Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	63×	body	640	valid
4.0ms	146×	body	80	valid
2.0ms	30×	body	320	valid
1.0ms	17×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	15	5
2	15	5

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 12.4b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
0.0b	(/ 1.0 (- x 1.0))
2.4b	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

168×	`*-un-lft-identity`
112×	`add-sqr-sqrt`
110×	`frac-sub`
103×	`associate-/r*`
72×	`add-cube-cbrt`
69×	`associate-/l*`
55×	`times-frac`
35×	`distribute-lft-out--`
23×	`frac-2neg` `clear-num`
21×	`distribute-lft-out`
18×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r/`
5×	`add-log-exp`
4×	`div-inv`
3×	`pow1` `flip--`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip-+`
1×	`sub-neg` `flip3-+` `diff-log`

Counts

3 → 211

Calls

3 calls:

5.0ms	(/ 1.0 (+ x 1.0))
5.0ms	(/ 1.0 (- x 1.0))
33.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

series264.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(/ 1.0 (+ x 1.0))
32.0ms	(/ 1.0 (- x 1.0))
200.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

simplify63.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1148	2299
1	5001	2177

prune285.0ms

Filtered

220 candidates to 129 candidates (41.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	218	2	220
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	219	2	221

Merged error: 0.5b

Counts

221 → 2

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b

(* (/ (+ x 1.0) (sqrt 1.0)) (/ (- x 1.0) (cbrt 1.0)))

0.0b

(/ (- (* (sqrt 1.0) (/ (- x 1.0) (cbrt 1.0))) (* (/ (+ x 1.0) (sqrt 1.0)) (* (cbrt 1.0) (cbrt 1.0)))) (* (/ (+ x 1.0) (sqrt 1.0)) (/ (- x 1.0) (cbrt 1.0))))

1.7b

(- (* (sqrt 1.0) (/ (- x 1.0) (cbrt 1.0))) (* (/ (+ x 1.0) (sqrt 1.0)) (* (cbrt 1.0) (cbrt 1.0))))

rewrite5.2s

Algorithm

rewrite-expression-head

Rules

99522×	`add-sqr-sqrt`
47522×	`times-frac`
36243×	`unswap-sqr`
18074×	`cbrt-prod`
16580×	`difference-of-squares`
14759×	`sqrt-prod`
13154×	`*-un-lft-identity`
7250×	`add-cube-cbrt`
6970×	`associate-r`
6052×	`associate-l`
3276×	`swap-sqr`
1843×	`*-commutative`
1636×	`distribute-lft-out--`
1302×	`distribute-lft-out`
888×	`associate-/r*`
865×	`associate-/l*`
604×	`associate-*l/`
570×	`frac-sub`
557×	`associate-/l/`
516×	`associate-*r/`
480×	`frac-times`
411×	`div-inv`
274×	`associate-/r/`
167×	`clear-num`
135×	`frac-2neg`
96×	`un-div-inv`
72×	`flip3-+` `flip-+`
64×	`flip3--` `flip--`
45×	`add-cbrt-cube`
33×	`add-exp-log`
21×	`cbrt-undiv`
13×	`div-exp`
12×	`cbrt-unprod`
8×	`prod-exp`
5×	`pow1` `add-log-exp`
4×	`sub-div`
1×	`sub-neg` `diff-log` `div-sub` `pow-prod-down`

Counts

3 → 17156

Calls

3 calls:

44.0ms

(* (/ (+ x 1.0) (sqrt 1.0)) (/ (- x 1.0) (cbrt 1.0)))

679.0ms

(/ (- (* (sqrt 1.0) (/ (- x 1.0) (cbrt 1.0))) (* (/ (+ x 1.0) (sqrt 1.0)) (* (cbrt 1.0) (cbrt 1.0)))) (* (/ (+ x 1.0) (sqrt 1.0)) (/ (- x 1.0) (cbrt 1.0))))

212.0ms

(- (* (sqrt 1.0) (/ (- x 1.0) (cbrt 1.0))) (* (/ (+ x 1.0) (sqrt 1.0)) (* (cbrt 1.0) (cbrt 1.0))))

series1.5s

Counts

3 → 9

Calls

3 calls:

252.0ms

(* (/ (+ x 1.0) (sqrt 1.0)) (/ (- x 1.0) (cbrt 1.0)))

