Details

Time bar (total: 4.9s)

sample34.0ms

Algorithm
intervals
Results
14.0ms290×body80valid
4.0ms79×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: 21.5b

localize112.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (* b b) (* (* 4.0 a) c))
23.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite20.0ms

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)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- (* b b) (* (* 4.0 a) c))
46.0ms
(- (* b b) (* (* 4.0 a) c))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
67.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify91.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0170540
1665506
22968498
35001488

prune307.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 9.1b

localize114.0ms

Local error

Found 4 expressions with local error:

7.9b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

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:
6.0ms
(+ (- 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)))
9.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series282.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
65.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms
(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

prune404.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.1b

localize118.0ms

Local error

Found 4 expressions with local error:

8.6b
(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

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)))
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:
78.0ms
(- (- 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)))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify179.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
02831391
19981121
247231013
350011013

prune426.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 9.1b

localize116.0ms

Local error

Found 4 expressions with local error:

23.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(cbrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(cbrt (- (* b b) (* (* 4.0 a) c)))
24.3b
(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 62
Calls
4 calls:
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)))
2.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

series354.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
93.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
100.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))
97.0ms
(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify86.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
0215657
1688619
22689612
35001611

prune377.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 9.1b

regimes178.0ms

Accuracy

90.5% (1.1b remaining)

Error of 8.6b against oracle of 7.5b and baseline of 19.5b

bsearch182.0ms

Steps
ItersRangePoint
8
1.9559514031553493e+101
2.0413668072230428e+104
5.8842313368253e+103
10
-6.365071861087975e+78
-2.694340871299081e+68
-4.1462667847686024e+73

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04958
14958

end0.0ms

sample825.0ms

Algorithm
intervals
Results
447.0ms8714×body80valid
137.0ms2849×body80nan