Details

Time bar (total: 4.1s)

sample72.0ms

Algorithm
intervals
Results
27.0ms49×body2560valid
13.0ms45×body640valid
12.0ms41×body1280valid
6.0ms36×body320valid
4.0ms69×body80valid
2.0ms16×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:

2.5b
(- 1.0 (cos x))
13.6b
(/ (- 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))
9.0ms
(/ (- 1.0 (cos x)) (* x x))

series67.0ms

Counts
2 → 6
Calls
2 calls:
24.0ms
(- 1.0 (cos x))
43.0ms
(/ (- 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

prune106.0ms

Pruning

9 alts after pruning (9 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))
0.2b
(* 1/24 (pow x 2))
11.0b
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite36.0ms

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))
6.0ms
(* 1/24 (pow x 2))
24.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series107.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(* 1/720 (pow x 4))
24.0ms
(* 1/24 (pow x 2))
45.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify39.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0268347
11132316
25001310

prune152.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- 1/576) (pow x 4))
0.2b
(* 1/24 (pow x 2))
18.4b
(+ (* (- 1/576) (pow x 4)) (* (+ (* 1/720 (pow x 4)) 1/2) (+ (* 1/720 (pow x 4)) 1/2)))
21.7b
(/ (+ (* (- 1/576) (pow x 4)) (* (+ (* 1/720 (pow x 4)) 1/2) (+ (* 1/720 (pow x 4)) 1/2))) (+ (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
16×add-exp-log
15×associate-*r*
13×associate-*l*
10×add-cbrt-cube
9×times-frac
8×unpow-prod-down
7×unswap-sqr
6×prod-exp add-log-exp
4×pow1 sqr-pow
3×distribute-lft-neg-in distribute-rgt-neg-in flip3-+ associate-/r* flip-+ associate-/l*
2×pow-to-exp associate-+r+ pow-exp associate-/r/ *-commutative cbrt-unprod associate-/l/ unpow2
1×cbrt-undiv +-commutative distribute-lft-neg-out distribute-rgt-in neg-mul-1 frac-2neg distribute-lft-in div-exp clear-num sum-log div-inv
Counts
4 → 104
Calls
4 calls:
8.0ms
(* (- 1/576) (pow x 4))
6.0ms
(* 1/24 (pow x 2))
5.0ms
(+ (* (- 1/576) (pow x 4)) (* (+ (* 1/720 (pow x 4)) 1/2) (+ (* 1/720 (pow x 4)) 1/2)))
34.0ms
(/ (+ (* (- 1/576) (pow x 4)) (* (+ (* 1/720 (pow x 4)) 1/2) (+ (* 1/720 (pow x 4)) 1/2))) (+ (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2))))

series265.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (- 1/576) (pow x 4))
23.0ms
(* 1/24 (pow x 2))
106.0ms
(+ (* (- 1/576) (pow x 4)) (* (+ (* 1/720 (pow x 4)) 1/2) (+ (* 1/720 (pow x 4)) 1/2)))
94.0ms
(/ (+ (* (- 1/576) (pow x 4)) (* (+ (* 1/720 (pow x 4)) 1/2) (+ (* 1/720 (pow x 4)) 1/2))) (+ (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2))))

simplify75.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
04751362
123061215
250011189

prune311.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) x)
0.1b
(/ (/ (- 1.0 (cos x)) x) x)
2.5b
(- 1.0 (cos x))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
103×add-sqr-sqrt *-un-lft-identity
69×add-cube-cbrt
24×associate-/l*
17×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 div-sub associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg diff-log
Counts
3 → 147
Calls
3 calls:
7.0ms
(/ (- 1.0 (cos x)) x)
15.0ms
(/ (/ (- 1.0 (cos x)) x) x)
3.0ms
(- 1.0 (cos x))

series106.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(/ (- 1.0 (cos x)) x)
47.0ms
(/ (/ (- 1.0 (cos x)) x) x)
18.0ms
(- 1.0 (cos x))

simplify49.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
05311270
118991197
250011186

prune256.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes40.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.4b

bsearch90.0ms

Steps
ItersRangePoint
9
0.00035723662727133143
33.11368705657117
0.02545355139751235
10
-29.541817090935037
-6.322351620237733e-11
-0.031030980254842244

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04523
14923
25023
35023

end0.0ms

sample2.1s

Algorithm
intervals
Results
908.0ms1621×body2560valid
389.0ms1238×body1280valid
342.0ms1531×body640valid
153.0ms954×body320valid
126.0ms2193×body80valid
52.0ms463×body160valid