Details

sample42.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

23.0ms	102×	body	1280	valid
5.0ms	117×	body	80	valid
4.0ms	20×	body	640	valid
1.0ms	12×	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

prune3.0ms

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: 19.8b

Counts

2 → 1

localize7.0ms

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))))))

rewrite21.0ms

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)))
10.0ms	(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))))))

series32.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot 1.0 x)
5.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
13.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify49.0ms

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

prune95.0ms

Filtered

40 candidates to 58 candidates (-45.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	3	59

Merged error: 19.4b

Counts

59 → 3

localize12.0ms

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	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.5b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
8×	`associate-*r/` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`distribute-lft-out`
4×	`pow1` `flip3--` `associate--l+` `associate-/r*` `frac-sub` `flip--` `associate-/l/`
3×	`sub-neg` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 75

Calls

4 calls:

1.0ms	(hypot 1.0 x)
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
11.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (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))))

series44.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot 1.0 x)
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
32.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (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))))

simplify48.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	398	1102
1	1424	1013
2	5002	1009

prune217.0ms

Filtered

61 candidates to 87 candidates (-42.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	85	5	90

Merged error: 19.3b

Counts

90 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
0.0b	(/ (/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
1.4b	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-exp-log` `add-cbrt-cube`
35×	`*-un-lft-identity`
34×	`times-frac`
28×	`associate-*r/`
21×	`add-sqr-sqrt`
19×	`add-cube-cbrt`
14×	`associate-/r/`
13×	`cbrt-undiv` `div-exp`
12×	`flip3-+` `flip-+`
9×	`prod-exp` `cbrt-unprod`
8×	`associate-l/` `frac-sub` `distribute-lft-out` `associate-/l`
7×	`div-inv` `associate-/l/`
6×	`pow1` `flip3--` `flip--` `add-log-exp`
5×	`associate-/r*`
3×	`associate-r` `associate-l`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `associate--r+`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 131

Calls

4 calls:

8.0ms	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
25.0ms	(/ (/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
28.0ms	(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
16.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

series58.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))
42.0ms	(/ (/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
10.0ms	(/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))
3.0ms	(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

simplify57.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	853	3937
1	5001	3367

prune686.0ms

Filtered

97 candidates to 143 candidates (-47.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	143	5	148

Merged error: 19.3b

Counts

148 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.1b	(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.4b	(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `associate-/r/`
5×	`flip3-+` `flip-+`
4×	`pow1` `cbrt-undiv` `times-frac` `div-exp` `associate-/r*` `distribute-lft-out`
3×	`distribute-rgt-out--` `div-inv`
2×	`+-commutative` `prod-exp` `sum-log` `cbrt-unprod`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `associate-r/` `clear-num` `frac-sub` `flip--` `associate-/l/` `associate-/l` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 71

Calls

4 calls:

5.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
5.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
7.0ms	(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
16.0ms	(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

series102.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
29.0ms	(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
60.0ms	(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

simplify46.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	403	1201
1	1643	1059
2	5002	1032

prune237.0ms

Filtered

57 candidates to 83 candidates (-45.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	82	6	88

Merged error: 19.0b

Counts

88 → 6

regimes432.0ms

Accuracy

0% (0.3b remaining)

Error of 15.5b against oracle of 15.2b and baseline of 15.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	22
1	22	22

end0.0ms

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

654.0ms	2860×	body	1280	valid
163.0ms	4014×	body	80	valid
117.0ms	658×	body	640	valid
42.0ms	322×	body	320	valid
12.0ms	146×	body	160	valid

Details

sample42.0ms

simplify8.0ms

prune3.0ms

localize7.0ms

rewrite21.0ms

series32.0ms

simplify49.0ms

prune95.0ms

localize12.0ms

rewrite26.0ms

series44.0ms

simplify48.0ms

prune217.0ms

localize22.0ms

rewrite82.0ms

series58.0ms

simplify57.0ms

prune686.0ms

localize16.0ms

rewrite36.0ms

series102.0ms

simplify46.0ms

prune237.0ms

regimes432.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling