Details

Time bar (total: 10.9s)

analyze1.2s (10.8%)

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
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)

sample150.0ms (1.4%)

Algorithm
intervals
Results
107.0ms98×body1024valid
15.0ms33×body2048valid
12.0ms61×body512valid
4.0ms26×body256valid
2.0ms38×body128valid
Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify12.0ms (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
36.7b
Counts
2 → 1
Alt Table
StatusErrorProgram
36.7b
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 27 to 18 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
1.8b
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.8b
(tan.f64 (+.f64 x eps))

series82.0ms (0.8%)

Counts
2 → 48
Calls

2 calls:

51.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
31.0ms
(tan.f64 (+.f64 x eps))

rewrite16.0ms (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:

11.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms
(tan.f64 (+.f64 x eps))

simplify108.0ms (1%)

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

prune87.0ms (0.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New88593
Fresh000
Picked101
Done000
Total89594
Error
0.2b
Counts
94 → 5
Alt Table
StatusErrorProgram
20.4b
(/.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)))))
33.8b
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
20.2b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
34.3b
(+.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)))))
34.1b
(+.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 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))
Compiler

Compiled 2849 to 1165 computations (59.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
0.1b
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.2b
(*.f64 (tan.f64 x) (tan.f64 eps))
3.1b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series504.0ms (4.6%)

Counts
4 → 96
Calls

4 calls:

294.0ms
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
132.0ms
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
40.0ms
(*.f64 (tan.f64 x) (tan.f64 eps))
38.0ms
(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

rewrite44.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
102×*-un-lft-identity_binary64
75×add-sqr-sqrt_binary64
68×add-cube-cbrt_binary64
61×times-frac_binary64
57×prod-diff_binary64
Counts
4 → 173
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 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

simplify367.0ms (3.4%)

Algorithm
egg-herbie
Rules
257×distribute-rgt-in_binary64
212×unswap-sqr_binary64
209×associate-+r+_binary64
205×cancel-sign-sub-inv_binary64
205×fma-neg_binary64
Counts
269 → 256
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
038310894
19129239
231888700
347948700
449848700
549928700
649298700

prune295.0ms (2.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New2479256
Fresh134
Picked101
Done000
Total24912261
Error
0.1b
Counts
261 → 12
Alt Table
StatusErrorProgram
20.2b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))))) (tan.f64 x))
20.2b
(-.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))
20.3b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (*.f64 (cbrt.f64 (*.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (*.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
20.3b
(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
20.5b
(/.f64 (fma.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) -1))) (*.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
21.3b
(fma.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
20.4b
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (cos.f64 x))) (/.f64 (sin.f64 eps) (*.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (cos.f64 eps)))) (/.f64 (sin.f64 x) (cos.f64 x)))
43.1b
(+.f64 (fma.f64 1 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (*.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (tan.f64 x))) (sqrt.f64 (tan.f64 x)) (*.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x)))))
34.3b
(+.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)))))
20.4b
(fma.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
34.1b
(+.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 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))
33.8b
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
Compiler

Compiled 9966 to 3433 computations (65.6% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))))
0.2b
(*.f64 (sin.f64 x) (sin.f64 eps))
0.3b
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))
3.1b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))))) (tan.f64 x))

series431.0ms (4%)

Counts
4 → 64
Calls

4 calls:

243.0ms
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))))) (tan.f64 x))
133.0ms
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))))
40.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))
13.0ms
(*.f64 (sin.f64 x) (sin.f64 eps))

rewrite81.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
220×*-un-lft-identity_binary64
163×add-sqr-sqrt_binary64
122×times-frac_binary64
93×add-cube-cbrt_binary64
90×prod-diff_binary64
Counts
4 → 239
Calls

4 calls:

19.0ms
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))))) (tan.f64 x))
9.0ms
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))))
5.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))
4.0ms
(*.f64 (sin.f64 x) (sin.f64 eps))

simplify291.0ms (2.7%)

