Details

sample37.0ms

Algorithm

intervals

Results

10.0ms	70×	body	1280	valid
7.0ms	241×	body	80	nan
4.0ms	33×	body	640	valid
3.0ms	123×	body	80	valid
2.0ms	24×	body	320	valid
0.0ms	6×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite121.0ms

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×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `hypot-def`

Counts

2 → 89

Calls

2 calls:

14.0ms	(sqrt (+ x 1.0))
101.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series120.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(sqrt (+ x 1.0))
83.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.1s

Counts

95 → 95

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	137	1993
1	301	1432
2	677	1124
3	1959	950
done	5000	846

prune119.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 84

Calls

3 calls:

8.0ms	(sqrt (+ x 1.0))
22.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
35.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

series238.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(sqrt (+ x 1.0))
65.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
139.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

simplify1.7s

Counts

93 → 93

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	158	1171
1	364	1060
2	967	972
3	2933	955
done	5000	954

prune277.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(cbrt x)
0.5b	(* (cbrt x) (cbrt x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
11.0ms	(* (cbrt x) (cbrt x))

series1.0s

Counts

4 → 12

Calls

4 calls:

257.0ms	(cbrt x)
273.0ms	(cbrt x)
210.0ms	(cbrt x)
291.0ms	(* (cbrt x) (cbrt x))

simplify4.9s

Counts

93 → 93

Iterations

Useful iterations: done (4.9s)

Iter	Nodes	Cost
0	65	554
1	119	443
2	325	423
3	1112	405
4	4532	400
done	5000	390

prune367.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
0.1b	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
0.1b	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
0.2b	(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

rewrite493.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 258

Calls

4 calls:

70.0ms	(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
64.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
52.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
287.0ms	(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

423.0ms	(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
188.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
188.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
236.0ms	(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

simplify1.6s

Counts

270 → 270

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	317	6276
1	674	4462
2	2105	4194
done	5000	4091

prune817.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes64.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.0s

Algorithm

intervals

Results

723.0ms	8200×	body	80	nan
410.0ms	1699×	body	1280	valid
259.0ms	4118×	body	80	valid
205.0ms	1186×	body	640	valid
109.0ms	687×	body	320	valid
25.0ms	310×	body	160	valid