Details

Time bar (total: 12.7s)

sample94.0ms

Algorithm
intervals
Results
49.0ms109×body1280valid
20.0ms82×body640valid
6.0ms227×body80nan
5.0ms37×body320valid
1.0ms15×body160valid
0.0ms13×body80valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0186
1256
2406
3616
4886
51046
61136
71136

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: 57.2b

Counts
2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ 1.0 x) (- 1.0 x))
5.0b
(log (/ (+ 1.0 x) (- 1.0 x)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
63×*-un-lft-identity
41×add-sqr-sqrt
40×times-frac
26×log-prod
23×add-cube-cbrt
11×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
7×add-exp-log
5×associate-/r*
4×associate-/r/ add-cbrt-cube associate-/l*
3×pow1
2×flip3-- div-exp rem-log-exp flip-- div-inv associate-/l/ add-log-exp
1×cbrt-undiv log-div frac-2neg flip3-+ clear-num log-pow flip-+
Counts
2 → 82
Calls
2 calls:
7.0ms
(/ (+ 1.0 x) (- 1.0 x))
7.0ms
(log (/ (+ 1.0 x) (- 1.0 x)))

series157.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(/ (+ 1.0 x) (- 1.0 x))
120.0ms
(log (/ (+ 1.0 x) (- 1.0 x)))

simplify120.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0318660
11025624
24261602
35001602

prune171.0ms

Filtered
88 candidates to 58 candidates (65.9%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New81788
Fresh000
Picked011
Done000
Total81889

Merged error: 0.1b

Counts
89 → 8

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow x 2) x)
0.0b
(+ (* 2.0 (+ (pow x 2) x)) (- (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))))
0.0b
(* 2.0 (/ (pow x 2) (pow 1.0 2)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
80×times-frac
72×add-sqr-sqrt
68×associate-*r*
56×unpow-prod-down
41×*-un-lft-identity
38×add-cube-cbrt
26×add-exp-log unpow2
24×sqr-pow
17×unswap-sqr
10×prod-exp
9×div-exp add-log-exp
8×add-cbrt-cube
6×pow-to-exp pow-exp
5×pow1 associate-+r+ associate-*r/
4×flip3-+ frac-add flip-+
3×log-prod associate-*l* associate--l+ sum-log
2×+-commutative associate-+l+ flip3-- flip-- cbrt-unprod
1×cbrt-undiv distribute-rgt-in associate-+r- sub-neg distribute-rgt-out distribute-lft-in distribute-lft1-in diff-log pow-prod-down *-commutative div-inv distribute-lft-out
Counts
3 → 148
Calls
3 calls:
5.0ms
(+ (pow x 2) x)
11.0ms
(+ (* 2.0 (+ (pow x 2) x)) (- (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))))
20.0ms
(* 2.0 (/ (pow x 2) (pow 1.0 2)))

series398.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(+ (pow x 2) x)
304.0ms
(+ (* 2.0 (+ (pow x 2) x)) (- (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))))
56.0ms
(* 2.0 (/ (pow x 2) (pow 1.0 2)))

simplify103.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
08241158
137491024
250011020

prune359.0ms

Filtered
157 candidates to 102 candidates (65.0%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1561157
Fresh066
Picked011
Done011
Total1569165

