Details

Time bar (total: 35.2s)

sample75.0ms

Algorithm
intervals
Results
21.0ms26×body320valid
19.0ms68×body640valid
9.0ms132×body80valid
6.0ms16×body1280valid
2.0ms14×body160valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
11815
23115
34115
48815
513515
616215
721115
844115
9120815
done500015

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.6b

localize29.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (/ 2.0 x) (/ 1.0 (+ x 1.0)))
2.0b
(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (/ 1.0 (+ x 1.0))))

rewrite713.0ms

Algorithm
rewrite-expression-head
Rules
1086×*-un-lft-identity
999×times-frac
924×add-sqr-sqrt
678×prod-diff
589×add-cube-cbrt
236×associate--r+
123×difference-of-squares
112×distribute-lft-out--
102×distribute-lft-out
74×associate-/r/ div-inv
34×fma-neg
26×flip3-+ flip-+
14×flip3-- flip--
9×add-log-exp
5×frac-sub
4×diff-log
3×sub-neg
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
1×associate--r-
Counts
2 → 763
Calls
2 calls:
101.0ms
(- (/ 2.0 x) (/ 1.0 (+ x 1.0)))
454.0ms
(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (/ 1.0 (+ x 1.0))))

series502.0ms

Counts
2 → 6
Calls
2 calls:
77.0ms
(- (/ 2.0 x) (/ 1.0 (+ x 1.0)))
424.0ms
(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (/ 1.0 (+ x 1.0))))

simplify2.1s

Counts
769 → 769
Iterations

Useful iterations: done (2.0s)

IterNodesCost
083038008
1206732945
done500127196

prune4.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (/ 2.0 x) (/ 1.0 (+ x 1.0)))
2.0b
(- (/ 1.0 (- x 1.0)) (* (/ 1 1) (- (/ 2.0 x) (/ 1.0 (+ x 1.0)))))

rewrite514.0ms

Algorithm
rewrite-expression-head
Rules
1003×times-frac
979×*-un-lft-identity
741×add-sqr-sqrt
723×prod-diff
717×add-cube-cbrt
472×associate--r+
236×distribute-rgt-in distribute-lft-in
118×distribute-lft-out
96×div-inv
82×associate-/r/
39×flip3-+ flip-+
34×fma-neg
12×distribute-lft-out--
10×frac-sub difference-of-squares
6×flip3-- flip-- add-log-exp
4×sub-neg
3×frac-times associate-*r/
2×pow1 add-exp-log expm1-log1p-u diff-log add-cbrt-cube log1p-expm1-u
1×associate-*l/
Counts
2 → 806
Calls
2 calls:
92.0ms
(- (/ 2.0 x) (/ 1.0 (+ x 1.0)))
257.0ms
(- (/ 1.0 (- x 1.0)) (* (/ 1 1) (- (/ 2.0 x) (/ 1.0 (+ x 1.0)))))

series457.0ms

Counts
2 → 6
Calls
2 calls:
75.0ms
(- (/ 2.0 x) (/ 1.0 (+ x 1.0)))
382.0ms
(- (/ 1.0 (- x 1.0)) (* (/ 1 1) (- (/ 2.0 x) (/ 1.0 (+ x 1.0)))))

simplify6.1s

Counts
812 → 812
Iterations

Useful iterations: done (6.0s)

IterNodesCost
0129132599
1366428268
done500124233

prune5.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

Local error

Found 3 expressions with local error:

