Details

sample14.0ms

Algorithm

intervals

Results

6.0ms

345×

body

valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	3
1	23	3
2	30	3
3	31	3
4	31	3

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: 4.6b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

4.3b	(* x (+ 1.0 (* y y)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `associate-r`
4×	`associate-l`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `associate-*r/` `distribute-lft-out`
1×	`expm1-log1p-u` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `log1p-expm1-u` `add-log-exp` `unswap-sqr`

Counts

1 → 28

Calls

1 calls:

9.0ms

(* x (+ 1.0 (* y y)))

series57.0ms

Counts

1 → 3

Calls

1 calls:

57.0ms

(* x (+ 1.0 (* y y)))

simplify84.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	144	129
1	714	109
2	3295	106
3	5001	106

prune43.0ms

Filtered

31 candidates to 23 candidates (74.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	28	3	31
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	4	32

Merged error: 4.4b

Counts

32 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
4.3b	(sqrt (+ 1.0 (* y y)))
4.3b	(sqrt (+ 1.0 (* y y)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
26×	`sqrt-prod`
25×	`associate-l`
16×	`sqrt-div` `associate-r`
14×	`unswap-sqr`
11×	`add-cube-cbrt`
10×	`pow1` `hypot-def`
8×	`add-exp-log` `flip3-+` `associate-*r/` `add-cbrt-cube` `flip-+` `distribute-lft-out`
4×	`frac-times` `*-commutative`
3×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `swap-sqr` `associate-*l/`

Counts

3 → 104

Calls

3 calls:

25.0ms	(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
7.0ms	(sqrt (+ 1.0 (* y y)))
7.0ms	(sqrt (+ 1.0 (* y y)))

series148.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
47.0ms	(sqrt (+ 1.0 (* y y)))
43.0ms	(sqrt (+ 1.0 (* y y)))

simplify45.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	304	813
1	1099	673
2	5001	606

prune191.0ms

Filtered

113 candidates to 78 candidates (69.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	111	6	117

Merged error: 4.4b

Counts

117 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sqrt (sqrt (+ 1.0 (* y y)))) 3)
1.5b	(* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (pow (sqrt (sqrt (+ 1.0 (* y y)))) 3))
4.3b	(sqrt (+ 1.0 (* y y)))
4.3b	(sqrt (+ 1.0 (* y y)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
79×	`sqrt-prod`
40×	`unswap-sqr`
39×	`*-un-lft-identity`
34×	`unpow-prod-down`
30×	`associate-l`
27×	`associate-r`
19×	`add-cube-cbrt`
18×	`add-exp-log`
14×	`pow1`
10×	`add-cbrt-cube` `hypot-def` `distribute-lft-out`
9×	`prod-exp`
8×	`sqrt-div`
6×	`sqrt-pow1` `sqr-pow`
5×	`pow-pow`
4×	`expm1-log1p-u` `pow1/2` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `flip3-+` `pow-prod-down` `pow-exp` `cbrt-unprod` `flip-+`
2×	`rem-sqrt-square` `unpow3` `associate-r/` `swap-sqr` `associate-l/`
1×	`sqrt-pow2` `rem-cube-cbrt`

Counts

4 → 162

Calls

4 calls:

8.0ms	(pow (sqrt (sqrt (+ 1.0 (* y y)))) 3)
33.0ms	(* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (pow (sqrt (sqrt (+ 1.0 (* y y)))) 3))
7.0ms	(sqrt (+ 1.0 (* y y)))
8.0ms	(sqrt (+ 1.0 (* y y)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(pow (sqrt (sqrt (+ 1.0 (* y y)))) 3)
57.0ms	(* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (pow (sqrt (sqrt (+ 1.0 (* y y)))) 3))
43.0ms	(sqrt (+ 1.0 (* y y)))
48.0ms	(sqrt (+ 1.0 (* y y)))

simplify98.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	550	1770
1	2611	1458
2	5001	1400

prune312.0ms

Filtered

174 candidates to 103 candidates (59.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	174	6	180

Merged error: 4.4b

Counts

180 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (pow (sqrt (sqrt (+ 1.0 (* y y)))) 3/2)) (pow (sqrt (sqrt (+ 1.0 (* y y)))) (/ 3 2)))
4.3b	(sqrt (+ 1.0 (* y y)))
4.3b	(sqrt (+ 1.0 (* y y)))
4.3b	(sqrt (+ 1.0 (* y y)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

455×	`add-sqr-sqrt`
321×	`unswap-sqr`
282×	`sqrt-prod`
157×	`unpow-prod-down`
93×	`associate-l`
60×	`add-exp-log`
48×	`prod-exp`
47×	`sqr-pow`
45×	`*-un-lft-identity`
41×	`associate-r`
21×	`add-cube-cbrt`
16×	`pow1`
15×	`hypot-def`
13×	`pow-to-exp` `pow-exp` `add-cbrt-cube`
12×	`distribute-lft-out`
10×	`sqrt-div`
6×	`pow-prod-down` `*-commutative` `cbrt-unprod`
4×	`expm1-log1p-u` `flip3-+` `associate-*l/` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `swap-sqr`
2×	`associate-*r/`

Counts

4 → 293

Calls

4 calls:

66.0ms	(* (* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (pow (sqrt (sqrt (+ 1.0 (* y y)))) 3/2)) (pow (sqrt (sqrt (+ 1.0 (* y y)))) (/ 3 2)))
8.0ms	(sqrt (+ 1.0 (* y y)))
7.0ms	(sqrt (+ 1.0 (* y y)))
8.0ms	(sqrt (+ 1.0 (* y y)))

series210.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (pow (sqrt (sqrt (+ 1.0 (* y y)))) 3/2)) (pow (sqrt (sqrt (+ 1.0 (* y y)))) (/ 3 2)))
50.0ms	(sqrt (+ 1.0 (* y y)))
48.0ms	(sqrt (+ 1.0 (* y y)))
43.0ms	(sqrt (+ 1.0 (* y y)))

simplify161.0ms

Algorithm

egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	629	6600
1	2604	5362
2	5002	5111

prune492.0ms

Filtered

305 candidates to 132 candidates (43.3%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	305	0	305
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	305	6	311

Merged error: 4.4b

Counts

311 → 6

regimes119.0ms

Accuracy

0% (0.2b remaining)

Error of 5.2b against oracle of 5.0b and baseline of 5.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	8
1	11	8

end0.0ms

sample346.0ms

Algorithm

intervals

Results

187.0ms

10655×

body

valid