285.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	487	18
1	487	18

prune9.0ms (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 → 2

Compiler

Compiled 38 to 35 computations (7.9% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
0.3b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
0.3b	(/.f64 1 (*.f64 x 9))
0.3b	(*.f64 3 (sqrt.f64 x))

rewrite66.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-exp-log_binary64_8641` `*-un-lft-identity_binary64_8603`
21×	`add-sqr-sqrt_binary64_8625`
16×	`add-cbrt-cube_binary64_8639`
15×	`add-cube-cbrt_binary64_8638`
14×	`cancel-sign-sub-inv_binary64_8569`
12×	`times-frac_binary64_8609`
9×	`add-log-exp_binary64_8642` `pow1_binary64_8664`
8×	`associate--l+_binary64_8540`
6×	`div-exp_binary64_8654` `associate-/l_binary64_8548` `associate-r*_binary64_8543`
5×	`distribute-lft-out--_binary64_8555` `div-inv_binary64_8600` `prod-exp_binary64_8652`
4×	`sqrt-prod_binary64_8619` `cbrt-undiv_binary64_8637`
3×	`cbrt-unprod_binary64_8636` `associate-l_binary64_8544` `diff-log_binary64_8695`
2×	`frac-sub_binary64_8612` `flip3--_binary64_8607` `associate-/r*_binary64_8547` `clear-num_binary64_8602` `1-exp_binary64_8647` `frac-2neg_binary64_8614` `flip--_binary64_8578` `rec-exp_binary64_8653` `sub-neg_binary64_8596` `pow-flip_binary64_8677` `pow-prod-down_binary64_8674` `unswap-sqr_binary64_8571`
1×	`difference-of-squares_binary64_8572` `associate--l-_binary64_8541` `inv-pow_binary64_8688` `*-commutative_binary64_8534`

Counts

4 → 105

Calls

4 calls:

29.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
7.0ms	(*.f64 3 (sqrt.f64 x))
6.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
6.0ms	(/.f64 1 (*.f64 x 9))

series260.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

101.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
84.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
45.0ms	(*.f64 3 (sqrt.f64 x))
29.0ms	(/.f64 1 (*.f64 x 9))

simplify110.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4986	1569
1	4986	1569

prune194.0ms (3.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	111	6	117
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	112	7	119

Merged error: 0b

Counts

119 → 7

Compiler

Compiled 2163 to 1552 computations (28.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
0.3b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
0.3b	(/.f64 (/.f64 1 x) 9)
0.3b	(*.f64 3 (sqrt.f64 x))

rewrite94.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

147×	`times-frac_binary64_8609`
94×	`add-sqr-sqrt_binary64_8625`
93×	`*-un-lft-identity_binary64_8603`
88×	`add-cube-cbrt_binary64_8638`
50×	`cancel-sign-sub-inv_binary64_8569`
44×	`associate--l+_binary64_8540`
20×	`add-exp-log_binary64_8641`
16×	`associate-/l*_binary64_8548` `add-cbrt-cube_binary64_8639`
11×	`div-inv_binary64_8600`
9×	`add-log-exp_binary64_8642`
8×	`div-exp_binary64_8654`
6×	`associate-r_binary64_8543` `pow1_binary64_8664`
5×	`cbrt-undiv_binary64_8637`
4×	`sqrt-prod_binary64_8619` `associate-/r*_binary64_8547`
3×	`associate-l_binary64_8544` `distribute-lft-out--_binary64_8555` `diff-log_binary64_8695`
2×	`frac-sub_binary64_8612` `flip3--_binary64_8607` `cbrt-unprod_binary64_8636` `clear-num_binary64_8602` `frac-2neg_binary64_8614` `prod-exp_binary64_8652` `flip--_binary64_8578` `sub-neg_binary64_8596` `unswap-sqr_binary64_8571`
1×	`difference-of-squares_binary64_8572` `associate--l-_binary64_8541` `associate-/l/_binary64_8550` `*-commutative_binary64_8534` `1-exp_binary64_8647` `rec-exp_binary64_8653` `pow-prod-down_binary64_8674`

Counts

4 → 184

Calls

4 calls:

42.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
15.0ms	(/.f64 (/.f64 1 x) 9)
11.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
6.0ms	(*.f64 3 (sqrt.f64 x))

series276.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

120.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
78.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
56.0ms	(*.f64 3 (sqrt.f64 x))
22.0ms	(/.f64 (/.f64 1 x) 9)

simplify118.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5216	3255

prune312.0ms (5.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	196	7	203

Merged error: 0b

Counts

203 → 7

Compiler

Compiled 3803 to 2697 computations (29.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 y (sqrt.f64 x))
0.2b	(/.f64 3 (/.f64 y (sqrt.f64 x)))
0.3b	(/.f64 1 (*.f64 x 9))
0.4b	(/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x))))

rewrite137.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

852×	`times-frac_binary64_8609`
416×	`add-cube-cbrt_binary64_8638` `add-sqr-sqrt_binary64_8625` `*-un-lft-identity_binary64_8603`
156×	`sqrt-prod_binary64_8619`
100×	`associate-/r*_binary64_8547`
43×	`add-exp-log_binary64_8641`
25×	`add-cbrt-cube_binary64_8639`
24×	`div-inv_binary64_8600`
23×	`div-exp_binary64_8654`
12×	`associate-/l*_binary64_8548` `cbrt-undiv_binary64_8637`
8×	`pow1_binary64_8664`
6×	`associate-/r/_binary64_8549`
5×	`1-exp_binary64_8647` `rec-exp_binary64_8653`
4×	`add-log-exp_binary64_8642` `clear-num_binary64_8602` `frac-2neg_binary64_8614`
3×	`prod-exp_binary64_8652` `pow-flip_binary64_8677`
2×	`inv-pow_binary64_8688`
1×	`cbrt-unprod_binary64_8636` `pow-prod-down_binary64_8674`

