Details

sample154.0ms

Algorithm

intervals

Results

67.0ms	102×	body	1280	valid
34.0ms	78×	body	640	valid
21.0ms	292×	body	80	valid
12.0ms	46×	body	320	valid
4.0ms	22×	body	160	valid

simplify74.0ms

Counts

1 → 1

Iterations

Iter	Nodes
7	36
6	36
5	35
4	33
3	29
2	22
1	14
0	7

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.6b

localize23.0ms

Local error

Found 1 expressions with local error:

5.8b	(- (exp x) (exp (- x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `add-cube-cbrt` `insert-posit16` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 15

Calls

1 calls:

21.0ms

(- (exp x) (exp (- x)))

series58.0ms

Counts

1 → 3

Calls

1 calls:

58.0ms

(- (exp x) (exp (- x)))

simplify4.7s

Counts

18 → 18

Iterations

Iter	Nodes
5	5103
4	1654
3	653
2	258
1	111
0	47

prune173.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (+ 2 (* 1/3 (* x x))) x) (* 1/60 (pow x 5)))
0.0b	(* (+ 2 (* 1/3 (* x x))) x)
0.1b	(* 1/60 (pow x 5))
0.2b	(* 1/3 (* x x))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`add-cbrt-cube`
11×	`pow1` `associate-r`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`associate-l`
7×	`prod-exp`
6×	`add-log-exp`
5×	`cbrt-unprod` `unswap-sqr`
4×	`unpow-prod-down` `pow-prod-down` `insert-posit16`
3×	`*-commutative`
2×	`flip3-+` `associate-*l/` `flip-+` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-exp`

Counts

4 → 79

Calls

4 calls:

11.0ms	(+ (* (+ 2 (* 1/3 (* x x))) x) (* 1/60 (pow x 5)))
13.0ms	(* (+ 2 (* 1/3 (* x x))) x)
16.0ms	(* 1/60 (pow x 5))
18.0ms	(* 1/3 (* x x))

series324.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (* (+ 2 (* 1/3 (* x x))) x) (* 1/60 (pow x 5)))
115.0ms	(* (+ 2 (* 1/3 (* x x))) x)
94.0ms	(* 1/60 (pow x 5))
49.0ms	(* 1/3 (* x x))

simplify3.0s

Counts

91 → 91

Iterations

Iter	Nodes
3	5776
2	1198
1	368
0	138

prune780.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize100.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/3 (* x x))
0.2b	(* 1/3 (* x x))
0.2b	(* 1/3 (* x x))
40.4b	(/ (+ (* (* 1/60 (* (* x x) (* (* x x) x))) (* (* 1/60 (* (* x x) (* (* x x) x))) (* 1/60 (* (* x x) (* (* x x) x))))) (* (* (* (* x x) x) (+ (* 1/3 (* x x)) 2)) (* (+ (* 1/3 (* x x)) 2) (+ (* 1/3 (* x x)) 2)))) (+ (* (* (+ (* 1/3 (* x x)) 2) (+ (* 1/3 (* x x)) 2)) (* x x)) (* (* 1/60 (* (* x x) (* (* x x) x))) (- (* 1/60 (* (* x x) (* (* x x) x))) (* (+ (* 1/3 (* x x)) 2) x)))))

rewrite10.8s

Algorithm

rewrite-expression-head

Rules

21×	`add-cbrt-cube` `add-exp-log`
20×	`associate-l/` `associate-r/`
19×	`pow1`
18×	`add-sqr-sqrt` `associate-/r/`
16×	`frac-add`
15×	`*-un-lft-identity` `add-cube-cbrt`
14×	`flip3-+` `flip-+`
9×	`times-frac` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`frac-times` `flip3--` `flip--`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-r` `-commutative` `associate-/l*` `unswap-sqr`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 108

Calls

4 calls:

13.0ms	(* 1/3 (* x x))
13.0ms	(* 1/3 (* x x))
13.0ms	(* 1/3 (* x x))
10.7s	(/ (+ (* (* 1/60 (* (* x x) (* (* x x) x))) (* (* 1/60 (* (* x x) (* (* x x) x))) (* 1/60 (* (* x x) (* (* x x) x))))) (* (* (* (* x x) x) (+ (* 1/3 (* x x)) 2)) (* (+ (* 1/3 (* x x)) 2) (+ (* 1/3 (* x x)) 2)))) (+ (* (* (+ (* 1/3 (* x x)) 2) (+ (* 1/3 (* x x)) 2)) (* x x)) (* (* 1/60 (* (* x x) (* (* x x) x))) (- (* 1/60 (* (* x x) (* (* x x) x))) (* (+ (* 1/3 (* x x)) 2) x)))))

series396.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 1/3 (* x x))
50.0ms	(* 1/3 (* x x))
35.0ms	(* 1/3 (* x x))
276.0ms	(/ (+ (* (* 1/60 (* (* x x) (* (* x x) x))) (* (* 1/60 (* (* x x) (* (* x x) x))) (* 1/60 (* (* x x) (* (* x x) x))))) (* (* (* (* x x) x) (+ (* 1/3 (* x x)) 2)) (* (+ (* 1/3 (* x x)) 2) (+ (* 1/3 (* x x)) 2)))) (+ (* (* (+ (* 1/3 (* x x)) 2) (+ (* 1/3 (* x x)) 2)) (* x x)) (* (* 1/60 (* (* x x) (* (* x x) x))) (- (* 1/60 (* (* x x) (* (* x x) x))) (* (+ (* 1/3 (* x x)) 2) x)))))

simplify2.3s

Counts

120 → 120

Iterations

Iter	Nodes
2	4089
1	818
0	223

prune1.9s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ -1 (exp x))
5.8b	(+ (/ -1 (exp x)) (exp x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`times-frac`
4×	`add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `add-exp-log` `associate-/l`
2×	`pow1` `insert-posit16`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `div-exp` `flip-+` `div-inv` `distribute-lft-out`

Counts

2 → 41

Calls

2 calls:

10.0ms	(/ -1 (exp x))
14.0ms	(+ (/ -1 (exp x)) (exp x))

series73.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(/ -1 (exp x))
63.0ms	(+ (/ -1 (exp x)) (exp x))

simplify6.9s

Counts

47 → 47

Iterations

Iter	Nodes
4	4903
3	1363
2	433
1	188
0	87

prune230.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes22.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	18
1	18
0	13

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.2s	3385×	body	1280	valid
1.1s	8062×	body	80	valid
1.0s	2483×	body	640	valid
432.0ms	1268×	body	320	valid
127.0ms	623×	body	160	valid