Details

Time bar (total: 4.1s)

sample42.0ms

Algorithm
intervals
Results
7.0ms189×body80valid
7.0ms36×body1280valid
6.0ms29×body2560valid
3.0ms95×body80nan
2.0ms11×body640valid
1.0ms10×body320valid
1.0ms11×body160valid
0.0ms1×body5120valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 34.3b

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))
1.0b
(- (* b b) (* 4.0 (* a c)))
2.8b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

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:
15.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series283.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms
(- (* b b) (* 4.0 (* a c)))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0404890
11481801
25001796

prune232.0ms

Filtered
89 candidates to 65 candidates (73.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New81889
Fresh000
Picked101
Done000
Total82890

Merged error: 5.2b

Counts
90 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.0b
(- (* b b) (* 4.0 (* a c)))
2.8b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

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) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series301.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
43.0ms
(- (* b b) (* 4.0 (* a c)))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify71.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05331804
125441605
250021531

prune233.0ms

Filtered
137 candidates to 72 candidates (52.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1352137
Fresh257
Picked011
Done000
Total1378145

Merged error: 5.1b

Counts
145 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.0b
(- (* b b) (* 4.0 (* a c)))
2.8b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

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
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
4.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series284.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
44.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify60.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0469991
12048866
25002857

prune205.0ms

Filtered
97 candidates to 65 candidates (67.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New97097
Fresh066
Picked011
Done011
Total978105

Merged error: 5.1b

Counts
105 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* 4.0 (* a c)))
14.3b
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
16.6b
(- (pow b 2) (pow b 2))
21.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
22×unpow-prod-down
19×add-exp-log *-un-lft-identity
16×difference-of-squares
15×add-cube-cbrt
13×add-cbrt-cube
12×unpow2 sqr-pow
10×distribute-rgt-out--
8×distribute-lft-out-- add-log-exp
7×div-exp
5×pow1 associate-/l/
4×cbrt-undiv prod-exp
3×flip3-- times-frac associate-/r* sqrt-prod flip--
2×frac-times sub-neg flip3-+ sqrt-div diff-log associate-*r/ cbrt-unprod flip-+
1×rem-sqrt-square rec-exp frac-2neg sqrt-pow1 pow1/2 +-inverses 1-exp associate-*l/ clear-num div-inv associate-/l*
Counts
4 → 104
Calls
4 calls:
4.0ms
(- (* b b) (* 4.0 (* a c)))
21.0ms
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
7.0ms
(- (pow b 2) (pow b 2))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series128.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
1.0ms
(- (pow b 2) (pow b 2))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify171.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (161.0ms)

IterNodesCost
0523718
13467529
25001480

prune266.0ms

Filtered
116 candidates to 73 candidates (62.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1142116
Fresh055
Picked101
Done022
Total1159124

Merged error: 5.0b

Counts
124 → 9

regimes249.0ms

Accuracy

92.2% (1.9b remaining)

Error of 7.4b against oracle of 5.5b and baseline of 29.4b

bsearch177.0ms

Steps
ItersRangePoint
7
4.4312058130773924e+95
1.951780157010812e+97
4.548896756142505e+96
8
2.9152441486958957e-294
8.554373099101626e-290
3.2642402951810927e-293
9
-5.70112062633313e+26
-1.2582724651754321e+21
-8.677842214331729e+23

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04424
14424

end0.0ms

sample1.2s

Algorithm
intervals
Results
244.0ms1038×body2560valid
230.0ms5927×body80valid
171.0ms882×body1280valid
114.0ms2979×body80nan
70.0ms478×body640valid
34.0ms121×body5120valid
24.0ms224×body320valid
8.0ms113×body160valid

Profiling

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