Details

Time bar (total: 11.5s)

analyze1.2s (10.1%)

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)

sample77.0ms (0.7%)

Algorithm
1×intervals
Results
34.0ms113×body1024valid
19.0ms39×body2048valid
8.0ms43×body512valid
3.0ms45×body128valid
2.0ms16×body256valid
Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify13.0ms (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

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
37.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶37.0b
(-.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
✓0.8b
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓3.1b
(tan.f64 (+.f64 x eps))

rewrite53.0ms (0.5%)

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:

44.0ms
(tan.f64 (+.f64 x eps))
6.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

series122.0ms (1.1%)

Counts
2 → 48
Calls

2 calls:

82.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
40.0ms
(tan.f64 (+.f64 x eps))

simplify130.0ms (1.1%)

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 → 138
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02072570
15072289
217872148
349652145
449862145
549432145

prune96.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1317138
Fresh000
Picked101
Done000
Total1327139
Error
0.2b
Counts
139 → 7
Alt Table
StatusErrorProgram
33.3b
(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
34.4b
(fma.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (*.f64 (*.f64 x x) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 3)) (/.f64 (sin.f64 eps) (cos.f64 eps))))))
19.2b
(/.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)))))
19.2b
(/.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)))
▶19.1b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
33.7b
(+.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)))))
33.8b
(+.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)))))))))))
Compiler

Compiled 3152 to 1347 computations (57.3% saved)

localize11.0ms (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))
✓1.7b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite40.0ms (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:

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))))
5.0ms
(*.f64 (tan.f64 x) (tan.f64 eps))
3.0ms
(+.f64 (tan.f64 x) (tan.f64 eps))

series810.0ms (7.1%)

Counts
4 → 96
Calls

4 calls:

418.0ms
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
237.0ms
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
84.0ms
(*.f64 (tan.f64 x) (tan.f64 eps))
70.0ms
(+.f64 (tan.f64 x) (tan.f64 eps))

simplify270.0ms (2.4%)

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 → 446
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
038510657
19259025
231708501
347678501
449238501

prune290.0ms (2.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New4388446
Fresh336
Picked101
Done000
Total44211453
Error
0.1b
Counts
453 → 11
Alt Table
StatusErrorProgram
19.1b
(+.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)
19.2b
(/.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)))))
19.1b
(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)))
27.9b
(log.f64 (exp.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))))
33.7b
(+.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)))))
19.1b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (tan.f64 x))
33.3b
(*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
▶19.1b
(-.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))
19.3b
(-.f64 (/.f64 (/.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)))))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
33.7b
(+.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))))))))
19.2b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (*.f64 (tan.f64 x) (*.f64 (cbrt.f64 (tan.f64 eps)) (cbrt.f64 (tan.f64 eps)))) (cbrt.f64 (tan.f64 eps))))) (tan.f64 x))
Compiler

Compiled 9565 to 3314 computations (65.4% saved)

localize17.0ms (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) (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)))
✓1.7b
(-.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))

rewrite67.0ms (0.6%)

Algorithm
1×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:

20.0ms
(-.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))
11.0ms
(/.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))

series799.0ms (7%)

Counts
4 → 64
Calls

4 calls:

444.0ms
(-.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))
243.0ms
(/.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)))))
85.0ms
(/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x)))
26.0ms
(*.f64 (sin.f64 x) (sin.f64 eps))

simplify321.0ms (2.8%)

Algorithm
1×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 → 554
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
045217021
1109713818
2421713065
3498613065

prune400.0ms (3.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New5486554
Fresh5510
Picked101
Done000
Total55411565
Error
0.1b
Counts
565 → 11
Alt Table
StatusErrorProgram
19.1b
(+.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)
19.2b
(/.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)))))
20.2b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (-.f64 1 (/.f64 (*.f64 (sin.f64 eps) (sin.f64 x)) (*.f64 (cos.f64 eps) (cos.f64 x)))))) (tan.f64 x))
19.1b
(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))))) (neg.f64 (tan.f64 x)))
33.7b
(+.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))))
27.9b
(log.f64 (exp.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))))
39.6b
(fma.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.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 (cbrt.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)))))) (neg.f64 (tan.f64 x)))
▶19.1b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (sin.f64 x) (/.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (sin.f64 eps))))) (tan.f64 x))
19.3b
(-.f64 (/.f64 (/.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)))))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
33.7b
(+.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))))))))
33.7b
(+.f64 (/.f64 eps (/.f64 (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3) eps)) (+.f64 (*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (/.f64 (*.f64 (sin.f64 x) (*.f64 eps eps)) (cos.f64 x))))
Compiler

