Details

sample38.0ms

Algorithm

intervals

Results

21.0ms	100×	body	1280	valid
5.0ms	125×	body	80	valid
3.0ms	18×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	5×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	6

prune7.0ms

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: 14.1b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.9b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity` `add-log-exp`
7×	`pow1`
6×	`add-sqr-sqrt`
4×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`+-commutative` `sub-neg` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `sum-log` `sqrt-prod` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 46

Calls

4 calls:

1.0ms	(hypot 1.0 x)
5.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
6.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series34.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot 1.0 x)
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
14.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify48.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	167	381
1	423	355
2	1736	353
3	5002	352

prune96.0ms

Filtered

40 candidates to 58 candidates (-45.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	2	59

Merged error: 13.6b

Counts

59 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.4b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-r/` `associate-/r` `associate-/l*` `add-log-exp`
4×	`associate--l+`
3×	`sub-neg`
2×	`cbrt-undiv` `distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `sqrt-div` `div-exp` `clear-num` `frac-sub` `flip--` `div-inv`
1×	`flip3-+` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod` `flip-+`

Counts

4 → 85

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series30.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(/ 1.0 (hypot 1.0 x))
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
8.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify37.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	299	576
1	1026	547
2	5001	541

prune216.0ms

Filtered

70 candidates to 97 candidates (-38.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	97	2	99

Merged error: 13.6b

Counts

99 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
0.5b	(* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.9b	(- 1.0 (* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
16×	`add-cube-cbrt`
11×	`sqrt-prod`
9×	`times-frac`
8×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-r`
6×	`associate-l`
4×	`unswap-sqr`
3×	`pow-prod-down` `associate-/r` `associate-/l`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `associate-*r/` `flip-+` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `sqrt-unprod` `diff-log` `div-exp` `prod-exp` `clear-num` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `div-inv`

Counts

4 → 84

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms	(/ 1.0 (hypot 1.0 x))
10.0ms	(* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(- 1.0 (* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series39.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
4.0ms	(/ 1.0 (hypot 1.0 x))
13.0ms	(* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
15.0ms	(- 1.0 (* (sqrt 0.5) (sqrt (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify99.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	272	656
1	1012	616
2	3572	611
3	5001	611

prune160.0ms

Filtered

63 candidates to 96 candidates (-52.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	96	2	98

Merged error: 13.6b

Counts

98 → 2

regimes107.0ms

Accuracy

0% (0.0b remaining)

Error of 15.2b against oracle of 15.2b and baseline of 15.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	13
1	19	13

end0.0ms

sample1.1s

Algorithm

intervals

Results

616.0ms	2844×	body	1280	valid
159.0ms	4041×	body	80	valid
108.0ms	632×	body	640	valid
39.0ms	329×	body	320	valid
12.0ms	154×	body	160	valid

Details

sample38.0ms

simplify8.0ms

prune7.0ms

localize8.0ms

rewrite17.0ms

series34.0ms

simplify48.0ms

prune96.0ms

localize13.0ms

rewrite20.0ms

series30.0ms

simplify37.0ms

prune216.0ms

localize11.0ms

rewrite23.0ms

series39.0ms

simplify99.0ms

prune160.0ms

regimes107.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling