Details

Time bar (total: 5.0s)

sample48.0ms

Algorithm
intervals
Results
9.0ms37×body1280valid
7.0ms191×body80valid
7.0ms33×body2560valid
3.0ms96×body80nan
2.0ms12×body640valid
1.0ms4×body5120valid
1.0ms8×body320valid
0.0ms3×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: 38.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite99.0ms

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:
61.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms
(- (* b b) (* (* 4.0 a) c))
19.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
42.0ms
(- (* b b) (* (* 4.0 a) c))
70.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
60.0ms
(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

prune231.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.8b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.6b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
27.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×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 → 154
Calls
4 calls:
21.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
55.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series436.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
132.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
167.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify110.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
06512692
131392439
250022426

prune445.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.7b
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
27.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite78.0ms

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:
7.0ms
(- (* b b) (* (* 4.0 a) c))
21.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
40.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* (* 4.0 a) c))
72.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
131.0ms
(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
64.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify73.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
0485953
12854745
25001737

prune232.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 4.0 (/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c))
0.8b
(- (* b b) (* (* 4.0 a) c))
0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
33×times-frac
26×add-sqr-sqrt
25×*-un-lft-identity
21×add-cube-cbrt
16×add-exp-log
13×add-cbrt-cube
10×add-log-exp
7×div-exp associate-/r*
5×pow1 cbrt-undiv div-inv
4×sqrt-prod
3×flip3-- diff-log flip-- associate-/l*
2×sub-neg sqrt-div prod-exp distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 1-exp neg-log clear-num associate-/r/ cbrt-unprod
Counts
4 → 94
Calls
4 calls:
26.0ms
(/ 4.0 (/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c))
8.0ms
(- (* b b) (* (* 4.0 a) c))
21.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series294.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(/ 4.0 (/ (* 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) c))
45.0ms
(- (* b b) (* (* 4.0 a) c))
68.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05421186
122311070
250011068

prune297.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.5b

regimes200.0ms

Accuracy

94.5% (1.3b remaining)

Error of 7.0b against oracle of 5.7b and baseline of 29.4b

bsearch184.0ms

Steps
ItersRangePoint
6
4.231934083523606e+52
2.717919616353272e+53
2.043334298601045e+53
10
-1.5811508713279925e-284
-6.201918159587988e-296
-7.499564665356541e-290
9
-4.3398659734944224e+136
-6.188138656270848e+129
-4.2975228517561493e+130

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05130
15330
25330

end0.0ms

sample1.2s

Algorithm
intervals
Results
242.0ms1090×body2560valid
237.0ms5831×body80valid
162.0ms909×body1280valid
107.0ms2813×body80nan
67.0ms471×body640valid
29.0ms109×body5120valid
24.0ms231×body320valid
9.0ms128×body160valid