Details

Time bar (total: 12.4s)

analyze937.0ms (7.6%)

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
12.5%87.4%0.1%5
18.7%81.2%0.1%6
21.9%78%0.1%7
23.4%76.5%0.1%8
24.2%75.7%0.1%9
24.6%75.3%0.1%10
24.8%75.1%0.1%11
24.9%75%0.1%12
24.9%75%0.1%13
25%75%0.1%14
Compiler

Compiled 10 to 7 computations (30% saved)

sample3.1s (25.4%)

Results
1.6s3631×body1024valid
861.0ms1245×body2048valid
404.0ms1392×body512valid
145.0ms1363×body128valid
117.0ms621×body256valid
5.0msbody4096valid
Compiler

Compiled 29 to 20 computations (31% saved)

simplify11.0ms (0.1%)

Algorithm
egg-herbie
Rules
39×fma-def_binary64
32×fma-neg_binary64
14×cancel-sign-sub-inv_binary64
12×sub-neg_binary64
10×distribute-rgt-in_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11011
21511
32211
42911
54611
67211
79311
811011
912011
1012411
1112611
1211211

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
37.3b
Counts
2 → 1
Alt Table
StatusErrorProgram
37.3b
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 27 to 18 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
1.8b
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.3b
(tan.f64 (+.f64 x eps))

series86.0ms (0.7%)

Counts
2 → 48
Calls

2 calls:

54.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
31.0ms
(tan.f64 (+.f64 x eps))

rewrite10.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
prod-diff_binary64
add-log-exp_binary64
Counts
2 → 43
Calls

2 calls:

6.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms
(tan.f64 (+.f64 x eps))

simplify109.0ms (0.9%)

Algorithm
egg-herbie
Rules
936×fma-def_binary64
909×times-frac_binary64
194×associate-+r+_binary64
142×unswap-sqr_binary64
125×+-commutative_binary64
Counts
91 → 93
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02072570
15072289
217872148
349652145
449862145
549432145

prune95.0ms (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New87693
Fresh000
Picked101
Done000
Total88694
Error
0.2b
Counts
94 → 6
Alt Table
StatusErrorProgram
31.4b
(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
24.4b
(/.f64 (fma.f64 (sin.f64 x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) -1) (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) (*.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
24.2b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
31.6b
(+.f64 (+.f64 eps (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (fma.f64 5/3 (/.f64 (pow.f64 eps 4) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3)) (fma.f64 (/.f64 (pow.f64 eps 4) (pow.f64 (cos.f64 x) 5)) (pow.f64 (sin.f64 x) 5) (fma.f64 4/3 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (fma.f64 1/3 (pow.f64 eps 3) (*.f64 2/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 eps 4)))))))))) (*.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
31.6b
(+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3)) (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)) (+.f64 eps (+.f64 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 (*.f64 5/3 (/.f64 (*.f64 (pow.f64 eps 4) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3))) (+.f64 (/.f64 (*.f64 (pow.f64 eps 4) (pow.f64 (sin.f64 x) 5)) (pow.f64 (cos.f64 x) 5)) (+.f64 (*.f64 4/3 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)) (+.f64 (*.f64 2/3 (/.f64 (*.f64 (pow.f64 eps 4) (sin.f64 x)) (cos.f64 x))) (*.f64 1/3 (pow.f64 eps 3)))))))))))
31.5b
(+.f64 (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (+.f64 (fma.f64 4/3 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (*.f64 1/3 (pow.f64 eps 3))) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps))) (*.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
Compiler

Compiled 3141 to 1357 computations (56.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.1b
(+.f64 (tan.f64 x) (tan.f64 eps))
0.2b
(*.f64 (tan.f64 x) (tan.f64 eps))
3.7b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series453.0ms (3.7%)

Counts
4 → 96
Calls

4 calls:

249.0ms
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
133.0ms
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
39.0ms
(*.f64 (tan.f64 x) (tan.f64 eps))
31.0ms
(+.f64 (tan.f64 x) (tan.f64 eps))

rewrite44.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
103×*-un-lft-identity_binary64
74×add-sqr-sqrt_binary64
67×add-cube-cbrt_binary64
61×times-frac_binary64
54×prod-diff_binary64
Counts
4 → 171
Calls

4 calls:

12.0ms
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
6.0ms
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
4.0ms
(*.f64 (tan.f64 x) (tan.f64 eps))
3.0ms
(+.f64 (tan.f64 x) (tan.f64 eps))

simplify240.0ms (1.9%)

