Details

Time bar (total: 6.7s)

sample99.0ms

Algorithm
intervals
Results
51.0ms156×body1280valid
19.0ms24×body2560valid
14.0ms48×body640valid
3.0ms21×body320valid
1.0ms5×body160valid
0.0ms2×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104
done104

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.9b

localize9.0ms

Local error

Found 2 expressions with local error:

1.3b
(- (cos (+ x eps)) (cos x))
2.2b
(cos (+ x eps))

rewrite24.0ms

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:
13.0ms
(- (cos (+ x eps)) (cos x))
10.0ms
(cos (+ x eps))

series73.0ms

Counts
2 → 6
Calls
2 calls:
57.0ms
(- (cos (+ x eps)) (cos x))
16.0ms
(cos (+ x eps))

simplify109.0ms

Counts
30 → 30
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
0134176
1281167
2840164
32958164
45002164
done5002164

prune86.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.1b
(* (cos x) (cos eps))
0.2b
(* (sin x) (sin eps))
3.6b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite98.0ms

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:
16.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
10.0ms
(* (cos x) (cos eps))
13.0ms
(* (sin x) (sin eps))
57.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series316.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
42.0ms
(* (cos x) (cos eps))
52.0ms
(* (sin x) (sin eps))
133.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify112.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0304632
11061601
24488583
35001583
done5001583

prune234.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 16.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos x) (cos eps))
0.2b
(* (sin x) (sin eps))
3.4b
(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
4.2b
(log (exp (* (sin x) (sin eps))))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×*-un-lft-identity
9×pow1 add-cube-cbrt add-log-exp
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
3×log-prod diff-log log-pow
2×sub-neg pow-prod-down prod-exp associate--l+ *-commutative cbrt-unprod unswap-sqr
1×associate--l- exp-prod flip3-- exp-to-pow rem-log-exp cos-mult flip-- sin-mult distribute-lft-out-- difference-of-squares
Counts
4 → 70
Calls
4 calls:
10.0ms
(* (cos x) (cos eps))
11.0ms
(* (sin x) (sin eps))
62.0ms
(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
7.0ms
(log (exp (* (sin x) (sin eps))))

series285.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (cos x) (cos eps))
48.0ms
(* (sin x) (sin eps))
136.0ms
(- (- (* (cos x) (cos eps)) (log (exp (* (sin x) (sin eps))))) (cos x))
52.0ms
(log (exp (* (sin x) (sin eps))))

simplify86.0ms

Counts
82 → 82
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0264602
1857524
23421510
35002510
done5002510

prune266.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 16.8b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite163.0ms

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:
36.0ms
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
3.0ms
(pow (cos x) 3)
20.0ms
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
101.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series906.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
28.0ms
(pow (cos x) 3)
117.0ms
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
652.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify99.0ms

Counts
112 → 112
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
05991433
128891321
250021280
done50021280

prune345.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 16.7b

regimes337.0ms

Accuracy

82.9% (1.7b remaining)

Error of 16.8b against oracle of 15.1b and baseline of 25.0b

bsearch131.0ms

Steps
ItersRangePoint
8
4.5561658934541904e-07
0.004858038437719416
1.1319847402439193e-06
9
-7.855206308743333e-09
-4.1211929036737376e-16
-1.1531548156266982e-10

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04741
14941
24941
done4941

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.5s4536×body1280valid
546.0ms627×body2560valid
369.0ms1809×body640valid
95.0ms695×body320valid
24.0ms254×body160valid
4.0ms79×body80valid