Details

sample30.0ms

Algorithm

intervals

Results

6.0ms	49×	body	1280	valid
5.0ms	269×	body	80	nan
4.0ms	43×	body	640	valid
3.0ms	143×	body	80	valid
1.0ms	11×	body	320	valid
0.0ms	10×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	6
1	14	6
2	14	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
2.4b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
69×	`times-frac`
50×	`sqrt-prod`
42×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip-+`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `frac-sub` `flip--`

Counts

4 → 133

Calls

4 calls:

7.0ms	(sqrt (+ x 1.0))
11.0ms	(/ 1.0 (sqrt (+ x 1.0)))
6.0ms	(/ 1.0 (sqrt x))
59.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series258.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (+ x 1.0))
65.0ms	(/ 1.0 (sqrt (+ x 1.0)))
40.0ms	(/ 1.0 (sqrt x))
121.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify44.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	443	1097
1	1434	1038
2	5001	992

prune297.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
2.4b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`sqrt-prod`
20×	`*-un-lft-identity`
18×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `add-cube-cbrt`
7×	`associate-r`
6×	`sqrt-div` `associate-r/` `associate-l*` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `div-exp` `difference-of-squares` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `distribute-lft-out` `distribute-lft-out--`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `times-frac` `sqrt-unprod` `diff-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 93

Calls

4 calls:

6.0ms	(sqrt (+ x 1.0))
54.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
25.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
38.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series400.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(sqrt (+ x 1.0))
246.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
57.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
70.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify62.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	511	883
1	2553	762
2	5001	749

prune247.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
1.5b	(+ x (- 1.0 x))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log` `add-cbrt-cube`
22×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`sqrt-prod`
11×	`add-log-exp`
8×	`pow1` `cbrt-undiv` `add-cube-cbrt` `div-exp` `prod-exp` `cbrt-unprod`
7×	`associate-r` `distribute-lft-out`
6×	`associate-l`
5×	`associate-*r/`
4×	`flip3-+` `sqrt-div` `flip-+` `unswap-sqr`
3×	`pow-prod-down` `sum-log`
2×	`+-commutative` `associate-+r+` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`associate-+r-` `sub-neg` `frac-2neg` `times-frac` `sqrt-unprod` `diff-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l/` `associate-/l*` `distribute-lft-out--`

Counts

4 → 92

Calls

4 calls:

28.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
52.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
27.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
14.0ms	(+ x (- 1.0 x))

series577.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
467.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
54.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(+ x (- 1.0 x))

simplify87.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	643	996
1	3509	806
2	5002	794

prune245.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
0.2b	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
31×	`sqrt-prod`
29×	`add-exp-log` `add-cbrt-cube`
27×	`add-sqr-sqrt`
21×	`distribute-lft-out`
19×	`add-cube-cbrt` `times-frac`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-/r*`
6×	`associate-l` `add-log-exp`
5×	`associate-*r/`
4×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `associate-/l*` `unswap-sqr`
3×	`pow-prod-down`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv`
1×	`+-commutative` `sqrt-unprod` `sum-log` `*-commutative` `associate-/l/`

Counts

4 → 116

Calls

4 calls:

28.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
41.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
24.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
44.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

series724.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
131.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
58.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
471.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

simplify82.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	671	1264
1	3525	1071
2	5002	1043

prune259.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

regimes51.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	10
1	14	10

end0.0ms

sample835.0ms

Algorithm

intervals

Results

161.0ms	7894×	body	80	nan
160.0ms	1779×	body	640	valid
134.0ms	1149×	body	1280	valid
100.0ms	4119×	body	80	valid
41.0ms	612×	body	320	valid
15.0ms	341×	body	160	valid