Details

Time bar (total: 3.8s)

sample58.0ms

Algorithm
intervals
Results
28.0ms59×body2560valid
9.0ms59×body640valid
8.0ms38×body1280valid
2.0ms70×body80valid
2.0ms18×body320valid
1.0ms12×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: 33.9b

localize6.0ms

Local error

Found 2 expressions with local error:

1.3b
(- 1.0 (cos x))
18.5b
(/ (- 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:
4.0ms
(- 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))

simplify61.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune105.0ms

Pruning

9 alts after pruning (8 fresh and 1 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))
13.4b
(- (+ (* 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)))

series113.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(* 1/720 (pow x 4))
25.0ms
(* 1/24 (pow x 2))
47.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify37.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0268347
11132316
25001310

prune152.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- 1/576) (pow x 4))
0.2b
(* 1/24 (pow x 2))
19.2b
(+ (* (- 1/576) (pow x 4)) (* (+ (* 1/720 (pow x 4)) 1/2) (+ (* 1/720 (pow x 4)) 1/2)))
21.3b
(/ (+ (* (- 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))))

rewrite35.0ms

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:
7.0ms
(* (- 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)))
14.0ms
(/ (+ (* (- 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))))

series270.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (- 1/576) (pow x 4))
24.0ms
(* 1/24 (pow x 2))
112.0ms
(+ (* (- 1/576) (pow x 4)) (* (+ (* 1/720 (pow x 4)) 1/2) (+ (* 1/720 (pow x 4)) 1/2)))
97.0ms
(/ (+ (* (- 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))))

simplify79.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
04751362
123061215
250011189

prune314.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- 1.0 (cos x))) x)
0.1b
(/ (sqrt (- 1.0 (cos x))) x)
1.3b
(- 1.0 (cos x))
1.3b
(- 1.0 (cos x))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt *-un-lft-identity
48×times-frac
40×sqrt-prod
38×add-cube-cbrt
16×associate-/l*
10×distribute-lft-out-- difference-of-squares
8×add-exp-log add-cbrt-cube add-log-exp
6×associate-/r*
4×pow1 flip3-- sqrt-div flip-- associate-/l/
2×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
4 → 126
Calls
4 calls:
6.0ms
(/ (sqrt (- 1.0 (cos x))) x)
6.0ms
(/ (sqrt (- 1.0 (cos x))) x)
4.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))

series221.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ (sqrt (- 1.0 (cos x))) x)
93.0ms
(/ (sqrt (- 1.0 (cos x))) x)
18.0ms
(- 1.0 (cos x))
18.0ms
(- 1.0 (cos x))

simplify98.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
02421020
1706972
22968960
35002960

prune278.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes85.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 32.1b

bsearch97.0ms

Steps
ItersRangePoint
10
4.9177062248324165e-05
42925490.781275615
0.03263027133962249
8
-1.0806682141483241
-0.0004106978961831668
-0.026802849257838823

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05636
16036
26136
36136

end0.0ms

sample1.6s

Algorithm
intervals
Results
752.0ms1585×body2560valid
304.0ms1257×body1280valid
231.0ms1538×body640valid
107.0ms905×body320valid
73.0ms2254×body80valid
34.0ms461×body160valid