Details

sample549.0ms

Algorithm

intervals

Results

289.0ms	101×	body	2560	valid
134.0ms	89×	body	1280	valid
51.0ms	20×	body	320	valid
45.0ms	34×	body	640	valid
11.0ms	256×	pre	80	true
5.0ms	11×	body	160	valid
0.0ms	1×	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: 60.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1 (tan x))
2.6b	(- (/ 1 x) (/ 1 (tan x)))

rewrite26.0ms

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:

10.0ms	(/ 1 (tan x))
14.0ms	(- (/ 1 x) (/ 1 (tan x)))

series135.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ 1 (tan x))
92.0ms	(- (/ 1 x) (/ 1 (tan x)))

simplify1.1s

Counts

69 → 69

Iterations

Iter	Nodes
done	2001
4	2001
3	1116
2	586
1	239
0	120

prune498.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

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))

rewrite140.0ms

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:

22.0ms	(+ (* (* x x) 1/45) 1/3)
9.0ms	(* 2/945 (pow x 5))
13.0ms	(* (* x x) 1/45)
94.0ms	(* x (+ (* (* x x) 1/45) 1/3))

series324.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ (* (* x x) 1/45) 1/3)
73.0ms	(* 2/945 (pow x 5))
40.0ms	(* (* x x) 1/45)
140.0ms	(* x (+ (* (* x x) 1/45) 1/3))

simplify1.2s

Counts

93 → 93

Iterations

Iter	Nodes
done	2028
3	2028
2	1205
1	383
0	134

prune684.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite284.0ms

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:

27.0ms	(* (* x x) 1/45)
76.0ms	(* (* (* x x) 1/45) 1/3)
24.0ms	(* (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125)) x)
155.0ms	(/ (* (+ 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))))

series654.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (* x x) 1/45)
27.0ms	(* (* (* x x) 1/45) 1/3)
207.0ms	(* (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125)) x)
379.0ms	(/ (* (+ 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))))

simplify1.1s

Counts

101 → 101

Iterations

Iter	Nodes
done	2001
2	2001
1	485
0	162

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) (* x x))
0.2b	(* 1/135 (* x x))
0.4b	(/ (+ (* (* (* x x) (* x x)) 1/2025) (- 1/9 (* 1/135 (* 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))

rewrite504.0ms

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:

21.0ms	(* (* x x) (* x x))
13.0ms	(* 1/135 (* x x))
250.0ms	(/ (+ (* (* (* x x) (* x x)) 1/2025) (- 1/9 (* 1/135 (* x x)))) x)
214.0ms	(/ (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125)) (/ (+ (* (* (* x x) (* x x)) 1/2025) (- 1/9 (* 1/135 (* x x)))) x))

series576.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (* x x) (* x x))
44.0ms	(* 1/135 (* x x))
96.0ms	(/ (+ (* (* (* x x) (* x x)) 1/2025) (- 1/9 (* 1/135 (* x x)))) x)
371.0ms	(/ (+ 1/27 (* (* (* (* x x) x) (* (* x x) x)) 1/91125)) (/ (+ (* (* (* x x) (* x x)) 1/2025) (- 1/9 (* 1/135 (* x x)))) x))

simplify1.3s

Counts

200 → 200

Iterations

Iter	Nodes
done	2001
2	2001
1	735
0	259

prune2.7s

Pruning

4 alts after pruning (2 fresh and 2 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

simplify8.0ms

Iterations

Iter	Nodes
done	31
1	31
0	23

end0.0ms

sample16.5s

Algorithm

intervals

Results

9.5s	3190×	body	2560	valid
4.8s	2568×	body	1280	valid
1.1s	1249×	body	640	valid
395.0ms	628×	body	320	valid
312.0ms	8000×	pre	80	true
164.0ms	322×	body	160	valid
31.0ms	43×	body	80	valid