Details

Time bar (total: 3.3s)

sample52.0ms

Algorithm
intervals
Results
25.0ms57×body2560valid
9.0ms58×body640valid
6.0ms28×body1280valid
3.0ms27×body320valid
2.0ms75×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

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: 31.5b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.3b
(- 1.0 (cos x))
16.0b
(/ (- 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))

series64.0ms

Counts
2 → 6
Calls
2 calls:
17.0ms
(- 1.0 (cos x))
46.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify63.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune107.0ms

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: 0.0b

Counts
49 → 10

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

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:
8.0ms
(/ (/ (- 1.0 (cos x)) x) x)
6.0ms
(/ (- 1.0 (cos x)) x)
4.0ms
(- 1.0 (cos x))

series109.0ms

Counts
3 → 9
Calls
3 calls:
45.0ms
(/ (/ (- 1.0 (cos x)) x) x)
42.0ms
(/ (- 1.0 (cos x)) x)
22.0ms
(- 1.0 (cos x))

simplify52.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
05311270
118991197
250011186

prune221.0ms

Filtered
156 candidates to 102 candidates (65.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1506156
Fresh549
Picked101
Done000
Total15610166

Merged error: 0.0b

Counts
166 → 10

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
0.1b
(/ (cos x) x)
1.5b
(- (/ 1.0 x) (/ (cos x) x))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
98×add-sqr-sqrt
95×times-frac
78×*-un-lft-identity
38×add-cube-cbrt
20×distribute-lft-out-- difference-of-squares
15×associate-/l*
12×div-inv
7×add-exp-log add-cbrt-cube
6×associate-/r*
5×distribute-rgt-out-- add-log-exp
4×associate-/l/
3×pow1
2×cbrt-undiv flip3-- frac-2neg div-exp clear-num frac-sub flip-- sub-div
1×sub-neg diff-log div-sub
Counts
3 → 118
Calls
3 calls:
16.0ms
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
4.0ms
(/ (cos x) x)
15.0ms
(- (/ 1.0 x) (/ (cos x) x))

series187.0ms

Counts
3 → 9
Calls
3 calls:
98.0ms
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
29.0ms
(/ (cos x) x)
59.0ms
(- (/ 1.0 x) (/ (cos x) x))

simplify46.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04631015
11518940
25001936

prune229.0ms

Filtered
127 candidates to 101 candidates (79.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1261127
Fresh099
Picked101
Done000
Total12710137

Merged error: 0.0b

Counts
137 → 10

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- (/ 1.0 x) (* (cos x) (/ 1 x))) x)
0.1b
(* (cos x) (/ 1 x))
1.5b
(- (/ 1.0 x) (* (cos x) (/ 1 x)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
23×times-frac
21×*-un-lft-identity
20×add-cube-cbrt
14×add-exp-log
13×associate-*r*
10×add-cbrt-cube
7×div-inv
6×associate-/l/
5×pow1 distribute-rgt-out-- associate-*r/ un-div-inv add-log-exp
4×prod-exp frac-sub associate-/l* sub-div
3×div-exp associate-*l* associate-/r* unswap-sqr
2×cbrt-undiv flip3-- flip-- cbrt-unprod
1×sub-neg rec-exp frac-2neg diff-log 1-exp div-sub pow-prod-down clear-num *-commutative
Counts
3 → 91
Calls
3 calls:
9.0ms
(/ (- (/ 1.0 x) (* (cos x) (/ 1 x))) x)
7.0ms
(* (cos x) (/ 1 x))
6.0ms
(- (/ 1.0 x) (* (cos x) (/ 1 x)))

series189.0ms

Counts
3 → 9
Calls
3 calls:
98.0ms
(/ (- (/ 1.0 x) (* (cos x) (/ 1 x))) x)
30.0ms
(* (cos x) (/ 1 x))
60.0ms
(- (/ 1.0 x) (* (cos x) (/ 1 x)))

simplify49.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0432678
11826583
25001560

prune148.0ms

Filtered
100 candidates to 75 candidates (75.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New991100
Fresh099
Picked011
Done000
Total9911110

Merged error: 0.0b

Counts
110 → 11

regimes49.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.0b

bsearch56.0ms

Steps
ItersRangePoint
6
0.011261476250181132
0.06406876111163662
0.03363822156293231
9
-3.7752751361666412
-2.6386627092684764e-08
-0.0354657383711672

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03512
13512

end0.0ms

sample1.6s

Algorithm
intervals
Results
734.0ms1603×body2560valid
283.0ms1241×body1280valid
222.0ms1541×body640valid
92.0ms918×body320valid
74.0ms2208×body80valid
40.0ms489×body160valid