Details

sample44.0ms

Algorithm

intervals

Results

12.0ms	40×	body	2560	valid
8.0ms	198×	body	80	valid
4.0ms	22×	body	1280	valid
4.0ms	103×	body	80	nan
3.0ms	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	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

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: 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))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-commutative`
8×	`prod-diff`
4×	`associate-r`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `fma-neg` `sqrt-div` `associate-/r*` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `fma-def` `frac-2neg` `pow1/2` `div-sub` `clear-num` `div-inv`

Counts

4 → 30

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))))

series299.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
43.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify136.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	318	329
1	1134	301
2	4750	289
3	5001	289

prune107.0ms

Filtered

42 candidates to 30 candidates (71.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	35	7	42
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	7	43

Merged error: 6.1b

Counts

43 → 7

localize13.0ms

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))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

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))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
42.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	357	579
1	1483	500
2	5002	469

prune142.0ms

Filtered

55 candidates to 39 candidates (70.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	51	4	55
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	55	7	62

Merged error: 6.1b

Counts

62 → 7

localize16.0ms

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))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-commutative`
8×	`prod-diff`
4×	`associate-r`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `fma-neg` `sqrt-div` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `fma-def` `frac-2neg` `pow1/2` `div-sub` `clear-num` `div-inv`

Counts

4 → 28

Calls

4 calls:

7.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
6.0ms	(- (* b b) (* 4.0 (* a c)))
6.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
6.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) a)
47.0ms	(- (* b b) (* 4.0 (* a c)))
79.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
66.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify124.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 3 (119.0ms)

Iter	Nodes	Cost
0	293	308
1	1036	281
2	4380	268
3	5001	266

prune99.0ms

Filtered

40 candidates to 28 candidates (70.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	40	7	47

Merged error: 6.1b

Counts

47 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-commutative`
10×	`frac-times`
8×	`prod-diff`
7×	`flip3-+` `flip-+`
6×	`associate-/r*`
5×	`associate-*l/`
4×	`associate-r`
3×	`+-commutative` `frac-2neg` `clear-num`
2×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `fma-neg` `sqrt-div` `associate-*r/` `flip--`
1×	`neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `fma-def` `pow1/2` `associate-l` `div-inv`

Counts

4 → 45

Calls

4 calls:

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

series329.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (/ 1 (* 2.0 a)) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
47.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify49.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	419	623
1	1916	540
2	5002	511

prune126.0ms

Filtered

57 candidates to 38 candidates (66.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	56	8	64

Merged error: 6.0b

Counts

64 → 8

regimes197.0ms

Accuracy

82% (5.1b remaining)

Error of 10.7b against oracle of 5.5b and baseline of 34.1b

bsearch110.0ms

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	33	16
1	33	16

end0.0ms

sample1.4s

Algorithm

intervals

Results

455.0ms	1092×	body	2560	valid
252.0ms	5871×	body	80	valid
169.0ms	874×	body	1280	valid
114.0ms	2855×	body	80	nan
69.0ms	452×	body	640	valid
37.0ms	117×	body	5120	valid
26.0ms	224×	body	320	valid
9.0ms	115×	body	160	valid