Details

Time bar (total: 16.2s)

sample166.0ms

Algorithm
intervals
Results
70.0ms98×body1280valid
42.0ms25×body2560valid
31.0ms61×body640valid
5.0ms19×body320valid
3.0ms40×body80valid
2.0ms13×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize8.0ms

Local error

Found 2 expressions with local error:

1.2b
(- (tan (+ x eps)) (tan x))
2.5b
(tan (+ x eps))

rewrite24.0ms

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:
16.0ms
(- (tan (+ x eps)) (tan x))
6.0ms
(tan (+ x eps))

series154.0ms

Counts
2 → 6
Calls
2 calls:
95.0ms
(- (tan (+ x eps)) (tan x))
59.0ms
(tan (+ x eps))

simplify1.8s

Counts
31 → 31
Iterations

Useful iterations: 4 (267.0ms)

IterNodesCost
068367
1135355
2278341
3528337
41109335
52471335
done5000335

prune94.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (tan x) (tan eps))
0.1b
(- 1 (* (tan x) (tan eps)))
0.2b
(* (tan x) (tan eps))
2.0b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×*-un-lft-identity add-log-exp
7×tan-quot
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
3×associate-*r* associate-*l*
2×sub-neg flip3-- diff-log flip-- difference-of-squares
1×+-commutative frac-times flip3-+ times-frac associate-*r/ pow-prod-down associate-*l/ frac-add prod-exp sum-log *-commutative frac-sub cbrt-unprod flip-+ distribute-lft-out distribute-lft-out-- unswap-sqr
Counts
4 → 62
Calls
4 calls:
9.0ms
(+ (tan x) (tan eps))
5.0ms
(- 1 (* (tan x) (tan eps)))
15.0ms
(* (tan x) (tan eps))
79.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series686.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(+ (tan x) (tan eps))
113.0ms
(- 1 (* (tan x) (tan eps)))
96.0ms
(* (tan x) (tan eps))
380.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.6s

Counts
74 → 74
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01461093
13431049
2921989
32450974
done5000972

prune222.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin x) (sin eps))
0.2b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.2b
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
2.0b
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

rewrite647.0ms

Algorithm
rewrite-expression-head
Rules
30×add-exp-log add-cbrt-cube
13×add-sqr-sqrt
11×*-un-lft-identity
9×prod-exp cbrt-unprod add-log-exp
8×cbrt-undiv div-exp
6×pow1 add-cube-cbrt
3×times-frac associate-*r* associate-*l* frac-sub sin-mult
2×frac-2neg diff-log clear-num associate-/r* associate-/r/ cos-mult div-inv associate-/l/ associate-/l* distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- flip3-+ pow-prod-down frac-add associate--l+ sum-log *-commutative flip-- flip-+ distribute-lft-out unswap-sqr
Counts
4 → 86
Calls
4 calls:
12.0ms
(* (sin x) (sin eps))
17.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
18.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
598.0ms
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

series668.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (sin x) (sin eps))
106.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
104.0ms
(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
404.0ms
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

simplify813.0ms

Counts
98 → 98
Iterations

Useful iterations: 2 (227.0ms)

IterNodesCost
01652902
14572834
219522500
done50002500

prune362.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin eps))
0.6b
(cbrt (sin eps))
0.6b
(cbrt (sin eps))
2.0b
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (* (sin x) (* (cbrt (sin eps)) (cbrt (sin eps)))) (cbrt (sin eps))) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

rewrite599.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity
9×cbrt-prod add-log-exp
7×add-cube-cbrt
4×pow1 add-exp-log add-cbrt-cube
3×pow1/3 frac-sub
2×diff-log distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- flip3-+ times-frac frac-add associate--l+ sum-log flip-- flip-+ distribute-lft-out
Counts
4 → 54
Calls
4 calls:
1.0ms
(cbrt (sin eps))
1.0ms
(cbrt (sin eps))
1.0ms
(cbrt (sin eps))
594.0ms
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (* (sin x) (* (cbrt (sin eps)) (cbrt (sin eps)))) (cbrt (sin eps))) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

series706.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(cbrt (sin eps))
101.0ms
(cbrt (sin eps))
101.0ms
(cbrt (sin eps))
401.0ms
(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (* (sin x) (* (cbrt (sin eps)) (cbrt (sin eps)))) (cbrt (sin eps))) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

simplify1.9s

Counts
66 → 66
Iterations

Useful iterations: 3 (717.0ms)

IterNodesCost
01222506
13292421
210832070
344371874
done50001874

prune486.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 14.4b

regimes136.0ms

Accuracy

0% (0.3b remaining)

Error of 13.1b against oracle of 12.8b and baseline of 13.1b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01845
12445
done2445

end0.0ms

sample5.0s

Algorithm
intervals
Results
2.4s3278×body1280valid
1.2s678×body2560valid
776.0ms1842×body640valid
215.0ms744×body320valid
107.0ms1116×body80valid
69.0ms342×body160valid