Details

sample75.0ms

Algorithm

intervals

Results

31.0ms	107×	body	1280	valid
15.0ms	93×	body	640	valid
6.0ms	374×	pre	80	true
4.0ms	36×	body	320	valid
3.0ms	125×	body	80	valid
1.0ms	13×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	6	4
2	7	4
done	7	4

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.8b

localize7.0ms

Local error

Found 1 expressions with local error:

4.9b	(- (exp x) 1.0)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 14

Calls

1 calls:

22.0ms

(- (exp x) 1.0)

series38.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

(- (exp x) 1.0)

simplify2.3s

Counts

17 → 17

Iterations

Useful iterations: 3 (160.0ms)

Iter	Nodes	Cost
0	39	132
1	83	127
2	224	119
3	690	117
4	2920	117
done	5000	117

prune67.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (pow x 2) (+ 1/2 (* x 1/6))) x)
0.0b	(* (pow x 2) (+ 1/2 (* x 1/6)))
0.4b	(* x 1/6)

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
11×	`associate-l`
10×	`add-exp-log`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`add-cbrt-cube`
6×	`associate-r`
5×	`pow1` `add-log-exp` `unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
2×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `flip3-+` `associate-r/` `-commutative` `cbrt-unprod` `flip-+` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow-prod-down` `pow-exp` `sum-log`

Counts

3 → 62

Calls

3 calls:

31.0ms	(+ (* (pow x 2) (+ 1/2 (* x 1/6))) x)
45.0ms	(* (pow x 2) (+ 1/2 (* x 1/6)))
13.0ms	(* x 1/6)

series193.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* (pow x 2) (+ 1/2 (* x 1/6))) x)
130.0ms	(* (pow x 2) (+ 1/2 (* x 1/6)))
27.0ms	(* x 1/6)

simplify1.5s

Counts

71 → 71

Iterations

Useful iterations: 2 (449.0ms)

Iter	Nodes	Cost
0	113	816
1	334	751
2	1762	674
done	5000	674

prune185.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(* x 1/6)
0.4b	(* x 1/6)
0.4b	(* x 1/6)
28.1b	(/ (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x)) (- (* (pow x 2) (+ 1/2 (* x 1/6))) x))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`times-frac` `associate-r` `associate-l`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `associate-/r` `-commutative` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

15.0ms	(* x 1/6)
15.0ms	(* x 1/6)
11.0ms	(* x 1/6)
161.0ms	(/ (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x)) (- (* (pow x 2) (+ 1/2 (* x 1/6))) x))

series183.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* x 1/6)
21.0ms	(* x 1/6)
19.0ms	(* x 1/6)
125.0ms	(/ (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x)) (- (* (pow x 2) (+ 1/2 (* x 1/6))) x))

simplify1.9s

Counts

98 → 98

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	112	1887
1	321	1847
2	1809	1689
done	5001	1643

prune414.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

14.5b	(* (* (cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x))) (cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x)))) (/ (cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x))) (- (* (pow x 2) (+ 1/2 (* x 1/6))) x)))
29.0b	(cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x)))
29.0b	(cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x)))
29.0b	(cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-div`
25×	`add-sqr-sqrt`
24×	`associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
19×	`cbrt-prod`
16×	`add-exp-log` `frac-times` `flip3--` `flip--`
12×	`associate-*l/`
10×	`add-cbrt-cube`
9×	`pow1`
6×	`prod-exp` `cbrt-unprod`
5×	`associate-*r/`
4×	`add-log-exp`
3×	`pow1/3` `pow-prod-down` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/`
1×	`associate-l` `*-commutative` `div-inv`

Counts

4 → 102

Calls

4 calls:

1.0s	(* (* (cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x))) (cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x)))) (/ (cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x))) (- (* (pow x 2) (+ 1/2 (* x 1/6))) x)))
79.0ms	(cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x)))
85.0ms	(cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x)))
62.0ms	(cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x)))

series531.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (* (cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x))) (cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x)))) (/ (cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x))) (- (* (pow x 2) (+ 1/2 (* x 1/6))) x)))
143.0ms	(cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x)))
136.0ms	(cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x)))
143.0ms	(cbrt (- (* (pow x 4) (* (+ 1/2 (* x 1/6)) (+ 1/2 (* x 1/6)))) (* x x)))

simplify3.5s

Counts

114 → 114

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	212	7978
1	629	7747
2	4110	6546
done	5002	5729

prune698.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes47.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	13	11
done	13	11

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.4s	3385×	body	1280	valid
438.0ms	2545×	body	640	valid
235.0ms	11936×	pre	80	true
120.0ms	1235×	body	320	valid
95.0ms	4096×	body	80	valid
41.0ms	675×	body	160	valid