Details

sample84.0ms

Algorithm

intervals

Results

31.0ms	88×	body	1280	valid
15.0ms	61×	body	640	valid
15.0ms	262×	body	80	valid
4.0ms	25×	body	320	valid
2.0ms	16×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	50	7
2	77	7
3	96	7
4	112	7
5	127	7
6	141	7
7	141	7

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.5b

Counts

2 → 1

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.3b	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (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-l` `sqrt-prod`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`pow1` `add-log-exp`
3×	`flip3-+` `associate-r` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative`

Counts

3 → 98

Calls

3 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
10.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt 2.0))

series299.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* a1 a1) (* a2 a2))
209.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
62.0ms	(/ (cos th) (sqrt 2.0))

simplify59.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	490	872
1	2426	805
2	5001	791

prune272.0ms

Filtered

107 candidates to 75 candidates (70.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	100	7	107
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	100	8	108

Merged error: 0b

Counts

108 → 8

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.1b	(* (cos th) (+ (* a1 a1) (* a2 a2)))
0.4b	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 62

Calls

3 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
6.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
8.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

series345.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* a1 a1) (* a2 a2))
109.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
210.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

simplify49.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	309	564
1	1642	490
2	5001	481

prune159.0ms

Filtered

71 candidates to 50 candidates (70.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	3	3	6
Picked	0	1	1
Done	1	0	1
Total	74	5	79

Merged error: 0b

Counts

79 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

1137×	`sqrt-prod`
1119×	`times-frac`
625×	`add-sqr-sqrt`
578×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-l`
34×	`associate-/l*`
22×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
13×	`unswap-sqr`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp`
3×	`flip3-+` `associate-r` `prod-exp` `cbrt-unprod` `flip-+`
2×	`frac-times` `frac-2neg` `associate-*r/` `clear-num`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `associate-/l/`

Counts

4 → 717

Calls

4 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
55.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
6.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
16.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* a1 a1) (* a2 a2))
216.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
97.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
66.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify136.0ms

Algorithm

egg-herbie

Counts

729 → 729

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	1961	10436
1	5001	9573

prune1.5s

Filtered

729 candidates to 374 candidates (51.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	729	0	729
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	729	5	734

Merged error: 0b

Counts

734 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.1b	(* (cos th) (+ (* a1 a1) (* a2 a2)))
0.2b	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt 2.0)))
0.3b	(/ (/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 224

Calls

4 calls:

4.0ms	(+ (* a1 a1) (* a2 a2))
6.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
10.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt 2.0)))
14.0ms	(/ (/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series665.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* a1 a1) (* a2 a2))
106.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
304.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt 2.0)))
222.0ms	(/ (/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify98.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	726	3535
1	3620	3074
2	5001	3074

prune383.0ms

Filtered

236 candidates to 112 candidates (47.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	235	1	236
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	237	4	241

Merged error: 0b

Counts

241 → 4

regimes132.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	7
1	13	7

end0.0ms

sample2.5s

Algorithm

intervals

Results

923.0ms	2525×	body	1280	valid
524.0ms	2081×	body	640	valid
466.0ms	7876×	body	80	valid
184.0ms	1020×	body	320	valid
70.0ms	545×	body	160	valid

Details

sample84.0ms

simplify17.0ms

prune7.0ms

localize15.0ms

rewrite23.0ms

series299.0ms

simplify59.0ms

prune272.0ms

localize11.0ms

rewrite21.0ms

series345.0ms

simplify49.0ms

prune159.0ms

localize16.0ms

rewrite140.0ms

series406.0ms

simplify136.0ms

prune1.5s

localize12.0ms

rewrite44.0ms

series665.0ms

simplify98.0ms

prune383.0ms

regimes132.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

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