Details

sample68.0ms

Algorithm

intervals

Results

23.0ms	65×	body	1280	valid
15.0ms	62×	body	640	valid
9.0ms	200×	body	80	valid
3.0ms	16×	body	320	valid
1.0ms	12×	body	160	valid

simplify27.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	15
3	15
2	13
1	10
0	5

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.2b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.4b	(- (exp x) 1.0)

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r*`
2×	`pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 52

Calls

2 calls:

53.0ms	(/ (- (exp x) 1.0) x)
42.0ms	(- (exp x) 1.0)

series110.0ms

Counts

2 → 6

Calls

2 calls:

81.0ms	(/ (- (exp x) 1.0) x)
29.0ms	(- (exp x) 1.0)

simplify2.7s

Counts

58 → 58

Iterations

Iter	Nodes
done	5008
3	1979
2	569
1	224
0	99

prune346.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 1/6 x) 1/2)
0.1b	(* x (+ (* 1/6 x) 1/2))
0.3b	(* 1/6 x)

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
7×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
5×	`add-log-exp`
2×	`flip3-+` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `sum-log`

Counts

3 → 51

Calls

3 calls:

19.0ms	(+ (* 1/6 x) 1/2)
60.0ms	(* x (+ (* 1/6 x) 1/2))
14.0ms	(* 1/6 x)

series200.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(+ (* 1/6 x) 1/2)
113.0ms	(* x (+ (* 1/6 x) 1/2))
30.0ms	(* 1/6 x)

simplify6.1s

Counts

60 → 60

Iterations

Iter	Nodes
done	5000
3	3729
2	690
1	222
0	77

prune361.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/6 x) 1/2)
0.1b	(* (* x x) (+ (* 1/6 x) 1/2))
0.3b	(* 1/6 x)
5.2b	(/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x)

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
9×	`times-frac`
6×	`associate-r` `add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`associate-r/` `-commutative` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 81

Calls

4 calls:

12.0ms	(+ (* 1/6 x) 1/2)
66.0ms	(* (* x x) (+ (* 1/6 x) 1/2))
15.0ms	(* 1/6 x)
148.0ms	(/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x)

series303.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (* 1/6 x) 1/2)
124.0ms	(* (* x x) (+ (* 1/6 x) 1/2))
24.0ms	(* 1/6 x)
90.0ms	(/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x)

simplify2.7s

Counts

93 → 93

Iterations

Iter	Nodes
done	5002
2	1428
1	380
0	136

prune582.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize95.0ms

Local error

Found 4 expressions with local error:

5.2b	(/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x)
5.2b	(/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x)
5.2b	(/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x)
8.7b	(cbrt (* (* (/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x) (/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x)) (/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x)))

rewrite774.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/r` `associate-/l`
7×	`cbrt-div`
6×	`associate-/l/`
5×	`frac-times` `associate-*l/`
4×	`pow1` `add-log-exp`
3×	`cbrt-undiv` `frac-2neg` `flip3-+` `associate-*r/` `div-exp` `clear-num` `flip-+` `div-inv`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 104

Calls

4 calls:

134.0ms	(/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x)
136.0ms	(/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x)
136.0ms	(/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x)
362.0ms	(cbrt (* (* (/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x) (/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x)) (/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x)
88.0ms	(/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x)
75.0ms	(/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x)
133.0ms	(cbrt (* (* (/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x) (/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x)) (/ (+ (* (* x x) (+ (* 1/6 x) 1/2)) x) x)))

simplify2.3s

Counts

116 → 116

Iterations

Iter	Nodes
done	5001
2	930
1	270
0	102

prune913.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes146.0ms

Accuracy

97.2% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 21.2b

bsearch2.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	24
1	24
0	18

end1.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	2289×	body	1280	valid
482.0ms	1599×	body	640	valid
271.0ms	845×	body	320	valid
254.0ms	5474×	body	80	valid
46.0ms	450×	body	160	valid