Details

Time bar (total: 4.6s)

sample546.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 5.867564%

Guaranteed chance to sample good point: 42.561744%

Results
12.0ms25×body2560valid
10.0ms193×body80valid
8.0ms32×body1280valid
4.0ms84×body80nan
3.0ms16×body640valid
2.0ms6×body5120valid
1.0ms4×body320valid
0.0ms2×body160valid

simplify16.0ms

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: 33.7b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b
(- (* b b) (* 4.0 (* a c)))
0.7b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.7b
(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
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
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))))

series66.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms
(- (* b b) (* 4.0 (* a c)))
20.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify51.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0398888
11466803
25001798

prune179.0ms

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

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New80989
Fresh000
Picked101
Done000
Total81990

Merged error: 6.7b

Counts
90 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.6b
(- (* b b) (* 4.0 (* a c)))
0.7b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite38.0ms

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:
17.0ms
(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
6.0ms
(- (* 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))))

series64.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
10.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify64.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0463989
12033868
25001860

prune161.0ms

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

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New94397
Fresh268
Picked011
Done000
Total9610106

Merged error: 6.7b

Counts
106 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* 4.0 (* a c)))
11.4b
(- (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
23.7b
(sqrt (- (* b b) (* 4.0 (* a c))))
23.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
9×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×associate--l- neg-sub0 neg-log difference-of-squares
Counts
4 → 57
Calls
4 calls:
6.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(- (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series58.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(- (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
15.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
16.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify143.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (135.0ms)

IterNodesCost
0237691
1923594
24204575
35003573

prune162.0ms

Filtered
54 candidates to 69 candidates (-27.8%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New69069
Fresh088
Picked011
Done011
Total691079

Merged error: 6.7b

Counts
79 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* 4.0 (* a c)))
4.7b
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
10.2b
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.7b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
61×*-un-lft-identity
52×times-frac
51×add-exp-log
30×add-cube-cbrt associate-*l*
27×add-cbrt-cube
20×prod-exp
18×difference-of-squares
16×div-exp
13×distribute-lft-out
12×sqrt-prod
9×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 → 149
Calls
4 calls:
4.0ms
(- (* b b) (* 4.0 (* a c)))
24.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
13.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series139.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(- (* b b) (* 4.0 (* a c)))
49.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
65.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
15.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify132.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 2 (107.0ms)

IterNodesCost
07582360
137522016
250011993

prune259.0ms

Filtered
102 candidates to 161 candidates (-57.8%)
Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New1565161
Fresh347
Picked011
Done022
Total15912171

Merged error: 6.7b

Counts
171 → 12

regimes390.0ms

Accuracy

86.9% (3.5b remaining)

Error of 9.1b against oracle of 5.7b and baseline of 32.3b

bsearch118.0ms

Steps
ItersRangePoint
8
1.5899226579934786e+86
1.772173797690106e+90
4.903783384436066e+89
10
-2.5797417726011165e-306
6.166956616948566e-300
1.242204110282341e-304
9
-4.614558500810685e+27
-1.5335959160462621e+22
-2.871993654387246e+26

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04034
14034

end0.0ms

sample1.8s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 5.867564%

Guaranteed chance to sample good point: 42.561744%

Results
327.0ms5913×body80valid
316.0ms1031×body2560valid
227.0ms904×body1280valid
121.0ms2212×body80nan
90.0ms461×body640valid
39.0ms100×body5120valid
31.0ms205×body320valid
13.0ms126×body160valid

Profiling

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