Details

Time bar (total: 24.4s)

sample22.0ms

Algorithm
intervals
Results
6.0ms188×body80valid
3.0ms27×body640valid
2.0ms19×body320valid
1.0ms10×body1280valid
1.0ms12×body160valid

simplify10.4s

Counts
1 → 1
Iterations

Useful iterations: 4 (34.0ms)

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.6b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- x 1.0) (+ y 1.0))
15.9b
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite38.0ms

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:
35.0ms
(/ (- x 1.0) (+ y 1.0))
1.0ms
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series131.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(/ (- x 1.0) (+ y 1.0))
93.0ms
(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

prune207.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ y 1.0))
0.0b
(/ x (+ y 1.0))
0.0b
(- (/ x (+ y 1.0)) (/ 1.0 (+ y 1.0)))
15.9b
(fma (- (/ x (+ y 1.0)) (/ 1.0 (+ y 1.0))) y 1.0)

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
582×*-un-lft-identity
484×times-frac
332×add-sqr-sqrt
324×prod-diff
320×add-cube-cbrt
123×distribute-lft-out
82×associate-/r/
41×flip3-+ flip-+ div-inv
18×fma-neg
8×add-exp-log associate-/r* add-cbrt-cube
7×distribute-lft-out--
6×associate-/l* add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u difference-of-squares
3×distribute-rgt-out--
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg flip3-- diff-log frac-sub flip-- fma-udef sub-div
Counts
4 → 452
Calls
4 calls:
22.0ms
(/ 1.0 (+ y 1.0))
17.0ms
(/ x (+ y 1.0))
120.0ms
(- (/ x (+ y 1.0)) (/ 1.0 (+ y 1.0)))
1.0ms
(fma (- (/ x (+ y 1.0)) (/ 1.0 (+ y 1.0))) y 1.0)

series249.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ 1.0 (+ y 1.0))
64.0ms
(/ x (+ y 1.0))
42.0ms
(- (/ x (+ y 1.0)) (/ 1.0 (+ y 1.0)))
97.0ms
(fma (- (/ x (+ y 1.0)) (/ 1.0 (+ y 1.0))) y 1.0)

simplify2.8s

Counts
464 → 464
Iterations

Useful iterations: done (2.8s)

IterNodesCost
047120743
1105418233
2239313844
done500010461

prune904.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ y 1.0))
0.1b
(* (/ 1 (+ y 1.0)) (- x 1.0))
0.1b
(* (* (/ 1 (+ y 1.0)) (- x 1.0)) y)
4.5b
(+ (* (* (/ 1 (+ y 1.0)) (- x 1.0)) y) 1.0)

rewrite252.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
44×add-sqr-sqrt
35×add-cube-cbrt
32×add-exp-log
26×times-frac
20×add-cbrt-cube
19×associate-*l*
18×prod-diff
13×prod-exp
12×pow1
11×distribute-rgt-in distribute-lft-in
8×associate-*r*
7×associate-*l/ cbrt-unprod distribute-lft-out
6×div-exp add-log-exp
4×expm1-log1p-u frac-times flip3-- associate-*r/ pow-prod-down associate-/r* associate-/r/ flip-- log1p-expm1-u
3×cbrt-undiv rec-exp flip3-+ 1-exp flip-+ associate-/l* unswap-sqr
2×sub-neg *-commutative div-inv
1×+-commutative pow-flip fma-def frac-2neg clear-num sum-log distribute-lft-out-- inv-pow difference-of-squares
Counts
4 → 152
Calls
4 calls:
22.0ms
(/ 1 (+ y 1.0))
55.0ms
(* (/ 1 (+ y 1.0)) (- x 1.0))
78.0ms
(* (* (/ 1 (+ y 1.0)) (- x 1.0)) y)
87.0ms
(+ (* (* (/ 1 (+ y 1.0)) (- x 1.0)) y) 1.0)

series210.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ 1 (+ y 1.0))
29.0ms
(* (/ 1 (+ y 1.0)) (- x 1.0))
44.0ms
(* (* (/ 1 (+ y 1.0)) (- x 1.0)) y)
110.0ms
(+ (* (* (/ 1 (+ y 1.0)) (- x 1.0)) y) 1.0)

simplify1.6s

Counts
164 → 164
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02602533
16482014
218951686
done50001644

prune379.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 1.0 (- (/ 1 y) (/ x y)) x)
0.3b
(- (/ 1 y) (/ x y))

rewrite63.0ms

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:
0.0ms
(fma 1.0 (- (/ 1 y) (/ x y)) x)
41.0ms
(- (/ 1 y) (/ x y))

series56.0ms

Counts
2 → 6
Calls
2 calls:
34.0ms
(fma 1.0 (- (/ 1 y) (/ x y)) x)
22.0ms
(- (/ 1 y) (/ x y))

simplify3.1s

Counts
228 → 228
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
03158117
16886842
213284644
341843416
done50003416

prune195.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.1b

regimes124.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 14.7b

bsearch87.0ms

Steps
ItersRangePoint
9
20796729.49276672
3744461241692.0635
150550976.72319537
6
-433630756157860.06
-60439154737701.01
-61215075097455.13

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01942
12533
done2533

end0.0ms

sample972.0ms

Algorithm
intervals
Results
334.0ms6059×body80valid
191.0ms724×body640valid
96.0ms554×body320valid
66.0ms362×body1280valid
22.0ms301×body160valid