Details

Time bar (total: 11.3s)

analyze1.1s (9.8%)

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
18.7%81.2%0.1%7
18.7%81.2%0.1%8
29.7%69.5%0.9%9
30.4%67.9%1.7%10
36.3%61.1%2.6%11
36.9%59.5%3.6%12
39.9%55.9%4.2%13
40.2%54.9%4.9%14
Compiler

Compiled 17 to 11 computations (35.3% saved)

sample3.5s (31.3%)

Results
1.2s1036×body2048valid
947.0ms1941×body1024valid
538.0ms4136×body128valid
286.0ms52×body4096valid
267.0ms743×body512valid
89.0ms348×body256valid
25.0ms183×body128invalid
8.0ms9×body2048invalid
1.0ms1×body8192exit
Compiler

Compiled 50 to 32 computations (36% saved)

simplify23.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
297×fma-def_binary64
157×fma-neg_binary64
50×cancel-sign-sub-inv_binary64
37×associate-/l*_binary64
33×sub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01123
12520
25020
312120
418120
524720
632120
738420
847020
948320
1050920
1146220

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
15.5b
Counts
3 → 2
Alt Table
StatusErrorProgram
▶15.5b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
16.0b
(-.f64 (*.f64 (PI.f64) l) (*.f64 (/.f64 1 (*.f64 F F)) (tan.f64 (*.f64 (PI.f64) l))))
Compiler

Compiled 88 to 48 computations (45.5% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
✓0.3b
(*.f64 (PI.f64) l)
✓3.1b
(/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F))
✓31.8b
(tan.f64 (*.f64 (PI.f64) l))

series115.0ms (1%)

Counts
4 → 60
Calls

4 calls:

59.0ms
(/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F))
40.0ms
(-.f64 (*.f64 (PI.f64) l) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
13.0ms
(tan.f64 (*.f64 (PI.f64) l))
3.0ms
(*.f64 (PI.f64) l)

rewrite18.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
14×add-sqr-sqrt_binary64
12×*-un-lft-identity_binary64
12×add-cube-cbrt_binary64
11×add-cbrt-cube_binary64
11×add-exp-log_binary64
Counts
4 → 82
Calls

4 calls:

6.0ms
(-.f64 (*.f64 (PI.f64) l) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
4.0ms
(/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F))
3.0ms
(*.f64 (PI.f64) l)
1.0ms
(tan.f64 (*.f64 (PI.f64) l))

simplify102.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
782×times-frac_binary64
624×fma-def_binary64
610×associate-/l*_binary64
223×fma-neg_binary64
147×cancel-sign-sub-inv_binary64
Counts
142 → 122
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01923051
14782877
215442771
349222768
448812768

prune223.0ms (2%)

Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New12221143
Fresh101
Picked101
Done000
Total12421145
Error
12.2b
Counts
145 → 21
Alt Table
StatusErrorProgram
15.6b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (tan.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (cbrt.f64 l))) (*.f64 F F)))
37.3b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (tan.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) l) 3))) (*.f64 F F)))
23.5b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (log.f64 (exp.f64 (tan.f64 (*.f64 (PI.f64) l)))) (*.f64 F F)))
39.8b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (tan.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 l)) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 l)))) (*.f64 F F)))
15.6b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (*.f64 (cbrt.f64 (tan.f64 (*.f64 (PI.f64) l))) (cbrt.f64 (tan.f64 (*.f64 (PI.f64) l)))) (/.f64 (*.f64 F F) (cbrt.f64 (tan.f64 (*.f64 (PI.f64) l))))))
39.8b
(-.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) l)) (sqrt.f64 (*.f64 (PI.f64) l))) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
15.5b
(-.f64 (*.f64 (PI.f64) l) (/.f64 1 (/.f64 (*.f64 F F) (tan.f64 (*.f64 (PI.f64) l)))))
44.4b
(-.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (*.f64 (*.f64 l l) l))) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
12.5b
(-.f64 (*.f64 (PI.f64) l) (*.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))
39.7b
(-.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 l)) (sqrt.f64 l)) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
16.2b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (PI.f64) l)) (cbrt.f64 (*.f64 (PI.f64) l))) (cbrt.f64 (*.f64 (PI.f64) l))) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
37.4b
(-.f64 (*.f64 (PI.f64) l) (*.f64 (/.f64 (sqrt.f64 (tan.f64 (*.f64 (PI.f64) l))) F) (/.f64 (sqrt.f64 (tan.f64 (*.f64 (PI.f64) l))) F)))
39.7b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (tan.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 l)) (sqrt.f64 l))) (*.f64 F F)))
12.7b
(-.f64 (*.f64 (PI.f64) l) (*.f64 (/.f64 (*.f64 (cbrt.f64 (tan.f64 (*.f64 (PI.f64) l))) (cbrt.f64 (tan.f64 (*.f64 (PI.f64) l)))) F) (/.f64 (cbrt.f64 (tan.f64 (*.f64 (PI.f64) l))) F)))
16.1b
(-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (cbrt.f64 l)) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
15.6b
(-.f64 (*.f64 (PI.f64) l) (*.f64 (*.f64 (cbrt.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F))) (cbrt.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))) (cbrt.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))))
15.6b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (tan.f64 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) l))) (*.f64 F F)))
40.0b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (tan.f64 (exp.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 l)))) (*.f64 F F)))
15.6b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (tan.f64 (*.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) l))) (*.f64 F F)))
19.6b
(-.f64 (*.f64 (PI.f64) l) (expm1.f64 (log1p.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))))
▶12.5b
(-.f64 (*.f64 (PI.f64) l) (/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F))))
Compiler

