Details

analyze1.0s (14.8%)

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
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.6%	0.1%	6
32.8%	67.1%	0.1%	7
34.3%	65.5%	0.1%	8
38.2%	61.2%	0.5%	9
39.6%	53%	7.4%	10
40.3%	52.4%	7.4%	11
41.6%	49.6%	8.8%	12
42%	39.9%	18.1%	13
42.3%	39.6%	18.2%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample46.0ms (0.7%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
10.0ms	118×	body	128	invalid
3.0ms	73×	body	128	nan

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify309.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (149.0ms)

Iter	Nodes	Cost
0	4740	19
1	4740	19

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 2.3b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 k (+.f64 k 10))
0.0b	(*.f64 a (pow.f64 k m))
2.3b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-exp-log_binary64_2134`
17×	`add-sqr-sqrt_binary64_2120`
12×	`add-cbrt-cube_binary64_2132` `*-un-lft-identity_binary64_2099`
11×	`associate-r_binary64_2041`
10×	`add-cube-cbrt_binary64_2131`
7×	`prod-exp_binary64_2145`
6×	`associate-l_binary64_2042`
5×	`pow1_binary64_2157`
4×	`unpow-prod-down_binary64_2175` `div-exp_binary64_2147` `unswap-sqr_binary64_2067`
3×	`times-frac_binary64_2105` `add-log-exp_binary64_2135` `associate-/r*_binary64_2045` `cbrt-unprod_binary64_2129`
2×	`sqr-pow_binary64_2071` `cbrt-undiv_binary64_2130` `associate-r/_binary64_2043` `flip3-+_binary64_2102` `pow-exp_binary64_2164` `-commutative_binary64_2032` `pow-to-exp_binary64_2165` `associate-/r/_binary64_2047` `flip-+_binary64_2073`
1×	`distribute-lft-out_binary64_2052` `distribute-rgt-in_binary64_2051` `distribute-lft-in_binary64_2050` `frac-2neg_binary64_2110` `pow-prod-down_binary64_2167` `clear-num_binary64_2098` `associate-/l*_binary64_2046` `div-inv_binary64_2096`

Counts

3 → 73

Calls

3 calls:

8.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))
7.0ms	(*.f64 k (+.f64 k 10))
6.0ms	(*.f64 a (pow.f64 k m))

series408.0ms (5.9%)

Counts

3 → 9

Calls

3 calls:

248.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))
106.0ms	(*.f64 a (pow.f64 k m))
53.0ms	(*.f64 k (+.f64 k 10))

simplify90.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4918	1205
1	4918	1205

prune80.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	3	83

Merged error: 2.2b

Counts

83 → 3

Compiler

Compiled 1585 to 853 computations (46.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 a (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
0.0b	(/.f64 (.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (pow.f64 k m)) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
16.4b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
16.4b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

rewrite39.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_2120` `add-exp-log_binary64_2134`
25×	`add-cube-cbrt_binary64_2131` `*-un-lft-identity_binary64_2099`
24×	`times-frac_binary64_2105` `sqrt-prod_binary64_2114`
15×	`add-cbrt-cube_binary64_2132`
12×	`associate-/r*_binary64_2045`
11×	`div-exp_binary64_2147`
8×	`sqrt-div_binary64_2115`
6×	`pow1_binary64_2157` `prod-exp_binary64_2145`
5×	`cbrt-undiv_binary64_2130`
4×	`flip3-+_binary64_2102` `associate-/r/_binary64_2047` `add-log-exp_binary64_2135` `associate-/l*_binary64_2046` `flip-+_binary64_2073`
2×	`pow-exp_binary64_2164` `pow-to-exp_binary64_2165` `frac-2neg_binary64_2110` `rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `clear-num_binary64_2098` `div-inv_binary64_2096` `sqrt-pow1_binary64_2116` `cbrt-unprod_binary64_2129`
1×	`associate-/l/_binary64_2048` `associate-*l/_binary64_2044`

Counts

4 → 107

Calls

4 calls:

15.0ms	(/.f64 (.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (pow.f64 k m)) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
6.0ms	(/.f64 a (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

series437.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

242.0ms	(/.f64 (.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (pow.f64 k m)) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
133.0ms	(/.f64 a (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
33.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
29.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4979	2854
1	4979	2854

prune173.0ms (2.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	118	4	122

Merged error: 2.2b

Counts

122 → 4

Compiler

Compiled 3520 to 2364 computations (32.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 k (+.f64 k 10))
0.0b	(*.f64 a (pow.f64 k m))
0.2b	(/.f64 1 (/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m))))
2.1b	(/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m)))