Algorithm
egg-herbie
Rules
228×unswap-sqr_binary64
225×associate-+r+_binary64
225×distribute-rgt-in_binary64
203×distribute-lft-in_binary64
184×associate-*l*_binary64
Counts
267 → 245
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
038510657
19259025
231708501
347678501
449238501

prune273.0ms (2.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2396245
Fresh055
Picked101
Done000
Total24011251
Error
0.1b
Counts
251 → 11
Alt Table
StatusErrorProgram
24.2b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x)))) (tan.f64 x))
24.2b
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (*.f64 1 1) (*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (tan.f64 x)))
31.6b
(+.f64 (+.f64 eps (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (fma.f64 5/3 (/.f64 (pow.f64 eps 4) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3)) (fma.f64 (/.f64 (pow.f64 eps 4) (pow.f64 (cos.f64 x) 5)) (pow.f64 (sin.f64 x) 5) (fma.f64 4/3 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (fma.f64 1/3 (pow.f64 eps 3) (*.f64 2/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 eps 4)))))))))) (*.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
24.8b
(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (pow.f64 1 3) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (*.f64 (cbrt.f64 (tan.f64 x)) (*.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (tan.f64 x))) (*.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))) (*.f64 (cbrt.f64 (tan.f64 x)) (*.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))))))
31.4b
(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
27.2b
(fma.f64 (/.f64 1 (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
24.4b
(/.f64 (fma.f64 (sin.f64 x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) -1) (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) (*.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
24.2b
(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (neg.f64 (tan.f64 x))) 0)
31.6b
(+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3)) (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)) (+.f64 eps (+.f64 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 (*.f64 5/3 (/.f64 (*.f64 (pow.f64 eps 4) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3))) (+.f64 (/.f64 (*.f64 (pow.f64 eps 4) (pow.f64 (sin.f64 x) 5)) (pow.f64 (cos.f64 x) 5)) (+.f64 (*.f64 4/3 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)) (+.f64 (*.f64 2/3 (/.f64 (*.f64 (pow.f64 eps 4) (sin.f64 x)) (cos.f64 x))) (*.f64 1/3 (pow.f64 eps 3)))))))))))
31.5b
(+.f64 (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (+.f64 (fma.f64 4/3 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (*.f64 1/3 (pow.f64 eps 3))) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps))) (*.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
24.4b
(-.f64 (/.f64 (+.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (/.f64 (sin.f64 eps) (cos.f64 eps))) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))))) (tan.f64 x))
Compiler

Compiled 9859 to 3466 computations (64.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(+.f64 (tan.f64 x) (tan.f64 eps))
0.2b
(*.f64 (tan.f64 x) (tan.f64 eps))
0.3b
(*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
3.7b
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (*.f64 1 1) (*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (tan.f64 x)))

series528.0ms (4.3%)

Counts
2 → 48
Calls

2 calls:

455.0ms
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (*.f64 1 1) (*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (tan.f64 x)))
72.0ms
(*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))

rewrite13.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
41×pow1_binary64
32×tan-quot_binary64
17×frac-times_binary64
17×pow-prod-down_binary64
14×add-cbrt-cube_binary64
Counts
2 → 61
Calls

2 calls:

7.0ms
(*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
0.0ms
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (*.f64 1 1) (*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (tan.f64 x)))

simplify138.0ms (1.1%)

Algorithm
egg-herbie
Rules
778×fma-def_binary64
744×associate-/r*_binary64
237×associate-/r/_binary64
226×associate-*r*_binary64
221×associate-*l*_binary64
Counts
109 → 106
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02536641
16826255
224335516
356625516

