Details

Time bar (total: 13.2s)

sample19.0ms

Algorithm
intervals
Results
5.0ms54×body1280valid
4.0ms49×body640valid
3.0ms123×body80valid
2.0ms27×body320valid
0.0ms3×body160valid

simplify114.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0713
11213
21613
31913
42113
52713
63913
75813
87613
99713
1012713
1113713
1214113
1314313
done14313

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
1.3b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite336.0ms

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:
5.0ms
(/ x (+ x 1.0))
11.0ms
(/ (+ x 1.0) (- x 1.0))
76.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series207.0ms

Counts
3 → 9
Calls
3 calls:
34.0ms
(/ x (+ x 1.0))
41.0ms
(/ (+ x 1.0) (- x 1.0))
131.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.2s

Counts
605 → 605
Iterations

Useful iterations: done (1.2s)

IterNodesCost
052334216
1115730851
2296722735
done500022021

prune604.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
0.1b
(/ (/ 1.0 x) x)
0.3b
(/ 3.0 (pow x 3))
6.4b
(- (- (/ (/ 1.0 x) x)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

rewrite522.0ms

Algorithm
rewrite-expression-head
Rules
3245×times-frac
2816×*-un-lft-identity
1528×add-sqr-sqrt
1526×add-cube-cbrt
1170×prod-diff
605×distribute-rgt-neg-in
602×distribute-lft-neg-in
459×unpow3
458×distribute-lft-out
364×distribute-rgt-out
301×div-inv
91×distribute-rgt1-in
90×fma-neg
16×associate-/l* add-log-exp
15×associate-/r*
14×add-exp-log neg-mul-1
13×fma-def
12×unpow-prod-down cube-prod
11×add-cbrt-cube
6×div-exp
5×distribute-lft-out--
4×pow1 cbrt-undiv expm1-log1p-u cube-mult diff-log log1p-expm1-u sqr-pow
3×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 flip-- associate-/l/ associate--r+ difference-of-squares
Counts
4 → 1464
Calls
4 calls:
32.0ms
(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
6.0ms
(/ (/ 1.0 x) x)
5.0ms
(/ 3.0 (pow x 3))
290.0ms
(- (- (/ (/ 1.0 x) x)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

series191.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
30.0ms
(/ (/ 1.0 x) x)
36.0ms
(/ 3.0 (pow x 3))
41.0ms
(- (- (/ (/ 1.0 x) x)) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

simplify1.2s

Counts
1476 → 1476
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0151182096
1284166843
done500166062

prune2.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
0.0b
(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
1.3b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite318.0ms

Algorithm
rewrite-expression-head
Rules
1139×*-un-lft-identity
796×times-frac
619×add-sqr-sqrt
468×prod-diff
415×add-cube-cbrt
215×distribute-lft-out
137×distribute-lft-out--
92×associate-/r/ difference-of-squares
46×div-inv
38×cbrt-prod
32×unpow-prod-down cube-prod
28×flip3-+ flip-+
21×flip3-- flip--
18×fma-neg
7×add-exp-log add-cbrt-cube
6×cube-div add-log-exp
5×pow1
4×expm1-log1p-u associate-/r* log1p-expm1-u
3×pow-unpow cbrt-div frac-sub associate-/l*
2×cube-mult unpow3 sqr-pow
1×cbrt-undiv pow-to-exp sub-neg pow-pow frac-2neg pow1/3 diff-log div-exp pow-exp clear-num rem-cbrt-cube rem-cube-cbrt
Counts
4 → 655
Calls
4 calls:
5.0ms
(/ x (+ x 1.0))
85.0ms
(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
87.0ms
(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
77.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series498.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ x (+ x 1.0))
134.0ms
(cbrt (pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3))
190.0ms
(pow (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))) 3)
134.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.3s

Counts
667 → 667
Iterations

Useful iterations: done (1.3s)

IterNodesCost
058736483
1132032660
2347124416
done500023858

prune740.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (/ x (+ x 1.0)))
0.3b
(cbrt (/ x (+ x 1.0)))
0.4b
(cbrt (pow (+ (fma (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0))) (/ (- (/ (+ x 1.0) (cbrt (- x 1.0)))) (* (cbrt (- x 1.0)) (cbrt (- x 1.0))))) (* (/ 1 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (+ (- (/ (+ x 1.0) (cbrt (- x 1.0)))) (/ (+ x 1.0) (cbrt (- x 1.0)))))) 3))
21.9b
(fma (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0))) (/ (- (/ (+ x 1.0) (cbrt (- x 1.0)))) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
48×cbrt-prod
35×*-un-lft-identity
24×times-frac
23×add-sqr-sqrt add-cube-cbrt
6×distribute-lft-out
4×pow1 add-exp-log expm1-log1p-u cbrt-div associate-/r/ add-cbrt-cube log1p-expm1-u add-log-exp
3×unpow-prod-down flip3-+ pow1/3 cube-prod flip-+
2×cube-div div-inv
1×cube-mult unpow3 rem-cbrt-cube fma-udef sqr-pow
Counts
4 → 93
Calls
4 calls:
3.0ms
(cbrt (/ x (+ x 1.0)))
3.0ms
(cbrt (/ x (+ x 1.0)))
3.0ms
(cbrt (pow (+ (fma (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0))) (/ (- (/ (+ x 1.0) (cbrt (- x 1.0)))) (* (cbrt (- x 1.0)) (cbrt (- x 1.0))))) (* (/ 1 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (+ (- (/ (+ x 1.0) (cbrt (- x 1.0)))) (/ (+ x 1.0) (cbrt (- x 1.0)))))) 3))
0.0ms
(fma (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0))) (/ (- (/ (+ x 1.0) (cbrt (- x 1.0)))) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))))

series1.6s

Counts
4 → 12
Calls
4 calls:
160.0ms
(cbrt (/ x (+ x 1.0)))
158.0ms
(cbrt (/ x (+ x 1.0)))
643.0ms
(cbrt (pow (+ (fma (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0))) (/ (- (/ (+ x 1.0) (cbrt (- x 1.0)))) (* (cbrt (- x 1.0)) (cbrt (- x 1.0))))) (* (/ 1 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (+ (- (/ (+ x 1.0) (cbrt (- x 1.0)))) (/ (+ x 1.0) (cbrt (- x 1.0)))))) 3))
656.0ms
(fma (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0))) (/ (- (/ (+ x 1.0) (cbrt (- x 1.0)))) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))))

simplify886.0ms

Counts
105 → 105
Iterations

Useful iterations: 2 (225.0ms)

IterNodesCost
02265096
15494648
218723468
done50013468

prune440.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes47.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.7b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02248
12648
22848
done2848

end0.0ms

sample518.0ms

Algorithm
intervals
Results
179.0ms1731×body1280valid
101.0ms1265×body640valid
97.0ms4084×body80valid
38.0ms618×body320valid
12.0ms302×body160valid