Details

sample23.0ms

Algorithm

intervals

Results

4.0ms	52×	body	1280	valid
4.0ms	229×	body	80	nan
3.0ms	46×	body	640	valid
2.0ms	135×	body	80	valid
1.0ms	17×	body	320	valid
0.0ms	6×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 29.2b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

1.9b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `sqrt-prod`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 19

Calls

1 calls:

8.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

series76.0ms

Counts

1 → 3

Calls

1 calls:

76.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

simplify48.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	129	175
1	383	159
2	1492	153
3	5002	149

prune39.0ms

Filtered

22 candidates to 14 candidates (36.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21	2	23

Merged error: 0.1b

Counts

23 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
20×	`sqrt-prod` `distribute-lft-out`
18×	`times-frac`
13×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 55

Calls

2 calls:

8.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series416.0ms

Counts

2 → 6

Calls

2 calls:

265.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
151.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify39.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	292	535
1	1048	482
2	5001	453

prune104.0ms

Filtered

61 candidates to 39 candidates (36.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	55	6	61
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	56	7	63

Merged error: 0.0b

Counts

63 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

540×	`*-un-lft-identity`
382×	`sqrt-prod`
324×	`sqrt-div`
224×	`distribute-lft-out`
174×	`associate-/r*`
173×	`add-sqr-sqrt`
157×	`times-frac`
144×	`frac-times`
142×	`add-cube-cbrt`
87×	`associate-/l*`
41×	`swap-sqr`
29×	`frac-2neg` `clear-num`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-r/` `associate-l/`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
5×	`pow-prod-up`
4×	`add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `div-exp`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 426

Calls

4 calls:

11.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
11.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
45.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series842.0ms

Counts

4 → 12

Calls

4 calls:

366.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
149.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
147.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
179.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify142.0ms

Algorithm

egg-herbie

Counts

438 → 438

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	793	5695
1	3467	5087
2	5001	5004

prune560.0ms

Filtered

438 candidates to 174 candidates (60.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	434	4	438
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	437	8	445

Merged error: 0.0b

Counts

445 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.3b	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (fabs (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

208×	`*-un-lft-identity`
198×	`sqrt-prod`
110×	`times-frac`
85×	`add-sqr-sqrt`
76×	`distribute-lft-out`
75×	`add-cube-cbrt`
27×	`associate-l` `associate-/r*`
26×	`sqrt-div`
15×	`associate-/l*`
12×	`associate-*l/`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/`
7×	`pow1`
4×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `div-exp`
1×	`sqrt-undiv` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 228

Calls

4 calls:

11.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
13.0ms	(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
21.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (fabs (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

367.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
154.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
369.0ms	(/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
317.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (fabs (/ (sqrt 1.0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))

simplify107.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	786	3408
1	3006	3209
2	5001	2886

prune505.0ms

Filtered

240 candidates to 135 candidates (43.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	240	0	240
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	240	8	248

Merged error: 0.0b

Counts

248 → 8

regimes37.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	5
1	9	5

end0.0ms

sample642.0ms

Algorithm

intervals

Results

145.0ms	1679×	body	1280	valid
127.0ms	7872×	body	80	nan
83.0ms	1255×	body	640	valid
76.0ms	4148×	body	80	valid
30.0ms	625×	body	320	valid
10.0ms	293×	body	160	valid