Details

Time bar (total: 19.7s)

sample172.0ms

Algorithm
intervals
Results
77.0ms104×body1280valid
26.0ms71×body640valid
23.0ms268×body80valid
8.0ms28×body320valid
5.0ms22×body160valid

simplify307.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
01219
12613
25712
38712
411412
513212
615112
717312
817512
done17512

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.5b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite51.0ms

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))
20.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
27.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series581.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(fma a1 a1 (* a2 a2))
204.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
336.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify1.3s

Counts
70 → 70
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0103947
1216911
21322777
done5000775

prune267.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
38×times-frac
32×add-cube-cbrt *-un-lft-identity
22×associate-*r* sqrt-prod
10×add-exp-log add-cbrt-cube
6×associate-/r*
5×pow1
3×expm1-log1p-u associate-*l* log1p-expm1-u associate-/l* add-log-exp unswap-sqr
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative fma-udef
Counts
3 → 95
Calls
3 calls:
1.0ms
(fma a1 a1 (* a2 a2))
50.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
7.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

series508.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(fma a1 a1 (* a2 a2))
309.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
148.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify2.2s

Counts
104 → 104
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01311616
12761537
220571325
done50001323

prune471.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize35.0ms

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
(/ (pow a1 2) (sqrt 2.0))
0.4b
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

rewrite100.0ms

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:
1.0ms
(fma (/ (pow a1 2) (sqrt 2.0)) (cos th) (/ (* (cos th) (pow a2 2)) (sqrt 2.0)))
30.0ms
(* (cos th) (pow a2 2))
21.0ms
(/ (pow a1 2) (sqrt 2.0))
39.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

series737.0ms

Counts
4 → 12
Calls
4 calls:
376.0ms
(fma (/ (pow a1 2) (sqrt 2.0)) (cos th) (/ (* (cos th) (pow a2 2)) (sqrt 2.0)))
77.0ms
(* (cos th) (pow a2 2))
122.0ms
(/ (pow a1 2) (sqrt 2.0))
160.0ms
(/ (* (cos th) (pow a2 2)) (sqrt 2.0))

simplify1.8s

Counts
160 → 160
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02292047
14331858
224221631
done50001630

prune653.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize16.0ms

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)))

rewrite100.0ms

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))
10.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
54.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
24.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
55.0ms
(fma a1 a1 (* a2 a2))
140.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
355.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
520.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

simplify1.8s

Counts
237 → 237
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02695586
16404970
233604599
done50004496

prune738.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes286.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01423
11523
done1523

end0.0ms

sample6.3s

Algorithm
intervals
Results
1.9s2619×body1280valid
1.7s2051×body640valid
1.4s8078×body80valid
380.0ms1001×body320valid
145.0ms507×body160valid