Details

Time bar (total: 8.1s)

analyze610.0ms (7.5%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
12.5%87.4%0.1%5
18.7%81.1%0.1%6
21.8%71.8%6.4%7
31.2%62.4%6.4%8
35.9%55.4%8.7%9
37.8%48.8%13.4%10
42.7%42.3%15%11
47.7%34.2%18.1%12
49.1%30.4%20.5%13
51.9%25.8%22.3%14
Compiler

Compiled 21 to 15 computations (28.6% saved)

sample130.0ms (1.6%)

Algorithm
intervals
Results
13.0ms176×body128valid
9.0ms28×body2048valid
7.0ms27×body1024valid
3.0msbody4096valid
2.0ms13×body512valid
2.0ms27×body128nan
1.0ms15×body128invalid
0.0msbody256valid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify264.0ms (3.3%)

Algorithm
egg-herbie
Rules
1743×fma-neg_binary64
1393×fma-def_binary64
800×div-sub_binary64
619×times-frac_binary64
473×associate-/r/_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01526
13322
26722
313822
420422
533822
655822
792422
8138822
9160422
10237522
11274222
12253322
13262122
14317122
15331322
16387322
17367922
18402922
19431722
20448522
21456122
22480522
23479322
24479722
25479722
26494822

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
32.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
32.9b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
32.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
Compiler

Compiled 111 to 74 computations (33.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
0.6b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
1.0b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
21.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

series208.0ms (2.6%)

Counts
4 → 96
Calls

4 calls:

90.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
61.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
46.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
11.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

rewrite29.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
10×fma-def_binary64
10×add-cube-cbrt_binary64
10×add-log-exp_binary64
Counts
4 → 90
Calls

4 calls:

10.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
7.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
4.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
3.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

simplify134.0ms (1.7%)

Algorithm
egg-herbie
Rules
701×fma-neg_binary64
334×cancel-sign-sub-inv_binary64
215×distribute-rgt-neg-in_binary64
159×associate-*r*_binary64
150×distribute-rgt-neg-out_binary64
Counts
186 → 207
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02434208
16953858
225123724
346943704
450313704

prune172.0ms (2.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1989207
Fresh011
Picked101
Done000
Total19910209
Error
5.8b
Counts
209 → 10
Alt Table
StatusErrorProgram
32.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
42.1b
(neg.f64 (/.f64 c b))
33.0b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
45.2b
(*.f64 (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b) (*.f64 a 2))) (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b) (*.f64 a 2))))
32.0b
(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a))
50.9b
(/.f64 (fma.f64 -2 (+.f64 (/.f64 (*.f64 c a) b) (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3))) (*.f64 (/.f64 (pow.f64 (*.f64 c a) 3) (pow.f64 b 5)) -4)) (*.f64 2 a))
35.7b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
37.4b
(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)))) (*.f64 2 a))
44.6b
(-.f64 (/.f64 c b) (/.f64 b a))
44.5b
(/.f64 (neg.f64 b) a)
Compiler

Compiled 5703 to 3337 computations (41.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a)
0.2b
(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a))
0.5b
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)
12.8b
(sqrt.f64 (*.f64 c (*.f64 a -4)))

series971.0ms (12%)

Counts
4 → 28
Calls

4 calls:

516.0ms
(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a)
278.0ms
(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a))
156.0ms
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)
21.0ms
(sqrt.f64 (*.f64 c (*.f64 a -4)))

rewrite58.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
111×add-sqr-sqrt_binary64
84×times-frac_binary64
81×*-un-lft-identity_binary64
59×add-cube-cbrt_binary64
57×sqrt-prod_binary64
Counts
4 → 182
Calls

4 calls:

23.0ms
(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a))
5.0ms
(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a)
3.0ms
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)
3.0ms
(sqrt.f64 (*.f64 c (*.f64 a -4)))

simplify261.0ms (3.2%)

Algorithm
egg-herbie
Rules
626×fma-def_binary64
314×cancel-sign-sub-inv_binary64
285×fma-neg_binary64
193×associate-*r/_binary64
182×associate-/l*_binary64
Counts
210 → 313
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03557676
18856951
229986668
347376472
449646472
550006472
648926472

prune368.0ms (4.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3942396
Fresh279
Picked101
Done000
Total3979406
Error
5.8b
Counts
406 → 9
Alt Table
StatusErrorProgram
50.6b
(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a))
32.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
42.1b
(neg.f64 (/.f64 c b))
36.4b
(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 -4 (*.f64 c a))) 3)) b) b)) a))
33.0b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))
50.9b
(/.f64 (fma.f64 -2 (+.f64 (/.f64 (*.f64 c a) b) (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3))) (*.f64 (/.f64 (pow.f64 (*.f64 c a) 3) (pow.f64 b 5)) -4)) (*.f64 2 a))
35.7b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
44.6b
(-.f64 (/.f64 c b) (/.f64 b a))
44.5b
(/.f64 (neg.f64 b) a)
Compiler

Compiled 16317 to 10594 computations (35.1% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
1.0b
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
21.0b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series184.0ms (2.3%)

Counts
3 → 60
Calls

3 calls:

