Details

sample16.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	22	17
2	33	17
3	48	17
4	58	17
5	64	17
6	86	17
7	116	17
8	144	17
9	167	17
10	311	17
11	518	17
12	847	17
13	1973	17
done	5000	17

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 0.99229 (* x 0.04481))
0.0b	(- x (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))))
0.1b	(* (+ 0.99229 (* x 0.04481)) x)
14.8b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
10×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
4×	`flip3-+` `flip-+`
3×	`associate-r` `associate-l` `associate-/r` `associate-/l`
2×	`associate-*l/` `associate-/r/` `associate-/l/` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

2.0ms	(+ 0.99229 (* x 0.04481))
13.0ms	(- x (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))))
8.0ms	(* (+ 0.99229 (* x 0.04481)) x)
9.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ 0.99229 (* x 0.04481))
85.0ms	(- x (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))))
60.0ms	(* (+ 0.99229 (* x 0.04481)) x)
58.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

simplify503.0ms

Counts

89 → 89

Iterations

Useful iterations: done (500.0ms)

Iter	Nodes	Cost
0	170	1668
1	421	1584
2	1405	1472
done	5000	1468

prune205.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))))
0.2b	(/ (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))) (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))))
14.8b	(sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))
14.8b	(sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `*-un-lft-identity`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`flip3-+` `associate-/r*` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 264

Calls

4 calls:

10.0ms	(/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))))
22.0ms	(/ (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))) (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))))
3.0ms	(sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))
3.0ms	(sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

series369.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))))
58.0ms	(/ (/ (+ 2.30753 (* x 0.27061)) (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))) (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))))
76.0ms	(sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))
80.0ms	(sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

simplify1.4s

Counts

276 → 276

Iterations

Useful iterations: 2 (296.0ms)

Iter	Nodes	Cost
0	384	12269
1	928	11071
2	3298	10277
done	5000	10277

prune557.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))) (+ 2.30753 (* x 0.27061)))
0.2b	(/ (/ 1 (/ (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))) (+ 2.30753 (* x 0.27061)))) (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))))
14.8b	(sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))
14.8b	(sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

1362×	`times-frac`
627×	`add-sqr-sqrt`
625×	`add-cube-cbrt` `*-un-lft-identity`
441×	`sqrt-prod`
83×	`associate-/l*`
53×	`associate-/r/`
30×	`div-inv`
26×	`flip3-+` `flip-+`
25×	`add-exp-log`
15×	`div-exp` `add-cbrt-cube`
9×	`associate-/r*`
8×	`sqrt-div`
7×	`cbrt-undiv`
6×	`pow1`
4×	`add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `rec-exp` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `clear-num`

Counts

4 → 641

Calls

4 calls:

9.0ms	(/ (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))) (+ 2.30753 (* x 0.27061)))
40.0ms	(/ (/ 1 (/ (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))) (+ 2.30753 (* x 0.27061)))) (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))))
3.0ms	(sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))
5.0ms	(sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))) (+ 2.30753 (* x 0.27061)))
58.0ms	(/ (/ 1 (/ (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))) (+ 2.30753 (* x 0.27061)))) (sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x))))
77.0ms	(sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))
82.0ms	(sqrt (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

simplify904.0ms

Counts

653 → 653

Iterations

Useful iterations: done (861.0ms)

Iter	Nodes	Cost
0	940	35589
1	2329	31596
done	5000	30594

prune902.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ 0.99229 (* x 0.04481)) x)
0.2b	(* (* (+ 0.99229 (* x 0.04481)) x) (* (+ 0.99229 (* x 0.04481)) x))
2.7b	(/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* (+ 0.99229 (* x 0.04481)) x) (* (+ 0.99229 (* x 0.04481)) x))))
20.7b	(* (/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* (+ 0.99229 (* x 0.04481)) x) (* (+ 0.99229 (* x 0.04481)) x)))) (- 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
31×	`add-sqr-sqrt`
25×	`add-exp-log` `times-frac` `add-cbrt-cube`
24×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-l`
19×	`pow-prod-down`
17×	`associate-*l/`
11×	`prod-exp` `cbrt-unprod`
8×	`flip3-+` `flip-+`
7×	`associate-r` `difference-of-squares`
6×	`frac-times`
4×	`flip3--` `associate-r/` `associate-/r` `associate-/r/` `pow-sqr` `pow-prod-up` `flip--` `add-log-exp`
3×	`-commutative` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-plus` `div-exp` `div-inv` `associate-/l/`
1×	`pow2` `frac-2neg` `swap-sqr` `clear-num`

Counts

4 → 142

Calls

4 calls:

8.0ms	(* (+ 0.99229 (* x 0.04481)) x)
24.0ms	(* (* (+ 0.99229 (* x 0.04481)) x) (* (+ 0.99229 (* x 0.04481)) x))
11.0ms	(/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* (+ 0.99229 (* x 0.04481)) x) (* (+ 0.99229 (* x 0.04481)) x))))
26.0ms	(* (/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* (+ 0.99229 (* x 0.04481)) x) (* (+ 0.99229 (* x 0.04481)) x)))) (- 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (+ 0.99229 (* x 0.04481)) x)
41.0ms	(* (* (+ 0.99229 (* x 0.04481)) x) (* (+ 0.99229 (* x 0.04481)) x))
73.0ms	(/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* (+ 0.99229 (* x 0.04481)) x) (* (+ 0.99229 (* x 0.04481)) x))))
118.0ms	(* (/ (+ 2.30753 (* x 0.27061)) (- (* 1.0 1.0) (* (* (+ 0.99229 (* x 0.04481)) x) (* (+ 0.99229 (* x 0.04481)) x)))) (- 1.0 (* (+ 0.99229 (* x 0.04481)) x)))

simplify1.4s

Counts

154 → 154

Iterations

Useful iterations: 2 (254.0ms)

Iter	Nodes	Cost
0	265	4598
1	732	4333
2	3404	3857
done	5000	3857

prune346.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes15.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	31
1	26	31
done	26	31

end0.0ms

sample346.0ms

Algorithm

intervals

Results

254.0ms

8000×

body

valid