Details

Time bar (total: 6.8s)

sample53.0ms

Algorithm
intervals
Results
24.0ms48×body2560valid
9.0ms43×body1280valid
6.0ms42×body640valid
3.0ms31×body320valid
3.0ms78×body80valid
1.0ms14×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

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize6.0ms

Local error

Found 2 expressions with local error:

2.2b
(- 1.0 (cos x))
14.6b
(/ (- 1.0 (cos x)) (* x x))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×prod-diff
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-log-exp
3×fma-neg distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv expm1-log1p-u flip3-- div-exp flip-- log1p-expm1-u associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 58
Calls
2 calls:
6.0ms
(- 1.0 (cos x))
13.0ms
(/ (- 1.0 (cos x)) (* x x))

series68.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(- 1.0 (cos x))
50.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0279446
11006326
25001317

prune132.0ms

Filtered
64 candidates to 43 candidates (67.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.2b
(/ (- 1.0 (cos x)) x)
2.2b
(- 1.0 (cos x))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
69×add-sqr-sqrt
54×*-un-lft-identity
46×times-frac
36×add-cube-cbrt
27×add-exp-log
19×associate-*r*
17×add-cbrt-cube
13×associate-*l*
9×div-exp prod-diff
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×expm1-log1p-u fma-neg associate-/r* log1p-expm1-u 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 → 132
Calls
3 calls:
21.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
11.0ms
(/ (- 1.0 (cos x)) x)
3.0ms
(- 1.0 (cos x))

series109.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
48.0ms
(/ (- 1.0 (cos x)) x)
19.0ms
(- 1.0 (cos x))

simplify72.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0582999
12640823
25001787

prune254.0ms

Filtered
141 candidates to 92 candidates (65.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
0.3b
(+ 1.0 (cos x))
0.3b
(pow (cos x) 3)
1.9b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
233×add-sqr-sqrt
165×*-un-lft-identity
144×prod-diff
138×unpow-prod-down cube-prod
113×add-cube-cbrt
80×difference-of-squares
75×times-frac
66×sqr-pow
26×cube-mult unpow3
25×associate-/l* distribute-lft-out--
12×fma-neg
8×add-log-exp
7×add-exp-log add-cbrt-cube
5×pow1 difference-cubes
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow fma-def associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv +-commutative pow-to-exp sub-neg pow-pow frac-2neg flip3-+ diff-log div-sub div-exp pow-exp clear-num sum-log flip-+ div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 354
Calls
4 calls:
57.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
3.0ms
(+ 1.0 (cos x))
1.0ms
(pow (cos x) 3)
20.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series212.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
10.0ms
(+ 1.0 (cos x))
35.0ms
(pow (cos x) 3)
49.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify151.0ms

Algorithm
egg-herbie
Counts
366 → 366
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
08284951
132444033
250023940

prune496.0ms

Filtered
366 candidates to 124 candidates (33.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ 1.0 (cos x))
0.3b
(+ 1.0 (cos x))
0.3b
(pow (cos x) 3)
2.2b
(- (/ (pow 1.0 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (/ (pow (cos x) 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))))

rewrite327.0ms

Algorithm
rewrite-expression-head
Rules
2986×times-frac
1881×add-sqr-sqrt
1837×*-un-lft-identity
1801×add-cube-cbrt
1600×prod-diff
754×unpow-prod-down cube-prod
254×sqr-pow
244×cube-mult unpow3
83×div-inv
40×fma-neg
25×difference-of-squares
16×distribute-lft-out--
10×add-log-exp
6×fma-def
5×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow
2×+-commutative flip3-+ sum-log flip-+ distribute-lft-out
1×pow-to-exp sub-neg flip3-- distribute-rgt-out-- pow-pow diff-log pow-exp frac-sub flip-- sub-div rem-cube-cbrt
Counts
4 → 1757
Calls
4 calls:
3.0ms
(+ 1.0 (cos x))
3.0ms
(+ 1.0 (cos x))
1.0ms
(pow (cos x) 3)
122.0ms
(- (/ (pow 1.0 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (/ (pow (cos x) 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))))

series428.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(+ 1.0 (cos x))
9.0ms
(+ 1.0 (cos x))
28.0ms
(pow (cos x) 3)
381.0ms
(- (/ (pow 1.0 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))) (/ (pow (cos x) 3) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0))))

simplify852.0ms

Algorithm
egg-herbie
Counts
1769 → 1769
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
02898118199
1500195507

prune1.6s

Filtered
1769 candidates to 338 candidates (19.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes52.0ms

Accuracy

99.4% (0.2b remaining)

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

bsearch72.0ms

Steps
ItersRangePoint
9
0.0004320794088804456
4086.0217424804537
0.0328884568480627
7
-0.37949367736095085
-0.007251023403816859
-0.034062018349277

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04948
14948

end0.0ms

sample1.6s

Algorithm
intervals
Results
737.0ms1593×body2560valid
302.0ms1297×body1280valid
223.0ms1435×body640valid
102.0ms928×body320valid
78.0ms2297×body80valid
38.0ms450×body160valid