Details

Time bar (total: 10.6s)

analyze1.1s (10.2%)

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
0%99.9%0.1%5
25%74.9%0.1%6
25%74.9%0.1%7
25%74.9%0.1%8
25%74.9%0.1%9
25%64%11.1%10
31.2%54.6%14.2%11
39%44.1%16.9%12
39%41.5%19.5%13
42.9%37%20.1%14
Compiler

Compiled 23 to 16 computations (30.4% saved)

sample137.0ms (1.3%)

Algorithm
intervals
Symmetry

(sort a1 a2)

Results
29.0ms58×body1024valid
27.0ms44×body1024invalid
18.0ms160×body128valid
8.0ms26×body512valid
3.0ms11×body512invalid
3.0ms15×body256invalid
2.0ms12×body256valid
1.0ms11×body128invalid
Compiler

Compiled 48 to 34 computations (29.2% saved)

simplify10.0ms (0.1%)

Algorithm
egg-herbie
Rules
32×fma-def_binary64
23×*-commutative_binary64
20×associate-/l*_binary64
11×associate-/r/_binary64
associate-*r/_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01320
12718
25318
37618
410318
511718
613218
713418
813618
913618

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.7b
(*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)))
0.7b
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
Compiler

Compiled 108 to 70 computations (35.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)))
0.6b
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series84.0ms (0.8%)

Counts
2 → 60
Calls

2 calls:

61.0ms
(*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)))
23.0ms
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite19.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt_binary64
38×times-frac_binary64
31×*-un-lft-identity_binary64
31×add-cube-cbrt_binary64
22×associate-*r*_binary64
Counts
2 → 85
Calls

2 calls:

7.0ms
(*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)))
3.0ms
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

simplify105.0ms (1%)

Algorithm
egg-herbie
Rules
456×associate-*l*_binary64
410×associate-*r*_binary64
396×fma-neg_binary64
332×associate-/l*_binary64
299×sub-neg_binary64
Counts
145 → 151
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01703315
13653012
212892968
343592968
450762968

prune156.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1447151
Fresh011
Picked101
Done000
Total1458153
Error
0.0b
Counts
153 → 8
Alt Table
StatusErrorProgram
0.7b
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
0.8b
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
1.5b
(*.f64 (cos.f64 th) (*.f64 (/.f64 (*.f64 (cbrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (cbrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 (sqrt.f64 2))) (/.f64 (cbrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2)))))
0.9b
(*.f64 (cos.f64 th) (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))))
0.5b
(*.f64 (cos.f64 th) (*.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
0.6b
(*.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
0.6b
(*.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
0.4b
(*.f64 (cos.f64 th) (*.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
Compiler

Compiled 3789 to 1798 computations (52.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (cos.f64 th) (*.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
0.1b
(/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
0.2b
(/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))
0.3b
(*.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))

series302.0ms (2.8%)

Counts
4 → 108
Calls

4 calls:

119.0ms
(*.f64 (cos.f64 th) (*.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
69.0ms
(/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
68.0ms
(*.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))
44.0ms
(/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))

rewrite123.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt_binary64
70×times-frac_binary64
61×add-exp-log_binary64
50×*-un-lft-identity_binary64
50×add-cube-cbrt_binary64
Counts
4 → 181
Calls

4 calls:

72.0ms
(*.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))
15.0ms
(*.f64 (cos.f64 th) (*.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
5.0ms
(/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
3.0ms
(/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))

simplify187.0ms (1.8%)

Algorithm
egg-herbie
Rules
517×cancel-sign-sub-inv_binary64
363×fma-neg_binary64
266×associate-*r*_binary64
250×associate-*l*_binary64
250×associate-*r/_binary64
Counts
289 → 309
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03479877
19387509
236177422
350797422

prune353.0ms (3.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New3081309
Fresh077
Picked011
Done000
Total3089317
Error
0b
Counts
317 → 9
Alt Table
StatusErrorProgram
0.9b
(*.f64 (cos.f64 th) (*.f64 (/.f64 1 (cbrt.f64 (sqrt.f64 2))) (*.f64 (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))))
0.5b
(*.f64 (cos.f64 th) (*.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
0.7b
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
0.8b
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
1.5b
(*.f64 (cos.f64 th) (*.f64 (/.f64 (*.f64 (cbrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (cbrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))) (sqrt.f64 (sqrt.f64 2))) (/.f64 (cbrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2)))))
0.9b
(*.f64 (cos.f64 th) (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))))
0.6b
(*.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
0.6b
(*.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
0.4b
(*.f64 (cos.f64 th) (*.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
Compiler

Compiled 10618 to 6967 computations (34.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (cos.f64 th) (*.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
0.2b
(*.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
0.5b
(/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))

series210.0ms (2%)

