Details

Time bar (total: 16.0s)

sample78.0ms

Algorithm
intervals
Results
25.0ms81×body1280valid
14.0ms284×body80valid
14.0ms67×body640valid
4.0ms25×body320valid
2.0ms15×body160valid

simplify18.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0267
1576
2876
31146
41326
51516
61716
71736
81736
done1736

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* sqrt-prod
4×pow1
3×associate-*r* associate-*l*
2×cbrt-undiv expm1-log1p-u div-exp prod-exp cbrt-unprod fma-udef log1p-expm1-u add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num *-commutative div-inv associate-/l* unswap-sqr
Counts
2 → 51
Calls
2 calls:
9.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
14.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series343.0ms

Counts
2 → 6
Calls
2 calls:
116.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
226.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify32.0ms

Counts
57 → 57
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0202424
1995365
25001359
done5001359

prune160.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
56×times-frac
36×cbrt-prod
35×add-exp-log add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
22×add-cbrt-cube
18×sqrt-prod
13×cbrt-undiv div-exp
12×div-inv
10×associate-/r*
9×prod-exp cbrt-unprod
6×associate-/l*
5×pow1
3×expm1-log1p-u associate-*r* associate-*l* log1p-expm1-u add-log-exp
2×frac-2neg clear-num fma-udef
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative associate-/l/ unswap-sqr
Counts
3 → 127
Calls
3 calls:
9.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
21.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
26.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series1.0s

Counts
3 → 9
Calls
3 calls:
115.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
685.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
228.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify73.0ms

Counts
136 → 136
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
04882207
125281901
250011871
done50011871

prune393.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))
0.3b
(/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))
0.3b
(* (/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
0.7b
(/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

rewrite706.0ms

Algorithm
rewrite-expression-head
Rules
1848×times-frac
1647×cbrt-prod
1173×add-sqr-sqrt
812×add-cube-cbrt *-un-lft-identity
510×sqrt-prod
376×associate-*r*
92×add-exp-log
85×unswap-sqr
65×associate-/l*
49×add-cbrt-cube
43×cbrt-undiv div-exp
35×associate-*l*
33×div-inv
23×prod-exp cbrt-unprod
22×associate-/r*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×associate-/l/
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 1109
Calls
4 calls:
26.0ms
(/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))
7.0ms
(/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))
534.0ms
(* (/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
28.0ms
(/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
434.0ms
(/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))
306.0ms
(/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0)))
239.0ms
(* (/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (fma a1 a1 (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
348.0ms
(/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

simplify236.0ms

Counts
1121 → 1121
Iterations

Useful iterations: 1 (61.0ms)

IterNodesCost
0363726959
1500226339
done500226339

prune4.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (sqrt (fma a1 a1 (* a2 a2))) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))
0.3b
(* (/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (* (hypot a1 a2) (/ (/ (sqrt (fma a1 a1 (* a2 a2))) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))))
0.7b
(/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
6.5b
(sqrt (fma a1 a1 (* a2 a2)))

rewrite399.0ms

Algorithm
rewrite-expression-head
Rules
1541×times-frac
1407×cbrt-prod
792×sqrt-prod
781×add-sqr-sqrt
780×add-cube-cbrt *-un-lft-identity
123×add-exp-log
89×associate-/l*
75×add-cbrt-cube
48×cbrt-undiv div-exp
45×prod-exp cbrt-unprod
35×associate-*l*
19×div-inv
13×associate-/r*
10×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r/ pow-prod-down
2×frac-2neg clear-num associate-/l/
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* associate-*l/ *-commutative fma-udef hypot-def
Counts
4 → 974
Calls
4 calls:
38.0ms
(/ (/ (sqrt (fma a1 a1 (* a2 a2))) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))
232.0ms
(* (/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (* (hypot a1 a2) (/ (/ (sqrt (fma a1 a1 (* a2 a2))) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))))
32.0ms
(/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
2.0ms
(sqrt (fma a1 a1 (* a2 a2)))

series1.1s

Counts
4 → 12
Calls
4 calls:
414.0ms
(/ (/ (sqrt (fma a1 a1 (* a2 a2))) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))
319.0ms
(* (/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (* (hypot a1 a2) (/ (/ (sqrt (fma a1 a1 (* a2 a2))) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))))
369.0ms
(/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
46.0ms
(sqrt (fma a1 a1 (* a2 a2)))

simplify200.0ms

Counts
986 → 986
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
0244022822
1500121550
done500121550

prune3.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes172.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01413
11413
done1413

end0.0ms

sample2.4s

Algorithm
intervals
Results
828.0ms2603×body1280valid
434.0ms2065×body640valid
402.0ms8087×body80valid
161.0ms1067×body320valid
55.0ms545×body160valid