Details

Time bar (total: 5.9s)

analyze767.0ms

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

sample82.0ms

Algorithm
intervals
Results
40.0ms95×body2560valid
24.0ms91×body1280valid
7.0ms38×body640valid
2.0ms15×body320valid
1.0ms12×body160valid
0.0ms5×body80valid

simplify88.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (86.0ms)

IterNodesCost
0579714

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.4b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 5.0 (* v v))
0.4b
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
4×add-sqr-sqrt
3×add-cube-cbrt *-un-lft-identity associate-*l* pow-prod-down prod-exp cbrt-unprod
2×add-log-exp
1×acos-asin associate-*r* *-commutative unswap-sqr
Counts
2 → 27
Calls
2 calls:
5.0ms
(* 5.0 (* v v))
1.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series6.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(* 5.0 (* v v))
3.0ms
(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify43.0ms

Algorithm
egg-herbie
Counts
33 → 33
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
04932310
14932310

prune45.0ms

Filtered
20 candidates to 33 candidates (-65.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New31233
Fresh000
Picked101
Done000
Total32234

Merged error: 0.4b

Counts
34 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
0.1b
(* 5.0 (* v v))
0.5b
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×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 difference-of-squares
1×sub-neg flip3-- times-frac diff-log associate-*r* *-commutative flip-- distribute-lft-out-- associate--r- unswap-sqr
Counts
3 → 42
Calls
3 calls:
7.0ms
(- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
6.0ms
(* 5.0 (* v v))
1.0ms
(asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series11.0ms

Counts
3 → 9
Calls
3 calls:
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)))

simplify47.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
05063767

prune75.0ms

Filtered
34 candidates to 51 candidates (-50.0%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New49251
Fresh101
Picked011
Done000
Total50353

Merged error: 0.4b

Counts
53 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0b
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0b
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0b
(* (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
50×cbrt-prod
35×*-un-lft-identity
18×cbrt-div
15×add-cube-cbrt
14×difference-of-squares
11×pow1 swap-sqr
9×flip3-- pow1/3 associate-*r* associate-*l* flip-- distribute-lft-out--
7×times-frac
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 107
Calls
4 calls:
6.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
8.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
6.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
17.0ms
(* (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))

series201.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
46.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
48.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
60.0ms
(* (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))

simplify63.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049573853
149573853

prune446.0ms

Filtered
78 candidates to 119 candidates (-52.6%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1163119
Fresh011
Picked101
Done011
Total1175122

Merged error: 0.4b

Counts
122 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
1.0b
(* (pow (cbrt (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))) 2) (cbrt (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))))
1.0b
(* (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))
1.0b
(pow (cbrt (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))) 2)

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
110×cbrt-prod
102×add-sqr-sqrt
46×*-un-lft-identity
33×unpow-prod-down
26×associate-*l*
24×add-cube-cbrt
22×unswap-sqr
21×associate-*r*
18×cbrt-div
16×difference-of-squares
13×pow1
12×add-exp-log
11×swap-sqr
10×distribute-lft-out--
8×flip3-- times-frac pow1/3 flip--
6×unpow2
5×add-cbrt-cube sqr-pow
4×frac-times associate-*r/ prod-exp add-log-exp
3×pow-unpow pow-prod-up
2×pow-to-exp pow-pow pow-plus pow-prod-down associate-*l/ pow-exp pow-sqr *-commutative cbrt-unprod
1×pow2 pow3
Counts
4 → 167
Calls
4 calls:
6.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
24.0ms
(* (pow (cbrt (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))) 2) (cbrt (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))))
17.0ms
(* (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))
9.0ms
(pow (cbrt (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))) 2)

series213.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))
48.0ms
(* (pow (cbrt (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))) 2) (cbrt (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))))
62.0ms
(* (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))) (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))))
56.0ms
(pow (cbrt (cbrt (- (/ PI 2) (asin (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))) 2)

simplify97.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
049376016
149376016

prune966.0ms

Filtered
112 candidates to 179 candidates (-59.8%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1763179
Fresh123
Picked101
Done011
Total1786184

Merged error: 0.4b

Counts
184 → 6

regimes148.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06418
16418

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.2s2993×body2560valid
673.0ms2508×body1280valid
253.0ms1266×body640valid
87.0ms605×body320valid
42.0ms400×body160valid
13.0ms228×body80valid
0.0ms4×body80nan

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