Details

Time bar (total: 6.7s)

sample86.0ms

Algorithm
intervals
Results
48.0ms142×body1280valid
15.0ms72×body640valid
12.0ms14×body2560valid
3.0ms20×body320valid
1.0ms7×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: 38.5b

localize8.0ms

Local error

Found 2 expressions with local error:

1.2b
(- (cos (+ x eps)) (cos x))
3.9b
(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))
4.0ms
(cos (+ x eps))

series67.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(- (cos (+ x eps)) (cos x))
14.0ms
(cos (+ x eps))

simplify108.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
0134176
1281167
2840164
32958164
45002164

prune89.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.3b

localize18.0ms

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))
3.7b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite34.0ms

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))
20.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series293.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (cos x) (cos eps))
81.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
49.0ms
(* (sin x) (sin eps))
126.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify111.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0304633
11061602
24487583
35002583

prune244.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 14.2b

localize19.0ms

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))
3.6b
(+ (* (cos x) (cos eps)) (- (- (* (sin x) (sin eps))) (cos x)))

rewrite29.0ms

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:
4.0ms
(* (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)))

series272.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (cos x) (cos eps))
53.0ms
(- (- (* (sin x) (sin eps))) (cos x))
49.0ms
(* (sin x) (sin eps))
126.0ms
(+ (* (cos x) (cos eps)) (- (- (* (sin x) (sin eps))) (cos x)))

simplify45.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0362707
11473662
25001640

prune275.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
0.4b
(pow (cos x) 3)
0.6b
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
3.5b
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
24×*-un-lft-identity
18×unpow-prod-down cube-prod
16×difference-of-squares
12×add-cube-cbrt
10×sqr-pow
8×pow1 add-exp-log frac-times cos-mult add-cbrt-cube sin-mult
6×pow-unpow add-log-exp
5×flip3-- flip3-+ flip-- flip-+ distribute-lft-out--
4×cube-div associate-*r* associate-*l/ frac-sub sub-div
3×associate-*l*
2×cube-mult pow-to-exp pow-pow unpow3 associate-*r/ pow-exp rem-cube-cbrt
1×difference-cubes distribute-rgt-in sub-neg distribute-lft-in diff-log pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out unswap-sqr
Counts
4 → 119
Calls
4 calls:
58.0ms
(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (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))

series953.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
28.0ms
(pow (cos x) 3)
110.0ms
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
612.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify181.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
08092240
148042061
250012061

prune507.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 14.0b

regimes361.0ms

Accuracy

83.5% (1.6b remaining)

Error of 16.2b against oracle of 14.6b and baseline of 24.5b

bsearch91.0ms

Steps
ItersRangePoint
5
1.7079491355729536e-10
3.529261774314728e-10
3.491110681506798e-10
6
-8.751105362266984e-13
-1.8057709034692785e-13
-8.668113418781679e-13

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07394
17794
27794

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.5s4494×body1280valid
551.0ms658×body2560valid
376.0ms1816×body640valid
92.0ms676×body320valid
25.0ms268×body160valid
4.0ms88×body80valid