Details

Time bar (total: 3.3s)

sample59.0ms

Algorithm
intervals
Results
29.0ms62×body2560valid
9.0ms35×body1280valid
7.0ms42×body640valid
3.0ms74×body80valid
3.0ms25×body320valid
1.0ms18×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 32.4b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.0b
(- 1.0 (cos x))
17.3b
(/ (- 1.0 (cos x)) (* x x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-cube-cbrt add-log-exp
3×distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 42
Calls
2 calls:
3.0ms
(- 1.0 (cos x))
7.0ms
(/ (- 1.0 (cos x)) (* x x))

series66.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(- 1.0 (cos x))
48.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify59.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune109.0ms

Filtered
48 candidates to 34 candidates (70.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New381048
Fresh000
Picked101
Done000
Total391049

Merged error: 0.1b

Counts
49 → 10

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 1/720 (pow x 4))
0.2b
(* 1/24 (pow x 2))
11.2b
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×associate-*r*
13×add-exp-log
9×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-log-exp
7×add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
4×sqr-pow
3×pow1
2×pow-to-exp diff-log pow-exp *-commutative cbrt-unprod unpow2
1×sub-neg flip3-- associate--l+ sum-log flip--
Counts
3 → 66
Calls
3 calls:
5.0ms
(* 1/720 (pow x 4))
5.0ms
(* 1/24 (pow x 2))
7.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series108.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(* 1/720 (pow x 4))
24.0ms
(* 1/24 (pow x 2))
48.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify44.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0268347
11132316
25001310

prune141.0ms

Filtered
75 candidates to 46 candidates (61.3%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New74175
Fresh099
Picked101
Done000
Total751085

Merged error: 0.1b

Counts
85 → 10

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 1/720 (pow x 4))
0.2b
(* 1/24 (pow x 2))
11.2b
(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×associate-*r*
13×add-exp-log
9×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-log-exp
7×add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
4×sqr-pow
3×pow1
2×pow-to-exp associate-+r+ pow-exp sum-log *-commutative cbrt-unprod unpow2
1×+-commutative associate-+r- sub-neg flip3-+ diff-log flip-+
Counts
3 → 67
Calls
3 calls:
5.0ms
(* 1/720 (pow x 4))
5.0ms
(* 1/24 (pow x 2))
6.0ms
(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

series108.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(* 1/720 (pow x 4))
29.0ms
(* 1/24 (pow x 2))
43.0ms
(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

simplify39.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0274345
11103314
25001314

prune140.0ms

Filtered
76 candidates to 47 candidates (61.8%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New76076
Fresh099
Picked011
Done000
Total761086

Merged error: 0.1b

Counts
86 → 10

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b
(/ (- 1.0 (cos x)) x)
2.0b
(- 1.0 (cos x))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
47×*-un-lft-identity
46×times-frac
29×add-cube-cbrt
27×add-exp-log
19×associate-*r*
17×add-cbrt-cube
13×associate-*l*
9×div-exp
8×prod-exp distribute-lft-out-- difference-of-squares
6×unswap-sqr
5×pow1 cbrt-undiv associate-/l* add-log-exp
4×cbrt-unprod
3×associate-/r* div-inv
2×rec-exp flip3-- 1-exp flip-- associate-/l/
1×frac-times sub-neg frac-2neg diff-log div-sub associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 114
Calls
3 calls:
17.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
6.0ms
(/ (- 1.0 (cos x)) x)
4.0ms
(- 1.0 (cos x))

series109.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
43.0ms
(/ (- 1.0 (cos x)) x)
18.0ms
(- 1.0 (cos x))

simplify62.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0521814
12334726
25001690

prune181.0ms

Filtered
123 candidates to 81 candidates (65.9%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1212123
Fresh268
Picked011
Done011
Total12310133

Merged error: 0.1b

Counts
133 → 10

regimes83.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.5b

bsearch71.0ms

Steps
ItersRangePoint
9
0.006602375602419948
2408.9151023461654
0.030982935793368763
10
-7888799.454350161
-0.0014566459989916651
-0.03319237955952178

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03411
13411

end0.0ms

sample1.8s

Algorithm
intervals
Results
809.0ms1630×body2560valid
338.0ms1245×body1280valid
260.0ms1484×body640valid
118.0ms921×body320valid
81.0ms2223×body80valid
42.0ms497×body160valid