Details

Time bar (total: 7.0s)

sample90.0ms

Algorithm
intervals
Results
50.0ms146×body1280valid
15.0ms18×body2560valid
12.0ms59×body640valid
3.0ms21×body320valid
1.0ms8×body160valid
0.0ms4×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 39.0b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.6b
(- (cos (+ x eps)) (cos x))
3.5b
(cos (+ x eps))

rewrite10.0ms

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))
4.0ms
(cos (+ x eps))

series68.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(- (cos (+ x eps)) (cos x))
15.0ms
(cos (+ x eps))

simplify113.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
0134176
1281167
2840164
32958164
45002164

prune86.0ms

Filtered
30 candidates to 23 candidates (76.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New191130
Fresh000
Picked101
Done000
Total201131

Merged error: 14.7b

Counts
31 → 11

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))
2.8b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite28.0ms

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))
13.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series289.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (cos x) (cos eps))
79.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
48.0ms
(* (sin x) (sin eps))
124.0ms
(- (- (* (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

prune250.0ms

Filtered
82 candidates to 57 candidates (69.5%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New671582
Fresh8210
Picked101
Done000
Total761793

Merged error: 14.5b

Counts
93 → 17

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (* (sin x) (sin eps)) 3)
0.4b
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
0.6b
(pow (* (cos x) (cos eps)) 3)
7.4b
(- (/ (- (pow (* (cos x) (cos eps)) 3) (pow (* (sin x) (sin eps)) 3)) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))) (cos x))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
49×pow1
22×add-exp-log add-cbrt-cube
19×pow-prod-down
11×add-sqr-sqrt
10×prod-exp cbrt-unprod
8×*-un-lft-identity
6×add-cube-cbrt pow-unpow add-log-exp
5×cos-mult
4×pow-pow pow-exp pow-sqr pow-prod-up rem-cube-cbrt
2×cube-div cube-mult pow-to-exp unpow-prod-down pow-plus unpow3 cube-prod difference-of-squares sqr-pow
1×associate--l- pow2 frac-times sub-neg flip3-- times-frac diff-log div-sub associate-*r/ swap-sqr associate-*r* associate-*l* associate-*l/ *-commutative flip-- sin-mult distribute-lft-out--
Counts
4 → 99
Calls
4 calls:
5.0ms
(pow (* (sin x) (sin eps)) 3)
8.0ms
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
4.0ms
(pow (* (cos x) (cos eps)) 3)
36.0ms
(- (/ (- (pow (* (cos x) (cos eps)) 3) (pow (* (sin x) (sin eps)) 3)) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))) (cos x))

series824.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(pow (* (sin x) (sin eps)) 3)
56.0ms
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
56.0ms
(pow (* (cos x) (cos eps)) 3)
651.0ms
(- (/ (- (pow (* (cos x) (cos eps)) 3) (pow (* (sin x) (sin eps)) 3)) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))) (cos x))

simplify76.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
04991280
122601141
250021141

prune377.0ms

Filtered
111 candidates to 61 candidates (55.0%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New1047111
Fresh41216
Picked101
Done000
Total10919128

Merged error: 14.5b

Counts
128 → 19

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
0.4b
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
0.6b
(pow (* (cos x) (cos eps)) 3)
7.4b
(- (/ (pow (* (cos x) (cos eps)) 3) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))) (+ (/ (pow (* (sin x) (sin eps)) 3) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))) (cos x)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
85×pow1
35×pow-prod-down
31×add-exp-log add-cbrt-cube
17×prod-exp cbrt-unprod
12×add-sqr-sqrt
10×*-un-lft-identity
9×cos-mult add-log-exp
8×pow-sqr pow-prod-up
5×add-cube-cbrt
4×pow-plus
3×pow-unpow difference-of-squares
2×pow2 frac-times pow-pow times-frac diff-log associate-*r/ swap-sqr associate-*r* associate-*l* associate-*l/ pow-exp *-commutative frac-sub distribute-lft-out-- rem-cube-cbrt sqr-pow
1×cube-div cube-mult pow-to-exp sub-neg unpow-prod-down flip3-- flip3-+ unpow3 cube-prod sum-log flip-- flip-+ distribute-lft-out associate--r+
Counts
4 → 118
Calls
4 calls:
9.0ms
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
8.0ms
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
4.0ms
(pow (* (cos x) (cos eps)) 3)
65.0ms
(- (/ (pow (* (cos x) (cos eps)) 3) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))) (+ (/ (pow (* (sin x) (sin eps)) 3) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))) (cos x)))

series841.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
53.0ms
(* (* (cos x) (cos eps)) (* (cos x) (cos eps)))
62.0ms
(pow (* (cos x) (cos eps)) 3)
668.0ms
(- (/ (pow (* (cos x) (cos eps)) 3) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))) (+ (/ (pow (* (sin x) (sin eps)) 3) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))) (cos x)))

simplify87.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
05212416
124392262
250012252

prune369.0ms

Filtered
130 candidates to 64 candidates (49.2%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New1264130
Fresh41418
Picked101
Done000
Total13118149

Merged error: 14.5b

Counts
149 → 18

regimes254.0ms

Accuracy

79.6% (2.0b remaining)

Error of 16.4b against oracle of 14.4b and baseline of 24.3b

bsearch120.0ms

Steps
ItersRangePoint
8
3.88064682879673e-06
0.018000635171863108
3.971057779343525e-06
9
-2.981750332052767e-33
-1.3727521311823731e-39
-2.9500525747086803e-33

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03942
13942

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.5s4480×body1280valid
556.0ms635×body2560valid
394.0ms1845×body640valid
104.0ms673×body320valid
28.0ms289×body160valid
4.0ms78×body80valid