Details

Time bar (total: 9.4s)

analyze1.7s (18.6%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
0%99.8%0.2%10
0%99.8%0.2%11
0%99.8%0.2%12
0%99.8%0.2%13
0%99.8%0.2%14
Compiler

Compiled 20 to 12 computations (40% saved)

sample1.3s (14.3%)

Results
1.1s8256×body128valid
169.0ms250×body8192exit
33.0ms261×body128invalid
Compiler

Compiled 39 to 23 computations (41% saved)

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Rules
fma-def_binary64
+-commutative_binary64
*-commutative_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01218
11818
22218
32218

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
27.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
27.3b
(/.f64 (fma.f64 a c (*.f64 b d)) (fma.f64 c c (*.f64 d d)))
27.3b
(/.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d)))
Compiler

Compiled 104 to 54 computations (48.1% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 c c) (*.f64 d d))
0.5b
(+.f64 (*.f64 a c) (*.f64 b d))
26.9b
(/.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d)))

series99.0ms (1.1%)

Counts
3 → 120
Calls

3 calls:

83.0ms
(/.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d)))
9.0ms
(+.f64 (*.f64 a c) (*.f64 b d))
6.0ms
(+.f64 (*.f64 c c) (*.f64 d d))

rewrite22.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
11×add-cube-cbrt_binary64
times-frac_binary64
add-log-exp_binary64
Counts
3 → 61
Calls

3 calls:

12.0ms
(/.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d)))
3.0ms
(+.f64 (*.f64 c c) (*.f64 d d))
3.0ms
(+.f64 (*.f64 a c) (*.f64 b d))

simplify128.0ms (1.4%)

Algorithm
egg-herbie
Rules
498×associate-*l*_binary64
491×fma-def_binary64
421×associate-*r*_binary64
343×times-frac_binary64
328×fma-neg_binary64
Counts
181 → 136
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01323026
13822904
212512820
347512808
449752808
549682808

prune94.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1288136
Fresh101
Picked101
Done000
Total1308138
Error
0.0b
Counts
138 → 8
Alt Table
StatusErrorProgram
18.4b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (cbrt.f64 (fma.f64 d b (*.f64 c a)))) (hypot.f64 d c)) (/.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (hypot.f64 d c)))
38.4b
(-.f64 (+.f64 (/.f64 a c) (/.f64 (*.f64 d b) (pow.f64 c 2))) (+.f64 (/.f64 (*.f64 (pow.f64 d 3) b) (pow.f64 c 4)) (/.f64 (*.f64 a (pow.f64 d 2)) (pow.f64 c 3))))
17.8b
(*.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c)))
27.7b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (cbrt.f64 (fma.f64 d b (*.f64 c a)))) (/.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (fma.f64 d d (*.f64 c c))))
29.2b
(fma.f64 (/.f64 d c) (/.f64 b c) (/.f64 a c))
47.9b
(/.f64 (+.f64 (pow.f64 (*.f64 a c) 3) (pow.f64 (*.f64 b d) 3)) (*.f64 (+.f64 (*.f64 c c) (*.f64 d d)) (+.f64 (*.f64 (*.f64 a c) (*.f64 a c)) (-.f64 (*.f64 (*.f64 b d) (*.f64 b d)) (*.f64 (*.f64 a c) (*.f64 b d))))))
27.3b
(*.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (/.f64 1 (fma.f64 d d (*.f64 c c))))
35.6b
(fma.f64 (/.f64 c d) (/.f64 a d) (/.f64 b d))
Compiler

Compiled 3558 to 745 computations (79.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (hypot.f64 d c))
0.3b
(fma.f64 d b (*.f64 c a))
0.3b
(*.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c)))
16.6b
(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))

series242.0ms (2.6%)

Counts
4 → 168
Calls

4 calls:

115.0ms
(*.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c)))
98.0ms
(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
19.0ms
(/.f64 1 (hypot.f64 d c))
9.0ms
(fma.f64 d b (*.f64 c a))

rewrite31.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt_binary64
43×times-frac_binary64
36×*-un-lft-identity_binary64
34×add-cube-cbrt_binary64
32×add-exp-log_binary64
Counts
4 → 130
Calls

4 calls:

9.0ms
(*.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c)))
8.0ms
(/.f64 (fma.f64 d b (*.f64 c a)) (hypot.f64 d c))
2.0ms
(/.f64 1 (hypot.f64 d c))
0.0ms
(fma.f64 d b (*.f64 c a))

simplify162.0ms (1.7%)

Algorithm
egg-herbie
Rules
845×times-frac_binary64
428×fma-neg_binary64
410×fma-def_binary64
335×cancel-sign-sub-inv_binary64
274×distribute-rgt-in_binary64
Counts
298 → 286
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02336205
16315720
221255547
348415539
450795539

prune204.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2815286
Fresh437
Picked101
Done000
Total2868294
Error
0.0b
Counts
294 → 8
Alt Table
StatusErrorProgram
35.6b
(fma.f64 (/.f64 c d) (/.f64 a d) (/.f64 b d))
22.1b
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c)) (/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c))))
17.8b
(*.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 1 (/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a)))))
45.1b
(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 d c) b a)))
18.4b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 a c (*.f64 d b))) (/.f64 (cbrt.f64 (fma.f64 a c (*.f64 d b))) (hypot.f64 d c))) (/.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (hypot.f64 d c)))
18.0b
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (/.f64 (/.f64 (fma.f64 a c (*.f64 d b)) (hypot.f64 d c)) (sqrt.f64 (hypot.f64 d c))))
29.2b
(fma.f64 (/.f64 d c) (/.f64 b c) (/.f64 a c))
27.3b
(*.f64 (+.f64 (*.f64 a c) (*.f64 b d)) (/.f64 1 (fma.f64 d d (*.f64 c c))))
Compiler

