Details

analyze699.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
6.2%	82.7%	11.1%	10
12.5%	73.7%	13.8%	11
15.6%	59.5%	25%	12
17.9%	53.3%	28.8%	13
22.4%	47.2%	30.4%	14

sample26.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
4.0ms	103×	body	80	invalid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	13
1	21	13

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: 7.8b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* z z) t)
0.0b	(- (* x x) (* (* y 4.0) (- (* z z) t)))
7.4b	(* (* y 4.0) (- (* z z) t))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 48

Calls

3 calls:

4.0ms	(- (* z z) t)
3.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
8.0ms	(* (* y 4.0) (- (* z z) t))

series38.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(- (* z z) t)
19.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
15.0ms	(* (* y 4.0) (- (* z z) t))

simplify36.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5049	632

prune89.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	51	6	57
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	51	7	58

Merged error: 3.2b

Counts

58 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

2.3b	(cbrt (+ (* x x) (* y (* 4.0 (- t (* z z))))))
7.4b	(* y (* 4.0 (- t (* z z))))
7.4b	(* y (* 4.0 (- t (* z z))))
7.4b	(* y (* 4.0 (- t (* z z))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/`
9×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`cbrt-prod` `flip3--` `associate-r` `*-commutative` `flip--`
2×	`cbrt-div`
1×	`flip3-+` `pow1/3` `flip-+`

Counts

4 → 85

Calls

4 calls:

3.0ms	(cbrt (+ (* x x) (* y (* 4.0 (- t (* z z))))))
6.0ms	(* y (* 4.0 (- t (* z z))))
6.0ms	(* y (* 4.0 (- t (* z z))))
7.0ms	(* y (* 4.0 (- t (* z z))))

series97.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(cbrt (+ (* x x) (* y (* 4.0 (- t (* z z))))))
15.0ms	(* y (* 4.0 (- t (* z z))))
15.0ms	(* y (* 4.0 (- t (* z z))))
15.0ms	(* y (* 4.0 (- t (* z z))))

simplify61.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4931	1143
1	4931	1143

prune163.0ms

Filtered

61 candidates to 97 candidates (-59.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	97	7	104

Merged error: 3.2b

Counts

104 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* y (* 4.0 (sqrt (- (* z z) t))))
0.2b	(* (* y (* 4.0 (sqrt (- (* z z) t)))) (sqrt (- (* z z) t)))
7.3b	(sqrt (- (* z z) t))
7.3b	(sqrt (- (* z z) t))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1`
18×	`add-exp-log` `sqrt-div` `associate-*r/` `add-cbrt-cube`
14×	`add-sqr-sqrt`
12×	`sqrt-prod`
9×	`add-cube-cbrt` `flip3--` `*-un-lft-identity` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
8×	`associate-r`
4×	`frac-times` `associate-l` `add-log-exp`
3×	`difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l/` `-commutative`

Counts

4 → 85

Calls

4 calls:

9.0ms	(* y (* 4.0 (sqrt (- (* z z) t))))
14.0ms	(* (* y (* 4.0 (sqrt (- (* z z) t)))) (sqrt (- (* z z) t)))
4.0ms	(sqrt (- (* z z) t))
4.0ms	(sqrt (- (* z z) t))

series38.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* y (* 4.0 (sqrt (- (* z z) t))))
12.0ms	(* (* y (* 4.0 (sqrt (- (* z z) t)))) (sqrt (- (* z z) t)))
6.0ms	(sqrt (- (* z z) t))
6.0ms	(sqrt (- (* z z) t))

simplify44.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5131	1084

prune115.0ms

Filtered

72 candidates to 97 candidates (-34.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	97	7	104

Merged error: 3.2b

Counts

104 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (- (pow z 4) (* t t)))
2.7b	(- (pow z 4) (* t t))
8.8b	(* y (* 4.0 (- (pow z 4) (* t t))))
22.1b	(/ (* y (* 4.0 (- (pow z 4) (* t t)))) (+ (* z z) t))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
15×	`add-sqr-sqrt`
11×	`pow1`
10×	`associate-*r/`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`sub-neg` `associate-r` `prod-exp` `cbrt-unprod`
6×	`associate-l` `add-log-exp` `difference-of-squares`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`flip3--` `pow-prod-down` `flip--`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/r*`
2×	`unpow-prod-down` `associate-/r/` `*-commutative` `associate-/l/` `sqr-pow`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `flip-+` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

7.0ms	(* 4.0 (- (pow z 4) (* t t)))
4.0ms	(- (pow z 4) (* t t))
7.0ms	(* y (* 4.0 (- (pow z 4) (* t t))))
12.0ms	(/ (* y (* 4.0 (- (pow z 4) (* t t)))) (+ (* z z) t))

series71.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* 4.0 (- (pow z 4) (* t t)))
6.0ms	(- (pow z 4) (* t t))
22.0ms	(* y (* 4.0 (- (pow z 4) (* t t))))
35.0ms	(/ (* y (* 4.0 (- (pow z 4) (* t t)))) (+ (* z z) t))

simplify40.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5304	1154

prune118.0ms

Filtered

65 candidates to 102 candidates (-56.9%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	2	3
Picked	0	1	1
Done	0	3	3
Total	102	7	109

Merged error: 3.2b

Counts

109 → 7

regimes904.0ms

Accuracy

78.4% (0.7b remaining)

Error of 3.4b against oracle of 2.7b and baseline of 6.1b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	55
1	33	55

end0.0ms

analyze696.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
6.2%	82.7%	11.1%	10
12.5%	73.7%	13.8%	11
15.6%	59.5%	25%	12
17.9%	53.3%	28.8%	13
22.4%	47.2%	30.4%	14

sample735.0ms

Algorithm

intervals

Results

331.0ms	8000×	body	80	valid
121.0ms	2840×	body	80	invalid

Details

analyze699.0ms

sample26.0ms

simplify3.0ms

prune7.0ms

localize9.0ms

rewrite16.0ms

series38.0ms

simplify36.0ms

prune89.0ms

localize16.0ms

rewrite25.0ms

series97.0ms

simplify61.0ms

prune163.0ms

localize12.0ms

rewrite36.0ms

series38.0ms

simplify44.0ms

prune115.0ms

localize15.0ms

rewrite34.0ms

series71.0ms

simplify40.0ms

prune118.0ms

regimes904.0ms

bsearch2.0ms

simplify1.0ms

end0.0ms

analyze696.0ms

sample735.0ms

Profiling