Details

Time bar (total: 3.2s)

sample28.0ms

Algorithm
intervals
Results
10.0ms203×body80valid
4.0ms23×body640valid
3.0ms13×body1280valid
1.0ms10×body320valid
1.0ms7×body160valid

simplify70.0ms

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: 22.9b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
1.5b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.6b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite35.0ms

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)
13.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
10.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series146.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(* (- 1.0 x) y)
71.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
45.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify47.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0338401
11456359
25001359

prune149.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
1.5b
(- 1.0 (/ (* 1 (* (- 1.0 x) y)) (+ y 1.0)))
9.6b
(/ (* 1 (* (- 1.0 x) y)) (+ y 1.0))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
15×*-un-lft-identity
14×add-cbrt-cube
13×add-sqr-sqrt
7×add-cube-cbrt prod-exp
5×pow1 div-exp associate-*l* add-log-exp
4×times-frac associate-*l/ associate-/r* cbrt-unprod
3×cbrt-undiv flip3-- associate-*r* flip--
2×1-exp associate-*r/ associate-/r/ 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 → 67
Calls
3 calls:
10.0ms
(* (- 1.0 x) y)
12.0ms
(- 1.0 (/ (* 1 (* (- 1.0 x) y)) (+ y 1.0)))
17.0ms
(/ (* 1 (* (- 1.0 x) y)) (+ y 1.0))

series142.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(* (- 1.0 x) y)
69.0ms
(- 1.0 (/ (* 1 (* (- 1.0 x) y)) (+ y 1.0)))
43.0ms
(/ (* 1 (* (- 1.0 x) y)) (+ y 1.0))

simplify55.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0398473
11831410
25001407

prune142.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

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)))
4.3b
(- 1.0 (* (/ (- 1.0 x) (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0)))))

rewrite91.0ms

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:
12.0ms
(/ (- 1.0 x) (sqrt (+ y 1.0)))
59.0ms
(* (/ (- 1.0 x) (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0))))
7.0ms
(/ y (sqrt (+ y 1.0)))
2.0ms
(- 1.0 (* (/ (- 1.0 x) (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0)))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ (- 1.0 x) (sqrt (+ y 1.0)))
44.0ms
(* (/ (- 1.0 x) (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0))))
115.0ms
(/ y (sqrt (+ y 1.0)))
71.0ms
(- 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 (68.0ms)

IterNodesCost
07902194
130802034
250011931

prune461.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
18×*-un-lft-identity
14×times-frac
6×add-log-exp difference-of-squares
5×div-inv distribute-lft-out--
4×add-cube-cbrt associate-+l+
3×sub-neg distribute-rgt-out--
2×pow1 add-exp-log distribute-rgt-in distribute-lft-in add-cbrt-cube
1×+-commutative flip3-- flip3-+ diff-log sum-log frac-sub flip-- flip-+ sub-div
Counts
2 → 43
Calls
2 calls:
21.0ms
(+ (* 1.0 (- (/ 1 y) (/ x y))) x)
18.0ms
(- (/ 1 y) (/ x y))

series50.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(+ (* 1.0 (- (/ 1 y) (/ x y))) x)
21.0ms
(- (/ 1 y) (/ x y))

simplify82.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 3 (77.0ms)

IterNodesCost
0224317
1627291
22889282
35001274

prune85.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.2b

regimes198.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 22.3b

bsearch88.0ms

Steps
ItersRangePoint
9
137964.03928948785
661184882896.0549
154919718.94598407
8
-591661204.423747
-45386.90934105675
-146664422.27513087

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03111
13311
23311

end0.0ms

sample794.0ms

Algorithm
intervals
Results
315.0ms6126×body80valid
136.0ms703×body640valid
89.0ms372×body1280valid
79.0ms541×body320valid
28.0ms258×body160valid