Details

sample78.0ms

Algorithm

intervals

Results

42.0ms	252×	body	80	nan
7.0ms	55×	body	1280	valid
4.0ms	45×	body	640	valid
3.0ms	125×	body	80	valid
1.0ms	18×	body	320	valid
1.0ms	13×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize9.0ms

Local error

Found 1 expressions with local error:

3.4b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

57×	`sqrt-prod`
50×	`*-un-lft-identity`
42×	`prod-diff`
37×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
8×	`distribute-lft-out`
7×	`fma-neg`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

1 → 70

Calls

1 calls:

73.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

series95.0ms

Counts

1 → 3

Calls

1 calls:

95.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

simplify2.4s

Counts

73 → 73

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	117	1805
1	254	1268
2	569	970
3	1667	800
done	5000	698

prune102.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 65

Calls

2 calls:

27.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
44.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

series277.0ms

Counts

2 → 6

Calls

2 calls:

105.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
172.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

simplify1.7s

Counts

71 → 71

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	132	983
1	313	898
2	848	818
3	2615	805
done	5001	804

prune208.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

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:

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

series1.5s

Counts

4 → 12

Calls

4 calls:

321.0ms	(* (cbrt x) (cbrt x))
610.0ms	(cbrt x)
251.0ms	(cbrt x)
282.0ms	(cbrt x)

simplify5.4s

Counts

93 → 93

Iterations

Useful iterations: done (5.4s)

Iter	Nodes	Cost
0	65	554
1	119	443
2	327	423
3	1104	405
4	4523	400
done	5001	390

prune395.0ms

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

rewrite497.0ms

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:

47.0ms	(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
76.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
69.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
261.0ms	(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

509.0ms	(sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0)))))
197.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
258.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
273.0ms	(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))

simplify1.7s

Counts

270 → 270

Iterations

Useful iterations: done (1.7s)

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

prune880.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes41.0ms

Accuracy

0% (0.2b 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	12	22
1	15	22
done	15	22

end0.0ms

sample2.1s

Algorithm

intervals

Results

559.0ms	4131×	body	80	valid
443.0ms	8150×	body	80	nan
385.0ms	1680×	body	1280	valid
175.0ms	1282×	body	640	valid
112.0ms	603×	body	320	valid
21.0ms	304×	body	160	valid