Details

Time bar (total: 10.3s)

analyze6.0ms (0.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%49.7%50.3%0
0%49.7%50.3%1
0%49.7%50.3%2
24.8%24.8%50.3%3
37.3%12.4%50.3%4
43.5%6.2%50.3%5
46.6%3.1%50.3%6
48.1%1.6%50.3%7
48.9%0.8%50.3%8
49.3%0.4%50.3%9
49.5%0.2%50.3%10
49.6%0.1%50.3%11
49.6%0%50.3%12
49.7%0%50.3%13
49.7%0%50.3%14
Compiler

Compiled 16 to 12 computations (25% saved)

sample298.0ms (2.9%)

Algorithm
intervals
Results
220.0ms127×body2048valid
22.0ms62×body1024valid
13.0ms11×body4096valid
5.0ms30×body512valid
5.0ms256×pre128true
2.0ms19×body256valid
0.0msbody128valid
Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify11.0ms (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
0712
11112
21712
32512
43312
55112
67612
79312
811012
912012
1012412
1112612
1211212

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
59.7b
Counts
2 → 1
Alt Table
StatusErrorProgram
59.7b
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (tan.f64 x))
3.9b
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

series34.0ms (0.3%)

Counts
2 → 24
Calls

2 calls:

18.0ms
(/.f64 1 (tan.f64 x))
15.0ms
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite54.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
288×times-frac_binary64
239×add-sqr-sqrt_binary64
231×*-un-lft-identity_binary64
215×add-cube-cbrt_binary64
182×prod-diff_binary64
Counts
2 → 273
Calls

2 calls:

15.0ms
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
3.0ms
(/.f64 1 (tan.f64 x))

simplify254.0ms (2.5%)

Algorithm
egg-herbie
Rules
770×fma-neg_binary64
466×fma-def_binary64
354×distribute-rgt-in_binary64
331×cancel-sign-sub-inv_binary64
277×associate-*l*_binary64
Counts
297 → 302
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01718645
13646130
29114575
328034281
442384246
549404246
647684246

prune194.0ms (1.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New3011302
Fresh000
Picked101
Done000
Total3021303
Error
0.3b
Counts
303 → 1
Alt Table
StatusErrorProgram
0.3b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 1/3 x)))
Compiler

Compiled 10348 to 6497 computations (37.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 1/3 x))
0.1b
(*.f64 2/945 (pow.f64 x 5))
0.1b
(*.f64 1/45 (pow.f64 x 3))
0.3b
(*.f64 1/3 x)

series11.0ms (0.1%)

Counts
4 → 9
Calls

4 calls:

3.0ms
(+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 1/3 x))
3.0ms
(*.f64 2/945 (pow.f64 x 5))
3.0ms
(*.f64 1/45 (pow.f64 x 3))
2.0ms
(*.f64 1/3 x)

rewrite19.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt_binary64
22×associate-*r*_binary64
16×add-exp-log_binary64
13×*-un-lft-identity_binary64
13×add-cube-cbrt_binary64
Counts
4 → 94
Calls

4 calls:

5.0ms
(+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 1/3 x))
5.0ms
(*.f64 1/45 (pow.f64 x 3))
4.0ms
(*.f64 2/945 (pow.f64 x 5))
3.0ms
(*.f64 1/3 x)

simplify89.0ms (0.9%)

Algorithm
egg-herbie
Rules
520×fma-neg_binary64
481×unswap-sqr_binary64
431×*-commutative_binary64
235×fma-def_binary64
234×sqr-pow_binary64
Counts
103 → 120
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01521094
13181020
28501004
318781004
43929968
54727965
64861965

prune112.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1137120
Fresh000
Picked011
Done000
Total1138121
Error
0.1b
Counts
121 → 8
Alt Table
StatusErrorProgram
1.6b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 (cbrt.f64 (*.f64 1/3 x)) (cbrt.f64 (*.f64 1/3 x))) (cbrt.f64 (*.f64 1/3 x)))))
0.3b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 1/3 x)))
30.8b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (/.f64 (*.f64 (*.f64 x x) (fma.f64 1/2025 (pow.f64 x 4) -1/9)) (*.f64 x (fma.f64 x (*.f64 x 1/45) -1/3))))
42.3b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (/.f64 (+.f64 (pow.f64 (*.f64 1/45 (pow.f64 x 3)) 3) (pow.f64 (*.f64 1/3 x) 3)) (+.f64 (*.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 1/45 (pow.f64 x 3))) (-.f64 (*.f64 (*.f64 1/3 x) (*.f64 1/3 x)) (*.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 1/3 x))))))
28.9b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 1/3 (sqrt.f64 x)) (sqrt.f64 x))))
1.4b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))
29.0b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (sqrt.f64 (*.f64 1/3 x)) (sqrt.f64 (*.f64 1/3 x)))))
40.1b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (cbrt.f64 (*.f64 (*.f64 (*.f64 1/3 1/3) 1/3) (*.f64 (*.f64 x x) x)))))
Compiler

