Details

sample33.0ms

Algorithm

intervals

Results

11.0ms	276×	body	80	valid
8.0ms	275×	body	80	nan

simplify101.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	7
1	65	7
2	182	7
3	338	7
4	488	7
5	757	7
6	1166	7
7	1729	7
8	2793	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)))
0.3b	(* 3.0 (sqrt x))
0.3b	(/ 1.0 (* x 9.0))
0.3b	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
16×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
12×	`associate-r`
11×	`pow1`
10×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`associate-l` `pow-prod-down` `sqrt-prod`
3×	`distribute-rgt-in` `distribute-lft-in` `times-frac` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `associate-r/` `div-exp` `associate--l+` `-commutative` `distribute-lft-out` `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 → 84

Calls

4 calls:

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

series142.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ y (/ 1.0 (* x 9.0)))
39.0ms	(* 3.0 (sqrt x))
15.0ms	(/ 1.0 (* x 9.0))
64.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	456	548
1	2172	486
2	5002	484

prune180.0ms

Filtered

96 candidates to 62 candidates (64.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	86	10	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	10	97

Merged error: 0.0b

Counts

97 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

5.0ms	(+ y (/ 1.0 (* x 9.0)))
11.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
14.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
4.0ms	(/ 1.0 (* x 9.0))

series162.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ y (/ 1.0 (* x 9.0)))
55.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
63.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
15.0ms	(/ 1.0 (* x 9.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	427	770
1	1858	694
2	5002	694

prune180.0ms

Filtered

110 candidates to 67 candidates (60.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	111	9	120

Merged error: 0.0b

Counts

120 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
57×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/l*`
12×	`associate-r`
11×	`pow1`
6×	`add-log-exp`
5×	`div-inv`
4×	`associate-l` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
3×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-/r*`
2×	`sub-neg` `associate-r/` `associate--l+` `-commutative` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `flip3--` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip--` `flip-+` `associate-/l/` `difference-of-squares`

Counts

4 → 133

Calls

4 calls:

13.0ms	(+ y (/ (/ 1.0 x) 9.0))
6.0ms	(/ (/ 1.0 x) 9.0)
5.0ms	(* 3.0 (sqrt x))
21.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))

series150.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ y (/ (/ 1.0 x) 9.0))
16.0ms	(/ (/ 1.0 x) 9.0)
42.0ms	(* 3.0 (sqrt x))
66.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))

simplify75.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	679	914
1	2999	846
2	5001	846

prune282.0ms

Filtered

145 candidates to 105 candidates (72.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	145	9	154

Merged error: 0.0b

Counts

154 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
0.3b	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))))
0.3b	(/ 1.0 (* x 9.0))
0.4b	(* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

51×	`distribute-rgt-in` `distribute-lft-in`
37×	`add-exp-log`
32×	`pow1`
25×	`add-cbrt-cube`
20×	`prod-exp` `cbrt-unprod`
19×	`pow-prod-down`
17×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`sub-neg` `associate--l+`
13×	`associate-l`
12×	`associate-*r/`
11×	`add-cube-cbrt`
8×	`associate-r`
4×	`sqrt-prod` `add-log-exp`
3×	`cbrt-prod` `flip3--` `times-frac` `-commutative` `flip--` `associate-/l`
2×	`cbrt-undiv` `div-exp` `distribute-lft-out--` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `distribute-lft-out` `difference-of-squares`

Counts

4 → 143

Calls

4 calls:

12.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
19.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))))
4.0ms	(/ 1.0 (* x 9.0))
13.0ms	(* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
95.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))))
16.0ms	(/ 1.0 (* x 9.0))
132.0ms	(* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

simplify75.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	681	1766
1	2737	1381
2	5003	1319

prune215.0ms

Filtered

155 candidates to 75 candidates (48.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	153	2	155
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	154	10	164

Merged error: 0b

Counts

164 → 10

regimes115.0ms

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

sample846.0ms

Algorithm

intervals

Results

285.0ms	8502×	body	80	valid
271.0ms	8417×	body	80	nan