Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	57×	body	1280	valid
3.0ms	139×	body	80	valid
3.0ms	39×	body	640	valid
1.0ms	14×	body	320	valid
0.0ms	7×	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

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.8b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite112.0ms

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))
44.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series205.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ x (+ x 1.0))
42.0ms	(/ (+ x 1.0) (- x 1.0))
130.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify208.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (76.0ms)

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

prune731.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(log (exp (/ (+ x 1.0) (- x 1.0))))
2.8b	(- (/ x (+ x 1.0)) (log (exp (/ (+ x 1.0) (- x 1.0)))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

1043×	`*-un-lft-identity`
785×	`times-frac`
649×	`add-sqr-sqrt`
540×	`prod-diff`
514×	`log-pow`
494×	`exp-prod`
482×	`add-cube-cbrt`
198×	`distribute-lft-out`
104×	`associate-/r/`
83×	`distribute-lft-out--` `difference-of-squares`
52×	`div-inv`
33×	`flip3-+` `flip-+`
24×	`pow1`
21×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
6×	`log-prod`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate--r+`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `diff-log` `rem-log-exp`

Counts

4 → 701

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
8.0ms	(/ (+ x 1.0) (- x 1.0))
10.0ms	(log (exp (/ (+ x 1.0) (- x 1.0))))
53.0ms	(- (/ x (+ x 1.0)) (log (exp (/ (+ x 1.0) (- x 1.0)))))

series257.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ x (+ x 1.0))
44.0ms	(/ (+ x 1.0) (- x 1.0))
39.0ms	(log (exp (/ (+ x 1.0) (- x 1.0))))
139.0ms	(- (/ x (+ x 1.0)) (log (exp (/ (+ x 1.0) (- x 1.0)))))

simplify229.0ms

Algorithm

egg-herbie

Counts

713 → 713

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1343	23868
1	3659	15044
2	5001	15044

prune768.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (exp (/ (+ x 1.0) (- x 1.0))))
0.0b	(log1p (/ x (+ x 1.0)))
0.0b	(expm1 (log1p (/ x (+ x 1.0))))
28.3b	(- (expm1 (log1p (/ x (+ x 1.0)))) (log (exp (/ (+ x 1.0) (- x 1.0)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

155×	`*-un-lft-identity`
114×	`add-sqr-sqrt`
109×	`log-pow`
104×	`exp-prod`
90×	`prod-diff`
80×	`add-cube-cbrt` `times-frac`
20×	`distribute-lft-out`
18×	`distribute-lft-out--`
17×	`difference-of-squares`
9×	`pow1`
8×	`associate-/r/`
6×	`log-prod`
5×	`expm1-log1p-u` `flip3--` `flip--` `add-log-exp`
4×	`add-exp-log` `add-cbrt-cube` `log1p-expm1-u` `div-inv`
3×	`fma-neg` `associate--r+`
2×	`expm1-udef`
1×	`associate--l-` `sub-neg` `log1p-udef` `expm1-log1p` `diff-log` `log1p-expm1` `rem-log-exp`

Counts

4 → 176

Calls

4 calls:

10.0ms	(log (exp (/ (+ x 1.0) (- x 1.0))))
1.0ms	(log1p (/ x (+ x 1.0)))
1.0ms	(expm1 (log1p (/ x (+ x 1.0))))
21.0ms	(- (expm1 (log1p (/ x (+ x 1.0)))) (log (exp (/ (+ x 1.0) (- x 1.0)))))

series540.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(log (exp (/ (+ x 1.0) (- x 1.0))))
100.0ms	(log1p (/ x (+ x 1.0)))
133.0ms	(expm1 (log1p (/ x (+ x 1.0))))
268.0ms	(- (expm1 (log1p (/ x (+ x 1.0)))) (log (exp (/ (+ x 1.0) (- x 1.0)))))

simplify79.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	732	4745
1	2151	2962
2	5001	2923

prune301.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
2.8b	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

544×	`*-un-lft-identity`
320×	`times-frac`
170×	`add-sqr-sqrt`
141×	`distribute-lft-out`
106×	`add-cube-cbrt`
72×	`swap-sqr`
52×	`distribute-lft-out--`
44×	`associate-r` `associate-l`
34×	`difference-of-squares`
30×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r/`
18×	`pow1` `frac-sub`
14×	`frac-times` `associate-r/` `associate-l/`
12×	`associate-/r*`
11×	`associate-/l/`
9×	`cbrt-undiv` `div-exp` `div-inv`
8×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`flip3--` `flip--` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `frac-add` `clear-num`

Counts

4 → 339

Calls

4 calls:

43.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
31.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
16.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
12.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series668.0ms

Counts

4 → 12

Calls

4 calls:

364.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
53.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
47.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
204.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify76.0ms

Algorithm

egg-herbie

Counts

351 → 351

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1339	5093
1	5001	4844

prune511.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes30.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 29.6b

bsearch98.0ms

Steps

Iters	Range		Point
10	4.9177062248324165e-05	42925490.781275615	9614.242799871034
9	-234806929230.2476	-1816.595590764893	-10426.928587191172

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	21
1	57	21
2	70	21
3	72	21
4	72	21

end0.0ms

sample558.0ms

Algorithm

intervals

Results

194.0ms	1724×	body	1280	valid
117.0ms	1270×	body	640	valid
99.0ms	4056×	body	80	valid
40.0ms	605×	body	320	valid
16.0ms	345×	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