Details

Time bar (total: 4.1s)

sample43.0ms

Algorithm
intervals
Results
8.0ms40×body2560valid
7.0ms187×body80valid
4.0ms21×body1280valid
3.0ms86×body80nan
2.0ms12×body640valid
1.0ms10×body320valid
1.0ms3×body5120valid
0.0ms4×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0299
1659
21219
31519
41609
51649
61649

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize12.0ms

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)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite129.0ms

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:
74.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms
(- (* b b) (* 4.0 (* a c)))
30.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series293.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
45.0ms
(- (* b b) (* 4.0 (* a c)))
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify78.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05903305
121012212
250022128

prune332.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

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)))
1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite104.0ms

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:
46.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms
(- (* b b) (* 4.0 (* a c)))
30.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series316.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
50.0ms
(- (* b b) (* 4.0 (* a c)))
81.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify96.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
07184221
130992976
250012863

prune352.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.2b

localize19.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))
22.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite70.0ms

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:
29.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
10.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series304.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify60.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03753008
112731987
250011900

prune395.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.2b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune0.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.2b

regimes225.0ms

Accuracy

82.7% (4.9b remaining)

Error of 10.6b against oracle of 5.7b and baseline of 34.1b

bsearch104.0ms

Steps
ItersRangePoint
7
7.363656180201337e+60
1.0503009045500217e+63
1.0273828621120979e+63
10
-1.566819529792693e-118
-1.4233178769563231e-129
-2.731633690849518e-121

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03616
13616

end0.0ms

sample1.2s

Algorithm
intervals
Results
231.0ms1089×body2560valid
221.0ms5871×body80valid
153.0ms857×body1280valid
93.0ms2807×body80nan
60.0ms459×body640valid
31.0ms119×body5120valid
23.0ms231×body320valid
10.0ms110×body160valid