Details

sample91.0ms

Algorithm

intervals

Results

32.0ms	94×	body	1280	valid
17.0ms	74×	body	640	valid
16.0ms	262×	body	80	valid
8.0ms	47×	body	320	valid
2.0ms	22×	body	160	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	26	7
1	57	6
2	87	6
3	114	6
4	132	6
5	151	6
6	171	6
7	173	6
8	173	6

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite15.0ms

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`
3×	`expm1-log1p-u` `associate-r` `associate-l` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 61

Calls

3 calls:

1.0ms	(fma a1 a1 (* a2 a2))
4.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
9.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series354.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(fma a1 a1 (* a2 a2))
107.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
211.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify34.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	205	467
1	1002	399
2	5001	393

prune185.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.1b	(* (cos th) (pow (fma a1 a1 (* a2 a2)) 1))
0.3b	(/ (* (cos th) (pow (fma a1 a1 (* a2 a2)) 1)) (sqrt 2.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log`
15×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
7×	`associate-r`
6×	`times-frac` `prod-exp` `associate-/r*` `sqrt-prod`
4×	`pow1` `unpow-prod-down` `div-exp`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `pow-to-exp` `pow-exp` `cbrt-unprod` `sqr-pow`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `fma-udef` `div-inv` `associate-/l`

Counts

3 → 69

Calls

3 calls:

1.0ms	(fma a1 a1 (* a2 a2))
5.0ms	(* (cos th) (pow (fma a1 a1 (* a2 a2)) 1))
6.0ms	(/ (* (cos th) (pow (fma a1 a1 (* a2 a2)) 1)) (sqrt 2.0))

series354.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(fma a1 a1 (* a2 a2))
107.0ms	(* (cos th) (pow (fma a1 a1 (* a2 a2)) 1))
213.0ms	(/ (* (cos th) (pow (fma a1 a1 (* a2 a2)) 1)) (sqrt 2.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	240	553
1	1191	473
2	5002	468

prune208.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
70×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l` `sqrt-prod`
32×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
12×	`prod-exp` `associate-/r*` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-r` `associate-l/` `clear-num` `-commutative`

Counts

4 → 176

Calls

4 calls:

9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms	(/ (cos th) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series334.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
107.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
60.0ms	(/ (cos th) (sqrt 2.0))
60.0ms	(/ (cos th) (sqrt 2.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	510	1324
1	2021	1196
2	5002	1174

prune461.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

1149×	`sqrt-prod`
1137×	`times-frac`
626×	`add-sqr-sqrt`
592×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-l`
37×	`associate-/l*`
34×	`add-exp-log` `add-cbrt-cube`
24×	`associate-/r*`
23×	`div-inv`
13×	`unswap-sqr`
11×	`cbrt-undiv` `div-exp`
9×	`pow1` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 752

Calls

4 calls:

50.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
6.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
16.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms	(/ (cos th) (sqrt 2.0))

series338.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
97.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
64.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
65.0ms	(/ (cos th) (sqrt 2.0))

simplify108.0ms

Algorithm

egg-herbie

Counts

764 → 764

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1552	9914
1	5002	8705

prune1.7s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes280.0ms

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	15	7
1	15	7

end0.0ms

sample2.3s

Algorithm

intervals

Results

866.0ms	2553×	body	1280	valid
478.0ms	2094×	body	640	valid
424.0ms	8064×	body	80	valid
171.0ms	1035×	body	320	valid
55.0ms	500×	body	160	valid