Details

Time bar (total: 4.9s)

sample306.0ms

Algorithm
intervals
Results
13.0ms39×body2560valid
12.0ms189×body80valid
8.0ms31×body1280valid
6.0ms72×body80nan
3.0ms12×body640valid
1.0ms7×body320valid
0.0ms1×body5120valid
0.0ms3×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1327
2417
3447
4447

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b
(- (* b_2 b_2) (* a c))
23.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 91
Calls
4 calls:
42.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
13.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0ms
(- (* b_2 b_2) (* a c))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
72.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms
(- (* b_2 b_2) (* a c))
75.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0368965
11241910
25001901

prune266.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b
(- (* b_2 b_2) (* a c))
23.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt
22×*-un-lft-identity
13×add-exp-log add-cube-cbrt associate-*r*
11×times-frac
10×add-log-exp
9×add-cbrt-cube
7×pow1 associate-*l*
5×flip3-- sqrt-prod flip--
4×prod-exp distribute-lft-out-- difference-of-squares
3×diff-log unswap-sqr
2×frac-times sub-neg distribute-rgt-neg-in sqrt-div div-exp associate-*l/ cbrt-unprod
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv
Counts
4 → 89
Calls
4 calls:
50.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series252.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
68.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
36.0ms
(- (* b_2 b_2) (* a c))
63.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify52.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0428881
11823791
25003771

prune242.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b
(- (* b_2 b_2) (* a c))
23.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
165×times-frac
130×add-sqr-sqrt
129×*-un-lft-identity
77×add-cube-cbrt
27×associate-/r*
26×distribute-lft-out-- difference-of-squares
16×sqrt-prod
15×add-exp-log
13×distribute-rgt-neg-in
10×add-log-exp
9×associate-/r/ add-cbrt-cube
7×flip3-- div-exp flip--
6×pow1
5×div-inv
3×cbrt-undiv diff-log associate-/l*
2×sub-neg rec-exp sqrt-div 1-exp
1×associate--l- neg-sub0 rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 neg-log clear-num inv-pow
Counts
4 → 177
Calls
4 calls:
26.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
12.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
71.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
33.0ms
(- (* b_2 b_2) (* a c))
64.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify76.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05912458
127062226
250012071

prune282.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.6b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b_2 b_2) (* a c))
1.2b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.7b
(/ (+ 0 (* a c)) (* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))
23.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
5×pow1
3×flip3-+ times-frac sqrt-prod flip-+ associate-/l*
2×cbrt-undiv flip3-- sqrt-div div-exp associate-*l/ sum-log associate-/r/ flip-- associate-/l/ distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 diff-log neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 67
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
11.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms
(/ (+ 0 (* a c)) (* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series320.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(- (* b_2 b_2) (* a c))
70.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
153.0ms
(/ (+ 0 (* a c)) (* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify65.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
0419709
12033603
25002591

prune192.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.6b

regimes218.0ms

Accuracy

90.5% (2.8b remaining)

Error of 8.3b against oracle of 5.5b and baseline of 34.6b

bsearch141.0ms

Steps
ItersRangePoint
8
6.881289457293598e+137
5.567978725714423e+140
1.1449768507266672e+139
8
-1.5398705077624364e-279
-4.8734111101062685e-284
-4.951878179078299e-284
6
-6.1500553607379255e+19
-5.724488702658166e+18
-1.3333671538923874e+19

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04224
14224

end0.0ms

sample1.6s

Algorithm
intervals
Results
387.0ms5797×body80valid
369.0ms1111×body2560valid
248.0ms913×body1280valid
170.0ms2908×body80nan
96.0ms454×body640valid
40.0ms102×body5120valid
37.0ms230×body320valid
14.0ms112×body160valid