Details

Time bar (total: 23.0s)

sample322.0ms

Algorithm
intervals
Results
147.0ms109×body1280valid
85.0ms23×body2560valid
46.0ms58×body640valid
11.0ms19×body320valid
5.0ms35×body80valid
5.0ms12×body160valid

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize82.0ms

Local error

Found 2 expressions with local error:

1.5b
(- (tan (+ x eps)) (tan x))
3.6b
(tan (+ x eps))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity tan-quot add-log-exp
2×pow1 tan-sum add-cbrt-cube add-exp-log frac-sub add-cube-cbrt
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 25
Calls
2 calls:
26.0ms
(- (tan (+ x eps)) (tan x))
10.0ms
(tan (+ x eps))

series225.0ms

Counts
2 → 6
Calls
2 calls:
135.0ms
(- (tan (+ x eps)) (tan x))
90.0ms
(tan (+ x eps))

simplify675.0ms

Counts
31 → 31
Iterations
IterNodes
done5000
31176
2355
1137
068

prune212.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
0.1b
(+ (tan x) (tan eps))
0.2b
(* (tan eps) (tan x))
2.9b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
22×add-sqr-sqrt
15×add-cube-cbrt
13×times-frac
9×tan-quot
8×add-cbrt-cube add-exp-log add-log-exp
6×pow1
5×distribute-lft-out
4×associate-/l*
3×associate-/r* associate-*r* associate-*l* associate-/l/
2×flip3-+ flip3-- frac-add associate-/r/ flip-+ flip-- difference-of-squares
1×frac-times cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg diff-log div-exp pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative frac-sub cbrt-unprod div-inv distribute-lft-out-- unswap-sqr
Counts
4 → 86
Calls
4 calls:
24.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
6.0ms
(+ (tan x) (tan eps))
11.0ms
(* (tan eps) (tan x))
70.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

series1.2s

Counts
4 → 12
Calls
4 calls:
353.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
164.0ms
(+ (tan x) (tan eps))
129.0ms
(* (tan eps) (tan x))
551.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

simplify791.0ms

Counts
98 → 98
Iterations
IterNodes
done5000
21596
1410
0173

prune613.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin eps) (* (cos eps) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))))
0.2b
(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
0.2b
(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
3.7b
(- (/ (/ (sin x) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (cos x)) (/ (sin x) (cos x)))

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
81×add-sqr-sqrt
62×times-frac
44×*-un-lft-identity
36×add-cube-cbrt
33×add-cbrt-cube add-exp-log
26×associate-*r* associate-*l*
10×cbrt-undiv div-exp
9×prod-exp cbrt-unprod
8×pow1 unswap-sqr
7×div-inv
6×add-log-exp difference-of-squares
4×associate-*r/ distribute-lft-out--
3×associate-/l*
2×frac-times flip3-- pow-prod-down associate-*l/ associate-/r/ *-commutative flip--
1×clear-num associate-/r* sub-neg frac-2neg distribute-rgt-out-- diff-log frac-sub sub-div
Counts
4 → 148
Calls
4 calls:
25.0ms
(/ (sin eps) (* (cos eps) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))))
44.0ms
(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
44.0ms
(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
119.0ms
(- (/ (/ (sin x) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (cos x)) (/ (sin x) (cos x)))

series883.0ms

Counts
4 → 12
Calls
4 calls:
244.0ms
(/ (sin eps) (* (cos eps) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))))
145.0ms
(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
154.0ms
(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
340.0ms
(- (/ (/ (sin x) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (cos x)) (/ (sin x) (cos x)))

simplify1.8s

Counts
160 → 160
Iterations
IterNodes
done5000
23638
1656
0240

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.6b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin x) (/ (sin eps) (cos eps)))
0.2b
(* (cos x) (cos x))
0.2b
(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
3.6b
(- (/ (sin x) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (sin x))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
33×times-frac
32×*-un-lft-identity
30×add-cube-cbrt
29×associate-*r*
23×add-cbrt-cube add-exp-log
19×associate-*l*
15×pow1
7×prod-exp cbrt-unprod unswap-sqr
6×add-log-exp
5×cbrt-undiv div-exp
3×swap-sqr pow-prod-down *-commutative div-inv
2×associate-*r/ difference-of-squares
1×pow2 frac-times sqr-cos sub-neg pow-plus flip3-- diff-log associate-*l/ pow-sqr cos-mult pow-prod-up flip-- distribute-lft-out--
Counts
4 → 124
Calls
4 calls:
15.0ms
(* (sin x) (/ (sin eps) (cos eps)))
8.0ms
(* (cos x) (cos x))
24.0ms
(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
117.0ms
(- (/ (sin x) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (sin x))

series606.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(* (sin x) (/ (sin eps) (cos eps)))
30.0ms
(* (cos x) (cos x))
163.0ms
(* (/ (sin eps) (cos eps)) (/ (sin x) (cos x)))
297.0ms
(- (/ (sin x) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (sin x))

simplify451.0ms

Counts
136 → 136
Iterations
IterNodes
done5001
1723
0245

prune1.0s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 12.6b

regimes299.0ms

Accuracy

0% (0.3b remaining)

Error of 12.5b against oracle of 12.3b and baseline of 12.5b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done29
129
022

end0.0ms

sample11.8s

Algorithm
intervals
Results
5.8s3210×body1280valid
2.4s1922×body640valid
2.2s622×body2560valid
648.0ms825×body320valid
247.0ms1067×body80valid
166.0ms354×body160valid