Details

Time bar (total: 4.6s)

sample97.0ms

Algorithm
intervals
Results
42.0ms107×body2560valid
17.0ms61×body1280valid
9.0ms241×body80nan
7.0ms35×body640valid
5.0ms32×body320valid
1.0ms10×body160valid
1.0ms11×body80valid

simplify99.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1427
2777
31467
42427
54177
627897
750027

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.7b

Counts
2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.1b
(* 5.0 (* v v))
0.7b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×times-frac
10×add-exp-log add-cbrt-cube
8×pow1
4×associate-/r* difference-of-squares
3×associate-*l* pow-prod-down prod-exp cbrt-unprod associate-/l* add-log-exp
2×flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv acos-asin frac-2neg div-sub div-exp associate-*r* clear-num *-commutative div-inv unswap-sqr
Counts
3 → 63
Calls
3 calls:
7.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
5.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series12.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
3.0ms
(* 5.0 (* v v))
3.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify37.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0336587
11261535
25002531

prune124.0ms

Filtered
55 candidates to 72 candidates (-30.9%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New67572
Fresh000
Picked101
Done000
Total68573

Merged error: 0.7b

Counts
73 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.0b
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.1b
(* 5.0 (* v v))
0.7b
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
16×*-un-lft-identity
14×add-cube-cbrt
13×times-frac
11×add-exp-log add-cbrt-cube
9×pow1
6×add-log-exp difference-of-squares
4×associate-/r*
3×flip3-- associate-*l* pow-prod-down prod-exp flip-- cbrt-unprod associate-/l*
2×asin-acos associate-/r/ associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp associate-*r* clear-num *-commutative div-inv distribute-lft-out-- associate--r- unswap-sqr
Counts
4 → 79
Calls
4 calls:
7.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
7.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
5.0ms
(* 5.0 (* v v))
1.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series16.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
5.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
3.0ms
(* 5.0 (* v v))
3.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify41.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0409840
11459784
25001780

prune155.0ms

Filtered
69 candidates to 91 candidates (-31.9%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New88391
Fresh224
Picked101
Done000
Total91596

Merged error: 0.7b

Counts
96 → 5

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow v 2) (pow v 4))
0.0b
(* 4.0 (+ (pow v 2) (pow v 4)))
0.7b
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
7×add-sqr-sqrt
5×pow1 add-exp-log add-cube-cbrt add-cbrt-cube add-log-exp
4×associate-*r*
3×associate-*l*
2×flip3-+ associate-*r/ flip-+ distribute-lft-out
1×+-commutative distribute-rgt-in acos-asin distribute-lft-in pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
3 → 43
Calls
3 calls:
6.0ms
(+ (pow v 2) (pow v 4))
9.0ms
(* 4.0 (+ (pow v 2) (pow v 4)))
1.0ms
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

series19.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(+ (pow v 2) (pow v 4))
8.0ms
(* 4.0 (+ (pow v 2) (pow v 4)))
3.0ms
(acos (- (* 4.0 (+ (pow v 2) (pow v 4))) 1.0))

simplify153.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0177315
1834276
24136273
35002273

prune99.0ms

Filtered
34 candidates to 52 candidates (-52.9%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New51152
Fresh134
Picked011
Done000
Total52557

Merged error: 0.7b

Counts
57 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
0.9b
(sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
0.9b
(sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0b
(* (sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
46×sqrt-prod
32×*-un-lft-identity
21×pow1
16×sqrt-div
14×add-cube-cbrt
13×swap-sqr
12×difference-of-squares
10×sqrt-pow1 pow1/2
9×associate-*r* associate-*l*
8×flip3-- flip-- distribute-lft-out--
6×add-exp-log times-frac add-cbrt-cube
5×pow-prod-up
4×frac-times add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/
1×pow2 asin-acos pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 112
Calls
4 calls:
1.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
6.0ms
(sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
6.0ms
(sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
18.0ms
(* (sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))

series33.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
12.0ms
(sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
12.0ms
(sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
6.0ms
(* (sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (sqrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))

simplify207.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 3 (188.0ms)

IterNodesCost
02202009
17661847
246021791
350011761

prune226.0ms

Filtered
68 candidates to 124 candidates (-82.4%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1204124
Fresh123
Picked011
Done011
Total1218129

Merged error: 0.6b

Counts
129 → 8

regimes237.0ms

Accuracy

0% (0.2b remaining)

Error of 0.7b against oracle of 0.5b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0136
1136

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.2s3050×body2560valid
673.0ms2483×body1280valid
299.0ms7796×body80nan
249.0ms1240×body640valid
90.0ms615×body320valid
43.0ms405×body160valid
12.0ms207×body80valid

Profiling

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