Details

analyze20.0ms

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

sample35.0ms

Algorithm

intervals

Results

10.0ms

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

prune6.0ms

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: 36.7b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.3b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.0b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

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

series52.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* x x) (* y y))
10.0ms	(+ (+ (* x x) (* y y)) (* z z))
12.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
25.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4946	1461
1	4946	1461

prune323.0ms

Filtered

72 candidates to 90 candidates (-25.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	83	7	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	7	91

Merged error: 16.2b

Counts

91 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y y) (* z z))
0.0b	(+ (* x x) (+ (* y y) (* z z)))
0.3b	(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
34.0b	(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

4.0ms	(+ (* y y) (* z z))
6.0ms	(+ (* x x) (+ (* 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))

series56.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* y y) (* z z))
10.0ms	(+ (* x x) (+ (* y y) (* z z)))
13.0ms	(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
28.0ms	(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

simplify61.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4945	928
1	4945	928

prune107.0ms

Filtered

47 candidates to 69 candidates (-46.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	69	7	76

Merged error: 16.2b

Counts

76 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y y) (* z z))
0.0b	(+ (* x x) (+ (* y y) (* z z)))
0.4b	(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
34.2b	(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

4.0ms	(+ (* y y) (* z z))
6.0ms	(+ (* x x) (+ (* y y) (* z z)))
9.0ms	(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
5.0ms	(sqrt (+ (* x x) (+ (* y y) (* z z))))

series64.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* y y) (* z z))
10.0ms	(+ (* x x) (+ (* y y) (* z z)))
31.0ms	(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
18.0ms	(sqrt (+ (* x x) (+ (* y y) (* z z))))

simplify51.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4948	2173
1	4948	2173

prune137.0ms

Filtered

71 candidates to 114 candidates (-60.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	111	10	121

Merged error: 16.0b

Counts

121 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (+ (* y y) (* z z)))
0.1b	(/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))
0.4b	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))))
34.2b	(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
75×	`times-frac` `sqrt-prod`
53×	`*-un-lft-identity`
49×	`add-cube-cbrt`
35×	`cbrt-prod`
25×	`associate-r`
16×	`unswap-sqr`
10×	`associate-l`
9×	`pow1` `add-log-exp`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/r*`
5×	`sqrt-div`
4×	`div-inv`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `sum-log` `associate-/l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-times` `associate-+r+` `frac-2neg` `sqrt-unprod` `associate-r/` `div-exp` `associate-l/` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 157

Calls

4 calls:

6.0ms	(+ (* x x) (+ (* y y) (* z z)))
9.0ms	(/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))
24.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))))
16.0ms	(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0)))

series115.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (* x x) (+ (* y y) (* z z)))
19.0ms	(/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))
42.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))))
43.0ms	(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0)))

simplify77.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4964	4093
1	4964	4093

prune377.0ms

Filtered

132 candidates to 169 candidates (-28.0%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	166	3	169
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	166	13	179

Merged error: 16.0b

Counts

179 → 13

regimes687.0ms

Accuracy

62.8% (7.2b remaining)

Error of 25.6b against oracle of 18.4b and baseline of 37.8b

bsearch38.0ms

Steps

Iters	Range		Point
7	2.638869520189117e+48	1.2558653627967038e+50	1.2356342879637884e+50
8	-1.1180956785317455e+155	-7.27269416187024e+151	-3.0495014106624294e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	43
1	59	43

end0.0ms

sample950.0ms

Algorithm

intervals

Results

331.0ms

8000×

body

valid

Details

analyze20.0ms

sample35.0ms

simplify3.0ms

prune6.0ms

localize9.0ms

rewrite28.0ms

series52.0ms

simplify45.0ms

prune323.0ms

localize9.0ms

rewrite26.0ms

series56.0ms

simplify61.0ms

prune107.0ms

localize12.0ms

rewrite28.0ms

series64.0ms

simplify51.0ms

prune137.0ms

localize15.0ms

rewrite61.0ms

series115.0ms

simplify77.0ms

prune377.0ms

regimes687.0ms

bsearch38.0ms

simplify2.0ms

end0.0ms

sample950.0ms

Profiling