Details

analyze234.0ms

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

sample20.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
1.0ms	15×	body	80	invalid

simplify99.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5084	11

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 5.1b

Counts

2 → 2

localize7.0ms

Local error

Found 2 expressions with local error:

3.3b	(* y (+ 1.0 (* z z)))
3.7b	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
20×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/l*`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `associate-*r/`
3×	`associate-r` `associate-l` `prod-exp` `cbrt-unprod` `div-inv`
2×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `associate-/l/` `unswap-sqr`

Counts

2 → 70

Calls

2 calls:

5.0ms	(* y (+ 1.0 (* z z)))
8.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series26.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(* y (+ 1.0 (* z z)))
17.0ms	(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify52.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4974	885
1	4974	885

prune132.0ms

Filtered

55 candidates to 76 candidates (-38.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	69	7	76
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	70	8	78

Merged error: 4.0b

Counts

78 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
3.7b	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
14.9b	(sqrt (+ 1.0 (* z z)))
14.9b	(sqrt (+ 1.0 (* z z)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
30×	`add-exp-log` `add-cbrt-cube`
28×	`sqrt-div`
24×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-*r/`
14×	`flip3-+` `flip-+`
13×	`associate-/l*`
11×	`pow1`
9×	`cbrt-undiv` `div-exp` `prod-exp` `sqrt-prod` `cbrt-unprod`
8×	`frac-times` `associate-/r/`
6×	`associate-r`
4×	`associate-*l/` `add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-2neg` `associate-l` `clear-num` `associate-/r` `-commutative` `associate-/l/`

Counts

4 → 117

Calls

4 calls:

13.0ms	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
14.0ms	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
3.0ms	(sqrt (+ 1.0 (* z z)))
3.0ms	(sqrt (+ 1.0 (* z z)))

series34.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
17.0ms	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
3.0ms	(sqrt (+ 1.0 (* z z)))
4.0ms	(sqrt (+ 1.0 (* z z)))

simplify65.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4962	1728
1	4962	1728

prune230.0ms

Filtered

91 candidates to 129 candidates (-41.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	128	9	137

Merged error: 4.0b

Counts

137 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

3.7b	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (* (fabs (cbrt (+ 1.0 (* z z)))) (sqrt (cbrt (+ 1.0 (* z z)))))))
14.9b	(sqrt (+ 1.0 (* z z)))
15.5b	(cbrt (+ 1.0 (* z z)))
15.5b	(cbrt (+ 1.0 (* z z)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
31×	`times-frac`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
16×	`prod-exp` `cbrt-unprod`
15×	`cbrt-undiv` `div-exp`
14×	`sqrt-div` `associate-*r/`
13×	`associate-/l*`
10×	`cbrt-div`
9×	`flip3-+` `flip-+`
8×	`associate-/r/`
6×	`cbrt-prod`
5×	`pow1`
4×	`frac-times` `add-log-exp`
3×	`sqrt-prod` `div-inv`
2×	`pow1/3` `associate-*l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r*` `associate-/l/`

Counts

4 → 107

Calls

4 calls:

19.0ms	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (* (fabs (cbrt (+ 1.0 (* z z)))) (sqrt (cbrt (+ 1.0 (* z z)))))))
3.0ms	(sqrt (+ 1.0 (* z z)))
2.0ms	(cbrt (+ 1.0 (* z z)))
3.0ms	(cbrt (+ 1.0 (* z z)))

series94.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (* (fabs (cbrt (+ 1.0 (* z z)))) (sqrt (cbrt (+ 1.0 (* z z)))))))
3.0ms	(sqrt (+ 1.0 (* z z)))
12.0ms	(cbrt (+ 1.0 (* z z)))
12.0ms	(cbrt (+ 1.0 (* z z)))

simplify75.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4966	2703
1	4966	2703

prune321.0ms

Filtered

91 candidates to 119 candidates (-30.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	119	9	128

Merged error: 4.0b

Counts

128 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1.0 x))
1.4b	(/ (+ 1.0 (* z z)) (cbrt (/ 1.0 x)))
3.0b	(/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) (* y (/ (+ 1.0 (* z z)) (cbrt (/ 1.0 x)))))
3.4b	(* y (/ (+ 1.0 (* z z)) (cbrt (/ 1.0 x))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

173×	`times-frac`
114×	`add-sqr-sqrt`
106×	`cbrt-prod`
102×	`add-cube-cbrt` `*-un-lft-identity`
53×	`associate-r`
32×	`add-exp-log`
22×	`add-cbrt-cube`
17×	`associate-/r*`
11×	`div-inv`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`cbrt-div`
6×	`pow1`
5×	`associate-/l/`
4×	`associate-/l*` `add-log-exp` `unswap-sqr`
3×	`associate-r/` `associate-l*` `associate-/r/`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `flip3-+` `pow1/3` `pow-prod-down` `associate-l/` `-commutative` `flip-+`

Counts

4 → 207

Calls

4 calls:

2.0ms	(cbrt (/ 1.0 x))
8.0ms	(/ (+ 1.0 (* z z)) (cbrt (/ 1.0 x)))
16.0ms	(/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) (* y (/ (+ 1.0 (* z z)) (cbrt (/ 1.0 x)))))
19.0ms	(* y (/ (+ 1.0 (* z z)) (cbrt (/ 1.0 x))))

series122.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (/ 1.0 x))
26.0ms	(/ (+ 1.0 (* z z)) (cbrt (/ 1.0 x)))
25.0ms	(/ (* (cbrt (/ 1.0 x)) (cbrt (/ 1.0 x))) (* y (/ (+ 1.0 (* z z)) (cbrt (/ 1.0 x)))))
46.0ms	(* y (/ (+ 1.0 (* z z)) (cbrt (/ 1.0 x))))

simplify98.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4928	3426
1	4928	3426

prune560.0ms

Filtered

172 candidates to 219 candidates (-27.3%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	219	9	228

Merged error: 4.0b

Counts

228 → 9

regimes586.0ms

Accuracy

79.1% (0.3b remaining)

Error of 5.3b against oracle of 5.0b and baseline of 6.5b

bsearch34.0ms

Steps

Iters	Range		Point
9	5.4996757602501314e-89	4.5606461353322675e-82	1.3999345631682573e-84
9	-8.787107463618577e-76	-2.512951095712576e-83	-1.3942200371202058e-79

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	72	33
1	72	33

end0.0ms

sample508.0ms

Algorithm

intervals

Results

302.0ms	8000×	body	80	valid
16.0ms	445×	body	80	invalid

Details

analyze234.0ms

sample20.0ms

simplify99.0ms

prune11.0ms

localize7.0ms

rewrite15.0ms

series26.0ms

simplify52.0ms

prune132.0ms

localize9.0ms

rewrite37.0ms

series34.0ms

simplify65.0ms

prune230.0ms

localize14.0ms

rewrite31.0ms

series94.0ms

simplify75.0ms

prune321.0ms

localize11.0ms

rewrite55.0ms

series122.0ms

simplify98.0ms

prune560.0ms

regimes586.0ms

bsearch34.0ms

simplify2.0ms

end0.0ms

sample508.0ms

Profiling