Details

Time bar (total: 18.9s)

sample20.0ms

Algorithm
intervals
Results
5.0ms189×body80valid
2.0ms26×body640valid
2.0ms14×body1280valid
1.0ms17×body320valid
0.0ms10×body160valid

simplify7.3s

Counts
1 → 1
Iterations

Useful iterations: 4 (28.0ms)

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

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- x 1.0) (+ y 1.0))
15.7b
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite34.0ms

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:
31.0ms
(/ (- x 1.0) (+ y 1.0))
0.0ms
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series100.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(/ (- x 1.0) (+ y 1.0))
66.0ms
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify1.5s

Counts
64 → 64
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0114834
1277799
2718745
31747739
done5000737

prune167.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* y y) (* 1.0 1.0))
4.0b
(/ (- x 1.0) (- (* y y) (* 1.0 1.0)))
11.0b
(* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0))
15.7b
(fma (* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0)) y 1.0)

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
58×*-un-lft-identity
41×times-frac
38×add-cube-cbrt
26×associate-*l*
22×difference-of-squares
19×prod-diff
11×add-exp-log distribute-rgt-in distribute-lft-in add-cbrt-cube
10×distribute-lft-out--
6×pow1 flip3-- flip-- add-log-exp
5×associate-*r* associate-/l*
4×expm1-log1p-u associate-/r* associate-/r/ log1p-expm1-u
3×sub-neg
2×cbrt-undiv frac-times associate-*r/ div-exp prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×frac-2neg fma-neg diff-log div-sub pow-prod-down associate-*l/ clear-num *-commutative fma-udef
Counts
4 → 150
Calls
4 calls:
12.0ms
(- (* y y) (* 1.0 1.0))
28.0ms
(/ (- x 1.0) (- (* y y) (* 1.0 1.0)))
80.0ms
(* (/ (- 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)

series291.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* y y) (* 1.0 1.0))
70.0ms
(/ (- x 1.0) (- (* y y) (* 1.0 1.0)))
65.0ms
(* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0))
113.0ms
(fma (* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0)) y 1.0)

simplify1.7s

Counts
162 → 162
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02663414
16823177
222362886
done50012450

prune420.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (/ 1 y) (/ x y))
0.0b
(fma 1.0 (- (/ 1 y) (/ x y)) x)

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
257×times-frac
210×add-sqr-sqrt
207×*-un-lft-identity
193×add-cube-cbrt
169×prod-diff
32×div-inv
13×fma-neg
6×difference-of-squares
5×distribute-lft-out--
4×add-log-exp
3×distribute-rgt-out--
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- diff-log frac-sub flip-- fma-udef sub-div
Counts
2 → 222
Calls
2 calls:
39.0ms
(- (/ 1 y) (/ x y))
0.0ms
(fma 1.0 (- (/ 1 y) (/ x y)) x)

series56.0ms

Counts
2 → 6
Calls
2 calls:
23.0ms
(- (/ 1 y) (/ x y))
33.0ms
(fma 1.0 (- (/ 1 y) (/ x y)) x)

simplify2.8s

Counts
228 → 228
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
03158117
16886842
213294644
341863416
done50003416

prune204.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (- (/ 1 y) (/ x y))) (cbrt (- (/ 1 y) (/ x y))))
5.8b
(cbrt (- (/ 1 y) (/ x y)))
5.8b
(cbrt (- (/ 1 y) (/ x y)))
5.8b
(cbrt (- (/ 1 y) (/ x y)))

rewrite264.0ms

Algorithm
rewrite-expression-head
Rules
156×add-sqr-sqrt
145×*-un-lft-identity
139×cbrt-prod
98×times-frac
52×cbrt-div
45×div-inv
43×distribute-lft-out--
42×difference-of-squares
29×add-cube-cbrt
28×swap-sqr
25×distribute-rgt-out--
20×associate-*r* associate-*l*
16×frac-times
13×flip3-- frac-sub flip-- sub-div
11×pow1
9×pow1/3
6×add-exp-log
4×expm1-log1p-u associate-*r/ associate-*l/ add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 209
Calls
4 calls:
181.0ms
(* (cbrt (- (/ 1 y) (/ x y))) (cbrt (- (/ 1 y) (/ x y))))
23.0ms
(cbrt (- (/ 1 y) (/ x y)))
21.0ms
(cbrt (- (/ 1 y) (/ x y)))
21.0ms
(cbrt (- (/ 1 y) (/ x y)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(* (cbrt (- (/ 1 y) (/ x y))) (cbrt (- (/ 1 y) (/ x y))))
87.0ms
(cbrt (- (/ 1 y) (/ x y)))
87.0ms
(cbrt (- (/ 1 y) (/ x y)))
85.0ms
(cbrt (- (/ 1 y) (/ x y)))

simplify2.1s

Counts
221 → 221
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02784785
15364445
213334203
333513837
done50003649

prune640.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

regimes108.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 21.7b

bsearch89.0ms

Steps
ItersRangePoint
9
211.08706756948936
882388454.4280733
122797968.695956
9
-5463081689.944393
-76786.820650899
-109215276.02048767

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02246
12837
done2837

end0.0ms

sample507.0ms

Algorithm
intervals
Results
160.0ms6133×body80valid
62.0ms719×body640valid
37.0ms339×body1280valid
33.0ms513×body320valid
17.0ms296×body160valid