Details

Time bar (total: 5.6s)

sample65.0ms

Algorithm
intervals
Results
33.0ms84×body1280valid
12.0ms49×body640valid
6.0ms23×body2560valid
2.0ms17×body320valid
2.0ms68×body80valid
1.0ms15×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1105

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: 52.0b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.7b
(+ x (sqrt (+ (* x x) 1.0)))
3.5b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.7b
(sqrt (+ (* x x) 1.0))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
14×*-un-lft-identity
6×add-cube-cbrt
5×pow1 sqrt-prod hypot-def add-log-exp
4×add-exp-log log-prod distribute-lft-out
3×expm1-log1p-u fma-def flip3-+ add-cbrt-cube flip-+ log1p-expm1-u
2×log-div sqrt-div
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 swap-sqr rem-log-exp associate-*l* sum-log log-pow *-commutative unswap-sqr
Counts
3 → 58
Calls
3 calls:
10.0ms
(+ x (sqrt (+ (* x x) 1.0)))
10.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
12.0ms
(sqrt (+ (* x x) 1.0))

series281.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(+ x (sqrt (+ (* x x) 1.0)))
180.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
43.0ms
(sqrt (+ (* x x) 1.0))

simplify168.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 3 (155.0ms)

IterNodesCost
0326430
11081394
24805372
35001371

prune157.0ms

Filtered
67 candidates to 57 candidates (85.1%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New63467
Fresh000
Picked101
Done000
Total64468

Merged error: 0.0b

Counts
68 → 4

localize12.0ms

Local error

Found 1 expressions with local error:

0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
100×unpow-prod-down times-frac
92×associate-*r*
85×add-sqr-sqrt
55×*-un-lft-identity
54×add-cube-cbrt
30×sqrt-prod
28×sqr-pow
24×add-exp-log
22×associate-*r/
21×unpow3
13×unswap-sqr
11×associate-/r*
10×prod-exp
9×div-exp associate-/l*
6×pow-to-exp pow-exp add-cbrt-cube
3×pow1 associate-*l*
2×clear-num un-div-inv cbrt-unprod
1×cbrt-undiv expm1-log1p-u frac-2neg pow-prod-down *-commutative log1p-expm1-u div-inv add-log-exp
Counts
1 → 155
Calls
1 calls:
30.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series147.0ms

Counts
1 → 3
Calls
1 calls:
147.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify92.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
0691933
13325867
25002867

prune339.0ms

Filtered
158 candidates to 96 candidates (60.8%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1580158
Fresh033
Picked011
Done000
Total1584162

Merged error: 0.0b

Counts
162 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
0.7b
(+ (hypot x (sqrt 1.0)) x)
3.5b
(log (+ (hypot x (sqrt 1.0)) x))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
5×add-sqr-sqrt add-cube-cbrt add-log-exp
4×pow1 add-exp-log log-prod
3×expm1-log1p-u fma-def add-cbrt-cube log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative hypot-udef rem-log-exp sum-log log-pow
Counts
3 → 44
Calls
3 calls:
1.0ms
(hypot x (sqrt 1.0))
3.0ms
(+ (hypot x (sqrt 1.0)) x)
3.0ms
(log (+ (hypot x (sqrt 1.0)) x))

series544.0ms

Counts
3 → 9
Calls
3 calls:
106.0ms
(hypot x (sqrt 1.0))
142.0ms
(+ (hypot x (sqrt 1.0)) x)
296.0ms
(log (+ (hypot x (sqrt 1.0)) x))

simplify96.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (91.0ms)

IterNodesCost
0266351
1859323
23421307
35002303

prune117.0ms

Filtered
53 candidates to 46 candidates (86.8%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New51253
Fresh202
Picked011
Done011
Total53457

Merged error: 0.0b

Counts
57 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1/8 (pow x 3))
0.4b
(/ (pow 1.0 3) (/ (pow x 5) 1/16))
10.9b
(log (fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16)))))
20.4b
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
413×times-frac
203×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
174×unpow-prod-down
58×sqr-pow
36×add-exp-log associate-/r*
30×unpow3
24×div-exp
18×associate-/l*
13×associate-/r/
11×add-cbrt-cube div-inv
8×pow-to-exp pow-exp
5×pow1
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×log-prod frac-2neg clear-num
1×rem-log-exp log-pow fma-udef
Counts
4 → 347
Calls
4 calls:
5.0ms
(/ 1/8 (pow x 3))
15.0ms
(/ (pow 1.0 3) (/ (pow x 5) 1/16))
1.0ms
(log (fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16)))))
1.0ms
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

series394.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ 1/8 (pow x 3))
89.0ms
(/ (pow 1.0 3) (/ (pow x 5) 1/16))
201.0ms
(log (fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16)))))
68.0ms
(fma (/ 1/8 (pow x 3)) (* 1.0 1.0) (- (* (- 1/2) (/ 1.0 x)) (/ (pow 1.0 3) (/ (pow x 5) 1/16))))

simplify82.0ms

Algorithm
egg-herbie
Counts
359 → 359
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
014753375
150013166

prune884.0ms

Filtered
359 candidates to 212 candidates (59.1%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New3590359
Fresh011
Picked011
Done022
Total3594363

Merged error: 0.0b

Counts
363 → 4

regimes32.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.2b

bsearch104.0ms

Steps
ItersRangePoint
10
1.0482644148039984e-06
3857898261607.3584
0.0009802275948138008
10
-1556119314.230081
-0.05767290693153419
-1.0189304134151242

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04428
14828
25128
35128

end0.0ms

sample1.9s

Algorithm
intervals
Results
948.0ms2277×body1280valid
396.0ms1634×body640valid
203.0ms737×body2560valid
116.0ms812×body320valid
68.0ms2093×body80valid
35.0ms447×body160valid