Details

Time bar (total: 5.0s)

sample48.0ms

Algorithm
intervals
Results
11.0ms173×body80valid
7.0ms30×body2560valid
7.0ms35×body1280valid
4.0ms103×body80nan
3.0ms18×body640valid
2.0ms6×body5120valid
1.0ms10×body320valid
0.0ms6×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: 34.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.2b
(- (* b b) (* 4.0 (* a c)))
1.8b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite75.0ms

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:
45.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series290.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
43.0ms
(- (* b b) (* 4.0 (* a c)))
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify88.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05903305
121012212
250022128

prune346.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.2b
(- (* b b) (* 4.0 (* a c)))
1.8b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite60.0ms

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:
28.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series294.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
42.0ms
(- (* b b) (* 4.0 (* a c)))
74.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify102.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
07184221
130992976
250012863

prune344.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
1.2b
(- (* b b) (* 4.0 (* a c)))
8.0b
(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
20.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
204×times-frac
141×prod-diff
101×*-un-lft-identity
98×add-sqr-sqrt
95×add-cube-cbrt
51×sqrt-prod
34×distribute-rgt-neg-in
33×distribute-lft-neg-in
28×div-inv
15×fma-neg
11×neg-mul-1
9×add-exp-log add-cbrt-cube
8×add-log-exp
6×associate-/l*
5×pow1
4×expm1-log1p-u flip3-- sqrt-div flip-- log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv sub-neg diff-log div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-out-- frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* frac-sub cbrt-unprod sub-div difference-of-squares
Counts
4 → 240
Calls
4 calls:
8.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
38.0ms
(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series348.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
47.0ms
(- (* b b) (* 4.0 (* a c)))
104.0ms
(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify128.0ms

Algorithm
egg-herbie
Counts
252 → 252
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
08478136
126765939
250015143

prune393.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.7b

localize18.0ms

Local error

Found 4 expressions with local error:

19.9b
(- (/ (- b) (* 2.0 a)) (* (* (cbrt (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))) (cbrt (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))) (cbrt (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))))
20.4b
(sqrt (- (* b b) (* 4.0 (* a c))))
20.4b
(sqrt (- (* b b) (* 4.0 (* a c))))
20.4b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
20×times-frac
18×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
14×fma-neg prod-diff
12×cbrt-div
9×sqrt-prod
7×pow1 frac-sub
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-div add-log-exp
5×frac-times associate-*l/
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/
2×neg-mul-1 div-inv
1×associate--l- neg-sub0 sub-neg diff-log div-sub
Counts
4 → 101
Calls
4 calls:
24.0ms
(- (/ (- b) (* 2.0 a)) (* (* (cbrt (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))) (cbrt (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))) (cbrt (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))))
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))))

series361.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(- (/ (- b) (* 2.0 a)) (* (* (cbrt (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))) (cbrt (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))) (cbrt (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
68.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify62.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04872962
115502201
250011836

prune388.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.7b

regimes226.0ms

Accuracy

84.7% (4.4b remaining)

Error of 10.0b against oracle of 5.6b and baseline of 34.5b

bsearch80.0ms

Steps
ItersRangePoint
6
2.6216430800597077e+98
1.6496650416179864e+99
1.3176462918432122e+99
6
-4.147465441909223e-81
-6.416385900146894e-82
-4.011579732710567e-81

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03517
13517

end0.0ms

sample1.1s

Algorithm
intervals
Results
245.0ms1041×body2560valid
229.0ms5853×body80valid
169.0ms876×body1280valid
104.0ms2872×body80nan
76.0ms489×body640valid
33.0ms117×body5120valid
28.0ms229×body320valid
8.0ms106×body160valid