Details

analyze228.0ms

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

sample21.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
0.0ms	14×	body	80	invalid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	82	11
1	82	11

prune9.0ms

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: 7.4b

Counts

2 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

3.1b	(* y (+ 1.0 (* z z)))
4.8b	(/ (/ 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))))

series27.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify48.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4985	885
1	4985	885

prune126.0ms

Filtered

55 candidates to 76 candidates (-38.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	69	7	76
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	71	7	78

Merged error: 5.0b

Counts

78 → 7

localize9.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ 1.0 (* x (+ 1.0 (* z z))))
3.2b	(* (/ 1 y) (/ 1.0 (* x (+ 1.0 (* z z)))))
4.8b	(* x (+ 1.0 (* z z)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 100

Calls

3 calls:

6.0ms	(/ 1.0 (* x (+ 1.0 (* z z))))
13.0ms	(* (/ 1 y) (/ 1.0 (* x (+ 1.0 (* z z)))))
5.0ms	(* x (+ 1.0 (* z z)))

series43.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(/ 1.0 (* x (+ 1.0 (* z z))))
19.0ms	(* (/ 1 y) (/ 1.0 (* x (+ 1.0 (* z z)))))
10.0ms	(* x (+ 1.0 (* z z)))

simplify73.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4944	1205
1	4944	1205

prune130.0ms

Filtered

73 candidates to 109 candidates (-49.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	108	8	116

Merged error: 2.3b

Counts

116 → 8

localize7.0ms

Local error

Found 2 expressions with local error:

3.7b	(/ (/ 1.0 y) (* x (+ 1.0 (* z z))))
4.8b	(* x (+ 1.0 (* z z)))

rewrite20.0ms

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:

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

series36.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(/ (/ 1.0 y) (* x (+ 1.0 (* z z))))
17.0ms	(* x (+ 1.0 (* z z)))

simplify47.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4985	885
1	4985	885

prune97.0ms

Filtered

54 candidates to 76 candidates (-40.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	76	8	84

Merged error: 2.3b

Counts

84 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
4.8b	(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
16.4b	(sqrt (+ 1.0 (* z z)))
16.4b	(sqrt (+ 1.0 (* z z)))

rewrite33.0ms

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:

10.0ms	(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
13.0ms	(/ (/ 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)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (* 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)))

simplify58.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4991	1716
1	4991	1716

prune167.0ms

Filtered

94 candidates to 129 candidates (-37.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	129	8	137

Merged error: 2.3b

Counts

137 → 8

regimes660.0ms

Accuracy

63% (1.6b remaining)

Error of 3.7b against oracle of 2.1b and baseline of 6.3b

bsearch31.0ms

Steps

Iters	Range		Point
8	5.568479895443027e+113	4.365753718355861e+116	7.39849454548267e+113
10	-1.3687775879370046e+135	-9.676269919675381e+123	-8.956704061217655e+126

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	29
1	27	29

end0.0ms

sample474.0ms

Algorithm

intervals

Results

281.0ms	8000×	body	80	valid
17.0ms	490×	body	80	invalid

Details

analyze228.0ms

sample21.0ms

simplify4.0ms

prune9.0ms

localize8.0ms

rewrite15.0ms

series27.0ms

simplify48.0ms

prune126.0ms

localize9.0ms

rewrite27.0ms

series43.0ms

simplify73.0ms

prune130.0ms

localize7.0ms

rewrite20.0ms

series36.0ms

simplify47.0ms

prune97.0ms

localize10.0ms

rewrite33.0ms

series36.0ms

simplify58.0ms

prune167.0ms

regimes660.0ms

bsearch31.0ms

simplify2.0ms

end0.0ms

sample474.0ms

Profiling