Details

Time bar (total: 3.1s)

sample57.0ms

Algorithm
intervals
Results
25.0ms58×body2560valid
12.0ms36×body1280valid
7.0ms54×body640valid
2.0ms24×body320valid
2.0ms73×body80valid
1.0ms11×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize6.0ms

Local error

Found 2 expressions with local error:

1.9b
(- 1.0 (cos x))
17.2b
(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

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))

series64.0ms

Counts
2 → 6
Calls
2 calls:
22.0ms
(- 1.0 (cos x))
42.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify61.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune103.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 1/720 (pow x 4))
0.4b
(* 1/24 (pow x 2))
13.6b
(- (+ (* 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 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)))

series106.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(* 1/720 (pow x 4))
28.0ms
(* 1/24 (pow x 2))
42.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify39.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0268347
11132316
25001310

prune152.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- 1.0 (cos x)))
1.9b
(- 1.0 (cos x))
1.9b
(- 1.0 (cos x))
1.9b
(- 1.0 (cos x))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity
10×add-log-exp
5×cbrt-prod add-cube-cbrt
4×pow1 add-exp-log flip3-- add-cbrt-cube flip-- distribute-lft-out-- difference-of-squares
3×sub-neg diff-log
2×cbrt-div
1×pow1/3
Counts
4 → 57
Calls
4 calls:
3.0ms
(cbrt (- 1.0 (cos x)))
4.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))

series175.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(cbrt (- 1.0 (cos x)))
18.0ms
(- 1.0 (cos x))
21.0ms
(- 1.0 (cos x))
18.0ms
(- 1.0 (cos x))

simplify51.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (46.0ms)

IterNodesCost
0150361
1391327
21222320
35001309

prune172.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.8b
(/ 1.0 (* x x))
0.8b
(/ (cos x) (* x x))
18.8b
(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-exp-log add-cbrt-cube
12×times-frac
11×*-un-lft-identity
7×add-cube-cbrt
6×associate-/l*
5×add-log-exp
4×cbrt-undiv div-exp div-inv difference-of-squares
3×pow1
2×frac-2neg prod-exp clear-num associate-/r* cbrt-unprod distribute-lft-out--
1×sub-neg flip3-- distribute-rgt-out-- diff-log frac-sub flip-- sub-div
Counts
3 → 63
Calls
3 calls:
4.0ms
(/ 1.0 (* x x))
5.0ms
(/ (cos x) (* x x))
12.0ms
(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

series131.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(/ 1.0 (* x x))
29.0ms
(/ (cos x) (* x x))
78.0ms
(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

simplify65.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0269413
1885365
23007362
35001362

prune131.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.1b

regimes39.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.3b

bsearch68.0ms

Steps
ItersRangePoint
9
1.2358748968334836e-07
0.22405535791780642
0.03173609678414467
9
-0.11986014733990268
-1.6789357321840064e-10
-0.032711082873140764

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03319
13319

end0.0ms

sample1.6s

Algorithm
intervals
Results
760.0ms1673×body2560valid
299.0ms1285×body1280valid
213.0ms1497×body640valid
87.0ms852×body320valid
73.0ms2215×body80valid
33.0ms478×body160valid