Details

Time bar (total: 32.2s)

sample392.0ms

Algorithm
intervals
Results
236.0ms115×body1280valid
53.0ms14×body2560valid
53.0ms50×body640valid
20.0ms28×body320valid
8.0ms15×body160valid
8.0ms34×body80valid

simplify7.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize26.0ms

Local error

Found 2 expressions with local error:

2.0b
(- (tan (+ x eps)) (tan x))
2.0b
(tan (+ x eps))

rewrite63.0ms

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 insert-posit16
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 27
Calls
2 calls:
52.0ms
(- (tan (+ x eps)) (tan x))
10.0ms
(tan (+ x eps))

series219.0ms

Counts
2 → 6
Calls
2 calls:
146.0ms
(- (tan (+ x eps)) (tan x))
74.0ms
(tan (+ x eps))

simplify1.8s

Counts
33 → 33
Iterations
IterNodes
done5001
42071
3808
2304
1139
070

prune164.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.1b

localize29.0ms

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))
3.1b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite162.0ms

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×insert-posit16 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 → 90
Calls
4 calls:
14.0ms
(+ (tan x) (tan eps))
43.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
16.0ms
(* (tan x) (tan eps))
86.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts
4 → 12
Calls
4 calls:
130.0ms
(+ (tan x) (tan eps))
285.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
140.0ms
(* (tan x) (tan eps))
570.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.6s

Counts
102 → 102
Iterations
IterNodes
done5030
34429
21214
1405
0174

prune648.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 12.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
0.2b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.1b
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
47×pow1
45×tan-quot
21×frac-times
20×add-cbrt-cube add-exp-log
19×pow-prod-down
15×associate-*r/
14×associate-*l/
12×add-sqr-sqrt
10×prod-exp cbrt-unprod
8×*-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l*
6×add-log-exp
5×frac-sub
4×pow-sqr pow-prod-up insert-posit16
3×*-commutative
2×flip3-+ pow-plus associate--l+ flip-+ unswap-sqr
1×pow2 distribute-rgt-in sub-neg distribute-lft-in flip3-- diff-log swap-sqr flip--
Counts
4 → 114
Calls
4 calls:
22.0ms
(* (tan x) (tan eps))
14.0ms
(* (tan x) (tan eps))
93.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
39.0ms
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.6s

Counts
4 → 12
Calls
4 calls:
122.0ms
(* (tan x) (tan eps))
98.0ms
(* (tan x) (tan eps))
146.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.3s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify1.6s

Counts
126 → 126
Iterations
IterNodes
done5002
22786
1655
0204

prune776.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.9b

localize78.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.2b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
0.2b
(* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps)))
3.1b
(+ (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) 1) (- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps))) (tan x)))

rewrite635.0ms

Algorithm
rewrite-expression-head
Rules
89×tan-quot
87×pow1
44×frac-times
40×add-cbrt-cube add-exp-log
39×associate-*l/
37×pow-prod-down
33×associate-*r/
24×associate-*l*
22×prod-exp cbrt-unprod
21×*-un-lft-identity
16×times-frac
13×add-sqr-sqrt add-cube-cbrt
10×frac-add
9×add-log-exp
8×pow-sqr pow-prod-up
7×frac-sub
4×pow-plus insert-posit16 distribute-lft-out difference-of-squares
3×associate-*r* *-commutative
2×pow2 cbrt-undiv associate-+r+ sum-log flip3-- swap-sqr div-exp associate-/r/ flip--
1×+-commutative associate-+r- sub-neg flip3-+ diff-log flip-+ div-inv sub-div
Counts
4 → 175
Calls
4 calls:
95.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
127.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
167.0ms
(* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps)))
240.0ms
(+ (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) 1) (- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps))) (tan x)))

series2.0s

Counts
4 → 12
Calls
4 calls:
144.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
149.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
491.0ms
(* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps)))
1.2s
(+ (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) 1) (- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (* (tan x) (tan eps))) (tan x)))

simplify2.6s

Counts
187 → 187
Iterations
IterNodes
done5001
24273
1966
0305

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.3b

regimes327.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

bsearch0.0ms

simplify13.0ms

Iterations
IterNodes
done37
137
029

end0.0ms

sample14.0s

Algorithm
intervals
Results
7.4s3317×body1280valid
2.5s618×body2560valid
2.3s1856×body640valid
1.1s765×body320valid
319.0ms1108×body80valid
222.0ms336×body160valid