Details

sample13.0ms

Algorithm

intervals

Results

5.0ms	256×	body	80	valid
1.0ms	66×	body	80	nan

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	4
1	8	4

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: 0.2b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 61

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series226.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(sqrt (+ x 1.0))
49.0ms	(+ 1.0 (sqrt (+ x 1.0)))
146.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify43.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	317	483
1	1159	435
2	5001	427

prune146.0ms

Filtered

70 candidates to 52 candidates (74.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	4	71

Merged error: 0b

Counts

71 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ x 1.0)))
0.0b	(sqrt (sqrt (+ x 1.0)))
0.2b	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
0.2b	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
64×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
30×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
16×	`distribute-lft-out`
15×	`times-frac`
14×	`associate-l`
10×	`associate-r`
9×	`flip3-+` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `associate-/r*` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
3×	`associate-/l*`
2×	`associate-r/` `associate-l/` `associate-/r/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 169

Calls

4 calls:

4.0ms	(sqrt (sqrt (+ x 1.0)))
4.0ms	(sqrt (sqrt (+ x 1.0)))
25.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
15.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series369.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sqrt (sqrt (+ x 1.0)))
93.0ms	(sqrt (sqrt (+ x 1.0)))
152.0ms	(/ x (+ 1.0 (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
32.0ms	(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify80.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	512	1361
1	2301	1177
2	5001	1151

prune313.0ms

Filtered

181 candidates to 93 candidates (51.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	181	4	185

Merged error: 0b

Counts

185 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
0.2b	(pow (sqrt (+ x 1.0)) 3)
3.3b	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
5.8b	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

160×	`add-sqr-sqrt`
152×	`*-un-lft-identity`
93×	`sqrt-prod`
62×	`sqrt-div`
46×	`associate-r`
38×	`add-cube-cbrt` `unswap-sqr`
37×	`distribute-lft-out`
36×	`times-frac`
33×	`difference-of-squares`
32×	`flip3-+` `flip-+`
28×	`associate-*r/`
26×	`distribute-rgt-out--`
23×	`unpow-prod-down` `cube-prod` `swap-sqr`
21×	`pow1`
19×	`pow-unpow`
16×	`sum-cubes` `frac-sub`
12×	`frac-times` `associate-/r*`
11×	`associate-l` `*-commutative`
9×	`add-exp-log` `sqrt-pow1` `pow1/2` `add-cbrt-cube`
8×	`associate-*l/`
6×	`distribute-lft-out--` `add-log-exp`
5×	`pow-prod-up`
4×	`sub-div`
3×	`pow-pow` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cube-div` `associate-/r/`
1×	`cbrt-undiv` `pow2` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `pow-plus` `sqrt-unprod` `diff-log` `unpow3` `div-exp` `pow-exp` `prod-exp` `clear-num` `rem-square-sqrt` `sqrt-pow2` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 260

Calls

4 calls:

11.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
5.0ms	(pow (sqrt (+ x 1.0)) 3)
46.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
21.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

series558.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (sqrt (+ x 1.0)) (sqrt (+ x 1.0)))
68.0ms	(pow (sqrt (+ x 1.0)) 3)
62.0ms	(- (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
410.0ms	(/ x (+ (pow 1.0 3) (pow (sqrt (+ x 1.0)) 3)))

simplify179.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 2 (148.0ms)

Iter	Nodes	Cost
0	921	2556
1	4433	2263
2	5001	2248

prune439.0ms

Filtered

272 candidates to 107 candidates (39.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	272	0	272
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	272	4	276

Merged error: 0b

Counts

276 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0))
0.0b	(+ (sqrt (+ x 1.0)) 1.0)
0.2b	(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
59×	`add-sqr-sqrt`
52×	`times-frac`
42×	`add-cube-cbrt` `sqrt-prod`
30×	`associate-r`
16×	`distribute-lft-out`
13×	`associate-r/` `associate-/l`
11×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*`
7×	`pow1`
6×	`associate-l` `add-log-exp` `unswap-sqr`
4×	`flip3-+` `associate-/r/` `flip-+`
3×	`clear-num`
2×	`cbrt-undiv` `frac-2neg` `sqrt-div` `div-exp` `prod-exp` `un-div-inv` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `sum-log` `*-commutative`

Counts

4 → 146

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
9.0ms	(/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0))
6.0ms	(+ (sqrt (+ x 1.0)) 1.0)
23.0ms	(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

series504.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ x 1.0))
294.0ms	(/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0))
42.0ms	(+ (sqrt (+ x 1.0)) 1.0)
138.0ms	(* (sqrt x) (/ (sqrt x) (+ (sqrt (+ x 1.0)) 1.0)))

simplify77.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	545	1323
1	2344	1171
2	5001	1139

prune282.0ms

Filtered

158 candidates to 99 candidates (62.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	158	4	162

Merged error: 0b

Counts

162 → 4

regimes39.0ms

Accuracy

0% (0.2b 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	8	4
1	8	4

end0.0ms

sample317.0ms

Algorithm

intervals

Results

155.0ms	7990×	body	80	valid
42.0ms	2595×	body	80	nan
1.0ms	10×	body	1280	valid