Details

Time bar (total: 14.1s)

analyze1.8s (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
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)

sample6.7s (47.7%)

Results
4.6s3643×body1024valid
742.0ms1362×body512valid
550.0ms2406×body128valid
428.0ms191×body2048valid
293.0ms654×body256valid
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify16.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
11314
21714
32014
42114
52114

prune4.0ms (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 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
Compiler

Compiled 45 to 27 computations (40% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(*.f64 r (sin.f64 b))
0.2b
(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
5.0b
(cos.f64 (+.f64 a b))

series135.0ms (1%)

Counts
3 → 68
Calls

3 calls:

104.0ms
(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
20.0ms
(*.f64 r (sin.f64 b))
10.0ms
(cos.f64 (+.f64 a b))

rewrite22.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
10×add-cbrt-cube_binary64
10×add-exp-log_binary64
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
3 → 53
Calls

3 calls:

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

simplify109.0ms (0.8%)

Algorithm
egg-herbie
Rules
558×fma-def_binary64
517×associate-/r*_binary64
394×associate-*l/_binary64
321×associate-/l/_binary64
308×associate-/r/_binary64
Counts
121 → 124
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02002011
15251879
220031831
350441831

prune229.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1168124
Fresh000
Picked101
Done000
Total1178125
Error
0.1b
Counts
125 → 8
Alt Table
StatusErrorProgram
14.9b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))) (cbrt.f64 (/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b))))) (cbrt.f64 (/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))))
0.2b
(/.f64 (*.f64 r (sin.f64 b)) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
14.2b
(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 b a))))
14.5b
(/.f64 (*.f64 r (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)))))
14.3b
(/.f64 (*.f64 r (sin.f64 b)) (cbrt.f64 (*.f64 (*.f64 (cos.f64 (+.f64 a b)) (cos.f64 (+.f64 a b))) (cos.f64 (+.f64 a b)))))
14.5b
(*.f64 (/.f64 r (*.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) (cbrt.f64 (cos.f64 (+.f64 a b))))) (/.f64 (sin.f64 b) (cbrt.f64 (cos.f64 (+.f64 a b)))))
25.0b
(fma.f64 (/.f64 (sin.f64 b) (cos.f64 b)) r (/.f64 (*.f64 (pow.f64 (sin.f64 b) 2) (*.f64 a r)) (pow.f64 (cos.f64 b) 2)))
14.2b
(*.f64 (*.f64 r (sin.f64 b)) (/.f64 1 (cos.f64 (+.f64 a b))))
Compiler

Compiled 2625 to 894 computations (65.9% saved)

localize16.0ms (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 r (sin.f64 b))
0.2b
(*.f64 (sin.f64 a) (sin.f64 b))
0.2b
(/.f64 (*.f64 r (sin.f64 b)) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

series162.0ms (1.2%)

Counts
3 → 64
Calls

3 calls:

127.0ms
(/.f64 (*.f64 r (sin.f64 b)) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
19.0ms
(*.f64 (sin.f64 a) (sin.f64 b))
16.0ms
(-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))

rewrite21.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×add-cbrt-cube_binary64
10×add-exp-log_binary64
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
3 → 66
Calls

3 calls:

9.0ms
(/.f64 (*.f64 r (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))

simplify226.0ms (1.6%)

Algorithm
egg-herbie
Rules
824×fma-def_binary64
381×fma-neg_binary64
329×cancel-sign-sub-inv_binary64
204×associate-*r*_binary64
204×distribute-rgt-neg-in_binary64
Counts
130 → 156
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02523500
16913279
225843054
345783049
449963049
549233049

prune363.0ms (2.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New18410194
Fresh707
Picked101
Done000
Total19210202
Error
0.0b
Counts
202 → 10
Alt Table
StatusErrorProgram
0.7b
(/.f64 1 (/.f64 (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (/.f64 (sin.f64 a) 1)) r))
0.3b
(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (/.f64 (sin.f64 a) 1)))
0.3b
(*.f64 (*.f64 r (sin.f64 b)) (/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
0.3b
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
0.5b
(/.f64 (*.f64 r (sin.f64 b)) (log.f64 (exp.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))))
0.3b
(/.f64 (*.f64 r (sin.f64 b)) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (*.f64 (*.f64 (*.f64 (sin.f64 a) (sin.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))) (*.f64 (sin.f64 a) (sin.f64 b))))))
0.2b
(/.f64 (*.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))
1.0b
(/.f64 (*.f64 (/.f64 r (*.f64 (cbrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))) (cbrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))) (sin.f64 b)) (cbrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
1.2b
(*.f64 (*.f64 (cbrt.f64 (/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (/.f64 (sin.f64 a) 1)))) (cbrt.f64 (/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (/.f64 (sin.f64 a) 1))))) (cbrt.f64 (/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (/.f64 (sin.f64 a) 1)))))
0.3b
(/.f64 r (/.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))) (sin.f64 b)))
Compiler

Compiled 5461 to 1517 computations (72.2% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series223.0ms (1.6%)

Counts
2 → 60
Calls

2 calls:

187.0ms
(/.f64 (*.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))
35.0ms
(fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b))))

rewrite13.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
Counts
2 → 33
Calls

