Details

sample26.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify2.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	21
1	32	21
2	70	21
3	130	21
4	280	21
5	500	21
6	827	21
7	1732	21
8	3546	21
done	5000	21

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
1.3b	(+ (* (+ x y) z) (* (+ t y) a))
2.8b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
24.8b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

38×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac`
13×	`distribute-lft-out`
11×	`add-log-exp`
10×	`associate-*l/`
8×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `flip-+`
6×	`pow1`
5×	`associate-/r*`
4×	`associate-l` `frac-add`
3×	`associate-r` `associate-/l*`
2×	`flip3--` `diff-log` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `associate--l+` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

10.0ms	(* (+ x y) z)
6.0ms	(+ (* (+ x y) z) (* (+ t y) a))
36.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
83.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series796.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (+ x y) z)
54.0ms	(+ (* (+ x y) z) (* (+ t y) a))
105.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
615.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify650.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (162.0ms)

Iter	Nodes	Cost
0	179	2307
1	532	2205
2	2153	2077
done	5000	2077

prune358.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))))
1.3b	(+ (* (+ x y) z) (* (+ t y) a))
2.8b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
24.9b	(/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

152×	`*-un-lft-identity`
138×	`times-frac`
72×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`distribute-lft-out`
24×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube` `add-log-exp`
8×	`div-exp` `associate-l/` `associate-/l`
6×	`flip3--` `flip3-+` `flip--` `flip-+` `div-inv`
5×	`pow1`
4×	`cbrt-undiv` `frac-add`
2×	`rec-exp` `frac-2neg` `diff-log` `1-exp` `clear-num` `sum-log` `associate-/l/`
1×	`+-commutative` `sub-neg` `pow-flip` `associate--l+` `inv-pow`

Counts

4 → 176

Calls

4 calls:

59.0ms	(/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))))
6.0ms	(+ (* (+ x y) z) (* (+ t y) a))
36.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
68.0ms	(/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

series862.0ms

Counts

4 → 12

Calls

4 calls:

596.0ms	(/ 1 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))))
53.0ms	(+ (* (+ x y) z) (* (+ t y) a))
104.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
108.0ms	(/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

simplify1.3s

Counts

188 → 188

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	262	6527
1	721	6159
2	2774	5714
done	5000	5706

prune407.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))) -1)
1.3b	(+ (* (+ x y) z) (* (+ t y) a))
2.8b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
24.9b	(/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
30×	`times-frac`
24×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`unpow-prod-down` `distribute-lft-out`
11×	`add-log-exp`
9×	`add-exp-log`
8×	`associate-*l/`
6×	`flip3-+` `add-cbrt-cube` `flip-+`
5×	`pow1` `associate-/l*`
4×	`frac-add` `associate-/r/`
3×	`pow-unpow` `flip3--` `associate-/r*` `flip--`
2×	`diff-log` `div-exp` `pow-exp` `sum-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `unpow-1` `pow-pow` `frac-2neg` `associate--l+` `clear-num` `sqr-pow`

Counts

4 → 105

Calls

4 calls:

60.0ms	(pow (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))) -1)
6.0ms	(+ (* (+ x y) z) (* (+ t y) a))
35.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
67.0ms	(/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

series2.3s

Counts

4 → 12

Calls

4 calls:

2.1s	(pow (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))) -1)
52.0ms	(+ (* (+ x y) z) (* (+ t y) a))
102.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
103.0ms	(/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))

simplify676.0ms

Counts

117 → 117

Iterations

Useful iterations: done (672.0ms)

Iter	Nodes	Cost
0	201	3583
1	613	3453
2	2392	3285
done	5000	3237

prune352.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ (+ x t) y) -1)
2.1b	(- (* (+ t y) a) (* y b))
2.2b	(+ (- (* (+ t y) a) (* y b)) (* (+ x y) z))
24.9b	(* (pow (+ (+ x t) y) -1) (+ (- (* (+ t y) a) (* y b)) (* (+ x y) z)))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`associate-*l/`
12×	`frac-add`
11×	`unpow-prod-down` `add-log-exp`
10×	`add-exp-log`
9×	`add-cube-cbrt` `flip3-+` `associate-l` `flip-+`
8×	`unpow-1`
7×	`flip3--` `flip--`
6×	`frac-times` `associate-*r/` `add-cbrt-cube` `distribute-lft-out`
5×	`pow1`
3×	`pow-unpow` `associate-r` `prod-exp` `unswap-sqr` `sqr-pow`
2×	`pow-to-exp` `sub-neg` `associate-+l+` `diff-log` `pow-exp` `sum-log`
1×	`+-commutative` `distribute-rgt-in` `associate-+l-` `pow-pow` `distribute-lft-in` `*-commutative` `cbrt-unprod`

Counts

4 → 93

Calls

4 calls:

20.0ms	(pow (+ (+ x t) y) -1)
5.0ms	(- (* (+ t y) a) (* y b))
24.0ms	(+ (- (* (+ t y) a) (* y b)) (* (+ x y) z))
144.0ms	(* (pow (+ (+ x t) y) -1) (+ (- (* (+ t y) a) (* y b)) (* (+ x y) z)))

series744.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(pow (+ (+ x t) y) -1)
33.0ms	(- (* (+ t y) a) (* y b))
94.0ms	(+ (- (* (+ t y) a) (* y b)) (* (+ x y) z))
563.0ms	(* (pow (+ (+ x t) y) -1) (+ (- (* (+ t y) a) (* y b)) (* (+ x y) z)))

simplify1.4s

Counts

105 → 105

Iterations

Useful iterations: 2 (194.0ms)

Iter	Nodes	Cost
0	171	2817
1	586	2652
2	3405	2475
done	5000	2475

prune306.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.1b

regimes825.0ms

Accuracy

85.9% (3.1b remaining)

Error of 7.5b against oracle of 4.4b and baseline of 26.4b

bsearch2.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	29	81
1	45	75
2	47	75
done	47	75

end0.0ms

sample617.0ms

Algorithm

intervals

Results

349.0ms

8000×

body

valid