Details

Time bar (total: 8.8s)

analyze614.0ms (7%)

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)

sample338.0ms (3.9%)

Algorithm
intervals
Results
12.0ms176×body128valid
9.0ms28×body2048valid
7.0ms27×body1024valid
3.0msbody4096valid
3.0ms13×body512valid
2.0ms27×body128nan
1.0ms15×body128invalid
1.0msbody256valid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify387.0ms (4.4%)

Algorithm
egg-herbie
Rules
2009×fma-neg_binary64
1508×div-sub_binary64
1334×associate-/l*_binary64
1156×fma-def_binary64
685×associate-/l/_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01526
13422
26422
313222
419822
532522
655222
791822
8135222
9155422
10235922
11315822
12256522
13265322
14321922
15336122
16346122
17398522
18417122
19443922
20465922
21470122
22475722
23494122
24494122
25336522
26305922
27298322
28298522
29299722
30299722
31299722
32299722
33273622

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 4 (*.f64 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)

localize13.0ms (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 4 (*.f64 a c))))) (*.f64 2 a))
0.6b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
1.0b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
21.0b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

series209.0ms (2.4%)

Counts
4 → 96
Calls

4 calls:

97.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
53.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
46.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
12.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))

rewrite28.0ms (0.3%)

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:

9.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
7.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
3.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))
3.0ms
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))

simplify129.0ms (1.5%)

Algorithm
egg-herbie
Rules
697×fma-neg_binary64
327×cancel-sign-sub-inv_binary64
226×distribute-rgt-neg-in_binary64
150×distribute-rgt-neg-out_binary64
146×associate-*r*_binary64
Counts
186 → 207
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02434202
16933825
224883724
346523704
449853704

prune179.0ms (2%)

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
44.5b
(/.f64 (neg.f64 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))
33.0b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))
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))
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))))
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))
Compiler

Compiled 5703 to 3198 computations (43.9% saved)

localize13.0ms (0.2%)

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)))

series965.0ms (11%)

Counts
4 → 28
Calls

4 calls:

530.0ms
(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a)
261.0ms
(*.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))
152.0ms
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)
21.0ms
(sqrt.f64 (*.f64 c (*.f64 a -4)))

rewrite54.0ms (0.6%)

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:

20.0ms
(*.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)))

simplify273.0ms (3.1%)

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

prune364.0ms (4.1%)

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))
44.6b
(-.f64 (/.f64 c b) (/.f64 b a))
44.5b
(/.f64 (neg.f64 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))
33.0b
(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 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))
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))
Compiler

Compiled 16317 to 10594 computations (35.1% saved)

localize14.0ms (0.2%)

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)))

series214.0ms (2.4%)

Counts
3 → 60
Calls

3 calls:

88.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
69.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
56.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)

rewrite23.0ms (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:

11.0ms
(*.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)))

simplify135.0ms (1.5%)

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

prune161.0ms (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
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 -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))
44.6b
(-.f64 (/.f64 c b) (/.f64 b a))
44.5b
(/.f64 (neg.f64 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))
31.8b
(/.f64 (*.f64 1/2 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) 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))
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)

localize16.0ms (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)))

series330.0ms (3.8%)

Counts
3 → 64
Calls

3 calls:

271.0ms
(/.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))
55.0ms
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
4.0ms
(*.f64 (+.f64 (*.f64 a (*.f64 c -4)) 0) (/.f64 1/2 a))

rewrite30.0ms (0.3%)

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:

12.0ms
(/.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))
8.0ms
(*.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)

simplify140.0ms (1.6%)

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

prune200.0ms (2.3%)

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
50.9b
(/.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))
28.3b
(/.f64 (*.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
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 -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))
44.6b
(-.f64 (/.f64 c b) (/.f64 b a))
44.5b
(/.f64 (neg.f64 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))
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)

regimes1.6s (18.3%)

Accuracy

Total 1.6b remaining (22.7%)

Threshold costs 0b (0%)

Counts
134 → 4
Compiler

Compiled 12532 to 8701 computations (30.6% saved)

bsearch99.0ms (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)

simplify6.0ms (0.1%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
03882
15980
27280
38580
49180
59480
69580
79480

end1.0ms (0%)

Compiler

Compiled 57 to 37 computations (35.1% saved)

sample2.2s (25.3%)

Algorithm
intervals
Results
642.0ms1134×body2048valid
369.0ms5175×body128valid
355.0ms398×body4096valid
207.0ms765×body1024valid
70.0ms355×body512valid
50.0ms641×body128nan
27.0ms365×body128invalid
23.0ms173×body256valid
Compiler

Compiled 269 to 182 computations (32.3% saved)

Profiling

Loading profile data...