Details

sample64.0ms

Algorithm

intervals

Results

14.0ms	309×	body	80	nan
14.0ms	59×	body	1280	valid
9.0ms	51×	body	640	valid
6.0ms	117×	body	80	valid
3.0ms	23×	body	320	valid
1.0ms	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: 33.2b

localize6.0ms

Local error

Found 1 expressions with local error:

2.4b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite71.0ms

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:

67.0ms

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

series127.0ms

Counts

1 → 3

Calls

1 calls:

127.0ms

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

simplify2.5s

Counts

73 → 73

Iterations

Useful iterations: done (2.5s)

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

prune154.0ms

Pruning

3 alts after pruning (3 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)))
0.2b	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

rewrite123.0ms

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:

40.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
78.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

series266.0ms

Counts

2 → 6

Calls

2 calls:

94.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
172.0ms	(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))

simplify2.1s

Counts

71 → 71

Iterations

Useful iterations: done (2.1s)

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

prune242.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(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:

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

series1.3s

Counts

4 → 12

Calls

4 calls:

309.0ms	(* (cbrt x) (cbrt x))
355.0ms	(cbrt x)
316.0ms	(cbrt x)
287.0ms	(cbrt x)

simplify5.8s

Counts

93 → 93

Iterations

Useful iterations: done (5.8s)

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

prune433.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
0.8b	(pow (sqrt (cbrt x)) 3)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-prod`
9×	`unpow-prod-down` `cube-prod`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-pow` `pow1/3` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`sqrt-pow1`
1×	`cube-mult` `pow-to-exp` `pow1/2` `unpow3` `pow-exp` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
5.0ms	(pow (sqrt (cbrt x)) 3)

series1.4s

Counts

4 → 12

Calls

4 calls:

338.0ms	(cbrt x)
304.0ms	(cbrt x)
325.0ms	(cbrt x)
419.0ms	(pow (sqrt (cbrt x)) 3)

simplify4.5s

Counts

92 → 92

Iterations

Useful iterations: 3 (1.9s)

Iter	Nodes	Cost
0	75	592
1	168	480
2	443	454
3	4022	434
done	5000	434

prune277.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes39.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample1.2s

Algorithm

intervals

Results

334.0ms	8101×	body	80	nan
235.0ms	1721×	body	1280	valid
183.0ms	4137×	body	80	valid
149.0ms	1224×	body	640	valid
42.0ms	610×	body	320	valid
15.0ms	308×	body	160	valid