Details

analyze1.0s (15.5%)

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)

sample43.0ms (0.7%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
7.0ms	88×	body	128	invalid
3.0ms	76×	body	128	nan

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify317.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (147.0ms)

Iter	Nodes	Cost
0	4740	19
1	4740	19

prune4.0ms (0.1%)

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: 1.8b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize9.0ms (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))
1.8b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))

rewrite29.0ms (0.5%)

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:

9.0ms	(*.f64 a (pow.f64 k m))
8.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))
6.0ms	(*.f64 k (+.f64 k 10))

series425.0ms (6.5%)

Counts

3 → 9

Calls

3 calls:

260.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))
110.0ms	(*.f64 a (pow.f64 k m))
55.0ms	(*.f64 k (+.f64 k 10))

simplify86.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4918	1205
1	4918	1205

prune84.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	4	83

Merged error: 1.8b

Counts

83 → 4

Compiler

Compiled 1584 to 850 computations (46.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 k)
0.6b	(cbrt.f64 k)
0.6b	(cbrt.f64 k)
1.8b	(/.f64 (.f64 (.f64 a (pow.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m)) (+.f64 1 (.f64 k (+.f64 k 10))))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-exp-log_binary64_2134`
30×	`prod-exp_binary64_2145`
16×	`div-exp_binary64_2147`
13×	`add-cbrt-cube_binary64_2132`
11×	`pow-exp_binary64_2164`
9×	`add-sqr-sqrt_binary64_2120` `add-cube-cbrt_binary64_2131` `*-un-lft-identity_binary64_2099` `cbrt-prod_binary64_2127`
8×	`pow-to-exp_binary64_2165`
4×	`pow1_binary64_2157` `add-log-exp_binary64_2135`
3×	`cbrt-undiv_binary64_2130` `pow1/3_binary64_2178` `times-frac_binary64_2105` `associate-/r*_binary64_2045` `cbrt-unprod_binary64_2129`
2×	`associate-/r/_binary64_2047`
1×	`flip3-+_binary64_2102` `frac-2neg_binary64_2110` `clear-num_binary64_2098` `associate-/l*_binary64_2046` `div-inv_binary64_2096` `flip-+_binary64_2073`

Counts

4 → 71

Calls

4 calls:

13.0ms	(/.f64 (.f64 (.f64 a (pow.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m)) (+.f64 1 (.f64 k (+.f64 k 10))))
1.0ms	(cbrt.f64 k)
1.0ms	(cbrt.f64 k)
1.0ms	(cbrt.f64 k)

series1.1s (16.9%)

Counts

4 → 12

Calls

4 calls:

650.0ms	(/.f64 (.f64 (.f64 a (pow.f64 (.f64 (cbrt.f64 k) (cbrt.f64 k)) m)) (pow.f64 (cbrt.f64 k) m)) (+.f64 1 (.f64 k (+.f64 k 10))))
157.0ms	(cbrt.f64 k)
154.0ms	(cbrt.f64 k)
139.0ms	(cbrt.f64 k)

simplify46.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5108	1630

prune95.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	83	4	87

Merged error: 1.8b

Counts

87 → 4

Compiler

Compiled 2168 to 1127 computations (48% saved)

localize10.0ms (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))
0.4b	(/.f64 1 (+.f64 1 (*.f64 k (+.f64 k 10))))
1.6b	(.f64 (.f64 a (pow.f64 k m)) (/.f64 1 (+.f64 1 (*.f64 k (+.f64 k 10)))))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-exp-log_binary64_2134`
32×	`prod-exp_binary64_2145`
31×	`add-sqr-sqrt_binary64_2120`
26×	`-un-lft-identity_binary64_2099` `associate-r*_binary64_2041`
24×	`add-cube-cbrt_binary64_2131`
22×	`add-cbrt-cube_binary64_2132`
18×	`times-frac_binary64_2105`
10×	`div-exp_binary64_2147`
9×	`pow1_binary64_2157`
8×	`cbrt-unprod_binary64_2129`
7×	`associate-l_binary64_2042`
5×	`1-exp_binary64_2140` `pow-exp_binary64_2164` `rec-exp_binary64_2146` `pow-to-exp_binary64_2165`
4×	`unpow-prod-down_binary64_2175` `associate-/r/_binary64_2047` `add-log-exp_binary64_2135` `unswap-sqr_binary64_2067`
3×	`cbrt-undiv_binary64_2130` `associate-r/_binary64_2043` `flip3-+_binary64_2102` `-commutative_binary64_2032` `associate-/r_binary64_2045` `associate-/l_binary64_2046` `flip-+_binary64_2073`
2×	`sqr-pow_binary64_2071` `pow-prod-down_binary64_2167` `div-inv_binary64_2096`
1×	`pow-flip_binary64_2170` `distribute-lft-out_binary64_2052` `un-div-inv_binary64_2097` `distribute-rgt-in_binary64_2051` `inv-pow_binary64_2181` `distribute-lft-in_binary64_2050` `frac-2neg_binary64_2110` `clear-num_binary64_2098`

