Details

Time bar (total: 4.6s)

sample49.0ms

Algorithm
intervals
Results
11.0ms29×body2560valid
10.0ms204×body80valid
6.0ms25×body1280valid
5.0ms98×body80nan
3.0ms15×body640valid
1.0ms2×body5120valid
1.0ms4×body320valid
0.0ms3×body160valid

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: 31.3b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
21.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×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:
11.0ms
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series310.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
81.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
50.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0398888
11466803
25001798

prune221.0ms

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: 5.2b

Counts
90 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
21.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

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
8×add-cube-cbrt
7×pow1 associate-*r* associate-*l*
5×flip3-- sqrt-prod flip--
4×div-exp cbrt-unprod distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp distribute-rgt-neg-in sqrt-div 1-exp associate-*l/
1×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:
14.0ms
(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
8.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series293.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
77.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
42.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify60.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0463989
12033868
25001860

prune207.0ms

Filtered
97 candidates to 64 candidates (66.0%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New95297
Fresh178
Picked011
Done000
Total9610106

Merged error: 5.2b

Counts
106 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
21.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

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
9×associate-/r/
8×sqrt-prod
7×flip3-- flip--
6×pow1
5×cbrt-undiv distribute-rgt-neg-in div-inv
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×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:
13.0ms
(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
8.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series351.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
79.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
48.0ms
(- (* b b) (* 4.0 (* a c)))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify76.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05381801
125731602
250021528

prune230.0ms

Filtered
137 candidates to 72 candidates (52.6%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1352137
Fresh448
Picked011
Done011
Total1398147

Merged error: 5.2b

Counts
147 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b
(- (* b b) (* 4.0 (* a c)))
13.9b
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
21.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log *-un-lft-identity add-cbrt-cube
10×add-log-exp
8×add-sqr-sqrt
7×add-cube-cbrt
5×pow1
4×times-frac distribute-lft-out associate-/l*
3×cbrt-undiv flip3-+ div-exp prod-exp sqrt-prod cbrt-unprod flip-+
2×flip3-- sqrt-div associate-*l/ sum-log associate-/r/ flip-- associate-/l/
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 diff-log neg-log clear-num associate-/r* div-inv
Counts
4 → 71
Calls
4 calls:
12.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
14.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series423.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
43.0ms
(- (* b b) (* 4.0 (* a c)))
226.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify102.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
0501969
13066816
25003798

prune215.0ms

Filtered
83 candidates to 62 candidates (74.7%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New82183
Fresh055
Picked011
Done022
Total82991

Merged error: 5.2b

Counts
91 → 9

regimes220.0ms

Accuracy

89% (3.1b remaining)

Error of 8.8b against oracle of 5.7b and baseline of 34.1b

bsearch208.0ms

Steps
ItersRangePoint
10
1.4182100026226751e+88
1.1634796338171106e+98
4.5720489322241335e+94
7
-2.6653979660135254e-122
-1.1110532800434707e-124
-1.6086867020358568e-124
9
-2.112079485172501e+81
-7.412295145025422e+71
-3.595919917945398e+76

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05233
15233

end0.0ms

sample1.4s

Algorithm
intervals
Results
321.0ms1107×body2560valid
317.0ms5833×body80valid
210.0ms903×body1280valid
142.0ms2897×body80nan
84.0ms438×body640valid
37.0ms105×body5120valid
30.0ms216×body320valid
10.0ms111×body160valid

Profiling

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