Details

Time bar (total: 5.2s)

sample39.0ms

Algorithm
intervals
Results
9.0ms37×body2560valid
8.0ms197×body80valid
5.0ms24×body1280valid
3.0ms77×body80nan
2.0ms16×body640valid
0.0ms4×body160valid
0.0ms2×body320valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize16.0ms

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))
0.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-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 neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
12.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
4.0ms
(- (* b b) (* (* 4.0 a) c))
9.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series323.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms
(- (* b b) (* (* 4.0 a) c))
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0438854
11702750
25001735

prune297.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.9b

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))
0.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
53×times-frac
48×*-un-lft-identity
29×add-sqr-sqrt
28×add-cube-cbrt
25×add-exp-log
13×add-cbrt-cube
12×div-exp
11×associate-/r*
10×fma-def distribute-lft-out add-log-exp
9×associate-/r/
8×distribute-rgt-neg-in
6×pow1
5×cbrt-undiv flip3-+ flip-+ div-inv
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in rec-exp 1-exp prod-exp sqrt-prod associate-/l*
2×flip3-- sqrt-div sum-log flip--
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff neg-log clear-num cbrt-unprod inv-pow
Counts
4 → 134
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))
8.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
88.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify71.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05561665
127071442
250011371

prune300.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.9b

localize26.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.9b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.4b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 232
Calls
4 calls:
10.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
23.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
7.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series464.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
148.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
174.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify145.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
08295119
137633863
250013860

prune533.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.9b
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
51×add-sqr-sqrt
50×*-un-lft-identity
46×add-cube-cbrt
34×sqrt-prod
25×add-exp-log add-cbrt-cube
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×prod-exp cbrt-unprod
7×neg-mul-1
6×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
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 frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 152
Calls
4 calls:
4.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series347.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
145.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify105.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
06683371
134822161
250012072

prune322.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.9b

regimes255.0ms

Accuracy

94.9% (1.3b remaining)

Error of 7.0b against oracle of 5.7b and baseline of 30.2b

bsearch174.0ms

Steps
ItersRangePoint
6
1.7071993853452014e+98
1.0593861995340862e+99
8.181926998189475e+98
9
-8.626468928177584e-227
-1.0460106670992606e-234
-1.1269687192740625e-234
8
-1.8835253050844136e+82
-1.7681891979126528e+79
-2.647259729659343e+81

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04828
14828

end0.0ms

sample1.2s

Algorithm
intervals
Results
254.0ms1045×body2560valid
240.0ms5938×body80valid
173.0ms852×body1280valid
118.0ms2870×body80nan
67.0ms442×body640valid
33.0ms112×body5120valid
26.0ms226×body320valid
9.0ms119×body160valid