Details

Time bar (total: 13.3s)

sample58.0ms

Algorithm
intervals
Results
16.0ms46×body1280valid
10.0ms27×body320valid
10.0ms37×body640valid
10.0ms135×body80valid
2.0ms11×body160valid

simplify2.2s

Counts
1 → 1
Iterations
IterNodes
done5001
143644
13892
12339
11229
10177
9109
855
742
632
526
423
322
219
115
07

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1))
0.0b
(/ (+ x 1) (- x 1))
3.2b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
110×*-un-lft-identity
60×times-frac
57×add-sqr-sqrt
25×add-cube-cbrt
20×distribute-lft-out
18×distribute-lft-out--
14×difference-of-squares
11×associate-/r*
7×add-cbrt-cube add-exp-log associate-/l*
5×difference-of-sqr-1 add-log-exp
4×associate-/r/
3×pow1 insert-posit16
2×cbrt-undiv clear-num frac-2neg flip3-+ flip3-- div-exp flip-+ div-inv flip-- associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 117
Calls
3 calls:
15.0ms
(/ x (+ x 1))
36.0ms
(/ (+ x 1) (- x 1))
58.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series151.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(/ x (+ x 1))
25.0ms
(/ (+ x 1) (- x 1))
97.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.0s

Counts
126 → 126
Iterations
IterNodes
done5000
21654
1413
0180

prune431.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ x (+ x 1))
0.0b
(/ (+ x 1) (- x 1))
3.1b
(log (exp (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
3.2b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite306.0ms

Algorithm
rewrite-expression-head
Rules
159×*-un-lft-identity
80×times-frac
72×add-sqr-sqrt
31×distribute-lft-out--
28×add-cube-cbrt distribute-lft-out
18×difference-of-squares
17×log-pow
16×exp-prod
11×associate-/r*
8×add-cbrt-cube add-exp-log
7×associate-/l*
6×add-log-exp
5×pow1 log-prod difference-of-sqr-1
4×associate-/r/ insert-posit16
2×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ flip3-- div-exp exp-sum flip-+ div-inv flip-- associate-/l/
1×log-div exp-diff diff-log rem-log-exp frac-sub
Counts
4 → 149
Calls
4 calls:
8.0ms
(/ x (+ x 1))
21.0ms
(/ (+ x 1) (- x 1))
206.0ms
(log (exp (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
68.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series301.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ x (+ x 1))
45.0ms
(/ (+ x 1) (- x 1))
103.0ms
(log (exp (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
118.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.3s

Counts
161 → 161
Iterations
IterNodes
done5001
21923
1483
0216

prune607.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

3.1b
(log (exp (cbrt (* (* (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))))
3.2b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
3.2b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
3.2b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
144×*-un-lft-identity
60×times-frac
42×add-sqr-sqrt
39×distribute-lft-out--
24×distribute-lft-out
12×difference-of-squares
10×add-log-exp
6×add-cube-cbrt
5×pow1 log-pow
4×exp-prod add-cbrt-cube add-exp-log insert-posit16
3×log-prod sub-neg flip3-- diff-log frac-sub flip--
1×cbrt-prod rem-log-exp
Counts
4 → 98
Calls
4 calls:
2.0ms
(log (exp (cbrt (* (* (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))))
55.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
57.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
59.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

series370.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(log (exp (cbrt (* (* (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))) (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))))
94.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
86.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
84.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify1.5s

Counts
110 → 110
Iterations
IterNodes
done5001
33354
2543
1192
093

prune485.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ x 1))
0.3b
(cbrt (+ x 1))
0.3b
(cbrt (+ x 1))
20.6b
(- (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (+ x 1) (- x 1)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
35×*-un-lft-identity
25×times-frac
16×cbrt-prod
10×difference-of-squares
7×add-cube-cbrt distribute-lft-out--
6×cbrt-div add-log-exp
5×distribute-lft-out
4×pow1 add-cbrt-cube add-exp-log insert-posit16
3×flip3-+ pow1/3 flip-+
1×sub-neg flip3-- diff-log frac-sub flip--
Counts
4 → 74
Calls
4 calls:
2.0ms
(cbrt (+ x 1))
3.0ms
(cbrt (+ x 1))
2.0ms
(cbrt (+ x 1))
89.0ms
(- (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (+ x 1) (- x 1)))

series245.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(cbrt (+ x 1))
52.0ms
(cbrt (+ x 1))
55.0ms
(cbrt (+ x 1))
80.0ms
(- (/ (/ x (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (cbrt (+ x 1))) (/ (+ x 1) (- x 1)))

simplify1.1s

Counts
86 → 86
Iterations
IterNodes
done5001
2975
1325
0135

prune390.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes108.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.9b

bsearch147.0ms

Steps
ItersRangePoint
7
986.1969312707462
23716.851585869685
12671.507747924104
9
-209901990.47645873
-0.28008678268591264
-15613.93143224409

simplify7.0ms

Iterations
IterNodes
done34
134
027

end0.0ms

sample2.1s

Algorithm
intervals
Results
961.0ms1701×body1280valid
460.0ms1331×body640valid
346.0ms4038×body80valid
175.0ms621×body320valid
42.0ms309×body160valid