Details

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

sample24.0ms

Algorithm

intervals

Results

18.0ms

256×

body

valid

simplify363.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (353.0ms)

Iter	Nodes	Cost
0	7545	20

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: 0.3b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64`
26×	`times-frac_binary64`
21×	`add-sqr-sqrt_binary64`
16×	`distribute-lft-out_binary64`
15×	`log-prod_binary64`
13×	`add-cube-cbrt_binary64`
12×	`div-inv_binary64`
11×	`sqrt-prod_binary64`
6×	`distribute-rgt-out_binary64`
5×	`add-log-exp_binary64` `pow1_binary64`
4×	`add-exp-log_binary64`
3×	`add-cbrt-cube_binary64` `log-div_binary64`
2×	`flip3-+_binary64` `frac-add_binary64` `distribute-rgt1-in_binary64` `difference-of-squares_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

3 → 68

Calls

3 calls:

41.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
5.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
38.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

series89.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
19.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
46.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

simplify82.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5042	1690

prune64.0ms

Filtered

57 candidates to 77 candidates (-35.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	76	2	78

Merged error: 0.0b

Counts

78 → 2

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.2b	(+.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (neg.f64 (log.f64 x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
10×	`distribute-lft-out_binary64` `add-sqr-sqrt_binary64`
9×	`pow1_binary64`
8×	`log-prod_binary64`
7×	`sqrt-prod_binary64`
6×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
5×	`log-pow_binary64` `associate-+l+_binary64`
4×	`distribute-rgt-neg-in_binary64`
3×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-neg-in_binary64` `flip-+_binary64` `associate-+r+_binary64` `sum-log_binary64`
2×	`associate-+l-_binary64` `difference-of-squares_binary64` `log-div_binary64` `+-commutative_binary64` `sqrt-div_binary64`
1×	`associate-+r-_binary64` `pow1/2_binary64` `flip3--_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `neg-log_binary64` `flip--_binary64` `unsub-neg_binary64`

Counts

3 → 60

Calls

3 calls:

6.0ms	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
11.0ms	(+.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (neg.f64 (log.f64 x)))

series85.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
20.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
52.0ms	(+.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (neg.f64 (log.f64 x)))

simplify104.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4885	1299
1	4885	1299

prune59.0ms

Filtered

53 candidates to 69 candidates (-30.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	69	2	71

Merged error: 0b

Counts

71 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (log.f64 x)))
0.2b	(-.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (log.f64 x))
0.2b	(-.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (log.f64 x))
0.5b	(.f64 (sqrt.f64 (-.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x))))) (log.f64 x))) (sqrt.f64 (-.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (log.f64 x))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

91×	`*-un-lft-identity_binary64`
88×	`sqrt-prod_binary64`
80×	`pow1_binary64`
60×	`log-pow_binary64` `distribute-lft-out--_binary64`
46×	`add-sqr-sqrt_binary64`
33×	`swap-sqr_binary64`
17×	`add-cube-cbrt_binary64`
16×	`log-prod_binary64`
14×	`sqrt-div_binary64`
11×	`associate-r_binary64` `associate-l_binary64`
10×	`associate--l+_binary64`
9×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `flip--_binary64`
7×	`difference-of-squares_binary64`
6×	`associate--r+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-up_binary64`
4×	`add-log-exp_binary64` `associate--l-_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `log-div_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-r/_binary64` `flip-+_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 164

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (log.f64 x)))
9.0ms	(-.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (log.f64 x))
10.0ms	(-.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (log.f64 x))
14.0ms	(.f64 (sqrt.f64 (-.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x))))) (log.f64 x))) (sqrt.f64 (-.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (log.f64 x))))

series230.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(sqrt.f64 (-.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (log.f64 x)))
50.0ms	(-.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (log.f64 x))
54.0ms	(-.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (log.f64 x))
61.0ms	(.f64 (sqrt.f64 (-.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x))))) (log.f64 x))) (sqrt.f64 (-.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (log.f64 x))))

simplify158.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4898	4787
1	4898	4787

prune159.0ms

Filtered

94 candidates to 176 candidates (-87.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	176	2	178

Merged error: 0b

Counts

178 → 2

regimes31.0ms

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	30	20
1	30	20

end0.0ms

sample498.0ms

Algorithm

intervals

Results

403.0ms	8000×	body	80	valid
0.0ms	7×	body	80	nan

Details

analyze5.0ms

sample24.0ms

simplify363.0ms

prune1.0ms

localize9.0ms

rewrite89.0ms

series89.0ms

simplify82.0ms

prune64.0ms

localize11.0ms

rewrite22.0ms

series85.0ms

simplify104.0ms

prune59.0ms

localize12.0ms

rewrite45.0ms

series230.0ms

simplify158.0ms

prune159.0ms

regimes31.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample498.0ms

Profiling