Details

sample27.0ms

Algorithm

intervals

Results

5.0ms	58×	body	1280	valid
4.0ms	226×	body	80	nan
3.0ms	42×	body	640	valid
3.0ms	123×	body	80	valid
1.0ms	23×	body	320	valid
0.0ms	10×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 31.7b

localize6.0ms

Local error

Found 1 expressions with local error:

3.0b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite31.0ms

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:

27.0ms

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

series71.0ms

Counts

1 → 3

Calls

1 calls:

71.0ms

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

simplify946.0ms

Counts

73 → 73

Iterations

Useful iterations: done (943.0ms)

Iter	Nodes	Cost
0	117	1805
1	248	1268
2	595	970
3	1902	800
done	5001	793

prune100.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (sqrt x) (sqrt (+ x 1.0)))
0.2b	(/ (+ 0 1.0) (+ (sqrt x) (sqrt (+ x 1.0))))

rewrite42.0ms

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:

13.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
26.0ms	(/ (+ 0 1.0) (+ (sqrt x) (sqrt (+ x 1.0))))

series199.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(+ (sqrt x) (sqrt (+ x 1.0)))
133.0ms	(/ (+ 0 1.0) (+ (sqrt x) (sqrt (+ x 1.0))))

simplify1.4s

Counts

80 → 80

Iterations

Useful iterations: 3 (719.0ms)

Iter	Nodes	Cost
0	143	1265
1	358	1018
2	969	937
3	3477	922
done	5000	922

prune187.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (sqrt (sqrt x)) (sqrt (sqrt x)) (sqrt (+ x 1.0)))
0.1b	(sqrt (sqrt x))
0.1b	(sqrt (sqrt x))
0.2b	(/ (+ 0 1.0) (fma (sqrt (sqrt x)) (sqrt (sqrt x)) (sqrt (+ x 1.0))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
20×	`sqrt-prod`
17×	`add-cube-cbrt`
12×	`times-frac`
8×	`pow1` `sqrt-pow1`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `rem-sqrt-square` `pow1/2` `log1p-expm1-u` `distribute-lft-out` `associate-/l*` `add-log-exp`
3×	`associate-/r*`
2×	`associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `fma-udef` `div-inv`

Counts

4 → 87

Calls

4 calls:

0.0ms	(fma (sqrt (sqrt x)) (sqrt (sqrt x)) (sqrt (+ x 1.0)))
1.0ms	(sqrt (sqrt x))
5.0ms	(sqrt (sqrt x))
8.0ms	(/ (+ 0 1.0) (fma (sqrt (sqrt x)) (sqrt (sqrt x)) (sqrt (+ x 1.0))))

series625.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(fma (sqrt (sqrt x)) (sqrt (sqrt x)) (sqrt (+ x 1.0)))
139.0ms	(sqrt (sqrt x))
138.0ms	(sqrt (sqrt x))
211.0ms	(/ (+ 0 1.0) (fma (sqrt (sqrt x)) (sqrt (sqrt x)) (sqrt (+ x 1.0))))

simplify693.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (270.0ms)

Iter	Nodes	Cost
0	209	1590
1	514	1156
2	1682	1033
done	5000	1033

prune282.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 0 1.0) (fma (* (sqrt (fabs (cbrt x))) (sqrt (sqrt (cbrt x)))) (sqrt (sqrt x)) (sqrt (+ x 1.0))))
0.3b	(* (sqrt (fabs (cbrt x))) (sqrt (sqrt (cbrt x))))
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
32×	`sqrt-prod`
29×	`*-un-lft-identity`
21×	`add-cube-cbrt`
12×	`times-frac` `associate-r`
11×	`cbrt-prod`
8×	`pow1` `add-exp-log` `add-cbrt-cube` `unswap-sqr`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out` `associate-/l*` `add-log-exp`
3×	`pow-prod-down` `associate-/r*`
2×	`sqrt-pow1` `pow1/2` `pow1/3` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `flip-+` `div-inv`

Counts

4 → 103

Calls

4 calls:

8.0ms	(/ (+ 0 1.0) (fma (* (sqrt (fabs (cbrt x))) (sqrt (sqrt (cbrt x)))) (sqrt (sqrt x)) (sqrt (+ x 1.0))))
11.0ms	(* (sqrt (fabs (cbrt x))) (sqrt (sqrt (cbrt x))))
0.0ms	(cbrt x)
1.0ms	(cbrt x)

series910.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(/ (+ 0 1.0) (fma (* (sqrt (fabs (cbrt x))) (sqrt (sqrt (cbrt x)))) (sqrt (sqrt x)) (sqrt (+ x 1.0))))
283.0ms	(* (sqrt (fabs (cbrt x))) (sqrt (sqrt (cbrt x))))
184.0ms	(cbrt x)
176.0ms	(cbrt x)

simplify819.0ms

Counts

115 → 115

Iterations

Useful iterations: done (815.0ms)

Iter	Nodes	Cost
0	280	2515
1	664	2279
2	2245	2140
done	5001	2137

prune484.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes37.0ms

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: 1 (1.0ms)

Iter	Nodes	Cost
0	16	21
1	19	19
done	19	19

end0.0ms

sample744.0ms

Algorithm

intervals

Results

171.0ms	1746×	body	1280	valid
153.0ms	7984×	body	80	nan
98.0ms	1276×	body	640	valid
84.0ms	4049×	body	80	valid
34.0ms	615×	body	320	valid
12.0ms	314×	body	160	valid