Details

Time bar (total: 9.1s)

sample106.0ms

Algorithm
intervals
Results
53.0ms131×body1280valid
21.0ms23×body2560valid
18.0ms73×body640valid
4.0ms17×body320valid
1.0ms9×body160valid
0.0ms3×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: 42.8b

localize8.0ms

Local error

Found 2 expressions with local error:

1.2b
(- (cos (+ x eps)) (cos x))
3.5b
(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))

series71.0ms

Counts
2 → 6
Calls
2 calls:
56.0ms
(- (cos (+ x eps)) (cos x))
15.0ms
(cos (+ x eps))

simplify114.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
0134176
1281167
2840164
32958164
45002164

prune89.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.5b

localize13.0ms

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))
3.9b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite37.0ms

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:
3.0ms
(* (cos x) (cos eps))
5.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
4.0ms
(* (sin x) (sin eps))
23.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series308.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (cos x) (cos eps))
87.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
51.0ms
(* (sin x) (sin eps))
130.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify116.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0304632
11061601
24487583
35002583

prune249.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 16.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos x) 3)
0.4b
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.5b
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
3.8b
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite67.0ms

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:
1.0ms
(pow (cos x) 3)
13.0ms
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
6.0ms
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
43.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series855.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(pow (cos x) 3)
97.0ms
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
108.0ms
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
617.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify111.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
05991433
128891321
250021280

prune410.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 16.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos x) 3)
0.4b
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.5b
(pow (* (cos x) (cos eps)) 3)
3.8b
(- (+ (pow (* (cos x) (cos eps)) 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)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
30×add-log-exp
15×*-un-lft-identity
11×sum-log
10×add-sqr-sqrt
9×flip3-+ flip-+
8×pow1 add-exp-log add-cube-cbrt frac-sub add-cbrt-cube
7×diff-log
6×pow-unpow
5×cube-div
4×unpow-prod-down cube-prod frac-add sin-mult
3×pow-pow pow-exp rem-cube-cbrt
2×cube-mult pow-to-exp sub-neg associate-+l+ unpow3 distribute-lft-out distribute-lft-out-- sqr-pow
1×+-commutative associate-+l- flip3-- pow-prod-down prod-exp associate--l+ cos-mult flip-- cbrt-unprod associate--r+ difference-of-squares
Counts
4 → 92
Calls
4 calls:
1.0ms
(pow (cos x) 3)
15.0ms
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
3.0ms
(pow (* (cos x) (cos eps)) 3)
1.2s
(- (+ (pow (* (cos x) (cos eps)) 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)))

series653.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(pow (cos x) 3)
99.0ms
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
58.0ms
(pow (* (cos x) (cos eps)) 3)
462.0ms
(- (+ (pow (* (cos x) (cos eps)) 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)))

simplify185.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (162.0ms)

IterNodesCost
08442997
146722779
250022775

prune658.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 16.2b

regimes514.0ms

Accuracy

83.4% (1.7b remaining)

Error of 16.8b against oracle of 15.1b and baseline of 25.4b

bsearch146.0ms

Steps
ItersRangePoint
9
2.5675937259375084e-20
4.470557786745182e-11
4.3834693427398484e-11
9
-5.033370145566524e-07
-1.9815489217883408e-12
-4.253274258796949e-10

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04448
14448

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.7s4420×body1280valid
603.0ms660×body2560valid
482.0ms1868×body640valid
123.0ms694×body320valid
43.0ms285×body160valid
6.0ms73×body80valid