Details

analyze3.0ms

Algorithm

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

sample11.0ms

Algorithm

intervals

Results

6.0ms	255×	body	128	valid
0.0ms	1×	body	2048	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	12
1	9	12

prune1.0ms

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: 0.2b

Counts

2 → 1

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
14×	`sqrt-prod_binary64`
6×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_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 → 71

Calls

3 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
9.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series193.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(sqrt.f64 (+.f64 x 1))
31.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
135.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify71.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4949	1549
1	4949	1549

prune71.0ms

Filtered

57 candidates to 80 candidates (-40.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	76	5	81

Merged error: 0b

Counts

81 → 5

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.1b	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.1b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64`
51×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
33×	`distribute-lft-out_binary64`
27×	`add-cube-cbrt_binary64`
24×	`associate-r_binary64`
20×	`sqrt-prod_binary64`
14×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64`
4×	`flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`
3×	`associate-l_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `div-inv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 120

Calls

4 calls:

4.0ms	(sqrt.f64 (+.f64 x 1))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
9.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
17.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series281.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(sqrt.f64 (+.f64 x 1))
32.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
90.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
132.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

simplify79.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4956	2465
1	4956	2465

prune105.0ms

Filtered

83 candidates to 132 candidates (-59.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	132	5	137

Merged error: 0b

Counts

137 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.0b	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.3b	(/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
0.5b	(/.f64 (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

602×	`*-un-lft-identity_binary64`
594×	`times-frac_binary64`
560×	`sqrt-prod_binary64`
394×	`add-sqr-sqrt_binary64`
280×	`distribute-lft-out_binary64`
252×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
28×	`sqrt-div_binary64`
24×	`associate-/r/_binary64`
18×	`associate-/r*_binary64`
14×	`flip3-+_binary64` `flip-+_binary64`
12×	`div-inv_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_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 → 445

Calls

4 calls:

7.0ms	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
10.0ms	(/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
30.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

series531.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
79.0ms	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
238.0ms	(/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
130.0ms	(/.f64 (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

simplify177.0ms

Algorithm

egg-herbie

Counts

457 → 457

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5163	16612

prune323.0ms

Filtered

152 candidates to 457 candidates (-200.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	457	0	457
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	457	5	462

Merged error: 0b

Counts

462 → 5

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x 1/2) (.f64 (.f64 x x) (-.f64 (.f64 x 1/16) 1/8)))
0.0b	(.f64 (.f64 x x) (-.f64 (*.f64 x 1/16) 1/8))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `sub-neg_binary64` `add-sqr-sqrt_binary64`
3×	`pow-prod-down_binary64` `-un-lft-identity_binary64` `cbrt-unprod_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
2×	`associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-+r+_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `associate-l_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

2 → 36

Calls

2 calls:

5.0ms	(+.f64 (.f64 x 1/2) (.f64 (.f64 x x) (-.f64 (.f64 x 1/16) 1/8)))
10.0ms	(.f64 (.f64 x x) (-.f64 (*.f64 x 1/16) 1/8))

series148.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(+.f64 (.f64 x 1/2) (.f64 (.f64 x x) (-.f64 (.f64 x 1/16) 1/8)))
112.0ms	(.f64 (.f64 x x) (-.f64 (*.f64 x 1/16) 1/8))

simplify40.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5799	731

prune27.0ms

Filtered

28 candidates to 42 candidates (-50.0%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	42	5	47

Merged error: 0b

Counts

47 → 5

regimes27.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	12
1	9	12

end0.0ms

sample296.0ms

Algorithm

intervals

Results

205.0ms	7997×	body	128	valid
0.0ms	3×	body	2048	valid

Details

analyze3.0ms

sample11.0ms

simplify8.0ms

prune1.0ms

localize5.0ms

rewrite25.0ms

series193.0ms

simplify71.0ms

prune71.0ms

localize6.0ms

rewrite47.0ms

series281.0ms

simplify79.0ms

prune105.0ms

localize8.0ms

rewrite140.0ms

series531.0ms

simplify177.0ms

prune323.0ms

localize8.0ms

rewrite18.0ms

series148.0ms

simplify40.0ms

prune27.0ms

regimes27.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample296.0ms

Profiling