Details

Time bar (total: 32.6s)

sample41.0ms

Algorithm
intervals
Results
12.0ms198×body80valid
5.0ms22×body640valid
3.0ms20×body320valid
2.0ms8×body1280valid
1.0ms8×body160valid

simplify10.7s

Counts
1 → 1
Iterations

Useful iterations: 4 (54.0ms)

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.4b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- x 1.0) (+ y 1.0))
13.7b
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite33.0ms

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:
30.0ms
(/ (- x 1.0) (+ y 1.0))
1.0ms
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series148.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(/ (- x 1.0) (+ y 1.0))
108.0ms
(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify2.4s

Counts
64 → 64
Iterations

Useful iterations: done (2.4s)

IterNodesCost
0114834
1277799
2718745
31747739
done5000737

prune185.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* y y) (* 1.0 1.0))
4.1b
(/ (- x 1.0) (- (* y y) (* 1.0 1.0)))
9.7b
(* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0))
13.7b
(fma (* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0)) y 1.0)

rewrite178.0ms

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:
18.0ms
(- (* y y) (* 1.0 1.0))
52.0ms
(/ (- x 1.0) (- (* y y) (* 1.0 1.0)))
95.0ms
(* (/ (- 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)

series384.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* y y) (* 1.0 1.0))
96.0ms
(/ (- x 1.0) (- (* y y) (* 1.0 1.0)))
92.0ms
(* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0))
146.0ms
(fma (* (/ (- x 1.0) (- (* y y) (* 1.0 1.0))) (- y 1.0)) y 1.0)

simplify3.2s

Counts
162 → 162
Iterations

Useful iterations: done (3.2s)

IterNodesCost
02663414
16823177
222362886
done50012450

prune600.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite87.0ms

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)
59.0ms
(- (/ 1 y) (/ x y))

series73.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(fma 1.0 (- (/ 1 y) (/ x y)) x)
24.0ms
(- (/ 1 y) (/ x y))

simplify3.7s

Counts
228 → 228
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
03158117
16886842
213284644
341843416
done50003416

prune305.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.8b
(pow (cbrt y) 3)
0.8b
(pow (cbrt y) 3)
0.8b
(pow (cbrt y) 3)
6.7b
(- (/ x (pow (cbrt y) 3)) (/ x (pow (cbrt y) 3)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
6916×times-frac
4445×add-sqr-sqrt
4403×*-un-lft-identity
4325×add-cube-cbrt
3364×prod-diff
2360×cbrt-prod unpow-prod-down cube-prod
380×sqr-pow
366×cube-mult unpow3
176×distribute-rgt-out--
121×div-inv
94×distribute-lft-out--
58×fma-neg
49×difference-of-squares
9×pow-unpow
7×pow1 add-exp-log
6×pow-pow add-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow-to-exp pow1/3 pow-exp rem-cube-cbrt
1×sub-neg flip3-- +-inverses diff-log frac-sub flip-- sub-div
Counts
4 → 3854
Calls
4 calls:
6.0ms
(pow (cbrt y) 3)
10.0ms
(pow (cbrt y) 3)
7.0ms
(pow (cbrt y) 3)
451.0ms
(- (/ x (pow (cbrt y) 3)) (/ x (pow (cbrt y) 3)))

series1.3s

Counts
4 → 12
Calls
4 calls:
412.0ms
(pow (cbrt y) 3)
424.0ms
(pow (cbrt y) 3)
433.0ms
(pow (cbrt y) 3)
5.0ms
(- (/ x (pow (cbrt y) 3)) (/ x (pow (cbrt y) 3)))

simplify3.4s

Counts
3866 → 3866
Iterations

Useful iterations: done (2.9s)

IterNodesCost
02018244837
14038164612
done5000117901

prune2.8s

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0.2b

regimes119.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 14.4b

bsearch121.0ms

Steps
ItersRangePoint
9
9556.682540875734
15966983906.555069
107669609.3560517
10
-9.405557600769291e+21
-1501.2167507114543
-197475236.47678238

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02246
12837
done2837

end0.0ms

sample1.4s

Algorithm
intervals
Results
544.0ms754×body640valid
279.0ms6091×body80valid
178.0ms505×body320valid
122.0ms354×body1280valid
24.0ms296×body160valid