Details

Time bar (total: 4.7s)

sample42.0ms

Algorithm
intervals
Results
10.0ms34×body2560valid
8.0ms209×body80valid
4.0ms22×body1280valid
3.0ms79×body80nan
3.0ms18×body640valid
0.0ms3×body320valid
0.0ms4×body160valid

simplify12.0ms

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: 34.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
23.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite56.0ms

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:
37.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series293.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms
(- (* b b) (* (* 4.0 a) c))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify48.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0405779
11563685
25001674

prune227.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.7b

localize21.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
4.4b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.6b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite84.0ms

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:
4.0ms
(- (* b b) (* (* 4.0 a) c))
42.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
26.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
140.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
179.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify109.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
06402579
131552333
250012320

prune413.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
14.1b
(/ (* 2.0 a) (* 4.0 (* a c)))
23.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

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×sqrt-prod
3×flip3-- diff-log flip--
2×sub-neg sqrt-div 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 → 70
Calls
4 calls:
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0ms
(- (* b b) (* (* 4.0 a) c))
7.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
6.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series198.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
0429637
12471542
25003534

prune220.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.8b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b
(- (* b b) (* (* 4.0 a) c))
23.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
113×add-exp-log
51×prod-exp
44×div-exp
29×add-cbrt-cube
16×rec-exp 1-exp
14×associate-/r/
12×add-sqr-sqrt
11×pow1 frac-times *-un-lft-identity
10×cbrt-undiv add-log-exp
9×cbrt-unprod
8×flip3-- flip--
7×add-cube-cbrt associate-*l/
5×associate-*r/
4×sqrt-prod
3×pow-flip times-frac diff-log pow-prod-down un-div-inv associate-/l*
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 neg-log clear-num associate-/r* div-inv inv-pow
Counts
4 → 116
Calls
4 calls:
63.0ms
(/ 1 (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
12.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series368.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ 1 (* (* (/ 2.0 4.0) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
76.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms
(- (* b b) (* (* 4.0 a) c))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify79.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07391499
134181216
250011210

prune245.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.6b

regimes245.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.5b against oracle of 5.3b and baseline of 29.3b

bsearch187.0ms

Steps
ItersRangePoint
8
1.9559514031553493e+101
2.0413668072230428e+104
9.373511171447418e+103
9
1.0311906074547519e-259
1.091011630730822e-254
1.0417939395900796e-259
9
-2.3467190644739184e+107
-3.2019781887028674e+101
-1.7431685240570133e+102

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04526
14526

end0.0ms

sample1.1s

Algorithm
intervals
Results
246.0ms1070×body2560valid
234.0ms5839×body80valid
168.0ms884×body1280valid
107.0ms2849×body80nan
81.0ms496×body640valid
28.0ms102×body5120valid
24.0ms220×body320valid
8.0ms103×body160valid