Merged error: 0.1b

Counts
165 → 9

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) (- (+ (pow x 4) (pow x 2)) (pow x 3)))
0.2b
(* (* 2.0 (/ (pow x 2) (pow 1.0 2))) (* 2.0 (/ (pow x 2) (pow 1.0 2))))
0.2b
(* (pow x 2) (pow x 2))
50.4b
(/ (+ (* (* 2.0 (+ (pow (pow x 2) 3) (pow x 3))) (+ (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2))))) (* (+ (* (pow x 2) (pow x 2)) (- (* x x) (* (pow x 2) x))) (- (* (log 1.0) (log 1.0)) (* (* 2.0 (/ (pow x 2) (pow 1.0 2))) (* 2.0 (/ (pow x 2) (pow 1.0 2))))))) (* (+ (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) (- (+ (pow x 4) (pow x 2)) (pow x 3))))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
551×add-exp-log
352×prod-exp
200×div-exp
138×pow-to-exp pow-exp
89×associate-*r/
79×flip3-+ flip-+
73×frac-times
66×associate-/l/
64×frac-add
49×add-cbrt-cube
45×pow1
41×add-sqr-sqrt
37×associate-*l/
30×flip3-- flip--
24×cbrt-unprod
21×unpow-prod-down *-un-lft-identity
19×pow-prod-down
18×associate-*r*
17×unswap-sqr
16×add-cube-cbrt
13×sqr-pow
12×associate-*l* unpow2
9×swap-sqr
8×cbrt-undiv associate-/r/
5×pow-sqr pow-prod-up
4×add-log-exp difference-of-squares
3×distribute-rgt-in distribute-lft-in times-frac *-commutative associate-/l*
2×pow2 sub-neg pow-plus associate--l+ distribute-lft-out--
1×frac-2neg cube-prod clear-num associate-/r* div-inv distribute-lft-out
Counts
4 → 354
Calls
4 calls:
23.0ms
(* (+ (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) (- (+ (pow x 4) (pow x 2)) (pow x 3)))
24.0ms
(* (* 2.0 (/ (pow x 2) (pow 1.0 2))) (* 2.0 (/ (pow x 2) (pow 1.0 2))))
8.0ms
(* (pow x 2) (pow x 2))
56.0ms
(/ (+ (* (* 2.0 (+ (pow (pow x 2) 3) (pow x 3))) (+ (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2))))) (* (+ (* (pow x 2) (pow x 2)) (- (* x x) (* (pow x 2) x))) (- (* (log 1.0) (log 1.0)) (* (* 2.0 (/ (pow x 2) (pow 1.0 2))) (* 2.0 (/ (pow x 2) (pow 1.0 2))))))) (* (+ (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) (- (+ (pow x 4) (pow x 2)) (pow x 3))))

series1.9s

Counts
4 → 12
Calls
4 calls:
74.0ms
(* (+ (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) (- (+ (pow x 4) (pow x 2)) (pow x 3)))
80.0ms
(* (* 2.0 (/ (pow x 2) (pow 1.0 2))) (* 2.0 (/ (pow x 2) (pow 1.0 2))))
31.0ms
(* (pow x 2) (pow x 2))
1.7s
(/ (+ (* (* 2.0 (+ (pow (pow x 2) 3) (pow x 3))) (+ (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2))))) (* (+ (* (pow x 2) (pow x 2)) (- (* x x) (* (pow x 2) x))) (- (* (log 1.0) (log 1.0)) (* (* 2.0 (/ (pow x 2) (pow 1.0 2))) (* 2.0 (/ (pow x 2) (pow 1.0 2))))))) (* (+ (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) (- (+ (pow x 4) (pow x 2)) (pow x 3))))

simplify117.0ms

Algorithm
egg-herbie
Counts
366 → 366
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
017357276
150026819

prune1.6s

Filtered
366 candidates to 162 candidates (44.3%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New3651366
Fresh066
Picked011
Done022
Total36510375

Merged error: 0.1b

Counts
375 → 10

localize38.0ms

Local error

Found 4 expressions with local error:

