Details

sample426.0ms

Algorithm

intervals

Results

241.0ms	102×	body	2560	valid
110.0ms	69×	body	1280	valid
37.0ms	51×	body	640	valid
9.0ms	256×	pre	80	true
9.0ms	19×	body	320	valid
4.0ms	13×	body	160	valid
0.0ms	2×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	14
2	14
1	10
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.8b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (tan x))
3.5b	(- (/ 1 x) (/ 1 (tan x)))

rewrite45.0ms

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))
36.0ms	(- (/ 1 x) (/ 1 (tan x)))

series449.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ 1 (tan x))
402.0ms	(- (/ 1 x) (/ 1 (tan x)))

simplify725.0ms

Counts

69 → 69

Iterations

Iter	Nodes
done	2001
3	1116
2	586
1	239
0	120

prune257.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

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))

rewrite111.0ms

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:

27.0ms	(+ (* (* x x) 1/45) 1/3)
13.0ms	(* 2/945 (pow x 5))
15.0ms	(* (* x x) 1/45)
53.0ms	(* x (+ (* (* x x) 1/45) 1/3))

series313.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ (* (* x x) 1/45) 1/3)
73.0ms	(* 2/945 (pow x 5))
29.0ms	(* (* x x) 1/45)
112.0ms	(* x (+ (* (* x x) 1/45) 1/3))

simplify613.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	2006
2	1205
1	383
0	134

prune372.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

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

rewrite250.0ms

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-*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:

14.0ms	(* (* x x) 1/45)
40.0ms	(* (* (* x x) 1/45) 1/3)
12.0ms	(* (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125)) x)
183.0ms	(/ (* (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125)) x) (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3))))

series751.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (* x x) 1/45)
29.0ms	(* (* (* x x) 1/45) 1/3)
229.0ms	(* (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125)) x)
450.0ms	(/ (* (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125)) x) (+ (* (* (* x x) 1/45) (* (* x x) 1/45)) (- (* 1/3 1/3) (* (* (* x x) 1/45) 1/3))))

simplify567.0ms

Counts

101 → 101

Iterations

Iter	Nodes
done	2001
1	485
0	162

prune411.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/135 (* x x))
0.2b	(* (* x x) (* x x))
0.4b	(/ (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125)) (/ (+ (* (* (* x x) (* x x)) 1/2025) (- 1/9 (* 1/135 (* x x)))) x))
0.4b	(/ (+ (* (* (* x x) (* x x)) 1/2025) (- 1/9 (* 1/135 (* x x)))) x)

rewrite403.0ms

Algorithm

rewrite-expression-head

Rules

120×	`pow1`
84×	`times-frac`
56×	`add-sqr-sqrt`
55×	`*-un-lft-identity` `add-cube-cbrt`
36×	`pow-prod-up`
28×	`add-cbrt-cube` `add-exp-log`
26×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus`
16×	`associate-/r*`
13×	`pow2`
11×	`prod-exp` `cbrt-unprod`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv` `div-exp` `associate-l` `insert-posit16` `add-log-exp` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3-+` `associate-r` `*-commutative` `flip-+` `unswap-sqr`
1×	`associate-+r-` `div-sub` `swap-sqr` `associate-/r/`

Counts

4 → 188

Calls

4 calls:

17.0ms	(* 1/135 (* x x))
30.0ms	(* (* x x) (* x x))
163.0ms	(/ (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125)) (/ (+ (* (* (* x x) (* x x)) 1/2025) (- 1/9 (* 1/135 (* x x)))) x))
189.0ms	(/ (+ (* (* (* x x) (* x x)) 1/2025) (- 1/9 (* 1/135 (* x x)))) x)

series505.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* 1/135 (* x x))
42.0ms	(* (* x x) (* x x))
339.0ms	(/ (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125)) (/ (+ (* (* (* x x) (* x x)) 1/2025) (- 1/9 (* 1/135 (* x x)))) x))
88.0ms	(/ (+ (* (* (* x x) (* x x)) 1/2025) (- 1/9 (* 1/135 (* x x)))) x)

simplify676.0ms

Counts

200 → 200

Iterations

Iter	Nodes
done	2000
1	745
0	259

prune902.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes37.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	31
1	31
0	23

end0.0ms

sample14.3s

Algorithm

intervals

Results

8.1s	3245×	body	2560	valid
3.9s	2491×	body	1280	valid
1.5s	1284×	body	640	valid
370.0ms	634×	body	320	valid
275.0ms	8000×	pre	80	true
99.0ms	304×	body	160	valid
7.0ms	42×	body	80	valid