Details

sample18.0ms

Algorithm

intervals

Results

9.0ms

296×

body

valid

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	5
1	29	5
2	45	5
3	56	5
4	74	5
5	86	5
6	120	5
7	136	5
8	146	5
9	150	5
10	160	5
11	446	5
12	2695	5
13	5001	5

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: 10.1b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(* x (+ (/ x y) 1.0))
9.4b	(/ (* x (+ (/ x y) 1.0)) (+ x 1.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
4×	`pow1` `times-frac` `associate-r/` `associate-r` `associate-/r`
3×	`flip3-+` `associate-l` `flip-+` `distribute-lft-out`
2×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

2 → 54

Calls

2 calls:

9.0ms	(* x (+ (/ x y) 1.0))
12.0ms	(/ (* x (+ (/ x y) 1.0)) (+ x 1.0))

series70.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(* x (+ (/ x y) 1.0))
45.0ms	(/ (* x (+ (/ x y) 1.0)) (+ x 1.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	306	352
1	1568	305
2	5001	304

prune104.0ms

Filtered

60 candidates to 42 candidates (70.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	51	9	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	9	61

Merged error: 0.0b

Counts

61 → 9

localize6.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (+ x 1.0) (+ (/ x y) 1.0))
0.1b	(/ x (/ (+ x 1.0) (+ (/ x y) 1.0)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

155×	`*-un-lft-identity`
146×	`times-frac`
71×	`add-sqr-sqrt` `add-cube-cbrt`
42×	`distribute-lft-out`
26×	`associate-/r*`
11×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/l*`
6×	`flip3-+` `flip-+` `div-inv`
4×	`cbrt-undiv` `div-exp`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `associate-/l/` `add-log-exp`

Counts

2 → 150

Calls

2 calls:

17.0ms	(/ (+ x 1.0) (+ (/ x y) 1.0))
13.0ms	(/ x (/ (+ x 1.0) (+ (/ x y) 1.0)))

series135.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(/ (+ x 1.0) (+ (/ x y) 1.0))
68.0ms	(/ x (/ (+ x 1.0) (+ (/ x y) 1.0)))

simplify65.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	504	1464
1	2390	1406
2	5002	1404

prune214.0ms

Filtered

156 candidates to 100 candidates (64.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	153	3	156
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	156	9	165

Merged error: 0b

Counts

165 → 9

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ x (/ 1 (/ (+ (/ x y) 1.0) (+ x 1.0))))
0.1b	(/ (+ (/ x y) 1.0) (+ x 1.0))
0.1b	(/ 1 (/ (+ (/ x y) 1.0) (+ x 1.0)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

815×	`times-frac`
620×	`*-un-lft-identity`
344×	`add-sqr-sqrt` `add-cube-cbrt`
138×	`distribute-lft-out`
97×	`associate-/r*`
40×	`associate-/r/`
35×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
19×	`add-cbrt-cube`
18×	`flip3-+` `flip-+`
10×	`cbrt-undiv` `associate-/l*`
4×	`pow1` `rec-exp` `1-exp`
3×	`expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

3 → 466

Calls

3 calls:

23.0ms	(/ x (/ 1 (/ (+ (/ x y) 1.0) (+ x 1.0))))
10.0ms	(/ (+ (/ x y) 1.0) (+ x 1.0))
13.0ms	(/ 1 (/ (+ (/ x y) 1.0) (+ x 1.0)))

series203.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(/ x (/ 1 (/ (+ (/ x y) 1.0) (+ x 1.0))))
48.0ms	(/ (+ (/ x y) 1.0) (+ x 1.0))
85.0ms	(/ 1 (/ (+ (/ x y) 1.0) (+ x 1.0)))

simplify118.0ms

Algorithm

egg-herbie

Counts

475 → 475

Iterations

Useful iterations: 1 (47.0ms)

Iter	Nodes	Cost
0	1297	5686
1	5001	5082

prune540.0ms

Filtered

475 candidates to 235 candidates (49.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	475	0	475
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	475	9	484

Merged error: 0b

Counts

484 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ (/ x y) 1.0))
0.2b	(cbrt (+ (/ x y) 1.0))
0.2b	(* (cbrt (+ (/ x y) 1.0)) (cbrt (+ (/ x y) 1.0)))
9.4b	(/ (* (* x (* (cbrt (+ (/ x y) 1.0)) (cbrt (+ (/ x y) 1.0)))) (cbrt (+ (/ x y) 1.0))) (+ x 1.0))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

70×	`cbrt-div`
38×	`*-un-lft-identity`
36×	`flip3-+` `flip-+`
34×	`associate-*r/`
32×	`cbrt-prod` `frac-times`
26×	`associate-/l/`
24×	`add-sqr-sqrt`
20×	`add-exp-log`
16×	`add-cube-cbrt` `associate-*l/`
13×	`add-cbrt-cube`
11×	`pow1`
10×	`distribute-lft-out`
9×	`swap-sqr`
8×	`pow1/3`
7×	`associate-r` `associate-l` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `times-frac` `div-exp` `associate-/r*` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-/r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-2neg` `pow-plus` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 144

Calls

4 calls:

6.0ms	(cbrt (+ (/ x y) 1.0))
6.0ms	(cbrt (+ (/ x y) 1.0))
19.0ms	(* (cbrt (+ (/ x y) 1.0)) (cbrt (+ (/ x y) 1.0)))
30.0ms	(/ (* (* x (* (cbrt (+ (/ x y) 1.0)) (cbrt (+ (/ x y) 1.0)))) (cbrt (+ (/ x y) 1.0))) (+ x 1.0))

series798.0ms

Counts

4 → 12

Calls

4 calls:

241.0ms	(cbrt (+ (/ x y) 1.0))
249.0ms	(cbrt (+ (/ x y) 1.0))
266.0ms	(* (cbrt (+ (/ x y) 1.0)) (cbrt (+ (/ x y) 1.0)))
41.0ms	(/ (* (* x (* (cbrt (+ (/ x y) 1.0)) (cbrt (+ (/ x y) 1.0)))) (cbrt (+ (/ x y) 1.0))) (+ x 1.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	530	1764
1	2466	1525
2	5001	1415

prune337.0ms

Filtered

156 candidates to 116 candidates (74.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	156	9	165

Merged error: 0b

Counts

165 → 9

regimes55.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	5
1	10	5

end0.0ms

sample461.0ms

Algorithm

intervals

Results

302.0ms

9130×

body

valid