rewrite46.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-exp-log_binary64_2134`
36×	`times-frac_binary64_2105`
34×	`add-sqr-sqrt_binary64_2120`
29×	`*-un-lft-identity_binary64_2099`
27×	`add-cube-cbrt_binary64_2131`
26×	`div-exp_binary64_2147`
22×	`add-cbrt-cube_binary64_2132`
16×	`prod-exp_binary64_2145`
11×	`associate-r_binary64_2041`
8×	`associate-/r*_binary64_2045`
7×	`cbrt-undiv_binary64_2130` `pow1_binary64_2157`
6×	`associate-l_binary64_2042` `associate-/l*_binary64_2046` `div-inv_binary64_2096`
5×	`1-exp_binary64_2140` `pow-exp_binary64_2164` `rec-exp_binary64_2146` `pow-to-exp_binary64_2165`
4×	`unpow-prod-down_binary64_2175` `add-log-exp_binary64_2135` `unswap-sqr_binary64_2067` `cbrt-unprod_binary64_2129`
2×	`sqr-pow_binary64_2071` `associate-r/_binary64_2043` `flip3-+_binary64_2102` `-commutative_binary64_2032` `associate-/l/_binary64_2048` `frac-2neg_binary64_2110` `clear-num_binary64_2098` `flip-+_binary64_2073`
1×	`pow-flip_binary64_2170` `distribute-lft-out_binary64_2052` `distribute-rgt-in_binary64_2051` `inv-pow_binary64_2181` `distribute-lft-in_binary64_2050` `associate-/r/_binary64_2047` `pow-prod-down_binary64_2167`

Counts

4 → 135

Calls

4 calls:

10.0ms	(/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m)))
10.0ms	(/.f64 1 (/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m))))
7.0ms	(*.f64 k (+.f64 k 10))
6.0ms	(*.f64 a (pow.f64 k m))

series564.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

211.0ms	(/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m)))
208.0ms	(/.f64 1 (/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m))))
91.0ms	(*.f64 a (pow.f64 k m))
54.0ms	(*.f64 k (+.f64 k 10))

simplify61.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5285	3007

prune156.0ms (2.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	1	1	2
Picked	0	1	1
Done	1	0	1
Total	148	3	151

Merged error: 0.1b

Counts

151 → 3

Compiler

Compiled 3150 to 1870 computations (40.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))))
16.4b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
16.4b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
16.4b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

rewrite98.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

396×	`times-frac_binary64_2105`
324×	`sqrt-prod_binary64_2114`
215×	`add-sqr-sqrt_binary64_2120`
212×	`add-cube-cbrt_binary64_2131` `*-un-lft-identity_binary64_2099`
30×	`sqrt-div_binary64_2115`
24×	`associate-/l*_binary64_2046`
22×	`associate-/r/_binary64_2047`
14×	`flip3-+_binary64_2102` `flip-+_binary64_2073`
11×	`div-inv_binary64_2096`
9×	`add-cbrt-cube_binary64_2132` `associate-/r*_binary64_2045` `add-exp-log_binary64_2134`
7×	`pow1_binary64_2157`
4×	`add-log-exp_binary64_2135`
3×	`cbrt-undiv_binary64_2130` `div-exp_binary64_2147` `rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `sqrt-pow1_binary64_2116`
1×	`associate-/l/_binary64_2048` `frac-2neg_binary64_2110` `clear-num_binary64_2098`

Counts

4 → 311

Calls

4 calls:

18.0ms	(/.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))))
5.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

series409.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

327.0ms	(/.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))))
29.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
27.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
25.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

simplify186.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

323 → 323

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4908	15881
1	4908	15881

prune1.1s (16.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	323	0	323
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	323	3	326

Merged error: 0.1b

Counts

326 → 3

Compiler

Compiled 16125 to 11598 computations (28.1% saved)

regimes53.0ms (0.8%)

Compiler: Compiled 228 to 198 computations (13.2% saved)

bsearch13.0ms (0.2%)

Steps

Iters	Range		Point
3	9.897213125238762e+26	1.1677742855101616e+27	1.134389353075233e+27

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	97
1	42	97

end0.0ms (0%)

sample1.4s (20.7%)

Algorithm

1×

intervals

Results

568.0ms	8000×	body	128	valid
284.0ms	3299×	body	128	invalid
96.0ms	1954×	body	128	nan

Compiler

Compiled 153 to 123 computations (19.6% saved)

Details

analyze1.0s (14.8%)

sample46.0ms (0.7%)

simplify309.0ms (4.5%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite27.0ms (0.4%)

series408.0ms (5.9%)

simplify90.0ms (1.3%)

prune80.0ms (1.2%)

localize12.0ms (0.2%)

rewrite39.0ms (0.6%)

series437.0ms (6.3%)

simplify71.0ms (1%)

prune173.0ms (2.5%)

localize14.0ms (0.2%)

rewrite46.0ms (0.7%)

series564.0ms (8.1%)

simplify61.0ms (0.9%)

prune156.0ms (2.3%)

localize14.0ms (0.2%)

rewrite98.0ms (1.4%)

series409.0ms (5.9%)

simplify186.0ms (2.7%)

prune1.1s (16.5%)

regimes53.0ms (0.8%)

bsearch13.0ms (0.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.4s (20.7%)

Profiling