Details

Time bar (total: 4.0s)

sample45.0ms

Algorithm
intervals
Results
10.0ms43×body2560valid
7.0ms38×body1280valid
7.0ms171×body80valid
4.0ms103×body80nan
3.0ms21×body640valid
1.0ms6×body320valid
0.0ms4×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0299
1659
21219
31519
41609
51649
61649

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 37.2b

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)))
1.1b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
10×*-commutative
8×prod-diff
4×flip3-- associate-*r* flip--
3×fma-neg
2×associate--l- neg-sub0 sub-neg sqrt-div div-sub associate-/r* associate-/l/
1×neg-mul-1 frac-2neg pow1/2 clear-num div-inv
Counts
4 → 32
Calls
4 calls:
8.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms
(- (* 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))))

series292.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
49.0ms
(- (* 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))))

simplify120.0ms

Algorithm
egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 3 (115.0ms)

IterNodesCost
0325356
11145329
24433316
35001314

prune112.0ms

Filtered
44 candidates to 31 candidates (70.5%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New37744
Fresh000
Picked101
Done000
Total38745

Merged error: 5.9b

Counts
45 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
5.2b
(/ (/ (fma a (* 4.0 c) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.5b
(/ (fma a (* 4.0 c) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
8×associate-/r/
6×flip3-- times-frac flip--
5×div-inv
4×*-commutative
3×frac-2neg clear-num associate-/l/ associate-/l*
2×sqrt-div associate-/r*
1×sub-neg pow1/2
Counts
4 → 29
Calls
4 calls:
6.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
9.0ms
(/ (/ (fma a (* 4.0 c) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
7.0ms
(/ (fma a (* 4.0 c) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
6.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series607.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
241.0ms
(/ (/ (fma a (* 4.0 c) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
219.0ms
(/ (fma a (* 4.0 c) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify38.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0330431
11057398
25001364

prune136.0ms

Filtered
41 candidates to 37 candidates (90.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New37441
Fresh336
Picked011
Done000
Total40848

Merged error: 5.8b

Counts
48 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* 4.0 (* a c)))
1.5b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.1b
(/ (fma a (* 4.0 c) 0) a)
23.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
9×*-commutative
8×prod-diff
4×associate-*r*
3×flip3-- flip--
2×sub-neg fma-neg sqrt-div
1×frac-2neg pow1/2 clear-num div-inv
Counts
4 → 24
Calls
4 calls:
5.0ms
(- (* b b) (* 4.0 (* a c)))
6.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.0ms
(/ (fma a (* 4.0 c) 0) a)
6.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series234.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
41.0ms
(/ (fma a (* 4.0 c) 0) a)
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify87.0ms

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0213237
1714224
22955216
35001216

prune89.0ms

Filtered
36 candidates to 20 candidates (55.6%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New35136
Fresh156
Picked101
Done011
Total37744

Merged error: 5.8b

Counts
44 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
11×*-commutative
9×associate-*r/
8×prod-diff
5×associate-*r* associate-/l/
4×flip3-- clear-num un-div-inv flip-- associate-/l*
3×div-inv
2×sub-neg frac-2neg fma-neg sqrt-div associate-*l* associate-/r/
1×pow1/2
Counts
4 → 38
Calls
4 calls:
10.0ms
(* (* 4.0 c) (/ (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
6.0ms
(- (* b b) (* 4.0 (* a c)))
6.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
6.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series390.0ms

Counts
4 → 12
Calls
4 calls:
195.0ms
(* (* 4.0 c) (/ (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
44.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify79.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0285312
11032290
25001279

prune98.0ms

Filtered
50 candidates to 30 candidates (60.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New49150
Fresh055
Picked011
Done011
Total49857

Merged error: 5.8b

Counts
57 → 8

regimes197.0ms

Accuracy

96% (1.0b remaining)

Error of 6.5b against oracle of 5.6b and baseline of 29.7b

bsearch132.0ms

Steps
ItersRangePoint
6
2.066422626357648e+110
1.9801395410105552e+111
1.703504653326294e+111
5
5.655525127217964e-251
1.9763919052369517e-250
5.949382726835493e-251
8
-2.083222696695489e+156
-8.927571262924557e+151
-1.3298367139250566e+153

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04726
14726

end0.0ms

sample1.1s

Algorithm
intervals
Results
246.0ms1094×body2560valid
225.0ms5866×body80valid
159.0ms878×body1280valid
103.0ms2855×body80nan
70.0ms481×body640valid
33.0ms106×body5120valid
21.0ms197×body320valid
8.0ms117×body160valid