Details

Time bar (total: 38.7s)

analyze4.1s (10.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%98.2%1.8%7
0%92%8%8
0%91.2%8.8%9
0.4%89.3%10.3%10
7.1%79.2%13.6%11
11.9%70.2%17.9%12
13.8%67.4%18.7%13
16.6%63.3%20.1%14
Compiler

Compiled 45 to 33 computations (26.7% saved)

sample248.0ms (0.6%)

Algorithm
intervals
Symmetry

(sort A C)

Results
29.0ms166×body128valid
25.0ms32×body1024valid
23.0ms23×body2048valid
21.0ms29×body1024nan
18.0ms19×body2048nan
16.0ms74×body128nan
13.0ms25×body512valid
9.0ms18×body512nan
3.0ms10×body256valid
2.0msbody256nan
Compiler

Compiled 93 to 69 computations (25.8% saved)

simplify51.0ms (0.1%)

Algorithm
egg-herbie
Rules
759×neg-mul-1_binary64
493×associate-*l*_binary64
463×associate-*r*_binary64
420×distribute-rgt-in_binary64
410×distribute-lft-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02361
16149
217649
364849
4272749
5486949
6551249

prune6.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
47.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
48.1b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
51.3b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)) F)) (-.f64 (+.f64 A C) (sqrt.f64 (+.f64 (pow.f64 (-.f64 A C) 2) (pow.f64 B 2))))))) (-.f64 (pow.f64 B 2) (*.f64 (*.f64 4 A) C)))
Compiler

Compiled 239 to 156 computations (34.7% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.0b
(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
3.7b
(*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
11.8b
(sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))
18.0b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))

series16.4s (42.4%)

Counts
4 → 124
Calls

4 calls:

9.5s
(sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))
6.6s
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
207.0ms
(*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
58.0ms
(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))

rewrite115.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
204×distribute-lft-in_binary64
204×distribute-rgt-in_binary64
164×*-un-lft-identity_binary64
108×prod-diff_binary64
105×add-sqr-sqrt_binary64
Counts
4 → 284
Calls

4 calls:

24.0ms
(sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))
15.0ms
(*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))
7.0ms
(-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))
6.0ms
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))

simplify637.0ms (1.6%)

Algorithm
egg-herbie
Rules
721×times-frac_binary64
670×fma-def_binary64
277×associate-/l*_binary64
190×associate-/r*_binary64
93×sub-neg_binary64
Counts
408 → 499
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0276555201
1484249427
2591149427

prune1.2s (3.1%)

Pruning

25 alts after pruning (25 fresh and 0 done)

PrunedKeptTotal
New47425499
Fresh101
Picked101
Done000
Total47625501
Error
18.6b
Counts
501 → 25
Alt Table
StatusErrorProgram
48.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))) (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B))))) (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))))
51.2b
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 4 (*.f64 A (*.f64 F (*.f64 B B))) (*.f64 -16 (*.f64 (*.f64 A A) (*.f64 C F)))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
57.4b
(/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 F (-.f64 C (hypot.f64 C B)))) (*.f64 (sqrt.f64 2) B))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
48.3b
(/.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (*.f64 (cbrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))) (cbrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))))) (cbrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))))
61.1b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A (fma.f64 1/2 (/.f64 (*.f64 A A) B) (fma.f64 1/2 (/.f64 (*.f64 C C) B) (+.f64 C B)))) (/.f64 (*.f64 A C) B))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
53.9b
(neg.f64 (*.f64 (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
48.1b
(/.f64 (sqrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))) (/.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))
51.6b
(*.f64 (/.f64 -1 (sqrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)))) (/.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (sqrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)))))
61.1b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (fma.f64 (sqrt.f64 (+.f64 A C)) (sqrt.f64 (+.f64 A C)) (neg.f64 (hypot.f64 B (-.f64 A C))))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
44.8b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (fma.f64 2 A (*.f64 -1/2 (/.f64 (*.f64 B B) C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
60.2b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 -2 (*.f64 F (pow.f64 B 3))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
46.0b
(neg.f64 (*.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 F C))) (sqrt.f64 2)))
48.4b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (+.f64 (fma.f64 1 (+.f64 A C) (neg.f64 (*.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C)))))) (fma.f64 (neg.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C)))) (sqrt.f64 (hypot.f64 B (-.f64 A C))) (*.f64 (sqrt.f64 (hypot.f64 B (-.f64 A C))) (sqrt.f64 (hypot.f64 B (-.f64 A C))))))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
48.1b
(*.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (/.f64 1 (fma.f64 A (*.f64 C -4) (*.f64 B B))))
57.0b
(/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))) (*.f64 (sqrt.f64 2) B))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
47.8b
(*.f64 (sqrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))) (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B))))
54.6b
(neg.f64 (*.f64 (sqrt.f64 (*.f64 F (-.f64 C (hypot.f64 B C)))) (/.f64 (sqrt.f64 2) B)))
44.4b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (*.f64 2 A)))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
50.7b
(/.f64 (neg.f64 (neg.f64 (*.f64 A (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 -8 (*.f64 C F))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
54.0b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (fma.f64 A (*.f64 C -4) (*.f64 B B))) (/.f64 (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))) (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))))
61.7b
(neg.f64 (*.f64 (sqrt.f64 (*.f64 -1/4 (/.f64 (*.f64 F (-.f64 (+.f64 A C) (sqrt.f64 (-.f64 (fma.f64 A A (*.f64 C C)) (*.f64 2 (*.f64 A C)))))) (*.f64 A C)))) (sqrt.f64 2)))
62.7b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 -16 (*.f64 A (*.f64 (pow.f64 C 2) F))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
61.3b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (pow.f64 B 3))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
60.6b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F B))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
50.6b
(/.f64 (neg.f64 (neg.f64 (fma.f64 A (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 -8 (*.f64 C F)))) (/.f64 (*.f64 F (*.f64 (sqrt.f64 2) (*.f64 B B))) (sqrt.f64 (*.f64 -8 (*.f64 C F))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
Compiler

