Details

sample36.0ms

Algorithm

intervals

Results

9.0ms	293×	body	80	nan
5.0ms	49×	body	640	valid
4.0ms	32×	body	1280	valid
4.0ms	141×	body	80	valid
1.0ms	18×	body	320	valid
1.0ms	16×	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: 20.3b

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))
4.4b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

1035×	`times-frac`
879×	`*-un-lft-identity`
747×	`add-sqr-sqrt`
714×	`add-cube-cbrt`
594×	`prod-diff`
566×	`sqrt-prod`
74×	`distribute-lft-out`
54×	`div-inv`
48×	`sqrt-div`
46×	`associate-/r/`
24×	`flip3-+` `flip-+`
22×	`fma-neg`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `frac-sub` `flip--` `hypot-def`

Counts

4 → 758

Calls

4 calls:

7.0ms	(sqrt (+ x 1.0))
12.0ms	(/ 1.0 (sqrt (+ x 1.0)))
6.0ms	(/ 1.0 (sqrt x))
81.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series279.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ x 1.0))
75.0ms	(/ 1.0 (sqrt (+ x 1.0)))
43.0ms	(/ 1.0 (sqrt x))
131.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify238.0ms

Algorithm

egg-herbie

Counts

770 → 770

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	1538	25021
1	4278	18390
2	5001	18355

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 19.6b

localize8.0ms

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)))
4.3b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
62×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
42×	`prod-diff`
37×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
10×	`distribute-lft-out`
9×	`pow1`
7×	`fma-neg` `associate-r`
6×	`sqrt-div` `associate-r/` `associate-l*` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `difference-of-squares` `unswap-sqr`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `pow-prod-down` `flip-+` `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` `hypot-def` `div-inv` `associate-/l*`

Counts

4 → 151

Calls

4 calls:

7.0ms	(sqrt (+ x 1.0))
84.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
24.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
49.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series412.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (+ x 1.0))
258.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
60.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
64.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify91.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	636	1811
1	2950	1369
2	5001	1271

prune338.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 18.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x (- 1.0 x)) (+ (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)))
3.6b	(+ x (- 1.0 x))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

112×	`*-un-lft-identity`
41×	`distribute-lft-out`
36×	`add-sqr-sqrt`
35×	`sqrt-prod`
31×	`times-frac`
29×	`add-exp-log` `add-cbrt-cube`
28×	`add-cube-cbrt`
11×	`associate-+r+`
9×	`cbrt-undiv` `div-exp` `prod-diff` `add-log-exp`
8×	`pow1` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
7×	`associate-r` `associate-/r*`
6×	`associate-l` `associate-/l*`
5×	`flip3-+` `associate-*r/` `flip-+`
4×	`expm1-log1p-u` `sqrt-div` `associate-/r/` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `pow-prod-down` `associate-/l/`
2×	`associate-+r-` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `sum-log` `div-inv`
1×	`+-commutative` `sub-neg` `sqrt-unprod` `diff-log` `div-sub` `*-commutative`

Counts

4 → 156

Calls

4 calls:

81.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
55.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
23.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
15.0ms	(+ x (- 1.0 x))

series666.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
468.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
59.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(+ x (- 1.0 x))

simplify104.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	799	1711
1	4236	1448
2	5001	1435

prune398.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

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

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
35×	`sqrt-prod`
29×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
22×	`distribute-lft-out`
21×	`add-cube-cbrt`
19×	`times-frac`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`fma-def` `associate-r` `associate-/r*`
6×	`associate-l` `add-log-exp`
5×	`associate-*r/`
4×	`expm1-log1p-u` `flip3-+` `sqrt-div` `associate-/r/` `flip-+` `log1p-expm1-u` `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 → 131

Calls

4 calls:

32.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
41.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
24.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
43.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

series733.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
137.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
60.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
477.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

simplify86.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	704	1320
1	3647	1120
2	5001	1050

prune306.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes96.0ms

Accuracy

0% (0.2b 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	11	9
1	11	9

end0.0ms

sample886.0ms

Algorithm

intervals

Results

172.0ms	1789×	body	640	valid
165.0ms	7890×	body	80	nan
142.0ms	1157×	body	1280	valid
109.0ms	4118×	body	80	valid
46.0ms	624×	body	320	valid
17.0ms	312×	body	160	valid