Details

Time bar (total: 5.2s)

sample36.0ms

Algorithm
intervals
Results
15.0ms281×body80valid
5.0ms103×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: 17.2b

localize117.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
2.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
37×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
7×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
3×diff-log
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 neg-log
Counts
4 → 140
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
17.0ms
(- (- b) (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)))

series262.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* (* 4.0 a) c))
77.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify65.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04062988
114311956
250021869

prune404.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.3b

localize116.0ms

Local error

Found 4 expressions with local error:

12.8b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.5b
(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))))))
5.0ms
(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)))

series288.0ms

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))))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify183.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
02831391
19981121
247231013
350011013

prune429.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.3b

localize124.0ms

Local error

Found 4 expressions with local error:

19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
19.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
20.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
20.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log expm1-log1p-u cbrt-div flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 64
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series334.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
97.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
96.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify82.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
0215634
1688602
22689596
35001594

prune464.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.3b

localize121.0ms

Local error

Found 4 expressions with local error:

20.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
20.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
20.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))
20.2b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u flip3-- pow1/3 add-cbrt-cube flip-- log1p-expm1-u add-log-exp
Counts
4 → 60
Calls
4 calls:
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
5.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series385.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
96.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
96.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
95.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify73.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0161680
1548636
22229628
35001628

prune494.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 7.3b

regimes207.0ms

Accuracy

87.5% (1.5b remaining)

Error of 9.2b against oracle of 7.8b and baseline of 19.5b

bsearch102.0ms

Steps
ItersRangePoint
6
2.6216430800597077e+98
1.6496650416179864e+99
1.0963004586600293e+99
4
-2.4628825350256635e+163
-1.5405955983178716e+163
-1.5694170650899903e+163

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05159
15159

end0.0ms

sample841.0ms

Algorithm
intervals
Results
457.0ms8774×body80valid
136.0ms2888×body80nan