635.0ms

(/ (- (* (sqrt 1.0) (/ (- x 1.0) (cbrt 1.0))) (* (/ (+ x 1.0) (sqrt 1.0)) (* (cbrt 1.0) (cbrt 1.0)))) (* (/ (+ x 1.0) (sqrt 1.0)) (/ (- x 1.0) (cbrt 1.0))))

587.0ms

(- (* (sqrt 1.0) (/ (- x 1.0) (cbrt 1.0))) (* (/ (+ x 1.0) (sqrt 1.0)) (* (cbrt 1.0) (cbrt 1.0))))

simplify7.2s

Algorithm

egg-herbie

Counts

17165 → 17165

Iterations

Useful iterations: 0 (163.0ms)

Iter	Nodes	Cost
0	7227	830613

prune19.7s

Filtered

17165 candidates to 4048 candidates (76.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	17164	1	17165
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	17164	3	17167

Merged error: 0.5b

Counts

17167 → 3

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (sqrt 1.0) (/ (- x 1.0) (cbrt 1.0))) (* (/ (+ x 1.0) (sqrt 1.0)) (* (cbrt 1.0) (cbrt 1.0)))) (* (- (* x x) (* 1.0 1.0)) (/ (- x 1.0) (cbrt 1.0))))
0.0b	(* (/ (- (* (sqrt 1.0) (/ (- x 1.0) (cbrt 1.0))) (* (/ (+ x 1.0) (sqrt 1.0)) (* (cbrt 1.0) (cbrt 1.0)))) (* (- (* x x) (* 1.0 1.0)) (/ (- x 1.0) (cbrt 1.0)))) (* (sqrt 1.0) (- x 1.0)))
0.0b	(* (- (* x x) (* 1.0 1.0)) (/ (- x 1.0) (cbrt 1.0)))
1.7b	(- (* (sqrt 1.0) (/ (- x 1.0) (cbrt 1.0))) (* (/ (+ x 1.0) (sqrt 1.0)) (* (cbrt 1.0) (cbrt 1.0))))

rewrite15.2s

Algorithm

rewrite-expression-head

Rules

203534×	`add-sqr-sqrt`
80510×	`times-frac`
73734×	`unswap-sqr`
43206×	`difference-of-squares`
35046×	`cbrt-prod`
31115×	`associate-l`
23084×	`sqrt-prod`
20206×	`*-un-lft-identity`
13997×	`associate-r`
11442×	`swap-sqr`
8518×	`add-cube-cbrt`
7778×	`*-commutative`
5304×	`distribute-lft-out--`
2402×	`associate-*r/`
2011×	`associate-*l/`
1768×	`associate-/l*`
1514×	`associate-/l/`
1425×	`frac-sub`
1394×	`associate-/r*`
1236×	`frac-times`
711×	`flip3--` `flip--`
413×	`div-inv`
261×	`clear-num`
234×	`un-div-inv`
183×	`frac-2neg`
106×	`associate-/r/`
95×	`flip3-+` `flip-+` `distribute-lft-out`
64×	`add-cbrt-cube`
50×	`add-exp-log`
27×	`cbrt-unprod`
20×	`cbrt-undiv` `prod-exp`
13×	`div-exp`
11×	`pow1`
10×	`sub-div`
8×	`distribute-rgt-in` `distribute-lft-in`
6×	`add-log-exp`
5×	`sub-neg`
4×	`pow-prod-down`
1×	`diff-log` `div-sub`

Counts

4 → 33562

Calls

4 calls:

677.0ms	(/ (- (* (sqrt 1.0) (/ (- x 1.0) (cbrt 1.0))) (* (/ (+ x 1.0) (sqrt 1.0)) (* (cbrt 1.0) (cbrt 1.0)))) (* (- (* x x) (* 1.0 1.0)) (/ (- x 1.0) (cbrt 1.0))))
5.2s	(* (/ (- (* (sqrt 1.0) (/ (- x 1.0) (cbrt 1.0))) (* (/ (+ x 1.0) (sqrt 1.0)) (* (cbrt 1.0) (cbrt 1.0)))) (* (- (* x x) (* 1.0 1.0)) (/ (- x 1.0) (cbrt 1.0)))) (* (sqrt 1.0) (- x 1.0)))
47.0ms	(* (- (* x x) (* 1.0 1.0)) (/ (- x 1.0) (cbrt 1.0)))
211.0ms	(- (* (sqrt 1.0) (/ (- x 1.0) (cbrt 1.0))) (* (/ (+ x 1.0) (sqrt 1.0)) (* (cbrt 1.0) (cbrt 1.0))))

series2.0s

Counts

4 → 12

Calls

4 calls:

