Details

Time bar (total: 2.2m)

sample451.0ms

Algorithm
intervals
Results
250.0ms127×body1280valid
72.0ms22×body2560valid
63.0ms53×body640valid
44.0ms21×body320valid
6.0ms25×body80valid
5.0ms8×body160valid

simplify4.0ms

Counts
1 → 1
Iterations
IterNodes
310
210
19
06

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.8b
(- (tan (+ x eps)) (tan x))
3.3b
(tan (+ x eps))

rewrite41.0ms

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:
36.0ms
(- (tan (+ x eps)) (tan x))
5.0ms
(tan (+ x eps))

series218.0ms

Counts
2 → 6
Calls
2 calls:
145.0ms
(- (tan (+ x eps)) (tan x))
72.0ms
(tan (+ x eps))

simplify3.7s

Counts
33 → 33
Iterations
IterNodes
53750
41478
3672
2285
1137
070

prune677.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.0b

localize28.0ms

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))
2.6b
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite149.0ms

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:
9.0ms
(+ (tan x) (tan eps))
30.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms
(* (tan x) (tan eps))
94.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.0s

Counts
4 → 12
Calls
4 calls:
127.0ms
(+ (tan x) (tan eps))
317.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
108.0ms
(* (tan x) (tan eps))
497.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.3s

Counts
102 → 102
Iterations
IterNodes
33692
21102
1402
0174

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 16.9b

localize107.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan eps))
0.3b
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.6b
(- (* (/ (+ (tan x) (tan eps)) (- 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))

rewrite270.0ms

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:
14.0ms
(* (tan x) (tan eps))
85.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
66.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
99.0ms
(- (* (/ (+ (tan x) (tan eps)) (- 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))

series2.5s

Counts
4 → 12
Calls
4 calls:
125.0ms
(* (tan x) (tan eps))
157.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
173.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.0s
(- (* (/ (+ (tan x) (tan eps)) (- 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))

simplify1.9s

Counts
154 → 154
Iterations
IterNodes
23611
1878
0273

prune2.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 16.8b

localize87.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.6b
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (cbrt (* (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (* (* (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))
12.0b
(cbrt (* (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
24645×tan-quot
20517×frac-times
8966×associate-*l/
8727×associate-*r/
4095×cbrt-div
82×pow1
34×pow-prod-down
28×add-cbrt-cube add-exp-log
16×prod-exp cbrt-unprod
8×pow-sqr pow-prod-up
6×add-log-exp
5×frac-sub
4×add-sqr-sqrt *-un-lft-identity pow-plus add-cube-cbrt insert-posit16
2×pow2 flip3-+ swap-sqr associate-*r* associate-*l* associate--l+ *-commutative flip-+
1×cbrt-prod distribute-rgt-in sub-neg distribute-lft-in flip3-- pow1/3 diff-log pow3 rem-cbrt-cube flip--
Counts
4 → 4226
Calls
4 calls:
92.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
75.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
92.0ms
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (cbrt (* (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (* (* (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))
1.3s
(cbrt (* (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))

series3.0s

Counts
4 → 12
Calls
4 calls:
147.0ms
(* (* (tan eps) (tan x)) (* (tan eps) (tan x)))
165.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.5s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (cbrt (* (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (* (* (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))
175.0ms
(cbrt (* (* (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))) (* (* (tan eps) (tan x)) (* (tan eps) (tan x)))))

simplify29.9s

Counts
4238 → 4238
Iterations
IterNodes
124742
011396

prune1.2m

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.4b

regimes173.0ms

Accuracy

57.5% (3.0b remaining)

Error of 15.5b against oracle of 12.5b and baseline of 19.5b

bsearch391.0ms

Steps
ItersRangePoint
10
8.848342155014433e-189
3.4736012736217745e-176
5.774589762410481e-177
5
-1.5360157608089411e-86
-6.232567035261237e-87
-9.72020893704794e-87

simplify40.0ms

Iterations
IterNodes
281
181
054

end0.0ms

sample9.8s

Algorithm
intervals
Results
5.4s3306×body1280valid
1.9s1850×body640valid
1.5s613×body2560valid
452.0ms754×body320valid
190.0ms1124×body80valid
124.0ms353×body160valid