Details

analyze1.1s (0.7%)

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
0%	99.9%	0.1%	4
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample198.0ms (0.1%)

Algorithm

1×

intervals

Results

46.0ms	93×	body	1024	valid
38.0ms	56×	body	2048	valid
37.0ms	45×	body	1024	nan
15.0ms	66×	body	128	overflowed
12.0ms	35×	body	512	valid
10.0ms	21×	body	512	nan
8.0ms	8×	body	1024	invalid
5.0ms	55×	body	128	valid
4.0ms	17×	body	256	valid
4.0ms	7×	body	512	invalid
3.0ms	11×	body	256	nan
2.0ms	19×	body	128	nan
1.0ms	8×	body	128	invalid
1.0ms	2×	body	256	invalid

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify51.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4814	19
1	4814	19

prune3.0ms (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: 33.4b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(pow.f64 x (/.f64 1 n))
2.3b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite21.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
16×	`unpow-prod-down_binary64`
13×	`pow-unpow_binary64`
12×	`add-cube-cbrt_binary64`
9×	`difference-of-squares_binary64` `times-frac_binary64`
8×	`sqr-pow_binary64`
7×	`cancel-sign-sub-inv_binary64`
4×	`add-log-exp_binary64`
3×	`pow1_binary64` `add-exp-log_binary64` `distribute-lft-out--_binary64`
2×	`add-cbrt-cube_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `div-inv_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

2 → 57

Calls

2 calls:

12.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
4.0ms	(pow.f64 x (/.f64 1 n))

series339.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

257.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
82.0ms	(pow.f64 x (/.f64 1 n))

simplify49.0ms (0%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5123	1288

prune373.0ms (0.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	7	64

Merged error: 20.9b

Counts

64 → 7

Compiler

Compiled 3889 to 2982 computations (23.3% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 x (/.f64 1 n))
0.0b	(pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))) 3)
0.1b	(cbrt.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))) 3))
2.3b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite62.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`unpow-prod-down_binary64`
80×	`add-sqr-sqrt_binary64`
55×	`*-un-lft-identity_binary64`
45×	`difference-of-squares_binary64`
36×	`cbrt-prod_binary64`
34×	`sqr-pow_binary64`
30×	`cube-prod_binary64`
20×	`add-cube-cbrt_binary64`
16×	`pow-unpow_binary64`
15×	`distribute-lft-out--_binary64`
9×	`times-frac_binary64`
7×	`cancel-sign-sub-inv_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64`
5×	`distribute-lft-out_binary64` `add-cbrt-cube_binary64`
4×	`cube-div_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`cbrt-div_binary64` `pow-to-exp_binary64` `pow-pow_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`sub-neg_binary64` `rem-cbrt-cube_binary64` `diff-log_binary64` `pow1/3_binary64` `rem-cube-cbrt_binary64` `div-inv_binary64`

Counts

4 → 153

Calls

4 calls:

14.0ms	(cbrt.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))) 3))
13.0ms	(pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))) 3)
12.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
4.0ms	(pow.f64 x (/.f64 1 n))

series963.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

393.0ms	(pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))) 3)
251.0ms	(cbrt.f64 (pow.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n))) 3))
242.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
76.0ms	(pow.f64 x (/.f64 1 n))

simplify69.0ms (0%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5353	4822

prune278.0ms (0.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	164	8	172

Merged error: 20.9b

Counts

172 → 8

Compiler

Compiled 4824 to 3561 computations (26.2% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 (sqrt.f64 (pow.f64 x (/.f64 1 n))) (pow.f64 (+.f64 x 1) (/.f64 1/2 n))) (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (sqrt.f64 (pow.f64 x (/.f64 1 n)))))
0.0b	(sqrt.f64 (pow.f64 x (/.f64 1 n)))
0.0b	(sqrt.f64 (pow.f64 x (/.f64 1 n)))
2.8b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (sqrt.f64 (pow.f64 x (/.f64 1 n))))

rewrite71.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary64`
53×	`sqrt-prod_binary64`
31×	`unpow-prod-down_binary64`
30×	`cancel-sign-sub-inv_binary64`
25×	`*-un-lft-identity_binary64`
24×	`difference-of-squares_binary64`
21×	`sqr-pow_binary64`
19×	`add-cube-cbrt_binary64`
16×	`associate-r_binary64`
11×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `rem-sqrt-square_binary64`
4×	`flip3--_binary64` `associate-l_binary64` `flip--_binary64` `frac-times_binary64`
3×	`flip3-+_binary64` `sub-neg_binary64` `flip-+_binary64`
2×	`pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `distribute-lft-out--_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 134

