Details

sample32.0ms

Algorithm

intervals

Results

13.0ms	277×	body	80	valid
4.0ms	116×	body	80	nan

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	7
1	45	7
2	67	7
3	94	7
4	115	7
5	115	7

prune3.0ms

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)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 19

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
3.0ms	(* (* x y) z)
8.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms	(sqrt (- (* z z) (* t a)))

series204.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* z z) (* t a))
23.0ms	(* (* x y) z)
85.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
62.0ms	(sqrt (- (* z z) (* t a)))

simplify130.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	150	154
1	452	152
2	1262	150
3	3689	150
4	5002	150

prune110.0ms

Filtered

31 candidates to 27 candidates (87.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	22	9	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	9	32

Merged error: 3.9b

Counts

32 → 9

localize10.0ms

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)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 25

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)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (sqrt (- (* z z) (* t a))) z)
33.0ms	(- (* z z) (* t a))
83.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
62.0ms	(sqrt (- (* z z) (* t a)))

simplify62.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	195	217
1	585	212
2	2230	208
3	5001	208

prune124.0ms

Filtered

37 candidates to 31 candidates (83.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	31	6	37
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	37	9	46

Merged error: 3.9b

Counts

46 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
0.2b	(* (sqrt (- (* z z) (* t a))) (/ 1 z))
3.4b	(/ (* x y) (* (sqrt (- (* z z) (* t a))) (/ 1 z)))
24.1b	(sqrt (- (* z z) (* t a)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

18×	`sqrt-div`
13×	`associate-/r/`
12×	`frac-times`
10×	`flip3--` `flip--`
9×	`clear-num`
8×	`*-commutative`
7×	`frac-2neg`
6×	`times-frac` `associate-*r/`
5×	`div-inv`
4×	`associate-r` `associate-*l/` `un-div-inv`
3×	`associate-/r*`
2×	`associate-/l*`
1×	`sub-neg` `pow1/2`

Counts

4 → 49

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
7.0ms	(* (sqrt (- (* z z) (* t a))) (/ 1 z))
9.0ms	(/ (* x y) (* (sqrt (- (* z z) (* t a))) (/ 1 z)))
4.0ms	(sqrt (- (* z z) (* t a)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* z z) (* t a))
69.0ms	(* (sqrt (- (* z z) (* t a))) (/ 1 z))
83.0ms	(/ (* x y) (* (sqrt (- (* z z) (* t a))) (/ 1 z)))
61.0ms	(sqrt (- (* z z) (* t a)))

simplify140.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	273	437
1	1051	422
2	4792	418
3	5002	418

prune178.0ms

Filtered

61 candidates to 46 candidates (75.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	61	9	70

Merged error: 3.9b

Counts

70 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.2b	(- (* z z) (* t a))
3.2b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.1b	(sqrt (- (* z z) (* t a)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 22

Calls

4 calls:

5.0ms	(/ z (sqrt (- (* z z) (* t a))))
4.0ms	(- (* z z) (* t a))
8.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ z (sqrt (- (* z z) (* t a))))
32.0ms	(- (* z z) (* t a))
83.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
62.0ms	(sqrt (- (* z z) (* t a)))

simplify57.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	154	157
1	539	155
2	1982	153
3	5001	153

prune92.0ms

Filtered

34 candidates to 28 candidates (82.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	31	3	34
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	33	10	43

Merged error: 3.9b

Counts

43 → 10

regimes304.0ms

Accuracy

84.3% (3.0b remaining)

Error of 6.1b against oracle of 3.1b and baseline of 22.4b

bsearch92.0ms

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	29	11
1	36	11
2	47	11
3	47	11

end0.0ms

sample787.0ms

Algorithm

intervals

Results

334.0ms	8834×	body	80	valid
105.0ms	2807×	body	80	nan