Details

analyze13.0ms

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

simplify560.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (31.0ms)

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

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

series74.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
35.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
24.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

simplify82.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5740	2062

prune94.0ms

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: 0b

Counts

110 → 2

localize9.0ms

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

98×	`sqrt-prod_binary64`
91×	`*-un-lft-identity_binary64`
71×	`add-sqr-sqrt_binary64`
63×	`times-frac_binary64`
42×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
11×	`distribute-lft-out_binary64`
9×	`associate-/l*_binary64` `distribute-lft-out--_binary64`
8×	`sqrt-div_binary64`
7×	`associate-/r*_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`
1×	`cbrt-undiv_binary64` `sqrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 137

Calls

4 calls:

3.0ms	(sqrt.f64 (+.f64 1 x))
4.0ms	(atan.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))
4.0ms	(sqrt.f64 (-.f64 1 x))
11.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt.f64 (+.f64 1 x))
12.0ms	(atan.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))
16.0ms	(sqrt.f64 (-.f64 1 x))
22.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))

simplify91.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5211	3200

prune100.0ms

Filtered

83 candidates to 149 candidates (-79.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	149	2	151

Merged error: 0b

Counts

151 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

84×	`add-sqr-sqrt_binary64`
79×	`*-un-lft-identity_binary64`
61×	`times-frac_binary64`
50×	`difference-of-squares_binary64`
36×	`associate-l_binary64`
30×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`associate-r_binary64` `associate-/l*_binary64`
5×	`associate-/r*_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `associate-*l/_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-prod_binary64` `*-commutative_binary64`

Counts

4 → 145

Calls

4 calls:

8.0ms	(/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x)))
1.0ms	(atan.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x))))
12.0ms	(sqrt.f64 (.f64 (/.f64 (-.f64 1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x)))
18.0ms	(.f64 (/.f64 (-.f64 1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x))

series66.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/.f64 (-.f64 1 x) (-.f64 1 (*.f64 x x)))
11.0ms	(atan.f64 (sqrt.f64 (.f64 (/.f64 (-.f64 1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x))))
22.0ms	(sqrt.f64 (.f64 (/.f64 (-.f64 1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x)))
20.0ms	(.f64 (/.f64 (-.f64 1 x) (-.f64 1 (.f64 x x))) (-.f64 1 x))

simplify109.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4967	3161
1	4967	3161

prune146.0ms

Filtered

117 candidates to 157 candidates (-34.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	157	2	159

Merged error: 0b

Counts

159 → 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	24	19
1	24	19

end0.0ms

sample488.0ms

Algorithm

intervals

Results

384.0ms

8000×

body

valid

Details

analyze13.0ms

sample20.0ms

simplify560.0ms

prune3.0ms

localize10.0ms

rewrite25.0ms

series74.0ms

simplify82.0ms

prune94.0ms

localize9.0ms

rewrite28.0ms

series64.0ms

simplify91.0ms

prune100.0ms

localize10.0ms

rewrite48.0ms

series66.0ms

simplify109.0ms

prune146.0ms

regimes10.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample488.0ms

Profiling