Details

sample121.0ms

Algorithm

intervals

Results

57.0ms	70×	body	1280	valid
24.0ms	51×	body	640	valid
11.0ms	20×	body	2560	valid
6.0ms	23×	body	320	valid
5.0ms	80×	body	80	valid
2.0ms	12×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 50.2b

localize22.0ms

Local error

Found 3 expressions with local error:

0.9b	(+ x (sqrt (+ (* x x) 1.0)))
3.8b	(log (+ x (sqrt (+ (* x x) 1.0))))
13.6b	(sqrt (+ (* x x) 1.0))

rewrite52.0ms

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:

19.0ms	(+ x (sqrt (+ (* x x) 1.0)))
21.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
10.0ms	(sqrt (+ (* x x) 1.0))

series454.0ms

Counts

3 → 9

Calls

3 calls:

110.0ms	(+ x (sqrt (+ (* x x) 1.0)))
278.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
66.0ms	(sqrt (+ (* x x) 1.0))

simplify1.3s

Counts

61 → 61

Iterations

Useful iterations: done (1.3s)

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

prune335.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

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:

0.0ms

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

series220.0ms

Counts

1 → 3

Calls

1 calls:

219.0ms

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

simplify1.1s

Counts

13 → 13

Iterations

Useful iterations: done (1.1s)

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

prune59.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot x (sqrt 1.0))
0.9b	(+ x (hypot x (sqrt 1.0)))
3.8b	(log (+ x (hypot x (sqrt 1.0))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 44

Calls

3 calls:

1.0ms	(hypot x (sqrt 1.0))
12.0ms	(+ x (hypot x (sqrt 1.0)))
10.0ms	(log (+ x (hypot x (sqrt 1.0))))

series775.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms	(hypot x (sqrt 1.0))
217.0ms	(+ x (hypot x (sqrt 1.0)))
423.0ms	(log (+ x (hypot x (sqrt 1.0))))

simplify1.1s

Counts

53 → 53

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	117	642
1	273	580
2	1054	542
done	5000	538

prune189.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ x (hypot x (sqrt 1.0)))
0.9b	(+ x (hypot x (sqrt 1.0)))
3.8b	(log (sqrt (+ x (hypot x (sqrt 1.0)))))
3.8b	(log (sqrt (+ x (hypot x (sqrt 1.0)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

9.0ms	(+ x (hypot x (sqrt 1.0)))
6.0ms	(+ x (hypot x (sqrt 1.0)))
6.0ms	(log (sqrt (+ x (hypot x (sqrt 1.0)))))
6.0ms	(log (sqrt (+ x (hypot x (sqrt 1.0)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

175.0ms	(+ x (hypot x (sqrt 1.0)))
157.0ms	(+ x (hypot x (sqrt 1.0)))
465.0ms	(log (sqrt (+ x (hypot x (sqrt 1.0)))))
377.0ms	(log (sqrt (+ x (hypot x (sqrt 1.0)))))

simplify724.0ms

Counts

90 → 90

Iterations

Useful iterations: done (721.0ms)

Iter	Nodes	Cost
0	124	1234
1	287	1164
2	1098	1034
done	5002	1030

prune385.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes36.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.7b

bsearch100.0ms

Steps

Iters	Range		Point
9	5.2366538615162886e-09	1.4124627081995123	0.0009192273826232663
7	-3.309911606533295	-0.03117879455470207	-1.016091287793054

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.7s	2340×	body	1280	valid
600.0ms	1585×	body	640	valid
397.0ms	763×	body	2560	valid
227.0ms	783×	body	320	valid
144.0ms	2109×	body	80	valid
56.0ms	420×	body	160	valid