Details

sample583.0ms

Algorithm

intervals

Results

357.0ms	113×	body	2560	valid
144.0ms	75×	body	1280	valid
41.0ms	45×	body	640	valid
12.0ms	256×	pre	80	true
11.0ms	16×	body	320	valid
3.0ms	6×	body	160	valid
0.0ms	1×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	10
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (tan x))
2.2b	(- (/ 1 x) (/ 1 (tan x)))

rewrite41.0ms

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:

6.0ms	(/ 1 (tan x))
33.0ms	(- (/ 1 x) (/ 1 (tan x)))

series137.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ 1 (tan x))
96.0ms	(- (/ 1 x) (/ 1 (tan x)))

simplify1.0s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
2	1026
1	242
0	120

prune249.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1/3 (* 1/45 (* x x)))
0.1b	(* 2/945 (pow x 5))
0.1b	(* 1/45 (* x x))
0.4b	(* x (+ 1/3 (* 1/45 (* x x))))

rewrite65.0ms

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-*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:

10.0ms	(+ 1/3 (* 1/45 (* x x)))
16.0ms	(* 2/945 (pow x 5))
27.0ms	(* 1/45 (* x x))
11.0ms	(* x (+ 1/3 (* 1/45 (* x x))))

series322.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ 1/3 (* 1/45 (* x x)))
86.0ms	(* 2/945 (pow x 5))
43.0ms	(* 1/45 (* x x))
117.0ms	(* x (+ 1/3 (* 1/45 (* x x))))

simplify1.3s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	2092
1	393
0	132

prune422.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/45 (* x x))
0.2b	(* 1/3 (* 1/45 (* x x)))
0.3b	(/ (* (+ (* (* x x) (* (* (* x x) (* x x)) 1/91125)) 1/27) x) (+ (* 1/3 1/3) (- (* (* 1/45 (* x x)) (* 1/45 (* x x))) (* 1/3 (* 1/45 (* x x))))))
0.4b	(* (+ (* (* x x) (* (* (* x x) (* x x)) 1/91125)) 1/27) x)

rewrite1.5s

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-l`
5×	`associate-r`
4×	`associate-*l/` `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×	`clear-num` `frac-2neg` `div-inv` `associate-/l*`

Counts

4 → 89

Calls

4 calls:

16.0ms	(* 1/45 (* x x))
36.0ms	(* 1/3 (* 1/45 (* x x)))
544.0ms	(/ (* (+ (* (* x x) (* (* (* x x) (* x x)) 1/91125)) 1/27) x) (+ (* 1/3 1/3) (- (* (* 1/45 (* x x)) (* 1/45 (* x x))) (* 1/3 (* 1/45 (* x x))))))
875.0ms	(* (+ (* (* x x) (* (* (* x x) (* x x)) 1/91125)) 1/27) x)

series748.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* 1/45 (* x x))
42.0ms	(* 1/3 (* 1/45 (* x x)))
383.0ms	(/ (* (+ (* (* x x) (* (* (* x x) (* x x)) 1/91125)) 1/27) x) (+ (* 1/3 1/3) (- (* (* 1/45 (* x x)) (* 1/45 (* x x))) (* 1/3 (* 1/45 (* x x))))))
294.0ms	(* (+ (* (* x x) (* (* (* x x) (* x x)) 1/91125)) 1/27) x)

simplify2.4s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	3079
1	473
0	159

prune507.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x 1/45)
0.2b	(* x 1/45)
0.3b	(/ x (+ (* (* x (* x 1/45)) (- (* x (* x 1/45)) 1/3)) 1/9))
0.4b	(* (+ 1/27 (* (* x (* x x)) (* (* x (* x x)) 1/91125))) (/ x (+ (* (* x (* x 1/45)) (- (* x (* x 1/45)) 1/3)) 1/9)))

rewrite421.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

6.0ms	(* x 1/45)
5.0ms	(* x 1/45)
124.0ms	(/ x (+ (* (* x (* x 1/45)) (- (* x (* x 1/45)) 1/3)) 1/9))
283.0ms	(* (+ 1/27 (* (* x (* x x)) (* (* x (* x x)) 1/91125))) (/ x (+ (* (* x (* x 1/45)) (- (* x (* x 1/45)) 1/3)) 1/9)))

series730.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* x 1/45)
18.0ms	(* x 1/45)
214.0ms	(/ x (+ (* (* x (* x 1/45)) (- (* x (* x 1/45)) 1/3)) 1/9))
482.0ms	(* (+ 1/27 (* (* x (* x x)) (* (* x (* x x)) 1/91125))) (/ x (+ (* (* x (* x 1/45)) (- (* x (* x 1/45)) 1/3)) 1/9)))

simplify2.0s

Counts

119 → 119

Iterations

Iter	Nodes
done	5002
2	2984
1	500
0	176

prune645.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	34
1	34
0	23

end0.0ms

sample16.9s

Algorithm

intervals

Results

10.2s	3214×	body	2560	valid
4.0s	2525×	body	1280	valid
1.6s	1266×	body	640	valid
437.0ms	629×	body	320	valid
309.0ms	8000×	pre	80	true
170.0ms	327×	body	160	valid
8.0ms	39×	body	80	valid