Details

sample28.0ms

Algorithm

intervals

Results

10.0ms	52×	body	1280	valid
5.0ms	41×	body	640	valid
4.0ms	124×	body	80	valid
2.0ms	25×	body	320	valid
1.0ms	14×	body	160	valid

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
3.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

22.0ms	(/ (+ x 1.0) (- x 1.0))
10.0ms	(/ x (+ x 1.0))
109.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series187.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ (+ x 1.0) (- x 1.0))
30.0ms	(/ x (+ x 1.0))
121.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify193.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	1208	18366
1	3687	13388
2	5001	13292

prune1.9s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
0.1b	(/ 1 (pow x 3))
0.4b	(/ (- 1.0) (pow x 2))
5.0b	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

440×	`times-frac`
354×	`add-sqr-sqrt`
344×	`*-un-lft-identity`
342×	`add-cube-cbrt`
252×	`prod-diff`
166×	`unpow-prod-down`
123×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
84×	`fma-neg`
56×	`sqr-pow`
52×	`unpow2`
41×	`neg-mul-1`
20×	`associate-/r*`
18×	`add-exp-log`
13×	`associate-/l*`
12×	`cube-prod`
9×	`div-exp`
8×	`add-cbrt-cube`
6×	`div-inv` `add-log-exp`
5×	`difference-of-squares`
4×	`pow1` `expm1-log1p-u` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `log1p-expm1-u`
3×	`rec-exp` `1-exp`
2×	`cbrt-undiv` `neg-sub0` `frac-2neg` `div-sub` `clear-num` `fma-udef`
1×	`associate--l-` `sub-neg` `flip3--` `pow-flip` `diff-log` `distribute-frac-neg` `flip--` `associate--r+` `distribute-lft-out--` `inv-pow`

Counts

4 → 559

Calls

4 calls:

0.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
9.0ms	(/ 1 (pow x 3))
10.0ms	(/ (- 1.0) (pow x 2))
92.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

series170.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
35.0ms	(/ 1 (pow x 3))
24.0ms	(/ (- 1.0) (pow x 2))
33.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

simplify177.0ms

Algorithm

egg-herbie

Counts

571 → 571

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	1159	12779
1	4167	7106
2	5001	7094

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 3.0 (/ 1 (pow x 3)))
0.1b	(/ 1 (pow x 3))
0.1b	(/ (/ 1.0 x) x)
5.0b	(- (fma -1 (/ (/ 1.0 x) x) (/ (- 3.0) x)) (* 3.0 (/ 1 (pow x 3))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

155×	`times-frac`
116×	`add-sqr-sqrt`
100×	`*-un-lft-identity`
96×	`add-cube-cbrt`
40×	`associate-r`
38×	`add-exp-log`
23×	`unpow-prod-down` `cube-prod`
16×	`add-cbrt-cube` `associate-/l*`
15×	`div-exp` `associate-/r*`
10×	`prod-exp`
9×	`unswap-sqr` `sqr-pow`
7×	`cube-mult` `unpow3` `div-inv`
6×	`pow1` `pow-to-exp` `rec-exp` `1-exp` `pow-exp` `add-log-exp`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `associate-l` `prod-diff`
2×	`frac-2neg` `clear-num` `cbrt-unprod`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `associate-r/` `pow-prod-down` `associate--l+` `un-div-inv` `-commutative` `flip--` `fma-udef` `associate-/l/` `inv-pow`

Counts

4 → 245

Calls

4 calls:

29.0ms	(* 3.0 (/ 1 (pow x 3)))
9.0ms	(/ 1 (pow x 3))
11.0ms	(/ (/ 1.0 x) x)
6.0ms	(- (fma -1 (/ (/ 1.0 x) x) (/ (- 3.0) x)) (* 3.0 (/ 1 (pow x 3))))

series133.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* 3.0 (/ 1 (pow x 3)))
30.0ms	(/ 1 (pow x 3))
29.0ms	(/ (/ 1.0 x) x)
32.0ms	(- (fma -1 (/ (/ 1.0 x) x) (/ (- 3.0) x)) (* 3.0 (/ 1 (pow x 3))))

simplify93.0ms

Algorithm

egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	760	1440
1	3959	1147
2	5001	1133

prune681.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
3.3b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite243.0ms

Algorithm

rewrite-expression-head

Rules

356×	`*-un-lft-identity`
220×	`times-frac`
160×	`add-sqr-sqrt`
96×	`add-cube-cbrt`
76×	`distribute-lft-out`
72×	`swap-sqr`
44×	`associate-r` `associate-l`
36×	`distribute-lft-out--`
28×	`add-exp-log` `add-cbrt-cube`
21×	`difference-of-squares`
18×	`pow1` `fma-def` `associate-/r/`
9×	`frac-sub` `div-inv`
8×	`cbrt-undiv` `frac-times` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
6×	`flip3-+` `flip-+`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`+-commutative` `sub-neg` `fma-neg` `diff-log` `prod-diff` `frac-add` `sum-log`

Counts

4 → 287

Calls

4 calls:

48.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
76.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
78.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
25.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series378.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
91.0ms	(+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))
54.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
194.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify60.0ms

Algorithm

egg-herbie

Counts

299 → 299

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1192	2826
1	5002	2626

prune1.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes43.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.8b

bsearch155.0ms

Steps

Iters	Range		Point
9	0.007285382865895221	15234496.061427226	9886.930048742035
9	-3013496178.120658	-569.2304264003914	-10044.420205958744

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	29
1	40	29

end0.0ms

sample691.0ms

Algorithm

intervals

Results

247.0ms	1753×	body	1280	valid
148.0ms	1233×	body	640	valid
127.0ms	4089×	body	80	valid
54.0ms	612×	body	320	valid
18.0ms	313×	body	160	valid

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6