Details

analyze266.0ms (5.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample64.0ms (1.3%)

Algorithm

1×

intervals

Results

28.0ms	75×	body	1024	valid
12.0ms	53×	body	512	valid
11.0ms	36×	body	2048	valid
4.0ms	77×	body	128	valid
2.0ms	14×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify168.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

prune2.0ms (0%)

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: 54.0b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.8b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
15.7b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_2436`
6×	`add-sqr-sqrt_binary64_2457`
5×	`add-log-exp_binary64_2472` `add-cube-cbrt_binary64_2468` `pow1_binary64_2494`
4×	`add-exp-log_binary64_2471` `log-prod_binary64_2519`
3×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `add-cbrt-cube_binary64_2469` `sqrt-prod_binary64_2451`
2×	`distribute-lft-out_binary64_2389` `log-div_binary64_2520` `sqrt-div_binary64_2452`
1×	`log-pow_binary64_2522` `pow1/2_binary64_2513` `sum-log_binary64_2524` `rem-sqrt-square_binary64_2449` `+-commutative_binary64_2368` `rem-log-exp_binary64_2474` `sqrt-pow1_binary64_2453`

Counts

3 → 42

Calls

3 calls:

7.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
6.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series183.0ms (3.7%)

Counts

3 → 9

Calls

3 calls:

90.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
58.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
35.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify84.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5385	862

prune63.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Merged error: 0b

Counts

52 → 4

Compiler

Compiled 812 to 538 computations (33.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
20.4b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_2457`
15×	`associate-l_binary64_2379`
13×	`add-exp-log_binary64_2471`
10×	`add-cube-cbrt_binary64_2468` `-un-lft-identity_binary64_2436` `associate-r*_binary64_2378`
8×	`unpow-prod-down_binary64_2512` `add-log-exp_binary64_2472`
7×	`unswap-sqr_binary64_2404` `add-cbrt-cube_binary64_2469`
6×	`prod-exp_binary64_2482`
4×	`cube-prod_binary64_2461` `sqr-pow_binary64_2408`
3×	`pow1_binary64_2494`
2×	`*-commutative_binary64_2369` `diff-log_binary64_2525` `cbrt-unprod_binary64_2466` `pow-to-exp_binary64_2502` `pow-exp_binary64_2501`
1×	`flip3--_binary64_2440` `sum-log_binary64_2524` `cube-mult_binary64_2463` `unpow3_binary64_2499` `flip--_binary64_2411` `associate--l+_binary64_2375` `sub-neg_binary64_2429`

Counts

3 → 69

Calls

3 calls:

6.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
6.0ms	(*.f64 3/40 (pow.f64 x 5))
6.0ms	(*.f64 (pow.f64 x 3) 1/6)

series181.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

63.0ms	(*.f64 3/40 (pow.f64 x 5))
63.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
55.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify73.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4845	999
1	4845	999

prune84.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	78	4	82

Merged error: 0b

Counts

82 → 4

Compiler

Compiled 1437 to 1113 computations (22.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 1/2 x))
0.0b	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
0.2b	(/.f64 1/8 (pow.f64 x 3))
9.7b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite76.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64_2436`
43×	`add-sqr-sqrt_binary64_2457`
40×	`times-frac_binary64_2442`
30×	`add-cube-cbrt_binary64_2468`
13×	`unpow-prod-down_binary64_2512` `cube-prod_binary64_2461`
12×	`associate-/r*_binary64_2382`
11×	`add-log-exp_binary64_2472`
10×	`add-exp-log_binary64_2471`
6×	`distribute-lft-out_binary64_2389` `add-cbrt-cube_binary64_2469` `log-prod_binary64_2519`
5×	`sqr-pow_binary64_2408` `pow1_binary64_2494` `difference-of-squares_binary64_2405`
4×	`distribute-lft-out--_binary64_2390` `cube-mult_binary64_2463` `unpow3_binary64_2499`
3×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `associate-/l*_binary64_2383` `div-exp_binary64_2484`
2×	`frac-sub_binary64_2445` `diff-log_binary64_2525` `sum-log_binary64_2524` `log-div_binary64_2520`
1×	`cbrt-undiv_binary64_2467` `log-pow_binary64_2522` `div-inv_binary64_2433` `flip3--_binary64_2440` `pow-to-exp_binary64_2502` `clear-num_binary64_2435` `pow-exp_binary64_2501` `+-commutative_binary64_2368` `frac-2neg_binary64_2447` `rem-log-exp_binary64_2474` `flip--_binary64_2411` `associate--l+_binary64_2375` `sub-neg_binary64_2429`

