Details

Time bar (total: 22.8s)

sample262.0ms

Algorithm
intervals
Results
153.0ms99×body1280valid
47.0ms76×body640valid
30.0ms15×body2560valid
11.0ms27×body320valid
3.0ms13×body160valid
3.0ms26×body80valid

simplify3.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.9b

localize20.0ms

Local error

Found 2 expressions with local error:

1.9b
(- (tan (+ x eps)) (tan x))
3.8b
(tan (+ x eps))

rewrite36.0ms

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:
25.0ms
(- (tan (+ x eps)) (tan x))
10.0ms
(tan (+ x eps))

series258.0ms

Counts
2 → 6
Calls
2 calls:
150.0ms
(- (tan (+ x eps)) (tan x))
107.0ms
(tan (+ x eps))

simplify583.0ms

Counts
31 → 31
Iterations
IterNodes
done5000
31176
2355
1137
068

prune203.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.7b

localize27.0ms

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))

rewrite152.0ms

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:
23.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
14.0ms
(+ (tan x) (tan eps))
23.0ms
(* (tan eps) (tan x))
90.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

series1.1s

Counts
4 → 12
Calls
4 calls:
293.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x))))
165.0ms
(+ (tan x) (tan eps))
127.0ms
(* (tan eps) (tan x))
534.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan eps) (tan x)))) (tan x))

simplify904.0ms

Counts
98 → 98
Iterations
IterNodes
done5000
21596
1410
0173

prune619.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin eps) (cos eps))
0.2b
(/ (sin eps) (cos eps))
0.2b
(/ (sin eps) (* (cos eps) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))))
2.7b
(- (/ (/ (sin x) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (cos x)) (/ (sin x) (cos x)))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
36×times-frac
32×*-un-lft-identity
24×add-cube-cbrt
13×add-cbrt-cube add-exp-log
9×associate-/l*
7×associate-/r*
6×add-log-exp difference-of-squares
5×div-inv
4×pow1 cbrt-undiv div-exp distribute-lft-out--
3×clear-num frac-2neg
2×quot-tan flip3-- associate-*r/ associate-/r/ flip--
1×sub-neg distribute-rgt-out-- diff-log prod-exp frac-sub cbrt-unprod sub-div
Counts
4 → 104
Calls
4 calls:
7.0ms
(/ (sin eps) (cos eps))
7.0ms
(/ (sin eps) (cos eps))
20.0ms
(/ (sin eps) (* (cos eps) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))))
125.0ms
(- (/ (/ (sin x) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (cos x)) (/ (sin x) (cos x)))

series616.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(/ (sin eps) (cos eps))
36.0ms
(/ (sin eps) (cos eps))
198.0ms
(/ (sin eps) (* (cos eps) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))))
362.0ms
(- (/ (/ (sin x) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))) (cos x)) (/ (sin x) (cos x)))

simplify965.0ms

Counts
116 → 116
Iterations
IterNodes
done5001
22005
1450
0189

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin eps) (cos eps))
0.2b
(/ (sin eps) (* (cos eps) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))))
0.3b
(* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))
2.7b
(- (/ (sin x) (- 1 (* (/ (sin eps) (cos x)) (/ (sin x) (cos eps))))) (sin x))

rewrite496.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
35×times-frac
30×*-un-lft-identity
28×add-cube-cbrt
23×add-cbrt-cube add-exp-log
13×associate-*r* associate-*l*
7×cbrt-undiv div-exp
6×pow1 associate-/l* add-log-exp
5×prod-exp cbrt-unprod
4×associate-/r* div-inv unswap-sqr
3×associate-*r/
2×clear-num frac-2neg flip3-- associate-/r/ flip-- difference-of-squares
1×frac-times quot-tan sub-neg diff-log pow-prod-down associate-*l/ *-commutative distribute-lft-out--
Counts
4 → 116
Calls
4 calls:
15.0ms
(/ (sin eps) (cos eps))
15.0ms
(/ (sin eps) (* (cos eps) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))))
29.0ms
(* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))
432.0ms
(- (/ (sin x) (- 1 (* (/ (sin eps) (cos x)) (/ (sin x) (cos eps))))) (sin x))

series653.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ (sin eps) (cos eps))
200.0ms
(/ (sin eps) (* (cos eps) (- 1 (* (/ (sin eps) (cos eps)) (/ (sin x) (cos x))))))
142.0ms
(* (/ (sin eps) (cos x)) (/ (sin x) (cos eps)))
275.0ms
(- (/ (sin x) (- 1 (* (/ (sin eps) (cos x)) (/ (sin x) (cos eps))))) (sin x))

simplify1.8s

Counts
128 → 128
Iterations
IterNodes
done5000
23884
1702
0256

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.0b

regimes271.0ms

Accuracy

0% (0.3b remaining)

Error of 12.9b against oracle of 12.6b and baseline of 12.9b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done31
131
024

end0.0ms

sample11.3s

Algorithm
intervals
Results
5.2s3318×body1280valid
2.8s1779×body640valid
1.9s656×body2560valid
643.0ms772×body320valid
169.0ms1114×body80valid
120.0ms361×body160valid