Details

Time bar (total: 5.9s)

sample75.0ms

Algorithm
intervals
Results
18.0ms47×body2560valid
13.0ms167×body80valid
10.0ms32×body1280valid
7.0ms107×body80nan
4.0ms16×body640valid
2.0ms4×body5120valid
2.0ms9×body320valid
1.0ms6×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.0b

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))
1.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
36.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms
(- (* b b) (* (* 4.0 a) c))
15.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms
(- (* b b) (* (* 4.0 a) c))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0405779
11563685
25001674

prune236.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.9b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
4.6b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.6b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
80×add-sqr-sqrt
79×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
20×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
13×sqrt-prod
10×distribute-rgt-neg-in
8×associate-/r*
7×cbrt-undiv div-exp
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log flip-+
Counts
4 → 148
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
48.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
28.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (* b b) (* (* 4.0 a) c))
153.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
187.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify109.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
06402581
131552333
250012320

prune451.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
16.5b
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt add-log-exp
9×*-un-lft-identity prod-exp cbrt-unprod
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×flip3-- sqrt-prod flip--
3×diff-log
2×sub-neg sqrt-div associate-*r/ associate-/r/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 72
Calls
4 calls:
13.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
18.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series545.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
349.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify76.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
0485952
12854745
25001737

prune230.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (/ (/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c) 4.0))
0.7b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
22.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
195×times-frac
92×add-sqr-sqrt
91×*-un-lft-identity
87×add-cube-cbrt
48×add-exp-log
31×div-exp
25×associate-/r*
18×add-cbrt-cube
17×div-inv
10×add-log-exp
9×cbrt-undiv
8×1-exp
6×pow1 prod-exp
5×rec-exp
4×sqrt-prod
3×flip3-- diff-log flip-- associate-/l*
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square pow-flip distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/r/ cbrt-unprod inv-pow
Counts
4 → 180
Calls
4 calls:
31.0ms
(/ 1 (/ (/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c) 4.0))
15.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series320.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(/ 1 (/ (/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c) 4.0))
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(- (* b b) (* (* 4.0 a) c))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify111.0ms

Algorithm
egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
09652811
144782486
250022326

prune379.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.8b

regimes178.0ms

Accuracy

94.4% (1.3b remaining)

Error of 6.9b against oracle of 5.6b and baseline of 29.1b

bsearch188.0ms

Steps
ItersRangePoint
6
5.779436182351587e+124
6.964873849469576e+125
5.026817155457435e+125
7
-9.439055548373166e-153
-1.4792713125191287e-154
-1.5018009284516093e-154
7
-2.3860448187824777e+68
-1.0929352752278947e+66
-2.3202538172935113e+68

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05131
15131

end0.0ms

sample1.9s

Algorithm
intervals
Results
443.0ms5747×body80valid
430.0ms1108×body2560valid
301.0ms926×body1280valid
191.0ms2804×body80nan
123.0ms481×body640valid
51.0ms106×body5120valid
41.0ms215×body320valid
15.0ms117×body160valid