Details

Time bar (total: 5.3s)

sample47.0ms

Algorithm
intervals
Results
20.0ms287×body80valid
10.0ms95×body80nan

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03918
18018
214318
317718
418918
519318
619318

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: 19.4b

Counts
2 → 1

localize119.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
2.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
37×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 neg-log
Counts
4 → 140
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series281.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
80.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify71.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04062988
114311956
250021869

prune389.0ms

Filtered
152 candidates to 80 candidates (52.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1448152
Fresh000
Picked101
Done000
Total1458153

Merged error: 7.1b

Counts
153 → 8

localize123.0ms

Local error

Found 4 expressions with local error:

8.3b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×add-cube-cbrt fma-def *-un-lft-identity
9×sqrt-prod
8×add-log-exp
7×pow1
6×sqrt-div
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in rem-sqrt-square flip3-- distribute-rgt-neg-in sqrt-pow1 pow1/2 flip--
2×sum-log
1×+-commutative neg-sub0 associate-+l- neg-mul-1 flip3-+ neg-log flip-+
Counts
4 → 76
Calls
4 calls:
5.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series312.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify115.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (107.0ms)

IterNodesCost
0249756
1969641
24038626
35001624

prune389.0ms

Filtered
88 candidates to 79 candidates (89.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New86288
Fresh257
Picked011
Done000
Total88896

Merged error: 7.1b

Counts
96 → 8

localize125.0ms

Local error

Found 4 expressions with local error:

21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log expm1-log1p-u rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- log1p-expm1-u add-log-exp
Counts
4 → 68
Calls
4 calls:
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series307.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
87.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify72.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 3 (65.0ms)

IterNodesCost
0139588
1510568
22129564
35001556

prune389.0ms

Filtered
80 candidates to 68 candidates (85.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New80080
Fresh066
Picked011
Done011
Total80888

Merged error: 7.1b

Counts
88 → 8

localize119.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.9b
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
6.1b
(/ (* a c) b)
21.9b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
55×add-sqr-sqrt
54×*-un-lft-identity
50×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
14×add-exp-log add-cbrt-cube
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×times-frac associate-/r*
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×flip3-- flip--
2×frac-2neg sqrt-div diff-log prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l* distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 155
Calls
4 calls:
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
4.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series241.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
63.0ms
(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
23.0ms
(/ (* a c) b)
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify93.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06203085
126922005
250021927

prune498.0ms

Filtered
167 candidates to 88 candidates (52.7%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1634167
Fresh235
Picked101
Done022
Total1669175

Merged error: 6.1b

Counts
175 → 9

regimes226.0ms

Accuracy

89.5% (1.6b remaining)

Error of 8.2b against oracle of 6.7b and baseline of 21.5b

bsearch179.0ms

Steps
ItersRangePoint
7
4.4312058130773924e+95
1.951780157010812e+97
1.6290075329134609e+97
9
-8.211399685419546e+34
-2.0557429965048975e+28
-4.027942602901873e+31

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05863
15863

end0.0ms

sample1.1s

Algorithm
intervals
Results
597.0ms8783×body80valid
193.0ms2979×body80nan