Details

sample55.0ms

Algorithm

intervals

Results

17.0ms	54×	body	1280	valid
8.0ms	223×	body	80	nan
5.0ms	42×	body	640	valid
5.0ms	130×	body	80	valid
2.0ms	20×	body	320	valid
1.0ms	10×	body	160	valid

simplify9.0ms

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: 29.7b

localize6.0ms

Local error

Found 1 expressions with local error:

3.1b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite81.0ms

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))

series119.0ms

Counts

1 → 3

Calls

1 calls:

119.0ms

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

simplify2.7s

Counts

73 → 73

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	117	1805
1	265	1282
2	827	970
3	4251	800
done	5000	799

prune182.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 74

Calls

2 calls:

21.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
67.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

series268.0ms

Counts

2 → 6

Calls

2 calls:

97.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
171.0ms	(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

simplify971.0ms

Counts

80 → 80

Iterations

Useful iterations: done (963.0ms)

Iter	Nodes	Cost
0	143	1265
1	368	1016
2	1620	938
done	5001	931

prune274.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite19.0ms

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:

12.0ms	(* (cbrt x) (cbrt x))
2.0ms	(cbrt x)
2.0ms	(cbrt x)
2.0ms	(cbrt x)

series1.3s

Counts

4 → 12

Calls

4 calls:

331.0ms	(* (cbrt x) (cbrt x))
334.0ms	(cbrt x)
287.0ms	(cbrt x)
360.0ms	(cbrt x)

simplify1.3s

Counts

93 → 93

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	65	554
1	143	443
2	719	423
done	5000	409

prune401.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt (cbrt x))
0.6b	(cbrt (* (cbrt x) (cbrt x)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt (cbrt x))
6.0ms	(cbrt (* (cbrt x) (cbrt x)))

series1.4s

Counts

4 → 12

Calls

4 calls:

286.0ms	(cbrt x)
280.0ms	(cbrt x)
462.0ms	(cbrt (cbrt x))
373.0ms	(cbrt (* (cbrt x) (cbrt x)))

simplify796.0ms

Counts

65 → 65

Iterations

Useful iterations: 3 (254.0ms)

Iter	Nodes	Cost
0	64	368
1	119	354
2	326	302
3	1177	290
done	5000	290

prune504.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes45.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	9	11
1	12	9
2	13	9
done	13	9

end0.0ms

sample2.1s

Algorithm

intervals

Results

776.0ms	1305×	body	640	valid
429.0ms	1792×	body	1280	valid
272.0ms	7921×	body	80	nan
196.0ms	3991×	body	80	valid
57.0ms	601×	body	320	valid
23.0ms	311×	body	160	valid