Details

Time bar (total: 5.4s)

sample67.0ms

Algorithm
intervals
Results
30.0ms72×body1280valid
13.0ms51×body640valid
9.0ms30×body2560valid
4.0ms26×body320valid
2.0ms62×body80valid
1.0ms15×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
095
195

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: 52.8b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.4b
(+ x (sqrt (+ (* x x) 1.0)))
3.5b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.5b
(sqrt (+ (* x x) 1.0))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod
3×flip3-+ sqrt-prod add-cbrt-cube flip-+
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow
Counts
3 → 42
Calls
3 calls:
5.0ms
(+ x (sqrt (+ (* x x) 1.0)))
5.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series276.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(+ x (sqrt (+ (* x x) 1.0)))
173.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
43.0ms
(sqrt (+ (* x x) 1.0))

simplify142.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (137.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune137.0ms

Filtered
51 candidates to 42 candidates (82.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New45651
Fresh000
Picked101
Done000
Total46652

Merged error: 0.1b

Counts
52 → 6

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.2b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
182×add-sqr-sqrt
140×unpow-prod-down cube-prod
118×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×add-exp-log unswap-sqr
10×prod-exp
9×div-exp
7×add-cbrt-cube
6×pow-to-exp pow-exp add-log-exp
4×pow1
3×associate-*r/ associate-*l*
2×diff-log frac-sub cbrt-unprod
1×cbrt-undiv sub-neg flip3-- flip3-+ pow-prod-down associate--l+ sum-log *-commutative flip-- flip-+ div-inv
Counts
2 → 286
Calls
2 calls:
13.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
48.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series289.0ms

Counts
2 → 6
Calls
2 calls:
151.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
138.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify123.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
08542089
146421654
250011654

prune392.0ms

Filtered
292 candidates to 111 candidates (38.0%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2920292
Fresh055
Picked011
Done000
Total2926298

Merged error: 0.1b

Counts
298 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 0.0625) (pow x 5))
0.5b
(/ 0.125 (pow x 3))
9.5b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
20.4b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
110×*-un-lft-identity
102×add-sqr-sqrt
76×add-cube-cbrt
47×unpow-prod-down
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
19×associate-/r*
17×sqr-pow
15×add-exp-log
14×cube-prod distribute-lft-out--
13×associate-/l*
12×log-prod
10×difference-of-squares
9×add-log-exp
8×neg-mul-1 frac-sub add-cbrt-cube
6×div-exp
5×pow1 log-div
4×cube-mult flip3-- unpow3 flip--
3×diff-log associate--r+
2×cbrt-undiv neg-sub0 pow-to-exp sub-neg frac-2neg div-sub pow-exp clear-num div-inv associate--r-
1×distribute-frac-neg rem-log-exp log-pow
Counts
4 → 223
Calls
4 calls:
6.0ms
(/ (- 0.0625) (pow x 5))
5.0ms
(/ 0.125 (pow x 3))
70.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
71.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series325.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ (- 0.0625) (pow x 5))
41.0ms
(/ 0.125 (pow x 3))
181.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
57.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify99.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
08371970
138171891
250021883

prune540.0ms

Filtered
235 candidates to 158 candidates (67.2%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New2350235
Fresh044
Picked011
Done011
Total2356241

Merged error: 0.1b

Counts
241 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (/ 0.5 x))
0.0b
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
0.5b
(/ 0.125 (pow x 3))
8.3b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
43×add-sqr-sqrt
40×times-frac
30×add-cube-cbrt
13×unpow-prod-down cube-prod
12×associate-/r*
11×add-log-exp
10×add-exp-log
6×log-prod add-cbrt-cube distribute-lft-out
5×pow1 difference-of-squares sqr-pow
4×cube-mult unpow3 distribute-lft-out--
3×flip3-+ div-exp flip-+ associate-/l*
2×log-div diff-log sum-log frac-sub
1×cbrt-undiv +-commutative pow-to-exp sub-neg flip3-- frac-2neg rem-log-exp pow-exp associate--l+ clear-num log-pow flip-- div-inv
Counts
4 → 117
Calls
4 calls:
5.0ms
(+ x (/ 0.5 x))
18.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
9.0ms
(/ 0.125 (pow x 3))
19.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series268.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(+ x (/ 0.5 x))
42.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
35.0ms
(/ 0.125 (pow x 3))
153.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify69.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0478849
12195809
25001807

prune199.0ms

Filtered
129 candidates to 77 candidates (59.7%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1290129
Fresh033
Picked011
Done022
Total1296135

Merged error: 0.1b

Counts
135 → 6

regimes123.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.0b

bsearch86.0ms

Steps
ItersRangePoint
10
0.475758948552502
3048118974.682059
0.888138877726932
9
-164485.30314980465
-0.009598081335721272
-1.0094339040681148

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample1.9s

Algorithm
intervals
Results
975.0ms2339×body1280valid
376.0ms1534×body640valid
222.0ms800×body2560valid
112.0ms785×body320valid
74.0ms2143×body80valid
33.0ms399×body160valid