Details

Time bar (total: 22.0s)

sample198.0ms

Algorithm
intervals
Results
63.0ms84×body1280valid
38.0ms237×body80valid
37.0ms69×body640valid
13.0ms35×body320valid
7.0ms25×body160valid

simplify681.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
01219
12613
25712
38712
411412
513212
615012
717012
817212
done17212

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize12.0ms

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))

rewrite36.0ms

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:
21.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
13.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series487.0ms

Counts
2 → 6
Calls
2 calls:
184.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
303.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify3.4s

Counts
57 → 57
Iterations

Useful iterations: done (3.4s)

IterNodesCost
0100839
1198806
2744692
33458674
done5000673

prune286.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite110.0ms

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:
19.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
54.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
28.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

series1.5s

Counts
3 → 9
Calls
3 calls:
152.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
314.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
1.0s
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

simplify1.1s

Counts
136 → 136
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02123744
14703409
217572941
done50002924

prune546.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize24.0ms

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))

rewrite45.0ms

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:
10.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
34.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series503.0ms

Counts
2 → 6
Calls
2 calls:
175.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
328.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify3.4s

Counts
57 → 57
Iterations

Useful iterations: done (3.4s)

IterNodesCost
0100839
1198806
2744692
33458674
done5000673

prune248.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
234×sqrt-prod
216×times-frac
95×add-sqr-sqrt
93×add-cube-cbrt *-un-lft-identity
19×add-exp-log add-cbrt-cube
18×associate-/r*
14×associate-/l*
12×div-inv
7×cbrt-undiv div-exp
5×pow1
3×expm1-log1p-u associate-*r* associate-*l* prod-exp cbrt-unprod 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 → 215
Calls
3 calls:
18.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
32.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
22.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

series964.0ms

Counts
3 → 9
Calls
3 calls:
170.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
358.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
435.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))

simplify1.2s

Counts
224 → 224
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02665478
16134865
217344448
done50004378

prune589.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes225.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01012
11112
done1112

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.3s2506×body1280valid
1.5s8004×body80valid
1.1s2088×body640valid
520.0ms1028×body320valid
106.0ms544×body160valid