Details

sample107.0ms

Algorithm

intervals

Results

59.0ms	91×	body	1280	valid
13.0ms	37×	body	640	valid
12.0ms	27×	body	2560	valid
5.0ms	23×	body	320	valid
3.0ms	59×	body	80	valid
3.0ms	19×	body	160	valid

simplify5.0ms

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: 53.8b

localize12.0ms

Local error

Found 3 expressions with local error:

0.9b	(+ x (sqrt (+ (* x x) 1.0)))
4.2b	(log (+ x (sqrt (+ (* x x) 1.0))))
14.3b	(sqrt (+ (* x x) 1.0))

rewrite88.0ms

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:

27.0ms	(+ x (sqrt (+ (* x x) 1.0)))
43.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
15.0ms	(sqrt (+ (* x x) 1.0))

series355.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(+ x (sqrt (+ (* x x) 1.0)))
211.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
63.0ms	(sqrt (+ (* x x) 1.0))

simplify1.0s

Counts

61 → 61

Iterations

Useful iterations: done (1.0s)

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

prune266.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 1 expressions with local error:

0.0b	(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))))

series203.0ms

Counts

1 → 3

Calls

1 calls:

203.0ms

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

simplify1.0s

Counts

13 → 13

Iterations

Useful iterations: done (1.0s)

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

prune67.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot x (sqrt 1.0))
0.9b	(+ x (hypot x (sqrt 1.0)))
4.2b	(log (+ x (hypot x (sqrt 1.0))))

rewrite21.0ms

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:

0.0ms	(hypot x (sqrt 1.0))
12.0ms	(+ x (hypot x (sqrt 1.0)))
8.0ms	(log (+ x (hypot x (sqrt 1.0))))

series671.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(hypot x (sqrt 1.0))
166.0ms	(+ x (hypot x (sqrt 1.0)))
383.0ms	(log (+ x (hypot x (sqrt 1.0))))

simplify496.0ms

Counts

53 → 53

Iterations

Useful iterations: done (494.0ms)

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

prune171.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot x (sqrt 1.0))
0.3b	(* (sqrt (hypot x (sqrt 1.0))) (sqrt (hypot x (sqrt 1.0))))
4.2b	(log (+ x (* (sqrt (hypot x (sqrt 1.0))) (sqrt (hypot x (sqrt 1.0))))))
10.7b	(+ x (* (sqrt (hypot x (sqrt 1.0))) (sqrt (hypot x (sqrt 1.0)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`pow1`
18×	`sqrt-prod`
14×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
7×	`add-exp-log`
6×	`associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`log-prod` `fma-def` `pow-prod-down` `pow-sqr`
2×	`log-div` `flip3-+` `flip-+`
1×	`+-commutative` `pow2` `hypot-udef` `pow-plus` `sqrt-unprod` `rem-log-exp` `prod-exp` `sum-log` `rem-square-sqrt` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 93

Calls

4 calls:

0.0ms	(hypot x (sqrt 1.0))
13.0ms	(* (sqrt (hypot x (sqrt 1.0))) (sqrt (hypot x (sqrt 1.0))))
4.0ms	(log (+ x (* (sqrt (hypot x (sqrt 1.0))) (sqrt (hypot x (sqrt 1.0))))))
6.0ms	(+ x (* (sqrt (hypot x (sqrt 1.0))) (sqrt (hypot x (sqrt 1.0)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

110.0ms	(hypot x (sqrt 1.0))
99.0ms	(* (sqrt (hypot x (sqrt 1.0))) (sqrt (hypot x (sqrt 1.0))))
331.0ms	(log (+ x (* (sqrt (hypot x (sqrt 1.0))) (sqrt (hypot x (sqrt 1.0))))))
474.0ms	(+ x (* (sqrt (hypot x (sqrt 1.0))) (sqrt (hypot x (sqrt 1.0)))))

simplify1.1s

Counts

105 → 105

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	160	1742
1	379	1007
2	1650	923
done	5001	908

prune323.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes28.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.6b

bsearch89.0ms

Steps

Iters	Range		Point
8	5.523051691372288e-07	0.022891638200552334	0.0008065403850916961
10	-911936.9907706906	-4.3470241882695893e-07	-1.0205349568144453

simplify24.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	56
1	37	56
done	37	56

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.3s	2409×	body	1280	valid
825.0ms	1557×	body	640	valid
373.0ms	786×	body	2560	valid
159.0ms	2059×	body	80	valid
138.0ms	764×	body	320	valid
48.0ms	425×	body	160	valid