Details

sample21.0ms

Algorithm

intervals

Results

6.0ms	48×	body	1280	valid
4.0ms	45×	body	640	valid
3.0ms	133×	body	80	valid
1.0ms	20×	body	320	valid
0.0ms	10×	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: 28.9b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
2.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite157.0ms

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:

11.0ms	(/ (+ x 1.0) (- x 1.0))
6.0ms	(/ x (+ x 1.0))
82.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series211.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(/ (+ x 1.0) (- x 1.0))
34.0ms	(/ x (+ x 1.0))
137.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify196.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (74.0ms)

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

prune751.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- x 1.0))
0.0b	(/ x (+ x 1.0))
0.1b	(* (+ x 1.0) (/ 1 (- x 1.0)))
7.3b	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity`
70×	`add-sqr-sqrt`
68×	`times-frac`
49×	`add-cube-cbrt`
21×	`associate-r`
19×	`add-exp-log`
18×	`fma-neg` `prod-diff`
13×	`add-cbrt-cube`
11×	`distribute-lft-out`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`pow1` `flip3-+` `flip-+` `distribute-lft-out--` `difference-of-squares`
6×	`frac-sub` `associate-/l*` `add-log-exp`
5×	`div-exp` `div-inv`
4×	`expm1-log1p-u` `frac-times` `associate-l` `associate-*l/` `prod-exp` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `flip--` `unswap-sqr`
2×	`rec-exp` `frac-2neg` `1-exp` `associate-*r/` `clear-num` `un-div-inv` `cbrt-unprod`
1×	`sub-neg` `pow-flip` `diff-log` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 185

Calls

4 calls:

6.0ms	(/ 1 (- x 1.0))
5.0ms	(/ x (+ x 1.0))
25.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
40.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

series236.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1 (- x 1.0))
34.0ms	(/ x (+ x 1.0))
43.0ms	(* (+ x 1.0) (/ 1 (- x 1.0)))
133.0ms	(- (/ x (+ x 1.0)) (* (+ x 1.0) (/ 1 (- x 1.0))))

simplify89.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	667	1458
1	3302	1271
2	5001	1212

prune333.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (- x 1.0) (* x (- x 1.0)) (* (- (+ x 1.0)) (- (* x x) (* 1.0 1.0)))) (* (+ x 1.0) (* (- x 1.0) (- x 1.0))))
0.1b	(* (- (+ x 1.0)) (- (* x x) (* 1.0 1.0)))
0.1b	(* (+ x 1.0) (* (- x 1.0) (- x 1.0)))
29.8b	(fma (- x 1.0) (* x (- x 1.0)) (* (- (+ x 1.0)) (- (* x x) (* 1.0 1.0))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

60×	`frac-times`
47×	`distribute-rgt-in` `distribute-lft-in`
41×	`*-un-lft-identity`
39×	`flip3--` `flip--`
38×	`add-sqr-sqrt` `prod-diff`
35×	`add-cube-cbrt`
30×	`associate-*r/`
26×	`associate-/r/`
21×	`flip3-+` `flip-+`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-*l/`
16×	`associate-l`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`sub-neg` `distribute-neg-frac`
5×	`associate-r`
4×	`distribute-lft-neg-in` `expm1-log1p-u` `distribute-rgt-neg-in` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `distribute-lft-out` `associate-/l*`
2×	`*-commutative` `unswap-sqr`
1×	`distribute-lft-neg-out` `neg-mul-1` `frac-2neg` `clear-num` `associate-/r*` `fma-udef` `div-inv` `difference-of-squares`

Counts

4 → 198

Calls

4 calls:

