Details

Time bar (total: 19.5s)

sample127.0ms

Algorithm
intervals
Results
41.0ms42×body10240exit
27.0ms318×body80nan
25.0ms253×body80valid
1.0ms1×body640valid
0.0ms1×body320valid
0.0ms1×body160valid

simplify3.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1139
2229
3459
41159
52689
68349
731979
done50019

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b
(pow (sqrt (atan2 b b)) (- b a))
0.5b
(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b
(sqrt (atan2 b b))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×*-un-lft-identity
7×add-cube-cbrt
6×pow1 unpow-prod-down sqrt-prod
5×pow-unpow
4×add-exp-log
3×pow-pow add-cbrt-cube add-log-exp
2×unpow-prod-up sqrt-pow1 pow1/2
1×pow-to-exp sub-neg rem-sqrt-square pow-exp sqrt-pow2 distribute-lft-out-- pow-sub difference-of-squares sqr-pow
Counts
3 → 48
Calls
3 calls:
11.0ms
(pow (sqrt (atan2 b b)) (- b a))
12.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
2.0ms
(sqrt (atan2 b b))

series136.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(pow (sqrt (atan2 b b)) (- b a))
80.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
12.0ms
(sqrt (atan2 b b))

simplify2.4s

Counts
57 → 57
Iterations

Useful iterations: 3 (296.0ms)

IterNodesCost
075614
1147571
2337536
3843527
42738527
done5000527

prune167.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.6b
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
15×sqrt-prod
14×add-sqr-sqrt
12×*-un-lft-identity
10×add-cube-cbrt
9×pow1 unpow-prod-down
6×sqrt-pow1
5×add-exp-log pow-unpow pow-pow
4×pow1/2 add-cbrt-cube add-log-exp
2×unpow-prod-up rem-sqrt-square
1×pow-to-exp sub-neg pow-exp sqrt-pow2 distribute-lft-out-- pow-sub difference-of-squares sqr-pow
Counts
4 → 66
Calls
4 calls:
11.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
40.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))

series203.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
136.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
16.0ms
(sqrt (atan2 b b))
12.0ms
(sqrt (atan2 b b))

simplify4.1s

Counts
78 → 78
Iterations

Useful iterations: 3 (437.0ms)

IterNodesCost
099950
1202794
2465756
31330735
44788735
done5000735

prune318.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (* (pow (sqrt (fabs (cbrt (atan2 b b)))) (- b a)) (pow (sqrt (sqrt (cbrt (atan2 b b)))) (- b a)))))
1.0b
(cbrt (atan2 b b))
1.0b
(cbrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×sqrt-prod
2×pow1/3
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 42
Calls
4 calls:
186.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (* (pow (sqrt (fabs (cbrt (atan2 b b)))) (- b a)) (pow (sqrt (sqrt (cbrt (atan2 b b)))) (- b a)))))
2.0ms
(cbrt (atan2 b b))
2.0ms
(cbrt (atan2 b b))
2.0ms
(sqrt (atan2 b b))

series713.0ms

Counts
4 → 12
Calls
4 calls:
367.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (* (pow (sqrt (fabs (cbrt (atan2 b b)))) (- b a)) (pow (sqrt (sqrt (cbrt (atan2 b b)))) (- b a)))))
191.0ms
(cbrt (atan2 b b))
141.0ms
(cbrt (atan2 b b))
14.0ms
(sqrt (atan2 b b))

simplify1.4s

Counts
54 → 54
Iterations

Useful iterations: done (1.4s)

IterNodesCost
084762
1166734
2435634
31682613
done5000601

prune359.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (sqrt (sqrt (atan2 b b)))) (- b a))
0.5b
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (* (log (sqrt (sqrt (atan2 b b)))) (- b a)))))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
10×*-un-lft-identity
8×add-cube-cbrt associate-*l*
6×add-exp-log sqrt-pow1 sqrt-prod add-cbrt-cube
5×associate-*r* log-pow
4×pow1/2 add-log-exp
2×distribute-rgt-in sub-neg rem-sqrt-square distribute-lft-in associate-*r/
1×flip3-- pow-prod-down prod-exp *-commutative flip-- cbrt-unprod distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 64
Calls
4 calls:
34.0ms
(* (log (sqrt (sqrt (atan2 b b)))) (- b a))
49.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (* (log (sqrt (sqrt (atan2 b b)))) (- b a)))))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))

series319.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(* (log (sqrt (sqrt (atan2 b b)))) (- b a))
129.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (* (log (sqrt (sqrt (atan2 b b)))) (- b a)))))
13.0ms
(sqrt (atan2 b b))
12.0ms
(sqrt (atan2 b b))

simplify1.5s

Counts
76 → 76
Iterations

Useful iterations: 3 (622.0ms)

IterNodesCost
097942
1198887
2576718
31775704
done5000704

prune331.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

regimes88.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01222
11422
done1422

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.1s1736×body10240exit
705.0ms9724×body80nan
685.0ms7993×body80valid
6.0ms2×body640valid
1.0ms3×body160valid
1.0ms2×body320valid