Details

analyze684.0ms

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

sample23.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	80×	body	80	invalid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	13
1	21	13

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: 7.6b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* z z) t)
0.0b	(- (* x x) (* (* y 4.0) (- (* z z) t)))
7.1b	(* (* y 4.0) (- (* z z) t))

rewrite15.0ms

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)
4.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
7.0ms	(* (* y 4.0) (- (* z z) t))

series37.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(- (* z z) t)
21.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
12.0ms	(* (* y 4.0) (- (* z z) t))

simplify33.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5049	632

prune78.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	52	5	57
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	6	58

Merged error: 3.0b

Counts

58 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

2.2b	(* y (* 4.0 (* (cbrt (- (* z z) t)) (cbrt (- (* z z) t)))))
7.8b	(cbrt (- (* z z) t))
7.8b	(cbrt (- (* z z) t))
7.8b	(cbrt (- (* z z) t))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

16.0ms	(* y (* 4.0 (* (cbrt (- (* z z) t)) (cbrt (- (* z z) t)))))
4.0ms	(cbrt (- (* z z) t))
4.0ms	(cbrt (- (* z z) t))
4.0ms	(cbrt (- (* z z) t))

series83.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* y (* 4.0 (* (cbrt (- (* z z) t)) (cbrt (- (* z z) t)))))
17.0ms	(cbrt (- (* z z) t))
17.0ms	(cbrt (- (* z z) t))
17.0ms	(cbrt (- (* z z) t))

simplify53.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4933	935
1	4933	935

prune117.0ms

Filtered

67 candidates to 83 candidates (-23.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	82	7	89

Merged error: 2.9b

Counts

89 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

1.1b	(sqrt (+ (* x x) (* y (* 4.0 (- t (* z z))))))
1.1b	(sqrt (+ (* x x) (* y (* 4.0 (- t (* z z))))))
7.1b	(* y (* 4.0 (- t (* z z))))
7.1b	(* y (* 4.0 (- t (* z z))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
14×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`distribute-rgt-in` `add-cube-cbrt` `sub-neg` `-un-lft-identity` `distribute-lft-in` `associate-r/`
6×	`associate-l` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`sqrt-div` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r` `*-commutative` `flip--` `flip-+`

Counts

4 → 78

Calls

4 calls:

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

series110.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (+ (* x x) (* y (* 4.0 (- t (* z z))))))
41.0ms	(sqrt (+ (* x x) (* y (* 4.0 (- t (* z z))))))
16.0ms	(* y (* 4.0 (- t (* z z))))
16.0ms	(* y (* 4.0 (- t (* z z))))

simplify50.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5506	1142

prune133.0ms

Filtered

62 candidates to 90 candidates (-45.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	89	8	97

Merged error: 2.9b

Counts

97 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

1.5b	(cbrt (+ (* y (* 4.0 (- t (* z z)))) (* x x)))
7.1b	(* y (* 4.0 (- t (* z z))))
7.1b	(* y (* 4.0 (- t (* z z))))
7.1b	(* y (* 4.0 (- t (* z z))))

rewrite28.0ms

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:

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

series145.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt (+ (* y (* 4.0 (- t (* z z)))) (* x x)))
16.0ms	(* y (* 4.0 (- t (* z z))))
15.0ms	(* y (* 4.0 (- t (* z z))))
18.0ms	(* y (* 4.0 (- t (* z z))))

simplify44.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5112	1136

prune153.0ms

Filtered

58 candidates to 97 candidates (-67.2%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	97	8	105

Merged error: 2.9b

Counts

105 → 8

regimes1.0s

Accuracy

79.5% (0.7b remaining)

Error of 3.3b against oracle of 2.6b and baseline of 5.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	36
1	27	36

end0.0ms

analyze615.0ms

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

sample683.0ms

Algorithm

intervals

Results

299.0ms	8000×	body	80	valid
114.0ms	2987×	body	80	invalid

Details

analyze684.0ms

sample23.0ms

simplify3.0ms

prune6.0ms

localize8.0ms

rewrite15.0ms

series37.0ms

simplify33.0ms

prune78.0ms

localize13.0ms

rewrite30.0ms

series83.0ms

simplify53.0ms

prune117.0ms

localize11.0ms

rewrite21.0ms

series110.0ms

simplify50.0ms

prune133.0ms

localize17.0ms

rewrite28.0ms

series145.0ms

simplify44.0ms

prune153.0ms

regimes1.0s

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze615.0ms

sample683.0ms

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