Details

Time bar (total: 16.1s)

analyze1.3s (8.3%)

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
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)

sample3.8s (23.3%)

Results
1.9s3599×body1024valid
957.0ms1220×body2048valid
492.0ms1446×body512valid
189.0ms1349×body128valid
155.0ms641×body256valid
1.0ms1×body4096valid
Compiler

Compiled 29 to 20 computations (31% 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

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
35.6b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶35.6b
(-.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
✓1.5b
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓4.4b
(tan.f64 (+.f64 x eps))

series76.0ms (0.5%)

Counts
2 → 48
Calls

2 calls:

48.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
28.0ms
(tan.f64 (+.f64 x eps))

rewrite10.0ms (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:

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

simplify107.0ms (0.7%)

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

prune92.0ms (0.6%)

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
20.9b
(/.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)))
32.6b
(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
33.0b
(+.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)))))
33.0b
(+.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)))))
33.0b
(+.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)))))
20.9b
(/.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)))))
▶20.8b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
Compiler

Compiled 2983 to 1243 computations (58.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(+.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))
✓2.3b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series390.0ms (2.4%)

Counts
4 → 96
Calls

4 calls:

213.0ms
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
115.0ms
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
33.0ms
(*.f64 (tan.f64 x) (tan.f64 eps))
28.0ms
(+.f64 (tan.f64 x) (tan.f64 eps))

rewrite44.0ms (0.3%)

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:

11.0ms
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
7.0ms
(/.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))

simplify232.0ms (1.4%)

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

prune366.0ms (2.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New2378245
Fresh156
Picked101
Done000
Total23913252
Error
0.1b
Counts
252 → 13
Alt Table
StatusErrorProgram
33.0b
(+.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)))))
20.8b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))) (tan.f64 x))
▶20.8b
(-.f64 (*.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))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
32.6b
(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
20.8b
(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)))
42.8b
(fma.f64 (sqrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (sqrt.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (neg.f64 (tan.f64 x)))
21.7b
(+.f64 (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 (*.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))))))
21.5b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))) (cbrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)))) (cbrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))))
21.9b
(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)))
33.0b
(+.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)))))
33.0b
(+.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)))))
20.9b
(/.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)))))
48.1b
(+.f64 (fma.f64 (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (-.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)))))
Compiler

Compiled 9859 to 3385 computations (65.7% 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 (tan.f64 x) (tan.f64 eps)) (*.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)))
✓2.1b
(-.f64 (*.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))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series2.0s (12.1%)

Counts
3 → 72
Calls

3 calls:

1.5s
(-.f64 (*.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))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
387.0ms
(/.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)))))
69.0ms
(*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))

rewrite39.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
42×pow1_binary64
39×tan-quot_binary64
33×*-un-lft-identity_binary64
21×add-sqr-sqrt_binary64
20×times-frac_binary64
Counts
3 → 126
Calls

3 calls:

11.0ms
(-.f64 (*.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))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
7.0ms
(*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
6.0ms
(/.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)))))

simplify208.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
400×associate-*l*_binary64
361×associate-*r*_binary64
331×unswap-sqr_binary64
206×fma-neg_binary64
176×*-commutative_binary64
Counts
198 → 198
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
039910922
1108610445
2408410360
3513910360

prune475.0ms (2.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New3273330
Fresh21012
Picked101
Done000
Total33013343
Error
0.1b
Counts
343 → 13
Alt Table
StatusErrorProgram
33.0b
(+.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)))))
▶20.8b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))) (tan.f64 x))
32.9b
(+.f64 (/.f64 eps (/.f64 (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3) eps)) (+.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 eps (+.f64 (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (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 (sin.f64 x) (*.f64 eps eps)) (cos.f64 x))))
32.6b
(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
20.8b
(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)))
21.5b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))) (cbrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)))) (cbrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))))
21.9b
(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)))
20.8b
(-.f64 (*.f64 (*.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 eps) 1)) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
33.0b
(+.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)))))
20.9b
(/.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)))))
48.1b
(+.f64 (fma.f64 (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (-.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)))))
20.8b
(-.f64 (*.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (cbrt.f64 (*.f64 (*.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (tan.f64 x)) (*.f64 (*.f64 (tan.f64 eps) (tan.f64 eps)) (tan.f64 eps))))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
21.7b
(+.f64 (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 (*.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))))))
Compiler

Compiled 15707 to 5231 computations (66.7% saved)

localize16.0ms (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 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))))
✓0.2b
(/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))
✓0.2b
(*.f64 (tan.f64 x) (sin.f64 eps))
✓2.3b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))) (tan.f64 x))

series405.0ms (2.5%)

Counts
4 → 96
Calls

4 calls:

227.0ms
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))) (tan.f64 x))
119.0ms
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))))
36.0ms
(/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps))
23.0ms
(*.f64 (tan.f64 x) (sin.f64 eps))

rewrite75.0ms (0.5%)

Algorithm
1×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:

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

simplify423.0ms (2.6%)

Algorithm
1×egg-herbie
Rules
243×unswap-sqr_binary64
222×associate-+r+_binary64
217×associate-/l*_binary64
201×associate-*l*_binary64
192×+-commutative_binary64
Counts
334 → 333
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
043715753
1104312970
2376412233
3475612233
4498512233
5499912233
6492412233

prune372.0ms (2.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New3321333
Fresh11112
Picked101
Done000
Total33412346
Error
0.1b
Counts
346 → 12
Alt Table
StatusErrorProgram
33.0b
(+.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)))))
32.9b
(+.f64 (/.f64 eps (/.f64 (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3) eps)) (+.f64 (+.f64 (/.f64 (*.f64 (pow.f64 eps 3) (pow.f64 (sin.f64 x) 4)) (pow.f64 (cos.f64 x) 4)) (+.f64 eps (+.f64 (*.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (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 (sin.f64 x) (*.f64 eps eps)) (cos.f64 x))))
21.7b
(+.f64 (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 (*.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))))))
20.8b
(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 eps)) (cos.f64 eps)))) (neg.f64 (tan.f64 x)))
21.5b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))) (cbrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x)))) (cbrt.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))))
21.9b
(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)))
20.8b
(-.f64 (*.f64 (*.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 eps) 1)) (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
33.0b
(+.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)))))
20.9b
(/.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)))))
32.6b
(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
48.1b
(+.f64 (fma.f64 (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (*.f64 (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (/.f64 (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (-.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)))))
20.8b
(-.f64 (*.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) (cbrt.f64 (*.f64 (*.f64 (*.f64 (tan.f64 x) (tan.f64 x)) (tan.f64 x)) (*.f64 (*.f64 (tan.f64 eps) (tan.f64 eps)) (tan.f64 eps))))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
Compiler

Compiled 13780 to 3983 computations (71.1% saved)

regimes5.2s (32.3%)

Accuracy

Total 0.2b remaining (61.8%)

Threshold costs 0.2b (61.8%)

Counts
566 → 3
Compiler

Compiled 58329 to 29459 computations (49.5% saved)

bsearch135.0ms (0.8%)

Steps
ItersRangePoint
9
1.3120128246323562e-11
1.4166182752465696e-6
1.4010817516092153e-6
11
-0.000377416288361673
-1.8190823126822755e-23
-0.0002511940692751289
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify12.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
19×+-commutative_binary64
16×*-commutative_binary64
13×sub-neg_binary64
7×neg-sub0_binary64
7×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
077274
1109274
2130274
3147274
4156274
5159274
6160274
7159274

end321.0ms (2%)

Compiler

Compiled 884 to 458 computations (48.2% saved)

Profiling

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