Details

Time bar (total: 9.4s)

analyze1.2s (12.6%)

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)

sample128.0ms (1.4%)

Algorithm
intervals
Results
29.0ms62×body1024invalid
27.0ms59×body1024valid
16.0ms152×body128valid
10.0ms37×body512invalid
10.0ms34×body512valid
6.0ms11×body256valid
3.0ms17×body256invalid
1.0ms12×body128invalid
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

prune4.0ms (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)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
0.3b
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1))
0.3b
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2))
0.7b
(/.f64 (cos.f64 th) (sqrt.f64 2))

series135.0ms (1.4%)

Counts
4 → 88
Calls

4 calls:

73.0ms
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
26.0ms
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1))
25.0ms
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2))
11.0ms
(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite38.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
58×times-frac_binary64
55×add-sqr-sqrt_binary64
45×*-un-lft-identity_binary64
45×add-cube-cbrt_binary64
44×associate-*l*_binary64
Counts
4 → 151
Calls

4 calls:

9.0ms
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2))
8.0ms
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
8.0ms
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1))
3.0ms
(/.f64 (cos.f64 th) (sqrt.f64 2))

simplify147.0ms (1.6%)

Algorithm
egg-herbie
Rules
652×fma-def_binary64
381×fma-neg_binary64
215×associate-*r*_binary64
196×*-commutative_binary64
194×associate-/r/_binary64
Counts
239 → 248
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02614527
17044412
222934278
348404278
450194278

prune418.0ms (4.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2918299
Fresh011
Picked101
Done000
Total2929301
Error
0b
Counts
301 → 9
Alt Table
StatusErrorProgram
0.5b
(+.f64 (*.f64 (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (*.f64 (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))) (*.f64 a1 a1))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
19.7b
(+.f64 (cbrt.f64 (*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) (pow.f64 a1 6))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
0.4b
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1)))) 2)
0.5b
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2) a2))
0.4b
(*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)))
0.5b
(+.f64 (*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
0.4b
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) (*.f64 a2 a2)))
0.6b
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (*.f64 a1 a1))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))
0.6b
(+.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 (sqrt.f64 2))) (*.f64 a2 a2))))
Compiler

Compiled 8932 to 4976 computations (44.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series125.0ms (1.3%)

Counts
4 → 112
Calls

4 calls:

56.0ms
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1)))) 2)
41.0ms
(*.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
26.0ms
(*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1)))
2.0ms
(cos.f64 th)

rewrite19.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube_binary64
20×add-exp-log_binary64
12×add-sqr-sqrt_binary64
11×pow1_binary64
10×*-un-lft-identity_binary64
Counts
4 → 83
Calls

4 calls:

6.0ms
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1)))) 2)
5.0ms
(*.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
3.0ms
(*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1)))
1.0ms
(cos.f64 th)

simplify152.0ms (1.6%)

Algorithm
egg-herbie
Rules
810×cancel-sign-sub-inv_binary64
531×fma-neg_binary64
313×associate-*r*_binary64
237×associate-*l*_binary64
222×fma-def_binary64
Counts
195 → 178
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02404283
16243788
226063691
343553689
449813689
549653689

prune174.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1726178
Fresh718
Picked101
Done000
Total1807187
Error
0b
Counts
187 → 7
Alt Table
StatusErrorProgram
0.4b
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (cos.f64 th) (hypot.f64 a1 a2)) (sqrt.f64 (fma.f64 a2 a2 (*.f64 a1 a1))))) 2)
0.4b
(/.f64 (*.f64 (cos.f64 th) (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 2))) 2)
0.4b
(*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)))
0.5b
(/.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))) 2)
0.4b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))) 2)
0.5b
(/.f64 (sqrt.f64 2) (/.f64 2 (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1)))))
0.5b
(/.f64 1 (/.f64 2 (*.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))))
Compiler

Compiled 4361 to 2300 computations (47.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series458.0ms (4.9%)

Counts
3 → 108
Calls

3 calls:

358.0ms
(*.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
56.0ms
(/.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))) 2)
44.0ms
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1)))))

rewrite45.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
58×add-exp-log_binary64
36×add-cbrt-cube_binary64
33×cbrt-unprod_binary64
33×prod-exp_binary64
29×pow1_binary64
Counts
3 → 101
Calls

3 calls:

13.0ms
(/.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))) 2)
11.0ms
(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1)))))
8.0ms
(*.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))

simplify129.0ms (1.4%)