Compiled 4002 to 1277 computations (68.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)
0.3b
(*.f64 (PI.f64) l)
✓0.3b
(/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))
31.8b
(tan.f64 (*.f64 (PI.f64) l))

series132.0ms (1.2%)

Counts
2 → 48
Calls

2 calls:

76.0ms
(/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)
55.0ms
(/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))

rewrite46.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
405×times-frac_binary64
195×*-un-lft-identity_binary64
195×add-sqr-sqrt_binary64
195×add-cube-cbrt_binary64
47×associate-/r*_binary64
Counts
2 → 236
Calls

2 calls:

10.0ms
(/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))
3.0ms
(/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)

simplify357.0ms (3.2%)

Algorithm
1×egg-herbie
Rules
587×fma-neg_binary64
352×*-commutative_binary64
291×fma-def_binary64
278×associate-/r/_binary64
242×unswap-sqr_binary64
Counts
284 → 341
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
02808467
15867416
218057073
321937067
428247067
540816913
644846901
749786901
848946901

prune815.0ms (7.2%)

Pruning

22 alts after pruning (21 fresh and 1 done)

PrunedKeptTotal
New3947401
Fresh61420
Picked011
Done000
Total40022422
Error
12.2b
Counts
422 → 22
Alt Table
StatusErrorProgram
16.4b
(-.f64 (*.f64 (PI.f64) l) (/.f64 1 (/.f64 F (expm1.f64 (log1p.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F))))))
40.0b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (tan.f64 (exp.f64 (+.f64 (log.f64 (PI.f64)) (log.f64 l)))) (*.f64 F F)))
15.6b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (tan.f64 (*.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (*.f64 (cbrt.f64 (PI.f64)) l))) (*.f64 F F)))
▶12.5b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (/.f64 1 (/.f64 F (tan.f64 (*.f64 (PI.f64) l)))) F))
39.8b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (tan.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 l)) (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 l)))) (*.f64 F F)))
15.6b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (*.f64 (cbrt.f64 (tan.f64 (*.f64 (PI.f64) l))) (cbrt.f64 (tan.f64 (*.f64 (PI.f64) l)))) (/.f64 (*.f64 F F) (cbrt.f64 (tan.f64 (*.f64 (PI.f64) l))))))
12.7b
(-.f64 (*.f64 (PI.f64) l) (/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 (*.f64 (cbrt.f64 (PI.f64)) (cbrt.f64 (PI.f64))) (*.f64 l (cbrt.f64 (PI.f64))))) F))))
39.8b
(-.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) l)) (sqrt.f64 (*.f64 (PI.f64) l))) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
15.5b
(-.f64 (*.f64 (PI.f64) l) (/.f64 1 (/.f64 (*.f64 F F) (tan.f64 (*.f64 (PI.f64) l)))))
12.7b
(-.f64 (*.f64 (PI.f64) l) (/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (cbrt.f64 l))) F))))
16.2b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (PI.f64) l)) (cbrt.f64 (*.f64 (PI.f64) l))) (cbrt.f64 (*.f64 (PI.f64) l))) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
39.7b
(-.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 l)) (sqrt.f64 l)) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
16.1b
(-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (cbrt.f64 l)) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
15.6b
(-.f64 (*.f64 (PI.f64) l) (*.f64 (*.f64 (cbrt.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F))) (cbrt.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))) (cbrt.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))))
37.3b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (tan.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) l) 3))) (*.f64 F F)))
37.4b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (/.f64 1 (sqrt.f64 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))) (sqrt.f64 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))))
15.6b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (tan.f64 (*.f64 (sqrt.f64 (PI.f64)) (*.f64 (sqrt.f64 (PI.f64)) l))) (*.f64 F F)))
12.5b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (/.f64 1 F) (/.f64 1 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F))))
19.6b
(-.f64 (*.f64 (PI.f64) l) (expm1.f64 (log1p.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))))
✓12.5b
(-.f64 (*.f64 (PI.f64) l) (/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F))))
44.4b
(-.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (*.f64 (*.f64 l l) l))) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
12.7b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (pow.f64 (cbrt.f64 F) 2)) (/.f64 (cbrt.f64 F) (/.f64 1 F))))
Compiler

