Details

Time bar (total: 3.2s)

sample20.0ms

Algorithm
intervals
Results
5.0ms199×body80valid
4.0ms17×body640valid
1.0ms16×body320valid
1.0ms9×body1280valid
1.0ms15×body160valid

simplify73.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0165
1355
2745
31285
42525
53745
65145
76425
87775
910105
1016865
1150015

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
3.8b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
10.1b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
13×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
7×add-cube-cbrt
5×pow1 associate-*l* add-log-exp
4×times-frac associate-*l/ associate-/r*
3×flip3-- associate-*r* flip--
2×cbrt-undiv div-exp prod-exp associate-/r/ cbrt-unprod associate-/l/ distribute-lft-out distribute-lft-out-- difference-of-squares
1×sub-neg frac-2neg flip3-+ diff-log pow-prod-down clear-num *-commutative flip-+ div-inv associate-/l* unswap-sqr
Counts
3 → 63
Calls
3 calls:
10.0ms
(* (- 1.0 x) y)
9.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series145.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(* (- 1.0 x) y)
65.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
47.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify43.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0338401
11456359
25001359

prune145.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ y (+ y 1.0))
0.0b
(* (- 1.0 x) (/ y (+ y 1.0)))
3.8b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
28×add-sqr-sqrt
25×times-frac
21×add-cube-cbrt
18×associate-*r*
10×add-exp-log add-cbrt-cube
7×distribute-lft-out
5×pow1 associate-*l* add-log-exp
4×associate-/r* associate-/r/
3×flip3-- flip-- associate-/l*
2×cbrt-undiv frac-times flip3-+ div-exp associate-*l/ prod-exp cbrt-unprod flip-+ div-inv unswap-sqr
1×sub-neg frac-2neg diff-log associate-*r/ pow-prod-down clear-num *-commutative distribute-lft-out-- difference-of-squares
Counts
3 → 88
Calls
3 calls:
9.0ms
(/ y (+ y 1.0))
37.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
2.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series191.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(/ y (+ y 1.0))
52.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
102.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify48.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0400572
11790526
25002526

prune178.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))
3.8b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
3.8b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
3.8b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log flip3-- add-cbrt-cube flip--
3×cbrt-prod sub-neg diff-log
2×cbrt-div
1×pow1/3
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))
2.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
2.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
2.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series409.0ms

Counts
4 → 12
Calls
4 calls:
204.0ms
(cbrt (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))))
77.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
67.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
61.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify91.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (79.0ms)

IterNodesCost
0228589
1680534
23306518
35001517

prune184.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 1.0 x) (sqrt (+ y 1.0)))
0.1b
(* (/ (- 1.0 x) (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0))))
0.1b
(/ y (sqrt (+ y 1.0)))
3.4b
(- 1.0 (* (/ (- 1.0 x) (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0)))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
138×*-un-lft-identity
132×add-sqr-sqrt
124×times-frac
78×sqrt-prod
72×add-cube-cbrt
41×associate-*l*
27×associate-*r*
20×add-exp-log add-cbrt-cube
18×distribute-lft-out
15×distribute-lft-out-- difference-of-squares
14×associate-/r*
9×unswap-sqr
8×sqrt-div associate-/r/ associate-/l*
6×pow1 cbrt-undiv div-exp add-log-exp
4×flip3-+ prod-exp cbrt-unprod flip-+ div-inv
2×flip3-- frac-2neg clear-num flip-- associate-/l/
1×frac-times sub-neg diff-log div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 218
Calls
4 calls:
11.0ms
(/ (- 1.0 x) (sqrt (+ y 1.0)))
55.0ms
(* (/ (- 1.0 x) (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0))))
6.0ms
(/ y (sqrt (+ y 1.0)))
2.0ms
(- 1.0 (* (/ (- 1.0 x) (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0)))))

series286.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(/ (- 1.0 x) (sqrt (+ y 1.0)))
46.0ms
(* (/ (- 1.0 x) (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0))))
109.0ms
(/ y (sqrt (+ y 1.0)))
68.0ms
(- 1.0 (* (/ (- 1.0 x) (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0)))))

simplify90.0ms

Algorithm
egg-herbie
Counts
230 → 230
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
07902194
130802034
250011931

prune445.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes81.0ms

Accuracy

100% (0.0b remaining)

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

bsearch82.0ms

Steps
ItersRangePoint
11
9.428505616792786e-16
4321407464.299789
185860506.9986492
8
-578421416.8415484
-838166.7342155329
-261468683.324989

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02910
12910

end0.0ms

sample439.0ms

Algorithm
intervals
Results
151.0ms6092×body80valid
72.0ms748×body640valid
37.0ms333×body1280valid
36.0ms539×body320valid
13.0ms288×body160valid