Details

sample120.0ms

Algorithm

intervals

Results

51.0ms	69×	body	1280	valid
21.0ms	43×	body	640	valid
21.0ms	30×	body	2560	valid
7.0ms	87×	body	80	valid
6.0ms	19×	body	320	valid
2.0ms	8×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
2	11
1	11
0	7

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 49.0b

localize52.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (sqrt (+ (* x x) 1)))
2.0b	(log (+ x (sqrt (+ (* x x) 1))))
18.2b	(sqrt (+ (* x x) 1))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `add-log-exp`
4×	`log-prod` `add-exp-log`
3×	`flip3-+` `add-cbrt-cube` `sqrt-prod` `flip-+` `insert-posit16`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `rem-log-exp` `log-pow`

Counts

3 → 45

Calls

3 calls:

24.0ms	(+ x (sqrt (+ (* x x) 1)))
24.0ms	(log (+ x (sqrt (+ (* x x) 1))))
14.0ms	(sqrt (+ (* x x) 1))

series266.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(+ x (sqrt (+ (* x x) 1)))
157.0ms	(log (+ x (sqrt (+ (* x x) 1))))
44.0ms	(sqrt (+ (* x x) 1))

simplify1.8s

Counts

54 → 54

Iterations

Iter	Nodes
4	3878
3	1588
2	647
1	272
0	121

prune508.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x x) x)
0.1b	(* (* x x) x)
0.1b	(* (* (* x x) x) 1/6)
23.6b	(- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x))

rewrite424.0ms

Algorithm

rewrite-expression-head

Rules

51×	`pow1`
23×	`add-cbrt-cube` `add-exp-log`
12×	`pow-plus` `pow-prod-down` `prod-exp` `pow-prod-up` `cbrt-unprod`
9×	`add-sqr-sqrt` `associate-r` `add-log-exp`
7×	`*-un-lft-identity` `add-cube-cbrt`
4×	`pow2` `pow-sqr` `insert-posit16`
3×	`diff-log` `associate-l` `*-commutative`
2×	`sub-neg` `pow3` `associate--r+` `unswap-sqr`
1×	`flip3--` `flip--` `associate--r-`

Counts

4 → 97

Calls

4 calls:

30.0ms	(* (* x x) x)
29.0ms	(* (* x x) x)
56.0ms	(* (* (* x x) x) 1/6)
307.0ms	(- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x))

series263.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* x x) x)
65.0ms	(* (* x x) x)
69.0ms	(* (* (* x x) x) 1/6)
81.0ms	(- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x))

simplify1.9s

Counts

109 → 109

Iterations

Iter	Nodes
3	3989
2	849
1	248
0	97

prune821.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 3/40 (* x x)) 1/6)
0.1b	(* (* x x) x)
0.1b	(* (* (* x x) x) (- (* 3/40 (* x x)) 1/6))
0.2b	(* 3/40 (* x x))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

37×	`pow1`
23×	`add-cbrt-cube` `add-exp-log`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
6×	`pow-plus` `pow-prod-up` `add-log-exp`
5×	`associate-l`
4×	`insert-posit16`
3×	`sub-neg` `*-commutative`
2×	`pow2` `distribute-rgt-in` `distribute-lft-in` `flip3--` `associate-*r/` `pow-sqr` `flip--` `unswap-sqr`
1×	`diff-log` `pow3`

Counts

4 → 90

Calls

4 calls:

29.0ms	(- (* 3/40 (* x x)) 1/6)
29.0ms	(* (* x x) x)
135.0ms	(* (* (* x x) x) (- (* 3/40 (* x x)) 1/6))
27.0ms	(* 3/40 (* x x))

series328.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (* 3/40 (* x x)) 1/6)
36.0ms	(* (* x x) x)
166.0ms	(* (* (* x x) x) (- (* 3/40 (* x x)) 1/6))
50.0ms	(* 3/40 (* x x))

simplify2.1s

Counts

102 → 102

Iterations

Iter	Nodes
3	4260
2	1014
1	318
0	112

prune682.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

13.8b	(cbrt (- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x)))
23.6b	(- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x))
23.6b	(- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x))
23.6b	(- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
9×	`diff-log`
6×	`sub-neg` `associate--r+`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--`
3×	`cbrt-prod` `associate--r-`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 65

Calls

4 calls:

242.0ms	(cbrt (- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x)))
282.0ms	(- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x))
241.0ms	(- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x))
271.0ms	(- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x))

series463.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(cbrt (- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x)))
87.0ms	(- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x))
89.0ms	(- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x))
77.0ms	(- (* 3/40 (* (* x x) (* (* x x) x))) (- (* (* (* x x) x) 1/6) x))

simplify2.1s

Counts

77 → 77

Iterations

Iter	Nodes
3	4239
2	783
1	254
0	108

prune849.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes120.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.0b

bsearch107.0ms

Steps

Iters	Range		Point
9	0.08974485042074802	9369.000823706243	0.9556310302201441
8	-15521.296822102611	-0.2777104116290821	-1.0529948069434159

simplify16.0ms

Iterations

Iter	Nodes
2	40
1	40
0	31

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.9s	2374×	body	1280	valid
1.3s	1539×	body	640	valid
575.0ms	790×	body	2560	valid
247.0ms	790×	body	320	valid
169.0ms	2131×	body	80	valid
69.0ms	376×	body	160	valid