Details

sample49.0ms

Algorithm

intervals

Results

18.0ms	285×	body	80	valid
6.0ms	108×	body	80	nan

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 24.7b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
6.7b	(* (* x y) z)
8.0b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.5b	(sqrt (- (* z z) (* t a)))

rewrite20.0ms

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))))
4.0ms	(sqrt (- (* z z) (* t a)))

series204.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* z z) (* t a))
22.0ms	(* (* x y) z)
78.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
69.0ms	(sqrt (- (* z z) (* t a)))

simplify115.0ms

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

prune104.0ms

Filtered

37 candidates to 29 candidates (78.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	30	7	37
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	31	7	38

Merged error: 2.7b

Counts

38 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.2b	(- (* z z) (* t a))
3.6b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.5b	(sqrt (- (* z z) (* t a)))

rewrite21.0ms

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)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ (sqrt (- (* z z) (* t a))) z)
46.0ms	(- (* z z) (* t a))
80.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
58.0ms	(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

prune115.0ms

Filtered

43 candidates to 33 candidates (76.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	40	3	43
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	43	7	50

Merged error: 2.6b

Counts

50 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
1.5b	(/ (/ (sqrt (- (* z z) (* t a))) z) x)
1.8b	(/ y (/ (/ (sqrt (- (* z z) (* t a))) z) x))
24.5b	(sqrt (- (* z z) (* t a)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 35

Calls

4 calls:

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

series231.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* z z) (* t a))
64.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) x)
77.0ms	(/ y (/ (/ (sqrt (- (* z z) (* t a))) z) x))
59.0ms	(sqrt (- (* z z) (* t a)))

simplify57.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	211	238
1	651	233
2	2568	226
3	5002	226

prune119.0ms

Filtered

47 candidates to 35 candidates (74.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	46	8	54

Merged error: 2.6b

Counts

54 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
1.5b	(* x (/ z (sqrt (- (* z z) (* t a)))))
1.6b	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
24.5b	(sqrt (- (* z z) (* t a)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 31

Calls

4 calls:

5.0ms	(- (* z z) (* t a))
6.0ms	(* x (/ z (sqrt (- (* z z) (* t a)))))
7.0ms	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* z z) (* t a))
53.0ms	(* x (/ z (sqrt (- (* z z) (* t a)))))
78.0ms	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
58.0ms	(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	170	170
1	583	167
2	2117	162
3	5002	149

prune107.0ms

Filtered

43 candidates to 32 candidates (74.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	41	2	43
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	42	9	51

Merged error: 2.6b

Counts

51 → 9

regimes432.0ms

Accuracy

78.8% (4.2b remaining)

Error of 7.7b against oracle of 3.4b and baseline of 23.4b

bsearch52.0ms

Steps

Iters	Range		Point
7	2.2820637225313194e+75	5.904464187258918e+76	2.3156939502955866e+75
3	-6.017134225162489e+36	-4.822947343404439e+36	-5.192230488731093e+36

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	15
1	41	15
2	44	15
3	44	15

end0.0ms

sample811.0ms

Algorithm

intervals

Results

355.0ms	8835×	body	80	valid
108.0ms	2946×	body	80	nan