Details

Time bar (total: 3.7s)

sample53.0ms

Algorithm
intervals
Results
24.0ms51×body2560valid
9.0ms39×body1280valid
7.0ms46×body640valid
3.0ms30×body320valid
2.0ms68×body80valid
2.0ms22×body160valid

simplify8.0ms

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: 30.5b

localize10.0ms

Local error

Found 2 expressions with local error:

2.4b
(- 1.0 (cos x))
15.3b
(/ (- 1.0 (cos x)) (* x x))

rewrite16.0ms

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:
3.0ms
(- 1.0 (cos x))
10.0ms
(/ (- 1.0 (cos x)) (* x x))

series68.0ms

Counts
2 → 6
Calls
2 calls:
24.0ms
(- 1.0 (cos x))
44.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0279446
11006326
25001317

prune136.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b
(/ (- 1.0 (cos x)) x)
2.4b
(- 1.0 (cos x))

rewrite43.0ms

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:
25.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
9.0ms
(/ (- 1.0 (cos x)) x)
3.0ms
(- 1.0 (cos x))

series109.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
42.0ms
(/ (- 1.0 (cos x)) x)
19.0ms
(- 1.0 (cos x))

simplify73.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0582999
12640823
25001787

prune261.0ms

Pruning

15 alts after pruning (15 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)) (/ 1 x)))
0.2b
(* (- 1.0 (cos x)) (/ 1 x))
2.4b
(- 1.0 (cos x))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
77×add-exp-log
40×prod-exp
36×add-sqr-sqrt
30×*-un-lft-identity
29×add-cbrt-cube
25×add-cube-cbrt
20×times-frac div-exp
18×associate-*l*
14×associate-*r*
12×frac-times cbrt-unprod
10×pow1 rec-exp 1-exp
9×associate-*r/ prod-diff
7×flip3-- associate-*l/ flip--
6×cbrt-undiv
5×add-log-exp
4×pow-prod-down
3×expm1-log1p-u fma-neg un-div-inv log1p-expm1-u unswap-sqr
2×*-commutative div-inv distribute-lft-out-- difference-of-squares
1×sub-neg diff-log
Counts
3 → 137
Calls
3 calls:
26.0ms
(* (/ 1 x) (* (- 1.0 (cos x)) (/ 1 x)))
15.0ms
(* (- 1.0 (cos x)) (/ 1 x))
3.0ms
(- 1.0 (cos x))

series111.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(* (/ 1 x) (* (- 1.0 (cos x)) (/ 1 x)))
43.0ms
(* (- 1.0 (cos x)) (/ 1 x))
22.0ms
(- 1.0 (cos x))

simplify67.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
06091041
12657783
25001759

prune240.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* x (cos x)) (+ 1.0 (cos x)))
0.3b
(pow (cos x) 3)
0.4b
(+ 1.0 (cos x))
2.2b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
144×prod-diff
108×add-sqr-sqrt
98×*-un-lft-identity
90×unpow-prod-down cube-prod
84×add-cube-cbrt
34×sqr-pow
26×cube-mult unpow3
16×difference-of-squares
12×fma-neg
10×pow1 add-exp-log add-cbrt-cube
8×add-log-exp
5×distribute-lft-out--
4×expm1-log1p-u associate-*r* log1p-expm1-u
3×pow-unpow fma-def pow-prod-down prod-exp cbrt-unprod
2×flip3-+ associate-*r/ flip-+ distribute-lft-out
1×difference-cubes +-commutative distribute-rgt-in pow-to-exp sub-neg flip3-- pow-pow distribute-lft-in diff-log associate-*l* pow-exp sum-log *-commutative flip-- rem-cube-cbrt
Counts
4 → 259
Calls
4 calls:
12.0ms
(* (* x (cos x)) (+ 1.0 (cos x)))
1.0ms
(pow (cos x) 3)
3.0ms
(+ 1.0 (cos x))
24.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series162.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (* x (cos x)) (+ 1.0 (cos x)))
28.0ms
(pow (cos x) 3)
10.0ms
(+ 1.0 (cos x))
54.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify136.0ms

Algorithm
egg-herbie
Counts
271 → 271
Iterations

Useful iterations: 2 (109.0ms)

IterNodesCost
06762846
130671936
250011907

prune305.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes69.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.3b

bsearch74.0ms

Steps
ItersRangePoint
9
0.004380743253548005
488.5072251079851
0.03299608739970331
9
-3.9934486818618
-6.3299436832828755e-06
-0.033320062920463786

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04226
14226

end0.0ms

sample1.6s

Algorithm
intervals
Results
724.0ms1551×body2560valid
287.0ms1180×body1280valid
232.0ms1552×body640valid
99.0ms950×body320valid
70.0ms2258×body80valid
38.0ms509×body160valid