Details

sample46.0ms

Algorithm

intervals

Results

10.0ms	62×	body	640	valid
9.0ms	275×	body	80	nan
6.0ms	140×	body	80	valid
5.0ms	27×	body	1280	valid
2.0ms	14×	body	320	valid
1.0ms	13×	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: 19.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
3.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite67.0ms

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))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
3.0ms	(/ 1.0 (sqrt x))
45.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series283.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ x 1.0))
76.0ms	(/ 1.0 (sqrt (+ x 1.0)))
42.0ms	(/ 1.0 (sqrt x))
134.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify45.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (34.0ms)

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

prune308.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.6b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
3.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite73.0ms

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:

4.0ms	(sqrt (+ x 1.0))
31.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
13.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
22.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series425.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ x 1.0))
265.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
57.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
73.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify66.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	511	884
1	2548	762
2	5002	749

prune259.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 17.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (+ x 1.0)) (sqrt x))
0.3b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.5b	(* (sqrt x) (sqrt x))
2.9b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
55×	`sqrt-prod`
40×	`*-un-lft-identity`
38×	`pow1`
24×	`add-cube-cbrt`
20×	`associate-l`
19×	`swap-sqr` `associate-r`
18×	`sqrt-pow1` `pow1/2`
14×	`sqrt-div`
12×	`unswap-sqr`
10×	`add-exp-log` `pow-prod-up` `add-cbrt-cube`
9×	`pow-prod-down`
7×	`flip3-+` `flip-+` `distribute-lft-out`
6×	`pow-sqr` `add-log-exp`
4×	`frac-times` `associate-*l/`
3×	`sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`
2×	`pow2` `pow-plus` `associate-*r/` `rem-square-sqrt`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`

Counts

4 → 157

Calls

4 calls:

14.0ms	(* (sqrt (+ x 1.0)) (sqrt x))
23.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
7.0ms	(* (sqrt x) (sqrt x))
12.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))

series108.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sqrt (+ x 1.0)) (sqrt x))
17.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
16.0ms	(* (sqrt x) (sqrt x))
14.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* (sqrt x) (sqrt x)))

simplify62.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	375	734
1	1736	639
2	5002	610

prune310.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (sqrt (+ x 1.0)) (sqrt x)) (+ x 1.0))
0.1b	(* (sqrt x) (+ (* (sqrt (+ x 1.0)) (sqrt x)) (+ x 1.0)))
0.3b	(* (sqrt (+ x 1.0)) (sqrt x))
0.4b	(/ (* 1.0 1.0) (* (sqrt x) (+ (* (sqrt (+ x 1.0)) (sqrt x)) (+ x 1.0))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`add-exp-log` `add-cbrt-cube`
16×	`flip3-+` `flip-+`
15×	`sqrt-prod`
14×	`sqrt-div` `associate-*l/`
13×	`-un-lft-identity` `associate-l*`
12×	`associate-*r/` `frac-add`
11×	`add-cube-cbrt`
10×	`pow1` `associate-r`
9×	`add-log-exp`
6×	`prod-exp` `associate-/r/` `cbrt-unprod` `unswap-sqr`
4×	`cbrt-undiv` `div-exp` `pow-prod-down`
3×	`sum-log` `distribute-lft-out`
2×	`sqrt-pow1` `pow1/2` `*-commutative`
1×	`+-commutative` `distribute-rgt-in` `associate-+r+` `frac-2neg` `distribute-lft-in` `times-frac` `sqrt-unprod` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 109

Calls

4 calls:

12.0ms	(+ (* (sqrt (+ x 1.0)) (sqrt x)) (+ x 1.0))
47.0ms	(* (sqrt x) (+ (* (sqrt (+ x 1.0)) (sqrt x)) (+ x 1.0)))
16.0ms	(* (sqrt (+ x 1.0)) (sqrt x))
18.0ms	(/ (* 1.0 1.0) (* (sqrt x) (+ (* (sqrt (+ x 1.0)) (sqrt x)) (+ x 1.0))))

series439.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(+ (* (sqrt (+ x 1.0)) (sqrt x)) (+ x 1.0))
135.0ms	(* (sqrt x) (+ (* (sqrt (+ x 1.0)) (sqrt x)) (+ x 1.0)))
56.0ms	(* (sqrt (+ x 1.0)) (sqrt x))
188.0ms	(/ (* 1.0 1.0) (* (sqrt x) (+ (* (sqrt (+ x 1.0)) (sqrt x)) (+ x 1.0))))

simplify87.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	696	1315
1	3457	1139
2	5001	1135

prune282.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes49.0ms

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	13	10
1	13	10

end0.0ms

sample855.0ms

Algorithm

intervals

Results

180.0ms	1782×	body	640	valid
171.0ms	7968×	body	80	nan
152.0ms	1174×	body	1280	valid
111.0ms	4128×	body	80	valid
45.0ms	607×	body	320	valid
15.0ms	309×	body	160	valid