24.0ms	(/ (fma (- x 1.0) (* x (- x 1.0)) (* (- (+ x 1.0)) (- (* x x) (* 1.0 1.0)))) (* (+ x 1.0) (* (- x 1.0) (- x 1.0))))
31.0ms	(* (- (+ x 1.0)) (- (* x x) (* 1.0 1.0)))
37.0ms	(* (+ x 1.0) (* (- x 1.0) (- x 1.0)))
0.0ms	(fma (- x 1.0) (* x (- x 1.0)) (* (- (+ x 1.0)) (- (* x x) (* 1.0 1.0))))

series380.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (fma (- x 1.0) (* x (- x 1.0)) (* (- (+ x 1.0)) (- (* x x) (* 1.0 1.0)))) (* (+ x 1.0) (* (- x 1.0) (- x 1.0))))
39.0ms	(* (- (+ x 1.0)) (- (* x x) (* 1.0 1.0)))
45.0ms	(* (+ x 1.0) (* (- x 1.0) (- x 1.0)))
102.0ms	(fma (- x 1.0) (* x (- x 1.0)) (* (- (+ x 1.0)) (- (* x x) (* 1.0 1.0))))

simplify51.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1157	3021
1	5001	2568

prune446.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- x 1.0) (- x 1.0))
0.1b	(* (+ x 1.0) (* (- x 1.0) (- x 1.0)))
0.1b	(* 3.0 (pow x 2))
19.2b	(/ (fma x 2.0 (- 1.0 (* 3.0 (pow x 2)))) (* (+ x 1.0) (* (- x 1.0) (- x 1.0))))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
66×	`*-un-lft-identity`
60×	`frac-times`
55×	`distribute-rgt-in` `distribute-lft-in`
54×	`prod-diff`
50×	`add-cube-cbrt`
42×	`flip3--` `flip--`
30×	`associate-*r/`
26×	`associate-/r/`
25×	`add-exp-log`
22×	`add-cbrt-cube`
18×	`flip3-+` `associate-*l/` `flip-+`
16×	`pow1`
14×	`associate-r`
12×	`associate-l`
10×	`prod-exp`
8×	`cbrt-unprod`
7×	`swap-sqr`
6×	`sub-neg` `distribute-lft-out--` `unswap-sqr`
4×	`expm1-log1p-u` `unpow-prod-down` `pow-prod-down` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`cbrt-undiv` `times-frac` `div-exp` `-commutative` `associate-/l`
2×	`unpow2` `sqr-pow`
1×	`pow2` `pow-to-exp` `frac-2neg` `pow-plus` `pow-exp` `clear-num` `associate-/r*` `pow-sqr` `pow-prod-up` `div-inv` `distribute-lft-out`

Counts

4 → 237

Calls

4 calls:

20.0ms	(* (- x 1.0) (- x 1.0))
36.0ms	(* (+ x 1.0) (* (- x 1.0) (- x 1.0)))
6.0ms	(* 3.0 (pow x 2))
28.0ms	(/ (fma x 2.0 (- 1.0 (* 3.0 (pow x 2)))) (* (+ x 1.0) (* (- x 1.0) (- x 1.0))))

series180.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (- x 1.0) (- x 1.0))
38.0ms	(* (+ x 1.0) (* (- x 1.0) (- x 1.0)))
24.0ms	(* 3.0 (pow x 2))
93.0ms	(/ (fma x 2.0 (- 1.0 (* 3.0 (pow x 2)))) (* (+ x 1.0) (* (- x 1.0) (- x 1.0))))

simplify49.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1052	2734
1	5002	2159

prune440.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

regimes32.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 16.7b

bsearch92.0ms

Steps

Iters	Range		Point
9	1.2499789889099044	556939279.5099251	125882.07557923895
9	-15640006985.087824	-4.508778152722845	-41855320.47834496

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	19
1	47	19
2	47	19

end0.0ms

sample521.0ms

Algorithm

intervals

Results

178.0ms	1719×	body	1280	valid
105.0ms	1232×	body	640	valid
89.0ms	4121×	body	80	valid
41.0ms	608×	body	320	valid
19.0ms	320×	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