Details

Time bar (total: 32.9s)

sample296.0ms

Algorithm
intervals
Results
158.0ms102×body1280valid
57.0ms24×body2560valid
45.0ms66×body640valid
11.0ms26×body320valid
5.0ms30×body80valid
3.0ms8×body160valid

simplify5.0ms

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: 37.5b

localize10.0ms

Local error

Found 2 expressions with local error:

1.3b
(- (tan (+ x eps)) (tan x))
3.6b
(tan (+ x eps))

rewrite45.0ms

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:
32.0ms
(- (tan (+ x eps)) (tan x))
12.0ms
(tan (+ x eps))

series213.0ms

Counts
2 → 6
Calls
2 calls:
127.0ms
(- (tan (+ x eps)) (tan x))
86.0ms
(tan (+ x eps))

simplify976.0ms

Counts
31 → 31
Iterations

Useful iterations: done (974.0ms)

IterNodesCost
068367
1135355
2349341
31136337
done5000335

prune124.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.9b

localize19.0ms

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))

rewrite180.0ms

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-exp-log add-cbrt-cube add-log-exp
6×pow1
5×distribute-lft-out
4×associate-/l*
3×associate-*r* associate-*l* associate-/r* associate-/l/
2×flip3-- flip3-+ frac-add associate-/r/ flip-- flip-+ difference-of-squares
1×cbrt-undiv +-commutative frac-times sub-neg frac-2neg diff-log associate-*r/ div-exp pow-prod-down associate-*l/ prod-exp clear-num sum-log *-commutative frac-sub cbrt-unprod div-inv distribute-lft-out-- unswap-sqr
Counts
4 → 86
Calls
4 calls:
11.0ms
(+ (tan x) (tan eps))
35.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
33.0ms
(* (tan x) (tan eps))
99.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts
4 → 12
Calls
4 calls:
120.0ms
(+ (tan x) (tan eps))
374.0ms
(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
140.0ms
(* (tan x) (tan eps))
551.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.2s

Counts
98 → 98
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01721724
14211649
216741579
done50011578

prune430.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (tan x) (tan eps))
0.3b
(pow (* (tan x) (tan eps)) 3)
0.3b
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
3.1b
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

rewrite272.0ms

Algorithm
rewrite-expression-head
Rules
48×pow1
45×tan-quot
21×add-exp-log frac-times add-cbrt-cube
19×pow-prod-down
15×associate-*r/
14×associate-*l/
10×prod-exp cbrt-unprod
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×add-log-exp
5×frac-sub
4×associate-*r* associate-*l* pow-sqr pow-prod-up
3×cube-div pow-unpow
2×pow-pow flip3-+ pow-plus pow-exp associate--l+ *-commutative flip-+ rem-cube-cbrt
1×pow2 distribute-rgt-in cube-mult pow-to-exp sub-neg unpow-prod-down flip3-- distribute-lft-in diff-log unpow3 cube-prod swap-sqr flip-- unswap-sqr sqr-pow
Counts
4 → 114
Calls
4 calls:
23.0ms
(* (tan x) (tan eps))
25.0ms
(pow (* (tan x) (tan eps)) 3)
87.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
132.0ms
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

series3.0s

Counts
4 → 12
Calls
4 calls:
117.0ms
(* (tan x) (tan eps))
198.0ms
(pow (* (tan x) (tan eps)) 3)
167.0ms
(* (* (tan x) (tan eps)) (* (tan x) (tan eps)))
2.5s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))

simplify644.0ms

Counts
126 → 126
Iterations

Useful iterations: done (640.0ms)

IterNodesCost
02743217
19822508
done50002300

prune564.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 15.8b

localize91.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (* (tan x) (tan eps)) 3)
0.3b
(pow (* (tan x) (tan eps)) 3)
0.3b
(pow (* (* (tan eps) (tan x)) (+ (* (tan eps) (tan x)) 1)) 3)
10.4b
(- (* (cos x) (* (+ (tan x) (tan eps)) (+ (pow (* (* (tan eps) (tan x)) (+ (* (tan eps) (tan x)) 1)) 3) 1))) (* (- 1 (pow (* (tan x) (tan eps)) 3)) (* (sin x) (+ (* (* (* (tan eps) (tan x)) (+ (* (tan eps) (tan x)) 1)) (- (* (* (tan eps) (tan x)) (+ (* (tan eps) (tan x)) 1)) 1)) 1))))

rewrite5.3s

Algorithm
rewrite-expression-head
Rules
199×associate-*r/
103×frac-times
93×flip3-+ flip-+
88×frac-sub
68×tan-quot
54×associate-*l/
34×flip3-- flip--
24×frac-add
17×cube-div
16×pow1 add-exp-log add-cbrt-cube
9×pow-unpow
8×distribute-rgt-in distribute-lft-in
7×add-sqr-sqrt add-cube-cbrt pow-pow *-un-lft-identity pow-exp rem-cube-cbrt
6×add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
4×associate--l+ associate--r+
3×cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod sqr-pow
1×sub-neg diff-log
Counts
4 → 194
Calls
4 calls:
17.0ms
(pow (* (tan x) (tan eps)) 3)
17.0ms
(pow (* (tan x) (tan eps)) 3)
78.0ms
(pow (* (* (tan eps) (tan x)) (+ (* (tan eps) (tan x)) 1)) 3)
5.2s
(- (* (cos x) (* (+ (tan x) (tan eps)) (+ (pow (* (* (tan eps) (tan x)) (+ (* (tan eps) (tan x)) 1)) 3) 1))) (* (- 1 (pow (* (tan x) (tan eps)) 3)) (* (sin x) (+ (* (* (* (tan eps) (tan x)) (+ (* (tan eps) (tan x)) 1)) (- (* (* (tan eps) (tan x)) (+ (* (tan eps) (tan x)) 1)) 1)) 1))))

series3.1s

Counts
4 → 12
Calls
4 calls:
155.0ms
(pow (* (tan x) (tan eps)) 3)
134.0ms
(pow (* (tan x) (tan eps)) 3)
294.0ms
(pow (* (* (tan eps) (tan x)) (+ (* (tan eps) (tan x)) 1)) 3)
2.5s
(- (* (cos x) (* (+ (tan x) (tan eps)) (+ (pow (* (* (tan eps) (tan x)) (+ (* (tan eps) (tan x)) 1)) 3) 1))) (* (- 1 (pow (* (tan x) (tan eps)) 3)) (* (sin x) (+ (* (* (* (tan eps) (tan x)) (+ (* (tan eps) (tan x)) 1)) (- (* (* (tan eps) (tan x)) (+ (* (tan eps) (tan x)) 1)) 1)) 1))))

simplify1.6s

Counts
206 → 206
Iterations

Useful iterations: done (1.5s)

IterNodesCost
071729781
1322025897
done500424715

prune2.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

regimes336.0ms

Accuracy

0% (0.4b remaining)

Error of 0.6b against oracle of 0.2b and baseline of 0.6b

bsearch0.0ms

simplify43.0ms

Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
090233
1129233
2132233
3134233
done134233

end0.0ms

sample10.7s

Algorithm
intervals
Results
5.3s3336×body1280valid
2.3s1843×body640valid
1.7s654×body2560valid
803.0ms767×body320valid
158.0ms1069×body80valid
108.0ms331×body160valid