Details

sample26.0ms

Algorithm

intervals

Results

5.0ms	56×	body	1280	valid
4.0ms	245×	body	80	nan
3.0ms	49×	body	640	valid
2.0ms	111×	body	80	valid
1.0ms	28×	body	320	valid
0.0ms	12×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 34.1b

localize8.0ms

Local error

Found 1 expressions with local error:

3.2b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite33.0ms

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:

29.0ms

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

series73.0ms

Counts

1 → 3

Calls

1 calls:

73.0ms

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

simplify139.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (131.0ms)

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

prune89.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

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)))

rewrite54.0ms

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:

20.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
31.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series207.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
141.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (37.0ms)

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

prune169.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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:

2.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))
2.0ms	(cbrt (+ x 1.0))
23.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (+ x 1.0))
88.0ms	(cbrt (+ x 1.0))
88.0ms	(cbrt (+ x 1.0))
104.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))

simplify158.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (148.0ms)

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

prune381.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

70×	`cbrt-div`
68×	`cbrt-prod`
52×	`sqrt-div`
47×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
36×	`sqrt-prod`
35×	`flip3-+` `flip-+`
32×	`frac-times`
22×	`add-cube-cbrt`
17×	`associate-l`
16×	`pow1` `associate-*r/`
15×	`swap-sqr`
11×	`add-exp-log` `pow1/3` `associate-r` `unswap-sqr`
10×	`associate-*l/`
9×	`distribute-lft-out`
7×	`pow-prod-down`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `pow-plus`

Counts

4 → 163

Calls

4 calls:

28.0ms	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
3.0ms	(cbrt (sqrt (+ x 1.0)))
3.0ms	(cbrt (sqrt (+ x 1.0)))
41.0ms	(* (cbrt (+ x 1.0)) (* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0)))))

series373.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
89.0ms	(cbrt (sqrt (+ x 1.0)))
88.0ms	(cbrt (sqrt (+ x 1.0)))
106.0ms	(* (cbrt (+ x 1.0)) (* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0)))))

simplify80.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	608	2051
1	2011	1950
2	5001	1701

prune610.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes31.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	13
1	18	13
2	18	13

end0.0ms

sample691.0ms

Algorithm

intervals

Results

161.0ms	1752×	body	1280	valid
142.0ms	8078×	body	80	nan
92.0ms	1322×	body	640	valid
78.0ms	3992×	body	80	valid
33.0ms	628×	body	320	valid
11.0ms	306×	body	160	valid