Details

analyze12.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

sample20.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify574.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	467	17
1	467	17

prune3.0ms

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: 0.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))
0.0b	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

79×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
30×	`sqrt-prod_binary64`
26×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
13×	`distribute-lft-out_binary64`
9×	`distribute-lft-out--_binary64`
6×	`associate-/l*_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64` `pow1_binary64` `associate-/r/_binary64`
3×	`add-log-exp_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64`

Counts

3 → 100

Calls

3 calls:

8.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
10.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

series71.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
34.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
24.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

simplify83.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5740	2062

prune89.0ms

Filtered

69 candidates to 109 candidates (-58.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	2	110

Merged error: 0.0b

Counts

110 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 x))
0.0b	(atan.f64 (*.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x)))))
0.0b	(/.f64 1 (+.f64 1 x))
0.0b	(*.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
47×	`*-un-lft-identity_binary64`
40×	`sqrt-prod_binary64`
28×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`
10×	`pow1_binary64` `add-exp-log_binary64`
9×	`associate-l_binary64` `sqrt-div_binary64`
8×	`add-cbrt-cube_binary64` `unswap-sqr_binary64`
7×	`distribute-lft-out_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `associate-/r/_binary64` `difference-of-squares_binary64`
3×	`pow-prod-down_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `prod-exp_binary64` `frac-2neg_binary64` `rec-exp_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

4 → 119

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 1 x))
1.0ms	(atan.f64 (*.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x)))))
6.0ms	(/.f64 1 (+.f64 1 x))
18.0ms	(*.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))

series57.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt.f64 (-.f64 1 x))
9.0ms	(atan.f64 (*.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x)))))
9.0ms	(/.f64 1 (+.f64 1 x))
24.0ms	(*.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (/.f64 1 (+.f64 1 x))))

simplify92.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4918	2187
1	4918	2187

prune110.0ms

Filtered

82 candidates to 131 candidates (-59.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	131	2	133

Merged error: 0b

Counts

133 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(sqrt.f64 (+.f64 1 (+.f64 x (*.f64 x x))))
0.0b	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 3))) (.f64 (sqrt.f64 (+.f64 1 (+.f64 x (.f64 x x)))) (sqrt.f64 (+.f64 1 x))))
0.0b	(.f64 (sqrt.f64 (+.f64 1 (+.f64 x (.f64 x x)))) (sqrt.f64 (+.f64 1 x)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
34×	`*-un-lft-identity_binary64`
30×	`sqrt-div_binary64`
16×	`difference-of-squares_binary64`
15×	`associate-/l*_binary64` `times-frac_binary64`
14×	`flip3-+_binary64` `add-cube-cbrt_binary64` `flip-+_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
8×	`associate-/r/_binary64` `frac-times_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `associate-l/_binary64`
3×	`pow-prod-down_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `div-exp_binary64`
1×	`associate-/r_binary64` `flip3--_binary64` `sqrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `-commutative_binary64`

Counts

4 → 128

Calls

4 calls:

3.0ms	(sqrt.f64 (+.f64 1 x))
5.0ms	(sqrt.f64 (+.f64 1 (+.f64 x (*.f64 x x))))
21.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 3))) (.f64 (sqrt.f64 (+.f64 1 (+.f64 x (.f64 x x)))) (sqrt.f64 (+.f64 1 x))))
14.0ms	(.f64 (sqrt.f64 (+.f64 1 (+.f64 x (.f64 x x)))) (sqrt.f64 (+.f64 1 x)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt.f64 (+.f64 1 x))
13.0ms	(sqrt.f64 (+.f64 1 (+.f64 x (*.f64 x x))))
38.0ms	(/.f64 (sqrt.f64 (-.f64 1 (pow.f64 x 3))) (.f64 (sqrt.f64 (+.f64 1 (+.f64 x (.f64 x x)))) (sqrt.f64 (+.f64 1 x))))
28.0ms	(.f64 (sqrt.f64 (+.f64 1 (+.f64 x (.f64 x x)))) (sqrt.f64 (+.f64 1 x)))

simplify90.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5122	3857

prune161.0ms

Filtered

100 candidates to 140 candidates (-40.0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	140	2	142

Merged error: 0b

Counts

142 → 2

regimes10.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	22
1	26	22

end0.0ms

sample472.0ms

Algorithm

intervals

Results

374.0ms

8000×

body

valid

Details

analyze12.0ms

sample20.0ms

simplify574.0ms

prune3.0ms

localize10.0ms

rewrite25.0ms

series71.0ms

simplify83.0ms

prune89.0ms

localize10.0ms

rewrite33.0ms

series57.0ms

simplify92.0ms

prune110.0ms

localize16.0ms

rewrite49.0ms

series94.0ms

simplify90.0ms

prune161.0ms

regimes10.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample472.0ms

Profiling