Details

Time bar (total: 6.0s)

sample289.0ms

Algorithm
intervals
Results
11.0ms45×body2560valid
11.0ms197×body80valid
5.0ms23×body1280valid
4.0ms97×body80nan
2.0ms10×body640valid
1.0msbody5120valid
1.0msbody320valid
0.0msbody160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1237
2307
3327
4347
5347

prune4.0ms

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: 35.1b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b
(- (* b_2 b_2) (* a c))
1.1b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
19×add-sqr-sqrt
18×add-cube-cbrt
15×times-frac
10×fma-def distribute-lft-out add-log-exp
distribute-rgt-neg-in
add-exp-log add-cbrt-cube
pow1 associate-/l*
expm1-log1p-u log1p-expm1-u
distribute-lft-neg-in associate-/r* sqrt-prod
neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
cbrt-undiv +-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub div-exp prod-diff neg-log clear-num div-inv
Counts
4 → 100
Calls
4 calls:
10.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms
(- (* b_2 b_2) (* a c))
9.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
36.0ms
(- (* b_2 b_2) (* a c))
77.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
70.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0389850
11366779
25001753

prune271.0ms

Filtered
112 candidates to 88 candidates (78.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1048112
Fresh000
Picked101
Done000
Total1058113

Merged error: 5.9b

Counts
113 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b_2 b_2) (* a c))
5.1b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.9b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
186×times-frac
154×add-sqr-sqrt
153×*-un-lft-identity
89×add-cube-cbrt
32×distribute-lft-out-- difference-of-squares
30×associate-/l*
19×sqrt-prod
16×distribute-rgt-neg-in
11×add-exp-log add-cbrt-cube
10×associate-/r* associate-/r/
flip3-- flip--
div-inv add-log-exp
pow1
cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
associate-/l/
frac-2neg sqrt-div clear-num
sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log prod-diff flip-+
Counts
4 → 210
Calls
4 calls:
4.0ms
(- (* b_2 b_2) (* a c))
20.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
13.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series402.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* b_2 b_2) (* a c))
141.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
166.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
63.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify120.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
07613434
134903258
250023250

prune463.0ms

Filtered
222 candidates to 152 candidates (68.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2193222
Fresh257
Picked011
Done000
Total2219230

Merged error: 5.8b

Counts
230 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (* b_2 b_2) (* a c))
1.6b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
5.1b
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
24.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
951×times-frac
585×add-sqr-sqrt
584×*-un-lft-identity
392×add-cube-cbrt
96×distribute-lft-out-- difference-of-squares
83×associate-/l*
51×sqrt-prod
48×distribute-rgt-neg-in
28×associate-/r*
22×div-inv
18×add-exp-log add-cbrt-cube
cbrt-undiv div-exp
add-log-exp
pow1 associate-/r/
expm1-log1p-u log1p-expm1-u
flip3-- frac-2neg sqrt-div clear-num flip--
sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-/l/
Counts
4 → 495
Calls
4 calls:
4.0ms
(- (* b_2 b_2) (* a c))
14.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
31.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series438.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* b_2 b_2) (* a c))
183.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
156.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify106.0ms

Algorithm
egg-herbie
Counts
507 → 507
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
015618690
150018042

prune971.0ms

Filtered
507 candidates to 308 candidates (60.7%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New5061507
Fresh077
Picked011
Done011
Total50610516

Merged error: 5.8b

Counts
516 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b
(- (* b_2 b_2) (* a c))
1.1b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.9b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
137×add-sqr-sqrt
110×*-un-lft-identity
84×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
24×associate-/r*
19×prod-diff
15×add-exp-log
13×distribute-lft-out--
associate-/r/ add-cbrt-cube
add-log-exp
flip3-- fma-neg div-exp flip--
pow1
div-inv
expm1-log1p-u log1p-expm1-u
cbrt-undiv associate-/l*
sub-neg rec-exp sqrt-div diff-log 1-exp
rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num inv-pow
Counts
4 → 196
Calls
4 calls:
14.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.0ms
(- (* b_2 b_2) (* a c))
8.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
33.0ms
(- (* b_2 b_2) (* a c))
72.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
59.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify85.0ms

Algorithm
egg-herbie
Counts
208 → 208
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
06582519
129432155
250012004

prune266.0ms

Filtered
208 candidates to 104 candidates (50.0%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New2080208
Fresh077
Picked011
Done022
Total20810218

Merged error: 5.8b

Counts
218 → 10

regimes216.0ms

Accuracy

87.8% (3.2b remaining)

Error of 9.0b against oracle of 5.8b and baseline of 32.0b

bsearch152.0ms

Steps
ItersRangePoint
9
5.612942259261838e-23
3.213408159798715e-15
2.39571434833311e-19
10
-6.42569108438854e-260
-2.403372424182918e-272
-5.097978013926245e-266
7
-1.337582615490612e+92
-9.459320394366776e+89
-2.864598576127613e+91

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04023
14023

end0.0ms

sample1.3s

Algorithm
intervals
Results
287.0ms1121×body2560valid
261.0ms5737×body80valid
193.0ms914×body1280valid
127.0ms2819×body80nan
86.0ms500×body640valid
32.0ms98×body5120valid
27.0ms222×body320valid
10.0ms113×body160valid

Profiling

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