Details

Time bar (total: 7.5s)

analyze648.0ms (8.7%)

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)

sample2.2s (29.2%)

Results
693.0ms5325×body128valid
584.0ms1149×body2048valid
314.0ms774×body1024valid
283.0ms470×body4096valid
138.0ms1113×body128invalid
115.0ms365×body512valid
38.0ms173×body256valid
Compiler

Compiled 42 to 30 computations (28.6% saved)

preprocess44.0ms (0.6%)

Algorithm
egg-herbie
Rules
807×fma-def_binary64
679×div-sub_binary64
295×fma-neg_binary64
214×associate-/l*_binary64
209×sub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
039104
19888
219888
344688
476888
5126188
6223688
7445888
033
Stop Event
saturated
node limit
Compiler

Compiled 20 to 14 computations (30% saved)

simplify29.0ms (0.4%)

Algorithm
egg-herbie
Rules
747×fma-neg_binary64
619×times-frac_binary64
338×fma-def_binary64
314×associate-/l*_binary64
262×div-sub_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01526
13422
26922
316122
425922
541722
673422
7132622
8261822
9387722
Stop Event
node limit
Counts
1 → 2

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
35.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
35.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
35.9b
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
Compiler

Compiled 111 to 75 computations (32.4% saved)

localize12.0ms (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 4 (*.f64 a c))))) (*.f64 2 a))
0.4b
(-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))
1.6b
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
25.5b
(sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))

series129.0ms (1.7%)

Counts
4 → 96
Calls

36 calls:

12.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
a
inf
10.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
a
-inf
9.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
c
inf
8.0ms
(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c))))) (*.f64 2 a))
c
-inf
7.0ms
(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))
c
-inf

rewrite75.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
277×log1p-udef_binary64
166×add-sqr-sqrt_binary64
162×log1p-expm1-u_binary64
162×expm1-log1p-u_binary64
161×add-cbrt-cube_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01574
134362
2485962
Stop Event
node limit
Counts
4 → 158

simplify52.0ms (0.7%)

Algorithm
egg-herbie
Rules
742×times-frac_binary64
467×associate-/l*_binary64
432×fma-def_binary64
422×associate-/r*_binary64
142×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01212241
14022164
214032078
Stop Event
node limit
Counts
254 → 232

prune193.0ms (2.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New22210232
Fresh011
Picked101
Done000
Total22311234
Error
6.7b
Counts
234 → 11
Alt Table
StatusErrorProgram
40.6b
(-.f64 (/.f64 c b) (/.f64 b a))
45.3b
(/.f64 (*.f64 -2 (/.f64 (*.f64 c a) b)) (*.f64 2 a))
40.5b
(/.f64 (neg.f64 b) a)
35.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
48.5b
(*.f64 1/2 (-.f64 (/.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) a) (/.f64 b a)))
50.8b
(pow.f64 (/.f64 (*.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) -1)
36.8b
(/.f64 (+.f64 (neg.f64 b) (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4)))))) (*.f64 2 a))
50.9b
(*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) (*.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) (/.f64 1/2 a)))
48.6b
(/.f64 (/.f64 (-.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4)) (*.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 b b (*.f64 (*.f64 a c) -4))))) (*.f64 2 a))
41.2b
(/.f64 (neg.f64 c) b)
56.3b
(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
Compiler

Compiled 6196 to 3602 computations (41.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
0.5b
(fma.f64 b b (*.f64 a (*.f64 c -4)))
1.6b
(-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b)
25.5b
(sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))))

series133.0ms (1.8%)

Counts
4 → 96
Calls

36 calls:

11.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
a
-inf
10.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
a
inf
9.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
c
inf
8.0ms
(-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b)
c
inf
7.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
c
-inf

rewrite71.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
737×prod-diff_binary64
158×egg-rr
139×add-sqr-sqrt_binary64
132×log1p-expm1-u_binary64
132×expm1-log1p-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01362
128159
2362659
Stop Event
node limit
Counts
4 → 158

simplify56.0ms (0.7%)

