Details

Time bar (total: 10.5s)

analyze1.2s (11.1%)

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)

sample157.0ms (1.5%)

Algorithm
intervals
Symmetry

(sort a1 a2)

Results
22.0ms42×body1024invalid
20.0ms43×body1024valid
18.0ms172×body128valid
8.0ms30×body512valid
8.0ms24×body512invalid
2.0ms22×body128invalid
2.0ms11×body256valid
1.0msbody256invalid
Compiler

Compiled 48 to 34 computations (29.2% saved)

simplify9.0ms (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

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.5b
(*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)))
0.5b
(+.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 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 a1 a1 (*.f64 a2 a2))
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))

series82.0ms (0.8%)

Counts
3 → 84
Calls

3 calls:

54.0ms
(*.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))
7.0ms
(fma.f64 a1 a1 (*.f64 a2 a2))

rewrite19.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt_binary64
38×times-frac_binary64
32×*-un-lft-identity_binary64
32×add-cube-cbrt_binary64
22×associate-*r*_binary64
Counts
3 → 95
Calls

3 calls:

9.0ms
(*.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))
0.0ms
(fma.f64 a1 a1 (*.f64 a2 a2))

simplify108.0ms (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
179 → 174
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01743607
13683275
212963231
343703231
451093231

prune176.0ms (1.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1677174
Fresh101
Picked101
Done000
Total1697176
Error
0b
Counts
176 → 7
Alt Table
StatusErrorProgram
0.6b
(*.f64 (cos.f64 th) (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))))
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))))
0.6b
(*.f64 (*.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
0.4b
(*.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))))
0.5b
(*.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th))
0.5b
(*.f64 (*.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (/.f64 1 (sqrt.f64 2)))
0.5b
(*.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
Compiler

Compiled 4063 to 1895 computations (53.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 a1 a1 (*.f64 a2 a2))
0.2b
(*.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))))
0.2b
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
0.3b
(/.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)))

series452.0ms (4.3%)

Counts
3 → 84
Calls

3 calls:

375.0ms
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
54.0ms
(*.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))))
22.0ms
(/.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)))

rewrite69.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
195×times-frac_binary64
110×add-sqr-sqrt_binary64
94×cbrt-prod_binary64
90×*-un-lft-identity_binary64
90×add-cube-cbrt_binary64
Counts
3 → 218
Calls

3 calls:

24.0ms
(*.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))))
10.0ms
(/.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)))
5.0ms
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

simplify260.0ms (2.5%)

Algorithm
egg-herbie
Rules
846×fma-neg_binary64
500×associate-/r/_binary64
260×fma-def_binary64
191×associate-/l*_binary64
181×associate-/l/_binary64
Counts
302 → 365
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03099806
16978974
225818924
345838924
453538924

prune403.0ms (3.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New3862388
Fresh246
Picked011
Done000
Total3887395
Error
0b
Counts
395 → 7
Alt Table
StatusErrorProgram
0.4b
(*.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 (*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (sqrt.f64 2)))
0.6b
(*.f64 (cos.f64 th) (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))))
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))))
0.6b
(*.f64 (*.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
0.5b
(*.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
0.4b
(*.f64 (cos.f64 th) (+.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
Compiler

Compiled 13315 to 8419 computations (36.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 a1 a1 (*.f64 a2 a2))
0.1b
(*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
0.2b
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
0.3b
(/.f64 (*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (sqrt.f64 2)))

series768.0ms (7.3%)

Counts
2 → 72
Calls

2 calls:

711.0ms
(*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))
56.0ms
(/.f64 (*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (sqrt.f64 2)))

rewrite82.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
25×add-exp-log_binary64
17×add-cbrt-cube_binary64
15×add-sqr-sqrt_binary64
13×times-frac_binary64
12×cbrt-prod_binary64
Counts
2 → 70
Calls

2 calls:

68.0ms
(/.f64 (*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (sqrt.f64 2)))
8.0ms
(*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))

simplify125.0ms (1.2%)