Compiled 11409 to 3719 computations (67.4% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 F (tan.f64 (*.f64 (PI.f64) l)))
0.3b
(*.f64 (PI.f64) l)
✓0.6b
(/.f64 1 (/.f64 F (tan.f64 (*.f64 (PI.f64) l))))
31.8b
(tan.f64 (*.f64 (PI.f64) l))

series119.0ms (1.1%)

Counts
2 → 48
Calls

2 calls:

77.0ms
(/.f64 F (tan.f64 (*.f64 (PI.f64) l)))
42.0ms
(/.f64 1 (/.f64 F (tan.f64 (*.f64 (PI.f64) l))))

rewrite17.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
87×times-frac_binary64
53×*-un-lft-identity_binary64
53×add-sqr-sqrt_binary64
53×add-cube-cbrt_binary64
17×associate-/r*_binary64
Counts
2 → 112
Calls

2 calls:

5.0ms
(/.f64 1 (/.f64 F (tan.f64 (*.f64 (PI.f64) l))))
3.0ms
(/.f64 F (tan.f64 (*.f64 (PI.f64) l)))

simplify128.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
495×distribute-rgt-neg-in_binary64
469×distribute-lft-neg-in_binary64
412×associate-*l*_binary64
397×associate-*r*_binary64
312×fma-neg_binary64
Counts
160 → 162
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01583444
13273146
29403099
330823095
448153095
550303095

prune318.0ms (2.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New2175222
Fresh13720
Picked101
Done011
Total23113244
Error
1.4b
Counts
244 → 13
Alt Table
StatusErrorProgram
▶1.9b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (/.f64 1 (-.f64 (/.f64 F (*.f64 (PI.f64) l)) (+.f64 (*.f64 1/3 (*.f64 (PI.f64) (*.f64 F l))) (+.f64 (*.f64 2/945 (*.f64 (pow.f64 (PI.f64) 5) (*.f64 (pow.f64 l 5) F))) (*.f64 1/45 (*.f64 (pow.f64 (PI.f64) 3) (*.f64 (pow.f64 l 3) F))))))) F))
37.4b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (/.f64 1 (sqrt.f64 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))) (sqrt.f64 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))))
39.8b
(-.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) l)) (sqrt.f64 (*.f64 (PI.f64) l))) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
15.5b
(-.f64 (*.f64 (PI.f64) l) (/.f64 1 (/.f64 (*.f64 F F) (tan.f64 (*.f64 (PI.f64) l)))))
12.7b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (/.f64 1 (*.f64 (*.f64 (cbrt.f64 F) (cbrt.f64 F)) (/.f64 (cbrt.f64 F) (tan.f64 (*.f64 (PI.f64) l))))) F))
44.4b
(-.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (*.f64 (*.f64 l l) l))) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
37.8b
(-.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 l)) (sqrt.f64 l)) (/.f64 (/.f64 1 (/.f64 F (tan.f64 (*.f64 (PI.f64) l)))) F))
3.0b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (/.f64 1 (+.f64 (/.f64 F (*.f64 (PI.f64) l)) (*.f64 F (fma.f64 (*.f64 (PI.f64) l) -1/3 (*.f64 (pow.f64 l 3) (*.f64 (pow.f64 (PI.f64) 3) -1/45)))))) F))
12.5b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (/.f64 1 F) (/.f64 1 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F))))
✓12.5b
(-.f64 (*.f64 (PI.f64) l) (/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F))))
16.2b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (PI.f64) l)) (cbrt.f64 (*.f64 (PI.f64) l))) (cbrt.f64 (*.f64 (PI.f64) l))) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
16.4b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (expm1.f64 (log1p.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F))) F))
16.1b
(-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (cbrt.f64 l)) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
Compiler

