Details

sample30.0ms

Algorithm

intervals

Results

10.0ms	277×	body	80	valid
4.0ms	116×	body	80	nan

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	7
1	46	7
2	72	7
3	99	7
4	120	7
5	120	7

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: 23.6b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
3.8b	(* (* x y) z)
10.5b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.1b	(sqrt (- (* z z) (* t a)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-commutative`
4×	`sqrt-div` `associate-l` `prod-diff` `associate-/l*`
3×	`flip3--` `flip--`
2×	`fma-neg` `associate-/r/`
1×	`sub-neg` `frac-2neg` `pow1/2` `clear-num` `div-inv`

Counts

4 → 25

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
3.0ms	(* (* x y) z)
7.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
7.0ms	(sqrt (- (* z z) (* t a)))

series192.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* z z) (* t a))
23.0ms	(* (* x y) z)
80.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
56.0ms	(sqrt (- (* z z) (* t a)))

simplify116.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 3 (36.0ms)

Iter	Nodes	Cost
0	165	180
1	504	177
2	1451	172
3	4133	160
4	5001	160

prune113.0ms

Filtered

37 candidates to 29 candidates (78.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	27	10	37
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	10	38

Merged error: 3.9b

Counts

38 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.2b	(- (* z z) (* t a))
3.4b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.1b	(sqrt (- (* z z) (* t a)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-commutative`
6×	`sqrt-div`
5×	`associate-/r/` `div-inv`
4×	`flip3--` `prod-diff` `flip--` `associate-/l/`
3×	`frac-2neg` `clear-num`
2×	`times-frac` `fma-neg` `associate-/l*`
1×	`sub-neg` `pow1/2` `associate-/r*`

Counts

4 → 31

Calls

4 calls:

5.0ms	(/ (sqrt (- (* z z) (* t a))) z)
4.0ms	(- (* z z) (* t a))
7.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms	(sqrt (- (* z z) (* t a)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (sqrt (- (* z z) (* t a))) z)
31.0ms	(- (* z z) (* t a))
78.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
59.0ms	(sqrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	212	243
1	643	237
2	2450	230
3	5001	230

prune141.0ms

Filtered

43 candidates to 33 candidates (76.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	41	2	43
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	44	9	53

Merged error: 3.9b

Counts

53 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
1.8b	(/ x (/ (sqrt (- (* z z) (* t a))) (* y z)))
9.4b	(/ (sqrt (- (* z z) (* t a))) (* y z))
24.1b	(sqrt (- (* z z) (* t a)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

7×	`associate-/r/` `*-commutative`
6×	`sqrt-div`
5×	`associate-/r*`
4×	`flip3--` `prod-diff` `flip--` `associate-/l/`
3×	`frac-2neg` `clear-num` `div-inv`
2×	`fma-neg`
1×	`sub-neg` `pow1/2`

Counts

4 → 31

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
7.0ms	(/ x (/ (sqrt (- (* z z) (* t a))) (* y z)))
6.0ms	(/ (sqrt (- (* z z) (* t a))) (* y z))
4.0ms	(sqrt (- (* z z) (* t a)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* z z) (* t a))
83.0ms	(/ x (/ (sqrt (- (* z z) (* t a))) (* y z)))
66.0ms	(/ (sqrt (- (* z z) (* t a))) (* y z))
62.0ms	(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	202	231
1	666	227
2	2282	220
3	5001	208

prune121.0ms

Filtered

43 candidates to 32 candidates (74.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	43	9	52

Merged error: 3.9b

Counts

52 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
3.8b	(* (* x y) z)
10.6b	(* (* (* x y) z) (/ 1 (sqrt (- (* z z) (* t a)))))
24.1b	(sqrt (- (* z z) (* t a)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-commutative`
8×	`associate-l`
4×	`sqrt-div` `prod-diff`
3×	`flip3--` `associate-r/` `associate-r*` `flip--`
2×	`fma-neg` `clear-num` `associate-/r/` `un-div-inv`
1×	`sub-neg` `frac-2neg` `pow1/2` `div-inv`

Counts

4 → 29

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
3.0ms	(* (* x y) z)
9.0ms	(* (* (* x y) z) (/ 1 (sqrt (- (* z z) (* t a)))))
5.0ms	(sqrt (- (* z z) (* t a)))

series202.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* z z) (* t a))
23.0ms	(* (* x y) z)
83.0ms	(* (* (* x y) z) (/ 1 (sqrt (- (* z z) (* t a)))))
60.0ms	(sqrt (- (* z z) (* t a)))

simplify71.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	185	173
1	707	166
2	3127	161
3	5001	161

prune87.0ms

Filtered

41 candidates to 27 candidates (65.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	41	9	50

Merged error: 3.9b

Counts

50 → 9

regimes297.0ms

Accuracy

83.1% (3.3b remaining)

Error of 6.2b against oracle of 2.9b and baseline of 22.5b

bsearch86.0ms

Steps

Iters	Range		Point
8	6.3736077767258876e+97	2.771218538638004e+101	3.0412120532343217e+100
10	-4.092990931352707e+163	-1.865346764731705e+152	-8.062579297869621e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	30	10
2	30	10

end0.0ms

sample792.0ms

Algorithm

intervals

Results

342.0ms	8834×	body	80	valid
112.0ms	2807×	body	80	nan