Counts

4 → 116

Calls

4 calls:

25.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
23.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
7.0ms	(+.f64 x (/.f64 1/2 x))
6.0ms	(/.f64 1/8 (pow.f64 x 3))

series232.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

81.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
65.0ms	(+.f64 x (/.f64 1/2 x))
47.0ms	(/.f64 1/8 (pow.f64 x 3))
39.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))

simplify66.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4907	2282
1	4907	2282

prune143.0ms (2.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	128	4	132

Merged error: 0b

Counts

132 → 4

Compiler

Compiled 2646 to 1888 computations (28.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1/16 (pow.f64 x 5))
0.2b	(/.f64 1/8 (pow.f64 x 3))
12.6b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
17.5b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite114.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64_2457`
71×	`times-frac_binary64_2442`
68×	`*-un-lft-identity_binary64_2436`
46×	`add-cube-cbrt_binary64_2468`
26×	`unpow-prod-down_binary64_2512`
19×	`associate-/r*_binary64_2382`
15×	`add-exp-log_binary64_2471`
14×	`cube-prod_binary64_2461`
11×	`log-prod_binary64_2519`
10×	`sqr-pow_binary64_2408` `difference-of-squares_binary64_2405`
9×	`add-log-exp_binary64_2472`
8×	`add-cbrt-cube_binary64_2469`
6×	`distribute-lft-out--_binary64_2390` `frac-sub_binary64_2445` `associate-/l*_binary64_2383` `div-exp_binary64_2484`
5×	`log-div_binary64_2520` `pow1_binary64_2494`
4×	`distribute-lft-out_binary64_2389` `cube-mult_binary64_2463` `unpow3_binary64_2499`
2×	`flip3-+_binary64_2439` `cbrt-undiv_binary64_2467` `flip-+_binary64_2410` `div-inv_binary64_2433` `diff-log_binary64_2525` `frac-add_binary64_2444` `flip3--_binary64_2440` `pow-to-exp_binary64_2502` `clear-num_binary64_2435` `pow-exp_binary64_2501` `frac-2neg_binary64_2447` `flip--_binary64_2411`
1×	`associate--r+_binary64_2374` `log-pow_binary64_2522` `sum-log_binary64_2524` `rem-log-exp_binary64_2474` `sub-neg_binary64_2429`

Counts

4 → 159

Calls

4 calls:

45.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
38.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
9.0ms	(/.f64 1/8 (pow.f64 x 3))
5.0ms	(/.f64 1/16 (pow.f64 x 5))

series229.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
56.0ms	(/.f64 1/16 (pow.f64 x 5))
50.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
50.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify63.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4929	3605
1	4929	3605

prune255.0ms (5.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	171	4	175

Merged error: 0b

Counts

175 → 4

Compiler

Compiled 4068 to 3235 computations (20.5% saved)

regimes124.0ms (2.5%)

Compiler: Compiled 775 to 596 computations (23.1% saved)

bsearch47.0ms (0.9%)

Steps

Iters	Range		Point
10	0.6133395137864166	213158136477.41104	0.9595302535145758
11	-7910618638.644347	-2.4053904822129223e-21	-1.0827450898202535

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms (0%)

sample2.4s (47.8%)

Algorithm

1×

intervals

Results

984.0ms	2522×	body	1024	valid
418.0ms	1219×	body	2048	valid
275.0ms	1267×	body	512	valid
114.0ms	2351×	body	128	valid
71.0ms	596×	body	256	valid
22.0ms	45×	body	4096	valid

Compiler

Compiled 316 to 244 computations (22.8% saved)

Details

analyze266.0ms (5.3%)

sample64.0ms (1.3%)

simplify168.0ms (3.4%)

prune2.0ms (0%)

localize8.0ms (0.2%)

rewrite21.0ms (0.4%)

series183.0ms (3.7%)

simplify84.0ms (1.7%)

prune63.0ms (1.3%)

localize9.0ms (0.2%)

rewrite24.0ms (0.5%)

series181.0ms (3.6%)

simplify73.0ms (1.5%)

prune84.0ms (1.7%)

localize10.0ms (0.2%)

rewrite76.0ms (1.5%)

series232.0ms (4.7%)

simplify66.0ms (1.3%)

prune143.0ms (2.9%)

localize12.0ms (0.2%)

rewrite114.0ms (2.3%)

series229.0ms (4.6%)

simplify63.0ms (1.3%)

prune255.0ms (5.1%)

regimes124.0ms (2.5%)

bsearch47.0ms (0.9%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.4s (47.8%)

Profiling