Details

Time bar (total: 5.2s)

sample43.0ms

Algorithm
intervals
Results
9.0ms33×body1280valid
7.0ms187×body80valid
6.0ms27×body2560valid
3.0ms76×body80nan
2.0ms13×body640valid
2.0ms6×body5120valid
1.0ms10×body320valid
0.0ms3×body160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0299
1659
21219
31519
41609
51649
61649

prune2.0ms

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: 33.5b

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))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
15.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
4.0ms
(- (* b b) (* 4.0 (* a c)))
10.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series289.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
47.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify76.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05903305
121012212
250022128

prune312.0ms

Filtered
169 candidates to 89 candidates (52.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New15910169
Fresh000
Picked101
Done000
Total16010170

Merged error: 5.9b

Counts
170 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
88×*-un-lft-identity
68×add-cube-cbrt
67×times-frac
61×prod-diff
38×sqrt-prod
26×distribute-rgt-neg-in
25×add-exp-log
21×distribute-lft-neg-in
13×associate-/r* add-cbrt-cube
12×div-exp
11×fma-neg
10×distribute-lft-out-- add-log-exp difference-of-squares
9×associate-/r/
7×neg-mul-1 flip3-- flip--
6×pow1
5×cbrt-undiv div-inv
4×expm1-log1p-u log1p-expm1-u
3×rec-exp diff-log 1-exp prod-exp associate-/l*
2×sub-neg sqrt-div
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 205
Calls
4 calls:
14.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series299.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
43.0ms
(- (* b b) (* 4.0 (* a c)))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify97.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
07184221
130992976
250012863

prune316.0ms

Filtered
217 candidates to 98 candidates (45.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2125217
Fresh639
Picked101
Done000
Total2198227

Merged error: 5.8b

Counts
227 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b
(- (* b b) (* 4.0 (* a c)))
1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
441×times-frac
291×add-sqr-sqrt
290×*-un-lft-identity
190×add-cube-cbrt
87×add-exp-log
61×prod-diff
58×div-exp sqrt-prod
50×distribute-lft-out-- difference-of-squares
46×distribute-rgt-neg-in
37×div-inv
27×associate-/r*
25×add-cbrt-cube
21×distribute-lft-neg-in
17×associate-/r/
15×rec-exp 1-exp
13×cbrt-undiv
12×prod-exp
11×flip3-- fma-neg flip--
10×add-log-exp
7×neg-mul-1 associate-/l*
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×diff-log
2×sub-neg sqrt-div cbrt-unprod
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/l/
Counts
4 → 394
Calls
4 calls:
23.0ms
(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
10.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series316.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
82.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
78.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify98.0ms

Algorithm
egg-herbie
Counts
406 → 406
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
014168436
150026798

prune561.0ms

Filtered
406 candidates to 158 candidates (38.9%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New4042406
Fresh167
Picked011
Done000
Total4059414

Merged error: 5.8b

Counts
414 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.6b
(sqrt (- (* b b) (* 4.0 (* a c))))
22.6b
(sqrt (- (* b b) (* 4.0 (* a c))))
22.6b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
55×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
40×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
8×add-log-exp
7×pow1 neg-mul-1
6×sqrt-div
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg neg-log
Counts
4 → 141
Calls
4 calls:
10.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series306.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify62.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03753008
112731987
250011900

prune364.0ms

Filtered
153 candidates to 83 candidates (54.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1530153
Fresh077
Picked011
Done011
Total1539162

Merged error: 5.8b

Counts
162 → 9

regimes482.0ms

Accuracy

81.8% (5.1b remaining)

Error of 10.6b against oracle of 5.5b and baseline of 33.7b

bsearch134.0ms

Steps
ItersRangePoint
9
1.314833454423355e+61
1.6016599845544569e+66
1.5877733204280517e+66
9
-7.062572886001061e-46
-7.97810515777731e-52
-1.438838017723487e-49

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03515
13515

end0.0ms

sample1.2s

Algorithm
intervals
Results
275.0ms1065×body2560valid
251.0ms5841×body80valid
180.0ms860×body1280valid
116.0ms2902×body80nan
80.0ms481×body640valid
30.0ms242×body320valid
27.0ms85×body5120valid
11.0ms114×body160valid