Details

Time bar (total: 13.2s)

analyze1.1s

Algorithm
search

sample257.0ms

Algorithm
intervals
Results
79.0ms112×body1280valid
57.0ms90×body1280nan
38.0ms73×body640valid
33.0ms72×body640nan
16.0ms44×body320valid
12.0ms35×body320nan
4.0ms16×body160valid
2.0ms8×body160nan
1.0ms11×body80valid

simplify422.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04222
19722
222322
356122
4121522
5281522
6500222

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 60.6b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ PI 4.0) f)
0.3b
(* (/ PI 4.0) f)
1.0b
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
4.1b
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
55×*-un-lft-identity
53×add-sqr-sqrt
40×times-frac
31×add-cube-cbrt
26×associate-*l*
16×add-exp-log add-cbrt-cube
8×pow1
6×associate-*r* distribute-lft-out distribute-lft-out-- add-log-exp difference-of-squares
5×associate-/r*
4×prod-exp cbrt-unprod associate-/l* unswap-sqr
3×cbrt-undiv div-exp div-inv
2×flip3-- pow-prod-down associate-*l/ associate-/r/ *-commutative flip-- associate-/l/
1×sub-neg frac-2neg flip3-+ diff-log clear-num flip-+
Counts
4 → 123
Calls
4 calls:
6.0ms
(* (/ PI 4.0) f)
27.0ms
(* (/ PI 4.0) f)
10.0ms
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
6.0ms
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

series48.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (/ PI 4.0) f)
3.0ms
(* (/ PI 4.0) f)
24.0ms
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
18.0ms
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

simplify51.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04391718
115131596
250011570

prune396.0ms

Filtered
99 candidates to 135 candidates (-36.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1314135
Fresh000
Picked101
Done000
Total1324136

Merged error: 1.5b

Counts
136 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(* f PI)
0.3b
(/ (/ 4.0 f) PI)
0.4b
(* (/ 1.0 (/ PI 4.0)) (log (+ (- (* 0.08333333333333334 (* f PI)) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3)))) (/ (/ 4.0 f) PI))))
1.0b
(pow PI 3)

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
100×add-sqr-sqrt
93×*-un-lft-identity
89×add-cube-cbrt
47×associate-*l*
21×add-exp-log add-cbrt-cube
13×associate-/l*
10×pow1
9×div-inv
8×log-prod
7×associate-*r*
6×cbrt-undiv div-exp
4×distribute-rgt-in distribute-lft-in prod-exp cbrt-unprod add-log-exp unswap-sqr
3×unpow-prod-down pow-unpow cube-prod associate-/r*
2×pow-prod-down *-commutative distribute-lft-out
1×cube-mult pow-to-exp pow-pow frac-2neg unpow3 associate-*l/ pow-exp clear-num associate-/r/ log-pow associate-/l/ rem-cube-cbrt sqr-pow
Counts
4 → 186
Calls
4 calls:
4.0ms
(* f PI)
6.0ms
(/ (/ 4.0 f) PI)
27.0ms
(* (/ 1.0 (/ PI 4.0)) (log (+ (- (* 0.08333333333333334 (* f PI)) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3)))) (/ (/ 4.0 f) PI))))
2.0ms
(pow PI 3)

series34.0ms

Counts
4 → 10
Calls
4 calls:
2.0ms
(* f PI)
4.0ms
(/ (/ 4.0 f) PI)
28.0ms
(* (/ 1.0 (/ PI 4.0)) (log (+ (- (* 0.08333333333333334 (* f PI)) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3)))) (/ (/ 4.0 f) PI))))
0.0ms
(pow PI 3)

simplify47.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010142033
150011866

prune507.0ms

Filtered
148 candidates to 196 candidates (-32.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1906196
Fresh123
Picked101
Done000
Total1928200

Merged error: 1.1b

Counts
200 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ 1.0 (/ PI 4.0))) (log (+ (- (* 0.08333333333333334 (* f PI)) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3)))) (/ (/ 4.0 f) PI))))
0.3b
(* f PI)
0.3b
(/ (/ 4.0 f) PI)
1.0b
(pow PI 3)