Compiled 2889 to 2310 computations (20% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (*.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
0.4b
(*.f64 1/3 (pow.f64 (cbrt.f64 x) 2))
0.4b
(pow.f64 (cbrt.f64 x) 2)
0.6b
(cbrt.f64 x)

series134.0ms (1.3%)

Counts
4 → 48
Calls

4 calls:

45.0ms
(*.f64 1/3 (pow.f64 (cbrt.f64 x) 2))
43.0ms
(pow.f64 (cbrt.f64 x) 2)
33.0ms
(cbrt.f64 x)
12.0ms
(*.f64 (*.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))

rewrite18.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt_binary64
20×add-exp-log_binary64
17×associate-*r*_binary64
14×unpow-prod-down_binary64
14×*-un-lft-identity_binary64
Counts
4 → 94
Calls

4 calls:

6.0ms
(*.f64 (*.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
5.0ms
(*.f64 1/3 (pow.f64 (cbrt.f64 x) 2))
2.0ms
(pow.f64 (cbrt.f64 x) 2)
1.0ms
(cbrt.f64 x)

simplify104.0ms (1%)

Algorithm
egg-herbie
Rules
732×fma-def_binary64
531×distribute-rgt-in_binary64
488×distribute-lft-in_binary64
391×*-commutative_binary64
260×sqr-pow_binary64
Counts
142 → 148
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01161266
12321141
26811075
311441069
42007980
54698980
64986980
74817980

prune176.0ms (1.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1607167
Fresh156
Picked101
Done011
Total16213175
Error
0.1b
Counts
175 → 13
Alt Table
StatusErrorProgram
40.1b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (cbrt.f64 (*.f64 1/27 (pow.f64 x 3)))))
2.0b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 1/3 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2))) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))) (cbrt.f64 x))))
30.8b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (/.f64 (*.f64 (*.f64 x x) (fma.f64 1/2025 (pow.f64 x 4) -1/9)) (*.f64 x (fma.f64 x (*.f64 x 1/45) -1/3))))
1.8b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x))))))
42.3b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (/.f64 (+.f64 (pow.f64 (*.f64 1/45 (pow.f64 x 3)) 3) (pow.f64 (*.f64 1/3 x) 3)) (+.f64 (*.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 1/45 (pow.f64 x 3))) (-.f64 (*.f64 (*.f64 1/3 x) (*.f64 1/3 x)) (*.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 1/3 x))))))
2.4b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 1/3 (pow.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (cbrt.f64 (cbrt.f64 x))) 2)) (cbrt.f64 x))))
1.6b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 (cbrt.f64 (*.f64 1/3 x)) (cbrt.f64 (*.f64 1/3 x))) (cbrt.f64 (*.f64 1/3 x)))))
0.3b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 1/3 x)))
2.0b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (cbrt.f64 (cbrt.f64 x))))))
1.7b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 (*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)) (*.f64 (cbrt.f64 1/3) (pow.f64 (cbrt.f64 x) 2))) (cbrt.f64 x))))
28.9b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 1/3 (sqrt.f64 x)) (sqrt.f64 x))))
31.5b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 1/3 (pow.f64 (exp.f64 (log.f64 (cbrt.f64 x))) 2)) (cbrt.f64 x))))
29.0b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (sqrt.f64 (*.f64 1/3 x)) (sqrt.f64 (*.f64 1/3 x)))))
Compiler

Compiled 4933 to 3565 computations (27.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 1/3 x)
0.3b
(*.f64 (*.f64 (cbrt.f64 (*.f64 1/3 x)) (cbrt.f64 (*.f64 1/3 x))) (cbrt.f64 (*.f64 1/3 x)))
0.5b
(*.f64 (cbrt.f64 (*.f64 1/3 x)) (cbrt.f64 (*.f64 1/3 x)))
0.7b
(cbrt.f64 (*.f64 1/3 x))

series144.0ms (1.4%)

Counts
3 → 36
Calls

3 calls:

77.0ms
(cbrt.f64 (*.f64 1/3 x))
46.0ms
(*.f64 (cbrt.f64 (*.f64 1/3 x)) (cbrt.f64 (*.f64 1/3 x)))
21.0ms
(*.f64 (*.f64 (cbrt.f64 (*.f64 1/3 x)) (cbrt.f64 (*.f64 1/3 x))) (cbrt.f64 (*.f64 1/3 x)))

rewrite25.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
29×pow1_binary64
16×pow1/3_binary64
11×pow-prod-up_binary64
11×add-sqr-sqrt_binary64
10×add-exp-log_binary64
Counts
3 → 79
Calls

