Details

Time bar (total: 7.6s)

sample97.0ms

Algorithm
intervals
Results
53.0ms145×body1280valid
19.0ms22×body2560valid
14.0ms61×body640valid
2.0ms16×body320valid
1.0ms11×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: 40.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.7b
(- (cos (+ x eps)) (cos x))
3.5b
(cos (+ x eps))

rewrite11.0ms

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:
6.0ms
(- (cos (+ x eps)) (cos x))
5.0ms
(cos (+ x eps))

series69.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(- (cos (+ x eps)) (cos x))
16.0ms
(cos (+ x eps))

simplify113.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
0134176
1281167
2840164
32958164
45002164

prune92.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.2b

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))
1.2b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite25.0ms

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)))
5.0ms
(* (sin x) (sin eps))
10.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series303.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (cos x) (cos eps))
83.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
45.0ms
(* (sin x) (sin eps))
131.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify117.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0304632
11061601
24487583
35002583

prune244.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 13.1b

localize26.0ms

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)
0.5b
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
1.0b
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite48.0ms

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:
19.0ms
(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
3.0ms
(pow (cos x) 3)
6.0ms
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
17.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series942.0ms

Counts
4 → 12
Calls
4 calls:
195.0ms
(* (- (* (cos eps) (cos x)) (* (sin x) (sin eps))) (+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x)))
28.0ms
(pow (cos x) 3)
111.0ms
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
607.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify175.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
08092265
147982078
250022078

prune580.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 12.9b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (* (sin x) (sin eps)) 3)
0.4b
(pow (cos x) 3)
0.5b
(pow (* (cos eps) (cos x)) 3)
0.9b
(+ (pow (* (cos eps) (cos x)) 3) (- (* 3 (* (cos x) (* (pow (sin x) 2) (* (pow (sin eps) 2) (cos eps))))) (+ (+ (pow (cos x) 3) (* 3 (* (pow (cos x) 2) (* (sin x) (* (sin eps) (pow (cos eps) 2)))))) (pow (* (sin x) (sin eps)) 3))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
18×add-log-exp
11×pow1 add-exp-log *-un-lft-identity add-cbrt-cube
9×add-sqr-sqrt add-cube-cbrt pow-unpow
7×sum-log
5×unpow-prod-down pow-pow cube-prod pow-exp rem-cube-cbrt
4×cube-div
3×cube-mult pow-to-exp diff-log unpow3 cos-mult sqr-pow
2×associate-+r+ pow-prod-down frac-add prod-exp cbrt-unprod
1×+-commutative associate-+r- sub-neg flip3-- flip3-+ flip-- flip-+ sin-mult distribute-lft-out
Counts
4 → 89
Calls
4 calls:
5.0ms
(pow (* (sin x) (sin eps)) 3)
3.0ms
(pow (cos x) 3)
4.0ms
(pow (* (cos eps) (cos x)) 3)
31.0ms
(+ (pow (* (cos eps) (cos x)) 3) (- (* 3 (* (cos x) (* (pow (sin x) 2) (* (pow (sin eps) 2) (cos eps))))) (+ (+ (pow (cos x) 3) (* 3 (* (pow (cos x) 2) (* (sin x) (* (sin eps) (pow (cos eps) 2)))))) (pow (* (sin x) (sin eps)) 3))))

series608.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(pow (* (sin x) (sin eps)) 3)
29.0ms
(pow (cos x) 3)
58.0ms
(pow (* (cos eps) (cos x)) 3)
456.0ms
(+ (pow (* (cos eps) (cos x)) 3) (- (* 3 (* (cos x) (* (pow (sin x) 2) (* (pow (sin eps) 2) (cos eps))))) (+ (+ (pow (cos x) 3) (* 3 (* (pow (cos x) 2) (* (sin x) (* (sin eps) (pow (cos eps) 2)))))) (pow (* (sin x) (sin eps)) 3))))

simplify134.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (121.0ms)

IterNodesCost
06061480
133731392
250021388

prune554.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.9b

regimes338.0ms

Accuracy

85.8% (1.5b remaining)

Error of 15.9b against oracle of 14.5b and baseline of 24.8b

bsearch219.0ms

Steps
ItersRangePoint
10
8.960609758249674e-23
4.5131138850246713e-07
1.2305748660245976e-07
11
-1.5073415317839904e-10
-5.397704668065765e-30
-1.4155618696900624e-10

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077123
182123
282123

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.5s4460×body1280valid
581.0ms663×body2560valid
393.0ms1836×body640valid
97.0ms675×body320valid
33.0ms287×body160valid
4.0ms79×body80valid