Details

Time bar (total: 51.0s)

sample301.0ms

Algorithm
intervals
Results
11.0ms43×body2560valid
10.0ms191×body80valid
5.0ms25×body1280valid
4.0ms88×body80nan
3.0ms17×body640valid
1.0ms3×body5120valid
0.0ms3×body320valid
0.0ms3×body160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1327
2417
3447
4447

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: 34.5b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* b_2 b_2) (* a c))
0.1b
(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 91
Calls
4 calls:
4.0ms
(- (* b_2 b_2) (* a c))
27.0ms
(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series257.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (* b_2 b_2) (* a c))
82.0ms
(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
75.0ms
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
68.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0368965
11241910
25001901

prune218.0ms

Filtered
103 candidates to 72 candidates (69.9%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New967103
Fresh000
Picked011
Done000
Total968104

Merged error: 6.9b

Counts
104 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.3b
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.6b
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
150×add-sqr-sqrt
115×*-un-lft-identity
81×add-cube-cbrt
34×difference-of-squares
27×associate-/l*
20×sqrt-prod
17×distribute-lft-out--
11×add-exp-log add-cbrt-cube
10×associate-/r/
9×associate-/r*
7×flip3-- flip--
6×div-inv add-log-exp
5×pow1
4×cbrt-undiv div-exp
3×associate-/l/
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 187
Calls
4 calls:
7.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series465.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
148.0ms
(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
189.0ms
(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify114.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 2 (83.0ms)

IterNodesCost
07302960
131632803
250022783

prune428.0ms

Filtered
199 candidates to 148 candidates (74.4%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1954199
Fresh336
Picked101
Done011
Total1998207

Merged error: 6.8b

Counts
207 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.6b
(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
4.3b
(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
23.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
3063×times-frac
1689×add-sqr-sqrt
1446×*-un-lft-identity
1204×add-cube-cbrt
242×difference-of-squares
237×associate-/l*
124×sqrt-prod
121×distribute-lft-out--
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×associate-/r/
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 diff-log
Counts
4 → 1025
Calls
4 calls:
7.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms
(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
57.0ms
(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series332.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
98.0ms
(/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)
96.0ms
(/ (/ 1 (/ (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a) c)) a)
67.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify256.0ms

Algorithm
egg-herbie
Counts
1037 → 1037
Iterations

Useful iterations: 1 (75.0ms)

IterNodesCost
0425921066
1500120478

prune2.0s

Filtered
1037 candidates to 576 candidates (55.5%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New103521037
Fresh066
Picked011
Done011
Total1035101045

Merged error: 6.8b

Counts
1045 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

1.9b
(/ (/ (cbrt 1) (/ (/ (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)) c)) (cbrt a))
23.5b
(sqrt (- (* b_2 b_2) (* a c)))
23.5b
(sqrt (- (* b_2 b_2) (* a c)))
23.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
28026×times-frac
14898×cbrt-prod
14065×add-sqr-sqrt
12550×*-un-lft-identity
11038×add-cube-cbrt
1512×difference-of-squares
1073×associate-/l*
765×sqrt-prod
756×distribute-lft-out--
176×div-inv
18×add-exp-log
10×cbrt-undiv div-exp
9×add-cbrt-cube
7×pow1 associate-/r/
6×sqrt-div associate-/r*
4×add-log-exp
3×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
1×frac-2neg clear-num associate-/l/
Counts
4 → 7581
Calls
4 calls:
299.0ms
(/ (/ (cbrt 1) (/ (/ (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)) c)) (cbrt a))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series491.0ms

Counts
4 → 12
Calls
4 calls:
312.0ms
(/ (/ (cbrt 1) (/ (/ (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt a)) c)) (cbrt a))
60.0ms
(sqrt (- (* b_2 b_2) (* a c)))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))
58.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Algorithm
egg-herbie
Counts
7593 → 7593
Iterations

Useful iterations: 0 (103.0ms)

IterNodesCost
08117244191

prune40.3s

Filtered
7593 candidates to 6077 candidates (80.0%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New759307593
Fresh077
Picked011
Done022
Total7593107603

Merged error: 6.8b

Counts
7603 → 10

regimes279.0ms

Accuracy

91.1% (2.2b remaining)

Error of 7.8b against oracle of 5.6b and baseline of 30.2b

bsearch165.0ms

Steps
ItersRangePoint
1
5.881644550024431e+60
6.142209670373015e+60
6.077068390285869e+60
11
-7.35233497352936e-257
-4.742264678162135e-280
-5.512280364913347e-262
9
-1.807486675368764e+43
-9.303647294761767e+36
-1.8788058561239443e+41

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05253
15253

end0.0ms

sample1.2s

Algorithm
intervals
Results
270.0ms1071×body2560valid
260.0ms5931×body80valid
184.0ms895×body1280valid
122.0ms2873×body80nan
70.0ms443×body640valid
35.0ms117×body5120valid
27.0ms227×body320valid
9.0ms111×body160valid

Profiling

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