Counts

4 → 128

Calls

4 calls:

12.0ms	(.f64 (.f64 a (pow.f64 k m)) (/.f64 1 (+.f64 1 (*.f64 k (+.f64 k 10)))))
7.0ms	(/.f64 1 (+.f64 1 (*.f64 k (+.f64 k 10))))
6.0ms	(*.f64 k (+.f64 k 10))
5.0ms	(*.f64 a (pow.f64 k m))

series450.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

254.0ms	(.f64 (.f64 a (pow.f64 k m)) (/.f64 1 (+.f64 1 (*.f64 k (+.f64 k 10)))))
111.0ms	(*.f64 a (pow.f64 k m))
59.0ms	(*.f64 k (+.f64 k 10))
26.0ms	(/.f64 1 (+.f64 1 (*.f64 k (+.f64 k 10))))

simplify76.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4965	2322
1	4965	2322

prune134.0ms (2.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	140	4	144

Merged error: 1.8b

Counts

144 → 4

Compiler

Compiled 2906 to 1716 computations (40.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
0.1b	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
15.2b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
15.2b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

rewrite86.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

146×	`add-sqr-sqrt_binary64_2120`
134×	`times-frac_binary64_2105`
76×	`add-cube-cbrt_binary64_2131` `*-un-lft-identity_binary64_2099` `sqrt-prod_binary64_2114`
48×	`associate-r_binary64_2041`
45×	`unpow-prod-down_binary64_2175`
33×	`add-exp-log_binary64_2134`
24×	`associate-l_binary64_2042`
21×	`unswap-sqr_binary64_2067`
19×	`sqr-pow_binary64_2071`
18×	`add-cbrt-cube_binary64_2132`
13×	`div-exp_binary64_2147`
10×	`sqrt-div_binary64_2115`
8×	`pow1_binary64_2157` `prod-exp_binary64_2145`
7×	`associate-/l*_binary64_2046`
6×	`associate-/r/_binary64_2047` `associate-/r*_binary64_2045`
5×	`cbrt-undiv_binary64_2130` `flip3-+_binary64_2102` `flip-+_binary64_2073`
4×	`add-log-exp_binary64_2135` `cbrt-unprod_binary64_2129`
3×	`pow-exp_binary64_2164` `pow-to-exp_binary64_2165` `div-inv_binary64_2096`
2×	`rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `sqrt-pow1_binary64_2116`
1×	`associate-r/_binary64_2043` `-commutative_binary64_2032` `associate-*l/_binary64_2044` `frac-2neg_binary64_2110` `pow-prod-down_binary64_2167` `clear-num_binary64_2098` `frac-times_binary64_2109`

Counts

4 → 218

Calls

4 calls:

40.0ms	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
8.0ms	(/.f64 (pow.f64 k m) (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))))

series460.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

255.0ms	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
137.0ms	(/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
37.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
30.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

simplify128.0ms (2%)

Algorithm

1×	egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4958	7864
1	4958	7864

prune424.0ms (6.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	230	4	234

Merged error: 1.8b

Counts

234 → 4

Compiler

Compiled 7929 to 5186 computations (34.6% saved)

regimes37.0ms (0.6%)

Compiler: Compiled 234 to 198 computations (15.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	34
1	22	34

end0.0ms (0%)

sample1.4s (20.8%)

Algorithm

1×

intervals

Results

544.0ms	8000×	body	128	valid
271.0ms	3157×	body	128	invalid
87.0ms	1966×	body	128	nan

Compiler

Compiled 114 to 91 computations (20.2% saved)

Details

analyze1.0s (15.5%)

sample43.0ms (0.7%)

simplify317.0ms (4.9%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

rewrite29.0ms (0.5%)

series425.0ms (6.5%)

simplify86.0ms (1.3%)

prune84.0ms (1.3%)

localize15.0ms (0.2%)

rewrite27.0ms (0.4%)

series1.1s (16.9%)

simplify46.0ms (0.7%)

prune95.0ms (1.5%)

localize10.0ms (0.2%)

rewrite43.0ms (0.7%)

series450.0ms (6.9%)

simplify76.0ms (1.2%)

prune134.0ms (2.1%)

localize12.0ms (0.2%)

rewrite86.0ms (1.3%)

series460.0ms (7.1%)

simplify128.0ms (2%)

prune424.0ms (6.5%)

regimes37.0ms (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.4s (20.8%)

Profiling