Details

analyze6.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

sample27.0ms

Algorithm

intervals

Results

6.0ms	45×	body	1024	valid
6.0ms	24×	body	256	valid
6.0ms	140×	body	128	valid
5.0ms	47×	body	512	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	192	22
1	192	22

prune2.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 11.7b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
56×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
18×	`distribute-lft-out--_binary64`
17×	`distribute-lft-out_binary64`
14×	`difference-of-squares_binary64`
11×	`associate-/r*_binary64` `add-log-exp_binary64`
10×	`add-exp-log_binary64`
8×	`add-cbrt-cube_binary64` `div-inv_binary64`
6×	`pow1_binary64` `associate-/l*_binary64`
4×	`difference-of-sqr-1_binary64` `associate-/r/_binary64`
3×	`flip3--_binary64` `frac-add_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-exp_binary64` `pow-flip_binary64` `flip-+_binary64` `frac-sub_binary64` `sum-log_binary64`
1×	`associate-+l+_binary64` `associate-+l-_binary64` `+-commutative_binary64`

Counts

4 → 133

Calls

4 calls:

6.0ms	(/.f64 1 (+.f64 x 1))
6.0ms	(/.f64 1 (-.f64 x 1))
20.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
45.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/.f64 1 (+.f64 x 1))
19.0ms	(/.f64 1 (-.f64 x 1))
29.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
107.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

simplify81.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5079	2560

prune129.0ms

Filtered

88 candidates to 145 candidates (-64.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	141	4	145
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	142	4	146

Merged error: 0.4b

Counts

146 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 x (+.f64 1 x))
0.0b	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
16.3b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt_binary64`
44×	`associate-*r/_binary64`
39×	`*-un-lft-identity_binary64`
32×	`frac-add_binary64`
31×	`flip3--_binary64` `flip--_binary64`
27×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
20×	`frac-times_binary64`
19×	`flip3-+_binary64` `flip-+_binary64`
18×	`associate-/l/_binary64` `difference-of-squares_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64` `associate-*l/_binary64`
9×	`associate-/r*_binary64`
8×	`pow1_binary64`
7×	`associate-r_binary64`
6×	`add-log-exp_binary64`
5×	`distribute-lft-out--_binary64`
4×	`sub-neg_binary64` `distribute-rgt-out--_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `unpow3_binary64`
3×	`associate-/l*_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-+l+_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-+r+_binary64` `*-commutative_binary64`
1×	`distribute-lft-out_binary64` `cbrt-undiv_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 157

Calls

4 calls:

7.0ms	(*.f64 x (+.f64 1 x))
21.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
10.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
12.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

series152.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(*.f64 x (+.f64 1 x))
59.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
24.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
8.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

simplify107.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4948	6630
1	4948	6630

prune324.0ms

Filtered

134 candidates to 169 candidates (-26.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	170	3	173

Merged error: 0.4b

Counts

173 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

0.4b	(/.f64 2 (-.f64 (pow.f64 x 3) x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64` `times-frac_binary64`
16×	`difference-of-squares_binary64`
15×	`add-cube-cbrt_binary64`
9×	`associate-/r*_binary64`
4×	`distribute-rgt-out--_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `distribute-lft-out--_binary64` `unpow3_binary64`
3×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
2×	`associate-/r/_binary64`
1×	`add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64`

Counts

1 → 53

Calls

1 calls:

9.0ms

(/.f64 2 (-.f64 (pow.f64 x 3) x))

series52.0ms

Counts

1 → 3

Calls

1 calls:

52.0ms

(/.f64 2 (-.f64 (pow.f64 x 3) x))

simplify68.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5210	1071

prune51.0ms

Filtered

42 candidates to 56 candidates (-33.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	55	4	59

Merged error: 0.0b

Counts

59 → 4

localize5.0ms

Local error

Found 1 expressions with local error:

0.1b	(/.f64 (/.f64 2 x) (-.f64 (*.f64 x x) 1))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

141×	`times-frac_binary64`
78×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
64×	`add-cube-cbrt_binary64`
28×	`difference-of-squares_binary64`
14×	`difference-of-sqr-1_binary64`
13×	`associate-/l*_binary64`
8×	`div-inv_binary64`
6×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`cbrt-undiv_binary64` `div-exp_binary64`
2×	`associate-/r/_binary64`
1×	`associate-/l/_binary64` `add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`

Counts

1 → 114

Calls

1 calls:

11.0ms

(/.f64 (/.f64 2 x) (-.f64 (*.f64 x x) 1))

series51.0ms

Counts

1 → 3

Calls

1 calls:

51.0ms

(/.f64 (/.f64 2 x) (-.f64 (*.f64 x x) 1))

simplify68.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5025	2916

prune78.0ms

Filtered

77 candidates to 117 candidates (-51.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	117	4	121

Merged error: 0.0b

Counts

121 → 4

regimes10.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	13
1	18	13

end0.0ms

sample652.0ms

Algorithm

intervals

Results

179.0ms	1270×	body	1024	valid
162.0ms	4473×	body	128	valid
160.0ms	1503×	body	512	valid
52.0ms	754×	body	256	valid

Details

analyze6.0ms

sample27.0ms

simplify13.0ms

prune2.0ms

localize8.0ms

rewrite89.0ms

series174.0ms

simplify81.0ms

prune129.0ms

localize13.0ms

rewrite78.0ms

series152.0ms

simplify107.0ms

prune324.0ms

localize5.0ms

rewrite14.0ms

series52.0ms

simplify68.0ms

prune51.0ms

localize5.0ms

rewrite25.0ms

series51.0ms

simplify68.0ms

prune78.0ms

regimes10.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample652.0ms

Profiling