Details

analyze223.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

sample18.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
0.0ms	13×	body	80	invalid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	110	11
1	110	11

prune2.0ms

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: 5.9b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

2.6b	(.f64 y (+.f64 1 (.f64 z z)))
4.3b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac_binary64`
26×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`
13×	`associate-/l*_binary64`
12×	`div-exp_binary64`
6×	`cbrt-undiv_binary64`
5×	`prod-exp_binary64`
4×	`pow1_binary64` `associate-*r/_binary64`
3×	`cbrt-unprod_binary64` `associate-r_binary64` `associate-l_binary64` `div-inv_binary64`
2×	`flip3-+_binary64` `add-log-exp_binary64` `1-exp_binary64` `associate-/r/_binary64` `rec-exp_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate-/r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `-commutative_binary64`

Counts

2 → 74

Calls

2 calls:

6.0ms	(.f64 y (+.f64 1 (.f64 z z)))
9.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))

series31.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(.f64 y (+.f64 1 (.f64 z z)))
17.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))

simplify49.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5072	883

prune68.0ms

Filtered

51 candidates to 80 candidates (-56.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	71	9	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	9	81

Merged error: 3.1b

Counts

81 → 9

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/.f64 (/.f64 1 x) y)
4.4b	(/.f64 (/.f64 (/.f64 1 x) y) (+.f64 1 (*.f64 z z)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

468×	`times-frac_binary64`
228×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
56×	`associate-/l*_binary64`
26×	`add-exp-log_binary64`
22×	`div-inv_binary64`
17×	`div-exp_binary64`
16×	`add-cbrt-cube_binary64`
9×	`cbrt-undiv_binary64`
6×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64` `pow1_binary64` `1-exp_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`flip3-+_binary64` `flip-+_binary64`

Counts

2 → 268

Calls

2 calls:

9.0ms	(/.f64 (/.f64 1 x) y)
15.0ms	(/.f64 (/.f64 (/.f64 1 x) y) (+.f64 1 (*.f64 z z)))

series19.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(/.f64 (/.f64 1 x) y)
16.0ms	(/.f64 (/.f64 (/.f64 1 x) y) (+.f64 1 (*.f64 z z)))

simplify80.0ms

Algorithm

egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5169	5115

prune182.0ms

Filtered

181 candidates to 274 candidates (-51.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	269	5	274
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	275	8	283

Merged error: 3.1b

Counts

283 → 8

localize7.0ms

Local error

Found 2 expressions with local error:

0.7b	(/.f64 -1 (*.f64 x y))
4.4b	(/.f64 (/.f64 -1 (.f64 x y)) (-.f64 -1 (.f64 z z)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

46×	`times-frac_binary64`
30×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/l*_binary64`
8×	`difference-of-squares_binary64`
7×	`cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
5×	`associate-/r*_binary64`
2×	`add-log-exp_binary64` `pow1_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64`
1×	`associate-/l/_binary64` `flip3--_binary64` `flip--_binary64`

Counts

2 → 79

Calls

2 calls:

5.0ms	(/.f64 -1 (*.f64 x y))
9.0ms	(/.f64 (/.f64 -1 (.f64 x y)) (-.f64 -1 (.f64 z z)))

series20.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(/.f64 -1 (*.f64 x y))
16.0ms	(/.f64 (/.f64 -1 (.f64 x y)) (-.f64 -1 (.f64 z z)))

simplify53.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4967	1160
1	4967	1160

prune65.0ms

Filtered

65 candidates to 85 candidates (-30.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	86	7	93

Merged error: 3.0b

Counts

93 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 z z)))) (/.f64 (/.f64 (/.f64 1 x) y) (sqrt.f64 (+.f64 1 (*.f64 z z)))))
2.2b	(/.f64 (/.f64 (/.f64 1 x) y) (sqrt.f64 (+.f64 1 (*.f64 z z))))
13.3b	(sqrt.f64 (+.f64 1 (*.f64 z z)))
13.3b	(sqrt.f64 (+.f64 1 (*.f64 z z)))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

1518×	`times-frac_binary64`
839×	`add-sqr-sqrt_binary64`
677×	`*-un-lft-identity_binary64`
649×	`add-cube-cbrt_binary64`
314×	`sqrt-prod_binary64`
264×	`associate-r_binary64`
113×	`add-exp-log_binary64`
67×	`div-exp_binary64`
55×	`div-inv_binary64`
45×	`add-cbrt-cube_binary64` `unswap-sqr_binary64`
43×	`associate-/l*_binary64`
24×	`associate-l_binary64` `prod-exp_binary64`
22×	`cbrt-undiv_binary64`
11×	`1-exp_binary64` `rec-exp_binary64`
10×	`sqrt-div_binary64`
8×	`pow1_binary64` `cbrt-unprod_binary64`
6×	`associate-/r*_binary64` `associate-/r/_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 735

Calls

4 calls:

133.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 z z)))) (/.f64 (/.f64 (/.f64 1 x) y) (sqrt.f64 (+.f64 1 (*.f64 z z)))))
20.0ms	(/.f64 (/.f64 (/.f64 1 x) y) (sqrt.f64 (+.f64 1 (*.f64 z z))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (.f64 z z)))) (/.f64 (/.f64 (/.f64 1 x) y) (sqrt.f64 (+.f64 1 (*.f64 z z)))))
22.0ms	(/.f64 (/.f64 (/.f64 1 x) y) (sqrt.f64 (+.f64 1 (*.f64 z z))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

simplify163.0ms

Algorithm

egg-herbie

Counts

747 → 747

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4956	17299
1	4956	17299

prune674.0ms

Filtered

382 candidates to 747 candidates (-95.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	747	0	747
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	747	7	754

Merged error: 3.0b

Counts

754 → 7

regimes391.0ms

Accuracy

84.3% (0.3b remaining)

Error of 5.2b against oracle of 4.9b and baseline of 6.7b

bsearch31.0ms

Steps

Iters	Range		Point
10	8.466201267373104e-05	1622373.1654913728	2231.9134022336957
9	-3.0455364354963784e-60	-8.705904786604096e-66	-5.3941269482623205e-62

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	53
1	30	53

end0.0ms

sample479.0ms

Algorithm

intervals

Results

287.0ms	8000×	body	80	valid
17.0ms	480×	body	80	invalid

Details

analyze223.0ms

sample18.0ms

simplify6.0ms

prune2.0ms

localize7.0ms

rewrite18.0ms

series31.0ms

simplify49.0ms

prune68.0ms

localize7.0ms

rewrite41.0ms

series19.0ms

simplify80.0ms

prune182.0ms

localize7.0ms

rewrite16.0ms

series20.0ms

simplify53.0ms

prune65.0ms

localize11.0ms

rewrite228.0ms

series40.0ms

simplify163.0ms

prune674.0ms

regimes391.0ms

bsearch31.0ms

simplify2.0ms

end0.0ms

sample479.0ms

Profiling