Details

Time bar (total: 14.4s)

analyze1.8s (12.4%)

Algorithm
1×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
0%99.9%0.1%7
0%99.9%0.1%8
0%99.9%0.1%9
0%99.9%0.1%10
0%99.9%0.1%11
0%99.9%0.1%12
0%99.9%0.1%13
0%99.9%0.1%14
Compiler

Compiled 10 to 7 computations (30% saved)

sample5.1s (35.3%)

Results
2.4s3603×body1024valid
1.5s1255×body2048valid
773.0ms1458×body512valid
213.0ms1339×body128valid
178.0ms599×body256valid
3.0ms2×body4096valid
Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify10.0ms (0.1%)

Algorithm
1×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

prune25.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
36.5b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶36.5b
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 27 to 18 computations (33.3% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓1.1b
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓2.5b
(tan.f64 (+.f64 x eps))

series92.0ms (0.6%)

Counts
2 → 48
Calls

2 calls:

55.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
37.0ms
(tan.f64 (+.f64 x eps))

rewrite20.0ms (0.1%)

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

2 calls:

11.0ms
(tan.f64 (+.f64 x eps))
6.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

simplify213.0ms (1.5%)

Algorithm
1×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

prune143.0ms (1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New86793
Fresh000
Picked101
Done000
Total87794
Error
0.2b
Counts
94 → 7
Alt Table
StatusErrorProgram
29.3b
(*.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)))))
29.7b
(+.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)))))))))))
29.7b
(+.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)))))
24.4b
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (*.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (*.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
29.6b
(+.f64 (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)))))
▶24.2b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
Compiler

Compiled 3139 to 1347 computations (57.1% saved)

localize10.0ms (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))
✓3.0b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series594.0ms (4.1%)

Counts
4 → 96
Calls

4 calls:

313.0ms
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
198.0ms
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
43.0ms
(*.f64 (tan.f64 x) (tan.f64 eps))
39.0ms
(+.f64 (tan.f64 x) (tan.f64 eps))

rewrite61.0ms (0.4%)

Algorithm
1×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:

26.0ms
(-.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))

simplify315.0ms (2.2%)

Algorithm
1×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

prune450.0ms (3.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New23411245
Fresh426
Picked101
Done000
Total23913252
Error
0.1b
Counts
252 → 13
Alt Table
StatusErrorProgram
▶24.2b
(-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
27.6b
(/.f64 (-.f64 (pow.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) 3) (pow.f64 (tan.f64 x) 3)) (+.f64 (*.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)))))
24.3b
(+.f64 (fma.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps))))) (fma.f64 (tan.f64 x) (tan.f64 eps) 1) (neg.f64 (tan.f64 x))) 0)
29.6b
(+.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps) (fma.f64 4/3 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (*.f64 (pow.f64 eps 3) 1/3)))) (*.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)) (sin.f64 x))))
25.3b
(fma.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) 1) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
27.3b
(-.f64 (/.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
24.2b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (cbrt.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)))) (tan.f64 x))
29.3b
(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
29.7b
(+.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)))))
29.6b
(+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)) (+.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 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 eps (+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)) (+.f64 (*.f64 4/3 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 1/3 (pow.f64 eps 3))))))))
24.4b
(-.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)))
25.3b
(+.f64 (-.f64 (pow.f64 (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) 3) (tan.f64 x)) 0)
24.8b
(+.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (*.f64 (neg.f64 (*.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x)))) (cbrt.f64 (tan.f64 x))))
Compiler

Compiled 9875 to 3462 computations (64.9% 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 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))
✓3.0b
(-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))

series671.0ms (4.7%)

Counts
2 → 48
Calls

2 calls:

543.0ms
(-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
128.0ms
(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))

rewrite27.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
19×add-sqr-sqrt_binary64
16×tan-quot_binary64
15×associate-*r*_binary64
15×*-un-lft-identity_binary64
12×add-cube-cbrt_binary64
Counts
2 → 75
Calls

2 calls:

12.0ms
(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
9.0ms
(-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))

simplify131.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
577×distribute-rgt-in_binary64
219×associate-*l*_binary64
211×cancel-sign-sub-inv_binary64
203×unswap-sqr_binary64
190×associate-+r+_binary64
Counts
123 → 149
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02955334
18045228
228825123
349345123