Compiled 69573 to 36748 computations (47.2% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.7b
(fma.f64 A (*.f64 C -4) (*.f64 B B))
4.5b
(*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (*.f64 2 A))))
15.7b
(sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (*.f64 2 A)))))
17.8b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (*.f64 2 A)))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))

series492.0ms (1.3%)

Counts
4 → 132
Calls

4 calls:

214.0ms
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (*.f64 2 A)))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
202.0ms
(sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (*.f64 2 A)))))
64.0ms
(*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (*.f64 2 A))))
12.0ms
(fma.f64 A (*.f64 C -4) (*.f64 B B))

rewrite32.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
36×times-frac_binary64
33×pow1_binary64
30×*-un-lft-identity_binary64
30×add-sqr-sqrt_binary64
30×add-cube-cbrt_binary64
Counts
4 → 119
Calls

4 calls:

8.0ms
(*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (*.f64 2 A))))
5.0ms
(sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (*.f64 2 A)))))
5.0ms
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (*.f64 2 A)))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
0.0ms
(fma.f64 A (*.f64 C -4) (*.f64 B B))

simplify137.0ms (0.4%)

Algorithm
egg-herbie
Rules
524×associate-*r*_binary64
408×associate-*l*_binary64
346×times-frac_binary64
278×associate-/r*_binary64
278×associate-/l*_binary64
Counts
251 → 269
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
045110270
113049211
252549211

prune341.0ms (0.9%)

Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New27413287
Fresh131124
Picked101
Done000
Total28824312
Error
15.2b
Counts
312 → 24
Alt Table
StatusErrorProgram
57.8b
(/.f64 (neg.f64 (*.f64 2 (*.f64 A (sqrt.f64 (*.f64 -4 (*.f64 C F)))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
48.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))) (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B))))) (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))))
57.4b
(/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 F (-.f64 C (hypot.f64 C B)))) (*.f64 (sqrt.f64 2) B))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
58.8b
(*.f64 2 (*.f64 (sqrt.f64 (*.f64 A F)) (/.f64 1 B)))
61.7b
(neg.f64 (*.f64 (sqrt.f64 (*.f64 -1/4 (/.f64 (*.f64 F (-.f64 (+.f64 A C) (sqrt.f64 (-.f64 (fma.f64 A A (*.f64 C C)) (*.f64 2 (*.f64 A C)))))) (*.f64 A C)))) (sqrt.f64 2)))
61.1b
(*.f64 -2 (*.f64 (sqrt.f64 (*.f64 A F)) (/.f64 1 B)))
61.3b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (pow.f64 B 3))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
44.5b
(*.f64 -1/4 (/.f64 (sqrt.f64 (*.f64 -16 (*.f64 C F))) C))
49.1b
(expm1.f64 (log1p.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))))
48.3b
(/.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (*.f64 (cbrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))) (cbrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))))) (cbrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))))
53.9b
(neg.f64 (*.f64 (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
44.8b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (fma.f64 2 A (*.f64 -1/2 (/.f64 (*.f64 B B) C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
60.2b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 -2 (*.f64 F (pow.f64 B 3))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
44.4b
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4))))) (/.f64 (neg.f64 (sqrt.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4)))))) (fma.f64 A (*.f64 C -4) (*.f64 B B))))
53.8b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (*.f64 2 A)))))) (cbrt.f64 (*.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (fma.f64 A (*.f64 C -4) (*.f64 B B))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))))
50.6b
(/.f64 (neg.f64 (neg.f64 (fma.f64 2 (/.f64 (*.f64 F (*.f64 B B)) (sqrt.f64 (*.f64 -16 (*.f64 F C)))) (*.f64 A (sqrt.f64 (*.f64 -16 (*.f64 F C))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
47.8b
(*.f64 (sqrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))) (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B))))
53.0b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (exp.f64 (log.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)))) (*.f64 2 (*.f64 F (*.f64 2 A)))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
44.4b
(/.f64 -1 (/.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4))))))
58.8b
(*.f64 2 (/.f64 (sqrt.f64 (*.f64 F A)) B))
62.7b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 -16 (*.f64 A (*.f64 (pow.f64 C 2) F))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
48.1b
(/.f64 (sqrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))) (/.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))
45.9b
(*.f64 -2 (sqrt.f64 (*.f64 -1/4 (/.f64 F C))))
50.7b
(/.f64 (neg.f64 (neg.f64 (*.f64 A (sqrt.f64 (*.f64 -16 (*.f64 F C)))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
Compiler