Algorithm
egg-herbie
Rules
742×times-frac_binary64
467×associate-/l*_binary64
432×fma-def_binary64
422×associate-/r*_binary64
142×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01212241
14022164
214032078
Stop Event
node limit
Counts
254 → 232

prune178.0ms (2.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New22111232
Fresh7310
Picked011
Done000
Total22815243
Error
6.7b
Counts
243 → 15
Alt Table
StatusErrorProgram
40.7b
(*.f64 (*.f64 2 (fma.f64 (/.f64 c b) a (neg.f64 b))) (/.f64 1/2 a))
32.5b
(/.f64 1 (/.f64 a (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) 1/2)))
45.3b
(*.f64 (*.f64 -2 (/.f64 (*.f64 c a) b)) (/.f64 1/2 a))
40.6b
(-.f64 (/.f64 c b) (/.f64 b a))
38.7b
(*.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) b) (/.f64 1/2 a))
40.5b
(/.f64 (neg.f64 b) a)
35.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
56.3b
(*.f64 (-.f64 b b) (/.f64 1/2 a))
41.2b
(/.f64 (neg.f64 c) b)
32.4b
(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (*.f64 a 2))
56.3b
(*.f64 (-.f64 (fma.f64 (*.f64 (/.f64 c b) a) -2 b) b) (/.f64 1/2 a))
34.4b
(*.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b))) (/.f64 1/2 a))
32.5b
(*.f64 (pow.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) 1) (/.f64 1/2 a))
49.5b
(*.f64 (/.f64 (-.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))) (*.f64 b b)) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) (/.f64 1/2 a))
49.5b
(/.f64 (*.f64 (-.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))) (*.f64 b b)) (/.f64 1/2 a)) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))
Compiler

Compiled 6052 to 3781 computations (37.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (*.f64 a 2))
0.7b
(-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b)
14.5b
(sqrt.f64 (*.f64 a (*.f64 c -4)))

series252.0ms (3.4%)

Counts
3 → 24
Calls

24 calls:

36.0ms
(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (*.f64 a 2))
a
-inf
28.0ms
(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (*.f64 a 2))
c
inf
26.0ms
(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (*.f64 a 2))
a
inf
22.0ms
(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (*.f64 a 2))
c
-inf
19.0ms
(-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b)
c
inf

rewrite189.0ms (2.5%)

Algorithm
batch-egg-rewrite
Rules
937×prod-diff_binary64
442×egg-rr
143×add-sqr-sqrt_binary64
136×log1p-expm1-u_binary64
136×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01345
128745
2391445
Stop Event
node limit
Counts
3 → 442

simplify54.0ms (0.7%)

Algorithm
egg-herbie
Rules
728×times-frac_binary64
385×associate-/l*_binary64
360×associate-/r*_binary64
271×associate-*r*_binary64
249×fma-def_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0102988
1323908
21054857
Stop Event
node limit
Counts
466 → 487

prune571.0ms (7.6%)

Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New4852487
Fresh31013
Picked011
Done011
Total48814502
Error
2.7b
Counts
502 → 14
Alt Table
StatusErrorProgram
40.7b
(*.f64 (*.f64 2 (fma.f64 (/.f64 c b) a (neg.f64 b))) (/.f64 1/2 a))
32.5b
(/.f64 1 (/.f64 a (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) 1/2)))
38.7b
(*.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) b) (/.f64 1/2 a))
40.5b
(/.f64 (neg.f64 b) a)
35.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
56.3b
(*.f64 (-.f64 b b) (/.f64 1/2 a))
41.2b
(/.f64 (neg.f64 c) b)
32.5b
(*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b) (/.f64 1/2 a))
49.5b
(/.f64 (*.f64 (-.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))) (*.f64 b b)) (/.f64 1/2 a)) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))
32.4b
(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (*.f64 a 2))
45.3b
(*.f64 (*.f64 -2 (/.f64 (*.f64 c a) b)) (/.f64 1/2 a))
56.3b
(*.f64 (-.f64 (fma.f64 (*.f64 (/.f64 c b) a) -2 b) b) (/.f64 1/2 a))
44.0b
(/.f64 (-.f64 (hypot.f64 b (*.f64 (sqrt.f64 (*.f64 c -4)) (sqrt.f64 a))) b) (*.f64 a 2))
49.5b
(*.f64 (/.f64 (-.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))) (*.f64 b b)) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) (/.f64 1/2 a))
Compiler

