Details

Time bar (total: 30.1s)

sample26.0ms

Algorithm
intervals
Results
6.0ms187×body80valid
4.0ms33×body640valid
2.0ms11×body1280valid
1.0ms14×body320valid
1.0ms11×body160valid

simplify11.9s

Counts
1 → 1
Iterations

Useful iterations: 4 (51.0ms)

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.8b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- x 1.0) (+ y 1.0))
16.1b
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite60.0ms

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:
56.0ms
(/ (- x 1.0) (+ y 1.0))
1.0ms
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series184.0ms

Counts
2 → 6
Calls
2 calls:
60.0ms
(/ (- x 1.0) (+ y 1.0))
123.0ms
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify2.3s

Counts
64 → 64
Iterations

Useful iterations: done (2.3s)

IterNodesCost
0114834
1277799
2718745
31747739
done5000737

prune235.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x 1.0) (+ y 1.0))
0.1b
(* (/ (- x 1.0) (+ y 1.0)) y)
4.4b
(+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0)

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
48×add-sqr-sqrt
41×times-frac
26×associate-*l*
25×add-cube-cbrt
11×distribute-lft-out
10×add-exp-log add-cbrt-cube
9×distribute-lft-out-- difference-of-squares
5×pow1 associate-/l* add-log-exp
4×associate-/r* associate-/r/
3×expm1-log1p-u flip3-+ associate-*r* flip-+ log1p-expm1-u
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative flip3-- fma-def frac-2neg div-sub pow-prod-down associate-*l/ clear-num sum-log *-commutative flip--
Counts
3 → 109
Calls
3 calls:
34.0ms
(/ (- x 1.0) (+ y 1.0))
67.0ms
(* (/ (- x 1.0) (+ y 1.0)) y)
31.0ms
(+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0)

series250.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(/ (- x 1.0) (+ y 1.0))
80.0ms
(* (/ (- x 1.0) (+ y 1.0)) y)
126.0ms
(+ (* (/ (- x 1.0) (+ y 1.0)) y) 1.0)

simplify4.0s

Counts
118 → 118
Iterations

Useful iterations: 3 (2.5s)

IterNodesCost
01721520
14601433
213181340
341391327
done50001327

prune370.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(* y (- y 1.0))
3.2b
(/ (- x 1.0) (- (* y y) (* 1.0 1.0)))
4.9b
(+ (* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (* y (- y 1.0))) 1.0)
16.1b
(* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (* y (- y 1.0)))

rewrite354.0ms

Algorithm
rewrite-expression-head
Rules
109×add-sqr-sqrt
107×*-un-lft-identity
99×distribute-rgt-in distribute-lft-in
90×prod-diff
87×add-cube-cbrt
44×associate-+l+
40×times-frac
29×associate-*l*
21×difference-of-squares
20×add-exp-log add-cbrt-cube
11×pow1
10×sub-neg distribute-lft-out--
8×associate-*r/
7×prod-exp cbrt-unprod
6×flip3-- associate-*r* flip-- add-log-exp
5×associate-/l*
4×expm1-log1p-u pow-prod-down associate-/r* associate-/r/ log1p-expm1-u
3×cbrt-undiv div-exp
2×frac-times *-commutative div-inv associate-/l/
1×+-commutative fma-def frac-2neg flip3-+ div-sub associate-*l/ clear-num sum-log flip-+ unswap-sqr
Counts
4 → 248
Calls
4 calls:
54.0ms
(* y (- y 1.0))
32.0ms
(/ (- x 1.0) (- (* y y) (* 1.0 1.0)))
67.0ms
(+ (* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (* y (- y 1.0))) 1.0)
172.0ms
(* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (* y (- y 1.0)))

series608.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* y (- y 1.0))
106.0ms
(/ (- x 1.0) (- (* y y) (* 1.0 1.0)))
266.0ms
(+ (* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (* y (- y 1.0))) 1.0)
144.0ms
(* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (* y (- y 1.0)))

simplify2.6s

Counts
260 → 260
Iterations

Useful iterations: done (2.6s)

IterNodesCost
03546480
19795596
230525034
done50014958

prune854.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 1 expressions with local error:

0.0b
(- (/ 1 y) (/ x y))

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
257×times-frac
209×add-sqr-sqrt
206×*-un-lft-identity
192×add-cube-cbrt
169×prod-diff
32×div-inv
13×fma-neg
6×difference-of-squares
5×distribute-lft-out--
3×distribute-rgt-out-- add-log-exp
1×pow1 add-exp-log expm1-log1p-u sub-neg flip3-- diff-log frac-sub add-cbrt-cube flip-- log1p-expm1-u sub-div
Counts
1 → 212
Calls
1 calls:
58.0ms
(- (/ 1 y) (/ x y))

series36.0ms

Counts
1 → 3
Calls
1 calls:
36.0ms
(- (/ 1 y) (/ x y))

simplify3.8s

Counts
215 → 215
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
02997937
16586662
212494493
337743265
done50003265

prune211.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

regimes122.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.1b

bsearch81.0ms

Steps
ItersRangePoint
9
5729.342694487068
8685649418.189968
165630154.1629503
4
-56513505501200.5
-30636816361710.875
-31112195187751.668

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
01939
12730
done2730

end0.0ms

sample1.7s

Algorithm
intervals
Results
683.0ms696×body640valid
478.0ms6129×body80valid
126.0ms534×body320valid
83.0ms343×body1280valid
28.0ms298×body160valid