2 calls:

8.0ms
(/.f64 (*.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))
1.0ms
(fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b))))

simplify132.0ms (0.9%)

Algorithm
egg-herbie
Rules
656×associate-*l*_binary64
468×fma-def_binary64
441×associate-/r*_binary64
304×associate-*l/_binary64
267×associate-/l/_binary64
Counts
93 → 88
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01702771
14512573
216502534
352102534

prune266.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1712173
Fresh279
Picked101
Done000
Total1749183
Error
0.0b
Counts
183 → 9
Alt Table
StatusErrorProgram
0.3b
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
0.3b
(/.f64 (*.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)))))
1.2b
(/.f64 (*.f64 (*.f64 (cbrt.f64 r) (cbrt.f64 r)) (*.f64 (sin.f64 b) (cbrt.f64 r))) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))
0.3b
(*.f64 (*.f64 r (sin.f64 b)) (/.f64 1 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
0.7b
(/.f64 1 (/.f64 (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (/.f64 (sin.f64 a) 1)) r))
0.5b
(/.f64 (*.f64 r (sin.f64 b)) (log.f64 (exp.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))))
1.0b
(/.f64 (*.f64 (/.f64 r (*.f64 (cbrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))) (cbrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))) (sin.f64 b)) (cbrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
1.2b
(*.f64 (*.f64 (cbrt.f64 (/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (/.f64 (sin.f64 a) 1)))) (cbrt.f64 (/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (/.f64 (sin.f64 a) 1))))) (cbrt.f64 (/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (/.f64 (sin.f64 a) 1)))))
0.3b
(/.f64 r (/.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))) (sin.f64 b)))
Compiler

Compiled 4782 to 1356 computations (71.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series302.0ms (2.1%)

Counts
4 → 76
Calls

4 calls:

141.0ms
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
117.0ms
(/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
32.0ms
(-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))
12.0ms
(*.f64 (sin.f64 b) (sin.f64 a))

rewrite60.0ms (0.4%)

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:

19.0ms
(*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
11.0ms
(/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
8.0ms
(-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))
7.0ms
(*.f64 (sin.f64 b) (sin.f64 a))

simplify325.0ms (2.3%)

Algorithm
egg-herbie
Rules
367×fma-neg_binary64
327×cancel-sign-sub-inv_binary64
299×associate-*r*_binary64
265×associate-*l*_binary64
203×associate-/l*_binary64
Counts
186 → 249
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03365467
18765149
233354803
345024797
449844797
549334797

prune417.0ms (3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2463249
Fresh268
Picked101
Done000
Total2499258
Error
0b
Counts
258 → 9
Alt Table
StatusErrorProgram
1.2b
(*.f64 (*.f64 r (*.f64 (cbrt.f64 (/.f64 1 (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (sin.f64 a)))) (cbrt.f64 (/.f64 1 (-.f64 (/.f64 (cos.f64 a) (/.f64 (sin.f64 b) (cos.f64 b))) (sin.f64 a)))))) (cbrt.f64 (/.f64 (sin.f64 b) (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))))
1.2b
(/.f64 (*.f64 (*.f64 (cbrt.f64 r) (cbrt.f64 r)) (*.f64 (sin.f64 b) (cbrt.f64 r))) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (*.f64 (sin.f64 a) (sin.f64 b)))))
0.3b
(*.f64 (*.f64 r (/.f64 (sin.f64 b) (-.f64 (*.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (cos.f64 a) (cos.f64 b))) (*.f64 (*.f64 (sin.f64 b) (sin.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))))) (+.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
0.3b
(*.f64 (*.f64 r (sin.f64 b)) (/.f64 1 (-.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 (pow.f64 (*.f64 (cos.f64 a) (cos.f64 b)) 3) (pow.f64 (*.f64 (sin.f64 a) (sin.f64 b)) 3)) (fma.f64 (*.f64 (sin.f64 a) (sin.f64 b)) (fma.f64 (sin.f64 a) (sin.f64 b) (*.f64 (cos.f64 a) (cos.f64 b))) (*.f64 (pow.f64 (cos.f64 a) 2) (pow.f64 (cos.f64 b) 2))))))
0.7b
(/.f64 1 (/.f64 (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (/.f64 (sin.f64 a) 1)) r))
0.3b
(/.f64 (*.f64 r (sin.f64 b)) (fma.f64 (cos.f64 a) (cos.f64 b) (neg.f64 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)))))
0.5b
(/.f64 (*.f64 r (sin.f64 b)) (log.f64 (exp.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))))
1.0b
(/.f64 (*.f64 (/.f64 r (*.f64 (cbrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))) (cbrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))) (sin.f64 b)) (cbrt.f64 (-.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
Compiler

Compiled 7409 to 1836 computations (75.2% saved)

regimes2.2s (15.6%)

Accuracy

Total 0.3b remaining (83.8%)

Threshold costs 0.3b (83.8%)

Counts
244 → 1
Compiler

Compiled 23432 to 13138 computations (43.9% saved)

simplify6.0ms (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
12226
23026
33526
43926
54126
64026

end295.0ms (2.1%)

Compiler

Compiled 336 to 179 computations (46.7% saved)

Profiling

Loading profile data...