Details

Time bar (total: 5.3s)

sample52.0ms

Algorithm
intervals
Results
26.0ms276×body80valid
11.0ms85×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03618
16718
212318
316018
417518
517718
617718

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.0b

localize112.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.0b
(- (* b b) (* (* 4.0 a) c))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 66
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
3.0ms
(- (* b b) (* (* 4.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series228.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (* b b) (* (* 4.0 a) c))
42.0ms
(- (* b b) (* (* 4.0 a) c))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify90.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (83.0ms)

IterNodesCost
0170540
1665506
22968498
35001488

prune304.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 10.6b

localize113.0ms

Local error

Found 4 expressions with local error:

6.8b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
10×fma-neg prod-diff
9×sqrt-prod
8×add-log-exp
7×pow1
6×distribute-lft-neg-in distribute-rgt-neg-in sqrt-div
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×neg-mul-1 diff-log
1×associate--l- neg-sub0 sub-neg neg-log difference-of-squares
Counts
4 → 88
Calls
4 calls:
8.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series282.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
68.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify174.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
02831391
19981121
247231013
350011013

prune416.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 10.6b

localize118.0ms

Local error

Found 4 expressions with local error:

12.1b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×add-cube-cbrt fma-def *-un-lft-identity
9×sqrt-prod
8×add-log-exp
7×pow1
6×sqrt-div
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in rem-sqrt-square flip3-- distribute-rgt-neg-in sqrt-pow1 pow1/2 flip--
2×sum-log
1×+-commutative neg-sub0 associate-+l- neg-mul-1 flip3-+ neg-log flip-+
Counts
4 → 76
Calls
4 calls:
7.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series287.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
66.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify117.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (109.0ms)

IterNodesCost
0249756
1969641
24038626
35001624

prune400.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 10.6b

localize121.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
5.0b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
6.6b
(/ (* a c) b)
23.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
14×add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt times-frac associate-/r*
6×add-log-exp
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u distribute-lft-out--
3×flip3-- sqrt-prod flip--
2×distribute-rgt-neg-in frac-2neg sqrt-div prod-exp clear-num associate-/r/ cbrt-unprod div-inv associate-/l* difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff
Counts
4 → 87
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
16.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
3.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* (* 4.0 a) c))
177.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
18.0ms
(/ (* a c) b)
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify53.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0423713
12101628
25002621

prune342.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 8.9b

regimes172.0ms

Accuracy

89.9% (1.3b remaining)

Error of 8.1b against oracle of 6.8b and baseline of 19.8b

bsearch181.0ms

Steps
ItersRangePoint
7
6.184155830638016e+27
1.3306260697673677e+30
8.864108110586416e+28
8
-7.940186999589029e+157
-2.4392292464634512e+153
-1.3442754169306616e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05962
15962

end0.0ms

sample1.3s

Algorithm
intervals
Results
802.0ms8710×body80valid
265.0ms2898×body80nan