Details

Time bar (total: 9.3s)

analyze674.0ms (7.3%)

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)

sample2.6s (27.6%)

Results
848.0ms5356×body128valid
598.0ms1127×body2048valid
315.0ms743×body1024valid
256.0ms402×body4096valid
247.0ms412×body512valid
143.0ms1061×body128invalid
48.0ms216×body256valid
Compiler

Compiled 62 to 44 computations (29% saved)

simplify256.0ms (2.8%)

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
33.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
33.5b
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
33.7b
(/.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)

localize9.0ms (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))
1.4b
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
23.1b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series180.0ms (1.9%)

Counts
3 → 60
Calls

3 calls:

82.0ms
(*.f64 (-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
58.0ms
(-.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
40.0ms
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

rewrite22.0ms (0.2%)

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)))

simplify126.0ms (1.4%)

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

prune172.0ms (1.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New19611207
Fresh101
Picked101
Done000
Total19811209
Error
7.9b
Counts
209 → 11
Alt Table
StatusErrorProgram
41.7b
(neg.f64 (/.f64 c b))
49.7b
(exp.f64 (log.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))))
36.0b
(*.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
44.2b
(*.f64 (*.f64 -2 b) (/.f64 1/2 a))
34.4b
(*.f64 (-.f64 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) b) (/.f64 1/2 a))
35.0b
(/.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))
44.2b
(-.f64 (/.f64 c b) (/.f64 b a))
44.2b
(/.f64 (neg.f64 b) a)
57.1b
(*.f64 (-.f64 b b) (/.f64 1/2 a))
42.2b
(/.f64 (*.f64 1/2 (+.f64 (*.f64 a (*.f64 c -4)) 0)) (*.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
45.9b
(*.f64 1/2 (/.f64 (sqrt.f64 (*.f64 a (*.f64 c -4))) a))
Compiler

Compiled 5902 to 3450 computations (41.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (-.f64 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) b) (/.f64 1/2 a))
0.5b
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))
12.8b
(-.f64 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) b)
23.1b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series475.0ms (5.1%)

Counts
3 → 60
Calls

3 calls:

350.0ms
(*.f64 (-.f64 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) b) (/.f64 1/2 a))
80.0ms
(-.f64 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) b)
44.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))

rewrite57.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt_binary64
74×sqrt-prod_binary64
32×sqrt-pow1_binary64
28×pow1_binary64
25×*-un-lft-identity_binary64
Counts
3 → 145
Calls

3 calls:

23.0ms
(*.f64 (-.f64 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) b) (/.f64 1/2 a))
8.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))
8.0ms
(-.f64 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) b)

simplify151.0ms (1.6%)

Algorithm
egg-herbie
Rules
569×fma-neg_binary64
335×distribute-rgt-in_binary64
261×cancel-sign-sub-inv_binary64
182×associate-*r*_binary64
182×associate-*l*_binary64
Counts
205 → 248
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02895142
17164775
226984534
347314534
448714534

prune310.0ms (3.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New3360336
Fresh01010
Picked011
Done000
Total33611347
Error
7.9b
Counts
347 → 11
Alt Table
StatusErrorProgram
41.7b
(neg.f64 (/.f64 c b))
49.7b
(exp.f64 (log.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))))
36.0b
(*.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
44.2b
(*.f64 (*.f64 -2 b) (/.f64 1/2 a))
34.4b
(*.f64 (-.f64 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) b) (/.f64 1/2 a))
35.0b
(/.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))
44.2b
(-.f64 (/.f64 c b) (/.f64 b a))
44.2b
(/.f64 (neg.f64 b) a)
57.1b
(*.f64 (-.f64 b b) (/.f64 1/2 a))
42.2b
(/.f64 (*.f64 1/2 (+.f64 (*.f64 a (*.f64 c -4)) 0)) (*.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
45.9b
(*.f64 1/2 (/.f64 (sqrt.f64 (*.f64 a (*.f64 c -4))) a))
Compiler

Compiled 11700 to 7056 computations (39.7% saved)

localize37.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(/.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))
1.1b
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
16.0b
(*.f64 (+.f64 (*.f64 a (*.f64 c -4)) 0) (/.f64 1/2 a))
23.1b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series383.0ms (4.1%)