Compiled 5602 to 2108 computations (62.4% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓1.0b
(pow.f64 (PI.f64) 5)
✓2.0b
(/.f64 (/.f64 1 (-.f64 (/.f64 F (*.f64 (PI.f64) l)) (+.f64 (*.f64 1/3 (*.f64 (PI.f64) (*.f64 F l))) (+.f64 (*.f64 2/945 (*.f64 (pow.f64 (PI.f64) 5) (*.f64 (pow.f64 l 5) F))) (*.f64 1/45 (*.f64 (pow.f64 (PI.f64) 3) (*.f64 (pow.f64 l 3) F))))))) F)
✓2.4b
(*.f64 (pow.f64 l 5) F)
✓6.2b
(*.f64 (pow.f64 l 3) F)

series527.0ms (4.7%)

Counts
4 → 48
Calls

4 calls:

498.0ms
(/.f64 (/.f64 1 (-.f64 (/.f64 F (*.f64 (PI.f64) l)) (+.f64 (*.f64 1/3 (*.f64 (PI.f64) (*.f64 F l))) (+.f64 (*.f64 2/945 (*.f64 (pow.f64 (PI.f64) 5) (*.f64 (pow.f64 l 5) F))) (*.f64 1/45 (*.f64 (pow.f64 (PI.f64) 3) (*.f64 (pow.f64 l 3) F))))))) F)
17.0ms
(*.f64 (pow.f64 l 5) F)
11.0ms
(*.f64 (pow.f64 l 3) F)
0.0ms
(pow.f64 (PI.f64) 5)

rewrite70.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
129×times-frac_binary64
109×add-sqr-sqrt_binary64
97×*-un-lft-identity_binary64
73×add-cube-cbrt_binary64
24×add-exp-log_binary64
Counts
4 → 193
Calls

4 calls:

24.0ms
(/.f64 (/.f64 1 (-.f64 (/.f64 F (*.f64 (PI.f64) l)) (+.f64 (*.f64 1/3 (*.f64 (PI.f64) (*.f64 F l))) (+.f64 (*.f64 2/945 (*.f64 (pow.f64 (PI.f64) 5) (*.f64 (pow.f64 l 5) F))) (*.f64 1/45 (*.f64 (pow.f64 (PI.f64) 3) (*.f64 (pow.f64 l 3) F))))))) F)
4.0ms
(*.f64 (pow.f64 l 3) F)
4.0ms
(*.f64 (pow.f64 l 5) F)
2.0ms
(pow.f64 (PI.f64) 5)

simplify357.0ms (3.2%)

Algorithm
1×egg-herbie
Rules
417×unswap-sqr_binary64
333×associate-*l*_binary64
310×associate-*r*_binary64
215×fma-neg_binary64
181×*-commutative_binary64
Counts
241 → 287
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
035614854
194513720
2360513688
3499513688
4495113688

