Details

Time bar (total: 18.4s)

sample38.0ms

Algorithm
intervals
Results
10.0ms53×body1280valid
7.0ms46×body640valid
5.0ms126×body80valid
2.0ms19×body320valid
1.0ms12×body160valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0713
11213
21613
31913
42113
52713
63913
75813
87913
918313
1053513
11170613
12358413
done500013

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ 1.0 x) (- x 1.0))
3.6b
(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

rewrite278.0ms

Algorithm
rewrite-expression-head
Rules
981×*-un-lft-identity
736×times-frac
585×add-sqr-sqrt
468×prod-diff
419×add-cube-cbrt
189×distribute-lft-out
94×associate-/r/
90×distribute-lft-out--
81×difference-of-squares
47×div-inv
29×flip3-+ flip-+
20×flip3-- flip--
18×fma-neg
9×associate-/r*
7×add-exp-log add-cbrt-cube associate-/l*
5×add-log-exp
3×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 596
Calls
3 calls:
11.0ms
(/ x (+ x 1.0))
29.0ms
(/ (+ 1.0 x) (- x 1.0))
164.0ms
(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

series326.0ms

Counts
3 → 9
Calls
3 calls:
62.0ms
(/ x (+ x 1.0))
61.0ms
(/ (+ 1.0 x) (- x 1.0))
202.0ms
(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

simplify2.7s

Counts
605 → 605
Iterations

Useful iterations: done (2.7s)

IterNodesCost
053634216
1130330941
2475523491
done500023490

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ 1.0 x) (- x 1.0))
2.7b
(log (exp (/ x (+ x 1.0))))
3.6b
(- (log (exp (/ x (+ x 1.0)))) (/ (+ 1.0 x) (- x 1.0)))

rewrite469.0ms

Algorithm
rewrite-expression-head
Rules
1094×*-un-lft-identity
809×times-frac
688×add-sqr-sqrt
572×prod-diff
533×log-pow
504×exp-prod
497×add-cube-cbrt
204×distribute-lft-out
104×associate-/r/
95×distribute-lft-out-- difference-of-squares
52×div-inv
33×pow1
30×flip3-+ flip-+
24×flip3-- flip--
22×fma-neg
9×associate-/r*
8×add-exp-log add-cbrt-cube
7×associate-/l*
6×log-prod
5×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×associate--l+
2×cbrt-undiv frac-2neg div-exp clear-num associate-/l/
1×sub-neg diff-log rem-log-exp
Counts
4 → 729
Calls
4 calls:
11.0ms
(/ x (+ x 1.0))
28.0ms
(/ (+ 1.0 x) (- x 1.0))
34.0ms
(log (exp (/ x (+ x 1.0))))
291.0ms
(- (log (exp (/ x (+ x 1.0)))) (/ (+ 1.0 x) (- x 1.0)))

series624.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ x (+ x 1.0))
67.0ms
(/ (+ 1.0 x) (- x 1.0))
49.0ms
(log (exp (/ x (+ x 1.0))))
471.0ms
(- (log (exp (/ x (+ x 1.0)))) (/ (+ 1.0 x) (- x 1.0)))

simplify829.0ms

Counts
741 → 741
Iterations

Useful iterations: done (780.0ms)

IterNodesCost
063142779
1145937441
done500028579

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
0.3b
(/ 1.0 (* x x))
0.5b
(/ 3.0 (pow x 3))
5.0b
(- (- (/ 1.0 (* x x))) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

rewrite444.0ms

Algorithm
rewrite-expression-head
Rules
493×*-un-lft-identity
425×times-frac
234×prod-diff
219×add-sqr-sqrt
217×add-cube-cbrt
102×unpow3
100×distribute-rgt-neg-in
98×distribute-lft-neg-in
97×distribute-lft-out
76×distribute-rgt-out
69×div-inv
40×fma-def
21×unpow-prod-down cube-prod
19×distribute-lft1-in
18×fma-neg
16×add-log-exp
14×add-exp-log neg-mul-1
13×associate-/r*
11×add-cbrt-cube
7×cube-mult sqr-pow
6×associate-/l*
5×div-exp
4×pow1 expm1-log1p-u diff-log log1p-expm1-u distribute-lft-out--
3×cbrt-undiv sum-log frac-sub distribute-neg-frac
2×frac-2neg flip3-+ neg-log frac-add clear-num flip-+
1×+-commutative associate--l- neg-sub0 pow-to-exp sub-neg flip3-- pow-exp prod-exp flip-- cbrt-unprod associate--r+ difference-of-squares
Counts
4 → 433
Calls
4 calls:
74.0ms
(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
8.0ms
(/ 1.0 (* x x))
8.0ms
(/ 3.0 (pow x 3))
310.0ms
(- (- (/ 1.0 (* x x))) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

series295.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(+ (/ 3.0 (pow x 3)) (/ 3.0 x))
50.0ms
(/ 1.0 (* x x))
79.0ms
(/ 3.0 (pow x 3))
47.0ms
(- (- (/ 1.0 (* x x))) (+ (/ 3.0 (pow x 3)) (/ 3.0 x)))

simplify771.0ms

Counts
445 → 445
Iterations

Useful iterations: done (749.0ms)

IterNodesCost
048516713
1124313870
done500112191

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- x 1.0))
0.3b
(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
2.7b
(log (exp (/ x (+ x 1.0))))
10.4b
(- (log (exp (/ x (+ x 1.0)))) (* (/ (sqrt (+ 1.0 x)) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ (sqrt (+ 1.0 x)) (cbrt (- x 1.0)))))

rewrite463.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
59×add-sqr-sqrt
57×log-pow
54×exp-prod
41×add-cube-cbrt
36×times-frac
33×cbrt-prod
22×fma-neg prod-diff
14×pow1 cbrt-div
10×swap-sqr
9×distribute-lft-out
8×flip3-- associate-*r* associate-*l* flip--
7×pow1/3 distribute-lft-out--
6×add-exp-log log-prod associate-/r/
5×add-log-exp difference-of-squares
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u unswap-sqr
3×flip3-+ associate--l+ flip-+ div-inv
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 sub-neg pow-plus diff-log rem-log-exp prod-exp *-commutative cbrt-unprod
Counts
4 → 168
Calls
4 calls:
4.0ms
(cbrt (- x 1.0))
79.0ms
(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
41.0ms
(log (exp (/ x (+ x 1.0))))
330.0ms
(- (log (exp (/ x (+ x 1.0)))) (* (/ (sqrt (+ 1.0 x)) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ (sqrt (+ 1.0 x)) (cbrt (- x 1.0)))))

series646.0ms

Counts
4 → 12
Calls
4 calls:
164.0ms
(cbrt (- x 1.0))
190.0ms
(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
47.0ms
(log (exp (/ x (+ x 1.0))))
245.0ms
(- (log (exp (/ x (+ x 1.0)))) (* (/ (sqrt (+ 1.0 x)) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ (sqrt (+ 1.0 x)) (cbrt (- x 1.0)))))

simplify1.9s

Counts
180 → 180
Iterations

Useful iterations: done (1.9s)

IterNodesCost
03184895
17444539
229944062
done50003610

prune820.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes56.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 31.7b

bsearch126.0ms

Steps
ItersRangePoint
9
0.00015484893005477947
28918.939680702064
7392.742446615246
10
-2676750800.736259
-2.9526231381329305e-09
-0.994187787075435

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03172
13857
done3857

end0.0ms

sample1.4s

Algorithm
intervals
Results
527.0ms1745×body1280valid
314.0ms4091×body80valid
266.0ms1240×body640valid
82.0ms627×body320valid
27.0ms297×body160valid