Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	44×	body	1280	valid
3.0ms	38×	body	640	valid
3.0ms	134×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	16×	body	160	valid

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

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: 28.6b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
4.4b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite116.0ms

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:

5.0ms	(/ x (+ x 1.0))
8.0ms	(/ (+ x 1.0) (- x 1.0))
41.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series210.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ x (+ x 1.0))
38.0ms	(/ (+ x 1.0) (- x 1.0))
136.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify222.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (85.0ms)

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

prune703.0ms

Filtered

605 candidates to 217 candidates (35.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	600	5	605
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	601	5	606

Merged error: 0.2b

Counts

606 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(exp (/ x (+ x 1.0)))
2.3b	(log (exp (/ x (+ x 1.0))))
4.4b	(- (log (exp (/ x (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

1091×	`*-un-lft-identity`
809×	`times-frac`
687×	`add-sqr-sqrt`
572×	`prod-diff`
533×	`log-pow`
522×	`exp-prod`
496×	`add-cube-cbrt`
203×	`distribute-lft-out`
104×	`associate-/r/`
95×	`distribute-lft-out--` `difference-of-squares`
52×	`div-inv`
33×	`pow1`
30×	`flip3-+` `flip-+`
24×	`flip3--` `flip--`
22×	`fma-neg`
6×	`add-exp-log` `log-prod` `add-cbrt-cube` `add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`associate--l+`
2×	`associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 722

Calls

4 calls:

8.0ms	(/ (+ x 1.0) (- x 1.0))
6.0ms	(exp (/ x (+ x 1.0)))
7.0ms	(log (exp (/ x (+ x 1.0))))
55.0ms	(- (log (exp (/ x (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (+ x 1.0) (- x 1.0))
54.0ms	(exp (/ x (+ x 1.0)))
35.0ms	(log (exp (/ x (+ x 1.0))))
138.0ms	(- (log (exp (/ x (+ x 1.0)))) (/ (+ x 1.0) (- x 1.0)))

simplify251.0ms

Algorithm

egg-herbie

Counts

734 → 734

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	1365	23449
1	3978	15399
2	5001	15325

prune693.0ms

Filtered

734 candidates to 242 candidates (33.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	734	0	734
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	734	5	739

Merged error: 0.2b

Counts

739 → 5

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ 1 (+ x 1.0))
29.0b	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
32×	`times-frac`
23×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`add-exp-log` `associate-/r*`
7×	`add-cbrt-cube` `associate-/l*`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`pow1` `associate-/r/`
3×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv` `associate-/l/`
1×	`rec-exp` `flip3--` `pow-flip` `1-exp` `flip--` `fma-udef` `inv-pow`

Counts

3 → 96

Calls

3 calls:

8.0ms	(/ (+ x 1.0) (- x 1.0))
6.0ms	(/ 1 (+ x 1.0))
1.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

series204.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(/ (+ x 1.0) (- x 1.0))
29.0ms	(/ 1 (+ x 1.0))
137.0ms	(fma x (/ 1 (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify42.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	352	622
1	1229	566
2	5001	540

prune155.0ms

Filtered

105 candidates to 66 candidates (62.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	105	5	110

Merged error: 0.2b

Counts

110 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (- x 1.0))
0.0b	(* (+ x 1.0) (+ x 1.0))
0.0b	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
17.6b	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
49×	`add-sqr-sqrt`
44×	`associate-*r/`
43×	`add-cube-cbrt`
37×	`prod-diff`
32×	`frac-sub`
30×	`flip3-+` `flip-+`
24×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate--l+`
20×	`frac-times` `flip3--` `flip--`
18×	`associate-/l/`
13×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `associate-*l/` `add-cbrt-cube`
9×	`associate-r`
7×	`associate-l`
6×	`swap-sqr` `distribute-lft-out` `add-log-exp`
5×	`sub-neg` `difference-of-squares`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`associate-/l*`
2×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate--r+` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `fma-neg` `diff-log` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv` `distribute-lft-out--`

Counts

4 → 198

Calls

4 calls:

7.0ms	(* x (- x 1.0))
8.0ms	(* (+ x 1.0) (+ x 1.0))
17.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
11.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

series155.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* x (- x 1.0))
16.0ms	(* (+ x 1.0) (+ x 1.0))
49.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
45.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	906	2204
1	5002	1888

prune400.0ms

Filtered

210 candidates to 139 candidates (66.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	208	2	210
Fresh	1	1	2
Picked	1	0	1
Done	2	0	2
Total	212	3	215

Merged error: 0.1b

Counts

215 → 3

regimes25.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 15.1b

bsearch104.0ms

Steps

Iters	Range		Point
9	860.9547529914067	28642596122.821114	666253.4914210141
10	-1.6881474944952877e+161	-4.262486889663285e+150	-1.3494192538472585e+154

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	18
1	67	18
2	79	18
3	81	18
4	81	18

end0.0ms

sample542.0ms

Algorithm

intervals

Results

198.0ms	1732×	body	1280	valid
102.0ms	1213×	body	640	valid
93.0ms	4091×	body	80	valid
44.0ms	650×	body	320	valid
14.0ms	314×	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