Details

Time bar (total: 10.8s)

sample19.0ms

Algorithm
intervals
Results
5.0ms195×body80valid
2.0ms27×body640valid
1.0ms17×body320valid
1.0ms9×body1280valid
0.0ms8×body160valid

simplify2.4s

Counts
1 → 1
Iterations

Useful iterations: 4 (20.0ms)

IterNodesCost
0811
11611
23511
37211
414110
528310
640110
751410
861610
986510
10120510
11170410
done500010

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- x 1.0) (+ y 1.0))
14.3b
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
23×add-sqr-sqrt
20×times-frac
13×add-cube-cbrt
6×distribute-lft-out
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log associate-/r* add-cbrt-cube
2×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv flip3-- frac-2neg flip3-+ div-sub div-exp clear-num flip-- flip-+ fma-udef div-inv
Counts
2 → 58
Calls
2 calls:
13.0ms
(/ (- x 1.0) (+ y 1.0))
1.0ms
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series103.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(/ (- x 1.0) (+ y 1.0))
72.0ms
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify2.0s

Counts
64 → 64
Iterations

Useful iterations: done (2.0s)

IterNodesCost
0114834
1277799
2801745
33560739
done5000738

prune162.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- x 1.0))
0.3b
(cbrt (- x 1.0))
0.3b
(cbrt (- x 1.0))
14.1b
(fma (* (/ (* (cbrt (- x 1.0)) (cbrt (- x 1.0))) (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ (cbrt (- x 1.0)) (cbrt (+ y 1.0)))) y 1.0)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity
7×add-cube-cbrt
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
1×fma-udef
Counts
4 → 61
Calls
4 calls:
2.0ms
(cbrt (- x 1.0))
2.0ms
(cbrt (- x 1.0))
2.0ms
(cbrt (- x 1.0))
0.0ms
(fma (* (/ (* (cbrt (- x 1.0)) (cbrt (- x 1.0))) (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ (cbrt (- x 1.0)) (cbrt (+ y 1.0)))) y 1.0)

series417.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(cbrt (- x 1.0))
109.0ms
(cbrt (- x 1.0))
106.0ms
(cbrt (- x 1.0))
87.0ms
(fma (* (/ (* (cbrt (- x 1.0)) (cbrt (- x 1.0))) (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ (cbrt (- x 1.0)) (cbrt (+ y 1.0)))) y 1.0)

simplify1.0s

Counts
73 → 73
Iterations

Useful iterations: 3 (287.0ms)

IterNodesCost
01191172
12721117
2740818
32524776
done5000776

prune306.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 3 expressions with local error:

2.7b
(/ (- x 1.0) (- (* y y) (* 1.0 1.0)))
8.9b
(* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0))
14.3b
(fma (* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0)) y 1.0)

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
57×*-un-lft-identity
41×times-frac
37×add-cube-cbrt
26×associate-*l*
21×difference-of-squares
18×prod-diff
11×distribute-rgt-in distribute-lft-in
10×add-exp-log add-cbrt-cube distribute-lft-out--
5×pow1 flip3-- associate-*r* flip-- associate-/l*
4×associate-/r* associate-/r/
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv frac-times sub-neg associate-*r/ div-exp prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×frac-2neg div-sub pow-prod-down associate-*l/ clear-num *-commutative fma-udef
Counts
3 → 133
Calls
3 calls:
13.0ms
(/ (- x 1.0) (- (* y y) (* 1.0 1.0)))
37.0ms
(* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0))
0.0ms
(fma (* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0)) y 1.0)

series245.0ms

Counts
3 → 9
Calls
3 calls:
70.0ms
(/ (- x 1.0) (- (* y y) (* 1.0 1.0)))
67.0ms
(* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0))
108.0ms
(fma (* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0)) y 1.0)

simplify1.5s

Counts
142 → 142
Iterations

Useful iterations: 2 (261.0ms)

IterNodesCost
02563206
16932990
231762695
done50002695

prune362.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
2.9b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.2b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite40.0ms

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:
11.0ms
(* (- 1.0 x) y)
14.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
10.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series159.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(* (- 1.0 x) y)
70.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
52.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify970.0ms

Counts
111 → 111
Iterations

Useful iterations: 2 (185.0ms)

IterNodesCost
02022757
15462323
222381851
done50011851

prune209.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

regimes131.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.6b

bsearch101.0ms

Steps
ItersRangePoint
9
2942.2625356967415
559751770.533176
184531412.1859252
9
-155084744.97222546
-3.3588146519216853
-126285643.80532795

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
01941
12631
done2631

end0.0ms

sample466.0ms

Algorithm
intervals
Results
158.0ms6059×body80valid
64.0ms712×body640valid
49.0ms380×body1280valid
35.0ms518×body320valid
15.0ms331×body160valid