Details

sample45.0ms

Algorithm

intervals

Results

9.0ms	40×	body	2560	valid
8.0ms	198×	body	80	valid
6.0ms	103×	body	80	nan
4.0ms	22×	body	1280	valid
2.0ms	17×	body	640	valid
1.0ms	2×	body	5120	valid
0.0ms	6×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

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: 34.2b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b	(- (* b b) (* 4.0 (* a c)))
1.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `associate-/r*` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `frac-2neg` `pow1/2` `div-sub` `clear-num` `*-commutative` `div-inv`

Counts

4 → 19

Calls

4 calls:

7.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
5.0ms	(- (* b b) (* 4.0 (* a c)))
5.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series321.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
47.0ms	(- (* b b) (* 4.0 (* a c)))
83.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify112.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	267	246
1	950	235
2	3703	225
3	5002	224

prune98.0ms

Filtered

31 candidates to 27 candidates (87.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	24	7	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	7	32

Merged error: 6.1b

Counts

32 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.2b	(- (* b b) (* 4.0 (* a c)))
1.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

10×	`frac-times`
7×	`flip3-+` `flip-+`
6×	`associate-/r*`
5×	`associate-*r/`
4×	`clear-num` `*-commutative`
3×	`frac-2neg`
2×	`flip3--` `sqrt-div` `associate-*l/` `un-div-inv` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `pow1/2` `associate-r` `div-inv`

Counts

4 → 32

Calls

4 calls:

9.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
5.0ms	(- (* b b) (* 4.0 (* a c)))
5.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series500.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
50.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
263.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify42.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	306	454
1	1320	434
2	5001	406

prune141.0ms

Filtered

44 candidates to 36 candidates (81.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	40	4	44
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	44	7	51

Merged error: 6.1b

Counts

51 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
0.2b	(- (* b b) (* 4.0 (* a c)))
1.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `frac-2neg` `pow1/2` `div-sub` `clear-num` `div-inv`

Counts

4 → 17

Calls

4 calls:

7.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
5.0ms	(- (* b b) (* 4.0 (* a c)))
5.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series299.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
45.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify103.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	242	225
1	853	215
2	3347	206
3	5001	205

prune89.0ms

Filtered

29 candidates to 25 candidates (86.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	27	2	29
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	29	7	36

Merged error: 6.1b

Counts

36 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 a))
0.2b	(- (* b b) (* 4.0 (* a c)))
1.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

6×	`frac-times`
5×	`flip3-+` `flip-+`
4×	`clear-num`
3×	`frac-2neg` `associate-*r/`
2×	`flip3--` `sqrt-div` `associate-*l/` `un-div-inv` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `pow1/2` `associate-r` `*-commutative` `div-inv`

Counts

4 → 26

Calls

4 calls:

7.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 a))
5.0ms	(- (* b b) (* 4.0 (* a c)))
5.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series302.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 a))
49.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify34.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	263	347
1	1087	330
2	5001	310

prune97.0ms

Filtered

38 candidates to 30 candidates (78.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	38	7	45

Merged error: 6.1b

Counts

45 → 7

regimes157.0ms

Accuracy

82.2% (5.1b remaining)

Error of 10.7b against oracle of 5.6b and baseline of 34.1b

bsearch111.0ms

Steps

Iters	Range		Point
9	6.997117448607536e-159	6.9825357345617866e-152	6.8956779722136e-152
8	-2.083222696695489e+156	-8.927571262924557e+151	-1.3324370156406744e+154

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	17
1	35	17

end0.0ms

sample1.1s

Algorithm

intervals

Results

256.0ms	1092×	body	2560	valid
229.0ms	5871×	body	80	valid
164.0ms	874×	body	1280	valid
102.0ms	2855×	body	80	nan
70.0ms	452×	body	640	valid
36.0ms	117×	body	5120	valid
27.0ms	224×	body	320	valid
8.0ms	115×	body	160	valid