Details

Time bar (total: 14.3s)

analyze2.3s (16.3%)

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
12.5%87.4%0.1%7
12.5%87.4%0.1%8
18.7%81.1%0.1%9
21.8%78%0.1%10
21.8%78%0.1%11
23.4%76.5%0.1%12
24.2%75.7%0.1%13
24.2%75.7%0.1%14
Compiler

Compiled 13 to 9 computations (30.8% saved)

sample5.7s (39.7%)

Results
3.6s3643×body1024valid
795.0ms1362×body512valid
532.0ms2406×body128valid
429.0ms191×body2048valid
282.0ms654×body256valid
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify13.0ms (0.1%)

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

prune6.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
14.2b
Counts
3 → 1
Alt Table
StatusErrorProgram
14.2b
(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
Compiler

Compiled 45 to 28 computations (37.8% saved)

localize15.0ms (0.1%)

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)))
5.0b
(cos.f64 (+.f64 a b))

series153.0ms (1.1%)

Counts
3 → 52
Calls

3 calls:

90.0ms
(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
56.0ms
(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
8.0ms
(cos.f64 (+.f64 a b))

rewrite28.0ms (0.2%)

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:

11.0ms
(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
6.0ms
(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
5.0ms
(cos.f64 (+.f64 a b))

simplify93.0ms (0.6%)

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

prune274.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New16012172
Fresh000
Picked101
Done000
Total16112173
Error
0.1b
Counts
173 → 12
Alt Table
StatusErrorProgram
14.8b
(*.f64 (*.f64 (cbrt.f64 (*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))) (cbrt.f64 (*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))))) (cbrt.f64 (*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))))
14.3b
(*.f64 r (log1p.f64 (expm1.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))))
24.9b
(*.f64 r (fma.f64 (/.f64 (pow.f64 (sin.f64 b) 2) (pow.f64 (cos.f64 b) 2)) a (/.f64 (sin.f64 b) (cos.f64 b))))
14.9b
(*.f64 r (/.f64 (*.f64 (cbrt.f64 (sin.f64 b)) (cbrt.f64 (sin.f64 b))) (/.f64 (cos.f64 (+.f64 a b)) (cbrt.f64 (sin.f64 b)))))
30.4b
(*.f64 r (+.f64 (/.f64 (*.f64 (sin.f64 a) (pow.f64 b 2)) (pow.f64 (cos.f64 a) 2)) (/.f64 b (cos.f64 a))))
14.2b
(*.f64 r (*.f64 (sin.f64 b) (/.f64 1 (cos.f64 (+.f64 a b)))))
14.5b
(*.f64 r (/.f64 (sin.f64 b) (*.f64 (*.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) (cbrt.f64 (cos.f64 (+.f64 a b)))) (cbrt.f64 (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)))))
14.8b
(*.f64 (*.f64 (cbrt.f64 r) (cbrt.f64 r)) (*.f64 (cbrt.f64 r) (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))))
42.5b
(*.f64 r (exp.f64 (log.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 b a))))))
14.2b
(/.f64 (*.f64 (sin.f64 b) r) (cos.f64 (+.f64 a b)))
14.3b
(*.f64 r (/.f64 (sin.f64 b) (log.f64 (exp.f64 (cos.f64 (+.f64 a b))))))
Compiler

Compiled 4039 to 1331 computations (67% saved)

localize20.0ms (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)))
0.2b
(/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.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 a) (sin.f64 b))

series231.0ms (1.6%)

Counts
4 → 80
Calls

4 calls:

125.0ms
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
71.0ms
(/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
20.0ms
(-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))
14.0ms
(*.f64 (sin.f64 a) (sin.f64 b))

rewrite33.0ms (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:

9.0ms
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
8.0ms
(/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
4.0ms
(-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))
4.0ms
(*.f64 (sin.f64 a) (sin.f64 b))

simplify239.0ms (1.7%)

Algorithm
egg-herbie
Rules
386×fma-neg_binary64
323×cancel-sign-sub-inv_binary64
292×associate-*r*_binary64
268×associate-*l*_binary64
198×distribute-rgt-neg-in_binary64
Counts
190 → 249
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03315599
18715281
232585029
345305023
449715023

prune1.6s (11.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2418249
Fresh10111
Picked101
Done000
Total2529261
Error
0b
Counts
261 → 9
Alt Table
StatusErrorProgram
1.2b
(*.f64 (*.f64 r (*.f64 (cbrt.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))) (cbrt.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))) (cbrt.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
0.4b
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (*.f64 (cbrt.f64 (sin.f64 a)) (cbrt.f64 (sin.f64 a))) (*.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b))))))
29.7b
(*.f64 (sqrt.f64 (/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))) (sqrt.f64 (/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))))
0.2b
(/.f64 (*.f64 (sin.f64 b) r) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
25.7b
(*.f64 (/.f64 r (sqrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))) (/.f64 (sin.f64 b) (sqrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
0.3b
(*.f64 r (*.f64 (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)))))
14.5b
(*.f64 r (/.f64 (sin.f64 b) (*.f64 (*.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) (cbrt.f64 (cos.f64 (+.f64 a b)))) (cbrt.f64 (cos.f64 (+.f64 a b))))))
0.3b
(/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))
Compiler

