Details

sample67.0ms

Algorithm

intervals

Results

35.0ms	77×	body	1280	valid
13.0ms	54×	body	640	valid
6.0ms	21×	body	2560	valid
3.0ms	78×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	10×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	7	9
1	10	8
done	10	8

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.7b

localize6.0ms

Local error

Found 3 expressions with local error:

0.5b	(+ (sqrt (fma x x 1.0)) x)
2.2b	(log (+ (sqrt (fma x x 1.0)) x))
15.5b	(sqrt (fma x x 1.0))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`fma-def` `sqrt-prod`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-prod`
3×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `flip3-+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow`

Counts

3 → 52

Calls

3 calls:

5.0ms	(+ (sqrt (fma x x 1.0)) x)
4.0ms	(log (+ (sqrt (fma x x 1.0)) x))
1.0ms	(sqrt (fma x x 1.0))

series310.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(+ (sqrt (fma x x 1.0)) x)
186.0ms	(log (+ (sqrt (fma x x 1.0)) x))
51.0ms	(sqrt (fma x x 1.0))

simplify1.1s

Counts

61 → 61

Iterations

Useful iterations: 3 (457.0ms)

Iter	Nodes	Cost
0	125	701
1	283	639
2	765	573
3	2710	571
done	5001	571

prune196.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma -1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

series155.0ms

Counts

1 → 3

Calls

1 calls:

155.0ms

(fma -1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify619.0ms

Counts

13 → 13

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	25	295
1	51	295
2	167	256
3	902	256
done	5001	256

prune50.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x 2 (- (/ 0.5 x) (/ 0.125 (pow x 3))))
0.0b	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.2b	(/ 0.125 (pow x 3))
10.2b	(log (fma x 2 (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

888×	`times-frac`
634×	`add-sqr-sqrt`
609×	`*-un-lft-identity`
603×	`add-cube-cbrt`
520×	`prod-diff`
131×	`unpow-prod-down` `cube-prod`
55×	`div-inv`
45×	`sqr-pow`
43×	`cube-mult` `unpow3`
13×	`fma-neg`
12×	`associate-/r*`
10×	`add-exp-log` `difference-of-squares`
6×	`add-cbrt-cube` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `div-exp` `associate-/l*`
2×	`distribute-lft-out--`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `rem-log-exp` `pow-exp` `clear-num` `log-pow` `frac-sub` `flip--` `fma-udef`

Counts

4 → 651

Calls

4 calls:

0.0ms	(fma x 2 (- (/ 0.5 x) (/ 0.125 (pow x 3))))
51.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
4.0ms	(/ 0.125 (pow x 3))
1.0ms	(log (fma x 2 (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

series351.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(fma x 2 (- (/ 0.5 x) (/ 0.125 (pow x 3))))
90.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
36.0ms	(/ 0.125 (pow x 3))
174.0ms	(log (fma x 2 (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

simplify1.4s

Counts

663 → 663

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	751	31474
1	1460	25632
2	3631	16708
done	5000	15031

prune514.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 0.0625 (pow x 5))
0.2b	(/ 0.125 (pow x 3))
12.2b	(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
18.9b	(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

rewrite840.0ms

Algorithm

rewrite-expression-head

Rules

1674×	`add-sqr-sqrt`
1602×	`times-frac`
1026×	`*-un-lft-identity`
895×	`prod-diff`
848×	`add-cube-cbrt`
522×	`associate--l+`
330×	`unpow-prod-down`
268×	`difference-of-squares`
181×	`cube-prod`
146×	`sqr-pow`
70×	`div-inv`
62×	`distribute-lft-out--`
43×	`cube-mult` `unpow3`
19×	`associate-/r*`
15×	`add-exp-log` `fma-neg`
10×	`log-prod`
9×	`add-log-exp`
8×	`frac-sub` `add-cbrt-cube`
6×	`div-exp` `associate-/l*`
5×	`pow1` `log-div`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`cbrt-undiv` `pow-to-exp` `sub-neg` `frac-2neg` `pow-exp` `clear-num`
1×	`associate--l-` `rem-log-exp` `log-pow`

Counts

4 → 1078

Calls

4 calls:

4.0ms	(/ 0.0625 (pow x 5))
4.0ms	(/ 0.125 (pow x 3))
260.0ms	(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
455.0ms	(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ 0.0625 (pow x 5))
37.0ms	(/ 0.125 (pow x 3))
192.0ms	(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
54.0ms	(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

simplify1.8s

Counts

1090 → 1090

Iterations

Useful iterations: 2 (1.0s)

Iter	Nodes	Cost
0	812	44329
1	1720	39950
2	4789	30323
done	5000	30323

prune3.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes33.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.2b

bsearch86.0ms

Steps

Iters	Range		Point
11	0.08347146558812443	3.320253512051989e+22	0.9004884393655546
9	-5.7596417613087905	-6.7357437175194845e-09	-1.03811431304858

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	55
1	34	55
done	34	55

end0.0ms

sample1.9s

Algorithm

intervals

Results

956.0ms	2308×	body	1280	valid
384.0ms	1563×	body	640	valid
220.0ms	786×	body	2560	valid
112.0ms	767×	body	320	valid
70.0ms	2171×	body	80	valid
33.0ms	405×	body	160	valid