Details

sample34.0ms

Algorithm

intervals

Results

14.0ms

529×

body

valid

simplify71.0ms

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: 5.3b

localize10.0ms

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))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 54

Calls

3 calls:

8.0ms	(- (* z z) t)
9.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
37.0ms	(* (* y 4.0) (- (* z z) t))

series161.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(- (* z z) t)
78.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
63.0ms	(* (* y 4.0) (- (* z z) t))

simplify41.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	292	385
1	1348	342
2	5001	337

prune125.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.7b

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)))
5.0b	(sqrt (- (* z z) t))
5.0b	(sqrt (- (* z z) t))

rewrite170.0ms

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:

36.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
109.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
10.0ms	(sqrt (- (* z z) t))
11.0ms	(sqrt (- (* z z) t))

series224.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
60.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
49.0ms	(sqrt (- (* z z) t))
45.0ms	(sqrt (- (* z z) t))

simplify52.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (44.0ms)

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

prune240.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t))))
5.0b	(sqrt (- (* z z) t))
5.0b	(sqrt (- (* z z) t))
5.0b	(sqrt (- (* z z) t))

rewrite145.0ms

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:

109.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t))))
10.0ms	(sqrt (- (* z z) t))
10.0ms	(sqrt (- (* z z) t))
13.0ms	(sqrt (- (* z z) t))

series243.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (sqrt (- (* z z) t))))
45.0ms	(sqrt (- (* z z) t))
48.0ms	(sqrt (- (* z z) t))
46.0ms	(sqrt (- (* z z) t))

simplify56.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (44.0ms)

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

prune317.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.7b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

9.0ms	(- (* x x) (* (* (* y 4.0) (+ z (sqrt t))) (- z (sqrt t))))
6.0ms	(+ z (sqrt t))
29.0ms	(* (* y 4.0) (+ z (sqrt t)))
87.0ms	(* (* (* y 4.0) (+ z (sqrt t))) (- z (sqrt t)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- (* x x) (* (* (* y 4.0) (+ z (sqrt t))) (- z (sqrt t))))
25.0ms	(+ z (sqrt t))
56.0ms	(* (* y 4.0) (+ z (sqrt t)))
96.0ms	(* (* (* y 4.0) (+ z (sqrt t))) (- z (sqrt t)))

simplify87.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	520	839
1	3082	698
2	5001	689

prune218.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 1.7b

regimes356.0ms

Accuracy

81.9% (0.6b remaining)

Error of 3.2b against oracle of 2.6b and baseline of 6.1b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	23
1	31	23

end0.0ms

sample914.0ms

Algorithm

intervals

Results

420.0ms

15625×

body

valid