Calls

4 calls:

32.0ms	(*.f64 (+.f64 (sqrt.f64 (pow.f64 x (/.f64 1 n))) (pow.f64 (+.f64 x 1) (/.f64 1/2 n))) (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (sqrt.f64 (pow.f64 x (/.f64 1 n)))))
13.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (sqrt.f64 (pow.f64 x (/.f64 1 n))))
3.0ms	(sqrt.f64 (pow.f64 x (/.f64 1 n)))
3.0ms	(sqrt.f64 (pow.f64 x (/.f64 1 n)))

series1.3s (0.9%)

Counts

4 → 12

Calls

4 calls:

725.0ms	(*.f64 (+.f64 (sqrt.f64 (pow.f64 x (/.f64 1 n))) (pow.f64 (+.f64 x 1) (/.f64 1/2 n))) (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (sqrt.f64 (pow.f64 x (/.f64 1 n)))))
365.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (sqrt.f64 (pow.f64 x (/.f64 1 n))))
116.0ms	(sqrt.f64 (pow.f64 x (/.f64 1 n)))
107.0ms	(sqrt.f64 (pow.f64 x (/.f64 1 n)))

simplify108.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4953	5280
1	4953	5280

prune405.0ms (0.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	145	9	154

Merged error: 20.9b

Counts

154 → 9

Compiler

Compiled 7054 to 5148 computations (27% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (sqrt.f64 (pow.f64 x (/.f64 1 n))))) (cbrt.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (sqrt.f64 (pow.f64 x (/.f64 1 n))))))
2.8b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (sqrt.f64 (pow.f64 x (/.f64 1 n))))
2.8b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (sqrt.f64 (pow.f64 x (/.f64 1 n))))
2.8b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (sqrt.f64 (pow.f64 x (/.f64 1 n))))

rewrite133.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

168×	`add-sqr-sqrt_binary64`
96×	`difference-of-squares_binary64`
90×	`sqrt-prod_binary64`
84×	`cbrt-prod_binary64`
62×	`unpow-prod-down_binary64`
56×	`sqr-pow_binary64`
41×	`*-un-lft-identity_binary64`
30×	`cancel-sign-sub-inv_binary64`
27×	`swap-sqr_binary64`
21×	`add-cube-cbrt_binary64`
19×	`associate-r_binary64` `associate-l_binary64`
12×	`cbrt-div_binary64`
11×	`pow1_binary64`
10×	`add-log-exp_binary64`
9×	`flip3--_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
6×	`pow1/3_binary64` `add-exp-log_binary64`
4×	`add-cbrt-cube_binary64` `unswap-sqr_binary64` `frac-times_binary64`
3×	`sub-neg_binary64` `diff-log_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 197

Calls

4 calls:

43.0ms	(*.f64 (cbrt.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (sqrt.f64 (pow.f64 x (/.f64 1 n))))) (cbrt.f64 (-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (sqrt.f64 (pow.f64 x (/.f64 1 n))))))
14.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (sqrt.f64 (pow.f64 x (/.f64 1 n))))
14.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (sqrt.f64 (pow.f64 x (/.f64 1 n))))
14.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (sqrt.f64 (pow.f64 x (/.f64 1 n))))

series2.4min (96.3%)

Calls

3 calls:

353.0ms

(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (sqrt.f64 (pow.f64 x (/.f64 1 n))))

346.0ms

(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (sqrt.f64 (pow.f64 x (/.f64 1 n))))

322.0ms

(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1/2 n)) (sqrt.f64 (pow.f64 x (/.f64 1 n))))

Details

analyze1.1s (0.7%)

sample198.0ms (0.1%)

simplify51.0ms (0%)

prune3.0ms (0%)

localize8.0ms (0%)

rewrite21.0ms (0%)

series339.0ms (0.2%)

simplify49.0ms (0%)

prune373.0ms (0.2%)

localize11.0ms (0%)

rewrite62.0ms (0%)

series963.0ms (0.6%)

simplify69.0ms (0%)

prune278.0ms (0.2%)

localize16.0ms (0%)

rewrite71.0ms (0%)

series1.3s (0.9%)

simplify108.0ms (0.1%)

prune405.0ms (0.3%)

localize17.0ms (0%)

rewrite133.0ms (0.1%)

series2.4min (96.3%)

Profiling