Details

Time bar (total: 4.8s)

sample328.0ms

Algorithm
intervals
Results
33.0ms73×body10240exit
16.0ms318×body80nan
15.0ms255×body80valid
1.0ms1×body160valid

simplify58.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0135
1225
2445
31145
43155
516095
650015

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(pow (sqrt (atan2 b b)) (- b a))
0.2b
(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b
(sqrt (atan2 b b))

rewrite30.0ms

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))
9.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
3.0ms
(sqrt (atan2 b b))

series97.0ms

Counts
3 → 9
Calls
3 calls:
18.0ms
(pow (sqrt (atan2 b b)) (- b a))
61.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
18.0ms
(sqrt (atan2 b b))

simplify50.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 3 (40.0ms)

IterNodesCost
0148324
1412298
21346292
35001290

prune180.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b
(pow (atan2 b b) (* 1/2 (- b a)))
0.2b
(sin (pow (atan2 b b) (* 1/2 (- b a))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
4×unpow-prod-up
3×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt unpow-prod-down *-un-lft-identity
2×distribute-rgt-in sub-neg distribute-lft-in add-cbrt-cube add-log-exp
1×pow-to-exp pow-unpow pow-pow pow-exp sqr-pow
Counts
2 → 26
Calls
2 calls:
4.0ms
(pow (atan2 b b) (* 1/2 (- b a)))
11.0ms
(sin (pow (atan2 b b) (* 1/2 (- b a))))

series79.0ms

Counts
2 → 6
Calls
2 calls:
19.0ms
(pow (atan2 b b) (* 1/2 (- b a)))
60.0ms
(sin (pow (atan2 b b) (* 1/2 (- b a))))

simplify57.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 3 (54.0ms)

IterNodesCost
0145236
1453212
21901202
35001199

prune105.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (sin (pow (atan2 b b) (* 1/2 (- b a)))) 3)
0.0b
(cbrt (pow (sin (pow (atan2 b b) (* 1/2 (- b a)))) 3))
0.1b
(pow (atan2 b b) (* 1/2 (- b a)))
0.2b
(sin (pow (atan2 b b) (* 1/2 (- b a))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×unpow-prod-down
6×pow1 add-exp-log cube-prod
5×add-cbrt-cube
4×unpow-prod-up pow-unpow add-log-exp
3×sqr-pow
2×distribute-rgt-in cube-mult pow-to-exp sub-neg pow-pow distribute-lft-in unpow3 pow-exp
1×pow1/3 rem-cbrt-cube rem-cube-cbrt
Counts
4 → 70
Calls
4 calls:
10.0ms
(pow (sin (pow (atan2 b b) (* 1/2 (- b a)))) 3)
9.0ms
(cbrt (pow (sin (pow (atan2 b b) (* 1/2 (- b a)))) 3))
4.0ms
(pow (atan2 b b) (* 1/2 (- b a)))
13.0ms
(sin (pow (atan2 b b) (* 1/2 (- b a))))

series245.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(pow (sin (pow (atan2 b b) (* 1/2 (- b a)))) 3)
57.0ms
(cbrt (pow (sin (pow (atan2 b b) (* 1/2 (- b a)))) 3))
19.0ms
(pow (atan2 b b) (* 1/2 (- b a)))
60.0ms
(sin (pow (atan2 b b) (* 1/2 (- b a))))

simplify44.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0270700
11042646
25001622

prune248.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize12.0ms

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)))
0.2b
(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))

rewrite78.0ms

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:
41.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
28.0ms
(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))

series141.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
85.0ms
(sin (* (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))

simplify49.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
02801645
111691507
250011483

prune553.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes85.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
095
195

end0.0ms

sample2.3s

Algorithm
intervals
Results
873.0ms1895×body10240exit
497.0ms9891×body80nan
491.0ms7995×body80valid
3.0ms1×body5120valid
0.0ms1×body640valid
0.0ms2×body160valid
0.0ms1×body320valid