Details

sample30.0ms

Algorithm

intervals

Results

14.0ms

492×

body

valid

simplify77.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.3b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* x x) (* (* y 4.0) (- (* z z) t)))
6.0b	(* (* y 4.0) (- (* z z) t))

rewrite19.0ms

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))

series141.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
65.0ms	(* (* y 4.0) (- (* z z) t))

simplify42.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (37.0ms)

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

prune101.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.0b

localize13.0ms

Local error

Found 4 expressions with local error:

3.6b	(cbrt (* (* y 4.0) (- (* z z) t)))
6.0b	(* (* y 4.0) (- (* z z) t))
6.0b	(* (* y 4.0) (- (* z z) t))
6.0b	(* (* y 4.0) (- (* z z) t))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

10.0ms	(cbrt (* (* y 4.0) (- (* z z) t)))
14.0ms	(* (* y 4.0) (- (* z z) t))
14.0ms	(* (* y 4.0) (- (* z z) t))
14.0ms	(* (* y 4.0) (- (* z z) t))

series334.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (* (* y 4.0) (- (* z z) t)))
63.0ms	(* (* y 4.0) (- (* z z) t))
63.0ms	(* (* y 4.0) (- (* z z) t))
61.0ms	(* (* y 4.0) (- (* z z) t))

simplify40.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	291	616
1	1138	518
2	5002	507

prune259.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.0b

localize11.0ms

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)))
5.9b	(sqrt (- (* z z) t))
5.9b	(sqrt (- (* z z) t))

rewrite76.0ms

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:

17.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
46.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
5.0ms	(sqrt (- (* z z) t))
5.0ms	(sqrt (- (* z z) t))

series230.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
61.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
50.0ms	(sqrt (- (* z z) t))
48.0ms	(sqrt (- (* z z) t))

simplify55.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (46.0ms)

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

prune267.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 3.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (* y 4.0) (sqrt (sqrt (- (* z z) t)))) (sqrt (sqrt (- (* z z) t))))
5.9b	(sqrt (- (* z z) t))
5.9b	(sqrt (- (* z z) t))
5.9b	(sqrt (- (* z z) t))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

30×	`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:

56.0ms	(* (* (* y 4.0) (sqrt (sqrt (- (* z z) t)))) (sqrt (sqrt (- (* z z) t))))
5.0ms	(sqrt (- (* z z) t))
5.0ms	(sqrt (- (* z z) t))
5.0ms	(sqrt (- (* z z) t))

series213.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (* (* y 4.0) (sqrt (sqrt (- (* z z) t)))) (sqrt (sqrt (- (* z z) t))))
46.0ms	(sqrt (- (* z z) t))
49.0ms	(sqrt (- (* z z) t))
47.0ms	(sqrt (- (* z z) t))

simplify47.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	349	813
1	1412	693
2	5001	682

prune295.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 3.0b

regimes473.0ms

Accuracy

64.4% (1.2b remaining)

Error of 3.9b against oracle of 2.7b and baseline of 6.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	16
1	25	16

end0.0ms

sample836.0ms

Algorithm

intervals

Results

458.0ms

15875×

body

valid