Details

analyze14.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
93.6%	6.2%	0.1%	8
96.7%	3.1%	0.1%	9
98.3%	1.6%	0.1%	10
99.1%	0.8%	0.1%	11
99.5%	0.4%	0.1%	12
99.7%	0.2%	0.1%	13
99.8%	0.1%	0.1%	14

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 40.5b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
37.5b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`times-frac`
17×	`add-cube-cbrt` `*-un-lft-identity`
13×	`sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`rem-sqrt-square` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `div-exp` `clear-num` `flip-+`

Counts

2 → 54

Calls

2 calls:

8.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series44.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
31.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify26.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5095	1102

prune127.0ms

Filtered

52 candidates to 60 candidates (-15.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	54	6	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	6	61

Merged error: 19.9b

Counts

61 → 6

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y y) (* z z))
0.1b	(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
37.5b	(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1`
7×	`add-sqr-sqrt`
5×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
4×	`associate-*l/`
3×	`flip3-+` `associate-r` `associate-l` `flip-+`
2×	`sqrt-pow1` `sqrt-div` `pow-prod-down`
1×	`+-commutative` `pow1/2` `prod-exp` `sum-log` `sqrt-prod` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 44

Calls

3 calls:

4.0ms	(+ (* y y) (* z z))
8.0ms	(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
7.0ms	(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

series50.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* y y) (* z z))
13.0ms	(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
32.0ms	(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

simplify50.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5370	700

prune77.0ms

Filtered

36 candidates to 53 candidates (-47.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	53	6	59

Merged error: 19.9b

Counts

59 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0))
0.3b	(* (sqrt (sqrt (+ (* x x) (+ (* y y) (* z z))))) (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0)))
37.4b	(sqrt (+ (* x x) (+ (* y y) (* z z))))
37.4b	(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

102×	`sqrt-prod`
73×	`add-sqr-sqrt`
44×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
25×	`associate-r`
16×	`sqrt-div`
12×	`unswap-sqr`
11×	`pow1`
9×	`associate-l`
6×	`add-exp-log` `add-cbrt-cube`
5×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`pow-prod-down`
2×	`frac-times` `associate-*l/` `div-inv`
1×	`sqrt-unprod` `associate-r/` `prod-exp` `-commutative` `cbrt-unprod`

Counts

4 → 130

Calls

4 calls:

8.0ms	(sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0))
25.0ms	(* (sqrt (sqrt (+ (* x x) (+ (* y y) (* z z))))) (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0)))
6.0ms	(sqrt (+ (* x x) (+ (* y y) (* z z))))
6.0ms	(sqrt (+ (* x x) (+ (* y y) (* z z))))

series151.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0))
50.0ms	(* (sqrt (sqrt (+ (* x x) (+ (* y y) (* z z))))) (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0)))
33.0ms	(sqrt (+ (* x x) (+ (* y y) (* z z))))
24.0ms	(sqrt (+ (* x x) (+ (* y y) (* z z))))

simplify48.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5477	3569

prune172.0ms

Filtered

95 candidates to 142 candidates (-49.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	142	6	148

Merged error: 19.9b

Counts

148 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y y) (* z z))
0.4b	(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
37.4b	(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 89

Calls

3 calls:

4.0ms	(+ (* y y) (* z z))
9.0ms	(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
6.0ms	(sqrt (+ (* x x) (+ (* y y) (* z z))))

series57.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* y y) (* z z))
31.0ms	(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
21.0ms	(sqrt (+ (* x x) (+ (* y y) (* z z))))

simplify47.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5240	1945

prune101.0ms

Filtered

60 candidates to 98 candidates (-63.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	95	9	104

Merged error: 19.8b

Counts

104 → 9

regimes530.0ms

Accuracy

59.4% (7.9b remaining)

Error of 26.7b against oracle of 18.8b and baseline of 38.3b

bsearch64.0ms

Steps

Iters	Range		Point
8	3.2159952724272873e+100	3.9346908559132804e+104	3.2526274382715766e+104
9	-1.8373988675773855e-266	-2.06660718003652e-271	-1.8125065743652247e-266
9	-4.063573378391617e-207	-1.9707636825743149e-215	-6.733605899691578e-215
8	-7.29483272344081e+113	-2.079637696625727e+111	-1.954455009610157e+112

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	57
1	57	57

end0.0ms

sample501.0ms

Algorithm

intervals

Results

355.0ms

8000×

body

valid

Details

analyze14.0ms

sample20.0ms

simplify3.0ms

prune7.0ms

localize9.0ms

rewrite17.0ms

series44.0ms

simplify26.0ms

prune127.0ms

localize9.0ms

rewrite20.0ms

series50.0ms

simplify50.0ms

prune77.0ms

localize13.0ms

rewrite50.0ms

series151.0ms

simplify48.0ms

prune172.0ms

localize10.0ms

rewrite22.0ms

series57.0ms

simplify47.0ms

prune101.0ms

regimes530.0ms

bsearch64.0ms

simplify2.0ms

end0.0ms

sample501.0ms

Profiling