Details

Time bar (total: 4.8s)

sample728.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 21.887207%

Guaranteed chance to sample good point: 86.240038%

Results
10.0ms183×body80valid
9.0ms29×body2560valid
8.0ms32×body1280valid
4.0ms9×body80nan
3.0ms13×body640valid
2.0ms11×body320valid
1.0ms4×body5120valid
0.0ms2×body160valid

simplify13.0ms

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: 34.6b

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))
0.6b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b
(- (* b b) (* 4.0 (* a c)))
24.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

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:
11.0ms
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series59.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
15.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0398888
11466803
25001798

prune177.0ms

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

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New791089
Fresh000
Picked101
Done000
Total801090

Merged error: 6.3b

Counts
90 → 10

localize13.0ms

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
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.6b
(- (* b b) (* 4.0 (* a c)))
24.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

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)))
8.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series58.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
17.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms
(- (* b b) (* 4.0 (* a c)))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify55.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0463989
12033868
25001860

prune142.0ms

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

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New94397
Fresh459
Picked011
Done000
Total989107

Merged error: 6.2b

Counts
107 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0b
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
10.6b
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
24.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite45.0ms

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:
6.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
18.0ms
(* (/ (+ 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))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series137.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
46.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
60.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
15.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify118.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
07582422
137172075
250022052

prune262.0ms

Filtered
106 candidates to 164 candidates (-54.7%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1604164
Fresh527
Picked011
Done011
Total1658173

Merged error: 6.2b

Counts
173 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* 4.0 (* a c)))
0.7b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.2b
(/ (* 4.0 (* a c)) (* 2.0 a))
24.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×prod-exp cbrt-unprod
8×add-log-exp
7×*-un-lft-identity
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 clear-num associate-/r* div-inv associate-/l* distribute-lft-out--
Counts
4 → 67
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
7.0ms
(- (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))))

series42.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
2.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify55.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0399575
12213498
25003498

prune92.0ms

Filtered
54 candidates to 79 candidates (-46.3%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New78179
Fresh145
Picked101
Done022
Total80787

Merged error: 6.2b

Counts
87 → 7

regimes299.0ms

Accuracy

95.2% (1.1b remaining)

Error of 7.0b against oracle of 5.8b and baseline of 29.7b

bsearch114.0ms

Steps
ItersRangePoint
9
3.547740726486026e+82
4.028771889956111e+87
1.0565439267036959e+86
10
1.1944347498966476e-295
6.57767071464998e-282
1.4782508651035191e-295
8
-5.768218291700969e+150
-9.419834664568275e+145
-1.277087256155046e+150

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04222
14222

end0.0ms

sample2.2s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 21.887207%

Guaranteed chance to sample good point: 86.240038%

Results
365.0ms1119×body2560valid
343.0ms5822×body80valid
245.0ms900×body1280valid
98.0ms450×body640valid
43.0ms103×body5120valid
36.0ms230×body320valid
20.0ms363×body80nan
11.0ms99×body160valid

Profiling

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