Details

sample118.0ms

Algorithm

intervals

Results

53.0ms	63×	body	1280	valid
28.0ms	64×	body	640	valid
12.0ms	23×	body	2560	valid
6.0ms	24×	body	320	valid
5.0ms	69×	body	80	valid
2.0ms	13×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (1.0ms)

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.6b	(+ (sqrt (fma x x 1.0)) x)
3.5b	(log (+ (sqrt (fma x x 1.0)) x))
13.1b	(sqrt (fma x x 1.0))

rewrite21.0ms

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:

10.0ms	(+ (sqrt (fma x x 1.0)) x)
7.0ms	(log (+ (sqrt (fma x x 1.0)) x))
2.0ms	(sqrt (fma x x 1.0))

series442.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(+ (sqrt (fma x x 1.0)) x)
251.0ms	(log (+ (sqrt (fma x x 1.0)) x))
75.0ms	(sqrt (fma x x 1.0))

simplify1.7s

Counts

61 → 61

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	125	701
1	283	639
2	768	573
3	2364	571
done	5000	556

prune222.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 1 expressions with local error:

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

1.0ms

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

series234.0ms

Counts

1 → 3

Calls

1 calls:

234.0ms

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

simplify868.0ms

Counts

13 → 13

Iterations

Useful iterations: done (867.0ms)

Iter	Nodes	Cost
0	25	295
1	51	295
2	171	256
3	989	256
done	5000	255

prune52.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.2b	(/ 0.125 (pow x 3))
14.1b	(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

888×	`times-frac`
633×	`add-sqr-sqrt`
608×	`*-un-lft-identity`
602×	`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×	`difference-of-squares`
9×	`add-exp-log`
5×	`add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `log-prod` `div-exp` `log1p-expm1-u` `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--`

Counts

3 → 641

Calls

3 calls:

69.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
9.0ms	(/ 0.125 (pow x 3))
2.0ms	(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

series622.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(- (/ 0.5 x) (/ 0.125 (pow x 3)))
315.0ms	(/ 0.125 (pow x 3))
214.0ms	(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

simplify2.0s

Counts

650 → 650

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	742	31264
1	1570	25431
2	3269	16537
done	5000	15817

prune905.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 0.125 (pow x 3))
0.5b	(/ 0.0625 (pow x 5))
15.1b	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
19.6b	(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

rewrite523.0ms

Algorithm

rewrite-expression-head

Rules

480×	`*-un-lft-identity`
367×	`times-frac`
244×	`add-sqr-sqrt`
218×	`add-cube-cbrt`
200×	`prod-diff`
84×	`distribute-lft-out`
80×	`unpow-prod-down`
68×	`cube-prod`
40×	`fma-neg`
28×	`sqr-pow`
22×	`cube-mult` `unpow3`
19×	`associate-/r*`
15×	`add-exp-log`
11×	`log-prod`
10×	`difference-of-squares`
9×	`add-log-exp`
8×	`add-cbrt-cube` `div-inv`
6×	`div-exp` `frac-sub` `associate-/l*` `distribute-lft-out--`
5×	`pow1` `log-div`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `flip3-+` `diff-log` `frac-add` `pow-exp` `clear-num` `flip--` `flip-+`
1×	`sub-neg` `rem-log-exp` `sum-log` `log-pow` `associate--r+`

Counts

4 → 408

Calls

4 calls:

9.0ms	(/ 0.125 (pow x 3))
8.0ms	(/ 0.0625 (pow x 5))
181.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
292.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

series466.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ 0.125 (pow x 3))
97.0ms	(/ 0.0625 (pow x 5))
257.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
66.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

simplify1.8s

Counts

420 → 420

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	466	17338
1	1017	11893
2	2802	9355
done	5000	9035

prune859.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes43.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.3b

bsearch98.0ms

Steps

Iters	Range		Point
10	1.0194597579740466e-06	20796729.49276672	0.9017023301953626
8	-11.923248480236845	-0.0008047768791668974	-1.002814715336328

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	55
1	35	55
done	35	55

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.9s	2305×	body	1280	valid
552.0ms	1572×	body	640	valid
472.0ms	828×	body	2560	valid
162.0ms	771×	body	320	valid
142.0ms	2130×	body	80	valid
48.0ms	394×	body	160	valid