Details

Time bar (total: 8.1s)

sample288.0ms

Algorithm
intervals
Results
10.0ms183×body80valid
10.0ms40×body2560valid
5.0ms27×body1280valid
4.0ms25×body640valid
4.0ms93×body80nan
1.0ms5×body320valid
0.0ms5×body160valid
0.0ms1×body5120valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 35.0b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.6b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.6b
(- (* b_2 b_2) (* a c))
23.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

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
8×distribute-rgt-neg-in
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×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:
22.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(- (* b_2 b_2) (* a c))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series277.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
74.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms
(- (* b_2 b_2) (* a c))
70.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0389850
11366779
25001753

prune280.0ms

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: 3.4b

Counts
113 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (* b_2 b_2) (* a c))
4.7b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.1b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite48.0ms

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/
7×flip3-- flip--
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×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))
16.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
15.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series407.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (* b_2 b_2) (* a c))
141.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
169.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
64.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify121.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
07613434
134903258
250023250

prune469.0ms

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: 3.4b

Counts
230 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (* b_2 b_2) (* a c))
2.9b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
4.7b
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
23.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite92.0ms

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
9×cbrt-undiv div-exp
6×add-log-exp
5×pow1 associate-/r/
4×expm1-log1p-u log1p-expm1-u
2×flip3-- frac-2neg sqrt-div clear-num flip--
1×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))
13.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
28.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (* b_2 b_2) (* a c))
181.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
154.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
59.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify109.0ms

Algorithm
egg-herbie
Counts
507 → 507
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
015618690
150018042

prune940.0ms

Filtered
507 candidates to 308 candidates (60.7%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New5061507
Fresh167
Picked011
Done101
Total5088516

Merged error: 3.4b

Counts
516 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (* b_2 b_2) (* a c))
1.8b
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
4.7b
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
23.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite214.0ms

Algorithm
rewrite-expression-head
Rules
3489×times-frac
1827×add-sqr-sqrt
1826×*-un-lft-identity
1346×add-cube-cbrt
267×associate-/l*
240×distribute-lft-out-- difference-of-squares
123×sqrt-prod
120×distribute-rgt-neg-in
58×div-inv
41×add-exp-log
28×div-exp
23×add-cbrt-cube
13×cbrt-undiv
6×associate-/r* add-log-exp
5×pow1
4×expm1-log1p-u associate-/r/ log1p-expm1-u
3×rec-exp 1-exp
2×flip3-- frac-2neg sqrt-div div-sub clear-num flip-- associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 1152
Calls
4 calls:
4.0ms
(- (* b_2 b_2) (* a c))
18.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
58.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series293.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* b_2 b_2) (* a c))
90.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
107.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
63.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify281.0ms

Algorithm
egg-herbie
Counts
1164 → 1164
Iterations

Useful iterations: 1 (72.0ms)

IterNodesCost
0427624795
1500124124

prune2.1s

Filtered
1164 candidates to 583 candidates (50.1%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New116401164
Fresh066
Picked011
Done011
Total116481172

Merged error: 3.4b

Counts
1172 → 8

regimes207.0ms

Accuracy

90% (2.7b remaining)

Error of 8.2b against oracle of 5.5b and baseline of 32.5b

bsearch177.0ms

Steps
ItersRangePoint
10
1.100420074551047e-18
0.0163835844060345
6.948103979107274e-08
9
1.1405585128681756e-186
1.2232775426196791e-178
1.164566682148749e-186
11
-3.334524116472281e+99
-2.3662890435539516e+79
-1.599359189869806e+99

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04023
14023

end0.0ms

sample1.2s

Algorithm
intervals
Results
263.0ms1089×body2560valid
252.0ms5799×body80valid
172.0ms879×body1280valid
124.0ms2960×body80nan
71.0ms446×body640valid
34.0ms118×body5120valid
28.0ms239×body320valid
12.0ms133×body160valid