Details

sample30.0ms

Algorithm

intervals

Results

8.0ms	55×	body	1280	valid
5.0ms	251×	body	80	nan
3.0ms	38×	body	640	valid
3.0ms	135×	body	80	valid
1.0ms	16×	body	320	valid
0.0ms	12×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite54.0ms

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:

51.0ms

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

series61.0ms

Counts

1 → 3

Calls

1 calls:

61.0ms

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

simplify139.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (130.0ms)

Iter	Nodes	Cost
0	252	1065
1	759	733
2	4363	623
3	5001	593

prune136.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
32×	`distribute-lft-out`
28×	`sqrt-prod`
24×	`times-frac`
16×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`fma-def`
6×	`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 → 75

Calls

2 calls:

33.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
56.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series186.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
128.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	356	693
1	1446	627
2	5001	586

prune232.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.2b	(cbrt (+ x 1.0))
0.2b	(cbrt (+ x 1.0))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

4.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))
38.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(cbrt (+ x 1.0))
79.0ms	(cbrt (+ x 1.0))
80.0ms	(cbrt (+ x 1.0))
94.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

simplify163.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (153.0ms)

Iter	Nodes	Cost
0	321	818
1	1071	769
2	4756	694
3	5001	692

prune586.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b	(cbrt (sqrt (+ x 1.0)))
0.3b	(cbrt (sqrt (+ x 1.0)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

86×	`cbrt-prod`
60×	`*-un-lft-identity`
58×	`add-sqr-sqrt`
36×	`sqrt-prod`
28×	`add-cube-cbrt` `cbrt-div`
23×	`swap-sqr`
18×	`pow1`
17×	`associate-r` `associate-l`
16×	`sqrt-div`
14×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
13×	`unswap-sqr`
8×	`add-exp-log` `frac-times`
4×	`expm1-log1p-u` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 164

Calls

4 calls:

43.0ms	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
39.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
5.0ms	(cbrt (sqrt (+ x 1.0)))
5.0ms	(cbrt (sqrt (+ x 1.0)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
97.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
83.0ms	(cbrt (sqrt (+ x 1.0)))
82.0ms	(cbrt (sqrt (+ x 1.0)))

simplify66.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	505	1591
1	1801	1499
2	5002	1374

prune924.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes47.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	16	6

end0.0ms

sample782.0ms

Algorithm

intervals

Results

175.0ms	8056×	body	80	nan
173.0ms	1742×	body	1280	valid
97.0ms	4130×	body	80	valid
95.0ms	1232×	body	640	valid
35.0ms	586×	body	320	valid
12.0ms	310×	body	160	valid