Details

Time bar (total: 4.9s)

sample54.0ms

Algorithm
intervals
Results
12.0ms43×body2560valid
10.0ms191×body80valid
9.0ms25×body1280valid
4.0ms88×body80nan
3.0ms16×body640valid
1.0ms3×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: 34.5b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* a c))
0.1b
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.5b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
20×*-un-lft-identity
14×add-exp-log add-cbrt-cube
10×pow1
8×add-cube-cbrt add-log-exp
7×times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
4×prod-exp cbrt-unprod
3×flip3-- distribute-rgt-neg-in associate-*l* pow-prod-down flip--
2×cbrt-undiv sqrt-div diff-log div-exp associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub associate-*r* neg-log clear-num associate-/r* *-commutative div-inv
Counts
4 → 83
Calls
4 calls:
5.0ms
(* 4.0 (* a c))
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)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series259.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* 4.0 (* a c))
95.0ms
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
75.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify48.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0451853
11636764
25001759

prune233.0ms

Filtered
95 candidates to 66 candidates (69.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New86995
Fresh000
Picked101
Done000
Total87996

Merged error: 6.9b

Counts
96 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* a c))
0.2b
(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.5b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
20×add-sqr-sqrt
18×add-cbrt-cube
17×*-un-lft-identity
13×prod-exp
12×pow1
10×associate-*l*
9×add-cube-cbrt
8×associate-*r* add-log-exp
7×cbrt-unprod
5×sqrt-prod
4×flip3-- div-exp pow-prod-down flip-- distribute-lft-out-- difference-of-squares
3×times-frac
2×cbrt-undiv frac-times rec-exp distribute-rgt-neg-in sqrt-div diff-log 1-exp associate-*l/ *-commutative
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ neg-log un-div-inv div-inv unswap-sqr
Counts
4 → 91
Calls
4 calls:
8.0ms
(* 4.0 (* a c))
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)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series261.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* 4.0 (* a c))
94.0ms
(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
76.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
67.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify60.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0516954
12203829
25001820

prune214.0ms

Filtered
103 candidates to 66 candidates (64.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New994103
Fresh448
Picked011
Done000
Total1039112

Merged error: 6.9b

Counts
112 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.4b
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
8.5b
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt
63×*-un-lft-identity
52×times-frac
51×add-exp-log
30×add-cube-cbrt associate-*l*
27×add-cbrt-cube
20×prod-exp difference-of-squares
16×div-exp
13×sqrt-prod distribute-lft-out
10×distribute-lft-out--
8×cbrt-undiv cbrt-unprod
7×pow1 associate-*r*
6×associate-/r* add-log-exp
4×rec-exp flip3-- 1-exp associate-/r/ flip-- associate-/l*
3×div-inv
2×sqrt-div associate-/l/ unswap-sqr
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 152
Calls
4 calls:
7.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
11.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series514.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
166.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
198.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify148.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (118.0ms)

IterNodesCost
07642421
136632067
250012044

prune384.0ms

Filtered
164 candidates to 106 candidates (64.6%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1604164
Fresh347
Picked011
Done011
Total16310173

Merged error: 6.8b

Counts
173 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ (* 4.0 (* a c)) (* 2.0 a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
0.9b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
12.2b
(/ (* 4.0 (* a c)) (* 2.0 a))
23.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
54×add-exp-log add-cbrt-cube
47×add-sqr-sqrt
38×times-frac
32×*-un-lft-identity
19×cbrt-undiv div-exp
18×add-cube-cbrt prod-exp cbrt-unprod
14×difference-of-squares
10×sqrt-prod
9×div-inv
7×associate-/r* distribute-lft-out--
6×associate-/l* add-log-exp
5×pow1
3×flip3-- flip--
2×frac-2neg sqrt-div clear-num associate-/r/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 123
Calls
4 calls:
14.0ms
(/ (/ (* 4.0 (* a c)) (* 2.0 a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
6.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
7.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series337.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(/ (/ (* 4.0 (* a c)) (* 2.0 a)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
80.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
9.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify99.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
06491787
137381534
250011533

prune234.0ms

Filtered
135 candidates to 82 candidates (60.7%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1341135
Fresh257
Picked011
Done022
Total1369145

Merged error: 6.8b

Counts
145 → 9

regimes170.0ms

Accuracy

82.3% (4.6b remaining)

Error of 10.2b against oracle of 5.6b and baseline of 31.7b

bsearch120.0ms

Steps
ItersRangePoint
10
2.564731655063431e+70
9.580498431628148e+82
4.11496261975277e+80
6
-3.644302906869421e-88
-3.979740892597312e-89
-1.0270535051017606e-88

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03716
13716

end0.0ms

sample1.6s

Algorithm
intervals
Results
489.0ms1068×body2560valid
302.0ms5928×body80valid
212.0ms899×body1280valid
138.0ms2877×body80nan
81.0ms440×body640valid
40.0ms117×body5120valid
31.0ms229×body320valid
14.0ms113×body160valid

Profiling

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