Details

sample29.0ms

Algorithm

intervals

Results

9.0ms	275×	body	80	valid
7.0ms	243×	body	80	nan

simplify118.0ms

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: 0.4b

Counts

2 → 1

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))
0.3b	(* 3.0 (sqrt x))
0.5b	(/ 1.0 (* x 9.0))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 183

Calls

4 calls:

13.0ms	(+ y (/ 1.0 (* x 9.0)))
25.0ms	(* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
5.0ms	(* 3.0 (sqrt x))
7.0ms	(/ 1.0 (* x 9.0))

series145.0ms

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))
37.0ms	(* 3.0 (sqrt x))
20.0ms	(/ 1.0 (* x 9.0))

simplify109.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	784	1575
1	3942	1323
2	5001	1319

prune397.0ms

Filtered

195 candidates to 124 candidates (63.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	185	10	195
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	186	10	196

Merged error: 0.0b

Counts

196 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (/ 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)))
0.5b	(/ 1.0 (* x 9.0))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 252

Calls

4 calls:

13.0ms	(+ y (/ 1.0 (* x 9.0)))
21.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
32.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
7.0ms	(/ 1.0 (* x 9.0))

series166.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ y (/ 1.0 (* x 9.0)))
59.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
65.0ms	(* 3.0 (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
16.0ms	(/ 1.0 (* x 9.0))

simplify123.0ms

Algorithm

egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	853	2873
1	4221	2223
2	5002	2217

prune403.0ms

Filtered

264 candidates to 133 candidates (50.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	262	2	264
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	265	9	274

Merged error: 0b

Counts

274 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 3.0 (sqrt x))
0.3b	(* (sqrt x) (sqrt 9.0))
0.3b	(* (sqrt x) (sqrt 9.0))
0.4b	(/ (/ 1.0 (* (sqrt x) (sqrt 9.0))) (* (sqrt x) (sqrt 9.0)))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

2793×	`times-frac`
2275×	`add-sqr-sqrt`
1374×	`sqrt-prod`
1175×	`add-cube-cbrt` `*-un-lft-identity`
828×	`associate-r`
825×	`associate-l`
550×	`unswap-sqr`
138×	`*-commutative`
70×	`associate-/l*`
42×	`associate-/r*`
31×	`add-exp-log` `add-cbrt-cube`
27×	`associate-/l/`
23×	`div-inv`
14×	`pow1`
10×	`cbrt-undiv` `div-exp`
8×	`prod-exp` `cbrt-unprod`
7×	`pow-prod-down`
4×	`expm1-log1p-u` `sqrt-pow1` `pow1/2` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `sqrt-unprod` `clear-num`

Counts

4 → 1634

Calls

4 calls:

5.0ms	(* 3.0 (sqrt x))
6.0ms	(* (sqrt x) (sqrt 9.0))
6.0ms	(* (sqrt x) (sqrt 9.0))
61.0ms	(/ (/ 1.0 (* (sqrt x) (sqrt 9.0))) (* (sqrt x) (sqrt 9.0)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* 3.0 (sqrt x))
70.0ms	(* (sqrt x) (sqrt 9.0))
70.0ms	(* (sqrt x) (sqrt 9.0))
131.0ms	(/ (/ 1.0 (* (sqrt x) (sqrt 9.0))) (* (sqrt x) (sqrt 9.0)))

simplify312.0ms

Algorithm

egg-herbie

Counts

1646 → 1646

Iterations

Useful iterations: 1 (77.0ms)

Iter	Nodes	Cost
0	4198	27343
1	5001	26423

prune2.5s

Filtered

1646 candidates to 592 candidates (36.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	1643	3	1646
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	1646	9	1655

Merged error: 0b

Counts

1655 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))))
0.3b	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
0.4b	(* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
0.5b	(/ 1.0 (* x 9.0))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

462×	`add-sqr-sqrt`
272×	`distribute-rgt-in` `distribute-lft-in`
251×	`*-un-lft-identity`
215×	`unswap-sqr`
168×	`prod-diff`
152×	`add-cube-cbrt`
110×	`associate-r`
97×	`cbrt-prod`
89×	`add-cbrt-cube`
83×	`cbrt-unprod`
75×	`associate-l`
45×	`distribute-lft-out`
37×	`add-exp-log`
36×	`times-frac`
34×	`sqrt-prod`
32×	`pow1`
28×	`associate--l+`
20×	`swap-sqr` `prod-exp`
19×	`pow-prod-down`
18×	`*-commutative`
14×	`+-commutative` `sub-neg`
12×	`associate-r/` `associate-/r`
6×	`distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--` `associate-/l*` `difference-of-squares`
2×	`cbrt-undiv` `div-exp`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 546

Calls

4 calls:

67.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))))
22.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
35.0ms	(* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
7.0ms	(/ 1.0 (* x 9.0))

series324.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (* (cbrt 3.0) (cbrt 3.0)) (* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))))
65.0ms	(* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0))
139.0ms	(* (cbrt 3.0) (* (sqrt x) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
17.0ms	(/ 1.0 (* x 9.0))

simplify136.0ms

Algorithm

egg-herbie

Counts

558 → 558

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2062	10478
1	5001	7789

prune845.0ms

Filtered

558 candidates to 223 candidates (40.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	555	3	558
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	559	8	567

Merged error: 0b

Counts

567 → 8

regimes70.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	13
1	18	13

end0.0ms

sample827.0ms

Algorithm

intervals

Results

274.0ms	8515×	body	80	valid
272.0ms	8653×	body	80	nan