Details

Time bar (total: 3.6s)

sample17.0ms

Algorithm
intervals
Results
5.0ms197×body80valid
2.0ms19×body640valid
2.0ms14×body1280valid
1.0ms18×body320valid
0.0ms8×body160valid

simplify78.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (12.0ms)

IterNodesCost
0165
1355
2765
31375
42854
54594
67194
78484
810644
913974
1021014
1150024

prune6.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 13.8b

Counts
2 → 2

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ y (+ y 1.0))
2.6b
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
12×times-frac
11×add-sqr-sqrt add-cube-cbrt
4×add-exp-log associate-/r* add-cbrt-cube distribute-lft-out
3×associate-/l*
2×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
1×cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ fma-udef div-inv
Counts
2 → 45
Calls
2 calls:
5.0ms
(/ y (+ y 1.0))
1.0ms
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series92.0ms

Counts
2 → 6
Calls
2 calls:
34.0ms
(/ y (+ y 1.0))
57.0ms
(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify110.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (104.0ms)

IterNodesCost
0203263
1708238
23148232
35002228

prune126.0ms

Filtered
51 candidates to 40 candidates (78.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New43851
Fresh011
Picked101
Done000
Total44953

Merged error: 7.0b

Counts
53 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ y 1.0))
0.3b
(cbrt (+ y 1.0))
0.3b
(cbrt (+ y 1.0))
9.1b
(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 flip-+ distribute-lft-out
1×fma-udef
Counts
4 → 58
Calls
4 calls:
7.0ms
(cbrt (+ y 1.0))
3.0ms
(cbrt (+ y 1.0))
3.0ms
(cbrt (+ y 1.0))
1.0ms
(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

series344.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(cbrt (+ y 1.0))
94.0ms
(cbrt (+ y 1.0))
98.0ms
(cbrt (+ y 1.0))
55.0ms
(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify74.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (65.0ms)

IterNodesCost
0230552
1657500
22252479
35001448

prune241.0ms

Filtered
70 candidates to 62 candidates (88.6%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New66470
Fresh178
Picked101
Done000
Total681179

Merged error: 7.0b

Counts
79 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ y 1.0))
0.3b
(cbrt (+ y 1.0))
0.3b
(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
9.1b
(fma (/ (/ y (* (cbrt (+ y 1.0)) (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-div
10×*-un-lft-identity
9×cbrt-prod
8×flip3-+ flip-+
6×add-sqr-sqrt add-cube-cbrt
4×pow1 add-exp-log expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
2×associate-*r/ associate-*l/ distribute-lft-out
1×fma-udef
Counts
4 → 61
Calls
4 calls:
3.0ms
(cbrt (+ y 1.0))
3.0ms
(cbrt (+ y 1.0))
8.0ms
(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
1.0ms
(fma (/ (/ y (* (cbrt (+ y 1.0)) (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

series368.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(cbrt (+ y 1.0))
96.0ms
(cbrt (+ y 1.0))
114.0ms
(cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))
61.0ms
(fma (/ (/ y (* (cbrt (+ y 1.0)) (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify104.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (95.0ms)

IterNodesCost
0363792
11019722
23582706
35001684

prune307.0ms

Filtered
73 candidates to 63 candidates (86.3%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New71273
Fresh01010
Picked101
Done000
Total721284

Merged error: 7.0b

Counts
84 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y)
0.6b
(cbrt y)
0.6b
(cbrt y)
9.4b
(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt y)
1.0ms
(cbrt y)
1.0ms
(cbrt y)
1.0ms
(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

series658.0ms

Counts
4 → 12
Calls
4 calls:
195.0ms
(cbrt y)
197.0ms
(cbrt y)
189.0ms
(cbrt y)
76.0ms
(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

simplify52.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (47.0ms)

IterNodesCost
0104277
1282243
21092232
35002228

prune159.0ms

Filtered
61 candidates to 53 candidates (86.9%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New59261
Fresh01111
Picked101
Done000
Total601373

Merged error: 7.0b

Counts
73 → 13

regimes294.0ms

Accuracy

95.9% (0.3b remaining)

Error of 7.8b against oracle of 7.4b and baseline of 15.4b

bsearch53.0ms

Steps
ItersRangePoint
6
3.3213059015388503e+18
1.620189034366253e+19
3.446482136760823e+18
5
-1.515253396550884e+39
-7.325238854406104e+38
-7.43549940857434e+38

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0239
1239

end0.0ms

sample443.0ms

Algorithm
intervals
Results
159.0ms6052×body80valid
65.0ms745×body640valid
39.0ms356×body1280valid
36.0ms546×body320valid
14.0ms301×body160valid