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

12.0ms

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: 34.3b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
32.0b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

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

series44.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* x x) (* y y))
13.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
26.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4941	1233
1	4941	1233

prune139.0ms

Filtered

62 candidates to 74 candidates (-19.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	6	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	68	7	75

Merged error: 16.1b

Counts

75 → 7

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (+ (* y y) (* z z)))
0.1b	(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
32.0b	(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 46

Calls

3 calls:

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))

series51.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(+ (* x x) (+ (* y y) (* z z)))
15.0ms	(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
26.0ms	(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

simplify45.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5057	797

prune75.0ms

Filtered

37 candidates to 55 candidates (-48.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	55	7	62

Merged error: 16.1b

Counts

62 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (+ (* y y) (* z z)))
0.2b	(/ (+ (* 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))))
31.9b	(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0)))

rewrite55.0ms

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)))
11.0ms	(/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))
23.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))))
8.0ms	(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0)))

series114.0ms

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))
45.0ms	(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))))
40.0ms	(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0)))

simplify86.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4964	4093
1	4964	4093

prune419.0ms

Filtered

132 candidates to 169 candidates (-28.0%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	166	3	169
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	166	10	176

Merged error: 16.1b

Counts

176 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (+ (* y y) (* z z)))
0.2b	(/ (/ (+ (* x x) (+ (* y y) (* z z))) (sqrt 3.0)) (sqrt 3.0))
0.2b	(/ (+ (* x x) (+ (* y y) (* z z))) (sqrt 3.0))
32.0b	(sqrt (/ (/ (+ (* x x) (+ (* y y) (* z z))) (sqrt 3.0)) (sqrt 3.0)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

526×	`times-frac`
405×	`sqrt-prod`
296×	`add-sqr-sqrt`
279×	`add-cube-cbrt` `*-un-lft-identity`
25×	`associate-/l*`
16×	`div-inv`
12×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
9×	`add-log-exp`
7×	`rem-sqrt-square`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`sum-log` `associate-/l/`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`+-commutative` `associate-+r+` `sqrt-pow1` `pow1/2` `sqrt-div`

Counts

4 → 382

Calls

4 calls:

7.0ms	(+ (* x x) (+ (* y y) (* z z)))
18.0ms	(/ (/ (+ (* x x) (+ (* y y) (* z z))) (sqrt 3.0)) (sqrt 3.0))
10.0ms	(/ (+ (* x x) (+ (* y y) (* z z))) (sqrt 3.0))
21.0ms	(sqrt (/ (/ (+ (* x x) (+ (* y y) (* z z))) (sqrt 3.0)) (sqrt 3.0)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* x x) (+ (* y y) (* z z)))
26.0ms	(/ (/ (+ (* x x) (+ (* y y) (* z z))) (sqrt 3.0)) (sqrt 3.0))
23.0ms	(/ (+ (* x x) (+ (* y y) (* z z))) (sqrt 3.0))
31.0ms	(sqrt (/ (/ (+ (* x x) (+ (* y y) (* z z))) (sqrt 3.0)) (sqrt 3.0)))

simplify152.0ms

Algorithm

egg-herbie

Counts

394 → 394

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4953	11441
1	4953	11441

prune402.0ms

Filtered

172 candidates to 394 candidates (-129.1%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	391	3	394
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	391	13	404

Merged error: 16.0b

Counts

404 → 13

regimes1.1s

Accuracy

58.3% (8.2b remaining)

Error of 26.3b against oracle of 18.1b and baseline of 37.8b

bsearch56.0ms

Steps

Iters	Range		Point
9	2.7770796570812462e+35	4.2396165874560057e+40	4.2028759973580324e+40
9	3.751567380081343e-285	4.166418763817453e-278	6.283003548996908e-285
4	-2.5018797972345417e-304	-1.677523558518056e-304	-1.6926737645350488e-304
9	-5.383788097406942e+155	-3.1840243950354578e+147	-5.128848087281205e+147

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	57
1	48	57

end0.0ms

sample529.0ms

Algorithm

intervals

Results

372.0ms

8000×

body

valid

Details

analyze14.0ms

sample20.0ms

simplify3.0ms

prune7.0ms

localize13.0ms

rewrite21.0ms

series44.0ms

simplify56.0ms

prune139.0ms

localize9.0ms

rewrite23.0ms

series51.0ms

simplify45.0ms

prune75.0ms

localize15.0ms

rewrite55.0ms

series114.0ms

simplify86.0ms

prune419.0ms

localize12.0ms

rewrite79.0ms

series91.0ms

simplify152.0ms

prune402.0ms

regimes1.1s

bsearch56.0ms

simplify2.0ms

end0.0ms

sample529.0ms

Profiling