Details

Time bar (total: 7.1s)

sample82.0ms

Algorithm
intervals
Results
27.0ms67×body1280valid
16.0ms70×body640valid
14.0ms257×body80valid
7.0ms39×body320valid
2.0ms17×body160valid

simplify19.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0267
1576
2876
31146
41326
51516
61716
71736
81736

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

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))

rewrite10.0ms

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:
0.0ms
(fma a1 a1 (* a2 a2))
3.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
5.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series355.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(fma a1 a1 (* a2 a2))
111.0ms
(* (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)

IterNodesCost
0205467
11002399
25001393

prune177.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (/ (pow a1 2) (sqrt 2.0)) (cos th) (/ (* (cos th) (pow a2 2)) (sqrt 2.0)))
0.1b
(* (cos th) (pow a2 2))
0.3b
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))
0.3b
(/ (pow a1 2) (sqrt 2.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
49×add-sqr-sqrt
43×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×unpow-prod-down
24×add-exp-log
13×add-cbrt-cube
12×associate-/r*
9×associate-/l* unpow2 sqr-pow
8×associate-*r*
7×div-exp
6×prod-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×cbrt-undiv pow-to-exp associate-*l* pow-exp
2×frac-2neg clear-num cbrt-unprod div-inv
1×*-commutative fma-udef
Counts
4 → 148
Calls
4 calls:
0.0ms
(fma (/ (pow a1 2) (sqrt 2.0)) (cos th) (/ (* (cos th) (pow a2 2)) (sqrt 2.0)))
9.0ms
(* (cos th) (pow a2 2))
5.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))
6.0ms
(/ (pow a1 2) (sqrt 2.0))

series457.0ms

Counts
4 → 12
Calls
4 calls:
240.0ms
(fma (/ (pow a1 2) (sqrt 2.0)) (cos th) (/ (* (cos th) (pow a2 2)) (sqrt 2.0)))
42.0ms
(* (cos th) (pow a2 2))
117.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))
58.0ms
(/ (pow a1 2) (sqrt 2.0))

simplify54.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04141106
11719958
25001948

prune404.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

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:
0.0ms
(fma a1 a1 (* a2 a2))
3.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
12.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

series652.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(fma a1 a1 (* a2 a2))
106.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
214.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
299.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

simplify79.0ms

Algorithm
egg-herbie
Counts
237 → 237
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
06263262
129992821
250012819

prune461.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 2.0)
1.0b
(cbrt 2.0)
1.0b
(/ 1 (sqrt (sqrt 2.0)))
1.0b
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
867×sqrt-prod
750×times-frac
403×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
102×cbrt-prod
34×associate-/l*
21×associate-/r*
17×add-exp-log
15×div-inv
11×sqrt-pow1 add-cbrt-cube
8×pow1 div-exp
7×pow-flip
4×cbrt-undiv expm1-log1p-u pow1/3 log1p-expm1-u add-log-exp
3×pow1/2
2×rec-exp frac-2neg 1-exp clear-num pow-div
1×associate-/l/ inv-pow
Counts
4 → 523
Calls
4 calls:
0.0ms
(cbrt 2.0)
0.0ms
(cbrt 2.0)
4.0ms
(/ 1 (sqrt (sqrt 2.0)))
21.0ms
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(cbrt 2.0)
0.0ms
(cbrt 2.0)
0.0ms
(/ 1 (sqrt (sqrt 2.0)))
0.0ms
(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))

simplify87.0ms

Algorithm
egg-herbie
Counts
527 → 527
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010787971
150027298

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes340.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02518
12518

end0.0ms

sample2.5s

Algorithm
intervals
Results
897.0ms2590×body1280valid
491.0ms2032×body640valid
454.0ms8026×body80valid
183.0ms1071×body320valid
67.0ms556×body160valid