Details

Time bar (total: 2.5s)

sample18.0ms

Algorithm
intervals
Results
5.0ms196×body80valid
2.0ms19×body640valid
2.0ms13×body1280valid
1.0ms18×body320valid
0.0ms10×body160valid

simplify62.0ms

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)
3.3b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
8.3b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite23.0ms

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:
6.0ms
(* (- 1.0 x) y)
7.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

series142.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(* (- 1.0 x) y)
68.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
46.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify44.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0338401
11456359
25001359

prune143.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ y (+ y 1.0))
0.0b
(* (- 1.0 x) (/ y (+ y 1.0)))
3.3b
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite22.0ms

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:
5.0ms
(/ y (+ y 1.0))
11.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
3.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series143.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(/ y (+ y 1.0))
41.0ms
(* (- 1.0 x) (/ y (+ y 1.0)))
66.0ms
(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify52.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0400572
11790526
25002526

prune171.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1 (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0))))
0.1b
(/ 1 (sqrt (+ y 1.0)))
0.1b
(/ y (sqrt (+ y 1.0)))
4.3b
(- 1.0 (* (- 1.0 x) (* (/ 1 (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0))))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
110×add-sqr-sqrt
106×times-frac
98×*-un-lft-identity
67×sqrt-prod
64×add-cube-cbrt
32×add-exp-log
27×associate-*r* associate-*l*
20×add-cbrt-cube
15×unswap-sqr
14×associate-/r* distribute-lft-out
11×div-exp
8×pow1 sqrt-div prod-exp associate-/r/
6×cbrt-undiv associate-/l* add-log-exp
4×flip3-+ cbrt-unprod flip-+ div-inv
3×rec-exp pow-flip 1-exp
2×frac-2neg clear-num
1×frac-times sub-neg flip3-- sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ *-commutative flip-- inv-pow
Counts
4 → 201
Calls
4 calls:
25.0ms
(* (/ 1 (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0))))
6.0ms
(/ 1 (sqrt (+ y 1.0)))
6.0ms
(/ y (sqrt (+ y 1.0)))
3.0ms
(- 1.0 (* (- 1.0 x) (* (/ 1 (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0))))))

series270.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (/ 1 (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0))))
53.0ms
(/ 1 (sqrt (+ y 1.0)))
111.0ms
(/ y (sqrt (+ y 1.0)))
68.0ms
(- 1.0 (* (- 1.0 x) (* (/ 1 (sqrt (+ y 1.0))) (/ y (sqrt (+ y 1.0))))))

simplify93.0ms

Algorithm
egg-herbie
Counts
213 → 213
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
07151890
135021632
250021493

prune357.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

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))

rewrite29.0ms

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:
15.0ms
(+ (* 1.0 (- (/ 1 y) (/ x y))) x)
12.0ms
(- (/ 1 y) (/ x y))

series49.0ms

Counts
2 → 6
Calls
2 calls:
30.0ms
(+ (* 1.0 (- (/ 1 y) (/ x y))) x)
19.0ms
(- (/ 1 y) (/ x y))

simplify71.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0224317
1627291
22889282
35001274

prune74.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

regimes91.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 14.5b

bsearch89.0ms

Steps
ItersRangePoint
10
0.10207175935539815
56238210404238.2
175576689.4578166
11
-358284796.04772377
-9.565599748882727e-17
-0.9909406107563364

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03315
13315

end0.0ms

sample456.0ms

Algorithm
intervals
Results
153.0ms6075×body80valid
70.0ms731×body640valid
45.0ms531×body320valid
42.0ms370×body1280valid
14.0ms293×body160valid