Algorithm
egg-herbie
Rules
841×fma-def_binary64
388×cancel-sign-sub-inv_binary64
345×fma-neg_binary64
216×unswap-sqr_binary64
164×associate-*r*_binary64
Counts
142 → 125
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02284520
15533551
223843446
347293434
449633434

prune206.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1901191
Fresh145
Picked011
Done011
Total1917198
Error
0b
Counts
198 → 7
Alt Table
StatusErrorProgram
0.4b
(*.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 (*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (sqrt.f64 2)))
0.6b
(*.f64 (cos.f64 th) (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))))
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))))
0.6b
(*.f64 (*.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
0.4b
(/.f64 (*.f64 (cos.f64 th) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 1/2))) (cbrt.f64 (sqrt.f64 2)))
0.5b
(*.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
Compiler

Compiled 5845 to 3702 computations (36.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 a1 a1 (*.f64 a2 a2))
0.1b
(*.f64 (cos.f64 th) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 1/2)))
0.3b
(/.f64 (*.f64 (cos.f64 th) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 1/2))) (cbrt.f64 (sqrt.f64 2)))
0.4b
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 1/2))

series478.0ms (4.6%)

Counts
3 → 96
Calls

3 calls:

415.0ms
(/.f64 (*.f64 (cos.f64 th) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 1/2))) (cbrt.f64 (sqrt.f64 2)))
45.0ms
(*.f64 (cos.f64 th) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 1/2)))
18.0ms
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 1/2))

rewrite26.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
19×add-exp-log_binary64
17×add-sqr-sqrt_binary64
16×cbrt-prod_binary64
13×*-un-lft-identity_binary64
13×add-cube-cbrt_binary64
Counts
3 → 81
Calls

3 calls:

12.0ms
(/.f64 (*.f64 (cos.f64 th) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 1/2))) (cbrt.f64 (sqrt.f64 2)))
5.0ms
(*.f64 (cos.f64 th) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 1/2)))
4.0ms
(*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 1/2))

simplify156.0ms (1.5%)

Algorithm
egg-herbie
Rules
603×fma-neg_binary64
565×cancel-sign-sub-inv_binary64
366×distribute-rgt-in_binary64
254×associate-*r*_binary64
247×associate-*l*_binary64
Counts
177 → 165
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02104659
15193989
221073943
344443935
449853935

prune195.0ms (1.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1871188
Fresh134
Picked011
Done112
Total1896195
Error
0b
Counts
195 → 6
Alt Table
StatusErrorProgram
0.6b
(*.f64 (*.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
0.4b
(*.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 (*.f64 (cos.f64 th) (*.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 1/2))) (cbrt.f64 (sqrt.f64 2)))
0.7b
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 (fabs.f64 (cbrt.f64 2)))) (*.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 (sqrt.f64 (cbrt.f64 2)))) (cbrt.f64 1/2)))
0.6b
(*.f64 (cos.f64 th) (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))))
0.5b
(*.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
Compiler

Compiled 4802 to 2842 computations (40.8% saved)

regimes2.0s (19.4%)

Accuracy

Total 0.4b remaining (83.8%)

Threshold costs 0.4b (83.8%)

Counts
205 → 1
Compiler

Compiled 36774 to 26877 computations (26.9% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01525
11725
21725

end8.0ms (0.1%)

Remove

(sort a1 a2)

Compiler

Compiled 57 to 42 computations (26.3% saved)

sample3.5s (33%)

Algorithm
intervals
Results
888.0ms1815×body1024valid
764.0ms1534×body1024invalid
492.0ms4815×body128valid
276.0ms917×body512valid
238.0ms765×body512invalid
89.0ms444×body256valid
72.0ms620×body128invalid
72.0ms368×body256invalid
8.0msbody2048valid
Compiler

Compiled 184 to 140 computations (23.9% saved)

Profiling

Loading profile data...