prune807.0ms (7.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New2825287
Fresh2911
Picked101
Done011
Total28515300
Error
1.2b
Counts
300 → 15
Alt Table
StatusErrorProgram
10.6b
(-.f64 (*.f64 (PI.f64) l) (/.f64 1 (*.f64 (-.f64 (/.f64 1 (*.f64 l (PI.f64))) (fma.f64 (*.f64 l (PI.f64)) 1/3 (fma.f64 2/945 (*.f64 (pow.f64 l 5) (pow.f64 (PI.f64) 5)) (*.f64 1/45 (pow.f64 (*.f64 l (PI.f64)) 3))))) (*.f64 F F))))
3.0b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (/.f64 1 (+.f64 (/.f64 F (*.f64 (PI.f64) l)) (*.f64 F (fma.f64 (*.f64 (PI.f64) l) -1/3 (*.f64 (pow.f64 l 3) (*.f64 (pow.f64 (PI.f64) 3) -1/45)))))) F))
2.1b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (/.f64 1 (-.f64 (/.f64 F (*.f64 (PI.f64) l)) (+.f64 (*.f64 1/3 (*.f64 (PI.f64) (*.f64 F l))) (+.f64 (*.f64 2/945 (*.f64 (pow.f64 (PI.f64) 5) (*.f64 (pow.f64 (*.f64 (cbrt.f64 l) (cbrt.f64 l)) 5) (*.f64 (pow.f64 (cbrt.f64 l) 5) F)))) (*.f64 1/45 (*.f64 (pow.f64 (PI.f64) 3) (*.f64 (pow.f64 l 3) F))))))) F))
39.8b
(-.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) l)) (sqrt.f64 (*.f64 (PI.f64) l))) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
1.7b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (/.f64 1 (-.f64 (/.f64 F (*.f64 (PI.f64) l)) (+.f64 (*.f64 1/3 (*.f64 (PI.f64) (*.f64 F l))) (+.f64 (*.f64 2/945 (*.f64 (pow.f64 (PI.f64) 5) (log1p.f64 (expm1.f64 (*.f64 (pow.f64 l 5) F))))) (*.f64 1/45 (*.f64 (pow.f64 (PI.f64) 3) (*.f64 (pow.f64 l 3) F))))))) F))
44.4b
(-.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (PI.f64) (PI.f64)) (PI.f64)) (*.f64 (*.f64 l l) l))) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
37.8b
(-.f64 (*.f64 (*.f64 (PI.f64) (sqrt.f64 l)) (sqrt.f64 l)) (/.f64 (/.f64 1 (/.f64 F (tan.f64 (*.f64 (PI.f64) l)))) F))
1.9b
(-.f64 (*.f64 (PI.f64) l) (/.f64 1 (*.f64 F (-.f64 (/.f64 F (*.f64 l (PI.f64))) (fma.f64 1/3 (*.f64 F (*.f64 l (PI.f64))) (fma.f64 2/945 (*.f64 F (*.f64 (pow.f64 l 5) (pow.f64 (PI.f64) 5))) (*.f64 1/45 (*.f64 F (pow.f64 (*.f64 l (PI.f64)) 3)))))))))
16.2b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (PI.f64) l)) (cbrt.f64 (*.f64 (PI.f64) l))) (cbrt.f64 (*.f64 (PI.f64) l))) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
37.4b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (/.f64 1 (sqrt.f64 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))) (sqrt.f64 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F)))))
12.5b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (/.f64 1 F) (/.f64 1 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F))))
✓12.5b
(-.f64 (*.f64 (PI.f64) l) (/.f64 1 (/.f64 F (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F))))
18.1b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (/.f64 1 (-.f64 (/.f64 F (*.f64 (PI.f64) l)) (+.f64 (*.f64 1/3 (*.f64 (PI.f64) (*.f64 F l))) (+.f64 (*.f64 2/945 (*.f64 (pow.f64 (PI.f64) 5) (exp.f64 (log.f64 (*.f64 F (pow.f64 l 5)))))) (*.f64 1/45 (*.f64 (pow.f64 (PI.f64) 3) (*.f64 (pow.f64 l 3) F))))))) F))
16.4b
(-.f64 (*.f64 (PI.f64) l) (/.f64 (expm1.f64 (log1p.f64 (/.f64 (tan.f64 (*.f64 (PI.f64) l)) F))) F))
16.1b
(-.f64 (*.f64 (*.f64 (PI.f64) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (cbrt.f64 l)) (/.f64 (tan.f64 (*.f64 (PI.f64) l)) (*.f64 F F)))
Compiler

Compiled 22089 to 12565 computations (43.1% saved)

regimes2.1s (18.8%)

Accuracy

Total 0.7b remaining (34.6%)

Threshold costs 0.7b (34.6%)

Counts
262 → 1
Compiler

Compiled 40508 to 25051 computations (38.2% saved)

simplify8.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
29×*-commutative_binary64
23×+-commutative_binary64
21×sub-neg_binary64
19×neg-sub0_binary64
19×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03376
15176
26476
38976
412576
516076
618876
720676
821476
921576
1021076

end297.0ms (2.6%)

Compiler

Compiled 552 to 350 computations (36.6% saved)

Profiling

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