Details

sample34.0ms

Algorithm

intervals

Results

11.0ms	271×	body	80	valid
9.0ms	292×	body	80	nan

simplify125.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 0.5b

Counts

2 → 1

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

rewrite32.0ms

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

series146.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ y (/ 1.0 (* x 9.0)))
18.0ms	(/ 1.0 (* x 9.0))
60.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
42.0ms	(* 3.0 (sqrt x))

simplify74.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (62.0ms)

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

prune229.0ms

Filtered

131 candidates to 75 candidates (57.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	119	12	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	12	132

Merged error: 0.0b

Counts

132 → 12

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

rewrite55.0ms

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

series149.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ y (/ (/ 1.0 x) 9.0))
16.0ms	(/ (/ 1.0 x) 9.0)
66.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
37.0ms	(* 3.0 (sqrt x))

simplify96.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	818	1496
1	3749	1238
2	5003	1234

prune335.0ms

Filtered

180 candidates to 118 candidates (65.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	176	4	180
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	182	10	192

Merged error: 0.0b

Counts

192 → 10

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

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 230

Calls

4 calls:

13.0ms	(+ y (/ (/ 1.0 x) 9.0))
6.0ms	(/ (/ 1.0 x) 9.0)
20.0ms	(* (sqrt x) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
27.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0)))

series167.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ y (/ (/ 1.0 x) 9.0))
17.0ms	(/ (/ 1.0 x) 9.0)
60.0ms	(* (sqrt x) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0))
65.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ (/ 1.0 x) 9.0)) 1.0)))

simplify113.0ms

Algorithm

egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	856	2770
1	3565	2116
2	5001	2110

prune344.0ms

Filtered

242 candidates to 127 candidates (52.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	241	1	242
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	241	11	252

Merged error: 0.0b

Counts

252 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (sqrt x))
0.3b	(/ 1.0 (sqrt x))
0.3b	(* (/ 1 (sqrt x)) (/ (/ 1.0 (sqrt x)) 9.0))
0.3b	(* 3.0 (sqrt x))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

215×	`times-frac`
189×	`add-sqr-sqrt`
120×	`*-un-lft-identity`
112×	`add-cube-cbrt`
77×	`sqrt-prod`
76×	`associate-r`
51×	`add-exp-log`
31×	`add-cbrt-cube`
25×	`associate-l`
22×	`unswap-sqr`
21×	`div-exp`
13×	`prod-exp`
12×	`associate-/r*`
11×	`cbrt-undiv`
10×	`pow1`
7×	`cbrt-unprod` `div-inv`
6×	`associate-/l*`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip`
2×	`frac-2neg` `pow-prod-down` `clear-num` `*-commutative`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `inv-pow`

Counts

4 → 256

Calls

4 calls:

4.0ms	(/ 1 (sqrt x))
4.0ms	(/ 1.0 (sqrt x))
42.0ms	(* (/ 1 (sqrt x)) (/ (/ 1.0 (sqrt x)) 9.0))
5.0ms	(* 3.0 (sqrt x))

series137.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ 1 (sqrt x))
36.0ms	(/ 1.0 (sqrt x))
27.0ms	(* (/ 1 (sqrt x)) (/ (/ 1.0 (sqrt x)) 9.0))
43.0ms	(* 3.0 (sqrt x))

simplify45.0ms

Algorithm

egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1068	2040
1	5002	1762

prune457.0ms

Filtered

268 candidates to 164 candidates (61.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	268	11	279

Merged error: 0.0b

Counts

279 → 11

regimes120.0ms

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	15	7
1	15	7

end0.0ms

sample811.0ms

Algorithm

intervals

Results

269.0ms	8564×	body	80	valid
260.0ms	8323×	body	80	nan