Details

Time bar (total: 18.0s)

sample155.0ms

Algorithm
intervals
Results
62.0ms87×body1280valid
40.0ms24×body2560valid
30.0ms77×body640valid
7.0ms28×body320valid
2.0ms30×body80valid
2.0ms10×body160valid

simplify4.0ms

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: 35.4b

localize14.0ms

Local error

Found 2 expressions with local error:

0.9b
(- (tan (+ x eps)) (tan x))
3.7b
(tan (+ x eps))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
4×tan-quot add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-exp-log add-cube-cbrt tan-sum frac-sub add-cbrt-cube
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 25
Calls
2 calls:
17.0ms
(- (tan (+ x eps)) (tan x))
6.0ms
(tan (+ x eps))

series143.0ms

Counts
2 → 6
Calls
2 calls:
92.0ms
(- (tan (+ x eps)) (tan x))
51.0ms
(tan (+ x eps))

simplify77.0ms

Counts
31 → 31
Iterations

Useful iterations: 3 (22.0ms)

IterNodesCost
0134211
1295202
2757200
32482199
45001199
done5001199

prune91.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (tan x) (tan eps))
0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b
(* (tan x) (tan eps))
2.4b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite128.0ms

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-exp-log add-cbrt-cube add-log-exp
6×pow1
5×distribute-lft-out
4×associate-/l*
3×associate-*r* associate-*l* associate-/r* associate-/l/
2×flip3-- flip3-+ frac-add associate-/r/ flip-- flip-+ difference-of-squares
1×cbrt-undiv +-commutative frac-times sub-neg frac-2neg diff-log associate-*r/ div-exp pow-prod-down associate-*l/ prod-exp clear-num sum-log *-commutative frac-sub cbrt-unprod div-inv distribute-lft-out-- unswap-sqr
Counts
4 → 86
Calls
4 calls:
8.0ms
(+ (tan x) (tan eps))
27.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
16.0ms
(* (tan x) (tan eps))
75.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series782.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(+ (tan x) (tan eps))
221.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
96.0ms
(* (tan x) (tan eps))
371.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify44.0ms

Counts
98 → 98
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03971050
114321005
25001995
done5001995

prune272.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan eps))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.3b
(pow (* (tan x) (tan eps)) 3)
2.4b
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
48×pow1
45×tan-quot
21×add-exp-log frac-times add-cbrt-cube
19×pow-prod-down
15×associate-*r/
14×associate-*l/
10×prod-exp cbrt-unprod
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×add-log-exp
5×frac-sub
4×associate-*r* associate-*l* pow-sqr pow-prod-up
3×cube-div pow-unpow
2×pow-pow flip3-+ pow-plus pow-exp associate--l+ *-commutative flip-+ rem-cube-cbrt
1×pow2 distribute-rgt-in cube-mult pow-to-exp sub-neg unpow-prod-down flip3-- distribute-lft-in diff-log unpow3 cube-prod swap-sqr flip-- unswap-sqr sqr-pow
Counts
4 → 114
Calls
4 calls:
14.0ms
(* (tan x) (tan eps))
65.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
11.0ms
(pow (* (tan x) (tan eps)) 3)
80.0ms
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

series2.0s

Counts
4 → 12
Calls
4 calls:
97.0ms
(* (tan x) (tan eps))
120.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
132.0ms
(pow (* (tan x) (tan eps)) 3)
1.6s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

simplify133.0ms

Counts
126 → 126
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
08481703
147861486
250011486
done50011486

prune424.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize66.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (cos eps) 3)
0.4b
(pow (cos eps) 3)
0.4b
(pow (cos eps) 3)
2.8b
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 3)))) (* (/ (pow (sin eps) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 2))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x)))) (/ (sin x) (cos x)))

rewrite5.9s

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt *-un-lft-identity frac-add
13×add-cube-cbrt add-log-exp
11×frac-sub
9×unpow-prod-down pow-unpow cube-prod
7×pow1 add-exp-log add-cbrt-cube
4×flip3-+ flip-+
3×cube-mult frac-times pow-to-exp pow-pow diff-log unpow3 associate-*r/ pow-exp sum-log rem-cube-cbrt sqr-pow
2×distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- times-frac associate-*l/ associate--l+ flip-- distribute-lft-out
Counts
4 → 99
Calls
4 calls:
3.0ms
(pow (cos eps) 3)
3.0ms
(pow (cos eps) 3)
3.0ms
(pow (cos eps) 3)
5.9s
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 3)))) (* (/ (pow (sin eps) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 2))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x)))) (/ (sin x) (cos x)))

series1.4s

Counts
4 → 12
Calls
4 calls:
33.0ms
(pow (cos eps) 3)
28.0ms
(pow (cos eps) 3)
27.0ms
(pow (cos eps) 3)
1.3s
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 3)))) (* (/ (pow (sin eps) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 2))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x)))) (/ (sin x) (cos x)))

simplify66.0ms

Counts
111 → 111
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010105756
150025532
done50025532

prune848.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

regimes272.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
063114
163114
done63114

end0.0ms

sample4.9s

Algorithm
intervals
Results
2.4s3360×body1280valid
1.1s646×body2560valid
764.0ms1815×body640valid
196.0ms746×body320valid
93.0ms1092×body80valid
59.0ms341×body160valid