29.8b
(cbrt (- (+ (pow x 4) (pow x 2)) (pow x 3)))
29.8b
(cbrt (- (+ (pow x 4) (pow x 2)) (pow x 3)))
29.8b
(cbrt (- (+ (pow x 4) (pow x 2)) (pow x 3)))
50.4b
(/ (+ (* (* 2.0 (+ (pow (pow x 2) 3) (pow x 3))) (+ (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2))))) (* (+ (* (pow x 2) (pow x 2)) (- (* x x) (* (pow x 2) x))) (- (* (log 1.0) (log 1.0)) (* (* 2.0 (/ (pow x 2) (pow 1.0 2))) (* 2.0 (/ (pow x 2) (pow 1.0 2))))))) (* (* (+ (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) (* (cbrt (- (+ (pow x 4) (pow x 2)) (pow x 3))) (cbrt (- (+ (pow x 4) (pow x 2)) (pow x 3))))) (cbrt (- (+ (pow x 4) (pow x 2)) (pow x 3)))))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
200×frac-times
168×cbrt-div
124×associate-*r/
108×flip3-- flip--
100×flip3-+ flip-+
82×associate-*l/
80×associate-/r/
66×associate-/l/
64×frac-add
30×add-sqr-sqrt
27×cbrt-prod
24×*-un-lft-identity
18×add-exp-log
13×add-cbrt-cube
12×difference-of-squares
9×add-cube-cbrt
6×prod-exp cbrt-unprod distribute-lft-out--
4×pow1 cbrt-undiv div-exp add-log-exp
3×unpow-prod-down times-frac pow1/3 cube-prod distribute-lft-out associate-/l* sqr-pow
1×frac-2neg clear-num associate-/r* div-inv
Counts
4 → 228
Calls
4 calls:
13.0ms
(cbrt (- (+ (pow x 4) (pow x 2)) (pow x 3)))
13.0ms
(cbrt (- (+ (pow x 4) (pow x 2)) (pow x 3)))
18.0ms
(cbrt (- (+ (pow x 4) (pow x 2)) (pow x 3)))
93.0ms
(/ (+ (* (* 2.0 (+ (pow (pow x 2) 3) (pow x 3))) (+ (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2))))) (* (+ (* (pow x 2) (pow x 2)) (- (* x x) (* (pow x 2) x))) (- (* (log 1.0) (log 1.0)) (* (* 2.0 (/ (pow x 2) (pow 1.0 2))) (* 2.0 (/ (pow x 2) (pow 1.0 2))))))) (* (* (+ (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) (* (cbrt (- (+ (pow x 4) (pow x 2)) (pow x 3))) (cbrt (- (+ (pow x 4) (pow x 2)) (pow x 3))))) (cbrt (- (+ (pow x 4) (pow x 2)) (pow x 3)))))

series1.7s

Counts
4 → 12
Calls
4 calls:
55.0ms
(cbrt (- (+ (pow x 4) (pow x 2)) (pow x 3)))
48.0ms
(cbrt (- (+ (pow x 4) (pow x 2)) (pow x 3)))
55.0ms
(cbrt (- (+ (pow x 4) (pow x 2)) (pow x 3)))
1.6s
(/ (+ (* (* 2.0 (+ (pow (pow x 2) 3) (pow x 3))) (+ (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2))))) (* (+ (* (pow x 2) (pow x 2)) (- (* x x) (* (pow x 2) x))) (- (* (log 1.0) (log 1.0)) (* (* 2.0 (/ (pow x 2) (pow 1.0 2))) (* 2.0 (/ (pow x 2) (pow 1.0 2))))))) (* (* (+ (log 1.0) (* 2.0 (/ (pow x 2) (pow 1.0 2)))) (* (cbrt (- (+ (pow x 4) (pow x 2)) (pow x 3))) (cbrt (- (+ (pow x 4) (pow x 2)) (pow x 3))))) (cbrt (- (+ (pow x 4) (pow x 2)) (pow x 3)))))

simplify155.0ms

Algorithm
egg-herbie
Counts
240 → 240
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0188013353
1500212978

prune2.3s

Filtered
240 candidates to 206 candidates (85.8%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New2382240
Fresh066
Picked101
Done033
Total23911250

Merged error: 0.1b

Counts
250 → 11

regimes242.0ms

Accuracy

0% (0.5b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02012
12012

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.5s3414×body1280valid
603.0ms2488×body640valid
213.0ms7846×body80nan
183.0ms1249×body320valid
57.0ms639×body160valid
8.0ms210×body80valid