Details

Time bar (total: 6.3s)

analyze683.0ms (10.9%)

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)

sample49.0ms (0.8%)

Algorithm
intervals
Results
14.0ms176×body128valid
9.0ms31×body2048valid
5.0ms22×body1024valid
4.0ms12×body4096valid
2.0ms11×body512valid
1.0ms19×body128nan
1.0ms13×body128invalid
0.0msbody256valid
Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify273.0ms (4.4%)

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 (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
34.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
34.5b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
34.5b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
Compiler

Compiled 111 to 74 computations (33.3% saved)

localize13.0ms (0.2%)

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))
1.1b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
1.4b
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))
24.6b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))

rewrite31.0ms (0.5%)

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:

11.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
8.0ms
(+.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))

series184.0ms (2.9%)

Counts
4 → 96
Calls

4 calls:

72.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))) (*.f64 2 a))
44.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))
38.0ms
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c)))
30.0ms
(-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))

simplify140.0ms (2.2%)

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 → 346
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02434208
16953858
225123724
346943704
450313704

prune159.0ms (2.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3388346
Fresh011
Picked101
Done000
Total3399348
Error
6.6b
Counts
348 → 9
Alt Table
StatusErrorProgram
33.8b
(*.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))
42.2b
(-.f64 (/.f64 c b) (/.f64 b a))
47.5b
(*.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))))
42.2b
(neg.f64 (/.f64 c b))
34.5b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
42.1b
(/.f64 (neg.f64 b) a)
56.5b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
50.6b
(/.f64 (-.f64 (*.f64 (neg.f64 b) (neg.f64 b)) (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)) (*.f64 a 2)))
39.1b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
Compiler

Compiled 5667 to 3309 computations (41.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.7b
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)
0.7b
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)
15.1b
(sqrt.f64 (*.f64 c (*.f64 a -4)))
15.1b
(sqrt.f64 (*.f64 c (*.f64 a -4)))

rewrite9.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
prod-diff_binary64
pow1_binary64
Counts
2 → 44
Calls

2 calls:

4.0ms
(sqrt.f64 (*.f64 c (*.f64 a -4)))
3.0ms
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)

series135.0ms (2.2%)

Counts
2 → 12
Calls

2 calls:

121.0ms
(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)
14.0ms
(sqrt.f64 (*.f64 c (*.f64 a -4)))

simplify104.0ms (1.7%)

Algorithm
egg-herbie
Rules
557×fma-neg_binary64
516×associate-/l*_binary64
399×associate-/r*_binary64
369×fma-def_binary64
191×*-commutative_binary64
Counts
56 → 101
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01341471
12831063
29901009
33952998
44749998
54875998
64845998

prune152.0ms (2.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2011202
Fresh088
Picked011
Done000
Total20110211
Error
6.6b
Counts
211 → 10
Alt Table
StatusErrorProgram
33.8b
(*.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))
42.2b
(-.f64 (/.f64 c b) (/.f64 b a))
47.5b
(*.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))))
42.2b
(neg.f64 (/.f64 c b))
39.1b
(/.f64 (/.f64 (*.f64 4 (*.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b))) (*.f64 2 a))
50.2b
(*.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))
34.5b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
42.1b
(/.f64 (neg.f64 b) a)
56.5b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
50.6b
(/.f64 (-.f64 (*.f64 (neg.f64 b) (neg.f64 b)) (*.f64 (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))) (*.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b)) (*.f64 a 2)))
Compiler

Compiled 6867 to 4422 computations (35.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 a (*.f64 c -4) (*.f64 b b))
0.2b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
1.1b
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
24.6b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

rewrite21.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt_binary64
32×*-un-lft-identity_binary64
28×add-cube-cbrt_binary64
18×prod-diff_binary64
17×sqrt-prod_binary64
Counts
4 → 109
Calls

4 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)))
0.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))

series187.0ms (3%)

Counts
4 → 96
Calls

4 calls:

71.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
49.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
35.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))
32.0ms
(fma.f64 a (*.f64 c -4) (*.f64 b b))

simplify216.0ms (3.4%)

Algorithm
egg-herbie
Rules
527×fma-neg_binary64
338×distribute-rgt-in_binary64
273×cancel-sign-sub-inv_binary64
155×associate-*l*_binary64
153×associate-*r*_binary64
Counts
205 → 384
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02675424
16734468
225244293
345504293
449914293
549944293
648844293

prune153.0ms (2.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New3804384
Fresh358
Picked011
Done011
Total38311394
Error
6.6b
Counts
394 → 11
Alt Table
StatusErrorProgram
33.8b
(*.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))
42.2b
(-.f64 (/.f64 c b) (/.f64 b a))
47.5b
(*.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))))
42.2b
(neg.f64 (/.f64 c b))
50.2b
(*.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))
35.6b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
42.9b
(/.f64 (*.f64 1/2 (+.f64 (*.f64 c (*.f64 a -4)) 0)) (*.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))))))
34.5b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
49.2b
(*.f64 (/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 c (*.f64 a -4)))) b) (sqrt.f64 a)) (/.f64 1/2 (sqrt.f64 a)))
42.1b
(/.f64 (neg.f64 b) a)
56.5b
(*.f64 (-.f64 b b) (/.f64 1/2 a))
Compiler

Compiled 6300 to 3688 computations (41.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
1.3b
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
16.8b
(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))
24.6b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

rewrite29.0ms (0.5%)

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:

13.0ms
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
8.0ms
(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))
3.0ms
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)

series267.0ms (4.2%)

Counts
3 → 64
Calls

3 calls:

214.0ms
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
42.0ms
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
10.0ms
(*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

simplify125.0ms (2%)

Algorithm
egg-herbie
Rules
616×fma-neg_binary64
248×associate-*l*_binary64
225×associate-/l*_binary64
220×associate-*r*_binary64
176×div-sub_binary64
Counts
156 → 269
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02503787
17083244
231323157
346133157
449323157

prune182.0ms (2.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New3244328
Fresh448
Picked101
Done022
Total32910339
Error
6.6b
Counts
339 → 10
Alt Table
StatusErrorProgram
33.8b
(*.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))
42.2b
(-.f64 (/.f64 c b) (/.f64 b a))
33.0b
(/.f64 (*.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
50.2b
(*.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))
35.7b
(/.f64 1 (/.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))))
34.5b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
35.6b
(/.f64 (/.f64 (*.f64 (*.f64 c a) -2) a) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
42.1b
(/.f64 (neg.f64 b) a)
42.2b
(neg.f64 (/.f64 c b))
45.8b
(/.f64 (*.f64 (+.f64 (*.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a)) (*.f64 2 (-.f64 b (/.f64 (*.f64 c a) b))))
Compiler

Compiled 7925 to 5007 computations (36.8% saved)

regimes1.3s (21.4%)

Accuracy

Total 1.4b remaining (19.9%)

Threshold costs 0b (0%)

Compiler

Compiled 10634 to 7466 computations (29.8% saved)

bsearch113.0ms (1.8%)

Steps
ItersRangePoint
10
8.981820027111466e+44
5.780594342752023e+56
5.705473668258076e+56
8
-3.046842614769162e-297
-2.2764529063929935e-301
-1.3269458115206028e-299
8
-7.171015674412679e+119
-1.5964967927357583e+116
-5.364212800122094e+119
Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
03984
16482
28882
310282
411082
511282
611082

end1.0ms (0%)

Compiler

Compiled 58 to 37 computations (36.2% saved)

sample1.7s (26.5%)

Algorithm
intervals
Results
364.0ms1145×body2048valid
350.0ms5183×body128valid
176.0ms707×body1024valid
161.0ms422×body4096valid
72.0ms359×body512valid
45.0ms677×body128nan
26.0ms405×body128invalid
26.0ms184×body256valid
Compiler

Compiled 277 to 189 computations (31.8% saved)

Profiling

Loading profile data...