Details

Time bar (total: 10.6s)

analyze1.3s (11.8%)

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)

sample115.0ms (1.1%)

Algorithm
intervals
Results
33.0ms65×body1024valid
23.0ms46×body1024invalid
15.0ms158×body128valid
6.0ms21×body512invalid
5.0ms19×body512valid
3.0ms14×body256valid
2.0ms12×body256invalid
2.0ms17×body128invalid
Compiler

Compiled 48 to 34 computations (29.2% saved)

simplify14.0ms (0.1%)

Algorithm
egg-herbie
Rules
23×*-commutative_binary64
20×associate-/l*_binary64
11×associate-/r/_binary64
associate-*r/_binary64
distribute-rgt-out_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01320
12620
24620
36620
48520
59720
610820
710620
810620

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.4b
Counts
2 → 2
Alt Table
StatusErrorProgram
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)))
0.4b
(*.f64 (cos.f64 th) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
Compiler

Compiled 92 to 63 computations (31.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (*.f64 a1 a1) (*.f64 a2 a2))
0.0b
(cos.f64 th)
0.1b
(*.f64 (cos.f64 th) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.4b
(/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2))

rewrite117.0ms (1.1%)

Algorithm
rewrite-expression-head
Error
0b
Rules
41×add-sqr-sqrt_binary64
38×times-frac_binary64
33×*-un-lft-identity_binary64
33×add-cube-cbrt_binary64
22×associate-*r*_binary64
Counts
4 → 101
Calls

4 calls:

9.0ms
(*.f64 (cos.f64 th) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
5.0ms
(/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2))
3.0ms
(+.f64 (*.f64 a1 a1) (*.f64 a2 a2))
1.0ms
(cos.f64 th)
Compiler

Compiled 2219 to 800 computations (63.9% saved)

series136.0ms (1.3%)

Error
0.3b
Counts
4 → 44
Calls

4 calls:

66.0ms
(*.f64 (cos.f64 th) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
32.0ms
(/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2))
19.0ms
(+.f64 (*.f64 a1 a1) (*.f64 a2 a2))
6.0ms
(cos.f64 th)
Compiler

Compiled 1419 to 1124 computations (20.8% saved)

simplify140.0ms (1.3%)

Algorithm
egg-herbie
Rules
508×associate-*l*_binary64
432×associate-*r*_binary64
343×unswap-sqr_binary64
313×cancel-sign-sub-inv_binary64
275×associate-/l*_binary64
Counts
145 → 126
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01523107
13772864
212242858
336022858
446392858
549692858

prune86.0ms (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1206126
Fresh101
Picked101
Done000
Total1226128
Error
0b
Counts
128 → 6
Alt Table
StatusErrorProgram
0.4b
(*.f64 (cos.f64 th) (*.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))))
0.4b
(*.f64 (*.f64 (cos.f64 th) (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
0.4b
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
0.5b
(*.f64 (cos.f64 th) (*.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2)))))
0.5b
(*.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
0.5b
(*.f64 (/.f64 (cos.f64 th) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
Compiler

Compiled 1914 to 819 computations (57.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
0.3b
(*.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
7.7b
(sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
7.7b
(sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))

rewrite262.0ms (2.5%)

Algorithm
rewrite-expression-head
Error
0b
Rules
149×add-sqr-sqrt_binary64
146×times-frac_binary64
127×sqrt-prod_binary64
90×cbrt-prod_binary64
87×*-un-lft-identity_binary64
Counts
4 → 226
Calls

4 calls:

29.0ms
(*.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
7.0ms
(/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
3.0ms
(sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
Compiler

Compiled 8394 to 3621 computations (56.9% saved)

series176.0ms (1.7%)

Error
0b
Counts
4 → 48
Calls

4 calls:

57.0ms
(/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
34.0ms
(*.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
29.0ms
(sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
28.0ms
(sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
Compiler

Compiled 3463 to 2660 computations (23.2% saved)

simplify286.0ms (2.7%)

Algorithm
egg-herbie
Rules
749×times-frac_binary64
379×associate-/r*_binary64
201×associate-*r/_binary64
199×associate-*l/_binary64
179×associate-/r/_binary64
Counts
274 → 252
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
024310532
16339576
222499112
346508892
450268892

prune148.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2520252
Fresh055
Picked011
Done000
Total2526258
Error
0b
Counts
258 → 6
Alt Table
StatusErrorProgram
0.4b
(*.f64 (cos.f64 th) (*.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))))
0.4b
(*.f64 (*.f64 (cos.f64 th) (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
0.4b
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
0.5b
(*.f64 (cos.f64 th) (*.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2)))))
0.5b
(*.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
0.5b
(*.f64 (/.f64 (cos.f64 th) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
Compiler

