Details

Time bar (total: 4.6s)

sample52.0ms

Algorithm
intervals
Results
11.0ms35×body2560valid
10.0ms187×body80valid
8.0ms31×body1280valid
5.0ms95×body80nan
2.0ms11×body640valid
1.0ms3×body5120valid
1.0ms4×body320valid
0.0ms4×body160valid

simplify15.0ms

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: 35.5b

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
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.1b
(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:
12.0ms
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms
(- (* b b) (* 4.0 (* a c)))
11.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
47.0ms
(- (* b b) (* 4.0 (* a c)))
76.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0398888
11466803
25001798

prune240.0ms

Filtered
89 candidates to 65 candidates (73.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New791089
Fresh000
Picked101
Done000
Total801090

Merged error: 6.4b

Counts
90 → 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
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite37.0ms

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

series363.0ms

Counts
4 → 12
Calls
4 calls:
160.0ms
(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
49.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify71.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05381801
125731602
250021528

prune239.0ms

Filtered
137 candidates to 73 candidates (53.3%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1352137
Fresh459
Picked101
Done000
Total1407147

Merged error: 6.4b

Counts
147 → 7

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
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.1b
(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
(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
3.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series304.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
45.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
76.0ms
(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

prune221.0ms

Filtered
97 candidates to 65 candidates (67.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New96197
Fresh156
Picked011
Done000
Total977104

Merged error: 6.4b

Counts
104 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
0.8b
(- (* b b) (* 4.0 (* a c)))
5.9b
(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
24.1b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
12×add-sqr-sqrt
10×times-frac
9×add-exp-log add-cube-cbrt sqrt-prod add-cbrt-cube
8×add-log-exp
6×associate-/l*
5×pow1
4×flip3-- sqrt-div flip--
3×div-inv distribute-lft-out--
2×cbrt-undiv sub-neg diff-log div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-out-- distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* frac-sub cbrt-unprod sub-div difference-of-squares
Counts
4 → 76
Calls
4 calls:
7.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
4.0ms
(- (* b b) (* 4.0 (* a c)))
15.0ms
(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series418.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
50.0ms
(- (* b b) (* 4.0 (* a c)))
115.0ms
(- (/ (neg b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
77.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0418881
11485823
25002813

prune209.0ms

Filtered
88 candidates to 68 candidates (77.3%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New88088
Fresh055
Picked011
Done011
Total88795

Merged error: 6.4b

Counts
95 → 7

regimes168.0ms

Accuracy

88.3% (3.3b remaining)

Error of 8.7b against oracle of 5.3b and baseline of 34.0b

bsearch241.0ms

Steps
ItersRangePoint
9
1.554603894687908e+31
4.1009785056144894e+37
4.056542178957228e+37
10
-4.316738762707921e-172
-5.0277934902974476e-185
-1.8339558115895393e-179
9
-6.551078454010515e+117
-3.119450221310465e+111
-2.3664063138986206e+112

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05334
15334

end0.0ms

sample1.5s

Algorithm
intervals
Results
339.0ms1113×body2560valid
323.0ms5859×body80valid
219.0ms864×body1280valid
148.0ms2880×body80nan
85.0ms430×body640valid
42.0ms110×body5120valid
34.0ms231×body320valid
13.0ms106×body160valid

Profiling

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