Details

sample568.0ms

Algorithm

intervals

Results

321.0ms	97×	body	2560	valid
144.0ms	76×	body	1280	valid
47.0ms	37×	body	640	valid
22.0ms	32×	body	320	valid
12.0ms	256×	pre	80	true
5.0ms	11×	body	160	valid
1.0ms	3×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	12
2	12
1	8
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.8b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`times-frac`
12×	`add-cube-cbrt`
9×	`difference-of-squares`
7×	`distribute-lft-out--`
6×	`add-exp-log`
5×	`div-inv`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow1` `associate-/r` `associate-/l`
2×	`div-exp` `insert-posit16`
1×	`cbrt-undiv` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `1-exp` `tan-quot` `associate-/r/` `frac-sub` `pow-flip` `flip--` `inv-pow`

Counts

2 → 63

Calls

2 calls:

9.0ms	(/ 1 (tan x))
14.0ms	(- (/ 1 x) (/ 1 (tan x)))

series168.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ 1 (tan x))
120.0ms	(- (/ 1 x) (/ 1 (tan x)))

simplify8.0s

Counts

69 → 69

Iterations

Iter	Nodes
4	2535
3	1222
2	567
1	235
0	120

prune516.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* x x) 1/45) 1/3)
0.1b	(* 2/945 (pow x 5))
0.2b	(* (* x x) 1/45)
0.3b	(* x (+ (* (* x x) 1/45) 1/3))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`add-cbrt-cube` `associate-r`
11×	`pow1`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l` `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-*r/` `flip-+` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `+-commutative` `sum-log` `distribute-lft-in` `pow-exp`

Counts

4 → 81

Calls

4 calls:

14.0ms	(+ (* (* x x) 1/45) 1/3)
8.0ms	(* 2/945 (pow x 5))
16.0ms	(* (* x x) 1/45)
68.0ms	(* x (+ (* (* x x) 1/45) 1/3))

series329.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ (* (* x x) 1/45) 1/3)
87.0ms	(* 2/945 (pow x 5))
34.0ms	(* (* x x) 1/45)
136.0ms	(* x (+ (* (* x x) 1/45) 1/3))

simplify1.6s

Counts

93 → 93

Iterations

Iter	Nodes
3	3462
2	958
1	342
0	134

prune862.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize98.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x x) 1/45)
0.2b	(* (* (* x x) 1/45) 1/3)
0.3b	(/ (* x (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125))) (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3))))
0.3b	(* x (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125)))

rewrite336.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-cbrt-cube` `add-exp-log`
20×	`pow1`
13×	`add-sqr-sqrt`
11×	`prod-exp` `cbrt-unprod`
10×	`*-un-lft-identity` `pow-prod-down` `add-cube-cbrt`
9×	`associate-r`
5×	`associate-l`
4×	`associate-*r/` `insert-posit16` `add-log-exp`
3×	`associate-/r` `flip3-+` `times-frac` `-commutative` `flip-+`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `unswap-sqr` `associate-/l/`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `div-inv` `associate-/l*`

Counts

4 → 91

Calls

4 calls:

29.0ms	(* (* x x) 1/45)
61.0ms	(* (* (* x x) 1/45) 1/3)
227.0ms	(/ (* x (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125))) (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3))))
16.0ms	(* x (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125)))

series787.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* x x) 1/45)
37.0ms	(* (* (* x x) 1/45) 1/3)
416.0ms	(/ (* x (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125))) (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3))))
287.0ms	(* x (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125)))

simplify1.1s

Counts

103 → 103

Iterations

Iter	Nodes
2	2062
1	481
0	165

prune1.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
0.1b	(* (* x x) (* x x))
0.1b	(* 2/945 (pow x 5))
0.2b	(* (* x x) -1/135)

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

231×	`pow1`
72×	`pow-prod-up`
49×	`pow-prod-down`
44×	`pow-sqr`
38×	`add-exp-log`
36×	`pow-plus`
35×	`add-cbrt-cube`
26×	`pow2`
22×	`prod-exp`
20×	`cbrt-unprod`
14×	`add-sqr-sqrt`
12×	`associate-r`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l` `unswap-sqr`
4×	`unpow-prod-down` `*-commutative` `insert-posit16` `add-log-exp`
2×	`swap-sqr` `sqr-pow`
1×	`pow-to-exp` `pow-exp`

Counts

4 → 174

Calls

4 calls:

45.0ms	(* (* x x) (* x x))
43.0ms	(* (* x x) (* x x))
23.0ms	(* 2/945 (pow x 5))
30.0ms	(* (* x x) -1/135)

series224.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (* x x) (* x x))
66.0ms	(* (* x x) (* x x))
65.0ms	(* 2/945 (pow x 5))
28.0ms	(* (* x x) -1/135)

simplify6.9s

Counts

186 → 186

Iterations

Iter	Nodes
4	9002
3	1871
2	629
1	277
0	118

prune2.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes31.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	31
1	31
0	22

end0.0ms

sample16.6s

Algorithm

intervals

Results

9.7s	3141×	body	2560	valid
4.1s	2598×	body	1280	valid
1.3s	1252×	body	640	valid
770.0ms	654×	body	320	valid
347.0ms	8000×	pre	80	true
117.0ms	307×	body	160	valid
9.0ms	48×	body	80	valid