Details

Time bar (total: 9.0s)

analyze618.0ms (6.9%)

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
18.7%76.5%4.8%7
28.1%66.3%5.6%8
34.7%55.4%9.9%9
36.1%51.1%12.8%10
42.1%42.4%15.5%11
47.5%33.8%18.7%12
48.8%30.7%20.6%13
51.8%25.6%22.5%14
Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.4s (27.2%)

Results
649.0ms1185×body2048valid
644.0ms5351×body128valid
291.0ms747×body1024valid
237.0ms420×body4096valid
132.0ms1106×body128invalid
108.0ms373×body512valid
41.0ms180×body256valid
Compiler

Compiled 50 to 32 computations (36% saved)

simplify88.0ms (1%)

Algorithm
egg-herbie
Rules
808×fma-neg_binary64
379×associate-/l*_binary64
361×div-sub_binary64
341×fma-def_binary64
224×times-frac_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01120
12318
23918
36918
410718
517818
627918
738218
854718
958718
1085518
11124718
12111718
13103518
14104318
15105118
16107718
17109318
18112918
19113118
20114318
21105018

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
34.4b
Counts
3 → 1
Alt Table
StatusErrorProgram
34.4b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
Compiler

Compiled 58 to 30 computations (48.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
0.4b
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))
1.5b
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
23.2b
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))

series461.0ms (5.1%)

Counts
4 → 96
Calls

4 calls:

281.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
100.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
69.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
10.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))

rewrite29.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt_binary64
41×*-un-lft-identity_binary64
31×add-cube-cbrt_binary64
20×sqrt-prod_binary64
19×prod-diff_binary64
Counts
4 → 120
Calls

4 calls:

8.0ms
(/.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) a)
7.0ms
(-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)
3.0ms
(sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))
3.0ms
(-.f64 (*.f64 b_2 b_2) (*.f64 a c))

simplify266.0ms (3%)

Algorithm
egg-herbie
Rules
682×fma-neg_binary64
364×cancel-sign-sub-inv_binary64
248×distribute-rgt-neg-in_binary64
220×distribute-lft-neg-in_binary64
172×distribute-rgt-in_binary64
Counts
216 → 237
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02725492
16834712
224844515
345214514
449154514
549904514
650004514
749994514
849324514

prune224.0ms (2.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New22710237
Fresh000
Picked101
Done000
Total22810238
Error
5.0b
Counts
238 → 10
Alt Table
StatusErrorProgram
32.0b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)) (cbrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a))) (cbrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)))
45.4b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
55.8b
(/.f64 (-.f64 b_2 b_2) a)
53.1b
(/.f64 (*.f64 (+.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 b_2)) (-.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 b_2))) a)
34.4b
(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
44.2b
(/.f64 (/.f64 (-.f64 (*.f64 b_2 b_2) (fma.f64 c a (*.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
39.6b
(*.f64 -1/2 (/.f64 c b_2))
31.5b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
40.5b
(/.f64 (/.f64 (-.f64 (pow.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) 3) (pow.f64 b_2 3)) (+.f64 (*.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (+.f64 (*.f64 b_2 b_2) (*.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2)))) a)
45.3b
(/.f64 (*.f64 -2 b_2) a)
Compiler

Compiled 5991 to 1696 computations (71.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
0.1b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
0.2b
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
12.0b
(sqrt.f64 (neg.f64 (*.f64 c a)))

series785.0ms (8.7%)

Counts
4 → 36
Calls

4 calls:

370.0ms
(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
254.0ms
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
142.0ms
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
19.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite37.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
138×times-frac_binary64
116×add-sqr-sqrt_binary64
115×*-un-lft-identity_binary64
81×add-cube-cbrt_binary64
26×associate-/r*_binary64
Counts
4 → 197
Calls

4 calls:

7.0ms
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
5.0ms
(/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
3.0ms
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
2.0ms
(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify194.0ms (2.2%)

Algorithm
egg-herbie
Rules
726×fma-def_binary64
384×cancel-sign-sub-inv_binary64
289×fma-neg_binary64
216×div-sub_binary64
164×distribute-neg-frac_binary64
Counts
233 → 300
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03157449
17196508
226046286
347446282
450146282

prune189.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2955300
Fresh549
Picked011
Done000
Total30010310
Error
0.2b
Counts
310 → 10
Alt Table
StatusErrorProgram
39.1b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
45.4b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
44.2b
(/.f64 (/.f64 (-.f64 (*.f64 b_2 b_2) (fma.f64 c a (*.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
39.6b
(*.f64 -1/2 (/.f64 c b_2))
53.1b
(/.f64 (*.f64 (+.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 b_2)) (-.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 b_2))) a)
31.5b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
47.1b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
45.9b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
31.5b
(*.f64 (/.f64 1 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
44.7b
(/.f64 1 (fma.f64 (/.f64 (*.f64 a (neg.f64 (*.f64 c a))) (pow.f64 b_2 3)) -1/8 (fma.f64 1/2 (/.f64 a b_2) (fma.f64 2 (/.f64 b_2 (neg.f64 c)) (*.f64 1/16 (/.f64 (*.f64 a (*.f64 (*.f64 c a) (*.f64 c a))) (pow.f64 b_2 5)))))))
Compiler

