Details

Time bar (total: 5.2s)

analyze808.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%100%0%3
0%100%0%4
0%100%0%5
0%100%0%6
0%100%0%7
0%100%0%8
0%100%0%9
0%100%0%10
0%100%0%11
0%100%0%12
3%46.9%50%13
3.1%46.8%50%14

sample85.0ms

Algorithm
intervals
Results
46.0ms112×body2560valid
19.0ms72×body1280valid
7.0ms35×body640valid
3.0ms22×body320valid
1.0ms9×body160valid
0.0ms6×body80valid

simplify90.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (89.0ms)

IterNodesCost
0579714

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.6b

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))
0.6b
(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)))

series11.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(/ (- 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)))

simplify63.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
049601050
149601050

prune111.0ms

Filtered
53 candidates to 72 candidates (-35.8%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New68472
Fresh000
Picked101
Done000
Total69473

Merged error: 0.6b

Counts
73 → 4

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(* v (* (+ v (pow v 3)) 4.0))
0.6b
(acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
3×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*l* pow-prod-down prod-exp cbrt-unprod
2×associate-*r/ associate-*l/ add-log-exp
1×acos-asin flip3-+ associate-*r* *-commutative flip-+
Counts
2 → 28
Calls
2 calls:
8.0ms
(* v (* (+ v (pow v 3)) 4.0))
1.0ms
(acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))

series14.0ms

Counts
2 → 6
Calls
2 calls:
11.0ms
(* v (* (+ v (pow v 3)) 4.0))
3.0ms
(acos (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))

simplify28.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
05085382

prune59.0ms

Filtered
21 candidates to 34 candidates (-61.9%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New31334
Fresh213
Picked101
Done000
Total34438

Merged error: 0.6b

Counts
38 → 4

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(* v (* (+ v (pow v 3)) 4.0))
0.0b
(- (/ PI 2) (asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)))
0.7b
(asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×pow1 add-exp-log add-cbrt-cube
6×*-un-lft-identity
5×add-log-exp
4×add-cube-cbrt
3×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×asin-acos associate-*r/ associate-*l/ difference-of-squares
1×sub-neg flip3-- flip3-+ times-frac diff-log associate-*r* *-commutative flip-- flip-+ distribute-lft-out-- associate--r-
Counts
3 → 43
Calls
3 calls:
9.0ms
(* v (* (+ v (pow v 3)) 4.0))
7.0ms
(- (/ PI 2) (asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)))
1.0ms
(asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))

series19.0ms

Counts
3 → 9
Calls
3 calls:
9.0ms
(* v (* (+ v (pow v 3)) 4.0))
6.0ms
(- (/ PI 2) (asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)))
3.0ms
(asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))

simplify30.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
05188791

prune98.0ms

Filtered
35 candidates to 52 candidates (-48.6%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New48452
Fresh303
Picked101
Done000
Total52456

Merged error: 0.6b

Counts
56 → 4

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ (- (/ (pow PI 3) 8) (pow (asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)) 3)) (+ (/ (* PI PI) 4) (* (asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)) (+ (/ PI 2) (asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))))))
1.0b
(pow (asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)) 3)
1.0b
(pow PI 3)
1.5b
(+ (/ PI 2) (asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
227×add-sqr-sqrt
136×times-frac
80×difference-of-squares
49×*-un-lft-identity
42×unpow-prod-down cube-prod
39×add-cube-cbrt
38×sqr-pow
24×associate-/l*
8×add-exp-log add-cbrt-cube
6×pow1 pow-unpow add-log-exp
4×associate-/r/ distribute-lft-out--
3×flip3-+ associate-/r* flip-+
2×cube-mult pow-to-exp pow-pow unpow3 associate-*r/ frac-add pow-exp associate-/l/ rem-cube-cbrt
1×cbrt-undiv +-commutative associate-+r- asin-acos flip3-- frac-2neg div-sub div-exp clear-num sum-log flip-- div-inv distribute-lft-out
Counts
4 → 177
Calls
4 calls:
34.0ms
(/ (- (/ (pow PI 3) 8) (pow (asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)) 3)) (+ (/ (* PI PI) 4) (* (asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)) (+ (/ PI 2) (asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))))))
2.0ms
(pow (asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)) 3)
2.0ms
(pow PI 3)
7.0ms
(+ (/ PI 2) (asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)))

series153.0ms

Counts
4 → 10
Calls
4 calls:
128.0ms
(/ (- (/ (pow PI 3) 8) (pow (asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)) 3)) (+ (/ (* PI PI) 4) (* (asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)) (+ (/ PI 2) (asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0))))))
20.0ms
(pow (asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)) 3)
0.0ms
(pow PI 3)
5.0ms
(+ (/ PI 2) (asin (- (* v (* (+ v (pow v 3)) 4.0)) 1.0)))

simplify91.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
0565812176

prune942.0ms

Filtered
97 candidates to 187 candidates (-92.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1852187
Fresh033
Picked101
Done000
Total1865191

Merged error: 0.6b

Counts
191 → 5

regimes50.0ms

Accuracy

0% (0.0b remaining)

Error of 0.8b against oracle of 0.7b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07598
17598

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.2s2961×body2560valid
685.0ms2506×body1280valid
262.0ms1296×body640valid
95.0ms627×body320valid
43.0ms427×body160valid
11.0ms183×body80valid
0.0ms5×body80nan

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