Details

sample32.0ms

Algorithm

intervals

Results

15.0ms

521×

body

valid

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	50	6
2	159	6
3	351	6
4	609	6
5	733	6
6	1068	6
7	1342	6
8	1506	6
9	1553	6
10	1553	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 4.8b

Counts

2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* x x) (* (* y 4.0) (- (* z z) t)))
4.5b	(* (* y 4.0) (- (* z z) t))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 41

Calls

2 calls:

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

series135.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
59.0ms	(* (* y 4.0) (- (* z z) t))

simplify41.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	269	322
1	1276	286
2	5001	281

prune92.0ms

Filtered

47 candidates to 29 candidates (61.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	43	4	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	5	48

Merged error: 2.7b

Counts

48 → 5

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)))
4.5b	(sqrt (- (* z z) t))
4.5b	(sqrt (- (* z z) t))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

9.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
15.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
4.0ms	(sqrt (- (* z z) t))
5.0ms	(sqrt (- (* z z) t))

series241.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
68.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
47.0ms	(sqrt (- (* z z) t))
52.0ms	(sqrt (- (* z z) t))

simplify52.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	372	769
1	1759	649
2	5001	641

prune229.0ms

Filtered

101 candidates to 69 candidates (68.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	100	6	106

Merged error: 2.7b

Counts

106 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t))))
4.5b	(sqrt (- (* z z) t))
4.5b	(sqrt (- (* z z) t))
4.5b	(sqrt (- (* z z) t))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

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

series238.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t))))
44.0ms	(sqrt (- (* z z) t))
49.0ms	(sqrt (- (* z z) t))
45.0ms	(sqrt (- (* z z) t))

simplify50.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	380	822
1	1670	755
2	5001	718

prune295.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	96	6	102

Merged error: 2.7b

Counts

102 → 6

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- z (sqrt t))
0.1b	(* (* y 4.0) (+ z (sqrt t)))
0.2b	(* (* (* y 4.0) (+ z (sqrt t))) (- z (sqrt t)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

4.0ms	(- z (sqrt t))
8.0ms	(* (* y 4.0) (+ z (sqrt t)))
18.0ms	(* (* (* y 4.0) (+ z (sqrt t))) (- z (sqrt t)))

series181.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(- z (sqrt t))
51.0ms	(* (* y 4.0) (+ z (sqrt t)))
95.0ms	(* (* (* y 4.0) (+ z (sqrt t))) (- z (sqrt t)))

simplify73.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	429	643
1	2654	522
2	5001	517

prune163.0ms

Filtered

83 candidates to 54 candidates (65.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	2	2
Picked	1	0	1
Done	0	3	3
Total	83	6	89

Merged error: 2.7b

Counts

89 → 6

regimes366.0ms

Accuracy

83% (0.6b remaining)

Error of 3.1b against oracle of 2.6b and baseline of 5.9b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	18
1	27	18

end0.0ms

sample840.0ms

Algorithm

intervals

Results

467.0ms

15770×

body

valid