Details

sample27.0ms

Algorithm

intervals

Results

5.0ms	63×	body	1280	valid
5.0ms	264×	body	80	nan
3.0ms	39×	body	640	valid
2.0ms	131×	body	80	valid
1.0ms	14×	body	320	valid
0.0ms	9×	body	160	valid

simplify6.0ms

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: 30.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

61×	`sqrt-prod`
54×	`*-un-lft-identity`
42×	`add-sqr-sqrt` `prod-diff`
31×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `distribute-lft-out--`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+` `hypot-def`

Counts

2 → 89

Calls

2 calls:

10.0ms	(sqrt (+ x 1.0))
50.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series101.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(sqrt (+ x 1.0))
65.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify40.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	299	1161
1	921	822
2	5001	744

prune143.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
33×	`distribute-lft-out`
32×	`sqrt-prod`
24×	`times-frac`
21×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
7×	`fma-def`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `hypot-def` `div-inv`

Counts

3 → 94

Calls

3 calls:

8.0ms	(sqrt (+ x 1.0))
34.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
58.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series234.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(sqrt (+ x 1.0))
60.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
137.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	409	789
1	1675	716
2	5001	675

prune230.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (* 1 (sqrt (+ x 1.0))) (sqrt x))
0.1b	(/ (+ 1.0 0) (+ (* 1 (sqrt (+ x 1.0))) (sqrt x)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
16×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3-+` `associate-/r` `sqrt-prod` `flip-+` `associate-/l`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `fma-def` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `hypot-def` `div-inv`

Counts

3 → 76

Calls

3 calls:

7.0ms	(sqrt (+ x 1.0))
14.0ms	(+ (* 1 (sqrt (+ x 1.0))) (sqrt x))
42.0ms	(/ (+ 1.0 0) (+ (* 1 (sqrt (+ x 1.0))) (sqrt x)))

series227.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(sqrt (+ x 1.0))
65.0ms	(+ (* 1 (sqrt (+ x 1.0))) (sqrt x))
133.0ms	(/ (+ 1.0 0) (+ (* 1 (sqrt (+ x 1.0))) (sqrt x)))

simplify58.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	429	756
1	1800	667
2	5002	651

prune224.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

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:

41.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
4.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))
4.0ms	(cbrt (+ x 1.0))

series368.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
88.0ms	(cbrt (+ x 1.0))
89.0ms	(cbrt (+ x 1.0))
91.0ms	(cbrt (+ x 1.0))

simplify150.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 3 (141.0ms)

Iter	Nodes	Cost
0	321	818
1	1064	769
2	4750	694
3	5001	688

prune379.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes29.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	7
1	22	7
2	22	7

end0.0ms

sample752.0ms

Algorithm

intervals

Results

149.0ms	1766×	body	1280	valid
147.0ms	7948×	body	80	nan
82.0ms	4094×	body	80	valid
81.0ms	1215×	body	640	valid
31.0ms	596×	body	320	valid
14.0ms	329×	body	160	valid