Details

Time bar (total: 14.7s)

analyze1.6s (11%)

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
0%99.9%0.1%6
6.2%93.6%0.1%7
9.4%90.5%0.1%8
14%85.8%0.1%9
19.5%80.4%0.1%10
20.7%79.2%0.1%11
22%77.8%0.1%12
23.5%76.4%0.1%13
23.8%76%0.1%14
Compiler

Compiled 13 to 9 computations (30.8% saved)

sample3.9s (26.2%)

Results
2.4s3513×body1024valid
595.0ms1451×body512valid
396.0ms2473×body128valid
271.0ms206×body2048valid
188.0ms613×body256valid
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify6.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
associate-/l*_binary64
+-commutative_binary64
associate-*r/_binary64
associate-*l/_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
11314
21614
32014
42114
52114

prune5.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
14.5b
Counts
3 → 1
Alt Table
StatusErrorProgram
14.5b
(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
Compiler

Compiled 45 to 28 computations (37.8% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
0.2b
(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
2.6b
(cos.f64 (+.f64 a b))

series76.0ms (0.5%)

Counts
3 → 52
Calls

3 calls:

45.0ms
(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
27.0ms
(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
4.0ms
(cos.f64 (+.f64 a b))

rewrite16.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt_binary64
19×times-frac_binary64
19×*-un-lft-identity_binary64
19×add-cube-cbrt_binary64
13×associate-*r*_binary64
Counts
3 → 73
Calls

3 calls:

5.0ms
(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
3.0ms
(cos.f64 (+.f64 a b))
3.0ms
(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))

simplify74.0ms (0.5%)

Algorithm
egg-herbie
Rules
696×fma-def_binary64
561×associate-/r*_binary64
437×associate-*l/_binary64
281×associate-/r/_binary64
239×associate-/l/_binary64
Counts
125 → 172
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02442790
16202642
222882580
353172580

prune155.0ms (1.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New16210172
Fresh000
Picked101
Done000
Total16310173
Error
0.1b
Counts
173 → 10
Alt Table
StatusErrorProgram
14.6b
(*.f64 r (/.f64 1 (/.f64 (cos.f64 (+.f64 a b)) (sin.f64 b))))
38.3b
(*.f64 (sqrt.f64 r) (*.f64 (sqrt.f64 r) (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))))
15.2b
(*.f64 (*.f64 (cbrt.f64 r) (cbrt.f64 r)) (*.f64 (cbrt.f64 r) (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))))
14.6b
(*.f64 (*.f64 r (sin.f64 b)) (/.f64 1 (cos.f64 (+.f64 a b))))
14.7b
(*.f64 r (/.f64 (sin.f64 b) (cbrt.f64 (*.f64 (*.f64 (cos.f64 (+.f64 a b)) (cos.f64 (+.f64 a b))) (cos.f64 (+.f64 a b))))))
30.4b
(*.f64 (/.f64 r (sqrt.f64 (cos.f64 (+.f64 b a)))) (/.f64 (sin.f64 b) (sqrt.f64 (cos.f64 (+.f64 a b)))))
38.4b
(*.f64 (*.f64 r (sqrt.f64 (sin.f64 b))) (/.f64 (sqrt.f64 (sin.f64 b)) (cos.f64 (+.f64 a b))))
0.3b
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
15.2b
(*.f64 (*.f64 r (*.f64 (cbrt.f64 (sin.f64 b)) (cbrt.f64 (sin.f64 b)))) (/.f64 (cbrt.f64 (sin.f64 b)) (cos.f64 (+.f64 a b))))
14.6b
(/.f64 (*.f64 (sin.f64 b) r) (cos.f64 (+.f64 a b)))
Compiler

Compiled 3929 to 1281 computations (67.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))
0.1b
(*.f64 (sin.f64 a) (sin.f64 b))
0.2b
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
0.2b
(/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

series197.0ms (1.3%)

Counts
4 → 80
Calls

4 calls:

109.0ms
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
63.0ms
(/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
15.0ms
(-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))
9.0ms
(*.f64 (sin.f64 a) (sin.f64 b))

rewrite30.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt_binary64
22×*-un-lft-identity_binary64
22×add-cube-cbrt_binary64
20×associate-*r*_binary64
19×times-frac_binary64
Counts
4 → 110
Calls

4 calls:

8.0ms
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
6.0ms
(/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
5.0ms
(*.f64 (sin.f64 a) (sin.f64 b))
4.0ms
(-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))

simplify155.0ms (1%)

Algorithm
egg-herbie
Rules
386×fma-neg_binary64
323×cancel-sign-sub-inv_binary64
290×associate-*r*_binary64
268×associate-*l*_binary64
198×distribute-rgt-neg-in_binary64
Counts
190 → 216
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03315599
18715281
232585029
345305023
449715023

prune216.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2088216
Fresh909
Picked101
Done000
Total2188226
Error
0.0b
Counts
226 → 8
Alt Table
StatusErrorProgram
0.4b
(*.f64 (*.f64 r (sin.f64 b)) (/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
1.2b
(*.f64 (*.f64 r (*.f64 (cbrt.f64 (sin.f64 b)) (cbrt.f64 (sin.f64 b)))) (/.f64 (cbrt.f64 (sin.f64 b)) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
1.1b
(*.f64 (*.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (cbrt.f64 r) (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1))))
0.4b
(/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))
22.7b
(*.f64 r (/.f64 (/.f64 (sin.f64 b) (sqrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))) (sqrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
0.5b
(*.f64 r (*.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (*.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2)))) (+.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
0.3b
(*.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))) r)
0.5b
(*.f64 (*.f64 r (/.f64 (sin.f64 b) (-.f64 (pow.f64 (*.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)))) (+.f64 (*.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (cos.f64 a) (cos.f64 b))) (+.f64 (*.f64 (*.f64 (sin.f64 a) (sin.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))) (*.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
Compiler

