Details

analyze664.0ms

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	99×	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

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: 5.3b

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)))
5.0b	(* (* y 4.0) (- (* z z) t))

rewrite17.0ms

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

series39.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(- (* z z) t)
19.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
16.0ms	(* (* y 4.0) (- (* z z) t))

simplify42.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4982	631
1	4982	631

prune75.0ms

Filtered

41 candidates to 57 candidates (-39.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	5	58

Merged error: 2.2b

Counts

58 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

1.7b	(cbrt (+ (* x x) (* y (* 4.0 (- t (* z z))))))
5.0b	(* y (* 4.0 (- t (* z z))))
5.0b	(* y (* 4.0 (- t (* z z))))
5.0b	(* 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:

3.0ms	(cbrt (+ (* x x) (* y (* 4.0 (- t (* z z))))))
6.0ms	(* y (* 4.0 (- t (* z z))))
9.0ms	(* y (* 4.0 (- t (* z z))))
6.0ms	(* y (* 4.0 (- t (* z z))))

series103.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(cbrt (+ (* x x) (* y (* 4.0 (- t (* z z))))))
15.0ms	(* y (* 4.0 (- t (* z z))))
16.0ms	(* y (* 4.0 (- t (* z z))))
16.0ms	(* y (* 4.0 (- t (* z z))))

simplify49.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5061	1138

prune161.0ms

Filtered

60 candidates to 97 candidates (-61.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	95	7	102

Merged error: 2.2b

Counts

102 → 7

localize23.0ms

Local error

Found 4 expressions with local error:

1.7b	(cbrt (+ (* x x) (* y (* 4.0 (- t (* z z))))))
4.2b	(* (* (cbrt y) (cbrt y)) (* 4.0 (* (- t (* z z)) (cbrt y))))
5.0b	(* y (* 4.0 (- t (* z z))))
5.0b	(* y (* 4.0 (- t (* z z))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

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

series106.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(cbrt (+ (* x x) (* y (* 4.0 (- t (* z z))))))
21.0ms	(* (* (cbrt y) (cbrt y)) (* 4.0 (* (- t (* z z)) (cbrt y))))
15.0ms	(* y (* 4.0 (- t (* z z))))
16.0ms	(* y (* 4.0 (- t (* z z))))

simplify42.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5031	1211

prune162.0ms

Filtered

60 candidates to 103 candidates (-71.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	103	7	110

Merged error: 2.2b

Counts

110 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (cbrt y) (* 4.0 (* (cbrt y) (* (- t (* z z)) (cbrt y)))))
2.4b	(* (cbrt y) (* (- t (* z z)) (cbrt y)))
5.0b	(* y (* 4.0 (- t (* z z))))
5.0b	(* y (* 4.0 (- t (* z z))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

33×	`pow1` `add-exp-log`
23×	`add-cbrt-cube`
19×	`pow-prod-down` `prod-exp` `cbrt-unprod`
18×	`associate-l`
16×	`associate-*r/`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
6×	`cbrt-prod`
4×	`flip3--` `associate-r` `associate-l/` `-commutative` `flip--` `add-log-exp`

Counts

4 → 100

Calls

4 calls:

13.0ms	(* (cbrt y) (* 4.0 (* (cbrt y) (* (- t (* z z)) (cbrt y)))))
11.0ms	(* (cbrt y) (* (- t (* z z)) (cbrt y)))
7.0ms	(* y (* 4.0 (- t (* z z))))
7.0ms	(* y (* 4.0 (- t (* z z))))

series111.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (cbrt y) (* 4.0 (* (cbrt y) (* (- t (* z z)) (cbrt y)))))
61.0ms	(* (cbrt y) (* (- t (* z z)) (cbrt y)))
15.0ms	(* y (* 4.0 (- t (* z z))))
15.0ms	(* y (* 4.0 (- t (* z z))))

simplify52.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4983	1211
1	4983	1211

prune162.0ms

Filtered

68 candidates to 112 candidates (-64.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	112	7	119

Merged error: 2.2b

Counts

119 → 7

regimes949.0ms

Accuracy

77% (0.9b remaining)

Error of 3.5b against oracle of 2.7b and baseline of 6.4b

bsearch0.0ms

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	359	36
1	359	36

end0.0ms

sample680.0ms

Algorithm

intervals

Results

304.0ms	8000×	body	80	valid
105.0ms	2914×	body	80	invalid

Details

analyze664.0ms

sample26.0ms

simplify28.0ms

prune7.0ms

localize9.0ms

rewrite17.0ms

series39.0ms

simplify42.0ms

prune75.0ms

localize13.0ms

rewrite28.0ms

series103.0ms

simplify49.0ms

prune161.0ms

localize23.0ms

rewrite36.0ms

series106.0ms

simplify42.0ms

prune162.0ms

localize24.0ms

rewrite41.0ms

series111.0ms

simplify52.0ms

prune162.0ms

regimes949.0ms

bsearch0.0ms

simplify5.0ms

end0.0ms

sample680.0ms

Profiling