Details

Time bar (total: 18.4s)

sample182.0ms

Algorithm
intervals
Results
76.0ms52×body10240exit
47.0ms339×body80nan
39.0ms256×body80valid

simplify1.4s

Counts
1 → 1
Iterations
IterNodes
done5000
5438
4117
345
222
113
07

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

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))

rewrite14.0ms

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 insert-posit16 add-log-exp
2×unpow-prod-up 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 → 51
Calls
3 calls:
7.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
5.0ms
(pow (sqrt (atan2 b b)) (- b a))
1.0ms
(sqrt (atan2 b b))

series133.0ms

Counts
3 → 9
Calls
3 calls:
90.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
25.0ms
(pow (sqrt (atan2 b b)) (- b a))
18.0ms
(sqrt (atan2 b b))

simplify2.1s

Counts
60 → 60
Iterations
IterNodes
done5001
34103
2656
1191
078

prune312.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

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))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
84×sqrt-prod
78×unpow-prod-down
76×add-sqr-sqrt
25×unswap-sqr
23×swap-sqr
22×*-un-lft-identity add-cube-cbrt
16×add-exp-log
15×associate-*r* associate-*l*
14×sqr-pow
12×unpow-prod-up
9×prod-exp
6×pow-to-exp pow1 sub-neg add-cbrt-cube pow-exp
4×insert-posit16 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 → 140
Calls
4 calls:
54.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
45.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0ms
(sqrt (atan2 b b))
2.0ms
(sqrt (atan2 b b))

series213.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
49.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
19.0ms
(sqrt (atan2 b b))
22.0ms
(sqrt (atan2 b b))

simplify1.8s

Counts
152 → 152
Iterations
IterNodes
done5002
21481
1327
0149

prune966.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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×add-cbrt-cube pow1/2 insert-posit16 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 → 73
Calls
3 calls:
30.0ms
(pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a)))
41.0ms
(sin (pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a))))
1.0ms
(sqrt (atan2 b b))

series161.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a)))
108.0ms
(sin (pow (sqrt (sqrt (atan2 b b))) (+ (- b a) (- b a))))
18.0ms
(sqrt (atan2 b b))

simplify1.1s

Counts
82 → 82
Iterations
IterNodes
done5002
21404
1357
0125

prune360.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize61.0ms

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))

rewrite154.0ms

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×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Counts
4 → 79
Calls
4 calls:
147.0ms
(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))

series110.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(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)))))
20.0ms
(sqrt (atan2 b b))
19.0ms
(sqrt (atan2 b b))
11.0ms
(sqrt (atan2 b b))

simplify2.0s

Counts
91 → 91
Iterations
IterNodes
done5000
33187
2655
1256
0143

prune616.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes85.0ms

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

sample6.3s

Algorithm
intervals
Results
2.3s1800×body10240exit
2.0s9820×body80nan
1.6s7991×body80valid
6.0ms1×body5120valid
3.0ms1×body2560valid
1.0ms1×body1280valid
1.0ms2×body320valid
1.0ms2×body640valid
1.0ms2×body160valid