Compiled 5912 to 2798 computations (52.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (*.f64 (cos.f64 th) (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
0.4b
(/.f64 (sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2))
7.7b
(sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))
7.7b
(sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))

rewrite158.0ms (1.5%)

Algorithm
rewrite-expression-head
Error
0b
Rules
84×sqrt-prod_binary64
72×times-frac_binary64
63×add-sqr-sqrt_binary64
59×*-un-lft-identity_binary64
59×add-cube-cbrt_binary64
Counts
4 → 158
Calls

4 calls:

16.0ms
(*.f64 (*.f64 (cos.f64 th) (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
12.0ms
(sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
6.0ms
(/.f64 (sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2))
3.0ms
(sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))
Compiler

Compiled 4795 to 1205 computations (74.9% saved)

series207.0ms (1.9%)

Error
0b
Counts
4 → 52
Calls

4 calls:

66.0ms
(*.f64 (*.f64 (cos.f64 th) (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
33.0ms
(/.f64 (sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2))
24.0ms
(sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))
24.0ms
(sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))
Compiler

Compiled 2831 to 1971 computations (30.4% saved)

simplify206.0ms (1.9%)

Algorithm
egg-herbie
Rules
807×times-frac_binary64
233×associate-*l*_binary64
217×associate-/l/_binary64
191×associate-*r*_binary64
186×distribute-rgt-in_binary64
Counts
210 → 149
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02465532
16005241
220385235
346895235
449855235
549765235

prune73.0ms (0.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1490149
Fresh044
Picked011
Done011
Total1496155
Error
0b
Counts
155 → 6
Alt Table
StatusErrorProgram
0.4b
(*.f64 (cos.f64 th) (*.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))))
0.4b
(*.f64 (*.f64 (cos.f64 th) (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
0.4b
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
0.5b
(*.f64 (cos.f64 th) (*.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2)))))
0.5b
(*.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
0.5b
(*.f64 (/.f64 (cos.f64 th) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
Compiler

Compiled 2864 to 1010 computations (64.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(cos.f64 th)
0.0b
(+.f64 (*.f64 a2 a2) (*.f64 a1 a1))
0.2b
(*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
0.4b
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))

rewrite72.0ms (0.7%)

Algorithm
rewrite-expression-head
Error
0b
Rules
12×add-sqr-sqrt_binary64
11×add-cbrt-cube_binary64
11×add-exp-log_binary64
10×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
Counts
4 → 67
Calls

4 calls:

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

Compiled 1404 to 435 computations (69% saved)

series152.0ms (1.4%)

Error
0b
Counts
4 → 48
Calls

4 calls:

68.0ms
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
48.0ms
(*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
20.0ms
(+.f64 (*.f64 a2 a2) (*.f64 a1 a1))
5.0ms
(cos.f64 th)
Compiler

Compiled 1599 to 1246 computations (22.1% saved)

simplify122.0ms (1.1%)

Algorithm
egg-herbie
Rules
574×associate-*l*_binary64
516×associate-/l*_binary64
363×times-frac_binary64
264×distribute-rgt-in_binary64
263×unswap-sqr_binary64
Counts
115 → 95
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01322185
13451918
212421832
343511832
449201832
549491832

prune47.0ms (0.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New95095
Fresh033
Picked011
Done022
Total956101
Error
0b
Counts
101 → 6
Alt Table
StatusErrorProgram
0.4b
(*.f64 (cos.f64 th) (*.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))))
0.4b
(*.f64 (*.f64 (cos.f64 th) (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
0.4b
(/.f64 (*.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
0.5b
(*.f64 (cos.f64 th) (*.f64 (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2))) (/.f64 (sqrt.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 (sqrt.f64 2)))))
0.5b
(*.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
0.5b
(*.f64 (/.f64 (cos.f64 th) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
Compiler

Compiled 1116 to 475 computations (57.4% saved)

regimes3.0s (28.3%)

Accuracy

Total 0.3b remaining (73.8%)

Threshold costs 0.3b (73.8%)

Compiler

Compiled 41030 to 26820 computations (34.6% saved)

simplify8.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01534
11734
21734

end12.0ms (0.1%)

Remove

(sort a1 a2)

Compiler

Compiled 75 to 39 computations (48% saved)

sample3.8s (35.5%)

Algorithm
intervals
Results
991.0ms1797×body1024valid
814.0ms1492×body1024invalid
560.0ms4846×body128valid
282.0ms898×body512valid
260.0ms785×body512invalid
100.0ms452×body256valid
91.0ms399×body256invalid
77.0ms638×body128invalid
7.0msbody2048valid
1.0msbody2048invalid
Compiler

Compiled 205 to 134 computations (34.6% saved)

Profiling

Loading profile data...