Compiled 7620 to 1963 computations (74.2% saved)

localize25.0ms (0.2%)

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

series236.0ms (1.6%)

Counts
2 → 28
Calls

2 calls:

222.0ms
(/.f64 (*.f64 (sin.f64 b) r) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
13.0ms
(*.f64 (sin.f64 b) r)

rewrite15.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
2 → 47
Calls

2 calls:

9.0ms
(/.f64 (*.f64 (sin.f64 b) r) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
3.0ms
(*.f64 (sin.f64 b) r)

simplify74.0ms (0.5%)

Algorithm
egg-herbie
Rules
542×associate-/r*_binary64
499×fma-def_binary64
346×associate-/l/_binary64
337×associate-/r/_binary64
159×associate-/l*_binary64
Counts
75 → 98
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01972205
15422011
221011931
350021931

prune316.0ms (2.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1883191
Fresh358
Picked101
Done000
Total1928200
Error
0b
Counts
200 → 8
Alt Table
StatusErrorProgram
1.2b
(*.f64 (*.f64 r (*.f64 (cbrt.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))) (cbrt.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))) (cbrt.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
0.4b
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (*.f64 (cbrt.f64 (sin.f64 a)) (cbrt.f64 (sin.f64 a))) (*.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b))))))
0.7b
(/.f64 (*.f64 (/.f64 (sin.f64 b) (*.f64 (cbrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))) (cbrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))) r) (cbrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
0.3b
(*.f64 r (*.f64 (sin.f64 b) (/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
0.3b
(/.f64 (sin.f64 b) (/.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))) r))
0.2b
(/.f64 (*.f64 (sin.f64 b) r) (fma.f64 (cos.f64 a) (cos.f64 b) (*.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))))
0.3b
(/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))
29.7b
(*.f64 (sqrt.f64 (/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))) (sqrt.f64 (/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))))
Compiler

Compiled 5319 to 1390 computations (73.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series212.0ms (1.5%)

Counts
3 → 84
Calls

3 calls:

158.0ms
(/.f64 (*.f64 (sin.f64 b) r) (fma.f64 (cos.f64 a) (cos.f64 b) (*.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))))
31.0ms
(fma.f64 (cos.f64 a) (cos.f64 b) (*.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))
23.0ms
(*.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))

rewrite25.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt_binary64
10×associate-*r*_binary64
10×add-cbrt-cube_binary64
10×add-exp-log_binary64
*-un-lft-identity_binary64
Counts
3 → 61
Calls

3 calls:

10.0ms
(*.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))
10.0ms
(/.f64 (*.f64 (sin.f64 b) r) (fma.f64 (cos.f64 a) (cos.f64 b) (*.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))))
1.0ms
(fma.f64 (cos.f64 a) (cos.f64 b) (*.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))

simplify178.0ms (1.2%)

Algorithm
egg-herbie
Rules
672×fma-def_binary64
317×fma-neg_binary64
253×associate-/l/_binary64
211×associate-*r*_binary64
206×associate-*l*_binary64
Counts
145 → 147
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02403500
16293274
223783207
348813202
450043202

prune221.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1850185
Fresh077
Picked011
Done000
Total1858193
Error
0b
Counts
193 → 8
Alt Table
StatusErrorProgram
1.2b
(*.f64 (*.f64 r (*.f64 (cbrt.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))) (cbrt.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))) (cbrt.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
0.4b
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (*.f64 (cbrt.f64 (sin.f64 a)) (cbrt.f64 (sin.f64 a))) (*.f64 (cbrt.f64 (sin.f64 a)) (sin.f64 b))))))
0.7b
(/.f64 (*.f64 (/.f64 (sin.f64 b) (*.f64 (cbrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))) (cbrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))) r) (cbrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
0.3b
(*.f64 r (*.f64 (sin.f64 b) (/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))))
0.3b
(/.f64 (sin.f64 b) (/.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))) r))
0.2b
(/.f64 (*.f64 (sin.f64 b) r) (fma.f64 (cos.f64 a) (cos.f64 b) (*.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))))
0.3b
(/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))
29.7b
(*.f64 (sqrt.f64 (/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))) (sqrt.f64 (/.f64 r (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (/.f64 (sin.f64 a) 1)))))
Compiler

Compiled 4734 to 1195 computations (74.8% saved)

regimes2.0s (14.3%)

Accuracy

Total 0.3b remaining (80.2%)

Threshold costs 0.3b (80.2%)

Counts
213 → 1
Compiler

Compiled 24994 to 14307 computations (42.8% 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
01326
12126
22826
33426
43726
53826
63826

end197.0ms (1.4%)

Compiler

Compiled 277 to 140 computations (49.5% saved)

Profiling

Loading profile data...