Details

Time bar (total: 14.8s)

sample20.0ms

Algorithm
intervals
Results
11.0ms293×body80valid

simplify360.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11911
22911
34411
45511
56911
68111
711411
812911
913511
1013911
1114911
1215311
1315511
done15511

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.6b

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b
(* x (+ (/ x y) 1.0))
7.1b
(/ (* x (+ (/ x y) 1.0)) (+ x 1.0))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
6×add-cube-cbrt
4×pow1 times-frac associate-*r/ associate-*r* associate-/r*
3×flip3-+ associate-*l* flip-+ distribute-lft-out
2×cbrt-undiv expm1-log1p-u div-exp prod-exp associate-/r/ cbrt-unprod log1p-expm1-u associate-/l/ add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num *-commutative div-inv associate-/l* unswap-sqr
Counts
2 → 54
Calls
2 calls:
96.0ms
(* x (+ (/ x y) 1.0))
70.0ms
(/ (* x (+ (/ x y) 1.0)) (+ x 1.0))

series103.0ms

Counts
2 → 6
Calls
2 calls:
46.0ms
(* x (+ (/ x y) 1.0))
57.0ms
(/ (* x (+ (/ x y) 1.0)) (+ x 1.0))

simplify3.0s

Counts
60 → 60
Iterations

Useful iterations: 3 (1.5s)

IterNodesCost
0107759
1302728
21120632
34510629
done5000629

prune215.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ x (/ (+ x 1.0) (+ (/ x y) 1.0)))
0.1b
(/ (+ x 1.0) (+ (/ x y) 1.0))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
155×*-un-lft-identity
146×times-frac
71×add-sqr-sqrt add-cube-cbrt
42×distribute-lft-out
26×associate-/r*
11×associate-/r/
9×add-exp-log add-cbrt-cube
7×associate-/l*
6×flip3-+ flip-+ div-inv
4×cbrt-undiv div-exp
2×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u associate-/l/ add-log-exp
Counts
2 → 150
Calls
2 calls:
70.0ms
(/ x (/ (+ x 1.0) (+ (/ x y) 1.0)))
43.0ms
(/ (+ x 1.0) (+ (/ x y) 1.0))

series173.0ms

Counts
2 → 6
Calls
2 calls:
78.0ms
(/ x (/ (+ x 1.0) (+ (/ x y) 1.0)))
95.0ms
(/ (+ x 1.0) (+ (/ x y) 1.0))

simplify1.5s

Counts
156 → 156
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02113002
14892812
217202698
done50002685

prune362.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ x y) (/ x y))
0.3b
(/ x (/ (+ x 1.0) (- (* (/ x y) (/ x y)) (* 1.0 1.0))))
3.2b
(/ (+ x 1.0) (- (* (/ x y) (/ x y)) (* 1.0 1.0)))
8.1b
(/ (/ x (/ (+ x 1.0) (- (* (/ x y) (/ x y)) (* 1.0 1.0)))) (- (/ x y) 1.0))

rewrite435.0ms

Algorithm
rewrite-expression-head
Rules
1482×times-frac
895×add-sqr-sqrt
877×*-un-lft-identity
523×add-cube-cbrt
249×difference-of-squares
105×distribute-lft-out
78×associate-/l*
72×distribute-lft-out--
62×associate-/r/
39×div-inv
32×add-exp-log associate-/r* add-cbrt-cube
27×flip3-- flip--
14×cbrt-undiv div-exp
13×swap-sqr associate-*r* associate-*l*
11×pow1
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
3×frac-2neg clear-num associate-/l/
1×pow2 frac-times flip3-+ pow-plus associate-*r/ pow-prod-down associate-*l/ pow-sqr *-commutative pow-prod-up flip-+
Counts
4 → 743
Calls
4 calls:
40.0ms
(* (/ x y) (/ x y))
67.0ms
(/ x (/ (+ x 1.0) (- (* (/ x y) (/ x y)) (* 1.0 1.0))))
60.0ms
(/ (+ x 1.0) (- (* (/ x y) (/ x y)) (* 1.0 1.0)))
155.0ms
(/ (/ x (/ (+ x 1.0) (- (* (/ x y) (/ x y)) (* 1.0 1.0)))) (- (/ x y) 1.0))

series381.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (/ x y) (/ x y))
131.0ms
(/ x (/ (+ x 1.0) (- (* (/ x y) (/ x y)) (* 1.0 1.0))))
98.0ms
(/ (+ x 1.0) (- (* (/ x y) (/ x y)) (* 1.0 1.0)))
120.0ms
(/ (/ x (/ (+ x 1.0) (- (* (/ x y) (/ x y)) (* 1.0 1.0)))) (- (/ x y) 1.0))

simplify2.3s

Counts
755 → 755
Iterations

Useful iterations: done (2.2s)

IterNodesCost
0100629565
1262227946
done500027356

prune2.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ x y) (/ x y))
0.3b
(/ x (/ (+ x 1.0) (- (* (/ x y) (/ x y)) (* 1.0 1.0))))
3.2b
(/ (+ x 1.0) (- (* (/ x y) (/ x y)) (* 1.0 1.0)))
8.0b
(* (/ x (/ (+ x 1.0) (- (* (/ x y) (/ x y)) (* 1.0 1.0)))) (/ 1 (- (/ x y) 1.0)))

rewrite325.0ms

Algorithm
rewrite-expression-head
Rules
336×times-frac
236×*-un-lft-identity
218×add-sqr-sqrt
161×add-cube-cbrt
84×associate-*l*
62×add-exp-log
44×add-cbrt-cube
39×difference-of-squares
37×associate-*r*
33×distribute-lft-out
26×div-exp associate-/r*
20×associate-/r/
17×cbrt-undiv
16×prod-exp
15×div-inv
13×pow1 swap-sqr unswap-sqr
10×cbrt-unprod
9×flip3-- flip--
7×associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rec-exp 1-exp distribute-lft-out--
2×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
1×pow2 flip3-+ pow-plus pow-sqr un-div-inv pow-prod-up flip-+
Counts
4 → 356
Calls
4 calls:
22.0ms
(* (/ x y) (/ x y))
54.0ms
(/ x (/ (+ x 1.0) (- (* (/ x y) (/ x y)) (* 1.0 1.0))))
50.0ms
(/ (+ x 1.0) (- (* (/ x y) (/ x y)) (* 1.0 1.0)))
176.0ms
(* (/ x (/ (+ x 1.0) (- (* (/ x y) (/ x y)) (* 1.0 1.0)))) (/ 1 (- (/ x y) 1.0)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (/ x y) (/ x y))
123.0ms
(/ x (/ (+ x 1.0) (- (* (/ x y) (/ x y)) (* 1.0 1.0))))
109.0ms
(/ (+ x 1.0) (- (* (/ x y) (/ x y)) (* 1.0 1.0)))
102.0ms
(* (/ x (/ (+ x 1.0) (- (* (/ x y) (/ x y)) (* 1.0 1.0)))) (/ 1 (- (/ x y) 1.0)))

simplify925.0ms

Counts
368 → 368
Iterations

Useful iterations: done (912.0ms)

IterNodesCost
05049476
114408843
done50008073

prune901.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes44.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11011
done1011

end0.0ms

sample635.0ms

Algorithm
intervals
Results
451.0ms9147×body80valid