Compiled 6451 to 1823 computations (71.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))
0.1b
(*.f64 (sin.f64 a) (sin.f64 b))
0.2b
(*.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))) r)
0.2b
(/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

series108.0ms (0.7%)

Counts
1 → 36
Calls

1 calls:

108.0ms
(*.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))) r)

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
17×associate-*l*_binary64
14×add-sqr-sqrt_binary64
10×times-frac_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
1 → 38
Calls

1 calls:

8.0ms
(*.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))) r)

simplify61.0ms (0.4%)

Algorithm
egg-herbie
Rules
975×times-frac_binary64
863×associate-/l*_binary64
472×fma-def_binary64
144×associate-/r/_binary64
117×associate-*r*_binary64
Counts
74 → 80
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01722443
14512277
214832241
350282241

prune233.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2190219
Fresh077
Picked011
Done000
Total2198227
Error
0.0b
Counts
227 → 8
Alt Table
StatusErrorProgram
0.4b
(*.f64 (*.f64 r (sin.f64 b)) (/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
1.2b
(*.f64 (*.f64 r (*.f64 (cbrt.f64 (sin.f64 b)) (cbrt.f64 (sin.f64 b)))) (/.f64 (cbrt.f64 (sin.f64 b)) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
1.1b
(*.f64 (*.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (cbrt.f64 r) (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1))))
0.4b
(/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))
22.7b
(*.f64 r (/.f64 (/.f64 (sin.f64 b) (sqrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))) (sqrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
0.5b
(*.f64 r (*.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (*.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2)))) (+.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
0.3b
(*.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))) r)
0.5b
(*.f64 (*.f64 r (/.f64 (sin.f64 b) (-.f64 (pow.f64 (*.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)))) (+.f64 (*.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (cos.f64 a) (cos.f64 b))) (+.f64 (*.f64 (*.f64 (sin.f64 a) (sin.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))) (*.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
Compiler

Compiled 6687 to 1767 computations (73.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1))
0.1b
(/.f64 (sin.f64 b) (cos.f64 b))
0.2b
(/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b)))
0.2b
(/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))

series168.0ms (1.1%)

Counts
4 → 88
Calls

4 calls:

116.0ms
(/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))
23.0ms
(-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1))
22.0ms
(/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b)))
7.0ms
(/.f64 (sin.f64 b) (cos.f64 b))

rewrite253.0ms (1.7%)

Algorithm
rewrite-expression-head
Rules
1540×times-frac_binary64
1028×add-sqr-sqrt_binary64
923×*-un-lft-identity_binary64
878×add-cube-cbrt_binary64
572×prod-diff_binary64
Counts
4 → 832
Calls

4 calls:

35.0ms
(-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1))
24.0ms
(/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))
5.0ms
(/.f64 (sin.f64 b) (cos.f64 b))
5.0ms
(/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b)))

simplify1.9s (13.2%)

Algorithm
egg-herbie
Rules
314×fma-neg_binary64
259×associate-/l*_binary64
252×fma-udef_binary64
228×associate-*r*_binary64
201×associate-*l/_binary64
Counts
920 → 1053
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
071535477
1109733287
2411829114
3471029113
4495729113
5493129113

prune1.4s (9.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New105211053
Fresh066
Picked011
Done011
Total105291061
Error
0b
Counts
1061 → 9
Alt Table
StatusErrorProgram
0.4b
(*.f64 (*.f64 r (sin.f64 b)) (/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
1.2b
(*.f64 (*.f64 r (*.f64 (cbrt.f64 (sin.f64 b)) (cbrt.f64 (sin.f64 b)))) (/.f64 (cbrt.f64 (sin.f64 b)) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
16.5b
(/.f64 r (-.f64 (*.f64 (*.f64 (sqrt.f64 (cos.f64 a)) (*.f64 (cbrt.f64 (cos.f64 b)) (cbrt.f64 (cos.f64 b)))) (/.f64 (sqrt.f64 (cos.f64 a)) (/.f64 (sin.f64 b) (cbrt.f64 (cos.f64 b))))) (/.f64 (sin.f64 a) 1)))
1.1b
(*.f64 (*.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (cbrt.f64 r) (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1))))
0.4b
(/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))
22.7b
(*.f64 r (/.f64 (/.f64 (sin.f64 b) (sqrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))) (sqrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
0.5b
(*.f64 r (*.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2)) (*.f64 (pow.f64 (sin.f64 a) 2) (pow.f64 (sin.f64 b) 2)))) (+.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
0.3b
(*.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))) r)
0.5b
(*.f64 (*.f64 r (/.f64 (sin.f64 b) (-.f64 (pow.f64 (*.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)))) (+.f64 (*.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (cos.f64 a) (cos.f64 b))) (+.f64 (*.f64 (*.f64 (sin.f64 a) (sin.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))) (*.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
Compiler

Compiled 50610 to 20260 computations (60% saved)

regimes4.0s (26.9%)

Accuracy

Total 0.3b remaining (84%)

Threshold costs 0.3b (84%)

Counts
511 → 1
Compiler

Compiled 75405 to 44343 computations (41.2% 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
01526
12626
23526
34126
44526
54626
64526

end163.0ms (1.1%)

Compiler

Compiled 312 to 172 computations (44.9% saved)

Profiling

Loading profile data...