0.0b
(* x (+ x 1.0))
1.1b
(- (/ 1.0 (- x 1.0)) (* (/ 1 1) (/ (- (* 2.0 (+ x 1.0)) (* x 1.0)) (* x (+ x 1.0)))))
15.3b
(/ (- (* 2.0 (+ x 1.0)) (* x 1.0)) (* x (+ x 1.0)))

rewrite288.0ms

Algorithm
rewrite-expression-head
Rules
44×*-un-lft-identity
39×add-sqr-sqrt
35×times-frac
25×add-cube-cbrt
21×fma-neg prod-diff
10×add-exp-log add-cbrt-cube
9×distribute-lft-out--
6×associate-/r/ difference-of-squares
5×pow1 associate-*r/ add-log-exp
4×flip3-- associate-*r* flip--
3×expm1-log1p-u associate-*l* frac-sub log1p-expm1-u div-inv associate-/l*
2×cbrt-undiv flip3-+ div-exp prod-exp cbrt-unprod flip-+ associate-/l/
1×distribute-rgt-in frac-times sub-neg frac-2neg distribute-lft-in diff-log div-sub pow-prod-down associate-*l/ clear-num associate-/r* *-commutative distribute-lft-out unswap-sqr
Counts
3 → 114
Calls
3 calls:
41.0ms
(* x (+ x 1.0))
144.0ms
(- (/ 1.0 (- x 1.0)) (* (/ 1 1) (/ (- (* 2.0 (+ x 1.0)) (* x 1.0)) (* x (+ x 1.0)))))
95.0ms
(/ (- (* 2.0 (+ x 1.0)) (* x 1.0)) (* x (+ x 1.0)))

series744.0ms

Counts
3 → 9
Calls
3 calls:
80.0ms
(* x (+ x 1.0))
549.0ms
(- (/ 1.0 (- x 1.0)) (* (/ 1 1) (/ (- (* 2.0 (+ x 1.0)) (* x 1.0)) (* x (+ x 1.0)))))
114.0ms
(/ (- (* 2.0 (+ x 1.0)) (* x 1.0)) (* x (+ x 1.0)))

simplify4.6s

Counts
123 → 123
Iterations

Useful iterations: 2 (1.4s)

IterNodesCost
02253595
16903101
248702679
done50002679

prune800.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 2.0 (pow x 5)) (+ (/ 2.0 (pow x 3)) (/ 2.0 (pow x 7))))
0.0b
(/ 2.0 (pow x 7))
0.1b
(/ 2.0 (pow x 5))
0.3b
(/ 2.0 (pow x 3))

rewrite582.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
92×*-un-lft-identity
78×add-sqr-sqrt add-cube-cbrt
45×unpow-prod-down
26×associate-/r*
25×fma-def
19×add-exp-log
15×sqr-pow
12×cube-prod
11×distribute-lft-out
10×add-cbrt-cube
9×div-exp associate-/l* add-log-exp
7×div-inv
4×pow1 expm1-log1p-u cube-mult unpow3 frac-add log1p-expm1-u
3×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num sum-log
2×flip3-+ flip-+
1×+-commutative associate-+r+
Counts
4 → 210
Calls
4 calls:
515.0ms
(+ (/ 2.0 (pow x 5)) (+ (/ 2.0 (pow x 3)) (/ 2.0 (pow x 7))))
16.0ms
(/ 2.0 (pow x 7))
15.0ms
(/ 2.0 (pow x 5))
18.0ms
(/ 2.0 (pow x 3))

series426.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(+ (/ 2.0 (pow x 5)) (+ (/ 2.0 (pow x 3)) (/ 2.0 (pow x 7))))
129.0ms
(/ 2.0 (pow x 7))
106.0ms
(/ 2.0 (pow x 5))
73.0ms
(/ 2.0 (pow x 3))

simplify2.3s

Counts
222 → 222
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
02942533
16892226
231962165
done50012165

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes113.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 26.5b

bsearch226.0ms

Steps
ItersRangePoint
10
2.8868360106527892e-08
453261925.93168354
120.21434515618485
8
-3934.6710789005906
-4.26929226401081
-109.15750550726749

simplify12.0ms

Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
03271
14451
24649
done4649

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.1s1889×body640valid
411.0ms4118×body80valid
347.0ms562×body1280valid
245.0ms904×body320valid
135.0ms530×body160valid