Details

Time bar (total: 17.1s)

sample121.0ms

Algorithm
intervals
Results
37.0ms47×body10240exit
26.0ms293×body80nan
24.0ms255×body80valid
5.0ms1×body5120valid

simplify1.7s

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b
(pow (sqrt (atan2 b b)) (- b a))
0.3b
(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b
(sqrt (atan2 b b))

rewrite30.0ms

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 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 → 63
Calls
3 calls:
7.0ms
(pow (sqrt (atan2 b b)) (- b a))
14.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
6.0ms
(sqrt (atan2 b b))

series140.0ms

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

simplify1.2s

Counts
72 → 72
Iterations
IterNodes
done5001
21102
1315
0117

prune383.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.2b
(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))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
18×*-un-lft-identity
16×add-cube-cbrt
15×sqrt-prod
11×unpow-prod-up
9×pow1 unpow-prod-down prod-diff
6×sqrt-pow1
5×pow-unpow pow-pow add-exp-log
4×expm1-log1p-u add-cbrt-cube pow1/2 log1p-expm1-u add-log-exp
2×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 → 83
Calls
4 calls:
15.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
42.0ms
(sin (* (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))

series205.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
130.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
12.0ms
(sqrt (atan2 b b))
19.0ms
(sqrt (atan2 b b))

simplify1.7s

Counts
95 → 95
Iterations
IterNodes
done5001
21427
1391
0146

prune484.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))
3.6b
(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
24×log-prod
18×add-sqr-sqrt
16×*-un-lft-identity add-cube-cbrt
15×sqrt-prod
11×unpow-prod-up
9×unpow-prod-down prod-diff
6×pow1 add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×pow-to-exp log-div sub-neg pow-exp log-pow pow-sub sqr-pow
Counts
4 → 77
Calls
4 calls:
56.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))
7.0ms
(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
13.0ms
(sqrt (atan2 b b))
12.0ms
(sqrt (atan2 b b))
96.0ms
(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify1.1s

Counts
89 → 89
Iterations
IterNodes
done5000
21032
1363
0164

prune683.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
23×add-sqr-sqrt
22×associate-*r*
12×add-cube-cbrt
11×pow1
10×distribute-lft-out--
8×associate-*l*
7×distribute-rgt-out add-exp-log distribute-lft-out
6×add-cbrt-cube associate-*r/ log-pow
5×sqrt-pow1
4×expm1-log1p-u flip3-- frac-add log1p-expm1-u flip-- add-log-exp difference-of-squares
3×log-prod pow1/2 sqrt-prod
2×distribute-lft1-in distribute-rgt1-in
1×distribute-rgt-in rem-sqrt-square distribute-lft-in flip3-+ count-2 rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 90
Calls
4 calls:
33.0ms
(sin (exp (* (log (sqrt (sqrt (atan2 b b)))) (+ (- b a) (- b a)))))
143.0ms
(* (log (sqrt (sqrt (atan2 b b)))) (+ (- b a) (- b a)))
45.0ms
(log (sin (exp (* (log (sqrt (sqrt (atan2 b b)))) (+ (- b a) (- b a))))))
2.0ms
(sqrt (atan2 b b))

series531.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(sin (exp (* (log (sqrt (sqrt (atan2 b b)))) (+ (- b a) (- b a)))))
215.0ms
(* (log (sqrt (sqrt (atan2 b b)))) (+ (- b a) (- b a)))
166.0ms
(log (sin (exp (* (log (sqrt (sqrt (atan2 b b)))) (+ (- b a) (- b a))))))
21.0ms
(sqrt (atan2 b b))

simplify1.7s

Counts
102 → 102
Iterations
IterNodes
done5000
21959
1438
0164

prune598.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes100.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done12
112
011

end0.0ms

sample5.5s

Algorithm
intervals
Results
1.7s7988×body80valid
1.6s1888×body10240exit
1.4s9645×body80nan
21.0ms5×body5120valid
1.0ms6×body160valid
1.0ms1×body320valid