86.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
54.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
43.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

rewrite22.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt_binary64
31×*-un-lft-identity_binary64
27×add-cube-cbrt_binary64
18×prod-diff_binary64
17×sqrt-prod_binary64
Counts
3 → 99
Calls

3 calls:

10.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
4.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
1.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

simplify130.0ms (1.6%)

Algorithm
egg-herbie
Rules
505×fma-neg_binary64
316×distribute-rgt-in_binary64
279×distribute-lft-in_binary64
261×cancel-sign-sub-inv_binary64
151×associate-*r*_binary64
Counts
159 → 207
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02584859
16623980
224793807
348593807
449663807

prune148.0ms (1.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2043207
Fresh268
Picked011
Done000
Total20610216
Error
5.8b
Counts
216 → 10
Alt Table
StatusErrorProgram
31.8b
(/.f64 (*.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b)) a)
44.6b
(*.f64 (*.f64 -2 b) (/.f64 1/2 a))
50.6b
(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a))
32.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
42.1b
(neg.f64 (/.f64 c b))
50.9b
(/.f64 (fma.f64 -2 (+.f64 (/.f64 (*.f64 c a) b) (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3))) (*.f64 (/.f64 (pow.f64 (*.f64 c a) 3) (pow.f64 b 5)) -4)) (*.f64 2 a))
35.7b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
44.6b
(-.f64 (/.f64 c b) (/.f64 b a))
44.5b
(/.f64 (neg.f64 b) a)
31.1b
(/.f64 (*.f64 (+.f64 (*.f64 a (*.f64 c -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
Compiler

Compiled 5882 to 3428 computations (41.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 (*.f64 (+.f64 (*.f64 a (*.f64 c -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
1.0b
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
13.5b
(*.f64 (+.f64 (*.f64 a (*.f64 c -4)) 0) (/.f64 1/2 a))
21.0b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series329.0ms (4.1%)

Counts
3 → 64
Calls

3 calls:

273.0ms
(/.f64 (*.f64 (+.f64 (*.f64 a (*.f64 c -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
52.0ms
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
3.0ms
(*.f64 (+.f64 (*.f64 a (*.f64 c -4)) 0) (/.f64 1/2 a))

rewrite30.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity_binary64
20×add-sqr-sqrt_binary64
17×add-cbrt-cube_binary64
17×add-exp-log_binary64
15×add-cube-cbrt_binary64
Counts
3 → 92
Calls

3 calls:

11.0ms
(/.f64 (*.f64 (+.f64 (*.f64 a (*.f64 c -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
9.0ms
(*.f64 (+.f64 (*.f64 a (*.f64 c -4)) 0) (/.f64 1/2 a))
3.0ms
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)

simplify138.0ms (1.7%)

Algorithm
egg-herbie
Rules
645×fma-neg_binary64
245×associate-*l*_binary64
225×associate-/l*_binary64
221×associate-*r*_binary64
177×div-sub_binary64
Counts
156 → 196
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02493787
17043238
231183153
345283153
449983153
549033153

prune206.0ms (2.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2391240
Fresh178
Picked011
Done011
Total24010250
Error
5.8b
Counts
250 → 10
Alt Table
StatusErrorProgram
50.6b
(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a))
32.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
42.1b
(neg.f64 (/.f64 c b))
28.3b
(/.f64 (*.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
50.9b
(/.f64 (fma.f64 -2 (+.f64 (/.f64 (*.f64 c a) b) (/.f64 (*.f64 (*.f64 c a) (*.f64 c a)) (pow.f64 b 3))) (*.f64 (/.f64 (pow.f64 (*.f64 c a) 3) (pow.f64 b 5)) -4)) (*.f64 2 a))
35.7b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
44.6b
(-.f64 (/.f64 c b) (/.f64 b a))
44.5b
(/.f64 (neg.f64 b) a)
44.6b
(*.f64 (*.f64 -2 b) (/.f64 1/2 a))
31.1b
(/.f64 (*.f64 (+.f64 (*.f64 a (*.f64 c -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
Compiler

Compiled 7935 to 5004 computations (36.9% saved)

regimes1.8s (22.7%)

Accuracy

Total 1.6b remaining (22.7%)

Threshold costs 0b (0%)

Counts
134 → 4
Compiler

Compiled 12532 to 8762 computations (30.1% saved)

bsearch92.0ms (1.1%)

Steps
ItersRangePoint
7
2.0899361396080252e+50
2.0917881741436121e+52
2.0607811355006304e+52
8
1.6316694668824063e-261
1.5782308949598633e-258
1.6513411710612578e-261
6
-5.2323290439070467e+76
-6.6269558394359654e+75
-5.1650230199605083e+76
Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
03580
15078
25778
36178
46278
56278

end1.0ms (0%)

Compiler

Compiled 56 to 36 computations (35.7% saved)

sample1.7s (21.2%)

Algorithm
intervals
Results
377.0ms1134×body2048valid
369.0ms5175×body128valid
202.0ms765×body1024valid
169.0ms398×body4096valid
70.0ms355×body512valid
42.0ms641×body128nan
25.0ms365×body128invalid
22.0ms173×body256valid
Compiler

Compiled 268 to 181 computations (32.5% saved)

Profiling

Loading profile data...