Details

sample113.0ms

Algorithm

intervals

Results

36.0ms	81×	body	1280	valid
19.0ms	63×	body	640	valid
19.0ms	267×	body	80	valid
8.0ms	37×	body	320	valid
4.0ms	24×	body	160	valid

simplify14.0ms

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

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.4b	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite21.0ms

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:

3.0ms	(+ (* a1 a1) (* a2 a2))
10.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt 2.0))

series54.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (* a1 a1) (* a2 a2))
38.0ms	(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
10.0ms	(/ (cos th) (sqrt 2.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (44.0ms)

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

prune199.0ms

Filtered

75 candidates to 107 candidates (-42.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	99	8	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	8	108

Merged error: 0.0b

Counts

108 → 8

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite19.0ms

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:

3.0ms	(+ (* a1 a1) (* a2 a2))
6.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
8.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

series69.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
26.0ms	(* (cos th) (+ (* a1 a1) (* a2 a2)))
37.0ms	(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (37.0ms)

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

prune116.0ms

Filtered

49 candidates to 71 candidates (-44.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	71	8	79

Merged error: 0.0b

Counts

79 → 8

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow a2 2) (pow a1 2))
0.2b	(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
0.4b	(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

96×	`*-un-lft-identity`
62×	`times-frac`
48×	`add-sqr-sqrt`
40×	`add-cube-cbrt`
34×	`associate-r` `sqrt-prod`
28×	`unpow-prod-down` `distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`pow1` `associate-/l*` `add-log-exp`
3×	`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 → 122

Calls

3 calls:

7.0ms	(+ (pow a2 2) (pow a1 2))
16.0ms	(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
10.0ms	(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

series56.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (pow a2 2) (pow a1 2))
37.0ms	(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
13.0ms	(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	344	1118
1	1561	1023
2	5001	1018

prune224.0ms

Filtered

69 candidates to 131 candidates (-89.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	131	8	139

Merged error: 0.0b

Counts

139 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a1 a1) (* a2 a2))
0.4b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.6b	(/ (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:

3.0ms	(+ (* a1 a1) (* a2 a2))
52.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
15.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* a1 a1) (* a2 a2))
43.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
8.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
6.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify120.0ms

Algorithm

egg-herbie

Counts

729 → 729

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1961	10436
1	5001	9573

prune1.5s

Filtered

374 candidates to 729 candidates (-94.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	728	1	729
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	728	9	737

Merged error: 0b

Counts

737 → 9

regimes560.0ms

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

sample3.2s

Algorithm

intervals

Results

1.1s	2488×	body	1280	valid
643.0ms	2039×	body	640	valid
573.0ms	8034×	body	80	valid
237.0ms	1067×	body	320	valid
78.0ms	505×	body	160	valid

Details

sample113.0ms

simplify14.0ms

prune9.0ms

localize11.0ms

rewrite21.0ms

series54.0ms

simplify53.0ms

prune199.0ms

localize10.0ms

rewrite19.0ms

series69.0ms

simplify44.0ms

prune116.0ms

localize12.0ms

rewrite39.0ms

series56.0ms

simplify48.0ms

prune224.0ms

localize12.0ms

rewrite140.0ms

series63.0ms

simplify120.0ms

prune1.5s

regimes560.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.2s

Profiling