Details

Time bar (total: 6.3s)

sample90.0ms

Algorithm
intervals
Results
46.0ms145×body1280valid
20.0ms24×body2560valid
11.0ms59×body640valid
3.0ms24×body320valid
0.0ms3×body160valid
0.0ms1×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.0b

localize14.0ms

Local error

Found 2 expressions with local error:

1.0b
(- (cos (+ x eps)) (cos x))
4.2b
(cos (+ x eps))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-exp-log add-cube-cbrt cos-sum add-cbrt-cube
1×associate--l- sub-neg flip3-- diff-log flip-- diff-cos distribute-lft-out-- difference-of-squares
Counts
2 → 24
Calls
2 calls:
7.0ms
(- (cos (+ x eps)) (cos x))
5.0ms
(cos (+ x eps))

series69.0ms

Counts
2 → 6
Calls
2 calls:
52.0ms
(- (cos (+ x eps)) (cos x))
16.0ms
(cos (+ x eps))

simplify117.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
0134176
1281167
2840164
32958164
45002164

prune90.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos x) (cos eps))
0.1b
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b
(* (sin x) (sin eps))
2.0b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×add-log-exp
10×*-un-lft-identity
8×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
6×associate-*r* associate-*l*
4×diff-log
3×sub-neg cos-mult sin-mult
2×flip3-- pow-prod-down prod-exp associate--l+ *-commutative flip-- cbrt-unprod unswap-sqr
1×associate--l- frac-sub distribute-lft-out-- sub-div difference-of-squares
Counts
4 → 70
Calls
4 calls:
4.0ms
(* (cos x) (cos eps))
5.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
4.0ms
(* (sin x) (sin eps))
21.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series313.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (cos x) (cos eps))
86.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
46.0ms
(* (sin x) (sin eps))
136.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify117.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0304632
11061601
24487583
35002583

prune249.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos x) (cos eps))
0.1b
(- (- (* (sin x) (sin eps))) (cos x))
0.2b
(* (sin x) (sin eps))
2.0b
(+ (* (cos x) (cos eps)) (- (- (* (sin x) (sin eps))) (cos x)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
16×add-log-exp
14×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
6×associate-*r* associate-*l*
4×diff-log
3×sum-log cos-mult
2×sub-neg associate-+r+ flip3-- pow-prod-down neg-log frac-add prod-exp *-commutative flip-- cbrt-unprod unswap-sqr
1×+-commutative associate--l- neg-sub0 associate-+r- flip3-+ flip-+ sin-mult distribute-lft-out-- difference-of-squares
Counts
4 → 72
Calls
4 calls:
6.0ms
(* (cos x) (cos eps))
6.0ms
(- (- (* (sin x) (sin eps))) (cos x))
4.0ms
(* (sin x) (sin eps))
14.0ms
(+ (* (cos x) (cos eps)) (- (- (* (sin x) (sin eps))) (cos x)))

series289.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (cos x) (cos eps))
56.0ms
(- (- (* (sin x) (sin eps))) (cos x))
51.0ms
(* (sin x) (sin eps))
135.0ms
(+ (* (cos x) (cos eps)) (- (- (* (sin x) (sin eps))) (cos x)))

simplify47.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0362707
11473662
25001640

prune276.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.4b
(pow (cos x) 3)
0.5b
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
1.8b
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
22×*-un-lft-identity
18×unpow-prod-down cube-prod
16×difference-of-squares
11×add-log-exp
10×add-cube-cbrt sqr-pow
6×pow1 add-exp-log pow-unpow add-cbrt-cube
5×distribute-lft-out--
4×cube-div
2×cube-mult pow-to-exp sub-neg associate-+l+ flip3-- pow-pow diff-log unpow3 pow-exp sum-log cos-mult flip-- sin-mult rem-cube-cbrt
1×difference-cubes +-commutative associate-+l- flip3-+ frac-sub flip-+ distribute-lft-out sub-div
Counts
4 → 100
Calls
4 calls:
14.0ms
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
1.0ms
(pow (cos x) 3)
6.0ms
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
44.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series875.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
34.0ms
(pow (cos x) 3)
111.0ms
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
627.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify98.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
05991433
128891321
250021280

prune344.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.1b

regimes252.0ms

Accuracy

82.5% (1.7b remaining)

Error of 16.4b against oracle of 14.7b and baseline of 24.4b

bsearch146.0ms

Steps
ItersRangePoint
11
2.28145452431431e-18
2231369.5462890854
2.8324086194409338e-08
10
-2.6466725305918305e-14
-3.863797843067215e-32
-2.605528298395092e-14

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04118
14318
24318

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.5s4511×body1280valid
560.0ms666×body2560valid
363.0ms1784×body640valid
99.0ms691×body320valid
24.0ms259×body160valid
5.0ms89×body80valid