Details

Time bar (total: 5.2s)

sample336.0ms

Algorithm
intervals
Results
28.0ms47×body10240exit
25.0ms295×body80nan
24.0ms256×body80valid

simplify57.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1225
2445
31145
43155
516095
650015

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

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))

rewrite22.0ms

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:
4.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms
(pow (sqrt (atan2 b b)) (- b a))
3.0ms
(sqrt (atan2 b b))

series104.0ms

Counts
3 → 9
Calls
3 calls:
65.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
22.0ms
(pow (sqrt (atan2 b b)) (- b a))
18.0ms
(sqrt (atan2 b b))

simplify47.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 3 (42.0ms)

IterNodesCost
0148324
1412298
21345292
35001290

prune124.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(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))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
93×sqrt-prod
87×unpow-prod-down
82×add-sqr-sqrt
28×*-un-lft-identity
26×add-cube-cbrt
25×unswap-sqr
23×swap-sqr
17×add-exp-log
15×associate-*r* associate-*l* sqr-pow
14×unpow-prod-up
9×pow1 prod-exp
7×pow-to-exp sub-neg pow-exp
6×sqrt-pow1 add-cbrt-cube
5×pow-unpow pow-pow pow-sub
4×pow1/2 add-log-exp
2×rem-sqrt-square
1×pow2 frac-times associate-*r/ pow-prod-down associate-*l/ pow-sqr *-commutative pow-prod-up sqrt-pow2 cbrt-unprod distribute-lft-out-- difference-of-squares
Counts
4 → 162
Calls
4 calls:
5.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
28.0ms
(* (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))

series88.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(pow (sqrt (sqrt (atan2 b b))) (- b a))
37.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
10.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))

simplify51.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
02921757
113511646
250011602

prune342.0ms

Pruning

2 alts after pruning (2 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)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a)))))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))
5.3b
(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
70×add-sqr-sqrt
66×sqrt-prod
60×unpow-prod-down
55×log-prod
40×exp-sum
30×unswap-sqr
19×add-cube-cbrt *-un-lft-identity
18×associate-*r*
15×associate-*l*
14×sqr-pow
8×add-exp-log
6×pow1 unpow-prod-up add-cbrt-cube
5×pow-sub
4×add-log-exp
3×sub-neg log-div rem-log-exp prod-exp
2×pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 exp-diff pow-exp
1×frac-times associate-*r/ associate-*l/ log-pow *-commutative cbrt-unprod
Counts
4 → 131
Calls
4 calls:
38.0ms
(* (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))
4.0ms
(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series142.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a)))))
10.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))
84.0ms
(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify45.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03161765
110691488
250011409

prune351.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite11.0ms

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:
5.0ms
(sin (* 1 (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
4.0ms
(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
1.0ms
(sqrt (atan2 b b))

series120.0ms

Counts
3 → 9
Calls
3 calls:
77.0ms
(sin (* 1 (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
30.0ms
(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
13.0ms
(sqrt (atan2 b b))

simplify168.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 3 (162.0ms)

IterNodesCost
0219471
1788427
24338399
35002379

prune129.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes43.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
11214

end0.0ms

sample2.9s

Algorithm
intervals
Results
957.0ms1850×body10240exit
765.0ms7990×body80valid
747.0ms9789×body80nan
5.0ms4×body2560valid
3.0ms1×body5120valid
1.0ms2×body1280valid
1.0ms2×body640valid
0.0ms1×body160valid