Details

Time bar (total: 10.0m)

sample157.0ms

Algorithm
intervals
Results
33.0ms63×body10240exit
18.0ms256×body80valid
17.0ms287×body80nan

simplify80.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(pow (sqrt (atan2 b b)) (- b a))
0.0b
(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b
(sqrt (atan2 b b))

rewrite24.0ms

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:
7.0ms
(pow (sqrt (atan2 b b)) (- b a))
10.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms
(sqrt (atan2 b b))

series126.0ms

Counts
3 → 9
Calls
3 calls:
23.0ms
(pow (sqrt (atan2 b b)) (- b a))
84.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
19.0ms
(sqrt (atan2 b b))

simplify41.0ms

Counts
57 → 57

prune144.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
0.0b
(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))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
84×sqrt-prod
78×unpow-prod-down
76×add-sqr-sqrt
25×unswap-sqr
23×swap-sqr
22×add-cube-cbrt *-un-lft-identity
16×add-exp-log
15×associate-*r* associate-*l*
14×sqr-pow
12×unpow-prod-up
9×prod-exp
6×pow1 pow-to-exp sub-neg pow-exp add-cbrt-cube
4×pow-sub add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×pow2 frac-times associate-*r/ pow-prod-down associate-*l/ pow-sqr *-commutative pow-prod-up cbrt-unprod
Counts
4 → 136
Calls
4 calls:
45.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
35.0ms
(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))

series175.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
103.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
15.0ms
(sqrt (atan2 b b))
12.0ms
(sqrt (atan2 b b))

simplify45.0ms

Counts
148 → 148

prune331.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
0.0b
(sin (* (pow (sqrt (sqrt 1)) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
1.0b
(sqrt (atan2 b b))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
12×sqrt-prod
9×unpow-prod-down
8×add-sqr-sqrt
7×pow1 add-cube-cbrt *-un-lft-identity
5×pow-pow sqrt-pow1
4×unpow-prod-up add-exp-log
3×pow1/2 add-cbrt-cube add-log-exp
2×distribute-rgt-in sub-neg distribute-lft-in
1×pow-to-exp rem-sqrt-square pow-unpow pow-exp sqrt-pow2 sqr-pow
Counts
3 → 50
Calls
3 calls:
8.0ms
(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
43.0ms
(sin (* (pow (sqrt (sqrt 1)) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
1.0ms
(sqrt (atan2 b b))

series8.3m

Counts
3 → 9
Calls
3 calls:
35.0ms
(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
8.3m
(sin (* (pow (sqrt (sqrt 1)) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
12.0ms
(sqrt (atan2 b b))

simplify142.0ms

Counts
59 → 59

prune963.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6))
0.0b
(sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)))
0.1b
(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)
1.0b
(sqrt (atan2 b b))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
48×unpow-prod-down
21×sqrt-prod
19×cbrt-prod
16×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
6×add-exp-log
5×pow1
4×unpow-prod-up pow-exp add-cbrt-cube add-log-exp sqr-pow
3×pow-unpow
2×pow-to-exp sub-neg
1×rem-sqrt-square pow-pow sqrt-pow1 pow1/2 pow1/3
Counts
4 → 78
Calls
4 calls:
10.0ms
(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6))
26.0ms
(sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)))
11.0ms
(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)
1.0ms
(sqrt (atan2 b b))

series217.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6))
94.0ms
(sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)))
65.0ms
(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)
15.0ms
(sqrt (atan2 b b))

simplify165.0ms

Counts
90 → 90

prune238.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes45.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.0s1797×body10240exit
883.0ms9570×body80nan
567.0ms7988×body80valid
6.0ms2×body5120valid
1.0ms2×body1280valid
1.0ms4×body320valid
0.0ms3×body160valid
0.0ms1×body640valid

end1.6m