Details

sample21.0ms

Algorithm

intervals

Results

7.0ms	57×	body	1280	valid
4.0ms	139×	body	80	valid
3.0ms	39×	body	640	valid
1.0ms	14×	body	320	valid
0.0ms	7×	body	160	valid

simplify22.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize9.0ms

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)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

5.0ms	(/ x (+ x 1.0))
7.0ms	(/ (+ x 1.0) (- x 1.0))
29.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series202.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ x (+ x 1.0))
37.0ms	(/ (+ x 1.0) (- x 1.0))
130.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	392	760
1	1379	726
2	5001	716

prune205.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

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)))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

87×	`*-un-lft-identity`
59×	`add-sqr-sqrt`
53×	`times-frac`
36×	`add-cube-cbrt`
28×	`log-pow`
26×	`exp-prod`
15×	`distribute-lft-out`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
6×	`pow1` `log-prod` `associate-/r/`
5×	`add-log-exp`
3×	`flip3--` `flip--` `div-inv` `associate--r+`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `associate-/l/`
1×	`sub-neg` `diff-log` `rem-log-exp`

Counts

4 → 135

Calls

4 calls:

5.0ms	(/ x (+ x 1.0))
8.0ms	(/ (+ x 1.0) (- x 1.0))
12.0ms	(log (exp (/ (+ x 1.0) (- x 1.0))))
35.0ms	(- (/ x (+ x 1.0)) (log (exp (/ (+ x 1.0) (- x 1.0)))))

series246.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ x (+ x 1.0))
37.0ms	(/ (+ x 1.0) (- x 1.0))
41.0ms	(log (exp (/ (+ x 1.0) (- x 1.0))))
128.0ms	(- (/ x (+ x 1.0)) (log (exp (/ (+ x 1.0) (- x 1.0)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	442	940
1	1437	871
2	5001	856

prune283.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite129.0ms

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×	`associate-/l*`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `frac-add` `clear-num`

Counts

4 → 329

Calls

4 calls:

30.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
44.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0))))
20.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
11.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

series669.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
352.0ms	(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0))))
47.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
210.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify83.0ms

Algorithm

egg-herbie

Counts

341 → 341

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1299	4984
1	5001	4721

prune481.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.1b	(exp (log (/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0))))))
1.7b	(log (/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ (+ x 1.0) (- 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))))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

485×	`*-un-lft-identity`
288×	`times-frac`
154×	`distribute-lft-out`
110×	`log-prod`
87×	`add-sqr-sqrt`
75×	`add-cube-cbrt`
55×	`exp-sum`
32×	`distribute-lft-out--`
25×	`difference-of-squares`
24×	`swap-sqr`
19×	`add-exp-log`
18×	`associate-r` `associate-l`
16×	`add-cbrt-cube`
14×	`associate-/r/`
13×	`pow1`
9×	`frac-sub`
7×	`frac-times` `associate-r/` `associate-l/`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
5×	`div-exp`
4×	`cbrt-undiv` `exp-prod` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`log-div` `rem-log-exp` `frac-add` `log-pow`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `exp-diff` `diff-log` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `rem-exp-log`

Counts

4 → 244

Calls

4 calls:

17.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
46.0ms	(exp (log (/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0))))))
40.0ms	(log (/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ (+ x 1.0) (- 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))))

series1.0s

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
368.0ms	(exp (log (/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0))))))
426.0ms	(log (/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (+ (/ (+ x 1.0) (- x 1.0)) (/ x (+ x 1.0)))))
210.0ms	(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))))

simplify152.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	1041	5546
1	4397	5314
2	5001	5261

prune425.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

regimes32.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.0b

bsearch88.0ms

Steps

Iters	Range		Point
10	4.9177062248324165e-05	42925490.781275615	7951.093111795664
9	-234806929230.2476	-1816.595590764893	-8016.61183921209

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	21
1	36	21

end0.0ms

sample574.0ms

Algorithm

intervals

Results

206.0ms	1724×	body	1280	valid
113.0ms	1270×	body	640	valid
106.0ms	4056×	body	80	valid
41.0ms	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