Details

sample19.0ms

Algorithm

intervals

Results

6.0ms	59×	body	1280	valid
3.0ms	139×	body	80	valid
2.0ms	24×	body	640	valid
1.0ms	24×	body	320	valid
0.0ms	10×	body	160	valid

simplify20.0ms

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: 27.6b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.3b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite54.0ms

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:

6.0ms	(/ x (+ x 1.0))
8.0ms	(/ (+ x 1.0) (- x 1.0))
35.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series208.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ x (+ x 1.0))
41.0ms	(/ (+ x 1.0) (- x 1.0))
132.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

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

prune211.0ms

Filtered

113 candidates to 76 candidates (67.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	5	114

Merged error: 0.0b

Counts

114 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
0.0b	(pow (/ x (+ x 1.0)) 3)
3.2b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

354×	`*-un-lft-identity`
216×	`times-frac`
190×	`add-sqr-sqrt`
104×	`unpow-prod-down` `cube-prod`
78×	`add-cube-cbrt`
66×	`distribute-lft-out`
61×	`distribute-lft-out--`
44×	`difference-of-squares`
24×	`swap-sqr`
22×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r` `associate-l`
16×	`associate-/r/`
14×	`sqr-pow`
13×	`pow1`
8×	`div-inv`
6×	`cbrt-undiv` `pow-unpow` `flip3-+` `div-exp` `flip-+` `add-log-exp`
4×	`cube-div` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`
3×	`flip3--` `flip--`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3`
1×	`difference-cubes` `pow2` `frac-times` `sub-neg` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `frac-sub`

Counts

4 → 303

Calls

4 calls:

19.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
13.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
8.0ms	(pow (/ x (+ x 1.0)) 3)
114.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series479.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
61.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
62.0ms	(pow (/ x (+ x 1.0)) 3)
308.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify62.0ms

Algorithm

egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1164	2932
1	5002	2690

prune553.0ms

Filtered

315 candidates to 141 candidates (44.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	313	2	315
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	315	5	320

Merged error: 0.0b

Counts

320 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
0.0b	(pow (/ x (+ x 1.0)) 3)
3.2b	(- (pow (/ x (+ x 1.0)) 3) (* (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))) (/ (+ x 1.0) (- x 1.0))))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

325×	`*-un-lft-identity`
216×	`times-frac`
169×	`add-sqr-sqrt`
105×	`add-cube-cbrt`
72×	`swap-sqr`
62×	`distribute-lft-out`
44×	`associate-r` `associate-l`
32×	`distribute-lft-out--`
31×	`add-exp-log` `add-cbrt-cube`
20×	`associate-/r/` `difference-of-squares`
19×	`pow1`
18×	`unpow-prod-down` `cube-prod`
10×	`div-inv`
9×	`cbrt-undiv` `div-exp`
8×	`cube-div` `prod-exp` `cbrt-unprod` `unswap-sqr`
7×	`frac-times` `associate-*l/` `frac-sub`
6×	`flip3-+` `flip-+` `add-log-exp`
5×	`flip3--` `associate-*r/` `flip--`
3×	`pow-unpow`
2×	`pow2` `pow-plus` `pow-prod-down` `pow-exp` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cube-cbrt`
1×	`difference-cubes` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `diff-log` `unpow3` `pow3` `sqr-pow`

Counts

4 → 292

Calls

4 calls:

22.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
29.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
8.0ms	(pow (/ x (+ x 1.0)) 3)
42.0ms	(- (pow (/ x (+ x 1.0)) 3) (* (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))) (/ (+ x 1.0) (- x 1.0))))

series482.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
60.0ms	(* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))
57.0ms	(pow (/ x (+ x 1.0)) 3)
316.0ms	(- (pow (/ x (+ x 1.0)) 3) (* (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0))) (/ (+ x 1.0) (- x 1.0))))

simplify64.0ms

Algorithm

egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1327	2957
1	5002	2651

prune616.0ms

Filtered

304 candidates to 157 candidates (51.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	302	2	304
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	304	5	309

Merged error: 0.0b

Counts

309 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (- x 1.0))
0.0b	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
0.0b	(* (+ x 1.0) (+ x 1.0))
19.0b	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

44×	`associate-*r/`
35×	`*-un-lft-identity`
32×	`frac-sub`
30×	`flip3-+` `flip-+`
25×	`add-sqr-sqrt`
20×	`frac-times` `flip3--` `flip--`
19×	`add-cube-cbrt`
18×	`associate-/l/`
13×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `associate-*l/` `add-cbrt-cube`
9×	`associate-r`
7×	`associate-l`
6×	`distribute-rgt-in` `distribute-lft-in` `swap-sqr` `distribute-lft-out` `add-log-exp`
5×	`sub-neg` `difference-of-squares`
4×	`associate--l+` `associate-/r*`
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` `diff-log` `div-sub` `div-exp` `clear-num` `pow-sqr` `pow-prod-up` `div-inv` `distribute-lft-out--`

Counts

4 → 152

Calls

4 calls:

7.0ms	(* x (- x 1.0))
15.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
13.0ms	(* (+ x 1.0) (+ x 1.0))
9.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

series156.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* x (- x 1.0))
50.0ms	(/ (- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0))) (- (* x x) (* 1.0 1.0)))
22.0ms	(* (+ x 1.0) (+ x 1.0))
39.0ms	(- (* x (- x 1.0)) (* (+ x 1.0) (+ x 1.0)))

simplify135.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (117.0ms)

Iter	Nodes	Cost
0	769	1735
1	4437	1626
2	5001	1621

prune359.0ms

Filtered

164 candidates to 110 candidates (67.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	166	3	169

Merged error: 0.0b

Counts

169 → 3

regimes26.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.1b

bsearch84.0ms

Steps

Iters	Range		Point
9	0.09117784756913819	2697524.489058797	316433.0155308468
8	-4.380867742722077e+39	-1.4003922086164443e+35	-1.2832315103805337e+38

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	15
1	44	15
2	44	15

end0.0ms

sample512.0ms

Algorithm

intervals

Results

183.0ms	1737×	body	1280	valid
100.0ms	1253×	body	640	valid
91.0ms	4086×	body	80	valid
34.0ms	584×	body	320	valid
14.0ms	340×	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