699.0ms	(/ (- (* (sqrt 1.0) (/ (- x 1.0) (cbrt 1.0))) (* (/ (+ x 1.0) (sqrt 1.0)) (* (cbrt 1.0) (cbrt 1.0)))) (* (- (* x x) (* 1.0 1.0)) (/ (- x 1.0) (cbrt 1.0))))
611.0ms	(* (/ (- (* (sqrt 1.0) (/ (- x 1.0) (cbrt 1.0))) (* (/ (+ x 1.0) (sqrt 1.0)) (* (cbrt 1.0) (cbrt 1.0)))) (* (- (* x x) (* 1.0 1.0)) (/ (- x 1.0) (cbrt 1.0)))) (* (sqrt 1.0) (- x 1.0)))
102.0ms	(* (- (* x x) (* 1.0 1.0)) (/ (- x 1.0) (cbrt 1.0)))
620.0ms	(- (* (sqrt 1.0) (/ (- x 1.0) (cbrt 1.0))) (* (/ (+ x 1.0) (sqrt 1.0)) (* (cbrt 1.0) (cbrt 1.0))))

simplify11.9s

Algorithm

egg-herbie

Counts

33574 → 33574

Iterations

Useful iterations: 0 (224.0ms)

Iter	Nodes	Cost
0	9453	1307059

prune38.7s

Filtered

33574 candidates to 6833 candidates (79.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	33574	0	33574
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	33574	3	33577

Merged error: 0.5b

Counts

33577 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 2.0 (/ 1 (pow x 2))) (* 2.0 (/ 1 (pow x 4))))
0.1b	(/ 1 (pow x 4))
0.1b	(/ 1 (pow x 6))
0.5b	(/ 1 (pow x 2))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

445×	`associate-*r/`
272×	`frac-add`
269×	`associate-/r*`
208×	`*-un-lft-identity`
159×	`add-sqr-sqrt` `add-cube-cbrt`
141×	`associate-/l*`
135×	`unpow-prod-down`
99×	`un-div-inv`
72×	`times-frac`
69×	`clear-num`
45×	`sqr-pow`
36×	`frac-2neg`
31×	`add-exp-log`
20×	`unpow2`
18×	`pow-flip` `div-exp`
14×	`associate-r` `distribute-lft-out`
10×	`pow1` `add-cbrt-cube`
9×	`pow-to-exp` `rec-exp` `pow-unpow` `1-exp` `pow-exp`
8×	`associate-l`
7×	`div-inv`
6×	`add-log-exp`
3×	`cbrt-undiv` `pow-pow` `inv-pow`
2×	`*-commutative`
1×	`+-commutative` `distribute-rgt-out` `flip3-+` `sum-log` `flip-+`

Counts

4 → 476

Calls

4 calls:

93.0ms	(+ (* 2.0 (/ 1 (pow x 2))) (* 2.0 (/ 1 (pow x 4))))
5.0ms	(/ 1 (pow x 4))
5.0ms	(/ 1 (pow x 6))
6.0ms	(/ 1 (pow x 2))

series206.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(+ (* 2.0 (/ 1 (pow x 2))) (* 2.0 (/ 1 (pow x 4))))
30.0ms	(/ 1 (pow x 4))
53.0ms	(/ 1 (pow x 6))
18.0ms	(/ 1 (pow x 2))

simplify112.0ms

Algorithm

egg-herbie

Counts

488 → 488

Iterations

Useful iterations: 1 (51.0ms)

Iter	Nodes	Cost
0	2282	4768
1	5001	3320

prune439.0ms

Filtered

488 candidates to 130 candidates (73.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	487	1	488
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	488	3	491

Merged error: 0.0b

Counts

491 → 3

regimes25.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 13.9b

bsearch112.0ms

Steps

Iters	Range		Point
9	0.0004381094517774334	96283.49646244562	424.6122658710841
8	-84260259616.65012	-46881322.55292306	-82806819079.29805

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	33
1	65	33
2	77	33
3	78	33
4	78	33

end0.0ms

sample468.0ms

Algorithm

intervals

Results

166.0ms	1963×	body	640	valid
98.0ms	4200×	body	80	valid
85.0ms	1241×	body	320	valid
25.0ms	596×	body	160	valid