Details

Time bar (total: 13.5s)

sample126.0ms

Algorithm
intervals
Results
40.0ms79×body1280valid
31.0ms91×body640valid
21.0ms254×body80valid
12.0ms50×body320valid
3.0ms15×body160valid

simplify18.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0267
1576
2876
31146
41326
51516
61716
71736
81736

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.2b
(* (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))

series70.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(fma a1 a1 (* a2 a2))
24.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
40.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify36.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0205467
11002399
25001393

prune429.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

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)))

series113.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(fma a1 a1 (* a2 a2))
25.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
38.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
42.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

simplify76.0ms

Algorithm
egg-herbie
Counts
237 → 237
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
06263262
129992821
250012819

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos th) (sqrt (sqrt (sqrt 2.0))))
0.2b
(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
0.3b
(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0))))
0.3b
(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0)))

rewrite382.0ms

Algorithm
rewrite-expression-head
Rules
2253×sqrt-prod
1726×times-frac
1186×add-sqr-sqrt
808×add-cube-cbrt *-un-lft-identity
376×associate-*r*
85×unswap-sqr
40×associate-*l*
37×associate-/l*
34×add-exp-log add-cbrt-cube
33×associate-/r*
30×div-inv
14×cbrt-undiv div-exp
6×pow1 prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 1077
Calls
4 calls:
6.0ms
(/ (cos th) (sqrt (sqrt (sqrt 2.0))))
254.0ms
(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
19.0ms
(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0))))
4.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0)))

series95.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(/ (cos th) (sqrt (sqrt (sqrt 2.0))))
43.0ms
(* (/ (cos th) (sqrt (sqrt (sqrt 2.0)))) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
27.0ms
(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0))))
13.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2.0)))

simplify197.0ms

Algorithm
egg-herbie
Counts
1089 → 1089
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
0259121519
1500220240

prune5.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.6b
(/ (cos th) (sqrt 2.0))
0.6b
(/ (cos th) (sqrt 2.0))

rewrite43.0ms

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:
15.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
14.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
4.0ms
(/ (cos th) (sqrt 2.0))
4.0ms
(/ (cos th) (sqrt 2.0))

series43.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
15.0ms
(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
7.0ms
(/ (cos th) (sqrt 2.0))
5.0ms
(/ (cos th) (sqrt 2.0))

simplify50.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
05101324
120211196
250021174

prune1.2s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes803.0ms

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)

IterNodesCost
01515
11515

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.3s2605×body1280valid
729.0ms2122×body640valid
662.0ms8075×body80valid
267.0ms1066×body320valid
92.0ms536×body160valid