Details

Time bar (total: 4.1s)

sample20.0ms

Algorithm
intervals
Results
7.0ms198×body80valid
2.0ms27×body640valid
1.0ms17×body320valid
1.0ms8×body1280valid
0.0ms6×body160valid

simplify68.0ms

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

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 22.5b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (- 1.0 x) y)
2.2b
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
8.3b
(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite24.0ms

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:
32.0ms
(* (- 1.0 x) y)
67.0ms
(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
42.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))

simplify44.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0338401
11456359
25001359

prune132.0ms

Filtered
72 candidates to 51 candidates (70.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New67572
Fresh000
Picked101
Done000
Total68573

Merged error: 0.2b

Counts
73 → 5

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (+ y 1.0) y)
0.3b
(/ (- 1.0 x) (/ (+ y 1.0) y))
2.2b
(- 1.0 (/ (- 1.0 x) (/ (+ y 1.0) y)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
167×times-frac
157×*-un-lft-identity
120×add-sqr-sqrt
77×add-cube-cbrt
22×distribute-lft-out
20×difference-of-squares
19×associate-/r*
18×distribute-lft-out--
10×add-exp-log add-cbrt-cube
9×associate-/l*
8×div-inv
5×add-log-exp
4×cbrt-undiv div-exp associate-/l/
3×pow1
2×flip3-- frac-2neg div-sub clear-num flip--
1×sub-neg flip3-+ diff-log associate-/r/ flip-+ associate--r-
Counts
3 → 169
Calls
3 calls:
6.0ms
(/ (+ y 1.0) y)
22.0ms
(/ (- 1.0 x) (/ (+ y 1.0) y))
35.0ms
(- 1.0 (/ (- 1.0 x) (/ (+ y 1.0) y)))

series156.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(/ (+ y 1.0) y)
40.0ms
(/ (- 1.0 x) (/ (+ y 1.0) y))
67.0ms
(- 1.0 (/ (- 1.0 x) (/ (+ y 1.0) y)))

simplify72.0ms

Algorithm
egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 1 (16.0ms)

IterNodesCost
06891514
126461460
250021460

prune252.0ms

Filtered
178 candidates to 117 candidates (65.7%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1780178
Fresh044
Picked011
Done000
Total1785183

Merged error: 0.2b

Counts
183 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 x) y)
2.1b
(/ (/ (* (- 1.0 x) y) (sqrt (+ y 1.0))) (sqrt (+ y 1.0)))
2.4b
(/ (* (- 1.0 x) y) (sqrt (+ y 1.0)))
3.9b
(- 1.0 (/ (/ (* (- 1.0 x) y) (sqrt (+ y 1.0))) (sqrt (+ y 1.0))))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
114×*-un-lft-identity
97×sqrt-prod
74×add-sqr-sqrt
62×add-cube-cbrt
24×distribute-lft-out
20×add-exp-log sqrt-div associate-/r/ add-cbrt-cube
14×associate-/r* associate-/l*
10×flip3-+ flip-+ div-inv
7×cbrt-undiv div-exp
6×pow1 add-log-exp
5×associate-*l*
4×associate-*l/ difference-of-squares
3×flip3-- associate-*r* prod-exp flip-- cbrt-unprod associate-/l/
2×frac-2neg clear-num distribute-lft-out--
1×sub-neg diff-log pow-prod-down *-commutative unswap-sqr
Counts
4 → 201
Calls
4 calls:
7.0ms
(* (- 1.0 x) y)
20.0ms
(/ (/ (* (- 1.0 x) y) (sqrt (+ y 1.0))) (sqrt (+ y 1.0)))
10.0ms
(/ (* (- 1.0 x) y) (sqrt (+ y 1.0)))
30.0ms
(- 1.0 (/ (/ (* (- 1.0 x) y) (sqrt (+ y 1.0))) (sqrt (+ y 1.0))))

series272.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (- 1.0 x) y)
51.0ms
(/ (/ (* (- 1.0 x) y) (sqrt (+ y 1.0))) (sqrt (+ y 1.0)))
105.0ms
(/ (* (- 1.0 x) y) (sqrt (+ y 1.0)))
70.0ms
(- 1.0 (/ (/ (* (- 1.0 x) y) (sqrt (+ y 1.0))) (sqrt (+ y 1.0))))

simplify101.0ms

Algorithm
egg-herbie
Counts
213 → 213
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
07152414
132772119
250032107

prune292.0ms

Filtered
213 candidates to 114 candidates (53.5%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New2130213
Fresh033
Picked011
Done011
Total2135218

Merged error: 0.2b

Counts
218 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

8.3b
(/ (* (- 1.0 x) y) (+ y 1.0))
8.3b
(/ (* (- 1.0 x) y) (+ y 1.0))
8.3b
(/ (* (- 1.0 x) y) (+ y 1.0))
14.3b
(/ (- (pow 1.0 3) (pow (/ (* (- 1.0 x) y) (+ y 1.0)) 3)) (+ (* (/ (* (- 1.0 x) y) (+ y 1.0)) (+ (/ (* (- 1.0 x) y) (+ y 1.0)) 1.0)) (* 1.0 1.0)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
136×add-sqr-sqrt
92×*-un-lft-identity
87×times-frac
64×difference-of-squares
48×unpow-prod-down cube-prod
40×add-cube-cbrt
32×sqr-pow
28×associate-/l*
21×add-exp-log add-cbrt-cube
20×distribute-lft-out--
15×associate-/r*
8×associate-/r/ associate-/l/
7×cbrt-undiv div-exp
6×associate-*l/ distribute-lft-out
4×pow1 difference-cubes flip3-- frac-2neg flip3-+ clear-num flip-- flip-+ div-inv add-log-exp
3×prod-exp cbrt-unprod
1×div-sub
Counts
4 → 201
Calls
4 calls:
12.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
9.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
9.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
43.0ms
(/ (- (pow 1.0 3) (pow (/ (* (- 1.0 x) y) (+ y 1.0)) 3)) (+ (* (/ (* (- 1.0 x) y) (+ y 1.0)) (+ (/ (* (- 1.0 x) y) (+ y 1.0)) 1.0)) (* 1.0 1.0)))

series941.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
227.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
51.0ms
(/ (* (- 1.0 x) y) (+ y 1.0))
620.0ms
(/ (- (pow 1.0 3) (pow (/ (* (- 1.0 x) y) (+ y 1.0)) 3)) (+ (* (/ (* (- 1.0 x) y) (+ y 1.0)) (+ (/ (* (- 1.0 x) y) (+ y 1.0)) 1.0)) (* 1.0 1.0)))

simplify123.0ms

Algorithm
egg-herbie
Counts
213 → 213
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
06604788
129544635
250024633

prune515.0ms

Filtered
213 candidates to 135 candidates (63.4%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New2112213
Fresh112
Picked101
Done022
Total2135218

Merged error: 0.2b

Counts
218 → 5

regimes138.0ms

Accuracy

99.7% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 13.9b

bsearch78.0ms

Steps
ItersRangePoint
11
164.2181510969774
7.805281752399305e+28
292785290.87269586
8
-20251402574.662838
-71914824.75180596
-215760841.30783328

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02810
12810

end0.0ms

sample436.0ms

Algorithm
intervals
Results
153.0ms6154×body80valid
62.0ms709×body640valid
44.0ms357×body1280valid
33.0ms504×body320valid
12.0ms276×body160valid