Details

Time bar (total: 5.0s)

sample39.0ms

Algorithm
intervals
Results
8.0ms36×body2560valid
7.0ms187×body80valid
4.0ms22×body1280valid
3.0ms76×body80nan
1.0ms5×body5120valid
1.0ms9×body640valid
1.0ms9×body320valid
0.0ms4×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0299
1659
21219
31519
41609
51649
61649

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

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)))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite44.0ms

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:
16.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
7.0ms
(- (* 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))))

series290.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
48.0ms
(- (* b b) (* 4.0 (* a c)))
73.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify78.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05903305
121012212
250022128

prune352.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.1b

localize13.0ms

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)))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite40.0ms

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:
13.0ms
(/ 1 (/ (* 2.0 a) (- (- 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))))

series303.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
47.0ms
(- (* b b) (* 4.0 (* a c)))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify95.0ms

Algorithm
egg-herbie
Counts
217 → 217
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07184221
130992976
250012863

prune350.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.0b

localize13.0ms

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)))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite40.0ms

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))))

series288.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
45.0ms
(- (* 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))))

simplify82.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
05903305
121012212
250022128

prune317.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.0b

localize14.0ms

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)))
1.2b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite65.0ms

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:
20.0ms
(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
13.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series304.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(/ (/ 1 (* 2.0 a)) (/ 1 (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
46.0ms
(- (* b b) (* 4.0 (* a c)))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify97.0ms

Algorithm
egg-herbie
Counts
406 → 406
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
014168437
150026798

prune583.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 8.0b

regimes245.0ms

Accuracy

84.6% (4.5b remaining)

Error of 10.3b against oracle of 5.8b and baseline of 34.7b

bsearch97.0ms

Steps
ItersRangePoint
6
1.7071993853452014e+98
1.0593861995340862e+99
1.0479007947857462e+99
8
-2.0898868129100636e-78
-1.06178241226232e-82
-4.653701756906352e-82

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04118
14718
24718

end0.0ms

sample1.2s

Algorithm
intervals
Results
258.0ms1068×body2560valid
239.0ms5772×body80valid
174.0ms919×body1280valid
103.0ms2858×body80nan
69.0ms466×body640valid
36.0ms127×body5120valid
25.0ms228×body320valid
10.0ms128×body160valid