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
103×add-sqr-sqrt
94×*-un-lft-identity
90×add-cube-cbrt
50×associate-*l*
47×sqrt-prod
14×add-exp-log add-cbrt-cube
13×associate-/l*
10×pow1
9×div-inv
8×log-prod
7×associate-*r*
5×unswap-sqr
4×distribute-rgt-in distribute-lft-in add-log-exp
3×cbrt-undiv unpow-prod-down pow-unpow cube-prod div-exp associate-/r*
2×pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out
1×cube-mult pow-to-exp pow-pow frac-2neg sqrt-div unpow3 associate-*l/ pow-exp clear-num associate-/r/ log-pow associate-/l/ rem-cube-cbrt sqr-pow
Counts
4 → 186
Calls
4 calls:
32.0ms
(* (sqrt (/ 1.0 (/ PI 4.0))) (log (+ (- (* 0.08333333333333334 (* f PI)) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3)))) (/ (/ 4.0 f) PI))))
3.0ms
(* f PI)
6.0ms
(/ (/ 4.0 f) PI)
2.0ms
(pow PI 3)

series38.0ms

Counts
4 → 10
Calls
4 calls:
32.0ms
(* (sqrt (/ 1.0 (/ PI 4.0))) (log (+ (- (* 0.08333333333333334 (* f PI)) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3)))) (/ (/ 4.0 f) PI))))
2.0ms
(* f PI)
4.0ms
(/ (/ 4.0 f) PI)
0.0ms
(pow PI 3)

simplify113.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
09592123
142152018
250032018

prune672.0ms

Filtered
153 candidates to 196 candidates (-28.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1942196
Fresh167
Picked011
Done000
Total1959204

Merged error: 1.1b

Counts
204 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (+ (* 4.0 (/ (log (/ 4.0 PI)) PI)) (* 0.08333333333333334 (* (pow f 2) PI))) (+ (* 0.01388888888888889 (/ (* (pow f 4) (pow PI 3)) (pow 4.0 2))) (+ (* 4.0 (/ (log f) PI)) (* 0.0003472222222222224 (* (pow f 4) (pow PI 3))))))
1.0b
(pow PI 3)
1.0b
(pow PI 3)
2.0b
(log (/ 4.0 PI))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
25×add-log-exp
19×add-sqr-sqrt *-un-lft-identity
17×add-cube-cbrt
13×log-prod
9×add-exp-log times-frac sum-log
8×flip3-+ frac-sub flip-+
7×pow1
6×unpow-prod-down pow-unpow diff-log cube-prod add-cbrt-cube
4×associate-*r/ frac-add
2×cube-mult pow-to-exp pow-pow unpow3 rem-log-exp pow-exp rem-cube-cbrt sqr-pow
1×sub-neg log-div flip3-- div-exp associate--l+ log-pow flip-- div-inv associate--r+ distribute-lft-out-- difference-of-squares
Counts
4 → 99
Calls
4 calls:
22.0ms
(- (+ (* 4.0 (/ (log (/ 4.0 PI)) PI)) (* 0.08333333333333334 (* (pow f 2) PI))) (+ (* 0.01388888888888889 (/ (* (pow f 4) (pow PI 3)) (pow 4.0 2))) (+ (* 4.0 (/ (log f) PI)) (* 0.0003472222222222224 (* (pow f 4) (pow PI 3))))))
2.0ms
(pow PI 3)
2.0ms
(pow PI 3)
3.0ms
(log (/ 4.0 PI))

series28.0ms

Counts
4 → 6
Calls
4 calls:
28.0ms
(- (+ (* 4.0 (/ (log (/ 4.0 PI)) PI)) (* 0.08333333333333334 (* (pow f 2) PI))) (+ (* 0.01388888888888889 (/ (* (pow f 4) (pow PI 3)) (pow 4.0 2))) (+ (* 4.0 (/ (log f) PI)) (* 0.0003472222222222224 (* (pow f 4) (pow PI 3))))))
0.0ms
(pow PI 3)
0.0ms
(pow PI 3)
0.0ms
(log (/ 4.0 PI))

simplify127.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (108.0ms)

IterNodesCost
07822052
142091953
250011945

prune391.0ms

Filtered
65 candidates to 105 candidates (-61.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1032105
Fresh167
Picked101
Done011
Total1059114

Merged error: 1.1b

Counts
114 → 9

regimes161.0ms

Accuracy

45.4% (0.4b remaining)

Error of 1.9b against oracle of 1.5b and baseline of 2.3b

bsearch2.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06146
17646
27646

end0.0ms

analyze880.0ms

Algorithm
search

sample7.6s

Algorithm
intervals
Results
2.3s3380×body1280valid
1.8s2886×body1280nan
1.2s2459×body640valid
1.0s2281×body640nan
473.0ms1325×body320valid
400.0ms1210×body320nan
146.0ms574×body160valid
56.0ms251×body160nan
33.0ms262×body80valid
0.0ms1×body80overflowed

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