Counts
3 → 84
Calls

3 calls:

120.0ms
(*.f64 (cos.f64 th) (*.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
68.0ms
(*.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
22.0ms
(/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))

rewrite26.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt_binary64
38×times-frac_binary64
33×*-un-lft-identity_binary64
33×add-cube-cbrt_binary64
23×associate-*r*_binary64
Counts
3 → 110
Calls

3 calls:

9.0ms
(*.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
6.0ms
(*.f64 (cos.f64 th) (*.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))))
3.0ms
(/.f64 (hypot.f64 a2 a1) (sqrt.f64 2))

simplify99.0ms (0.9%)

Algorithm
egg-herbie
Rules
731×associate-/l*_binary64
669×times-frac_binary64
233×fma-def_binary64
218×associate-/l/_binary64
166×associate-*r*_binary64
Counts
194 → 177
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02414340
15864018
220163928
350923928

prune163.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1752177
Fresh347
Picked101
Done011
Total1797186
Error
0b
Counts
186 → 7
Alt Table
StatusErrorProgram
0.7b
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
0.8b
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
0.6b
(*.f64 (cos.f64 th) (*.f64 (*.f64 (hypot.f64 a2 a1) (sqrt.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))) (sqrt.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))))
0.5b
(*.f64 (cos.f64 th) (*.f64 (hypot.f64 a2 a1) (/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))))
0.6b
(*.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
0.6b
(*.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
0.4b
(*.f64 (cos.f64 th) (*.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
Compiler

Compiled 4435 to 2403 computations (45.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (cos.f64 th) (*.f64 (hypot.f64 a2 a1) (/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))))
0.2b
(*.f64 (hypot.f64 a2 a1) (/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
0.3b
(/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))
0.3b
(/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

series238.0ms (2.2%)

Counts
4 → 108
Calls

4 calls:

114.0ms
(*.f64 (cos.f64 th) (*.f64 (hypot.f64 a2 a1) (/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))))
69.0ms
(*.f64 (hypot.f64 a2 a1) (/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
29.0ms
(/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))
25.0ms
(/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

rewrite235.0ms (2.2%)

Algorithm
rewrite-expression-head
Rules
1137×sqrt-prod_binary64
1119×times-frac_binary64
626×add-sqr-sqrt_binary64
579×*-un-lft-identity_binary64
579×add-cube-cbrt_binary64
Counts
4 → 734
Calls

4 calls:

56.0ms
(*.f64 (hypot.f64 a2 a1) (/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
22.0ms
(*.f64 (cos.f64 th) (*.f64 (hypot.f64 a2 a1) (/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))))
15.0ms
(/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
4.0ms
(/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))

simplify619.0ms (5.8%)

Algorithm
egg-herbie
Rules
478×fma-def_binary64
435×associate-/l/_binary64
383×associate-/l*_binary64
304×associate-*r*_binary64
299×associate-*l*_binary64
Counts
842 → 781
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
058326485
1143524343
2474024247
3525624247

prune797.0ms (7.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New7783781
Fresh415
Picked011
Done011
Total7826788
Error
0b
Counts
788 → 6
Alt Table
StatusErrorProgram
0.7b
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2) (/.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 2)))
0.6b
(*.f64 (cos.f64 th) (*.f64 (*.f64 (hypot.f64 a2 a1) (sqrt.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))) (sqrt.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))))
0.6b
(*.f64 (cos.f64 th) (*.f64 (*.f64 (hypot.f64 a2 a1) (hypot.f64 a2 a1)) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))))
0.5b
(*.f64 (cos.f64 th) (*.f64 (hypot.f64 a2 a1) (/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))))
0.4b
(*.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
0.4b
(*.f64 (cos.f64 th) (*.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
Compiler

Compiled 25750 to 16323 computations (36.6% saved)

regimes2.1s (19.5%)

Accuracy

Total 0.4b remaining (93.7%)

Threshold costs 0.4b (93.7%)

Counts
226 → 1
Compiler

Compiled 40041 to 27112 computations (32.3% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01436
11636
21636

end7.0ms (0.1%)

Remove

(sort a1 a2)

Compiler

Compiled 75 to 57 computations (24% saved)

sample3.5s (33.4%)

Algorithm
intervals
Results
943.0ms1818×body1024valid
795.0ms1553×body1024invalid
487.0ms4823×body128valid
266.0ms908×body512valid
227.0ms747×body512invalid
99.0ms447×body256valid
88.0ms393×body256invalid
73.0ms616×body128invalid
4.0msbody2048valid
Compiler

Compiled 187 to 134 computations (28.3% saved)

Profiling

Loading profile data...