Details

sample21.0ms

Algorithm

intervals

Results

6.0ms	53×	body	1280	valid
3.0ms	131×	body	80	valid
3.0ms	33×	body	640	valid
2.0ms	28×	body	320	valid
1.0ms	11×	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: 29.6b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
4.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite206.0ms

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:

12.0ms	(/ x (+ x 1.0))
23.0ms	(/ (+ x 1.0) (- x 1.0))
114.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series205.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ x (+ x 1.0))
37.0ms	(/ (+ x 1.0) (- x 1.0))
133.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify190.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (76.0ms)

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

prune747.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
4.0b	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
4.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite591.0ms

Algorithm

rewrite-expression-head

Rules

1898×	`*-un-lft-identity`
1428×	`times-frac`
1132×	`add-sqr-sqrt`
936×	`prod-diff`
810×	`add-cube-cbrt`
473×	`log-prod`
470×	`exp-sum`
365×	`distribute-lft-out`
182×	`associate-/r/`
175×	`distribute-lft-out--`
157×	`difference-of-squares`
91×	`div-inv`
55×	`flip3-+` `flip-+`
38×	`flip3--` `flip--`
18×	`fma-neg`
17×	`log-pow`
16×	`exp-prod`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`log-div` `exp-diff` `diff-log` `rem-log-exp` `frac-sub`

Counts

4 → 1097

Calls

4 calls:

10.0ms	(/ x (+ x 1.0))
24.0ms	(/ (+ x 1.0) (- x 1.0))
311.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
115.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ x (+ x 1.0))
38.0ms	(/ (+ x 1.0) (- x 1.0))
135.0ms	(log (exp (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
134.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify329.0ms

Algorithm

egg-herbie

Counts

1109 → 1109

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	1837	36120
1	4689	26172
2	5001	26146

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
13.6b	(/ x (- (* x x) (* 1.0 1.0)))
30.0b	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ (+ x 1.0) (- x 1.0))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 92

Calls

3 calls:

23.0ms	(/ (+ x 1.0) (- x 1.0))
12.0ms	(/ x (- (* x x) (* 1.0 1.0)))
0.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ (+ x 1.0) (- x 1.0))))

series269.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ (+ x 1.0) (- x 1.0))
70.0ms	(/ x (- (* x x) (* 1.0 1.0)))
162.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ (+ x 1.0) (- x 1.0))))

simplify47.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	426	756
1	1608	697
2	5001	684

prune239.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

13.6b	(/ x (- (* x x) (* 1.0 1.0)))
30.0b	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ (+ x 1.0) (- x 1.0))))
30.0b	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ (+ x 1.0) (- x 1.0))))
30.0b	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ (+ x 1.0) (- x 1.0))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
3×	`fma-udef` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`

Counts

4 → 65

Calls

4 calls:

12.0ms	(/ x (- (* x x) (* 1.0 1.0)))
0.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ (+ x 1.0) (- x 1.0))))
0.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ (+ x 1.0) (- x 1.0))))
4.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ (+ x 1.0) (- x 1.0))))

series562.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ x (- (* x x) (* 1.0 1.0)))
168.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ (+ x 1.0) (- x 1.0))))
160.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ (+ x 1.0) (- x 1.0))))
162.0ms	(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (/ (+ x 1.0) (- x 1.0))))

simplify37.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	258	770
1	979	676
2	5001	655

prune273.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes26.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.9b

bsearch86.0ms

Steps

Iters	Range		Point
10	26.826342714152005	1.350953981158519e+19	11258.21718550442
8	-5184857.938787598	-4116.604674393256	-14610.347047709978

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	20
1	37	20

end0.0ms

sample588.0ms

Algorithm

intervals

Results

188.0ms	1716×	body	1280	valid
121.0ms	1241×	body	640	valid
96.0ms	4094×	body	80	valid
45.0ms	665×	body	320	valid
13.0ms	284×	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