Compiled 23744 to 15298 computations (35.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 -4 (*.f64 a c))
0.2b
(*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b) (/.f64 1/2 a))
0.7b
(-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b)
14.5b
(sqrt.f64 (*.f64 -4 (*.f64 a c)))

series267.0ms (3.6%)

Counts
4 → 48
Calls

30 calls:

37.0ms
(*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b) (/.f64 1/2 a))
a
-inf
31.0ms
(*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b) (/.f64 1/2 a))
c
inf
27.0ms
(*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b) (/.f64 1/2 a))
a
inf
23.0ms
(*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b) (/.f64 1/2 a))
c
-inf
20.0ms
(-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b)
c
inf

rewrite73.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
568×prod-diff_binary64
249×log1p-udef_binary64
140×add-sqr-sqrt_binary64
133×log1p-expm1-u_binary64
133×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01352
128452
2363452
Stop Event
node limit
Counts
4 → 132

simplify37.0ms (0.5%)

Algorithm
egg-herbie
Rules
728×times-frac_binary64
385×associate-/l*_binary64
360×associate-/r*_binary64
271×associate-*r*_binary64
249×fma-def_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01021156
13231076
210541025
Stop Event
node limit
Counts
180 → 178

prune129.0ms (1.7%)

Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New1771178
Fresh3811
Picked011
Done022
Total18012192
Error
0.1b
Counts
192 → 12
Alt Table
StatusErrorProgram
40.7b
(*.f64 (*.f64 2 (fma.f64 (/.f64 c b) a (neg.f64 b))) (/.f64 1/2 a))
32.5b
(/.f64 1 (/.f64 a (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) 1/2)))
40.5b
(/.f64 (neg.f64 b) a)
35.9b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 b b (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))
32.5b
(*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 -4 (*.f64 a c)))) b) (/.f64 1/2 a))
49.5b
(/.f64 (*.f64 (-.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))) (*.f64 b b)) (/.f64 1/2 a)) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))
32.4b
(/.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (*.f64 a 2))
45.3b
(*.f64 (*.f64 -2 (/.f64 (*.f64 c a) b)) (/.f64 1/2 a))
47.2b
(*.f64 (-.f64 (hypot.f64 b (*.f64 (sqrt.f64 (*.f64 -4 a)) (sqrt.f64 c))) b) (/.f64 1/2 a))
41.2b
(/.f64 (neg.f64 c) b)
44.0b
(/.f64 (-.f64 (hypot.f64 b (*.f64 (sqrt.f64 (*.f64 c -4)) (sqrt.f64 a))) b) (*.f64 a 2))
49.5b
(*.f64 (/.f64 (-.f64 (fma.f64 b b (*.f64 a (*.f64 c -4))) (*.f64 b b)) (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) (/.f64 1/2 a))
Compiler

Compiled 4458 to 2864 computations (35.8% saved)

regimes1.8s (24.5%)

Accuracy

Total 9.6b remaining (97.7%)

Threshold costs 0b (0%)

Counts
156 → 3
Compiler

Compiled 13468 to 9382 computations (30.3% saved)

bsearch91.0ms (1.2%)

Algorithm
binary-search
Calls

2 calls:

54.0ms
b
30.0ms
b
Steps
ItersPointRange
2.4043657819526966e-95
∈ [
6.495536785335216e-99
,
7.555548468790224e-94
]
-1.7835917271326807e+116
∈ [
-3.571763802003995e+116
,
-1.8834001322573645e+113
]
Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

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
02448
13846
24746
35346
45546
Stop Event
saturated

end144.0ms (1.9%)

Stop Event
fuel
Compiler

Compiled 279 to 189 computations (32.3% saved)

Profiling

Loading profile data...