Details

sample105.0ms

Algorithm

intervals

Results

44.0ms	62×	body	1280	valid
24.0ms	60×	body	640	valid
12.0ms	24×	body	2560	valid
6.0ms	25×	body	320	valid
4.0ms	72×	body	80	valid
2.0ms	13×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	9	9
done	9	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) 1.0)
0.3b	(+ x (sqrt (+ (* x x) 1.0)))
3.8b	(log (+ x (sqrt (+ (* x x) 1.0))))
12.8b	(sqrt (+ (* x x) 1.0))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

9.0ms	(+ (* x x) 1.0)
21.0ms	(+ x (sqrt (+ (* x x) 1.0)))
32.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
13.0ms	(sqrt (+ (* x x) 1.0))

series427.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (* x x) 1.0)
63.0ms	(+ x (sqrt (+ (* x x) 1.0)))
243.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
66.0ms	(sqrt (+ (* x x) 1.0))

simplify1.9s

Counts

65 → 65

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	141	885
1	331	804
2	935	719
3	3071	703
done	5000	701

prune265.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.1b	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite494.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
182×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
118×	`add-cube-cbrt` `*-un-lft-identity`
80×	`sqrt-prod`
40×	`sqr-pow`
30×	`cube-mult` `unpow3`
25×	`add-exp-log` `unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
4×	`pow1`
3×	`associate-r/` `associate-l*`
2×	`diff-log` `frac-sub` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `flip-+` `div-inv`

Counts

2 → 286

Calls

2 calls:

292.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
162.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series461.0ms

Counts

2 → 6

Calls

2 calls:

252.0ms	(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
208.0ms	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify1.3s

Counts

292 → 292

Iterations

Useful iterations: 2 (519.0ms)

Iter	Nodes	Cost
0	336	4436
1	727	3364
2	2594	2955
done	5000	2955

prune567.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.0b	(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
0.1b	(/ 0.125 (pow x 3))
11.2b	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
51×	`times-frac`
30×	`add-cube-cbrt`
15×	`add-log-exp`
14×	`unpow-prod-down` `cube-prod`
12×	`associate-/r*`
10×	`add-exp-log` `distribute-lft-out` `difference-of-squares`
6×	`log-prod` `add-cbrt-cube` `sqr-pow`
5×	`pow1` `sum-log`
4×	`cube-mult` `unpow3` `distribute-lft-out--`
3×	`div-exp` `associate-/l*`
2×	`associate-+r-` `log-div` `flip3-+` `diff-log` `flip-+`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `associate-+r+` `flip3--` `frac-2neg` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `frac-sub` `flip--` `div-inv`

Counts

4 → 125

Calls

4 calls:

76.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
579.0ms	(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
9.0ms	(/ 0.125 (pow x 3))
515.0ms	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

series485.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
63.0ms	(+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))
42.0ms	(/ 0.125 (pow x 3))
253.0ms	(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

simplify1.0s

Counts

137 → 137

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	225	2109
1	473	1903
2	1354	1761
done	5000	1751

prune389.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 0.0625 (pow x 5))
0.1b	(/ 0.125 (pow x 3))
12.9b	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
18.7b	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite331.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
71×	`times-frac`
68×	`*-un-lft-identity`
46×	`add-cube-cbrt`
26×	`unpow-prod-down`
19×	`associate-/r*`
15×	`add-exp-log`
14×	`cube-prod`
11×	`log-prod`
10×	`difference-of-squares` `sqr-pow`
9×	`add-log-exp`
8×	`add-cbrt-cube`
6×	`div-exp` `frac-sub` `associate-/l*` `distribute-lft-out--`
5×	`pow1` `log-div`
4×	`cube-mult` `unpow3` `distribute-lft-out`
2×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `flip3-+` `diff-log` `frac-add` `pow-exp` `clear-num` `flip--` `flip-+` `div-inv`
1×	`sub-neg` `rem-log-exp` `sum-log` `log-pow` `associate--r+`

Counts

4 → 160

Calls

4 calls:

8.0ms	(/ 0.0625 (pow x 5))
11.0ms	(/ 0.125 (pow x 3))
135.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
170.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series485.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ 0.0625 (pow x 5))
50.0ms	(/ 0.125 (pow x 3))
280.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
83.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify1.2s

Counts

172 → 172

Iterations

Useful iterations: 2 (475.0ms)

Iter	Nodes	Cost
0	318	2936
1	678	2663
2	2083	2515
done	5001	2515

prune608.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes33.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.0b

bsearch92.0ms

Steps

Iters	Range		Point
10	1.5244367550608482e-07	9556.682540875734	0.8981400227354687
9	-1501.2167507114543	-0.006495210018506858	-1.017049376431383

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	57
1	39	57
done	39	57

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.5s	2224×	body	1280	valid
657.0ms	1649×	body	640	valid
340.0ms	836×	body	2560	valid
196.0ms	820×	body	320	valid
166.0ms	2075×	body	80	valid
45.0ms	396×	body	160	valid