Algorithm
egg-herbie
Rules
294×times-frac_binary64
240×unswap-sqr_binary64
227×associate-*r*_binary64
224×associate-*l*_binary64
217×associate-/l*_binary64
Counts
303 → 333
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
045217021
1109713818
2421713065
3498613065

prune434.0ms (4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New3312333
Fresh11011
Picked101
Done000
Total33312345
Error
0.1b
Counts
345 → 12
Alt Table
StatusErrorProgram
20.5b
(-.f64 (/.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 x) (cos.f64 eps)))) (tan.f64 x))
20.5b
(/.f64 (fma.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) -1))) (*.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
21.3b
(fma.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
20.2b
(-.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))
20.4b
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (cos.f64 x))) (/.f64 (sin.f64 eps) (*.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (cos.f64 eps)))) (/.f64 (sin.f64 x) (cos.f64 x)))
38.9b
(-.f64 (/.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 1 (sqrt.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))))) (-.f64 1 (sqrt.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))))) (tan.f64 x))
20.3b
(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
43.1b
(+.f64 (fma.f64 1 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (*.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (tan.f64 x))) (sqrt.f64 (tan.f64 x)) (*.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x)))))
34.3b
(+.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)))))
20.4b
(fma.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
34.1b
(+.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 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))
33.8b
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
Compiler

Compiled 15638 to 4269 computations (72.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x))))
0.2b
(/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x))
0.2b
(*.f64 (sin.f64 x) (tan.f64 eps))
3.1b
(-.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))

series503.0ms (4.6%)

Counts
4 → 96
Calls

4 calls:

266.0ms
(-.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))
172.0ms
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x))))
39.0ms
(/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x))
25.0ms
(*.f64 (sin.f64 x) (tan.f64 eps))

rewrite74.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
222×*-un-lft-identity_binary64
165×add-sqr-sqrt_binary64
124×times-frac_binary64
95×add-cube-cbrt_binary64
90×prod-diff_binary64
Counts
4 → 238
Calls

4 calls:

16.0ms
(-.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))
8.0ms
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x))))
5.0ms
(*.f64 (sin.f64 x) (tan.f64 eps))
4.0ms
(/.f64 (*.f64 (sin.f64 x) (tan.f64 eps)) (cos.f64 x))

simplify445.0ms (4.1%)

Algorithm
egg-herbie
Rules
222×associate-+r+_binary64
202×associate-/l*_binary64
192×+-commutative_binary64
190×associate-*l*_binary64
184×associate-*r*_binary64
Counts
334 → 323
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
044115753
1104812960
2371012235
3481512235
4497312235
5499712235
6492812235

prune367.0ms (3.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New3230323
Fresh01111
Picked011
Done000
Total32312335
Error
0.1b
Counts
335 → 12
Alt Table
StatusErrorProgram
20.5b
(-.f64 (/.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (*.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (*.f64 (cos.f64 x) (cos.f64 eps)))) (tan.f64 x))
20.5b
(/.f64 (fma.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (sin.f64 x) (+.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) -1))) (*.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
21.3b
(fma.f64 (*.f64 (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (cbrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
20.2b
(-.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))
20.4b
(-.f64 (+.f64 (/.f64 (sin.f64 x) (*.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (cos.f64 x))) (/.f64 (sin.f64 eps) (*.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))) (cos.f64 eps)))) (/.f64 (sin.f64 x) (cos.f64 x)))
38.9b
(-.f64 (/.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (+.f64 1 (sqrt.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))))) (-.f64 1 (sqrt.f64 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))))) (tan.f64 x))
20.3b
(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
43.1b
(+.f64 (fma.f64 1 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (*.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x))))) (fma.f64 (neg.f64 (sqrt.f64 (tan.f64 x))) (sqrt.f64 (tan.f64 x)) (*.f64 (sqrt.f64 (tan.f64 x)) (sqrt.f64 (tan.f64 x)))))
34.3b
(+.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)))))
20.4b
(fma.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
34.1b
(+.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 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)))))
33.8b
(fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps)
Compiler

Compiled 13504 to 3917 computations (71% saved)

regimes2.5s (22.7%)

Accuracy

Total 0.2b remaining (58.1%)

Threshold costs 0.2b (58.1%)

Counts
373 → 3
Compiler

Compiled 32733 to 18809 computations (42.5% saved)

bsearch92.0ms (0.8%)

Steps
ItersRangePoint
8
8.535838914561808e-5
2.7657861693978445
0.00020226632576998254
10
-127770193335.10165
-6.157174127538602e-8
-0.00021540980790189893
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify10.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
071241
195241
2113241
3127241
4137241
5141241
6142241
7141241

end3.0ms (0%)

Compiler

Compiled 155 to 89 computations (42.6% saved)

sample2.8s (25.6%)

Algorithm
intervals
Results
1.1s3498×body1024valid
680.0ms1267×body2048valid
263.0ms1345×body512valid
82.0ms631×body256valid
80.0ms1258×body128valid
1.0msbody4096valid
Compiler

Compiled 648 to 355 computations (45.2% saved)

Profiling

Loading profile data...