Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

sample12.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

valid

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	8	8
1	8	8

prune4.0ms (0.2%)

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 → 1

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1.0))
0.0b	(+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
0.1b	(/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

rewrite19.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
6×	`distribute-lft-out_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64` `pow1_binary64` `sqrt-prod_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 61

Calls

3 calls:

8.0ms	(/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
6.0ms	(+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
3.0ms	(sqrt.f64 (+.f64 x 1.0))

series41.0ms (1.8%)

Counts

3 → 9

Calls

3 calls:

30.0ms	(/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
7.0ms	(+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
5.0ms	(sqrt.f64 (+.f64 x 1.0))

simplify27.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	4963	1021
1	4963	1021

prune95.0ms (4.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	4	71

Merged error: 0b

Counts

71 → 4

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
0.1b	(sqrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
0.3b	(/.f64 x (sqrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))))
0.4b	(/.f64 (/.f64 x (sqrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))) (sqrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))))

rewrite64.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

378×	`times-frac_binary64`
306×	`*-un-lft-identity_binary64`
232×	`sqrt-prod_binary64`
192×	`add-sqr-sqrt_binary64`
190×	`add-cube-cbrt_binary64`
58×	`distribute-lft-out_binary64`
30×	`associate-/l*_binary64`
24×	`sqrt-div_binary64`
20×	`associate-/r/_binary64`
14×	`associate-/r*_binary64`
12×	`flip3-+_binary64` `flip-+_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`div-inv_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64`

Counts

4 → 317

Calls

4 calls:

21.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))) (sqrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))))
9.0ms	(/.f64 x (sqrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))))
8.0ms	(sqrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
6.0ms	(sqrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

series108.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(/.f64 x (sqrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))))
25.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))) (sqrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))))
16.0ms	(sqrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
16.0ms	(sqrt.f64 (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))

simplify81.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

329 → 329

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5484	8179

prune744.0ms (32.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	329	0	329
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	329	4	333

Merged error: 0b

Counts

333 → 4

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
0.1b	(/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
0.2b	(pow.f64 (/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))) 3)
33.2b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))) 3))

rewrite43.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`*-un-lft-identity_binary64`
60×	`times-frac_binary64`
47×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
42×	`cbrt-prod_binary64`
36×	`unpow-prod-down_binary64` `cube-prod_binary64`
17×	`distribute-lft-out_binary64`
10×	`associate-/r/_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64`
5×	`pow1_binary64` `div-inv_binary64`
4×	`associate-/r*_binary64`
3×	`pow-unpow_binary64` `associate-/l*_binary64`
2×	`cbrt-undiv_binary64` `sqr-pow_binary64` `cube-div_binary64` `rem-cube-cbrt_binary64` `div-exp_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `rem-cbrt-cube_binary64` `pow1/3_binary64` `pow-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 153

Calls

4 calls:

12.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))) 3))
10.0ms	(pow.f64 (/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))) 3)
9.0ms	(/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
6.0ms	(+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))

series118.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

56.0ms	(pow.f64 (/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))) 3)
31.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))) 3))
25.0ms	(/.f64 x (+.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
6.0ms	(+.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))

simplify52.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5218	3002

prune237.0ms (10.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	165	4	169

Merged error: 0b

Counts

169 → 4

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1.0))
0.0b	(.f64 (/.f64 x (-.f64 (.f64 1.0 1.0) (+.f64 x 1.0))) (-.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
3.3b	(-.f64 (*.f64 1.0 1.0) (+.f64 x 1.0))
3.3b	(-.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))

rewrite40.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
18×	`associate-l_binary64`
14×	`add-cube-cbrt_binary64`
13×	`times-frac_binary64`
11×	`add-log-exp_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`difference-of-squares_binary64`
7×	`pow1_binary64`
6×	`associate-r_binary64` `sqrt-prod_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`sub-neg_binary64`
3×	`diff-log_binary64`
2×	`cbrt-unprod_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `frac-times_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `associate--r+_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `associate-l/_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 90

Calls

4 calls:

19.0ms	(.f64 (/.f64 x (-.f64 (.f64 1.0 1.0) (+.f64 x 1.0))) (-.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
7.0ms	(-.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
7.0ms	(-.f64 (*.f64 1.0 1.0) (+.f64 x 1.0))
3.0ms	(sqrt.f64 (+.f64 x 1.0))

series25.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

10.0ms	(.f64 (/.f64 x (-.f64 (.f64 1.0 1.0) (+.f64 x 1.0))) (-.f64 1.0 (sqrt.f64 (+.f64 x 1.0))))
7.0ms	(-.f64 1.0 (sqrt.f64 (+.f64 x 1.0)))
5.0ms	(sqrt.f64 (+.f64 x 1.0))
2.0ms	(-.f64 (*.f64 1.0 1.0) (+.f64 x 1.0))

simplify32.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5418	1359

prune139.0ms (6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	102	4	106

Merged error: 0b

Counts

106 → 4

regimes61.0ms (2.6%)

Accuracy

Total 0.2b remaining (95.7%)

Threshold costs 0.2b (95.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	8
1	8	8

end0.0ms (0%)

sample317.0ms (13.8%)

Algorithm

1×

intervals

Results

222.0ms	7998×	body	80	valid
0.0ms	2×	body	1280	valid

Details

analyze3.0ms (0.1%)

sample12.0ms (0.5%)

simplify5.0ms (0.2%)

prune4.0ms (0.2%)

localize5.0ms (0.2%)

rewrite19.0ms (0.8%)

series41.0ms (1.8%)

simplify27.0ms (1.2%)

prune95.0ms (4.1%)

localize8.0ms (0.3%)

rewrite64.0ms (2.8%)

series108.0ms (4.7%)

simplify81.0ms (3.5%)

prune744.0ms (32.4%)

localize8.0ms (0.4%)

rewrite43.0ms (1.9%)

series118.0ms (5.2%)

simplify52.0ms (2.3%)

prune237.0ms (10.3%)

localize8.0ms (0.4%)

rewrite40.0ms (1.7%)

series25.0ms (1.1%)

simplify32.0ms (1.4%)

prune139.0ms (6%)

regimes61.0ms (2.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample317.0ms (13.8%)

Profiling