Details

Time bar (total: 9.4s)

sample278.0ms

Algorithm
intervals
Results
7.0ms36×body2560valid
6.0ms192×body80valid
4.0ms26×body1280valid
4.0ms83×body80nan
2.0ms12×body640valid
1.0ms9×body320valid
1.0ms3×body5120valid
0.0ms2×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0147
1227
2257
3277
4297
5297

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: 31.0b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b
(- (* b_2 b_2) (* a c))
0.5b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
51×*-un-lft-identity
20×difference-of-squares
17×sqrt-prod
15×add-cube-cbrt times-frac
14×unswap-sqr
10×distribute-lft-out add-log-exp
8×associate-*l* distribute-lft-out--
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in associate-/l*
4×swap-sqr *-commutative
3×associate-/r*
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp neg-log clear-num div-inv
Counts
4 → 108
Calls
4 calls:
29.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.0ms
(- (* b_2 b_2) (* a c))
23.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
29.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series288.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
38.0ms
(- (* b_2 b_2) (* a c))
80.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
73.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0397996
11372933
25002912

prune198.0ms

Filtered
120 candidates to 77 candidates (64.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1128120
Fresh000
Picked101
Done000
Total1138121

Merged error: 4.4b

Counts
121 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.6b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
7.9b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
20.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
383×*-un-lft-identity
298×times-frac
253×add-sqr-sqrt
115×add-cube-cbrt
74×distribute-lft-out
66×difference-of-squares
60×distribute-lft-out--
51×associate-/l*
45×sqrt-prod
41×associate-*l*
28×distribute-rgt-neg-in
21×associate-/l/
17×associate-/r*
11×add-exp-log add-cbrt-cube
10×associate-/r/
8×add-log-exp
7×flip3-- flip-- unswap-sqr
6×div-inv
5×pow1
4×cbrt-undiv div-exp
3×frac-2neg clear-num
2×flip3-+ sqrt-div diff-log swap-sqr *-commutative flip-+
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 308
Calls
4 calls:
23.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
43.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
31.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series458.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
145.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
180.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify136.0ms

Algorithm
egg-herbie
Counts
320 → 320
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
08014888
135444626
250024600

prune408.0ms

Filtered
320 candidates to 160 candidates (50.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3164320
Fresh257
Picked101
Done000
Total3199328

Merged error: 4.3b

Counts
328 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.8b
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
3.6b
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
20.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite337.0ms

Algorithm
rewrite-expression-head
Rules
3846×times-frac
2123×add-sqr-sqrt
2105×*-un-lft-identity
1509×add-cube-cbrt
450×associate-/l*
304×difference-of-squares
298×distribute-lft-out--
184×associate-/r/
170×associate-/l/
164×sqrt-prod
147×distribute-rgt-neg-in
112×associate-/r*
66×div-inv
41×add-exp-log
28×div-exp
23×add-cbrt-cube
13×cbrt-undiv
12×frac-2neg clear-num
8×add-log-exp
7×flip3-- flip-- unswap-sqr
5×pow1
4×div-sub associate-*l*
3×rec-exp 1-exp
2×associate--l- neg-sub0 sqrt-div diff-log swap-sqr *-commutative
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 1441
Calls
4 calls:
24.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
37.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
96.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
16.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series349.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
96.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
113.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify269.0ms

Algorithm
egg-herbie
Counts
1453 → 1453
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
0500128854

prune3.2s

Filtered
1453 candidates to 907 candidates (62.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New145031453
Fresh358
Picked101
Done000
Total145481462

Merged error: 4.3b

Counts
1462 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.8b
(/ c (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))
3.6b
(/ (/ c (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)) a)
20.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
1014×times-frac
682×add-sqr-sqrt
664×*-un-lft-identity
428×add-cube-cbrt
135×associate-/l*
124×difference-of-squares
118×distribute-lft-out--
75×associate-/r/
74×sqrt-prod
68×associate-/r*
57×distribute-rgt-neg-in
41×associate-/l/
23×div-inv
18×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
8×frac-2neg clear-num add-log-exp
7×flip3-- flip-- unswap-sqr
5×pow1
4×associate-*l*
2×sqrt-div diff-log swap-sqr *-commutative
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 605
Calls
4 calls:
24.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms
(/ c (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))
48.0ms
(/ (/ c (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)) a)
17.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series500.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
184.0ms
(/ c (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))
174.0ms
(/ (/ c (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)) a)
69.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify129.0ms

Algorithm
egg-herbie
Counts
617 → 617
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
018519984
150029440

prune1.1s

Filtered
617 candidates to 378 candidates (61.3%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New6152617
Fresh257
Picked101
Done000
Total6187625

Merged error: 4.3b

Counts
625 → 7

regimes137.0ms

Accuracy

94.7% (1.3b remaining)

Error of 7.1b against oracle of 5.8b and baseline of 29.5b

bsearch149.0ms

Steps
ItersRangePoint
9
2.8787744468916765e+83
8.390568855339406e+90
7.775131276953344e+90
10
-1.627973268244592e-198
-2.2998085647908577e-213
-1.972370344124578e-212
8
-2.4252735757472657e+138
-4.116420024851893e+134
-1.8890263868387462e+136

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04123
14323
24323

end0.0ms

sample1.0s

Algorithm
intervals
Results
208.0ms5954×body80valid
204.0ms1028×body2560valid
142.0ms853×body1280valid
96.0ms2983×body80nan
59.0ms466×body640valid
24.0ms88×body5120valid
21.0ms220×body320valid
6.0ms101×body160valid