prune504.0ms (4.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New2674271
Fresh2810
Picked101
Done000
Total27012282
Error
0.1b
Counts
282 → 12
Alt Table
StatusErrorProgram
0.7b
(+.f64 (fma.f64 (/.f64 (sin.f64 eps) (*.f64 (cos.f64 eps) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2)))))) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 eps) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2))))))) (-.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) 1) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2))))))) (/.f64 (sin.f64 x) (cos.f64 x))))
24.4b
(/.f64 (fma.f64 (sin.f64 x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) -1) (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) (*.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
24.7b
(fma.f64 (/.f64 (fma.f64 (*.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))) (cbrt.f64 (tan.f64 x)) (tan.f64 eps)) (-.f64 (*.f64 1 1) (*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (tan.f64 x)))
31.6b
(+.f64 (+.f64 eps (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (fma.f64 5/3 (/.f64 (pow.f64 eps 4) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3)) (fma.f64 (/.f64 (pow.f64 eps 4) (pow.f64 (cos.f64 x) 5)) (pow.f64 (sin.f64 x) 5) (fma.f64 4/3 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (fma.f64 1/3 (pow.f64 eps 3) (*.f64 2/3 (*.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 eps 4)))))))))) (*.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
24.8b
(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (pow.f64 1 3) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (*.f64 (cbrt.f64 (tan.f64 x)) (*.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (tan.f64 x))) (*.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))) (*.f64 (cbrt.f64 (tan.f64 x)) (*.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))))))
31.4b
(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
27.2b
(fma.f64 (/.f64 1 (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
24.2b
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (*.f64 1 1) (/.f64 (*.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (tan.f64 x)))
24.2b
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (*.f64 1 1) (*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (tan.f64 x)))
24.2b
(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3))) (fma.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) 1) (neg.f64 (tan.f64 x))) 0)
31.6b
(+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3)) (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)) (+.f64 eps (+.f64 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 (*.f64 5/3 (/.f64 (*.f64 (pow.f64 eps 4) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3))) (+.f64 (/.f64 (*.f64 (pow.f64 eps 4) (pow.f64 (sin.f64 x) 5)) (pow.f64 (cos.f64 x) 5)) (+.f64 (*.f64 4/3 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)) (+.f64 (*.f64 2/3 (/.f64 (*.f64 (pow.f64 eps 4) (sin.f64 x)) (cos.f64 x))) (*.f64 1/3 (pow.f64 eps 3)))))))))))
31.5b
(+.f64 (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (+.f64 (fma.f64 4/3 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (*.f64 1/3 (pow.f64 eps 3))) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps))) (*.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
Compiler

Compiled 13323 to 4881 computations (63.4% saved)

localize32.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(pow.f64 (sin.f64 x) 2)
0.3b
(pow.f64 (cos.f64 x) 2)
0.3b
(pow.f64 (cos.f64 eps) 2)
2.3b
(-.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) 1) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2))))))) (/.f64 (sin.f64 x) (cos.f64 x)))

series1.0s (8.4%)

Counts
4 → 36
Calls

4 calls:

1.0s
(-.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) 1) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2))))))) (/.f64 (sin.f64 x) (cos.f64 x)))
3.0ms
(pow.f64 (sin.f64 x) 2)
3.0ms
(pow.f64 (cos.f64 eps) 2)
3.0ms
(pow.f64 (cos.f64 x) 2)

rewrite47.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity_binary64
24×add-sqr-sqrt_binary64
24×add-cube-cbrt_binary64
18×times-frac_binary64
13×cancel-sign-sub-inv_binary64
Counts
4 → 105
Calls

4 calls:

31.0ms
(-.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) 1) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2))))))) (/.f64 (sin.f64 x) (cos.f64 x)))
4.0ms
(pow.f64 (sin.f64 x) 2)
2.0ms
(pow.f64 (cos.f64 eps) 2)
2.0ms
(pow.f64 (cos.f64 x) 2)

simplify168.0ms (1.4%)

Algorithm
egg-herbie
Rules
262×associate-*r*_binary64
238×associate-*l*_binary64
208×fma-def_binary64
200×associate-/l*_binary64
187×times-frac_binary64
Counts
141 → 174
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04427478
112206667
245256649
350386649

