Details

sample33.0ms

Algorithm

intervals

Results

17.0ms

486×

body

valid

simplify79.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* x x) (* (* y 4.0) (- (* z z) t)))
6.7b	(* (* y 4.0) (- (* z z) t))

rewrite18.0ms

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:

3.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
14.0ms	(* (* y 4.0) (- (* z z) t))

series140.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
65.0ms	(* (* y 4.0) (- (* z z) t))

simplify40.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (36.0ms)

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

prune97.0ms

Filtered

47 candidates to 29 candidates (61.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* x x) (* (- (* z z) t) (* y 4.0)))
6.7b	(* (- (* z z) t) (* y 4.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

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

series105.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(- (* x x) (* (- (* z z) t) (* y 4.0)))
43.0ms	(* (- (* z z) t) (* y 4.0))

simplify123.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	231	277
1	900	241
2	4520	237
3	5001	237

prune86.0ms

Filtered

39 candidates to 25 candidates (64.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 3.5b

localize11.0ms

Local error

Found 4 expressions with local error:

1.1b	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
1.1b	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
6.7b	(* (* y 4.0) (- (* z z) t))
6.7b	(* (* y 4.0) (- (* z z) t))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

4.0ms	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
4.0ms	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
13.0ms	(* (* y 4.0) (- (* z z) t))
14.0ms	(* (* y 4.0) (- (* z z) t))

series391.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
130.0ms	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
63.0ms	(* (* y 4.0) (- (* z z) t))
62.0ms	(* (* y 4.0) (- (* z z) t))

simplify44.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	270	654
1	1170	602
2	5002	598

prune239.0ms

Filtered

92 candidates to 62 candidates (67.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 3.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (- (* z z) t)) (* y 4.0))
0.2b	(* (sqrt (- (* z z) t)) (* (sqrt (- (* z z) t)) (* y 4.0)))
6.6b	(sqrt (- (* z z) t))
6.6b	(sqrt (- (* z z) t))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1`
18×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
16×	`add-sqr-sqrt` `sqrt-prod`
14×	`associate-l`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-l/`
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-r/` `associate-r` `-commutative`

Counts

4 → 89

Calls

4 calls:

16.0ms	(* (sqrt (- (* z z) t)) (* y 4.0))
44.0ms	(* (sqrt (- (* z z) t)) (* (sqrt (- (* z z) t)) (* y 4.0)))
4.0ms	(sqrt (- (* z z) t))
5.0ms	(sqrt (- (* z z) t))

series211.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (sqrt (- (* z z) t)) (* y 4.0))
42.0ms	(* (sqrt (- (* z z) t)) (* (sqrt (- (* z z) t)) (* y 4.0)))
49.0ms	(sqrt (- (* z z) t))
44.0ms	(sqrt (- (* z z) t))

simplify127.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 3 (119.0ms)

Iter	Nodes	Cost
0	351	761
1	1207	641
2	4827	639
3	5001	637

prune262.0ms

Filtered

101 candidates to 71 candidates (70.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 3.5b

regimes402.0ms

Accuracy

82.5% (0.6b remaining)

Error of 3.2b against oracle of 2.7b and baseline of 5.9b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	16
1	25	16

end0.0ms

sample829.0ms

Algorithm

intervals

Results

462.0ms

15479×

body

valid