Details

sample57.0ms

Algorithm

intervals

Results

12.0ms	59×	body	1280	valid
10.0ms	260×	body	80	nan
7.0ms	44×	body	640	valid
5.0ms	126×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	8×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize33.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
1.6b	(- (sqrt (+ 1.0 x)) (sqrt x))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
54×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `prod-diff`
31×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `diff-log` `flip-+` `hypot-def` `flip--`

Counts

2 → 89

Calls

2 calls:

6.0ms	(sqrt (+ 1.0 x))
43.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

series109.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(sqrt (+ 1.0 x))
75.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

simplify609.0ms

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	1090
1	323
0	139

prune256.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (sqrt (+ 1.0 x)) (sqrt x))
0.0b	(sqrt (+ 1.0 x))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
33×	`distribute-lft-out`
32×	`sqrt-prod`
24×	`times-frac`
21×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
7×	`fma-def`
6×	`associate-/r*`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `hypot-def` `div-inv`

Counts

3 → 94

Calls

3 calls:

38.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
6.0ms	(sqrt (+ 1.0 x))
65.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))

series315.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
42.0ms	(sqrt (+ 1.0 x))
188.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))

simplify1.3s

Counts

103 → 103

Iterations

Iter	Nodes
done	5001
2	2041
1	439
0	173

prune495.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ 1.0 x))
0.3b	(cbrt (+ 1.0 x))
0.3b	(cbrt (+ 1.0 x))
0.3b	(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

6.0ms	(cbrt (+ 1.0 x))
5.0ms	(cbrt (+ 1.0 x))
3.0ms	(cbrt (+ 1.0 x))
29.0ms	(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))

series561.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(cbrt (+ 1.0 x))
139.0ms	(cbrt (+ 1.0 x))
129.0ms	(cbrt (+ 1.0 x))
166.0ms	(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))

simplify792.0ms

Counts

115 → 115

Iterations

Iter	Nodes
done	5001
2	1247
1	347
0	143

prune838.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ 1.0 x))
0.3b	(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))
0.3b	(cbrt (sqrt (+ x 1.0)))
0.3b	(cbrt (sqrt (+ x 1.0)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

42×	`cbrt-prod`
37×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
18×	`cbrt-div`
17×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
8×	`sqrt-prod`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `sqrt-div` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 109

Calls

4 calls:

3.0ms	(cbrt (+ 1.0 x))
40.0ms	(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))
4.0ms	(cbrt (sqrt (+ x 1.0)))
4.0ms	(cbrt (sqrt (+ x 1.0)))

series508.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(cbrt (+ 1.0 x))
154.0ms	(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))
119.0ms	(cbrt (sqrt (+ x 1.0)))
131.0ms	(cbrt (sqrt (+ x 1.0)))

simplify1.2s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
2	2078
1	498
0	216

prune947.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes79.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	13
2	13
1	12
0	9

end0.0ms

sample2.1s

Algorithm

intervals

Results

857.0ms	8020×	body	80	nan
345.0ms	1724×	body	1280	valid
219.0ms	1214×	body	640	valid
190.0ms	4115×	body	80	valid
64.0ms	622×	body	320	valid
23.0ms	325×	body	160	valid