Details

sample23.0ms

Algorithm

intervals

Results

7.0ms	55×	body	1280	valid
4.0ms	38×	body	640	valid
4.0ms	132×	body	80	valid
2.0ms	22×	body	320	valid
0.0ms	9×	body	160	valid

simplify23.0ms

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

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: 29.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite108.0ms

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))
7.0ms	(/ (+ x 1.0) (- x 1.0))
39.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series220.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ x (+ x 1.0))
39.0ms	(/ (+ x 1.0) (- x 1.0))
142.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify218.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (81.0ms)

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

prune708.0ms

Filtered

605 candidates to 217 candidates (35.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	602	3	605
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	603	3	606

Merged error: 0.2b

Counts

606 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(exp (/ (+ x 1.0) (- x 1.0)))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.0b	(- (/ x (+ x 1.0)) (log (exp (/ (+ x 1.0) (- x 1.0)))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

1042×	`*-un-lft-identity`
785×	`times-frac`
648×	`add-sqr-sqrt`
540×	`prod-diff`
494×	`exp-prod`
487×	`log-pow`
481×	`add-cube-cbrt`
198×	`distribute-lft-out`
104×	`associate-/r/`
83×	`distribute-lft-out--` `difference-of-squares`
52×	`div-inv`
33×	`flip3-+` `flip-+`
23×	`pow1`
21×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`log-prod` `associate--r+`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `diff-log` `rem-exp-log`

Counts

4 → 697

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
9.0ms	(exp (/ (+ x 1.0) (- x 1.0)))
7.0ms	(/ (+ x 1.0) (- x 1.0))
50.0ms	(- (/ x (+ x 1.0)) (log (exp (/ (+ x 1.0) (- x 1.0)))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ x (+ x 1.0))
83.0ms	(exp (/ (+ x 1.0) (- x 1.0)))
39.0ms	(/ (+ x 1.0) (- x 1.0))
142.0ms	(- (/ x (+ x 1.0)) (log (exp (/ (+ x 1.0) (- x 1.0)))))

simplify249.0ms

Algorithm

egg-herbie

Counts

709 → 709

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1389	23876
1	3891	15042
2	5001	15042

prune737.0ms

Filtered

709 candidates to 243 candidates (34.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	709	0	709
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	709	3	712

Merged error: 0.2b

Counts

712 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))
5.7b	(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
10.0b	(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
14.9b	(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

303×	`add-sqr-sqrt`
286×	`*-un-lft-identity`
225×	`times-frac`
144×	`difference-of-squares`
108×	`unpow-prod-down` `cube-prod`
106×	`associate-l`
82×	`add-cube-cbrt`
72×	`sqr-pow`
57×	`distribute-lft-out`
45×	`distribute-lft-out--`
25×	`associate-/r*`
18×	`fma-neg` `prod-diff`
11×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
9×	`difference-cubes`
8×	`flip3-+` `associate-/r/` `flip-+`
6×	`pow1`
5×	`frac-sub`
4×	`expm1-log1p-u` `frac-times` `associate-r/` `log1p-expm1-u` `div-inv` `associate-/l`
3×	`flip3--` `associate-r` `sum-log` `flip--`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `associate-/l/` `associate--r+` `unswap-sqr`
1×	`+-commutative` `sub-neg` `associate-+r+` `fma-def` `frac-2neg` `diff-log` `pow-prod-down` `clear-num` `*-commutative`

Counts

4 → 353

Calls

4 calls:

6.0ms	(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))
20.0ms	(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
11.0ms	(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
34.0ms	(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

series329.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))
59.0ms	(/ (+ x 1.0) (- (pow x 3) (pow 1.0 3)))
176.0ms	(- (/ x (+ x 1.0)) (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))))
75.0ms	(* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))))

simplify79.0ms

Algorithm

egg-herbie

Counts

365 → 365

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1313	4807
1	5002	4489

prune945.0ms

Filtered

365 candidates to 205 candidates (56.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	364	1	365
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	364	4	368

Merged error: 0.2b

Counts

368 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
0.4b	(/ 1 (pow x 3))
0.5b	(/ (- 1.0) (pow x 2))
4.6b	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

rewrite89.0ms

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:

1.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
6.0ms	(/ 1 (pow x 3))
7.0ms	(/ (- 1.0) (pow x 2))
40.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

series188.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
35.0ms	(/ 1 (pow x 3))
26.0ms	(/ (- 1.0) (pow x 2))
44.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

simplify195.0ms

Algorithm

egg-herbie

Counts

571 → 571

Iterations

Useful iterations: 2 (87.0ms)

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

prune730.0ms

Filtered

571 candidates to 218 candidates (38.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	568	3	571
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	570	5	575

Merged error: 0.0b

Counts

575 → 5

regimes35.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.0b

bsearch103.0ms

Steps

Iters	Range		Point
10	6.398614580632226	3002406562115.273	12773.683991769165
11	-55383.34621353126	-7.66540900750845e-16	-12155.681664534535

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	16
1	35	16

end0.0ms

sample639.0ms

Algorithm

intervals

Results

221.0ms	1763×	body	1280	valid
133.0ms	1251×	body	640	valid
117.0ms	4018×	body	80	valid
51.0ms	644×	body	320	valid
17.0ms	324×	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