Details

Time bar (total: 38.4s)

sample147.0ms

Algorithm
intervals
Results
89.0ms105×body1280valid
35.0ms91×body640valid
5.0ms26×body320valid
4.0ms256×pre80true
3.0ms27×body160valid
0.0ms7×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0105
1115
2115

prune6.0ms

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: 60.7b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
7.2b
(log (- 1.0 x))
7.3b
(log (+ 1.0 x))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
17×add-sqr-sqrt
16×times-frac
15×pow1 add-cube-cbrt
12×log-pow
9×log-prod
7×add-exp-log
6×log-div
5×add-cbrt-cube
4×associate-/r* associate-/l*
3×add-log-exp
2×flip3-- div-sub rem-log-exp flip--
1×cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
3 → 69
Calls
3 calls:
6.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
3.0ms
(log (- 1.0 x))
3.0ms
(log (+ 1.0 x))

series238.0ms

Counts
3 → 9
Calls
3 calls:
140.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
53.0ms
(log (- 1.0 x))
44.0ms
(log (+ 1.0 x))

simplify48.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0421668
11543624
25002599

prune173.0ms

Filtered
78 candidates to 55 candidates (70.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New70878
Fresh000
Picked011
Done000
Total70979

Merged error: 58.0b

Counts
79 → 9

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
7.2b
(log (- 1.0 x))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
388×add-sqr-sqrt
284×times-frac
212×*-un-lft-identity
114×unpow-prod-down
102×unswap-sqr
91×difference-of-squares
87×add-cube-cbrt
70×unpow2 sqr-pow
68×associate-*r*
58×pow1
57×associate-*r/
55×associate-/r*
53×log-pow
51×distribute-lft-out--
48×associate-*l*
44×associate-/r/
42×frac-sub
40×distribute-lft-out
31×associate-/l*
29×add-exp-log
21×flip3-+ flip-+
10×div-exp prod-exp add-cbrt-cube
7×clear-num
6×pow-to-exp pow-exp un-div-inv
5×log-prod
4×log-div frac-2neg
3×flip3-- flip-- add-log-exp
2×cbrt-undiv div-sub cbrt-unprod div-inv
1×rem-log-exp pow-prod-down *-commutative
Counts
3 → 363
Calls
3 calls:
28.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
74.0ms
(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
3.0ms
(log (- 1.0 x))

series256.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
150.0ms
(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
55.0ms
(log (- 1.0 x))

simplify95.0ms

Algorithm
egg-herbie
Counts
372 → 372
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
016125342
150014993

prune735.0ms

Filtered
372 candidates to 192 candidates (51.6%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New3711372
Fresh347
Picked101
Done011
Total3756381

Merged error: 0.1b

Counts
381 → 6

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite296.0ms

Algorithm
rewrite-expression-head
Rules
1234×*-un-lft-identity
1061×add-sqr-sqrt
834×times-frac
470×distribute-lft-out--
397×associate-*l*
376×distribute-lft-out
302×difference-of-squares
289×unswap-sqr
256×unpow-prod-down
227×pow1
220×log-pow
176×unpow2 sqr-pow
136×associate-*r*
134×add-cube-cbrt
76×associate-*r/
63×associate-/r*
51×add-exp-log
50×associate-/l*
44×associate-/r/
42×frac-sub
21×flip3-+ flip-+
20×prod-exp
19×div-exp
15×add-cbrt-cube
12×pow-to-exp pow-exp
9×clear-num
8×un-div-inv
5×frac-2neg
4×cbrt-unprod
3×cbrt-undiv div-sub div-inv add-log-exp
2×flip3-- pow-prod-down *-commutative flip-- associate-/l/ associate--r+
1×+-commutative
Counts
3 → 800
Calls
3 calls:
24.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
23.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
148.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series243.0ms

Counts
3 → 9
Calls
3 calls:
56.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
57.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
130.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify198.0ms

Algorithm
egg-herbie
Counts
809 → 809
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
0179116888
1500215555

prune1.1s

Filtered
809 candidates to 273 candidates (33.7%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New8081809
Fresh134
Picked011
Done011
Total8096815

Merged error: 0.0b

Counts
815 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(/ (* 1.0 x) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
0.0b
(- (/ (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (/ (* 1.0 x) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
29.7b
(/ (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite12.3s

Algorithm
rewrite-expression-head
Rules
14108×*-un-lft-identity
13878×add-sqr-sqrt
7990×times-frac
6751×distribute-lft-out--
5217×associate-*l*
4434×difference-of-squares
4294×unswap-sqr
3771×associate-/r*
3120×distribute-lft-out
3078×frac-sub
2286×pow1
2280×log-pow
2102×unpow-prod-down
2048×associate-/l*
2010×unpow2 sqr-pow
599×add-cube-cbrt
347×associate-*r*
280×associate-/r/
243×associate-*r/
165×sub-div
159×clear-num
136×flip3-+ flip-+
120×frac-2neg
97×distribute-rgt-out--
94×*-commutative associate-/l/
52×flip3-- flip--
50×un-div-inv
34×add-exp-log
16×add-cbrt-cube
12×div-exp
11×prod-exp
6×pow-to-exp pow-exp add-log-exp
5×div-inv
4×cbrt-undiv
3×cbrt-unprod
2×div-sub
1×associate--l- sub-neg diff-log pow-prod-down
Counts
4 → 5991
Calls
4 calls:
27.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
77.0ms
(/ (* 1.0 x) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
10.7s
(- (/ (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (/ (* 1.0 x) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
127.0ms
(/ (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series847.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
148.0ms
(/ (* 1.0 x) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
265.0ms
(- (/ (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (/ (* 1.0 x) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
383.0ms
(/ (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify2.6s

Algorithm
egg-herbie
Counts
6003 → 6003
Iterations

Useful iterations: 0 (117.0ms)

IterNodesCost
08149270665

prune14.5s

Filtered
6003 candidates to 2614 candidates (43.5%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New600306003
Fresh033
Picked011
Done022
Total600366009

Merged error: 0.0b

Counts
6009 → 6

regimes48.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01926
11926

end0.0ms

sample4.4s

Algorithm
intervals
Results
2.8s3342×body1280valid
1.0s2515×body640valid
247.0ms1262×body320valid
99.0ms8000×pre80true
75.0ms651×body160valid
11.0ms230×body80valid