Details

sample81.0ms

Algorithm

intervals

Results

30.0ms	81×	body	1280	valid
16.0ms	71×	body	640	valid
13.0ms	256×	body	80	valid
5.0ms	30×	body	320	valid
1.0ms	14×	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: 0.4b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite12.0ms

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)))
6.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series363.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(fma a1 a1 (* a2 a2))
113.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
216.0ms	(/ (* (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

prune191.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize15.0ms

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))
0.4b	(/ (* (cos th) (pow (fma a1 a1 (* a2 a2)) 1)) (sqrt 2.0))

rewrite15.0ms

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))
7.0ms	(/ (* (cos th) (pow (fma a1 a1 (* a2 a2)) 1)) (sqrt 2.0))

series363.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(fma a1 a1 (* a2 a2))
107.0ms	(* (cos th) (pow (fma a1 a1 (* a2 a2)) 1))
216.0ms	(/ (* (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

prune210.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 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 (sqrt 2.0)))
0.3b	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite41.0ms

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

Counts

4 → 225

Calls

4 calls:

1.0ms	(fma a1 a1 (* a2 a2))
4.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
7.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
18.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series685.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(fma a1 a1 (* a2 a2))
110.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
321.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
220.0ms	(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	626	3262
1	2999	2821
2	5001	2813

prune665.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite3.5s

Algorithm

rewrite-expression-head

Rules

56612×	`times-frac`
55503×	`sqrt-prod`
23771×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
790×	`div-inv`
429×	`associate-/r*`
55×	`associate-/l*`
43×	`associate-/r/`
34×	`add-exp-log` `add-cbrt-cube`
20×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`associate-/l/`

Counts

4 → 15587

Calls

4 calls:

7.0ms	(/ (cos th) (sqrt (sqrt (sqrt 2.0))))
401.0ms	(/ (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (sqrt (sqrt 2.0)) (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt (sqrt 2.0))))))
7.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt (sqrt 2.0))))
21.0ms	(/ (sqrt (sqrt 2.0)) (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt (sqrt 2.0)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

243.0ms	(/ (cos th) (sqrt (sqrt (sqrt 2.0))))
217.0ms	(/ (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (sqrt (sqrt 2.0)) (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt (sqrt 2.0))))))
289.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt (sqrt 2.0))))
386.0ms	(/ (sqrt (sqrt 2.0)) (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt (sqrt 2.0)))))

simplify4.3s

Algorithm

egg-herbie

Counts

15599 → 15599

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	10005	590034

prune50.8s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes143.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	15

end0.0ms

sample2.3s

Algorithm

intervals

Results

829.0ms	2492×	body	1280	valid
483.0ms	2157×	body	640	valid
404.0ms	7961×	body	80	valid
164.0ms	1004×	body	320	valid
62.0ms	572×	body	160	valid