prune2.3s (18.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New4467453
Fresh5611
Picked101
Done000
Total45213465
Error
0.0b
Counts
465 → 13
Alt Table
StatusErrorProgram
0.7b
(+.f64 (fma.f64 (/.f64 (sin.f64 eps) (*.f64 (cos.f64 eps) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2)))))) (/.f64 (expm1.f64 (log1p.f64 (pow.f64 (sin.f64 x) 2))) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 eps) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2))))))) (-.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) 1) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2))))))) (/.f64 (sin.f64 x) (cos.f64 x))))
0.9b
(+.f64 (fma.f64 (/.f64 (sin.f64 eps) (*.f64 (cos.f64 eps) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2)))))) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (*.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) 2) (pow.f64 (cbrt.f64 (cos.f64 x)) 2))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 eps) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2))))))) (-.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) 1) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2))))))) (/.f64 (sin.f64 x) (cos.f64 x))))
0.7b
(+.f64 (fma.f64 (/.f64 (sin.f64 eps) (*.f64 (cos.f64 eps) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2)))))) (/.f64 (pow.f64 (sin.f64 x) 2) (exp.f64 (log.f64 (pow.f64 (cos.f64 x) 2)))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 eps) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2))))))) (-.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) 1) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2))))))) (/.f64 (sin.f64 x) (cos.f64 x))))
27.2b
(fma.f64 (/.f64 1 (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
2.1b
(+.f64 (fma.f64 (/.f64 (sin.f64 eps) (*.f64 (cos.f64 eps) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2)))))) (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 eps) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2))))))) (/.f64 (-.f64 (*.f64 (*.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2))) (*.f64 1 1)) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2))))))) (cos.f64 x)) (*.f64 (-.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) 1) (sin.f64 x))) (*.f64 (-.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) 1) (cos.f64 x))))
24.4b
(/.f64 (fma.f64 (sin.f64 x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) -1) (*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) (*.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
0.7b
(+.f64 (fma.f64 (/.f64 (sin.f64 eps) (*.f64 (cos.f64 eps) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2)))))) (/.f64 (pow.f64 (sin.f64 x) 2) (cbrt.f64 (pow.f64 (pow.f64 (cos.f64 x) 2) 3))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 eps) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2))))))) (-.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) 1) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2))))))) (/.f64 (sin.f64 x) (cos.f64 x))))
0.7b
(+.f64 (fma.f64 (/.f64 (sin.f64 eps) (*.f64 (cos.f64 eps) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2)))))) (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (sin.f64 x) 2) 3)) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 eps) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2))))))) (-.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) 1) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2))))))) (/.f64 (sin.f64 x) (cos.f64 x))))
24.2b
(fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (*.f64 1 1) (*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (tan.f64 x)))
24.8b
(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 (pow.f64 1 3) (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (*.f64 1 1) (+.f64 (*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (*.f64 (cbrt.f64 (tan.f64 x)) (*.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (tan.f64 x))) (*.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))) (*.f64 (cbrt.f64 (tan.f64 x)) (*.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))))))
31.6b
(+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3)) (+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)) (+.f64 eps (+.f64 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 (*.f64 5/3 (/.f64 (*.f64 (pow.f64 eps 4) (pow.f64 (sin.f64 x) 3)) (pow.f64 (cos.f64 x) 3))) (+.f64 (/.f64 (*.f64 (pow.f64 eps 4) (pow.f64 (sin.f64 x) 5)) (pow.f64 (cos.f64 x) 5)) (+.f64 (*.f64 4/3 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)) (+.f64 (*.f64 2/3 (/.f64 (*.f64 (pow.f64 eps 4) (sin.f64 x)) (cos.f64 x))) (*.f64 1/3 (pow.f64 eps 3)))))))))))
31.5b
(+.f64 (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (+.f64 (fma.f64 4/3 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (*.f64 1/3 (pow.f64 eps 3))) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps))) (*.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
0.9b
(+.f64 (fma.f64 (/.f64 (sin.f64 eps) (*.f64 (cos.f64 eps) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2)))))) (/.f64 (pow.f64 (sin.f64 x) 2) (*.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 4) (pow.f64 (cbrt.f64 (cos.f64 x)) 2))) (/.f64 (sin.f64 eps) (*.f64 (cos.f64 eps) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2))))))) (-.f64 (*.f64 (+.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) 1) (/.f64 (sin.f64 x) (*.f64 (cos.f64 x) (-.f64 1 (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (sin.f64 x) 2)) (*.f64 (pow.f64 (cos.f64 eps) 2) (pow.f64 (cos.f64 x) 2))))))) (/.f64 (sin.f64 x) (cos.f64 x))))
Compiler

Compiled 55629 to 31083 computations (44.1% saved)

regimes1.5s (12.1%)

Accuracy

Total 0.5b remaining (83.5%)

Threshold costs 0.5b (83.5%)

Counts
280 → 1
Compiler

Compiled 45560 to 26056 computations (42.8% saved)

simplify9.0ms (0.1%)

Algorithm
egg-herbie
Rules
11×*-commutative_binary64
10×+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
031180
144180
255180
369180
479180
585180
687180
786180

end686.0ms (5.5%)

Compiler

Compiled 1440 to 861 computations (40.2% saved)

Profiling

Loading profile data...