Compiled 13990 to 8205 computations (41.4% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.7b
(fma.f64 A (*.f64 C -4) (*.f64 B B))
4.5b
(*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4)))
15.7b
(sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4))))
17.6b
(/.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4)))))

series677.0ms (1.7%)

Counts
3 → 96
Calls

3 calls:

409.0ms
(/.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4)))))
209.0ms
(sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4))))
58.0ms
(*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4)))

rewrite20.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
22×pow1_binary64
14×add-cbrt-cube_binary64
14×add-exp-log_binary64
13×*-un-lft-identity_binary64
13×add-sqr-sqrt_binary64
Counts
3 → 71
Calls

3 calls:

6.0ms
(/.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4)))))
5.0ms
(*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4)))
4.0ms
(sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4))))

simplify153.0ms (0.4%)

Algorithm
egg-herbie
Rules
791×fma-def_binary64
367×associate-*r*_binary64
281×associate-*l*_binary64
260×fma-neg_binary64
209×times-frac_binary64
Counts
167 → 189
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03276476
19515935
237615917
349295917
450075917

prune245.0ms (0.6%)

Pruning

27 alts after pruning (26 fresh and 1 done)

PrunedKeptTotal
New2178225
Fresh51823
Picked011
Done000
Total22227249
Error
15.2b
Counts
249 → 27
Alt Table
StatusErrorProgram
57.8b
(/.f64 (neg.f64 (*.f64 2 (*.f64 A (sqrt.f64 (*.f64 -4 (*.f64 C F)))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
48.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))) (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B))))) (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))))
57.4b
(/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 F (-.f64 C (hypot.f64 C B)))) (*.f64 (sqrt.f64 2) B))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
58.8b
(*.f64 2 (/.f64 (sqrt.f64 (*.f64 F A)) B))
61.9b
(/.f64 -1 (-.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 A F))) B)) (*.f64 (sqrt.f64 (/.f64 A F)) (/.f64 C B))))
58.8b
(*.f64 2 (*.f64 (sqrt.f64 (*.f64 A F)) (/.f64 1 B)))
61.7b
(neg.f64 (*.f64 (sqrt.f64 (*.f64 -1/4 (/.f64 (*.f64 F (-.f64 (+.f64 A C) (sqrt.f64 (-.f64 (fma.f64 A A (*.f64 C C)) (*.f64 2 (*.f64 A C)))))) (*.f64 A C)))) (sqrt.f64 2)))
61.1b
(*.f64 -2 (*.f64 (sqrt.f64 (*.f64 A F)) (/.f64 1 B)))
61.3b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (pow.f64 B 3))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
44.5b
(/.f64 -1 (*.f64 4 (/.f64 C (sqrt.f64 (*.f64 -16 (*.f64 C F))))))
44.5b
(*.f64 -1/4 (/.f64 (sqrt.f64 (*.f64 -16 (*.f64 C F))) C))
51.7b
(/.f64 -1 (fma.f64 1/2 (sqrt.f64 (*.f64 -4 (/.f64 C F))) (*.f64 1/4 (/.f64 (*.f64 B B) (*.f64 A (*.f64 F (sqrt.f64 (*.f64 -4 (/.f64 C F)))))))))
49.1b
(expm1.f64 (log1p.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))))
48.3b
(/.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (*.f64 (cbrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))) (cbrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))))) (cbrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))))
53.9b
(neg.f64 (*.f64 (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
48.1b
(/.f64 (sqrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))) (/.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))
53.0b
(/.f64 -1 (/.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (sqrt.f64 (*.f64 (exp.f64 (log.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)))) (*.f64 F (*.f64 A 4))))))
46.1b
(/.f64 -1 (*.f64 1/2 (sqrt.f64 (*.f64 -4 (/.f64 C F)))))
44.8b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (fma.f64 2 A (*.f64 -1/2 (/.f64 (*.f64 B B) C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
60.2b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 -2 (*.f64 F (pow.f64 B 3))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
44.4b
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4))))) (/.f64 (neg.f64 (sqrt.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4)))))) (fma.f64 A (*.f64 C -4) (*.f64 B B))))
47.8b
(*.f64 (sqrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))) (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B))))
44.4b
(/.f64 -1 (/.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4))))))
45.9b
(*.f64 -2 (sqrt.f64 (*.f64 -1/4 (/.f64 F C))))
50.7b
(/.f64 -1 (/.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (neg.f64 (*.f64 A (sqrt.f64 (*.f64 -16 (*.f64 C F)))))))
44.4b
(/.f64 -1 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (/.f64 1 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4)))))))
60.8b
(/.f64 -1 (fma.f64 (*.f64 B (sqrt.f64 (/.f64 1 (*.f64 F A)))) -1/2 (*.f64 (sqrt.f64 (/.f64 A F)) (/.f64 C B))))
Compiler

