Details

Time bar (total: 4.5s)

sample43.0ms

Algorithm
intervals
Results
8.0ms203×body80valid
6.0ms31×body1280valid
6.0ms23×body2560valid
4.0ms4×body5120valid
3.0ms79×body80nan
3.0ms17×body640valid
0.0ms4×body320valid
0.0ms4×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: 32.9b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

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

series290.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
43.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0404890
11481801
25001796

prune246.0ms

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: 6.2b

Counts
90 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite38.0ms

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:
18.0ms
(/ 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))))

series303.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
48.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
66.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify65.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05331804
125441605
250021531

prune268.0ms

Filtered
137 candidates to 73 candidates (53.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1343137
Fresh347
Picked011
Done000
Total1378145

Merged error: 6.2b

Counts
145 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.8b
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.1b
(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
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:
16.0ms
(* (- (- 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))))

series288.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
48.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify55.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0469991
12048866
25002857

prune225.0ms

Filtered
97 candidates to 65 candidates (67.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New96197
Fresh156
Picked011
Done011
Total978105

Merged error: 6.2b

Counts
105 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* 4.0 (* a c)))
1.2b
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.3b
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
22.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

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:
4.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series358.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* 4.0 (* a c)))
81.0ms
(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
163.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (* (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a)))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify101.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
0502969
13079812
25002794

prune285.0ms

Filtered
83 candidates to 62 candidates (74.7%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New81283
Fresh145
Picked011
Done022
Total82991

Merged error: 6.2b

Counts
91 → 9

regimes207.0ms

Accuracy

85% (4.0b remaining)

Error of 9.3b against oracle of 5.4b and baseline of 31.9b

bsearch155.0ms

Steps
ItersRangePoint
9
4.546949039871578e+116
7.0067478635952275e+121
7.369869774752497e+119
4
2.7062129888597453e-95
4.861630376334293e-95
2.7444235711350233e-95
9
-6.621891359339352e+42
-4.1115514380901975e+36
-4.8085485579241775e+39

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05031
15031

end0.0ms

sample1.4s

Algorithm
intervals
Results
465.0ms1063×body2560valid
240.0ms5846×body80valid
173.0ms849×body1280valid
109.0ms2863×body80nan
71.0ms463×body640valid
31.0ms105×body5120valid
27.0ms231×body320valid
10.0ms126×body160valid