Details

Time bar (total: 4.4s)

sample55.0ms

Algorithm
intervals
Results
21.0ms46×body2560valid
11.0ms41×body1280valid
8.0ms53×body640valid
4.0ms31×body320valid
3.0ms70×body80valid
1.0ms15×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: 30.7b

localize6.0ms

Local error

Found 2 expressions with local error:

1.9b
(- 1.0 (cos x))
14.8b
(/ (- 1.0 (cos x)) (* x x))

rewrite18.0ms

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))

series60.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(- 1.0 (cos x))
42.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify32.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0279446
11006326
25001317

prune134.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) x)
0.1b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
1.9b
(- 1.0 (cos x))

rewrite38.0ms

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:
8.0ms
(/ (- 1.0 (cos x)) x)
21.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
3.0ms
(- 1.0 (cos x))

series111.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(/ (- 1.0 (cos x)) x)
42.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
22.0ms
(- 1.0 (cos x))

simplify69.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
0582999
12640823
25001787

prune244.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

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
(pow (cos x) 3)
0.4b
(+ 1.0 (cos x))
1.7b
(- (pow 1.0 3) (pow (cos x) 3))

rewrite101.0ms

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)))
1.0ms
(pow (cos x) 3)
3.0ms
(+ 1.0 (cos x))
20.0ms
(- (pow 1.0 3) (pow (cos x) 3))

series211.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ (- (pow 1.0 3) (pow (cos x) 3)) (fma (cos x) (+ 1.0 (cos x)) (* 1.0 1.0)))
28.0ms
(pow (cos x) 3)
10.0ms
(+ 1.0 (cos x))
53.0ms
(- (pow 1.0 3) (pow (cos x) 3))

simplify146.0ms

Algorithm
egg-herbie
Counts
366 → 366
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
08284951
132444033
250023940

prune504.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos x) 3)
0.3b
(pow (pow (cos x) 3) 3)
0.4b
(+ 1.0 (cos x))
1.7b
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
400×cbrt-prod
396×prod-diff
374×unpow-prod-down cube-prod
278×add-sqr-sqrt
217×*-un-lft-identity
213×add-cube-cbrt
97×sqr-pow
74×cube-mult unpow3
44×difference-of-squares
12×fma-neg
8×add-log-exp
7×add-exp-log
6×pow-unpow add-cbrt-cube
5×pow1 pow-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-to-exp fma-def
2×pow-pow rem-cube-cbrt
1×+-commutative sub-neg flip3-- flip3-+ diff-log sum-log flip-- flip-+ distribute-lft-out distribute-lft-out--
Counts
4 → 554
Calls
4 calls:
1.0ms
(pow (cos x) 3)
3.0ms
(pow (pow (cos x) 3) 3)
3.0ms
(+ 1.0 (cos x))
49.0ms
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

series153.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(pow (cos x) 3)
58.0ms
(pow (pow (cos x) 3) 3)
10.0ms
(+ 1.0 (cos x))
56.0ms
(- (pow 1.0 3) (cbrt (pow (pow (cos x) 3) 3)))

simplify175.0ms

Algorithm
egg-herbie
Counts
566 → 566
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
09279840
127405065
250014777

prune364.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes61.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.7b

bsearch100.0ms

Steps
ItersRangePoint
10
4.8244160186105205e-08
257763.20554958374
0.03363901833902096
10
-772.3369502403921
-4.163765984402517e-10
-0.03168275196437828

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04641
14641

end0.0ms

sample1.7s

Algorithm
intervals
Results
778.0ms1587×body2560valid
307.0ms1247×body1280valid
243.0ms1482×body640valid
117.0ms962×body320valid
104.0ms2289×body80valid
38.0ms433×body160valid