Details

Time bar (total: 4.7s)

sample327.0ms

Algorithm
intervals
Results
26.0ms53×body10240exit
17.0ms328×body80nan
15.0ms255×body80valid
1.0ms1×body1280valid

simplify57.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0135
1225
2445
31145
43215
516275
650015

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

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))

rewrite29.0ms

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 sub-neg rem-sqrt-square pow-exp sqrt-pow2 distribute-lft-out-- pow-sub difference-of-squares sqr-pow
Counts
3 → 63
Calls
3 calls:
5.0ms
(pow (sqrt (atan2 b b)) (- b a))
6.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
3.0ms
(sqrt (atan2 b b))

series106.0ms

Counts
3 → 9
Calls
3 calls:
25.0ms
(pow (sqrt (atan2 b b)) (- b a))
62.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
19.0ms
(sqrt (atan2 b b))

simplify76.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (70.0ms)

IterNodesCost
0255514
1714433
22703425
35001408

prune160.0ms

Filtered
72 candidates to 43 candidates (59.7%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (sin (pow (sqrt (atan2 b b)) (- b a))))
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))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
11×unpow-prod-up
9×prod-diff
7×pow1
6×unpow-prod-down sqrt-prod
5×add-exp-log pow-unpow log1p-expm1-u
4×expm1-log1p-u add-cbrt-cube add-log-exp
3×pow-pow
2×sqrt-pow1 pow1/2
1×pow-to-exp sub-neg rem-sqrt-square expm1-log1p pow-exp sqrt-pow2 distribute-lft-out-- expm1-udef pow-sub difference-of-squares sqr-pow
Counts
4 → 74
Calls
4 calls:
0.0ms
(expm1 (sin (pow (sqrt (atan2 b b)) (- b a))))
5.0ms
(pow (sqrt (atan2 b b)) (- b a))
6.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms
(sqrt (atan2 b b))

series188.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(expm1 (sin (pow (sqrt (atan2 b b)) (- b a))))
19.0ms
(pow (sqrt (atan2 b b)) (- b a))
61.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
10.0ms
(sqrt (atan2 b b))

simplify96.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 3 (89.0ms)

IterNodesCost
0296636
1869542
23455526
35001509

prune229.0ms

Filtered
86 candidates to 53 candidates (61.6%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (exp (expm1 (sin (pow (sqrt (atan2 b b)) (- b a))))))
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))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×*-un-lft-identity
16×add-cube-cbrt
11×unpow-prod-up
9×prod-diff
8×pow1
6×unpow-prod-down sqrt-prod
5×add-exp-log pow-unpow
4×expm1-log1p-u log-pow add-cbrt-cube log1p-expm1-u add-log-exp
3×log-prod exp-prod pow-pow
2×sqrt-pow1 pow1/2
1×pow-to-exp sub-neg rem-sqrt-square log-div exp-diff rem-log-exp pow-exp sqrt-pow2 distribute-lft-out-- expm1-udef pow-sub difference-of-squares sqr-pow
Counts
4 → 81
Calls
4 calls:
1.0ms
(log (exp (expm1 (sin (pow (sqrt (atan2 b b)) (- b a))))))
5.0ms
(pow (sqrt (atan2 b b)) (- b a))
7.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms
(sqrt (atan2 b b))

series188.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(log (exp (expm1 (sin (pow (sqrt (atan2 b b)) (- b a))))))
19.0ms
(pow (sqrt (atan2 b b)) (- b a))
61.0ms
(sin (pow (sqrt (atan2 b b)) (- b a)))
10.0ms
(sqrt (atan2 b b))

simplify98.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 3 (90.0ms)

IterNodesCost
0320728
1901617
23545601
35003584

prune273.0ms

Filtered
93 candidates to 59 candidates (63.4%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (cbrt (sqrt (atan2 b b))) (cbrt (sqrt (atan2 b b))))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))
1.0b
(sqrt (atan2 b b))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
40×cbrt-prod
29×sqrt-prod
19×add-cube-cbrt *-un-lft-identity
14×pow1
11×swap-sqr
9×associate-*r* associate-*l* unswap-sqr
6×add-exp-log pow1/3
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 103
Calls
4 calls:
9.0ms
(* (cbrt (sqrt (atan2 b b))) (cbrt (sqrt (atan2 b b))))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))
1.0ms
(sqrt (atan2 b b))

series138.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (cbrt (sqrt (atan2 b b))) (cbrt (sqrt (atan2 b b))))
10.0ms
(sqrt (atan2 b b))
10.0ms
(sqrt (atan2 b b))
13.0ms
(sqrt (atan2 b b))

simplify119.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 4 (111.0ms)

IterNodesCost
0103742
1354703
21193651
33475614
45002598

prune391.0ms

Filtered
115 candidates to 67 candidates (58.3%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

regimes37.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02023
12023

end0.0ms

sample2.1s

Algorithm
intervals
Results
775.0ms1769×body10240exit
462.0ms7996×body80valid
452.0ms9746×body80nan
1.0ms1×body1280valid
0.0ms1×body640valid
0.0ms1×body320valid
0.0ms1×body160valid