Counts
3 → 64
Calls

3 calls:

330.0ms
(/.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))
50.0ms
(+.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))

rewrite31.0ms (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))
10.0ms
(*.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)

simplify135.0ms (1.5%)

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

prune194.0ms (2.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2373240
Fresh279
Picked101
Done011
Total24011251
Error
7.9b
Counts
251 → 11
Alt Table
StatusErrorProgram
36.6b
(*.f64 (/.f64 (+.f64 (*.f64 a (*.f64 c -4)) 0) (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)) (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)))) (/.f64 (/.f64 1/2 a) (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))))
32.7b
(/.f64 (*.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
34.4b
(*.f64 (-.f64 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) b) (/.f64 1/2 a))
37.5b
(/.f64 (*.f64 (*.f64 a (*.f64 (*.f64 c -4) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
44.2b
(-.f64 (/.f64 c b) (/.f64 b a))
41.7b
(neg.f64 (/.f64 c b))
49.7b
(exp.f64 (log.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))))
36.0b
(*.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
44.2b
(*.f64 (*.f64 -2 b) (/.f64 1/2 a))
44.2b
(/.f64 (neg.f64 b) a)
42.2b
(/.f64 (*.f64 1/2 (+.f64 (*.f64 a (*.f64 c -4)) 0)) (*.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
Compiler

Compiled 8213 to 5194 computations (36.8% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.4b
(/.f64 (*.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
1.1b
(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)
23.1b
(sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))

series255.0ms (2.8%)

Counts
1 → 20
Calls

1 calls:

255.0ms
(/.f64 (*.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))

rewrite9.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
associate-/r*_binary64
times-frac_binary64
Counts
1 → 27
Calls

1 calls:

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

simplify64.0ms (0.7%)

Algorithm
egg-herbie
Rules
769×times-frac_binary64
615×associate-/l*_binary64
357×associate-/r*_binary64
352×fma-neg_binary64
235×fma-def_binary64
Counts
47 → 67
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01271488
13661333
211801254
348441254
450781254

prune150.0ms (1.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1601161
Fresh189
Picked011
Done011
Total16111172
Error
7.9b
Counts
172 → 11
Alt Table
StatusErrorProgram
32.7b
(/.f64 (*.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
34.4b
(*.f64 (-.f64 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) b) (/.f64 1/2 a))
37.5b
(/.f64 (*.f64 (*.f64 a (*.f64 (*.f64 c -4) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a))))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a))) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))
44.2b
(-.f64 (/.f64 c b) (/.f64 b a))
41.7b
(neg.f64 (/.f64 c b))
49.7b
(exp.f64 (log.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (/.f64 1/2 a))))
36.0b
(*.f64 (*.f64 (-.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))) b) (/.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (*.f64 (cbrt.f64 a) (cbrt.f64 a)))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 a)))
44.2b
(*.f64 (*.f64 -2 b) (/.f64 1/2 a))
44.2b
(/.f64 (neg.f64 b) a)
33.1b
(/.f64 (/.f64 (*.f64 -2 c) (*.f64 (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)) (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)))) (cbrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)))
42.2b
(/.f64 (*.f64 1/2 (+.f64 (*.f64 a (*.f64 c -4)) 0)) (*.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))
Compiler

Compiled 4298 to 2596 computations (39.6% saved)

regimes2.7s (29.3%)

Accuracy

Total 1.1b remaining (16.3%)

Threshold costs 0b (0%)

Counts
185 → 4
Compiler

Compiled 18796 to 12906 computations (31.3% saved)

bsearch103.0ms (1.1%)

Steps
ItersRangePoint
6
4.304271055690811e+116
1.95276327175828e+117
1.2519627697101639e+117
10
-2.0173403581532023e-244
-4.546614556968612e-259
-1.1866595270317575e-257
1
-3.5130526354900675e+110
-3.4815467862880304e+102
-3.4155395926676587e+106
Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03178
14578
25678
36378
46678
56678

end168.0ms (1.8%)

Compiler

Compiled 352 to 228 computations (35.2% saved)

Profiling

Loading profile data...