Details

Time bar (total: 20.4s)

sample643.0ms

Algorithm
intervals
Results
187.0ms339×body80nan
116.0ms52×body10240exit
110.0ms256×body80valid

simplify1.8s

Counts
1 → 1
Iterations
IterNodes
done5000
5444
4117
345
222
113
07

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 3 expressions with local error:

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
15×*-un-lft-identity
13×add-cube-cbrt
11×unpow-prod-up
9×prod-diff
6×pow1 unpow-prod-down sqrt-prod
5×pow-unpow
4×add-exp-log
3×expm1-log1p-u pow-pow add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×sqrt-pow1 pow1/2
1×pow-to-exp rem-sqrt-square sub-neg pow-exp sqrt-pow2 distribute-lft-out-- pow-sub difference-of-squares sqr-pow
Counts
3 → 66
Calls
3 calls:
25.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
11.0ms
(pow (sqrt (atan2 b b)) (- b a))
5.0ms
(sqrt (atan2 b b))

series138.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
32.0ms
(pow (sqrt (atan2 b b)) (- b a))
31.0ms
(sqrt (atan2 b b))

simplify1.1s

Counts
75 → 75
Iterations
IterNodes
done5000
21105
1318
0120

prune344.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
100×add-sqr-sqrt
84×sqrt-prod
78×unpow-prod-down
48×unpow-prod-up
46×*-un-lft-identity add-cube-cbrt
36×prod-diff
32×swap-sqr
25×unswap-sqr
24×associate-*r* associate-*l*
16×add-exp-log
14×sqr-pow
9×prod-exp
6×pow-to-exp pow1 sub-neg add-cbrt-cube pow-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u pow-sub add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×pow2 frac-times pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up cbrt-unprod
Counts
4 → 175
Calls
4 calls:
49.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
34.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
2.0ms
(sqrt (atan2 b b))
2.0ms
(sqrt (atan2 b b))

series218.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
68.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
12.0ms
(sqrt (atan2 b b))
12.0ms
(sqrt (atan2 b b))

simplify2.5s

Counts
187 → 187
Iterations
IterNodes
done5001
22608
1514
0217

prune871.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 3 expressions with local error:

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

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
22×pow-unpow
21×add-sqr-sqrt
12×add-cube-cbrt sqrt-prod
10×distribute-lft-out--
9×unpow-prod-down
7×pow1 distribute-rgt-out distribute-lft-out
5×pow-pow sqrt-pow1
4×add-exp-log difference-of-squares
3×expm1-log1p-u add-cbrt-cube pow1/2 insert-posit16 log1p-expm1-u add-log-exp
2×distribute-lft1-in distribute-rgt1-in pow-sub
1×pow-to-exp unpow-prod-up rem-sqrt-square associate-+r- count-2 pow-exp associate-+l- sqrt-pow2 sqr-pow
Counts
3 → 79
Calls
3 calls:
29.0ms
(pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a)))
41.0ms
(sin (pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a))))
2.0ms
(sqrt (atan2 b b))

series170.0ms

Counts
3 → 9
Calls
3 calls:
59.0ms
(pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a)))
99.0ms
(sin (pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a))))
11.0ms
(sqrt (atan2 b b))

simplify1.8s

Counts
88 → 88
Iterations
IterNodes
done5002
21423
1365
0131

prune369.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (* (* (pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a))) (pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a)))) (pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a)))))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
54×pow-sub
28×frac-times
27×associate-+r- associate-+l-
26×cbrt-div
14×associate-*l/
10×add-sqr-sqrt
9×sqrt-prod
8×associate-*r/
7×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 87
Calls
4 calls:
175.0ms
(cbrt (* (* (pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a))) (pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a)))) (pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a)))))
2.0ms
(sqrt (atan2 b b))
2.0ms
(sqrt (atan2 b b))
2.0ms
(sqrt (atan2 b b))

series85.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(cbrt (* (* (pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a))) (pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a)))) (pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a)))))
18.0ms
(sqrt (atan2 b b))
17.0ms
(sqrt (atan2 b b))
12.0ms
(sqrt (atan2 b b))

simplify2.1s

Counts
99 → 99
Iterations
IterNodes
done5000
33209
2665
1260
0147

prune671.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes74.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done13
113
012

end0.0ms

sample6.9s

Algorithm
intervals
Results
2.9s1800×body10240exit
1.9s7991×body80valid
1.6s9820×body80nan
6.0ms1×body5120valid
3.0ms1×body2560valid
2.0ms2×body640valid
2.0ms1×body1280valid
1.0ms2×body320valid
1.0ms2×body160valid