Compiled 8527 to 2459 computations (71.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)
0.2b
(*.f64 (/.f64 1 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
0.2b
(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
12.0b
(sqrt.f64 (neg.f64 (*.f64 c a)))

series319.0ms (3.6%)

Counts
2 → 26
Calls

2 calls:

212.0ms
(*.f64 (/.f64 1 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
107.0ms
(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)

rewrite44.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt_binary64
27×*-un-lft-identity_binary64
24×add-cube-cbrt_binary64
18×prod-diff_binary64
13×associate-*l*_binary64
Counts
2 → 79
Calls

2 calls:

37.0ms
(*.f64 (/.f64 1 a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2))
0.0ms
(hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)

simplify99.0ms (1.1%)

Algorithm
egg-herbie
Rules
676×fma-def_binary64
341×neg-mul-1_binary64
288×fma-neg_binary64
226×cancel-sign-sub-inv_binary64
201×distribute-rgt-in_binary64
Counts
105 → 153
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02382794
15622517
219412327
344732325
449952325

prune147.0ms (1.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2272229
Fresh088
Picked101
Done011
Total22811239
Error
0.1b
Counts
239 → 11
Alt Table
StatusErrorProgram
39.1b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
45.4b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
45.9b
(*.f64 (/.f64 1 a) (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2))
53.1b
(/.f64 (*.f64 (+.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 b_2)) (-.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 b_2))) a)
47.0b
(*.f64 (/.f64 1 a) (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2))
31.5b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
44.2b
(/.f64 (/.f64 (-.f64 (*.f64 b_2 b_2) (fma.f64 c a (*.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
39.6b
(*.f64 -1/2 (/.f64 c b_2))
47.1b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
45.9b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
44.7b
(/.f64 1 (fma.f64 (/.f64 (*.f64 a (neg.f64 (*.f64 c a))) (pow.f64 b_2 3)) -1/8 (fma.f64 1/2 (/.f64 a b_2) (fma.f64 2 (/.f64 b_2 (neg.f64 c)) (*.f64 1/16 (/.f64 (*.f64 a (*.f64 (*.f64 c a) (*.f64 c a))) (pow.f64 b_2 5)))))))
Compiler

Compiled 6380 to 2227 computations (65.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(*.f64 2 (/.f64 b_2 (neg.f64 c)))
0.0b
(fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c))))
0.7b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))

series55.0ms (0.6%)

Counts
3 → 96
Calls

3 calls:

30.0ms
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
18.0ms
(fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c))))
6.0ms
(*.f64 2 (/.f64 b_2 (neg.f64 c)))

rewrite21.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
40×times-frac_binary64
37×add-sqr-sqrt_binary64
34×associate-*r*_binary64
32×*-un-lft-identity_binary64
32×add-cube-cbrt_binary64
Counts
3 → 98
Calls

3 calls:

13.0ms
(*.f64 2 (/.f64 b_2 (neg.f64 c)))
2.0ms
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
0.0ms
(fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c))))

simplify106.0ms (1.2%)

Algorithm
egg-herbie
Rules
702×associate-/l*_binary64
621×associate-/r*_binary64
486×fma-def_binary64
240×associate-/l/_binary64
185×associate-/r/_binary64
Counts
194 → 161
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02053714
14893347
215603323
348153321
450753321

prune95.0ms (1.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1610161
Fresh099
Picked011
Done011
Total16111172
Error
0.1b
Counts
172 → 11
Alt Table
StatusErrorProgram
39.1b
(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (*.f64 2 (/.f64 b_2 (neg.f64 c)))))
45.4b
(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
45.9b
(*.f64 (/.f64 1 a) (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2))
53.1b
(/.f64 (*.f64 (+.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 b_2)) (-.f64 (sqrt.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (sqrt.f64 b_2))) a)
47.0b
(*.f64 (/.f64 1 a) (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2))
31.5b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
44.2b
(/.f64 (/.f64 (-.f64 (*.f64 b_2 b_2) (fma.f64 c a (*.f64 b_2 b_2))) (+.f64 b_2 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) a)
39.6b
(*.f64 -1/2 (/.f64 c b_2))
47.1b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)))
45.9b
(/.f64 1 (/.f64 a (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2)))
44.7b
(/.f64 1 (fma.f64 (/.f64 (*.f64 a (neg.f64 (*.f64 c a))) (pow.f64 b_2 3)) -1/8 (fma.f64 1/2 (/.f64 a b_2) (fma.f64 2 (/.f64 b_2 (neg.f64 c)) (*.f64 1/16 (/.f64 (*.f64 a (*.f64 (*.f64 c a) (*.f64 c a))) (pow.f64 b_2 5)))))))
Compiler

Compiled 3616 to 1897 computations (47.5% saved)

regimes2.5s (27.9%)

Accuracy

Total 9.8b remaining (98.7%)

Threshold costs 0b (0%)

Counts
149 → 3
Compiler

Compiled 13316 to 7426 computations (44.2% saved)

bsearch59.0ms (0.7%)

Steps
ItersRangePoint
5
2.7554873207805907e-78
1.0019616692019509e-77
4.879063262869388e-78
9
-2.577727491636072e+158
-9.756569196677351e+149
-3.4328189515268776e+153
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: 0 (0.0ms)

IterNodesCost
03056
14556
25756
36456
46756
56656

end155.0ms (1.7%)

Compiler

Compiled 301 to 193 computations (35.9% saved)

Profiling

Loading profile data...