Details

sample32.0ms

Algorithm

intervals

Results

15.0ms

506×

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.3b

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))

rewrite20.0ms

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:

4.0ms	(- (* z z) t)
7.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
8.0ms	(* (* y 4.0) (- (* z z) t))

series159.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(- (* z z) t)
77.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
60.0ms	(* (* y 4.0) (- (* z z) t))

simplify41.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (36.0ms)

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

prune139.0ms

Filtered

63 candidates to 41 candidates (65.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* z z) t)
0.0b	(- (* x x) (* (* y 4.0) (pow (- (* z z) t) 1)))
5.0b	(* (* y 4.0) (pow (- (* z z) t) 1))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 52

Calls

3 calls:

4.0ms	(- (* z z) t)
3.0ms	(- (* x x) (* (* y 4.0) (pow (- (* z z) t) 1)))
9.0ms	(* (* y 4.0) (pow (- (* z z) t) 1))

series169.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(- (* z z) t)
80.0ms	(- (* x x) (* (* y 4.0) (pow (- (* z z) t) 1)))
66.0ms	(* (* y 4.0) (pow (- (* z z) t) 1))

simplify48.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	311	392
1	1355	344
2	5001	341

prune158.0ms

Filtered

61 candidates to 40 candidates (65.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.5b

localize14.0ms

Local error

Found 4 expressions with local error:

2.7b	(cbrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
5.0b	(* (* y 4.0) (- (* z z) t))
5.0b	(* (* y 4.0) (- (* z z) t))
5.0b	(* (* y 4.0) (- (* z z) t))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

3.0ms	(cbrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
8.0ms	(* (* y 4.0) (- (* z z) t))
8.0ms	(* (* y 4.0) (- (* z z) t))
8.0ms	(* (* y 4.0) (- (* z z) t))

series327.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(cbrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
65.0ms	(* (* y 4.0) (- (* z z) t))
65.0ms	(* (* y 4.0) (- (* z z) t))
65.0ms	(* (* y 4.0) (- (* z z) t))

simplify42.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	312	671
1	1323	596
2	5001	590

prune245.0ms

Filtered

100 candidates to 62 candidates (62.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* y 4.0) (pow (- (* z z) t) 1/2))
0.2b	(* (* (* y 4.0) (pow (- (* z z) t) 1/2)) (pow (sqrt (- (* z z) t)) 1))
5.0b	(sqrt (- (* z z) t))
5.0b	(pow (- (* z z) t) 1/2)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-exp-log`
57×	`prod-exp`
19×	`associate-r`
18×	`add-cbrt-cube`
17×	`add-sqr-sqrt`
16×	`pow-to-exp` `pow-exp`
15×	`unpow-prod-down`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-unprod`
8×	`sqrt-prod`
7×	`pow1`
4×	`add-log-exp` `difference-of-squares`
3×	`pow-unpow` `sqr-pow`
2×	`sqrt-div` `associate-l` `*-commutative`
1×	`rem-sqrt-square` `flip3--` `pow-pow` `sqrt-pow1` `pow1/2` `pow-prod-down` `flip--` `unpow1/2`

Counts

4 → 105

Calls

4 calls:

9.0ms	(* (* y 4.0) (pow (- (* z z) t) 1/2))
15.0ms	(* (* (* y 4.0) (pow (- (* z z) t) 1/2)) (pow (sqrt (- (* z z) t)) 1))
4.0ms	(sqrt (- (* z z) t))
8.0ms	(pow (- (* z z) t) 1/2)

series253.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (* y 4.0) (pow (- (* z z) t) 1/2))
66.0ms	(* (* (* y 4.0) (pow (- (* z z) t) 1/2)) (pow (sqrt (- (* z z) t)) 1))
45.0ms	(sqrt (- (* z z) t))
71.0ms	(pow (- (* z z) t) 1/2)

simplify73.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	509	911
1	2293	694
2	5003	674

prune272.0ms

Filtered

117 candidates to 70 candidates (59.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.5b

regimes412.0ms

Accuracy

87.4% (0.4b remaining)

Error of 3.0b against oracle of 2.5b and baseline of 5.8b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	18
1	32	18

end0.0ms

sample904.0ms

Algorithm

intervals

Results

488.0ms

15697×

body

valid