Compiled 10437 to 5975 computations (42.8% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.7b
(fma.f64 A (*.f64 C -4) (*.f64 B B))
4.5b
(*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4)))
15.7b
(sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4))))
17.5b
(*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (/.f64 1 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4))))))

series394.0ms (1%)

Counts
1 → 24
Calls

1 calls:

394.0ms
(*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (/.f64 1 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4))))))

rewrite17.0ms (0%)

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt_binary64
16×associate-*r*_binary64
14×times-frac_binary64
11×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
Counts
1 → 41
Calls

1 calls:

12.0ms
(*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (/.f64 1 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4))))))

simplify98.0ms (0.3%)

Algorithm
egg-herbie
Rules
424×associate-*l/_binary64
383×fma-def_binary64
206×fma-neg_binary64
191×unswap-sqr_binary64
168×cancel-sign-sub-inv_binary64
Counts
65 → 96
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01883128
15272885
220472881
347972881
449872881

prune213.0ms (0.5%)

Pruning

27 alts after pruning (25 fresh and 2 done)

PrunedKeptTotal
New2310231
Fresh02525
Picked011
Done011
Total23127258
Error
15.2b
Counts
258 → 27
Alt Table
StatusErrorProgram
57.8b
(/.f64 (neg.f64 (*.f64 2 (*.f64 A (sqrt.f64 (*.f64 -4 (*.f64 C F)))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
48.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))) (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B))))) (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))))
57.4b
(/.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 F (-.f64 C (hypot.f64 C B)))) (*.f64 (sqrt.f64 2) B))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
58.8b
(*.f64 2 (/.f64 (sqrt.f64 (*.f64 F A)) B))
61.9b
(/.f64 -1 (-.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 (*.f64 A F))) B)) (*.f64 (sqrt.f64 (/.f64 A F)) (/.f64 C B))))
58.8b
(*.f64 2 (*.f64 (sqrt.f64 (*.f64 A F)) (/.f64 1 B)))
61.7b
(neg.f64 (*.f64 (sqrt.f64 (*.f64 -1/4 (/.f64 (*.f64 F (-.f64 (+.f64 A C) (sqrt.f64 (-.f64 (fma.f64 A A (*.f64 C C)) (*.f64 2 (*.f64 A C)))))) (*.f64 A C)))) (sqrt.f64 2)))
61.1b
(*.f64 -2 (*.f64 (sqrt.f64 (*.f64 A F)) (/.f64 1 B)))
61.3b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (pow.f64 B 3))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
44.5b
(/.f64 -1 (*.f64 4 (/.f64 C (sqrt.f64 (*.f64 -16 (*.f64 C F))))))
44.5b
(*.f64 -1/4 (/.f64 (sqrt.f64 (*.f64 -16 (*.f64 C F))) C))
51.7b
(/.f64 -1 (fma.f64 1/2 (sqrt.f64 (*.f64 -4 (/.f64 C F))) (*.f64 1/4 (/.f64 (*.f64 B B) (*.f64 A (*.f64 F (sqrt.f64 (*.f64 -4 (/.f64 C F)))))))))
49.1b
(expm1.f64 (log1p.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))))
48.3b
(/.f64 (/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))) (*.f64 (cbrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))) (cbrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))))) (cbrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))))
