Details

Time bar (total: 5.3s)

sample37.0ms

Algorithm
intervals
Results
14.0ms285×body80valid
5.0ms103×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03618
16718
212318
316018
417518
517718
617718

prune4.0ms

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: 21.3b

Counts
2 → 1

localize123.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.2b
(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)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify67.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04062988
114311956
250021869

prune385.0ms

Filtered
152 candidates to 80 candidates (52.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1466152
Fresh000
Picked101
Done000
Total1476153

Merged error: 8.5b

Counts
153 → 6

localize127.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.3b
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
6.3b
(/ (* a c) b)
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
62×*-un-lft-identity
60×prod-diff
55×add-sqr-sqrt
50×add-cube-cbrt
34×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
14×add-exp-log add-cbrt-cube
10×fma-neg
8×times-frac add-log-exp
7×neg-mul-1
6×associate-/l*
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp associate-/r* log1p-expm1-u distribute-lft-out
2×neg-sub0 flip3-- frac-2neg sqrt-div diff-log div-sub prod-exp clear-num flip-- cbrt-unprod div-inv associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- associate-+l- associate-+r- sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 161
Calls
4 calls:
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
5.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series240.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
62.0ms
(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
19.0ms
(/ (* a c) b)
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify85.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06503173
126652081
250022000

prune431.0ms

Filtered
173 candidates to 90 candidates (52.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1685173
Fresh235
Picked101
Done000
Total1718179

Merged error: 7.4b

Counts
179 → 8

localize119.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/r*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/r/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 156
Calls
4 calls:
12.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series382.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
50.0ms
(- (* b b) (* (* 4.0 a) c))
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify76.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05453278
121142181
250022098

prune411.0ms

Filtered
168 candidates to 88 candidates (52.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1635168
Fresh257
Picked101
Done000
Total16610176

Merged error: 7.1b

Counts
176 → 10

localize117.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 2.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
169×add-sqr-sqrt
168×*-un-lft-identity
159×times-frac
116×add-cube-cbrt
61×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
26×distribute-lft-out-- difference-of-squares
25×associate-/r*
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv flip3-- diff-log div-exp flip-- associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/r/
Counts
4 → 243
Calls
4 calls:
14.0ms
(/ 2.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))
4.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series337.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ 2.0 (/ (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) c))
45.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify115.0ms

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
08524907
133583766
250023725

prune600.0ms

Filtered
255 candidates to 139 candidates (54.5%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2514255
Fresh369
Picked011
Done000
Total25411265

Merged error: 6.1b

Counts
265 → 11

regimes242.0ms

Accuracy

91.7% (1.3b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 20.7b

bsearch171.0ms

Steps
ItersRangePoint
8
3.6696373663460875e+72
1.716395662560696e+75
1.700743369447203e+75
10
-3.525651047217798e+97
-2.6938476684742574e+82
-8.919295405006286e+96

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05543
15543

end0.0ms

sample828.0ms

Algorithm
intervals
Results
447.0ms8714×body80valid
133.0ms2946×body80nan