Details

Time bar (total: 3.4s)

sample57.0ms

Algorithm
intervals
Results
9.0ms182×body80valid
9.0ms32×body2560valid
6.0ms24×body1280valid
5.0ms106×body80nan
4.0ms19×body640valid
1.0ms4×body5120valid
1.0ms8×body320valid
0.0ms5×body160valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.2b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.5b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.6b
(- (* b b) (* 4.0 (* a c)))
20.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

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:
12.0ms
(/ (- (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))))

series60.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
17.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(- (* b b) (* 4.0 (* a c)))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0398888
11466803
25001798

prune167.0ms

Filtered
65 candidates to 89 candidates (-36.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New81889
Fresh000
Picked101
Done000
Total82890

Merged error: 4.4b

Counts
90 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
1.5b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.6b
(- (* b b) (* 4.0 (* a c)))
20.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
159×times-frac
128×add-sqr-sqrt
127×*-un-lft-identity
75×add-cube-cbrt
26×distribute-lft-out-- difference-of-squares
25×associate-/l*
16×sqrt-prod
13×distribute-rgt-neg-in
10×add-log-exp
9×add-exp-log add-cbrt-cube
5×pow1 div-inv
3×cbrt-undiv flip3-- diff-log div-exp associate-/r* flip--
2×sub-neg sqrt-div div-sub
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 164
Calls
4 calls:
16.0ms
(/ (/ (- (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))))

series57.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(/ (/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
15.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(- (* b b) (* 4.0 (* a c)))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify76.0ms

Algorithm
egg-herbie
Counts
176 → 176
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
06722534
125432443
250012443

prune263.0ms

Filtered
113 candidates to 176 candidates (-55.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1760176
Fresh077
Picked011
Done000
Total1768184

Merged error: 4.4b

Counts
184 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.5b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.6b
(- (* b b) (* 4.0 (* a c)))
20.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

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:
15.0ms
(* (- (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)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series61.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
16.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(- (* b b) (* 4.0 (* a c)))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0463989
12033868
25001860

prune137.0ms

Filtered
65 candidates to 97 candidates (-49.2%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New96197
Fresh156
Picked011
Done011
Total978105

Merged error: 4.4b

Counts
105 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
1.5b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.6b
(- (* b b) (* 4.0 (* a c)))
20.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

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-/r*
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-/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 → 76
Calls
4 calls:
13.0ms
(/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
8.0ms
(- (neg 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))))

series91.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
16.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms
(- (* b b) (* 4.0 (* a c)))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0369865
11548770
25001760

prune112.0ms

Filtered
63 candidates to 88 candidates (-39.7%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New87188
Fresh055
Picked011
Done022
Total87996

Merged error: 4.4b

Counts
96 → 9

regimes298.0ms

Accuracy

87.8% (3.5b remaining)

Error of 8.8b against oracle of 5.3b and baseline of 33.7b

bsearch106.0ms

Steps
ItersRangePoint
9
1.4207218227508602e+125
1.7687561556963888e+130
4.381882541249602e+126
10
-2.167522402930775e-204
-3.11138610555295e-222
-4.248212506849557e-211
6
-4357518.715743097
-340480.61858828116
-999239.1209736161

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04430
14430

end0.0ms

sample1.6s

Algorithm
intervals
Results
342.0ms1148×body2560valid
303.0ms5786×body80valid
207.0ms839×body1280valid
143.0ms2824×body80nan
89.0ms470×body640valid
38.0ms100×body5120valid
34.0ms240×body320valid
12.0ms119×body160valid

Profiling

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