Details

analyze757.0ms

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
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

sample94.0ms

Algorithm

intervals

Results

19.0ms	45×	body	1280	valid
14.0ms	32×	body	1280	invalid
13.0ms	138×	body	80	valid
13.0ms	45×	body	640	valid
9.0ms	29×	body	640	invalid
4.0ms	17×	body	320	invalid
3.0ms	15×	body	320	valid
2.0ms	13×	body	160	valid
2.0ms	20×	body	80	invalid
1.0ms	8×	body	160	invalid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	105	13
1	105	13

prune12.0ms

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: 0.4b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
0.4b	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`times-frac`
32×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-r` `sqrt-prod`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`pow1` `add-log-exp`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/`
1×	`+-commutative` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

3 → 94

Calls

3 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
10.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
6.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series55.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
39.0ms	(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
11.0ms	(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4965	1529
1	4965	1529

prune186.0ms

Filtered

69 candidates to 103 candidates (-49.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	95	10	105

Merged error: 0b

Counts

105 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.2b	(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))
0.3b	(/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

195×	`times-frac`
111×	`add-sqr-sqrt`
94×	`cbrt-prod`
91×	`add-cube-cbrt` `*-un-lft-identity`
67×	`associate-r`
47×	`sqrt-prod`
32×	`add-exp-log`
22×	`div-inv`
20×	`add-cbrt-cube`
12×	`cbrt-undiv` `div-exp`
10×	`associate-/r` `associate-/l`
7×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`pow1` `add-log-exp`
3×	`associate-l` `associate-/l/`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`+-commutative` `associate-r/` `pow-prod-down` `sum-log` `-commutative`

Counts

4 → 225

Calls

4 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
9.0ms	(/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
25.0ms	(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))
13.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series93.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
36.0ms	(/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
41.0ms	(* (cos th) (/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))
11.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify69.0ms

Algorithm

egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5231	4587

prune502.0ms

Filtered

169 candidates to 237 candidates (-40.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	235	2	237
Fresh	6	3	9
Picked	0	1	1
Done	0	0	0
Total	241	6	247

Merged error: 0b

Counts

247 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.2b	(* (cos th) (/ (* (cbrt (/ 1 2.0)) (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
0.3b	(/ (* (cbrt (/ 1 2.0)) (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
0.4b	(* (cbrt (/ 1 2.0)) (+ (* a1 a1) (* a2 a2)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
34×	`cbrt-prod`
29×	`times-frac`
25×	`*-un-lft-identity`
24×	`add-cube-cbrt`
20×	`add-exp-log`
19×	`associate-l`
16×	`associate-r`
13×	`add-cbrt-cube`
9×	`associate-/r*` `sqrt-prod`
8×	`pow1`
6×	`cbrt-div` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`flip3-+` `associate-*r/` `flip-+` `associate-/l/` `unswap-sqr`
4×	`cbrt-undiv` `frac-times` `div-exp`
3×	`div-inv`
2×	`pow-prod-down` `associate-l/` `-commutative`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `sum-log` `associate-/l*`

Counts

4 → 123

Calls

4 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
14.0ms	(* (cos th) (/ (* (cbrt (/ 1 2.0)) (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
13.0ms	(/ (* (cbrt (/ 1 2.0)) (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
9.0ms	(* (cbrt (/ 1 2.0)) (+ (* a1 a1) (* a2 a2)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
71.0ms	(* (cos th) (/ (* (cbrt (/ 1 2.0)) (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0))))
31.0ms	(/ (* (cbrt (/ 1 2.0)) (+ (* a1 a1) (* a2 a2))) (cbrt (sqrt 2.0)))
10.0ms	(* (cbrt (/ 1 2.0)) (+ (* a1 a1) (* a2 a2)))

simplify48.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4967	2138
1	4967	2138

prune267.0ms

Filtered

105 candidates to 135 candidates (-28.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	135	6	141

Merged error: 0b

Counts

141 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.2b	(/ (cos th) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
0.2b	(/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
0.2b	(* (/ (cos th) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

285×	`times-frac`
245×	`cbrt-prod`
173×	`add-sqr-sqrt`
121×	`add-cube-cbrt` `*-un-lft-identity`
88×	`associate-r`
77×	`add-exp-log`
49×	`sqrt-prod`
45×	`add-cbrt-cube`
32×	`cbrt-undiv` `div-exp`
30×	`div-inv`
22×	`prod-exp` `cbrt-unprod`
18×	`unswap-sqr`
14×	`associate-/r*`
13×	`associate-/l*`
7×	`associate-l`
6×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip-+`

Counts

4 → 313

Calls

4 calls:

9.0ms	(/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
9.0ms	(/ (cos th) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
14.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
43.0ms	(* (/ (cos th) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))

series155.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
32.0ms	(/ (cos th) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
45.0ms	(/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0))))
41.0ms	(* (/ (cos th) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (+ (* a1 a1) (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (cbrt (sqrt 2.0)))))

simplify90.0ms

Algorithm

egg-herbie

Counts

325 → 325

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5048	9991

prune1.6s

Filtered

249 candidates to 325 candidates (-30.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	325	0	325
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	325	6	331

Merged error: 0b

Counts

331 → 6

regimes359.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	19
1	20	19

end0.0ms

sample2.7s

Algorithm

intervals

Results

593.0ms	1379×	body	1280	valid
518.0ms	1216×	body	1280	invalid
348.0ms	4663×	body	80	valid
346.0ms	1137×	body	640	valid
288.0ms	941×	body	640	invalid
115.0ms	535×	body	320	valid
112.0ms	484×	body	320	invalid
42.0ms	286×	body	160	valid
41.0ms	277×	body	160	invalid
40.0ms	471×	body	80	invalid

Details

analyze757.0ms

sample94.0ms

simplify4.0ms

prune12.0ms

localize10.0ms

rewrite23.0ms

series55.0ms

simplify68.0ms

prune186.0ms

localize16.0ms

rewrite62.0ms

series93.0ms

simplify69.0ms

prune502.0ms

localize15.0ms

rewrite44.0ms

series117.0ms

simplify48.0ms

prune267.0ms

localize17.0ms

rewrite91.0ms

series155.0ms

simplify90.0ms

prune1.6s

regimes359.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.7s

Profiling