Details

Time bar (total: 6.1s)

sample286.0ms

Algorithm
intervals
Results
10.0ms179×body80valid
8.0ms34×body2560valid
6.0ms30×body1280valid
4.0ms86×body80nan
3.0ms17×body640valid
1.0ms5×body5120valid
1.0ms8×body320valid
0.0ms3×body160valid

simplify15.0ms

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: 35.7b

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)
1.0b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b
(- (* b_2 b_2) (* a c))
23.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite46.0ms

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:
24.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms
(+ (- 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)))

series270.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
72.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms
(- (* b_2 b_2) (* a c))
69.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify48.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0389850
11366779
25001753

prune274.0ms

Filtered
112 candidates to 88 candidates (78.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1057112
Fresh000
Picked101
Done000
Total1067113

Merged error: 4.9b

Counts
113 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.2b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.1b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
199×add-sqr-sqrt
198×*-un-lft-identity
186×times-frac
130×add-cube-cbrt
60×prod-diff
50×sqrt-prod
38×distribute-rgt-neg-in
34×distribute-lft-out-- difference-of-squares
30×associate-/l*
21×distribute-lft-neg-in
11×add-exp-log add-cbrt-cube
10×fma-neg associate-/r* associate-/r/
8×add-log-exp
7×neg-mul-1 flip3-- flip--
6×div-inv
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg sqrt-div diff-log clear-num
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 284
Calls
4 calls:
10.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
135.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
163.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
62.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify147.0ms

Algorithm
egg-herbie
Counts
296 → 296
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
09195579
139184508
250014505

prune529.0ms

Filtered
296 candidates to 172 candidates (58.1%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2933296
Fresh156
Picked101
Done000
Total2958303

Merged error: 4.8b

Counts
303 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

1.3b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
2.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.2b
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
23.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
951×times-frac
630×add-sqr-sqrt
629×*-un-lft-identity
433×add-cube-cbrt
98×distribute-lft-out-- difference-of-squares
83×associate-/l*
82×sqrt-prod
70×distribute-rgt-neg-in
60×prod-diff
28×associate-/r*
22×div-inv
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
9×cbrt-undiv div-exp
8×add-log-exp
7×neg-mul-1
5×pow1 associate-/r/
4×expm1-log1p-u log1p-expm1-u
2×flip3-- frac-2neg sqrt-div diff-log clear-num flip--
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 569
Calls
4 calls:
17.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
10.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
26.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series469.0ms

Counts
4 → 12
Calls
4 calls:
185.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
66.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
153.0ms
(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify125.0ms

Algorithm
egg-herbie
Counts
581 → 581
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0175510833
150019431

prune997.0ms

Filtered
581 candidates to 329 candidates (56.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New5792581
Fresh257
Picked011
Done000
Total5818589

Merged error: 4.8b

Counts
589 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
1.0b
(- (* b_2 b_2) (* a c))
2.8b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.5b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
169×add-sqr-sqrt
168×*-un-lft-identity
159×times-frac
116×add-cube-cbrt
61×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
26×distribute-lft-out-- difference-of-squares
25×associate-/r*
21×distribute-lft-neg-in
15×add-exp-log
11×fma-neg
10×add-log-exp
9×add-cbrt-cube
7×neg-mul-1 div-exp
6×pow1
5×div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv flip3-- diff-log flip-- associate-/l*
2×sub-neg rec-exp sqrt-div 1-exp
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/r/ inv-pow
Counts
4 → 249
Calls
4 calls:
13.0ms
(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
4.0ms
(- (* b_2 b_2) (* a c))
10.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series263.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(/ 1 (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
31.0ms
(- (* b_2 b_2) (* a c))
67.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify105.0ms

Algorithm
egg-herbie
Counts
261 → 261
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
08024369
132033287
250023111

prune278.0ms

Filtered
261 candidates to 107 candidates (41.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2601261
Fresh156
Picked011
Done011
Total2618269

Merged error: 4.8b

Counts
269 → 8

regimes157.0ms

Accuracy

90.7% (2.3b remaining)

Error of 7.6b against oracle of 5.3b and baseline of 29.7b

bsearch178.0ms

Steps
ItersRangePoint
9
14028.172733867412
3007116902181.375
2947728123750.7354
11
-7.158612012333694e-224
-2.980406596944262e-243
-5.266108209623796e-239
10
-1.552489725432399e+46
-8.211399685419546e+34
-1.310778137866809e+45

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03922
13922

end0.0ms

sample1.2s

Algorithm
intervals
Results
278.0ms1100×body2560valid
253.0ms5800×body80valid
175.0ms889×body1280valid
125.0ms2951×body80nan
73.0ms468×body640valid
36.0ms119×body5120valid
29.0ms212×body320valid
9.0ms112×body160valid