prune278.0ms (1.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2233226
Fresh4812
Picked101
Done000
Total22811239
Error
0.1b
Counts
239 → 11
Alt Table
StatusErrorProgram
▶25.0b
(-.f64 (*.f64 (log1p.f64 (expm1.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
25.3b
(+.f64 (-.f64 (pow.f64 (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) 3) (tan.f64 x)) 0)
25.3b
(fma.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) 1) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
27.3b
(-.f64 (/.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
27.6b
(/.f64 (-.f64 (pow.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) 3) (pow.f64 (tan.f64 x) 3)) (+.f64 (*.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)))))
29.3b
(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
29.7b
(+.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)))))
29.6b
(+.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps) (fma.f64 4/3 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (*.f64 (pow.f64 eps 3) 1/3)))) (*.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)) (sin.f64 x))))
29.6b
(+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)) (+.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 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 eps (+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)) (+.f64 (*.f64 4/3 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 1/3 (pow.f64 eps 3))))))))
25.7b
(/.f64 (-.f64 (*.f64 (*.f64 (-.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 (tan.f64 eps) (tan.f64 eps))) 1) (cos.f64 x)) (*.f64 (*.f64 (-.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (sin.f64 x))) (*.f64 (*.f64 (-.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (cos.f64 x)))
27.9b
(/.f64 (fma.f64 (cos.f64 x) (+.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3)) (*.f64 (*.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) (*.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x))))) (+.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) -1))) (*.f64 (cos.f64 x) (*.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (fma.f64 (tan.f64 x) (tan.f64 x) (*.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)))))))
Compiler

Compiled 8444 to 3415 computations (59.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (tan.f64 x) (tan.f64 eps))
✓0.3b
(expm1.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))
✓0.7b
(log1p.f64 (expm1.f64 (+.f64 (tan.f64 x) (tan.f64 eps))))
✓7.1b
(-.f64 (*.f64 (log1p.f64 (expm1.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))

series379.0ms (2.6%)

Counts
3 → 72
Calls

3 calls:

254.0ms
(-.f64 (*.f64 (log1p.f64 (expm1.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
87.0ms
(log1p.f64 (expm1.f64 (+.f64 (tan.f64 x) (tan.f64 eps))))
37.0ms
(expm1.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))

rewrite9.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
5×add-log-exp_binary64
5×*-un-lft-identity_binary64
5×add-sqr-sqrt_binary64
5×add-cube-cbrt_binary64
4×log1p-expm1-u_binary64
Counts
3 → 44
Calls

3 calls:

7.0ms
(-.f64 (*.f64 (log1p.f64 (expm1.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
0.0ms
(expm1.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))
0.0ms
(log1p.f64 (expm1.f64 (+.f64 (tan.f64 x) (tan.f64 eps))))

simplify100.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
675×associate-/l*_binary64
413×associate-/r*_binary64
191×distribute-rgt-in_binary64
186×distribute-lft-in_binary64
142×unswap-sqr_binary64
Counts
116 → 111
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02413834
16233663
221403573
351433573

prune194.0ms (1.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1541155
Fresh01010
Picked101
Done000
Total15511166
Error
0.1b
Counts
166 → 11
Alt Table
StatusErrorProgram
25.3b
(fma.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) 1) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
27.3b
(-.f64 (/.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (sqrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
27.6b
(/.f64 (-.f64 (pow.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) 3) (pow.f64 (tan.f64 x) 3)) (+.f64 (*.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)))))
27.6b
(-.f64 (*.f64 (log1p.f64 (log1p.f64 (expm1.f64 (expm1.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))))) (/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
29.3b
(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
29.7b
(+.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)))))
29.6b
(+.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps) (fma.f64 4/3 (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (*.f64 (pow.f64 eps 3) 1/3)))) (*.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)) (sin.f64 x))))
29.6b
(+.f64 (/.f64 (*.f64 (pow.f64 eps 2) (sin.f64 x)) (cos.f64 x)) (+.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 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 eps (+.f64 (/.f64 (*.f64 eps (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2)) (+.f64 (*.f64 4/3 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 2)) (pow.f64 (cos.f64 x) 2))) (*.f64 1/3 (pow.f64 eps 3))))))))
25.3b
(+.f64 (-.f64 (pow.f64 (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) 3) (tan.f64 x)) 0)
25.7b
(/.f64 (-.f64 (*.f64 (*.f64 (-.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (*.f64 (tan.f64 eps) (tan.f64 eps))) 1) (cos.f64 x)) (*.f64 (*.f64 (-.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (sin.f64 x))) (*.f64 (*.f64 (-.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (cos.f64 x)))
27.9b
(/.f64 (fma.f64 (cos.f64 x) (+.f64 (pow.f64 (tan.f64 x) 3) (pow.f64 (tan.f64 eps) 3)) (*.f64 (*.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 x) (*.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x))))) (+.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) -1))) (*.f64 (cos.f64 x) (*.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (fma.f64 (tan.f64 x) (tan.f64 x) (*.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) (tan.f64 x)))))))
Compiler

Compiled 5490 to 2227 computations (59.4% saved)

regimes3.3s (22.6%)

Accuracy

Total 0.2b remaining (53%)

Threshold costs 0.2b (53%)

Counts
388 → 3
Compiler

Compiled 36063 to 19931 computations (44.7% saved)

bsearch133.0ms (0.9%)

Steps
ItersRangePoint
10
5.489262752659868e-7
11897.890833890428
0.00031230127715924045
9
-9.28533629159753
-0.00012520256540215095
-0.00021560437678393656
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify8.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
064225
183225
294225
3100225
4104225
5105225
6104225

end388.0ms (2.7%)

Compiler

Compiled 854 to 475 computations (44.4% saved)

Profiling

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