Details

Time bar (total: 28.8s)

sample44.0ms

Algorithm
intervals
Results
12.0ms195×body80valid
7.0ms29×body640valid
2.0ms14×body320valid
2.0ms8×body1280valid
1.0ms10×body160valid

simplify11.7s

Counts
1 → 1
Iterations

Useful iterations: 4 (56.0ms)

IterNodesCost
0811
11611
23511
37611
413110
524210
630910
737410
842410
951310
1058210
1159110
1261010
1364810
1477710
1591510
16123310
17168910
18227010
19243610
20244210
done244210

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.4b

localize17.0ms

Local error

Found 1 expressions with local error:

13.7b
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
1.0ms
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series96.0ms

Counts
1 → 3
Calls
1 calls:
95.0ms
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify4.2s

Counts
13 → 13
Iterations

Useful iterations: 5 (2.2s)

IterNodesCost
029178
163177
2141153
3329149
4990147
54868145
done5000145

prune47.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
1.8b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
8.9b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
30×add-sqr-sqrt prod-diff
24×add-cube-cbrt
16×times-frac
10×add-exp-log add-cbrt-cube
8×associate-/r/
5×pow1 associate-*l* distribute-lft-out add-log-exp
4×flip3-+ associate-*l/ associate-/r* flip-+ div-inv
3×expm1-log1p-u flip3-- fma-neg associate-*r* flip-- log1p-expm1-u
2×cbrt-undiv div-exp prod-exp cbrt-unprod associate-/l/ distribute-lft-out-- difference-of-squares
1×sub-neg frac-2neg diff-log pow-prod-down clear-num *-commutative associate-/l* unswap-sqr
Counts
3 → 102
Calls
3 calls:
30.0ms
(* (- 1.0 x) y)
27.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
48.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series261.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(* (- 1.0 x) y)
139.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
75.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify2.8s

Counts
111 → 111
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02022757
15282323
219651851
done50001619

prune311.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ y (+ y 1.0))
0.0b
(* (- 1.0 x) (/ y (+ y 1.0)))
1.8b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
30×add-sqr-sqrt
25×times-frac
23×add-cube-cbrt
18×associate-*r*
10×add-exp-log add-cbrt-cube
7×distribute-lft-out
5×pow1 associate-*l* add-log-exp
4×associate-/r* associate-/r/
3×expm1-log1p-u flip3-- fma-neg prod-diff flip-- log1p-expm1-u associate-/l*
2×cbrt-undiv frac-times flip3-+ div-exp associate-*l/ prod-exp cbrt-unprod flip-+ div-inv unswap-sqr
1×sub-neg frac-2neg diff-log associate-*r/ pow-prod-down clear-num *-commutative distribute-lft-out-- difference-of-squares
Counts
3 → 100
Calls
3 calls:
13.0ms
(/ y (+ y 1.0))
50.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
13.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series206.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(/ y (+ y 1.0))
70.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
87.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify1.8s

Counts
109 → 109
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01721418
14321330
215251216
done50001204

prune352.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (* (/ y (+ y 1.0)) (- 1.0 x)) (fma (- 1.0 x) (/ y (+ y 1.0)) 1.0) (* 1.0 1.0))
0.2b
(pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)
1.7b
(- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3))
14.6b
(/ (- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)) (fma (* (/ y (+ y 1.0)) (- 1.0 x)) (fma (- 1.0 x) (/ y (+ y 1.0)) 1.0) (* 1.0 1.0)))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
112×add-sqr-sqrt
96×prod-diff
72×*-un-lft-identity
62×add-cube-cbrt
52×sqr-pow
50×unpow-prod-down cube-prod
40×difference-of-squares
39×times-frac
22×cube-mult unpow3
13×associate-/l*
12×add-exp-log fma-neg add-cbrt-cube
7×pow1
6×add-log-exp
5×difference-cubes cube-div distribute-lft-out--
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×pow-unpow pow-exp associate-/r* rem-cube-cbrt
2×cbrt-undiv frac-times pow-pow div-exp associate-*l/ prod-exp cbrt-unprod associate-/l/
1×pow-to-exp sub-neg frac-2neg diff-log div-sub associate-*r/ pow-prod-down clear-num fma-udef div-inv
Counts
4 → 245
Calls
4 calls:
0.0ms
(fma (* (/ y (+ y 1.0)) (- 1.0 x)) (fma (- 1.0 x) (/ y (+ y 1.0)) 1.0) (* 1.0 1.0))
21.0ms
(pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)
54.0ms
(- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3))
101.0ms
(/ (- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)) (fma (* (/ y (+ y 1.0)) (- 1.0 x)) (fma (- 1.0 x) (/ y (+ y 1.0)) 1.0) (* 1.0 1.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
144.0ms
(fma (* (/ y (+ y 1.0)) (- 1.0 x)) (fma (- 1.0 x) (/ y (+ y 1.0)) 1.0) (* 1.0 1.0))
125.0ms
(pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)
238.0ms
(- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3))
675.0ms
(/ (- (pow 1.0 3) (pow (* (- 1.0 x) (/ y (+ y 1.0))) 3)) (fma (* (/ y (+ y 1.0)) (- 1.0 x)) (fma (- 1.0 x) (/ y (+ y 1.0)) 1.0) (* 1.0 1.0)))

simplify2.6s

Counts
257 → 257
Iterations

Useful iterations: done (2.5s)

IterNodesCost
034914378
187210252
231618762
done50028712

prune884.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

regimes158.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 14.2b

bsearch113.0ms

Steps
ItersRangePoint
9
137362616.0762091
1439059428709982.0
237947981.8392704
7
-2445851338.3862987
-30461436.183609415
-295491748.0547483

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01734
12327
done2327

end0.0ms

sample1.7s

Algorithm
intervals
Results
999.0ms6123×body80valid
190.0ms755×body640valid
81.0ms364×body1280valid
67.0ms506×body320valid
23.0ms252×body160valid