Details

Time bar (total: 5.7s)

sample47.0ms

Algorithm
intervals
Results
8.0ms26×body1280valid
8.0ms192×body80valid
8.0ms33×body2560valid
4.0ms113×body80nan
2.0ms10×body640valid
1.0ms4×body5120valid
1.0ms9×body320valid
1.0ms7×body160valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.4b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b
(- (* b b) (* 4.0 (* a c)))
2.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
205×add-sqr-sqrt
114×*-un-lft-identity
84×times-frac
58×difference-of-squares
44×unswap-sqr
42×add-cube-cbrt
36×sqrt-prod distribute-lft-out--
32×associate-*l*
24×associate-*r*
14×distribute-rgt-neg-in *-commutative
12×associate-/r*
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×associate-/l*
6×swap-sqr
5×pow1
4×flip3-- flip--
3×diff-log
2×cbrt-undiv associate--l- neg-sub0 sub-neg sqrt-div div-sub div-exp associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num cbrt-unprod div-inv
Counts
4 → 204
Calls
4 calls:
45.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
22.0ms
(- (* b b) (* 4.0 (* a c)))
37.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series318.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
52.0ms
(- (* b b) (* 4.0 (* a c)))
83.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
79.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify95.0ms

Algorithm
egg-herbie
Counts
216 → 216
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
07282858
127642769
250012764

prune368.0ms

Filtered
216 candidates to 120 candidates (44.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2088216
Fresh000
Picked101
Done000
Total2098217

Merged error: 5.0b

Counts
217 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
0.4b
(- (* b b) (* 4.0 (* a c)))
2.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
224×add-sqr-sqrt
159×times-frac
149×*-un-lft-identity
77×add-cube-cbrt
58×difference-of-squares
36×sqrt-prod distribute-lft-out-- unswap-sqr
32×associate-/l*
17×associate-/l/
14×distribute-rgt-neg-in
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×associate-*l*
6×swap-sqr associate-/r* *-commutative
5×pow1 div-inv
4×flip3-- div-sub flip--
3×cbrt-undiv diff-log div-exp
2×associate--l- neg-sub0 sub-neg frac-2neg sqrt-div clear-num
1×rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 217
Calls
4 calls:
44.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
25.0ms
(- (* b b) (* 4.0 (* a c)))
34.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
26.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series314.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) 2.0) a)
52.0ms
(- (* b b) (* 4.0 (* a c)))
83.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
76.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify105.0ms

Algorithm
egg-herbie
Counts
229 → 229
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
07943047
128942946
250012946

prune390.0ms

Filtered
229 candidates to 135 candidates (41.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2272229
Fresh257
Picked011
Done000
Total2298237

Merged error: 5.0b

Counts
237 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b
(- (* b b) (* 4.0 (* a c)))
2.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
606×times-frac
585×add-sqr-sqrt
454×*-un-lft-identity
236×add-cube-cbrt
130×difference-of-squares
108×distribute-lft-out--
97×associate-/r*
96×associate-*l*
87×associate-*r*
72×sqrt-prod
65×unswap-sqr
50×distribute-rgt-neg-in
35×*-commutative
30×associate-/r/
25×add-exp-log
17×associate-/l*
13×add-cbrt-cube
12×div-exp
10×add-log-exp
7×flip3-- flip--
6×pow1 swap-sqr
5×cbrt-undiv div-inv
3×rec-exp diff-log 1-exp prod-exp clear-num remove-double-div
2×sub-neg frac-2neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip sqrt-pow1 pow1/2 neg-log cbrt-unprod inv-pow
Counts
4 → 495
Calls
4 calls:
61.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
26.0ms
(- (* b b) (* 4.0 (* a c)))
34.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series337.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
52.0ms
(- (* b b) (* 4.0 (* a c)))
84.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
81.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify117.0ms

Algorithm
egg-herbie
Counts
507 → 507
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
013588207
150027647

prune639.0ms

Filtered
507 candidates to 205 candidates (59.6%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New5043507
Fresh246
Picked101
Done011
Total5078515

Merged error: 5.0b

Counts
515 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))
22.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
149×add-sqr-sqrt
67×sqrt-prod
54×unswap-sqr
47×difference-of-squares
35×*-un-lft-identity
14×distribute-lft-out--
12×associate-*l*
9×swap-sqr *-commutative
8×add-log-exp
7×pow1 add-cube-cbrt
6×sqrt-div
4×add-exp-log flip3-- add-cbrt-cube flip--
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log
1×associate--l- neg-sub0 sub-neg distribute-rgt-neg-in neg-log
Counts
4 → 120
Calls
4 calls:
37.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
23.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
27.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series314.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
77.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
76.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
78.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify141.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 3 (127.0ms)

IterNodesCost
02741257
19061236
235401225
350011209

prune356.0ms

Filtered
132 candidates to 78 candidates (40.9%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1320132
Fresh066
Picked011
Done011
Total1328140

Merged error: 5.0b

Counts
140 → 8

regimes201.0ms

Accuracy

85.1% (4.3b remaining)

Error of 9.8b against oracle of 5.5b and baseline of 34.3b

bsearch67.0ms

Steps
ItersRangePoint
0
1.3836563058951246e+50
1.390978468581987e+50
1.3873173872385558e+50
9
-2.816841330355383e-75
-7.368877589091801e-81
-1.0996442222619662e-75

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03115
13115

end0.0ms

sample1.2s

Algorithm
intervals
Results
273.0ms1103×body2560valid
248.0ms5872×body80valid
177.0ms890×body1280valid
108.0ms2796×body80nan
71.0ms453×body640valid
32.0ms102×body5120valid
27.0ms231×body320valid
9.0ms116×body160valid