Details

Time bar (total: 7.8s)

sample80.0ms

Algorithm
intervals
Results
25.0ms74×body1280valid
16.0ms69×body640valid
13.0ms260×body80valid
6.0ms36×body320valid
2.0ms17×body160valid

simplify18.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0267
1576
2876
31146
41326
51516
61716
71736
81736
done1736

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite27.0ms

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:
13.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
12.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series340.0ms

Counts
2 → 6
Calls
2 calls:
116.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
224.0ms
(/ (* (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

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
38×times-frac
31×add-cube-cbrt *-un-lft-identity
22×associate-*r* sqrt-prod
9×add-exp-log add-cbrt-cube
6×associate-/r*
4×pow1
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv expm1-log1p-u div-exp prod-exp cbrt-unprod log1p-expm1-u div-inv add-log-exp
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
2 → 85
Calls
2 calls:
20.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
6.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

series335.0ms

Counts
2 → 6
Calls
2 calls:
230.0ms
(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
104.0ms
(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify39.0ms

Counts
91 → 91
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0253776
11117684
25001659
done5001659

prune225.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite60.0ms

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:
9.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
14.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
26.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series667.0ms

Counts
3 → 9
Calls
3 calls:
117.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
319.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0)))
231.0ms
(/ (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify76.0ms

Counts
224 → 224
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
06233219
129922787
250022779
done50022779

prune428.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos th) (fma a1 a1 (* a2 a2)))
0.2b
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt (sqrt 2.0))))
0.3b
(* (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
1.0b
(/ 1 (sqrt (sqrt 2.0)))

rewrite310.0ms

Algorithm
rewrite-expression-head
Rules
1038×sqrt-prod
799×times-frac
494×add-sqr-sqrt
406×*-un-lft-identity
394×add-cube-cbrt
379×associate-*r*
75×add-exp-log
49×add-cbrt-cube
32×div-exp
30×unswap-sqr
22×prod-exp
21×associate-/r*
19×associate-*l*
18×cbrt-undiv
16×div-inv
14×cbrt-unprod
11×pow1
5×pow-flip
4×expm1-log1p-u rec-exp sqrt-pow1 1-exp log1p-expm1-u associate-/l* add-log-exp
2×frac-2neg pow1/2 pow-prod-down clear-num *-commutative fma-udef
1×distribute-rgt-in frac-times distribute-lft-in associate-*r/ associate-*l/ inv-pow
Counts
4 → 583
Calls
4 calls:
9.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
17.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt (sqrt 2.0))))
220.0ms
(* (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
13.0ms
(/ 1 (sqrt (sqrt 2.0)))

series1.1s

Counts
4 → 10
Calls
4 calls:
113.0ms
(* (cos th) (fma a1 a1 (* a2 a2)))
514.0ms
(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt (sqrt 2.0))))
455.0ms
(* (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt (sqrt 2.0)))) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
0.0ms
(/ 1 (sqrt (sqrt 2.0)))

simplify113.0ms

Counts
593 → 593
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
0226210311
150029229
done50029229

prune1.1s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes142.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02016
12016
done2016

end0.0ms

sample2.5s

Algorithm
intervals
Results
848.0ms2504×body1280valid
470.0ms2115×body640valid
431.0ms8016×body80valid
163.0ms1035×body320valid
57.0ms495×body160valid