Details

analyze653.0ms

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

sample30.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	98×	body	80	invalid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	720	13
1	720	13

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 6.8b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(- t (* z z))
0.0b	(+ (* x x) (* y (* 4.0 (- t (* z z)))))
6.4b	(* y (* 4.0 (- t (* z z))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 51

Calls

3 calls:

3.0ms	(- t (* z z))
5.0ms	(+ (* x x) (* y (* 4.0 (- t (* z z)))))
7.0ms	(* y (* 4.0 (- t (* z z))))

series48.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(- t (* z z))
26.0ms	(+ (* x x) (* y (* 4.0 (- t (* z z)))))
15.0ms	(* y (* 4.0 (- t (* z z))))

simplify32.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5903	661

prune83.0ms

Filtered

41 candidates to 60 candidates (-46.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	54	6	60
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	7	61

Merged error: 5.6b

Counts

61 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
2.1b	(* (- t (* z z)) (cbrt y))
4.7b	(* (* (cbrt y) (cbrt y)) (* 4.0 (* (- t (* z z)) (cbrt y))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1` `add-exp-log`
18×	`add-cbrt-cube`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
14×	`add-sqr-sqrt`
10×	`cbrt-prod`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r`
5×	`associate-l`
4×	`associate-r/` `associate-l/` `add-log-exp`
2×	`flip3--` `pow1/3` `*-commutative` `flip--` `unswap-sqr`
1×	`difference-of-squares`

Counts

4 → 77

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
7.0ms	(* (- t (* z z)) (cbrt y))
16.0ms	(* (* (cbrt y) (cbrt y)) (* 4.0 (* (- t (* z z)) (cbrt y))))

series94.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt y)
21.0ms	(cbrt y)
29.0ms	(* (- t (* z z)) (cbrt y))
20.0ms	(* (* (cbrt y) (cbrt y)) (* 4.0 (* (- t (* z z)) (cbrt y))))

simplify49.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5013	697

prune103.0ms

Filtered

54 candidates to 89 candidates (-64.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	86	10	96

Merged error: 5.1b

Counts

96 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.7b	(* (* (- t (* z z)) (cbrt (pow (cbrt y) 2))) (cbrt (cbrt y)))
1.6b	(* (- t (* z z)) (cbrt (pow (cbrt y) 2)))
4.7b	(* (* (cbrt y) (cbrt y)) (* 4.0 (* (* (- t (* z z)) (cbrt (pow (cbrt y) 2))) (cbrt (cbrt y)))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

43×	`pow1` `add-exp-log`
32×	`cbrt-prod`
28×	`pow-prod-down` `prod-exp` `cbrt-unprod`
25×	`add-cbrt-cube`
24×	`add-sqr-sqrt` `associate-r`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-*l/`
8×	`unpow-prod-down`
6×	`associate-l` `unswap-sqr`
4×	`associate-*r/` `add-log-exp`
3×	`flip3--` `*-commutative` `flip--`
2×	`unpow2` `sqr-pow`
1×	`pow1/3` `difference-of-squares`

Counts

4 → 110

Calls

4 calls:

1.0ms	(cbrt y)
11.0ms	(* (* (- t (* z z)) (cbrt (pow (cbrt y) 2))) (cbrt (cbrt y)))
10.0ms	(* (- t (* z z)) (cbrt (pow (cbrt y) 2)))
19.0ms	(* (* (cbrt y) (cbrt y)) (* 4.0 (* (* (- t (* z z)) (cbrt (pow (cbrt y) 2))) (cbrt (cbrt y)))))

series124.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt y)
30.0ms	(* (* (- t (* z z)) (cbrt (pow (cbrt y) 2))) (cbrt (cbrt y)))
50.0ms	(* (- t (* z z)) (cbrt (pow (cbrt y) 2)))
23.0ms	(* (* (cbrt y) (cbrt y)) (* 4.0 (* (* (- t (* z z)) (cbrt (pow (cbrt y) 2))) (cbrt (cbrt y)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4932	1831
1	4932	1831

prune180.0ms

Filtered

77 candidates to 122 candidates (-58.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	123	9	132

Merged error: 5.1b

Counts

132 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
1.5b	(* (cbrt y) (* (cbrt y) (* 4.0 (* (- t (* z z)) (* (cbrt (pow (cbrt y) 2)) (cbrt (cbrt y)))))))
2.1b	(* (- t (* z z)) (* (cbrt (pow (cbrt y) 2)) (cbrt (cbrt y))))
3.5b	(* (cbrt y) (* 4.0 (* (- t (* z z)) (* (cbrt (pow (cbrt y) 2)) (cbrt (cbrt y))))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

43×	`pow1` `add-exp-log`
28×	`pow-prod-down` `prod-exp` `cbrt-unprod`
24×	`add-cbrt-cube`
16×	`associate-l`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r/`
9×	`cbrt-prod`
6×	`associate-*l/`
4×	`add-log-exp`
3×	`flip3--` `associate-r` `*-commutative` `flip--`
1×	`pow1/3` `difference-of-squares`

Counts

4 → 93

Calls

4 calls:

1.0ms	(cbrt y)
18.0ms	(* (cbrt y) (* (cbrt y) (* 4.0 (* (- t (* z z)) (* (cbrt (pow (cbrt y) 2)) (cbrt (cbrt y)))))))
11.0ms	(* (- t (* z z)) (* (cbrt (pow (cbrt y) 2)) (cbrt (cbrt y))))
18.0ms	(* (cbrt y) (* 4.0 (* (- t (* z z)) (* (cbrt (pow (cbrt y) 2)) (cbrt (cbrt y))))))

series140.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt y)
21.0ms	(* (cbrt y) (* (cbrt y) (* 4.0 (* (- t (* z z)) (* (cbrt (pow (cbrt y) 2)) (cbrt (cbrt y)))))))
28.0ms	(* (- t (* z z)) (* (cbrt (pow (cbrt y) 2)) (cbrt (cbrt y))))
68.0ms	(* (cbrt y) (* 4.0 (* (- t (* z z)) (* (cbrt (pow (cbrt y) 2)) (cbrt (cbrt y))))))

simplify61.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4957	1677
1	4957	1677

prune147.0ms

Filtered

69 candidates to 105 candidates (-52.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	105	9	114

Merged error: 5.1b

Counts

114 → 9

regimes466.0ms

Accuracy

-3.2% (1.7b remaining)

Error of 6.0b against oracle of 4.3b and baseline of 6.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	28
1	41	28

end0.0ms

sample667.0ms

Algorithm

intervals

Results

290.0ms	8000×	body	80	valid
110.0ms	3053×	body	80	invalid

Details

analyze653.0ms

sample30.0ms

simplify28.0ms

prune8.0ms

localize9.0ms

rewrite16.0ms

series48.0ms

simplify32.0ms

prune83.0ms

localize12.0ms

rewrite28.0ms

series94.0ms

simplify49.0ms

prune103.0ms

localize19.0ms

rewrite46.0ms

series124.0ms

simplify62.0ms

prune180.0ms

localize19.0ms

rewrite51.0ms

series140.0ms

simplify61.0ms

prune147.0ms

regimes466.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample667.0ms

Profiling