3 calls:

7.0ms
(*.f64 (*.f64 (cbrt.f64 (*.f64 1/3 x)) (cbrt.f64 (*.f64 1/3 x))) (cbrt.f64 (*.f64 1/3 x)))
5.0ms
(*.f64 (cbrt.f64 (*.f64 1/3 x)) (cbrt.f64 (*.f64 1/3 x)))
2.0ms
(cbrt.f64 (*.f64 1/3 x))

simplify102.0ms (1%)

Algorithm
egg-herbie
Rules
582×fma-def_binary64
489×*-commutative_binary64
469×associate-*r*_binary64
415×sqr-pow_binary64
368×unswap-sqr_binary64
Counts
115 → 105
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0801128
11491049
2420985
31173924
42297830
53346830
64439830
74846830

prune193.0ms (1.9%)

Pruning

16 alts after pruning (14 fresh and 2 done)

PrunedKeptTotal
New2024206
Fresh11011
Picked011
Done011
Total20316219
Error
0.0b
Counts
219 → 16
Alt Table
StatusErrorProgram
40.1b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (cbrt.f64 (*.f64 1/27 (pow.f64 x 3)))))
2.0b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 1/3 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2))) (cbrt.f64 (pow.f64 (cbrt.f64 x) 2)))) (cbrt.f64 x))))
30.8b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (/.f64 (*.f64 (*.f64 x x) (fma.f64 1/2025 (pow.f64 x 4) -1/9)) (*.f64 x (fma.f64 x (*.f64 x 1/45) -1/3))))
1.6b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 (*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)) (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (*.f64 1/3 x)))))
1.8b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x))))))
42.3b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (/.f64 (+.f64 (pow.f64 (*.f64 1/45 (pow.f64 x 3)) 3) (pow.f64 (*.f64 1/3 x) 3)) (+.f64 (*.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 1/45 (pow.f64 x 3))) (-.f64 (*.f64 (*.f64 1/3 x) (*.f64 1/3 x)) (*.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 1/3 x))))))
2.4b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 1/3 (pow.f64 (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (cbrt.f64 (cbrt.f64 x))) 2)) (cbrt.f64 x))))
28.9b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 1/3 (sqrt.f64 x)) (sqrt.f64 x))))
1.6b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 (cbrt.f64 1/3) (pow.f64 (cbrt.f64 (*.f64 1/3 x)) 2)) (cbrt.f64 x))))
29.0b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (sqrt.f64 (*.f64 1/3 x)) (sqrt.f64 (*.f64 1/3 x)))))
2.0b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 (cbrt.f64 (*.f64 1/3 x)) (cbrt.f64 (*.f64 1/3 x))) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 1/3 x))) 2) (cbrt.f64 (cbrt.f64 (*.f64 1/3 x)))))))
1.6b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 (cbrt.f64 (*.f64 1/3 x)) (cbrt.f64 (*.f64 1/3 x))) (cbrt.f64 (*.f64 1/3 x)))))
0.3b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 1/3 x)))
2.0b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 1/3 (pow.f64 (cbrt.f64 x) 2)) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (cbrt.f64 (cbrt.f64 x))))))
31.5b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 1/3 (pow.f64 (exp.f64 (log.f64 (cbrt.f64 x))) 2)) (cbrt.f64 x))))
1.8b
(+.f64 (*.f64 2/945 (pow.f64 x 5)) (+.f64 (*.f64 1/45 (pow.f64 x 3)) (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 1/3 x)) (cbrt.f64 (*.f64 1/3 x))) (cbrt.f64 (*.f64 1/3 x)))) (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 1/3 x)) (cbrt.f64 (*.f64 1/3 x))) (cbrt.f64 (*.f64 1/3 x))))) (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 1/3 x)) (cbrt.f64 (*.f64 1/3 x))) (cbrt.f64 (*.f64 1/3 x)))))))
Compiler

Compiled 6516 to 5271 computations (19.1% saved)

regimes212.0ms (2.1%)

Accuracy

Total 0.2b remaining (71.9%)

Threshold costs 0.2b (71.9%)

Counts
89 → 1
Compiler

Compiled 4438 to 3534 computations (20.4% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01422
11922
21922

end1.0ms (0%)

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample8.0s (78.2%)

Algorithm
intervals
Results
5.9s4013×body2048valid
844.0ms2022×body1024valid
224.0ms1007×body512valid
155.0ms8000×pre128true
116.0ms198×body4096valid
100.0ms532×body256valid
13.0ms228×body128valid
Compiler

Compiled 510 to 401 computations (21.4% saved)

Profiling

Loading profile data...