53.9b
(neg.f64 (*.f64 (sqrt.f64 (*.f64 F (-.f64 A (hypot.f64 A B)))) (/.f64 (sqrt.f64 2) B)))
48.1b
(/.f64 (sqrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))) (/.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C)))))))))
53.0b
(/.f64 -1 (/.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (sqrt.f64 (*.f64 (exp.f64 (log.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)))) (*.f64 F (*.f64 A 4))))))
46.1b
(/.f64 -1 (*.f64 1/2 (sqrt.f64 (*.f64 -4 (/.f64 C F)))))
44.8b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 2 (*.f64 F (fma.f64 2 A (*.f64 -1/2 (/.f64 (*.f64 B B) C)))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
60.2b
(/.f64 (neg.f64 (sqrt.f64 (*.f64 -2 (*.f64 F (pow.f64 B 3))))) (fma.f64 A (*.f64 C -4) (*.f64 B B)))
44.4b
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4))))) (/.f64 (neg.f64 (sqrt.f64 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4)))))) (fma.f64 A (*.f64 C -4) (*.f64 B B))))
47.8b
(*.f64 (sqrt.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B))) (/.f64 (neg.f64 (sqrt.f64 (*.f64 2 (*.f64 F (-.f64 (+.f64 A C) (hypot.f64 B (-.f64 A C))))))) (fma.f64 A (*.f64 C -4) (*.f64 B B))))
44.4b
(/.f64 -1 (/.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4))))))
45.9b
(*.f64 -2 (sqrt.f64 (*.f64 -1/4 (/.f64 F C))))
50.7b
(/.f64 -1 (/.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (neg.f64 (*.f64 A (sqrt.f64 (*.f64 -16 (*.f64 C F)))))))
44.4b
(/.f64 -1 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (/.f64 1 (sqrt.f64 (*.f64 (fma.f64 A (*.f64 C -4) (*.f64 B B)) (*.f64 F (*.f64 A 4)))))))
60.8b
(/.f64 -1 (fma.f64 (*.f64 B (sqrt.f64 (/.f64 1 (*.f64 F A)))) -1/2 (*.f64 (sqrt.f64 (/.f64 A F)) (/.f64 C B))))
Compiler

Compiled 10240 to 6084 computations (40.6% saved)

regimes6.2s (15.9%)

Accuracy

Total 20.5b remaining (58.2%)

Threshold costs 0b (0%)

Counts
258 → 8
Compiler

Compiled 59591 to 37379 computations (37.3% saved)

bsearch726.0ms (1.9%)

Steps
ItersRangePoint
9
4.777337762782758e+297
5.214060497737751e+306
1.9355356954408794e+298
4
1.4163411158344141e+178
2.402597081061553e+178
2.1421053442050514e+178
5
8.799491867932524e+102
2.2619829352120735e+103
1.4999553372101038e+103
7
6.739942499631027e+65
3.984584806874062e+67
1.3072799572480792e+67
8
2.3813086470808913e-97
1.0054225607517286e-94
2.595610150498829e-95
8
-4.2557946078497334e-268
-2.4382994163758725e-272
-4.1890341447133404e-268
8
-4.6579681589414485e-60
-1.1756814188391766e-64
-4.583468965674152e-60
Compiler

Compiled 5 to 4 computations (20% saved)

simplify11.0ms (0%)

Algorithm
egg-herbie
Rules
21×*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
075287
1102287
2115287
3125287
4131287
5132287
6132287

end15.0ms (0%)

Compiler

Compiled 591 to 348 computations (41.1% saved)

sample6.2s (16%)

Algorithm
intervals
Results
1.0s5518×body128valid
754.0ms677×body2048valid
700.0ms873×body1024valid
593.0ms590×body2048nan
560.0ms769×body1024nan
457.0ms2507×body128nan
356.0ms565×body512nan
350.0ms630×body512valid
117.0ms318×body256nan
110.0ms301×body256valid
1.0msbody4096valid
Compiler

Compiled 1044 to 668 computations (36% saved)

Profiling

Loading profile data...