Details

sample32.0ms

Algorithm

intervals

Results

9.0ms	302×	body	80	nan
9.0ms	274×	body	80	valid

simplify111.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	7
1	65	7
2	190	7
3	412	7
4	644	7
5	1083	7
6	1628	7
7	2273	7
8	3723	7
9	5001	7

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.4b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (/ 1.0 (* x 9.0)))
0.2b	(/ 1.0 (* x 9.0))
0.2b	(* 3.0 (sqrt x))
0.3b	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
25×	`add-cube-cbrt`
24×	`prod-diff`
16×	`add-exp-log` `add-cbrt-cube`
15×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-r`
11×	`pow1`
8×	`distribute-lft-out`
6×	`add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `sqrt-prod` `log1p-expm1-u`
3×	`fma-def` `times-frac` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `associate-r/` `div-exp` `associate--l+` `-commutative` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `flip3--` `frac-2neg` `flip3-+` `clear-num` `associate-/r*` `sum-log` `flip--` `flip-+` `div-inv` `difference-of-squares`

Counts

4 → 119

Calls

4 calls:

5.0ms	(+ y (/ 1.0 (* x 9.0)))
4.0ms	(/ 1.0 (* x 9.0))
5.0ms	(* 3.0 (sqrt x))
16.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))

series139.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ y (/ 1.0 (* x 9.0)))
15.0ms	(/ 1.0 (* x 9.0))
39.0ms	(* 3.0 (sqrt x))
60.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))

simplify75.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	594	1130
1	2890	878
2	5001	872

prune225.0ms

Filtered

131 candidates to 75 candidates (57.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	121	10	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	10	132

Merged error: 0.0b

Counts

132 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (/ 1.0 (* x 9.0)))
0.2b	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
0.2b	(/ 1.0 (* x 9.0))
0.3b	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

96×	`*-un-lft-identity`
75×	`distribute-rgt-in` `distribute-lft-in`
72×	`prod-diff`
59×	`add-sqr-sqrt`
53×	`add-cube-cbrt`
20×	`distribute-lft-out`
16×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
9×	`associate-l`
7×	`associate-r`
6×	`sub-neg` `associate-*r/` `associate--l+` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `pow-prod-down` `sqrt-prod` `log1p-expm1-u`
3×	`fma-def` `times-frac` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `*-commutative` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `clear-num` `associate-/r*` `sum-log` `flip-+` `div-inv` `difference-of-squares`

Counts

4 → 181

Calls

4 calls:

5.0ms	(+ y (/ 1.0 (* x 9.0)))
14.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
4.0ms	(/ 1.0 (* x 9.0))
12.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))

series162.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ y (/ 1.0 (* x 9.0)))
63.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
15.0ms	(/ 1.0 (* x 9.0))
59.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))

simplify83.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	633	2404
1	2665	1754
2	5002	1748

prune225.0ms

Filtered

193 candidates to 84 candidates (43.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	191	2	193
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	193	10	203

Merged error: 0b

Counts

203 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (/ (/ 1.0 x) 9.0))
0.2b	(* 3.0 (sqrt x))
0.3b	(* (* 3.0 (sqrt x)) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
0.3b	(/ (/ 1.0 x) 9.0)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

84×	`*-un-lft-identity`
75×	`times-frac`
71×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
24×	`prod-diff`
16×	`add-exp-log` `add-cbrt-cube`
15×	`distribute-rgt-in` `distribute-lft-in`
13×	`associate-/l*`
12×	`associate-r`
11×	`pow1`
8×	`distribute-lft-out`
6×	`add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod` `log1p-expm1-u`
3×	`cbrt-undiv` `fma-def` `div-exp` `associate-/r*`
2×	`sub-neg` `associate-r/` `associate--l+` `-commutative` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `flip3--` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip--` `flip-+` `associate-/l/` `difference-of-squares`

Counts

4 → 168

Calls

4 calls:

12.0ms	(+ y (/ (/ 1.0 x) 9.0))
5.0ms	(* 3.0 (sqrt x))
23.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
6.0ms	(/ (/ 1.0 x) 9.0)

series144.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ y (/ (/ 1.0 x) 9.0))
36.0ms	(* 3.0 (sqrt x))
64.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
16.0ms	(/ (/ 1.0 x) 9.0)

simplify96.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	818	1496
1	3771	1238
2	5002	1234

prune300.0ms

Filtered

180 candidates to 118 candidates (65.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	180	10	190

Merged error: 0b

Counts

190 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (* x 9.0))
0.3b	(* (* (* 3.0 (sqrt (sqrt x))) (sqrt (sqrt x))) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
0.3b	(* 3.0 (sqrt (sqrt x)))
0.3b	(* (* 3.0 (sqrt (sqrt x))) (sqrt (sqrt x)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
36×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
25×	`add-exp-log` `add-cbrt-cube`
24×	`associate-r` `prod-diff`
21×	`sqrt-prod`
20×	`pow1`
15×	`distribute-rgt-in` `distribute-lft-in`
11×	`prod-exp` `cbrt-unprod`
10×	`pow-prod-down`
7×	`distribute-lft-out`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `sub-neg` `associate-*r/` `div-exp` `associate--l+` `distribute-lft-out--`
1×	`flip3--` `frac-2neg` `clear-num` `associate-/r*` `flip--` `div-inv` `difference-of-squares`

Counts

4 → 135

Calls

4 calls:

4.0ms	(/ 1.0 (* x 9.0))
17.0ms	(* (* (* 3.0 (sqrt (sqrt x))) (sqrt (sqrt x))) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
6.0ms	(* 3.0 (sqrt (sqrt x)))
9.0ms	(* (* 3.0 (sqrt (sqrt x))) (sqrt (sqrt x)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 1.0 (* x 9.0))
65.0ms	(* (* (* 3.0 (sqrt (sqrt x))) (sqrt (sqrt x))) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
154.0ms	(* 3.0 (sqrt (sqrt x)))
40.0ms	(* (* 3.0 (sqrt (sqrt x))) (sqrt (sqrt x)))

simplify91.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	686	1655
1	3579	1067
2	5001	1053

prune218.0ms

Filtered

147 candidates to 79 candidates (53.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	148	9	157

Merged error: 0b

Counts

157 → 9

regimes101.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	7
1	16	7

end0.0ms

sample826.0ms

Algorithm

intervals

Results

287.0ms	8535×	body	80	valid
271.0ms	8645×	body	80	nan