Compiled 15566 to 4270 computations (72.6% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (sin.f64 x) (/.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (sin.f64 eps)))))
✓0.2b
(/.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (sin.f64 eps))
✓0.3b
(/.f64 (sin.f64 x) (/.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (sin.f64 eps)))
✓1.7b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (sin.f64 x) (/.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (sin.f64 eps))))) (tan.f64 x))

rewrite91.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
300×add-sqr-sqrt_binary64
295×*-un-lft-identity_binary64
239×times-frac_binary64
127×add-cube-cbrt_binary64
114×prod-diff_binary64
Counts
4 → 309
Calls

4 calls:

25.0ms
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (sin.f64 x) (/.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (sin.f64 eps))))) (tan.f64 x))
18.0ms
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (sin.f64 x) (/.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (sin.f64 eps)))))
5.0ms
(/.f64 (sin.f64 x) (/.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (sin.f64 eps)))
4.0ms
(/.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (sin.f64 eps))

series991.0ms (8.6%)

Counts
4 → 80
Calls

4 calls:

511.0ms
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (sin.f64 x) (/.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (sin.f64 eps))))) (tan.f64 x))
257.0ms
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (sin.f64 x) (/.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (sin.f64 eps)))))
156.0ms
(/.f64 (sin.f64 x) (/.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (sin.f64 eps)))
65.0ms
(/.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (sin.f64 eps))

simplify600.0ms (5.2%)

Algorithm
1×egg-herbie
Rules
229×associate-/l*_binary64
215×associate-+r+_binary64
193×+-commutative_binary64
193×associate-*r*_binary64
191×associate-*l*_binary64
Counts
389 → 708
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
053220985
1123617854
2443417623
3497017623
4500217623

prune524.0ms (4.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New7062708
Fresh1910
Picked011
Done000
Total70712719
Error
0.1b
Counts
719 → 12
Alt Table
StatusErrorProgram
19.1b
(+.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)
19.2b
(/.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)))))
33.7b
(+.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))))
27.9b
(log.f64 (exp.f64 (-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))))
39.6b
(fma.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.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 (cbrt.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)))))) (neg.f64 (tan.f64 x)))
✓19.1b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (sin.f64 x) (/.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (sin.f64 eps))))) (tan.f64 x))
19.2b
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (sin.f64 x) (*.f64 (/.f64 (cos.f64 eps) (*.f64 (cbrt.f64 (sin.f64 eps)) (cbrt.f64 (sin.f64 eps)))) (/.f64 (cos.f64 x) (cbrt.f64 (sin.f64 eps))))))) (tan.f64 x))
19.3b
(-.f64 (/.f64 (/.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)))))) (cbrt.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
33.7b
(+.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))))))))
24.7b
(fma.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps)))) (sqrt.f64 (-.f64 1 (/.f64 (sin.f64 x) (/.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (sin.f64 eps)))))) (/.f64 (cbrt.f64 (+.f64 (tan.f64 x) (tan.f64 eps))) (sqrt.f64 (-.f64 1 (/.f64 (sin.f64 x) (/.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (sin.f64 eps)))))) (neg.f64 (tan.f64 x)))
19.1b
(fma.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (*.f64 (cos.f64 eps) (cos.f64 x))))) (neg.f64 (tan.f64 x)))
33.7b
(+.f64 (/.f64 eps (/.f64 (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3) eps)) (+.f64 (*.f64 eps (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))) (/.f64 (*.f64 (sin.f64 x) (*.f64 eps eps)) (cos.f64 x))))
Compiler

Compiled 19170 to 4784 computations (75% saved)

regimes1.8s (15.6%)

Accuracy

Total 0.9b remaining (86.5%)

Threshold costs 0.9b (86.5%)

Compiler

Compiled 22455 to 12365 computations (44.9% saved)

bsearch72.0ms (0.6%)

Steps
ItersRangePoint
6
4.350858919875792e-32
3.5568736646225677e-31
3.5100561387016338e-31
8
-0.0009492728119689005
-7.97526552862672e-7
-7.034024772968383e-5
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify9.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
061204
190204
2108204
3125204
4134204
5137204
6135204

end3.0ms (0%)

Compiler

Compiled 131 to 73 computations (44.3% saved)

sample2.7s (23.5%)

Algorithm
1×intervals
Results
1.0s3520×body1024valid
616.0ms1211×body2048valid
302.0ms1426×body512valid
80.0ms1246×body128valid
76.0ms595×body256valid
2.0ms2×body4096valid
Compiler

Compiled 644 to 365 computations (43.3% saved)

Profiling

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