Compiled 7417 to 2231 computations (69.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 1 (/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a))))
0.3b
(fma.f64 d b (*.f64 c a))
0.3b
(*.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 1 (/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a)))))
16.6b
(/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a)))

series288.0ms (3.1%)

Counts
3 → 144
Calls

3 calls:

114.0ms
(*.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 1 (/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a)))))
103.0ms
(/.f64 1 (/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a))))
71.0ms
(/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a)))

rewrite59.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
187×times-frac_binary64
142×add-sqr-sqrt_binary64
106×*-un-lft-identity_binary64
99×add-exp-log_binary64
95×add-cube-cbrt_binary64
Counts
3 → 230
Calls

3 calls:

20.0ms
(*.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 1 (/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a)))))
4.0ms
(/.f64 1 (/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a))))
2.0ms
(/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a)))

simplify219.0ms (2.3%)

Algorithm
egg-herbie
Rules
774×fma-def_binary64
309×fma-neg_binary64
283×associate-/l*_binary64
273×times-frac_binary64
264×sub-neg_binary64
Counts
374 → 452
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
032511693
194510154
236049911
350989911

prune312.0ms (3.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New4722474
Fresh257
Picked101
Done000
Total4757482
Error
0.0b
Counts
482 → 7
Alt Table
StatusErrorProgram
29.2b
(fma.f64 (/.f64 d c) (/.f64 b c) (/.f64 a c))
27.3b
(*.f64 (/.f64 1 (fma.f64 d d (*.f64 c c))) (fma.f64 d b (*.f64 c a)))
35.6b
(fma.f64 (/.f64 c d) (/.f64 a d) (/.f64 b d))
22.1b
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c)) (/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c))))
45.1b
(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 d c) b a)))
18.4b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 a c (*.f64 d b))) (/.f64 (cbrt.f64 (fma.f64 a c (*.f64 d b))) (hypot.f64 d c))) (/.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (hypot.f64 d c)))
17.9b
(/.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a))))
Compiler

Compiled 14616 to 4785 computations (67.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (hypot.f64 d c))
0.3b
(fma.f64 d b (*.f64 c a))
0.3b
(/.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a))))
16.6b
(/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a)))

series106.0ms (1.1%)

Counts
1 → 48
Calls

1 calls:

105.0ms
(/.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a))))

rewrite53.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
421×times-frac_binary64
197×*-un-lft-identity_binary64
197×add-sqr-sqrt_binary64
197×add-cube-cbrt_binary64
29×div-inv_binary64
Counts
1 → 221
Calls

1 calls:

8.0ms
(/.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a))))

simplify334.0ms (3.6%)

Algorithm
egg-herbie
Rules
565×associate-*r/_binary64
484×fma-def_binary64
428×*-commutative_binary64
397×distribute-rgt-in_binary64
248×associate-/l/_binary64
Counts
269 → 310
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
025112060
167111066
2201610235
3313710024
4497910024
5496810024

prune310.0ms (3.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New4940494
Fresh066
Picked011
Done000
Total4947501
Error
0.0b
Counts
501 → 7
Alt Table
StatusErrorProgram
29.2b
(fma.f64 (/.f64 d c) (/.f64 b c) (/.f64 a c))
27.3b
(*.f64 (/.f64 1 (fma.f64 d d (*.f64 c c))) (fma.f64 d b (*.f64 c a)))
35.6b
(fma.f64 (/.f64 c d) (/.f64 a d) (/.f64 b d))
22.1b
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 d c))) (hypot.f64 d c)) (/.f64 (fma.f64 d b (*.f64 c a)) (sqrt.f64 (hypot.f64 d c))))
45.1b
(*.f64 (/.f64 1 (hypot.f64 d c)) (neg.f64 (fma.f64 (/.f64 d c) b a)))
18.4b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 a c (*.f64 d b))) (/.f64 (cbrt.f64 (fma.f64 a c (*.f64 d b))) (hypot.f64 d c))) (/.f64 (cbrt.f64 (fma.f64 d b (*.f64 c a))) (hypot.f64 d c)))
17.9b
(/.f64 (/.f64 1 (hypot.f64 d c)) (/.f64 (hypot.f64 d c) (fma.f64 d b (*.f64 c a))))
Compiler

Compiled 16181 to 4953 computations (69.4% saved)

regimes3.3s (35.5%)

Accuracy

Total 10.2b remaining (97.9%)

Threshold costs 0b (0%)

Counts
219 → 5
Compiler

Compiled 25756 to 14049 computations (45.5% saved)

bsearch126.0ms (1.3%)

Steps
ItersRangePoint
10
2.703815564337194e+137
5.13643420591158e+149
3.6305850563522157e+137
9
1.12321756707486e-218
2.9635878340197967e-210
1.2661331500288663e-210
11
-4.639582689177046e-139
-1.179798966901837e-160
-9.690011489311247e-152
8
-1.7002869485250527e+173
-4.281030473688284e+170
-4.3216122432969205e+170
Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0.1%)

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

Useful iterations: 2 (0.0ms)

IterNodesCost
036111
145111
252109
360109
463109
564109
662109

end126.0ms (1.3%)

Compiler

Compiled 305 to 143 computations (53.1% saved)

Profiling

Loading profile data...