Details

sample127.0ms

Algorithm

intervals

Results

65.0ms	77×	body	1280	valid
22.0ms	53×	body	640	valid
12.0ms	25×	body	2560	valid
7.0ms	28×	body	320	valid
4.0ms	61×	body	80	valid
2.0ms	12×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.9b

localize20.0ms

Local error

Found 3 expressions with local error:

0.3b	(+ x (sqrt (+ (* x x) 1.0)))
3.5b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.2b	(sqrt (+ (* x x) 1.0))

rewrite459.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

410.0ms	(+ x (sqrt (+ (* x x) 1.0)))
29.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
17.0ms	(sqrt (+ (* x x) 1.0))

series413.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(+ x (sqrt (+ (* x x) 1.0)))
258.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
65.0ms	(sqrt (+ (* x x) 1.0))

simplify1.2s

Counts

61 → 61

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	139	813
1	342	677
2	1454	609
done	5001	597

prune433.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize32.0ms

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))))

series237.0ms

Counts

1 → 3

Calls

1 calls:

237.0ms

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

simplify1.4s

Counts

13 → 13

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	25	295
1	51	295
2	177	256
3	1271	256
done	5002	255

prune96.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 0.0625 (pow x 5))
0.2b	(/ 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))))

rewrite670.0ms

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:

13.0ms	(/ 0.0625 (pow x 5))
14.0ms	(/ 0.125 (pow x 3))
274.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
323.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series583.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ 0.0625 (pow x 5))
67.0ms	(/ 0.125 (pow x 3))
333.0ms	(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
96.0ms	(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify3.6s

Counts

420 → 420

Iterations

Useful iterations: 2 (1.7s)

Iter	Nodes	Cost
0	466	17336
1	1080	12011
2	4599	9527
done	5000	9527

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b	(+ x (hypot x (sqrt 1.0)))
3.5b	(log (+ x (hypot x (sqrt 1.0))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

9.0ms	(+ x (hypot x (sqrt 1.0)))
7.0ms	(log (+ x (hypot x (sqrt 1.0))))

series606.0ms

Counts

2 → 6

Calls

2 calls:

181.0ms	(+ x (hypot x (sqrt 1.0)))
425.0ms	(log (+ x (hypot x (sqrt 1.0))))

simplify789.0ms

Counts

40 → 40

Iterations

Useful iterations: done (787.0ms)

Iter	Nodes	Cost
0	102	509
1	243	487
2	999	433
done	5001	431

prune240.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes63.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.4b

bsearch142.0ms

Steps

Iters	Range		Point
10	2.8868360106527892e-08	453261925.93168354	0.0008623768125089599
9	-4.26929226401081	-3.26160511802404e-08	-1.0390866699268784

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	49
1	35	49
done	35	49

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.7s	2277×	body	1280	valid
1.1s	1538×	body	640	valid
537.0ms	822×	body	2560	valid
298.0ms	815×	body	320	valid
169.0ms	2158×	body	80	valid
55.0ms	390×	body	160	valid