Details

Time bar (total: 4.6s)

sample56.0ms

Algorithm
intervals
Results
13.0ms38×body2560valid
9.0ms181×body80valid
7.0ms29×body1280valid
5.0ms96×body80nan
4.0ms20×body640valid
2.0msbody5120valid
1.0msbody320valid
0.0msbody160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

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: 35.9b

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))
0.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.4b
(- (* b b) (* 4.0 (* a c)))
25.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
add-exp-log add-cbrt-cube
add-cube-cbrt times-frac associate-/l*
sqrt-prod distribute-lft-out-- difference-of-squares
pow1
flip3-- flip--
distribute-rgt-neg-in diff-log
cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
15.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series297.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
51.0ms
(- (* b b) (* 4.0 (* a c)))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0404890
11481801
25001796

prune259.0ms

Filtered
89 candidates to 65 candidates (73.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New80989
Fresh000
Picked101
Done000
Total81990

Merged error: 5.8b

Counts
90 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.4b
(- (* b b) (* 4.0 (* a c)))
25.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
67×times-frac
48×add-sqr-sqrt
47×*-un-lft-identity
27×add-cube-cbrt
25×add-exp-log
13×associate-/r* add-cbrt-cube
12×div-exp
10×distribute-lft-out-- add-log-exp difference-of-squares
associate-/r/
sqrt-prod
flip3-- flip--
pow1
cbrt-undiv distribute-rgt-neg-in div-inv
rec-exp diff-log 1-exp prod-exp associate-/l*
sub-neg sqrt-div
associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 125
Calls
4 calls:
14.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
8.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series319.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
80.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
50.0ms
(- (* b b) (* 4.0 (* a c)))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify69.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05331804
125441605
250021531

prune257.0ms

Filtered
137 candidates to 72 candidates (52.6%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1352137
Fresh448
Picked011
Done000
Total1397146

Merged error: 5.7b

Counts
146 → 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)))
0.3b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.4b
(- (* b b) (* 4.0 (* a c)))
25.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×add-sqr-sqrt
16×*-un-lft-identity
13×add-cbrt-cube
10×prod-exp add-log-exp
add-cube-cbrt
pow1 associate-*r* associate-*l*
flip3-- sqrt-prod flip--
div-exp cbrt-unprod distribute-lft-out-- difference-of-squares
times-frac diff-log
cbrt-undiv frac-times sub-neg rec-exp distribute-rgt-neg-in sqrt-div 1-exp associate-*l/
associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 85
Calls
4 calls:
16.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
8.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series296.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
45.0ms
(- (* b b) (* 4.0 (* a c)))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify62.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0469991
12048866
25002857

prune222.0ms

Filtered
97 candidates to 65 candidates (67.0%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New97097
Fresh055
Picked011
Done011
Total977104

Merged error: 5.7b

Counts
104 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

1.1b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.4b
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
20.5b
(- (pow b 2) (pow b 2))
25.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
23×*-un-lft-identity
22×unpow-prod-down
19×add-exp-log
16×difference-of-squares
15×add-cube-cbrt
13×add-cbrt-cube
12×unpow2 sqr-pow
10×distribute-rgt-out-- add-log-exp
distribute-lft-out--
div-exp
pow1 associate-/l/
cbrt-undiv prod-exp
flip3-+ times-frac associate-/r* sqrt-prod flip-+
frac-times flip3-- sqrt-div associate-*r/ sum-log flip-- cbrt-unprod distribute-lft-out
+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square rec-exp distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 +-inverses diff-log 1-exp neg-log associate-*l/ clear-num div-inv associate-/l*
Counts
4 → 107
Calls
4 calls:
8.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0ms
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
8.0ms
(- (pow b 2) (pow b 2))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series170.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
13.0ms
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
1.0ms
(- (pow b 2) (pow b 2))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify200.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (190.0ms)

IterNodesCost
0595778
13991571
25002555

prune313.0ms

Filtered
119 candidates to 79 candidates (66.4%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1172119
Fresh134
Picked101
Done022
Total1197126

Merged error: 5.7b

Counts
126 → 7

regimes198.0ms

Accuracy

92.1% (2.0b remaining)

Error of 7.8b against oracle of 5.9b and baseline of 30.7b

bsearch184.0ms

Steps
ItersRangePoint
6
2087876908255263.8
9946277058360104.0
9787957843074626.0
10
2.6524235870522762e-238
1.0968859070725262e-227
1.4261987494619949e-235
7
-1.337582615490612e+92
-9.459320394366776e+89
-1.608252882176146e+91

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04425
14425

end0.0ms

sample1.4s

Algorithm
intervals
Results
314.0ms5940×body80valid
314.0ms1064×body2560valid
205.0ms854×body1280valid
145.0ms2835×body80nan
82.0ms435×body640valid
42.0ms108×body5120valid
31.0ms213×body320valid
13.0ms111×body160valid

Profiling

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