Details

Time bar (total: 11.3s)

analyze1.1s (9.6%)

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)

sample4.9s (43.4%)

Symmetry

(sort a1 a2)

Results
1.4s1825×body1024valid
1.2s1627×body1024invalid
920.0ms5077×body128valid
504.0ms921×body512valid
461.0ms858×body512invalid
146.0ms426×body256valid
144.0ms408×body256invalid
118.0ms636×body128invalid
7.0msbody2048valid
Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify14.0ms (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

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.4b
(*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)))
0.4b
(+.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
0.2b
(*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)))
0.4b
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series84.0ms (0.7%)

Counts
2 → 60
Calls

2 calls:

62.0ms
(*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)))
21.0ms
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite18.0ms (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:

8.0ms
(*.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))

simplify110.0ms (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

prune155.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1447151
Fresh011
Picked011
Done000
Total1449153
Error
0b
Counts
153 → 9
Alt Table
StatusErrorProgram
0.7b
(*.f64 (*.f64 (cos.f64 th) (/.f64 1 (sqrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
0.7b
(*.f64 (*.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) (*.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))))
0.4b
(*.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
1.2b
(*.f64 (cos.f64 th) (/.f64 (*.f64 (cbrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (cbrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))) (/.f64 (sqrt.f64 2) (cbrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))))))
0.7b
(*.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)))))
0.4b
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
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)))))
0.4b
(*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)))
0.5b
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)))))
Compiler

Compiled 3820 to 1798 computations (52.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series291.0ms (2.6%)

Counts
4 → 108
Calls

4 calls:

113.0ms
(*.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)))))
67.0ms
(/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
66.0ms
(*.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))))
45.0ms
(/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))

rewrite64.0ms (0.6%)

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:

22.0ms
(*.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))))
12.0ms
(*.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)))))
7.0ms
(/.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)))

simplify198.0ms (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

prune355.0ms (3.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New3081309
Fresh257
Picked011
Done011
Total3108318
Error
0b
Counts
318 → 8
Alt Table
StatusErrorProgram
0.7b
(*.f64 (*.f64 (cos.f64 th) (/.f64 1 (sqrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
0.7b
(*.f64 (*.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) (*.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))))
0.7b
(*.f64 (cos.f64 th) (*.f64 (/.f64 (sqrt.f64 (hypot.f64 a2 a1)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (/.f64 (sqrt.f64 (hypot.f64 a2 a1)) (cbrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))))
0.4b
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
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)))))
0.4b
(*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)))
0.4b
(*.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
0.5b
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)))))
Compiler

Compiled 10549 to 6907 computations (34.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
0.3b
(*.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
0.4b
(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2))
6.5b
(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

series301.0ms (2.7%)

Counts
4 → 120
Calls

4 calls:

232.0ms
(*.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
35.0ms
(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
21.0ms
(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2))
13.0ms
(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

rewrite35.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
81×sqrt-prod_binary64
72×times-frac_binary64
65×add-sqr-sqrt_binary64
60×*-un-lft-identity_binary64
60×add-cube-cbrt_binary64
Counts
4 → 162
Calls

4 calls:

11.0ms
(*.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
4.0ms
(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2))
3.0ms
(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
1.0ms
(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

simplify218.0ms (1.9%)

Algorithm
egg-herbie
Rules
621×fma-def_binary64
376×cancel-sign-sub-inv_binary64
345×associate-*l*_binary64
317×sub-neg_binary64
308×fma-neg_binary64
Counts
282 → 332
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03477564
19366108
233646008
347996003
449326003
550386003

prune301.0ms (2.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New3311332
Fresh145
Picked101
Done022
Total3337340
Error
0b
Counts
340 → 7
Alt Table
StatusErrorProgram
0.7b
(*.f64 (*.f64 (cos.f64 th) (/.f64 1 (sqrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))))
0.7b
(*.f64 (*.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) (*.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (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)))))
0.4b
(*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)))
0.5b
(*.f64 (cos.f64 th) (*.f64 (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)))))
0.7b
(*.f64 (cos.f64 th) (*.f64 (/.f64 (sqrt.f64 (hypot.f64 a2 a1)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (/.f64 (sqrt.f64 (hypot.f64 a2 a1)) (cbrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))))
0.3b
(*.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
Compiler

Compiled 9352 to 3959 computations (57.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)
0.2b
(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
0.3b
(*.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
6.6b
(sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2))

series127.0ms (1.1%)

Counts
3 → 84
Calls

3 calls:

94.0ms
(*.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
23.0ms
(sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2))
11.0ms
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)

rewrite19.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt_binary64
28×times-frac_binary64
26×*-un-lft-identity_binary64
26×sqrt-prod_binary64
26×add-cube-cbrt_binary64
Counts
3 → 90
Calls

3 calls:

7.0ms
(*.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
3.0ms
(sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2))
2.0ms
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)

simplify149.0ms (1.3%)

Algorithm
egg-herbie
Rules
767×times-frac_binary64
619×fma-neg_binary64
488×cancel-sign-sub-inv_binary64
293×associate-*r*_binary64
260×associate-*l*_binary64
Counts
174 → 211
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02935151
17524553
227413865
350003865
452833865

prune258.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New2772279
Fresh224
Picked101
Done022
Total2806286
Error
0b
Counts
286 → 6
Alt Table
StatusErrorProgram
0.5b
(*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
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)))))
0.7b
(*.f64 (*.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) (*.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))))
0.4b
(*.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 2 (hypot.f64 a2 a1)))))
0.4b
(*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)))
0.7b
(*.f64 (cos.f64 th) (*.f64 (/.f64 (sqrt.f64 (hypot.f64 a2 a1)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (/.f64 (sqrt.f64 (hypot.f64 a2 a1)) (cbrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))))
Compiler

Compiled 7728 to 3423 computations (55.7% saved)

regimes2.4s (21.6%)

Accuracy

Total 0.3b remaining (89%)

Threshold costs 0.3b (89%)

Counts
271 → 1
Compiler

Compiled 48425 to 32382 computations (33.1% 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
01626
12426
22826
33126
43226
53126

end124.0ms (1.1%)

Remove

(sort a1 a2)

Compiler

Compiled 214 to 139 computations (35% saved)

Profiling

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