Counts

4 → 485

Calls

4 calls:

34.0ms	(/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x))))
10.0ms	(/.f64 3 (/.f64 y (sqrt.f64 x)))
6.0ms	(/.f64 1 (*.f64 x 9))
5.0ms	(/.f64 y (sqrt.f64 x))

series325.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(/.f64 1 (/.f64 3 (/.f64 y (sqrt.f64 x))))
105.0ms	(/.f64 3 (/.f64 y (sqrt.f64 x)))
81.0ms	(/.f64 y (sqrt.f64 x))
33.0ms	(/.f64 1 (*.f64 x 9))

simplify301.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 0 (133.0ms)

Iter	Nodes	Cost
0	4925	11028
1	4925	11028

prune1.3s (21.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	497	0	497
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	497	7	504

Merged error: 0b

Counts

504 → 7

Compiler

Compiled 12622 to 7674 computations (39.2% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1/3 (sqrt.f64 x))))
0.2b	(*.f64 y (/.f64 1/3 (sqrt.f64 x)))
0.3b	(/.f64 1 (*.f64 x 9))
0.4b	(/.f64 1/3 (sqrt.f64 x))

rewrite48.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64_8625`
44×	`times-frac_binary64_8609`
37×	`add-cube-cbrt_binary64_8638` `*-un-lft-identity_binary64_8603`
22×	`add-exp-log_binary64_8641` `sqrt-prod_binary64_8619` `associate-r_binary64_8543`
16×	`add-cbrt-cube_binary64_8639`
9×	`add-log-exp_binary64_8642` `pow1_binary64_8664`
8×	`cancel-sign-sub-inv_binary64_8569` `associate--l+_binary64_8540`
7×	`associate-/r*_binary64_8547`
6×	`div-exp_binary64_8654` `associate-/l*_binary64_8548`
5×	`prod-exp_binary64_8652`
4×	`cbrt-undiv_binary64_8637` `div-inv_binary64_8600`
3×	`cbrt-unprod_binary64_8636` `associate-l_binary64_8544` `associate-*r/_binary64_8545` `diff-log_binary64_8695` `unswap-sqr_binary64_8571`
2×	`frac-sub_binary64_8612` `flip3--_binary64_8607` `clear-num_binary64_8602` `1-exp_binary64_8647` `frac-2neg_binary64_8614` `flip--_binary64_8578` `rec-exp_binary64_8653` `sub-neg_binary64_8596` `pow-flip_binary64_8677` `pow-prod-down_binary64_8674`
1×	`associate--l-_binary64_8541` `inv-pow_binary64_8688` `*-commutative_binary64_8534`

Counts

4 → 133

Calls

4 calls:

13.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1/3 (sqrt.f64 x))))
12.0ms	(*.f64 y (/.f64 1/3 (sqrt.f64 x)))
5.0ms	(/.f64 1 (*.f64 x 9))
5.0ms	(/.f64 1/3 (sqrt.f64 x))

series284.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

105.0ms	(*.f64 y (/.f64 1/3 (sqrt.f64 x)))
82.0ms	(/.f64 1/3 (sqrt.f64 x))
71.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 y (/.f64 1/3 (sqrt.f64 x))))
25.0ms	(/.f64 1 (*.f64 x 9))

simplify125.0ms (2%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4926	1981
1	4926	1981

prune218.0ms (3.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	145	7	152

Merged error: 0b

Counts

152 → 7

Compiler

Compiled 2728 to 1888 computations (30.8% saved)

regimes181.0ms (2.9%)

Compiler: Compiled 1370 to 1237 computations (9.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	67	21
1	67	21

end0.0ms (0%)

sample1.4s (22%)

Algorithm

1×

intervals

Results

493.0ms	8000×	body	128	valid
6.0ms	100×	body	128	invalid

Compiler

Compiled 489 to 443 computations (9.4% saved)

Details

analyze42.0ms (0.7%)

sample19.0ms (0.3%)

simplify285.0ms (4.6%)

prune9.0ms (0.1%)

localize20.0ms (0.3%)

rewrite66.0ms (1.1%)

series260.0ms (4.2%)

simplify110.0ms (1.8%)

prune194.0ms (3.1%)

localize10.0ms (0.2%)

rewrite94.0ms (1.5%)

series276.0ms (4.5%)

simplify118.0ms (1.9%)

prune312.0ms (5.1%)

localize12.0ms (0.2%)

rewrite137.0ms (2.2%)

series325.0ms (5.3%)

simplify301.0ms (4.9%)

prune1.3s (21.8%)

localize17.0ms (0.3%)

rewrite48.0ms (0.8%)

series284.0ms (4.6%)

simplify125.0ms (2%)

prune218.0ms (3.5%)

regimes181.0ms (2.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (22%)

Profiling