Details

Time bar (total: 31.5s)

sample186.0ms

Algorithm
intervals
Results
81.0ms85×body1280valid
28.0ms55×body640valid
26.0ms250×body80valid
12.0ms35×body320valid
5.0ms21×body160valid

simplify152.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
01219
13713
29612
316212
417012
done17012

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.2b
(* (fma a1 a1 (* a2 a2)) (cos th))
0.4b
(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (sqrt 2.0))

rewrite43.0ms

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* log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod
1×frac-2neg pow-prod-down clear-num *-commutative fma-udef div-inv associate-/l* unswap-sqr
Counts
3 → 59
Calls
3 calls:
0.0ms
(fma a1 a1 (* a2 a2))
14.0ms
(* (fma a1 a1 (* a2 a2)) (cos th))
27.0ms
(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (sqrt 2.0))

series501.0ms

Counts
3 → 9
Calls
3 calls:
71.0ms
(fma a1 a1 (* a2 a2))
165.0ms
(* (fma a1 a1 (* a2 a2)) (cos th))
265.0ms
(/ (* (fma a1 a1 (* a2 a2)) (cos th)) (sqrt 2.0))

simplify7.7s

Counts
68 → 68
Iterations

Useful iterations: done (7.7s)

IterNodesCost
0100919
11397883
done5000746

prune333.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma a1 a1 (* a2 a2))
0.1b
(/ (cos th) (cbrt (sqrt 2.0)))
0.2b
(/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.3b
(* (/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (cos th) (cbrt (sqrt 2.0))))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
71×add-sqr-sqrt
70×times-frac
49×add-cube-cbrt *-un-lft-identity
46×cbrt-prod
32×add-exp-log
31×associate-*r*
23×sqrt-prod
22×add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
9×prod-exp cbrt-unprod
8×unswap-sqr
7×associate-*l*
6×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
2×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative fma-udef
Counts
4 → 158
Calls
4 calls:
1.0ms
(fma a1 a1 (* a2 a2))
24.0ms
(/ (cos th) (cbrt (sqrt 2.0)))
23.0ms
(/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
67.0ms
(* (/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (cos th) (cbrt (sqrt 2.0))))

series1.4s

Counts
4 → 12
Calls
4 calls:
53.0ms
(fma a1 a1 (* a2 a2))
364.0ms
(/ (cos th) (cbrt (sqrt 2.0)))
671.0ms
(/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
263.0ms
(* (/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (cos th) (cbrt (sqrt 2.0))))

simplify897.0ms

Counts
170 → 170
Iterations

Useful iterations: done (889.0ms)

IterNodesCost
02303419
done50003295

prune995.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite281.0ms

Algorithm
rewrite-expression-head
Rules
285×times-frac
245×cbrt-prod
173×add-sqr-sqrt
121×add-cube-cbrt *-un-lft-identity
88×associate-*r*
77×add-exp-log
49×sqrt-prod
45×add-cbrt-cube
32×cbrt-undiv div-exp
30×div-inv
22×prod-exp cbrt-unprod
18×unswap-sqr
14×associate-/r*
13×associate-/l*
7×associate-*l*
6×pow1
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 → 319
Calls
4 calls:
20.0ms
(/ (cos th) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
13.0ms
(/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
163.0ms
(* (/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (/ (cos th) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0)))))
51.0ms
(/ (/ (cos th) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0))))

series1.8s

Counts
4 → 12
Calls
4 calls:
524.0ms
(/ (cos th) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
587.0ms
(/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
323.0ms
(* (/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (/ (cos th) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0)))))
395.0ms
(/ (/ (cos th) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0))))

simplify578.0ms

Counts
331 → 331
Iterations

Useful iterations: done (556.0ms)

IterNodesCost
043510519
done500110082

prune2.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite504.0ms

Algorithm
rewrite-expression-head
Rules
365×add-exp-log
277×times-frac
238×cbrt-prod
153×div-exp prod-exp
152×add-sqr-sqrt
134×*-un-lft-identity
132×add-cube-cbrt
120×add-cbrt-cube
110×associate-*r*
77×cbrt-undiv cbrt-unprod
45×sqrt-prod
30×div-inv
20×pow1
16×rec-exp 1-exp
13×associate-/r*
10×associate-/l*
8×associate-*l* unswap-sqr
6×frac-times pow-flip pow1/3 associate-*l/ pow-div
4×expm1-log1p-u associate-*r/ pow-prod-down log1p-expm1-u add-log-exp
2×frac-2neg clear-num pow-sqr *-commutative pow-prod-up
1×pow2 pow-plus associate-/l/
Counts
4 → 410
Calls
4 calls:
110.0ms
(* (/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (cos th) (cbrt 1)))
18.0ms
(/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
276.0ms
(* (* (/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (cos th) (cbrt 1))) (/ (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0)))))
56.0ms
(/ (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0))))

series2.2s

Counts
4 → 10
Calls
4 calls:
898.0ms
(* (/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (cos th) (cbrt 1)))
617.0ms
(/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
727.0ms
(* (* (/ (fma a1 a1 (* a2 a2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (cos th) (cbrt 1))) (/ (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0)))))
0.0ms
(/ (/ 1 (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (cbrt (cbrt (sqrt 2.0))))

simplify2.6s

Counts
420 → 420
Iterations

Useful iterations: done (2.6s)

IterNodesCost
053714730
done500012502

prune2.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes262.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: done (5.0ms)

IterNodesCost
02037
12436
done2434

end0.0ms

sample6.0s

Algorithm
intervals
Results
1.9s2515×body1280valid
1.5s2125×body640valid
1.4s8074×body80valid
365.0ms1041×body320valid
101.0ms511×body160valid