Algorithm
egg-herbie
Rules
864×cancel-sign-sub-inv_binary64
487×associate-*r*_binary64
413×associate-*l*_binary64
401×unswap-sqr_binary64
314×fma-neg_binary64
Counts
209 → 184
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02925843
17384870
233154856
357614856

prune235.0ms (2.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2350235
Fresh066
Picked011
Done000
Total2357242
Error
0b
Counts
242 → 7
Alt Table
StatusErrorProgram
0.4b
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (cos.f64 th) (hypot.f64 a1 a2)) (sqrt.f64 (fma.f64 a2 a2 (*.f64 a1 a1))))) 2)
0.4b
(/.f64 (*.f64 (cos.f64 th) (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 2))) 2)
0.4b
(*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)))
0.5b
(/.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))) 2)
0.4b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))) 2)
0.5b
(/.f64 (sqrt.f64 2) (/.f64 2 (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1)))))
0.5b
(/.f64 1 (/.f64 2 (*.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))))
Compiler

Compiled 7825 to 4938 computations (36.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (cos.f64 th) (hypot.f64 a1 a2))
0.2b
(*.f64 (*.f64 (cos.f64 th) (hypot.f64 a1 a2)) (sqrt.f64 (fma.f64 a2 a2 (*.f64 a1 a1))))
0.3b
(*.f64 (sqrt.f64 2) (*.f64 (*.f64 (cos.f64 th) (hypot.f64 a1 a2)) (sqrt.f64 (fma.f64 a2 a2 (*.f64 a1 a1)))))
7.1b
(sqrt.f64 (fma.f64 a2 a2 (*.f64 a1 a1)))

series396.0ms (4.2%)

Counts
4 → 132
Calls

4 calls:

181.0ms
(*.f64 (sqrt.f64 2) (*.f64 (*.f64 (cos.f64 th) (hypot.f64 a1 a2)) (sqrt.f64 (fma.f64 a2 a2 (*.f64 a1 a1)))))
124.0ms
(*.f64 (*.f64 (cos.f64 th) (hypot.f64 a1 a2)) (sqrt.f64 (fma.f64 a2 a2 (*.f64 a1 a1))))
78.0ms
(*.f64 (cos.f64 th) (hypot.f64 a1 a2))
12.0ms
(sqrt.f64 (fma.f64 a2 a2 (*.f64 a1 a1)))

rewrite21.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
21×pow1_binary64
20×add-cbrt-cube_binary64
20×add-exp-log_binary64
14×add-sqr-sqrt_binary64
11×*-un-lft-identity_binary64
Counts
4 → 85
Calls

4 calls:

7.0ms
(*.f64 (sqrt.f64 2) (*.f64 (*.f64 (cos.f64 th) (hypot.f64 a1 a2)) (sqrt.f64 (fma.f64 a2 a2 (*.f64 a1 a1)))))
5.0ms
(*.f64 (*.f64 (cos.f64 th) (hypot.f64 a1 a2)) (sqrt.f64 (fma.f64 a2 a2 (*.f64 a1 a1))))
3.0ms
(*.f64 (cos.f64 th) (hypot.f64 a1 a2))
1.0ms
(sqrt.f64 (fma.f64 a2 a2 (*.f64 a1 a1)))

simplify109.0ms (1.2%)

Algorithm
egg-herbie
Rules
746×cancel-sign-sub-inv_binary64
600×times-frac_binary64
373×associate-*r*_binary64
340×associate-*l*_binary64
301×fma-neg_binary64
Counts
217 → 221
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02754825
17863943
227913938
350623938

prune170.0ms (1.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2210221
Fresh055
Picked011
Done011
Total2217228
Error
0b
Counts
228 → 7
Alt Table
StatusErrorProgram
0.4b
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (cos.f64 th) (hypot.f64 a1 a2)) (sqrt.f64 (fma.f64 a2 a2 (*.f64 a1 a1))))) 2)
0.4b
(/.f64 (*.f64 (cos.f64 th) (*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 2))) 2)
0.4b
(*.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)))
0.5b
(/.f64 (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))) 2)
0.4b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))) 2)
0.5b
(/.f64 (sqrt.f64 2) (/.f64 2 (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1)))))
0.5b
(/.f64 1 (/.f64 2 (*.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))))
Compiler

Compiled 6290 to 2919 computations (53.6% saved)

regimes1.9s (20.5%)

Accuracy

Total 0.4b remaining (90.8%)

Threshold costs 0.4b (90.8%)

Counts
199 → 1
Compiler

Compiled 41005 to 29600 computations (27.8% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
*-lft-identity_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01421
11921
21821

end7.0ms (0.1%)

Remove

(sort a1 a2)

Compiler

Compiled 51 to 36 computations (29.4% saved)

sample3.3s (35.4%)

Algorithm
intervals
Results
841.0ms1735×body1024valid
728.0ms1541×body1024invalid
483.0ms4912×body128valid
273.0ms894×body512valid
246.0ms815×body512invalid
90.0ms451×body256valid
70.0ms357×body256invalid
64.0ms614×body128invalid
7.0msbody2048valid
Compiler

Compiled 182 to 135 computations (25.8% saved)

Profiling

Loading profile data...