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

simplify455.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	465	11
1	465	11

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

localize9.0ms

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))

rewrite36.0ms

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))))
9.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
21.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

series22.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
5.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
12.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

simplify53.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5925	1355

prune77.0ms

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

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

714×	`times-frac_binary64`
690×	`*-un-lft-identity_binary64`
480×	`add-sqr-sqrt_binary64`
424×	`sqrt-prod_binary64`
286×	`add-cube-cbrt_binary64`
128×	`difference-of-squares_binary64`
106×	`distribute-lft-out_binary64`
64×	`distribute-lft-out--_binary64`
54×	`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`
3×	`associate-/l/_binary64` `div-sub_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3--_binary64` `flip--_binary64`

Counts

4 → 513

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 1 x))
6.0ms	(sqrt.f64 (+.f64 1 x))
24.0ms	(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 1 x)))
10.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))

series19.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 1 x))
4.0ms	(sqrt.f64 (+.f64 1 x))
3.0ms	(/.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (+.f64 1 x)))
8.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))

simplify110.0ms

Algorithm

egg-herbie

Counts

525 → 525

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5111	10068

prune242.0ms

Filtered

178 candidates to 525 candidates (-194.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	524	1	525
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	524	3	527

Merged error: 0b

Counts

527 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

1617×	`times-frac_binary64`
1566×	`*-un-lft-identity_binary64`
1100×	`add-sqr-sqrt_binary64`
932×	`sqrt-prod_binary64`
918×	`cbrt-prod_binary64`
656×	`add-cube-cbrt_binary64`
480×	`unpow-prod-down_binary64` `cube-prod_binary64`
296×	`difference-of-squares_binary64`
233×	`distribute-lft-out_binary64`
148×	`distribute-lft-out--_binary64`
111×	`associate-/l*_binary64`
44×	`associate-/r/_binary64` `sqrt-div_binary64`
22×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
14×	`associate-/r*_binary64`
11×	`add-exp-log_binary64`
10×	`sqr-pow_binary64` `add-cbrt-cube_binary64` `unpow3_binary64` `cube-mult_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/l/_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `cube-div_binary64` `div-exp_binary64`
2×	`cbrt-div_binary64` `clear-num_binary64` `rem-cube-cbrt_binary64` `frac-2neg_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `rem-cbrt-cube_binary64` `flip3--_binary64` `pow1/3_binary64` `pow-pow_binary64` `div-sub_binary64` `flip--_binary64`

Counts

4 → 1162

Calls

4 calls:

17.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) 3))
52.0ms	(/.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) 3)) (sqrt.f64 (+.f64 1 x)))
10.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))
15.0ms	(pow.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) 3)

series30.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) 3))
3.0ms	(/.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) 3)) (sqrt.f64 (+.f64 1 x)))
7.0ms	(/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x)))
13.0ms	(pow.f64 (/.f64 (-.f64 1 x) (sqrt.f64 (+.f64 1 x))) 3)

simplify232.0ms

Algorithm

egg-herbie

Counts

1174 → 1174

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5024	22636

prune401.0ms

Filtered

242 candidates to 1174 candidates (-385.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	1174	0	1174
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	1174	3	1177

Merged error: 0b

Counts

1177 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(atan.f64 (+.f64 (-.f64 1 x) (.f64 (.f64 x x) 1/2)))
0.0b	(+.f64 (-.f64 1 x) (.f64 (.f64 x x) 1/2))
0.0b	(.f64 (.f64 x x) 1/2)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `prod-exp_binary64`
2×	`sum-log_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-+l+_binary64` `associate-l_binary64` `associate-+l-_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

3 → 40

Calls

3 calls:

3.0ms	(atan.f64 (+.f64 (-.f64 1 x) (.f64 (.f64 x x) 1/2)))
8.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 x x) 1/2))
6.0ms	(.f64 (.f64 x x) 1/2)

series9.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(atan.f64 (+.f64 (-.f64 1 x) (.f64 (.f64 x x) 1/2)))
3.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 x x) 1/2))
4.0ms	(.f64 (.f64 x x) 1/2)

simplify50.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5073	438

prune25.0ms

Filtered

31 candidates to 49 candidates (-58.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	49	3	52

Merged error: 0b

Counts

52 → 3

regimes19.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	17
1	23	17

end0.0ms

sample475.0ms

Algorithm

intervals

Results

376.0ms

8000×

body

valid

Details

analyze12.0ms

sample20.0ms

simplify455.0ms

prune3.0ms

localize9.0ms

rewrite36.0ms

series22.0ms

simplify53.0ms

prune77.0ms

localize9.0ms

rewrite83.0ms

series19.0ms

simplify110.0ms

prune242.0ms

localize12.0ms

rewrite223.0ms

series30.0ms

simplify232.0ms

prune401.0ms

localize8.0ms

rewrite19.0ms

series9.0ms

simplify50.0ms

prune25.0ms

regimes19.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample475.0ms

Profiling