Details

Time bar (total: 32.8s)

sample392.0ms

Algorithm
intervals
Results
174.0ms106×body1280valid
94.0ms21×body2560valid
80.0ms56×body640valid
17.0ms21×body320valid
9.0ms15×body160valid
9.0ms37×body80valid

simplify4.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize13.0ms

Local error

Found 2 expressions with local error:

1.5b
(- (tan (+ x eps)) (tan x))
2.5b
(tan (+ x eps))

rewrite35.0ms

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:
25.0ms
(- (tan (+ x eps)) (tan x))
9.0ms
(tan (+ x eps))

series216.0ms

Counts
2 → 6
Calls
2 calls:
133.0ms
(- (tan (+ x eps)) (tan x))
83.0ms
(tan (+ x eps))

simplify1.8s

Counts
33 → 33
Iterations
IterNodes
done5001
41821
3719
2300
1139
070

prune194.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.6b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b
(+ (tan x) (tan eps))
0.2b
(* (tan x) (tan eps))
3.0b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite120.0ms

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:
23.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
7.0ms
(+ (tan x) (tan eps))
21.0ms
(* (tan x) (tan eps))
69.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.1s

Counts
4 → 12
Calls
4 calls:
295.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
131.0ms
(+ (tan x) (tan eps))
125.0ms
(* (tan x) (tan eps))
517.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.9s

Counts
102 → 102
Iterations
IterNodes
done5008
34112
21148
1405
0174

prune504.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.5b

localize105.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan eps) (tan x))
0.3b
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.0b
(- (* (/ (+ (tan eps) (tan x)) (- 1 (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

rewrite307.0ms

Algorithm
rewrite-expression-head
Rules
84×pow1
73×tan-quot
37×frac-times
35×pow-prod-down
30×add-cbrt-cube add-exp-log
25×associate-*r/
24×associate-*l/
17×prod-exp cbrt-unprod
8×add-sqr-sqrt pow-sqr pow-prod-up
6×*-un-lft-identity add-cube-cbrt add-log-exp
5×associate-*r* associate-*l* frac-sub
4×pow-plus insert-posit16
3×*-commutative
2×pow2 flip3-+ swap-sqr associate--l+ flip-+
1×distribute-rgt-in sub-neg distribute-lft-in flip3-- diff-log flip-- unswap-sqr
Counts
4 → 142
Calls
4 calls:
13.0ms
(* (tan eps) (tan x))
90.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
89.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
113.0ms
(- (* (/ (+ (tan eps) (tan x)) (- 1 (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

series2.4s

Counts
4 → 12
Calls
4 calls:
144.0ms
(* (tan eps) (tan x))
158.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
148.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.0s
(- (* (/ (+ (tan eps) (tan x)) (- 1 (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

simplify2.8s

Counts
154 → 154
Iterations
IterNodes
done5009
23794
1889
0273

prune939.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.3b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan eps) (tan x))
0.2b
(* (tan x) (* (tan eps) (tan x)))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.0b
(- (* (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan eps) (* (tan x) (* (tan eps) (tan x)))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
53×tan-quot
50×pow1
25×frac-times
23×add-cbrt-cube add-exp-log
21×pow-prod-down
19×associate-*r/
16×associate-*l/
12×prod-exp cbrt-unprod
9×add-sqr-sqrt
7×*-un-lft-identity associate-*l* add-cube-cbrt
6×add-log-exp
5×associate-*r* frac-sub
4×pow-sqr pow-prod-up insert-posit16
3×*-commutative
2×flip3-+ pow-plus associate--l+ flip-+
1×pow2 distribute-rgt-in sub-neg distribute-lft-in flip3-- diff-log swap-sqr flip-- unswap-sqr
Counts
4 → 118
Calls
4 calls:
23.0ms
(* (tan eps) (tan x))
40.0ms
(* (tan x) (* (tan eps) (tan x)))
86.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
97.0ms
(- (* (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan eps) (* (tan x) (* (tan eps) (tan x)))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

series2.3s

Counts
4 → 12
Calls
4 calls:
152.0ms
(* (tan eps) (tan x))
124.0ms
(* (tan x) (* (tan eps) (tan x)))
163.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
1.9s
(- (* (/ (+ (tan eps) (tan x)) (- 1 (* (* (tan eps) (* (tan x) (* (tan eps) (tan x)))) (* (tan eps) (tan x))))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

simplify3.1s

Counts
130 → 130
Iterations
IterNodes
done5013
23726
1858
0269

prune828.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 12.3b

regimes331.0ms

Accuracy

93.8% (0.5b remaining)

Error of 13.8b against oracle of 13.2b and baseline of 21.8b

bsearch475.0ms

Steps
ItersRangePoint
8
6.608106750126326e-54
3.070722928872959e-51
2.106612565673929e-51
9
-1.9094137902975774e-15
-1.0692349298420692e-20
-5.135442363002646e-18

simplify16.0ms

Iterations
IterNodes
done55
155
038

end0.0ms

sample11.4s

Algorithm
intervals
Results
5.7s3287×body1280valid
2.7s1828×body640valid
1.8s629×body2560valid
524.0ms758×body320valid
337.0ms1138×body80valid
141.0ms360×body160valid