Details

Time bar (total: 6.0s)

sample60.0ms

Algorithm
intervals
Results
26.0ms61×body1280valid
12.0ms49×body640valid
9.0ms32×body2560valid
3.0ms22×body320valid
2.0ms73×body80valid
1.0ms19×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

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.0b

localize6.0ms

Local error

Found 3 expressions with local error:

1.0b
(+ x (sqrt (+ (* x x) 1.0)))
4.0b
(log (+ x (sqrt (+ (* x x) 1.0))))
17.1b
(sqrt (+ (* x x) 1.0))

rewrite21.0ms

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:
8.0ms
(+ x (sqrt (+ (* x x) 1.0)))
8.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series271.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(+ x (sqrt (+ (* x x) 1.0)))
167.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
46.0ms
(sqrt (+ (* x x) 1.0))

simplify141.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (135.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune153.0ms

Filtered
51 candidates to 42 candidates (82.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

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

rewrite196.0ms

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:
109.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
68.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series294.0ms

Counts
2 → 6
Calls
2 calls:
156.0ms
(- (+ (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)))

simplify112.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08542089
146421654
250011654

prune421.0ms

Filtered
292 candidates to 111 candidates (38.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 0.125 (pow x 3)) (* 2 x))
0.0b
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
0.1b
(/ 0.125 (pow x 3))
10.2b
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
38×times-frac
34×*-un-lft-identity
30×add-cube-cbrt
12×unpow-prod-down cube-prod associate-/r*
11×add-log-exp
10×add-exp-log
6×log-prod add-cbrt-cube
5×pow1 flip3-- flip--
4×cube-mult log-div diff-log unpow3 frac-sub difference-of-squares sqr-pow
3×sub-neg div-exp associate-/l*
2×associate--r+ distribute-lft-out--
1×cbrt-undiv pow-to-exp frac-2neg rem-log-exp pow-exp clear-num log-pow div-inv associate--r-
Counts
4 → 117
Calls
4 calls:
29.0ms
(- (/ 0.125 (pow x 3)) (* 2 x))
54.0ms
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
4.0ms
(/ 0.125 (pow x 3))
50.0ms
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

series331.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(- (/ 0.125 (pow x 3)) (* 2 x))
45.0ms
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
35.0ms
(/ 0.125 (pow x 3))
150.0ms
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

simplify68.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
0484987
12212936
25002934

prune256.0ms

Filtered
129 candidates to 80 candidates (62.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.125 (pow x 3))
0.4b
(/ (- 0.0625) (pow x 5))
13.1b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
16.4b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite360.0ms

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:
4.0ms
(/ 0.125 (pow x 3))
6.0ms
(/ (- 0.0625) (pow x 5))
164.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
176.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series324.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ 0.125 (pow x 3))
54.0ms
(/ (- 0.0625) (pow x 5))
178.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
56.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify100.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
08371970
138171891
250021883

prune590.0ms

Filtered
235 candidates to 158 candidates (67.2%)
Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.1b

regimes143.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.1b

bsearch73.0ms

Steps
ItersRangePoint
8
0.8818080259852756
19555.519105776155
0.8958997819542213
9
-1052513.600169936
-0.041603525395973645
-1.0296783040954165

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127

end0.0ms

sample1.9s

Algorithm
intervals
Results
948.0ms2307×body1280valid
364.0ms1538×body640valid
217.0ms801×body2560valid
114.0ms797×body320valid
78.0ms2130×body80valid
34.0ms427×body160valid