Details

Time bar (total: 8.4s)

sample143.0ms

Algorithm
intervals
Results
87.0ms103×body1280valid
32.0ms80×body640valid
6.0ms35×body320valid
3.0ms31×body160valid
3.0ms256×pre80true
0.0ms7×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115
done115

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
8.4b
(log (+ 1.0 x))
8.4b
(log (- 1.0 x))

rewrite29.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 75
Calls
3 calls:
16.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
4.0ms
(log (+ 1.0 x))
6.0ms
(log (- 1.0 x))

series205.0ms

Counts
3 → 9
Calls
3 calls:
120.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
40.0ms
(log (+ 1.0 x))
45.0ms
(log (- 1.0 x))

simplify44.0ms

Counts
84 → 84
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0452686
11669638
25001623
done5001623

prune219.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 57.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (log (- (pow 1.0 3) (pow x 3))) (log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))) (log (+ 1.0 x)))
2.2b
(log (- (pow 1.0 3) (pow x 3)))
8.4b
(log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
8.4b
(log (+ 1.0 x))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
53×*-un-lft-identity
36×pow1
32×log-prod times-frac log-pow
25×distribute-lft-out--
21×add-cube-cbrt difference-of-squares
12×unpow-prod-down cube-prod
9×add-exp-log
8×associate-/l* sqr-pow
6×log-div add-cbrt-cube
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
3×rem-log-exp
2×flip3-- flip3-+ flip-- flip-+ associate-/l/
1×difference-cubes cbrt-undiv frac-2neg div-sub div-exp clear-num div-inv distribute-lft-out
Counts
4 → 132
Calls
4 calls:
65.0ms
(/ (- (log (- (pow 1.0 3) (pow x 3))) (log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))) (log (+ 1.0 x)))
30.0ms
(log (- (pow 1.0 3) (pow x 3)))
16.0ms
(log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
5.0ms
(log (+ 1.0 x))

series602.0ms

Counts
4 → 12
Calls
4 calls:
244.0ms
(/ (- (log (- (pow 1.0 3) (pow x 3))) (log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))) (log (+ 1.0 x)))
255.0ms
(log (- (pow 1.0 3) (pow x 3)))
61.0ms
(log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
41.0ms
(log (+ 1.0 x))

simplify82.0ms

Counts
144 → 144
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
08312105
133551990
250011987
done50011987

prune434.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 57.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(cbrt (pow (log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x)))) 3))
2.2b
(log (- (pow 1.0 3) (pow x 3)))
8.4b
(log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
8.4b
(log (+ 1.0 x))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
32×log-prod
22×*-un-lft-identity
16×unpow-prod-down cube-prod difference-of-squares
14×cbrt-prod
10×add-cube-cbrt
9×pow1 sqr-pow
7×add-exp-log
6×log-div
5×log-pow distribute-lft-out--
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-log-exp
2×flip3-+ flip-+
1×difference-cubes cube-mult flip3-- pow1/3 unpow3 flip-- rem-cbrt-cube distribute-lft-out
Counts
4 → 96
Calls
4 calls:
3.0ms
(cbrt (pow (log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x)))) 3))
29.0ms
(log (- (pow 1.0 3) (pow x 3)))
15.0ms
(log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
5.0ms
(log (+ 1.0 x))

series414.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(cbrt (pow (log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x)))) 3))
251.0ms
(log (- (pow 1.0 3) (pow x 3)))
62.0ms
(log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
40.0ms
(log (+ 1.0 x))

simplify50.0ms

Counts
108 → 108
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0486950
11740908
25001900
done5001900

prune395.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 57.5b

localize23.0ms

Local error

Found 4 expressions with local error:

8.4b
(log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
8.4b
(log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
8.4b
(log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
8.4b
(log (+ 1.0 x))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
13×log-prod
10×*-un-lft-identity
8×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt log-div
4×expm1-log1p-u flip3-+ rem-log-exp log-pow add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
1×distribute-lft-out
Counts
4 → 65
Calls
4 calls:
16.0ms
(log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
18.0ms
(log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
15.0ms
(log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
5.0ms
(log (+ 1.0 x))

series213.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
60.0ms
(log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
59.0ms
(log (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
39.0ms
(log (+ 1.0 x))

simplify105.0ms

Counts
77 → 77
Iterations

Useful iterations: 3 (93.0ms)

IterNodesCost
0242687
1851611
23413599
35001595
done5001595

prune411.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 57.5b

regimes131.0ms

Accuracy

82.7% (0.4b remaining)

Error of 59.3b against oracle of 58.9b and baseline of 61.2b

bsearch141.0ms

Steps
ItersRangePoint
8
3.658274249114263e-20
1.6623346108088312e-15
1.1340365921574058e-16
7
-7.688829805793637e-17
-3.5004566919240794e-19
-5.5247076957621224e-17

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048103
148103
done48103

end0.0ms

sample4.4s

Algorithm
intervals
Results
2.9s3385×body1280valid
965.0ms2476×body640valid
242.0ms1263×body320valid
92.0ms8000×pre80true
72.0ms675×body160valid
9.0ms201×body80valid