Details

Time bar (total: 10.4s)

analyze27.0ms (0.3%)

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)

sample246.0ms (2.4%)

Algorithm
intervals
Results
198.0ms133×body2048valid
23.0ms56×body1024valid
5.0ms38×body512valid
4.0ms256×pre128true
3.0msbody4096valid
1.0ms11×body256valid
1.0ms13×body128valid
Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify12.0ms (0.1%)

Algorithm
egg-herbie
Rules
15×sub-neg_binary64
14×cancel-sign-sub-inv_binary64
10×distribute-rgt-in_binary64
neg-mul-1_binary64
associate--r+_binary64
Counts
1 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0712
11112
21712
32412
43112
54712
66912
77812
89012
99212
108612
117212

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
59.3b
Counts
1 → 1
Alt Table
StatusErrorProgram
59.3b
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
Compiler

Compiled 18 to 14 computations (22.2% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b
(/.f64 1 (tan.f64 x))
3.8b
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite102.0ms (1%)

Algorithm
rewrite-expression-head
Error
58.8b
Rules
43×add-sqr-sqrt_binary64
36×times-frac_binary64
35×*-un-lft-identity_binary64
19×add-cube-cbrt_binary64
14×cancel-sign-sub-inv_binary64
Counts
2 → 74
Calls

2 calls:

16.0ms
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
4.0ms
(/.f64 1 (tan.f64 x))
Compiler

Compiled 1107 to 719 computations (35% saved)

series42.0ms (0.4%)

Error
0.3b
Counts
2 → 13
Calls

2 calls:

20.0ms
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
13.0ms
(/.f64 1 (tan.f64 x))
Compiler

Compiled 312 to 232 computations (25.6% saved)

simplify127.0ms (1.2%)

Algorithm
egg-herbie
Rules
694×times-frac_binary64
514×sub-neg_binary64
431×div-sub_binary64
347×associate-/l*_binary64
319×cancel-sign-sub-inv_binary64
Counts
87 → 56
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01031185
12411151
25091148
313831148
436211133
542061113
647091113
750041113

prune36.0ms (0.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New47956
Fresh000
Picked011
Done000
Total471057
Error
58.9b
Counts
57 → 10
Alt Table
StatusErrorProgram
61.9b
(/.f64 (-.f64 (/.f64 1 (pow.f64 x 3)) (pow.f64 (/.f64 1 (tan.f64 x)) 3)) (+.f64 (/.f64 (/.f64 1 x) x) (/.f64 (+.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x))) (tan.f64 x))))
61.4b
(/.f64 (-.f64 (tan.f64 x) x) (*.f64 x (tan.f64 x)))
59.3b
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
59.3b
(cbrt.f64 (pow.f64 (-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x))) 3))
61.1b
(-.f64 (/.f64 1 x) (*.f64 (pow.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) 2) (cbrt.f64 (/.f64 1 (tan.f64 x)))))
62.1b
(-.f64 (/.f64 1 x) (cbrt.f64 (pow.f64 (/.f64 1 (tan.f64 x)) 3)))
62.0b
(-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (/.f64 1 (tan.f64 x))) (sqrt.f64 (tan.f64 x))))
62.1b
(*.f64 (+.f64 (sqrt.f64 (/.f64 1 (tan.f64 x))) (/.f64 1 (sqrt.f64 x))) (-.f64 (/.f64 1 (sqrt.f64 x)) (sqrt.f64 (/.f64 1 (tan.f64 x)))))
61.1b
(-.f64 (/.f64 1 x) (/.f64 (pow.f64 (cbrt.f64 (/.f64 1 (tan.f64 x))) 2) (cbrt.f64 (tan.f64 x))))
61.6b
(/.f64 (-.f64 (/.f64 (/.f64 1 x) x) (/.f64 (/.f64 1 (tan.f64 x)) (tan.f64 x))) (+.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x))))
Compiler

Compiled 639 to 444 computations (30.5% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(/.f64 1 (tan.f64 x))
0.1b
(pow.f64 (-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x))) 3)
0.1b
(cbrt.f64 (pow.f64 (-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x))) 3))
3.8b
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite247.0ms (2.4%)

Algorithm
rewrite-expression-head
Error
58.7b
Rules
155×add-sqr-sqrt_binary64
115×*-un-lft-identity_binary64
108×times-frac_binary64
45×difference-of-squares_binary64
44×cbrt-prod_binary64
Counts
4 → 188
Calls

4 calls:

18.0ms
(cbrt.f64 (pow.f64 (-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x))) 3))
16.0ms
(pow.f64 (-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x))) 3)
15.0ms
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
4.0ms
(/.f64 1 (tan.f64 x))
Compiler

Compiled 2849 to 2048 computations (28.1% saved)

series108.0ms (1%)

Error
40.7b
Counts
4 → 28
Calls

4 calls:

23.0ms
(pow.f64 (-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x))) 3)
22.0ms
(cbrt.f64 (pow.f64 (-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x))) 3))
20.0ms
(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))
14.0ms
(/.f64 1 (tan.f64 x))
Compiler

Compiled 884 to 677 computations (23.4% saved)

simplify156.0ms (1.5%)

Algorithm
egg-herbie
Rules
394×distribute-rgt-in_binary64
386×distribute-lft-in_binary64
224×times-frac_binary64
206×unswap-sqr_binary64
168×associate-/l*_binary64
Counts
216 → 162
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01984366
14774175
213194132
345254099
449284099

prune72.0ms (0.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New1611162
Fresh808
Picked101
Done101
Total1711172
Error
40.7b
Counts
172 → 1
Alt Table
StatusErrorProgram
40.7b
(cbrt.f64 (+.f64 (+.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/27) (*.f64 (pow.f64 x 5) 1/135)) (*.f64 17/14175 (pow.f64 x 7))) (*.f64 16/91125 (pow.f64 x 9))))
Compiler

Compiled 1090 to 744 computations (31.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 17/14175 (pow.f64 x 7))
0.1b
(*.f64 (pow.f64 x 5) 1/135)
0.1b
(*.f64 (pow.f64 x 3) 1/27)
40.7b
(cbrt.f64 (+.f64 (+.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/27) (*.f64 (pow.f64 x 5) 1/135)) (*.f64 17/14175 (pow.f64 x 7))) (*.f64 16/91125 (pow.f64 x 9))))

rewrite251.0ms (2.4%)

Algorithm
rewrite-expression-head
Error
40.5b
Rules
32×add-sqr-sqrt_binary64
22×associate-*l*_binary64
19×add-exp-log_binary64
15×add-cube-cbrt_binary64 *-un-lft-identity_binary64
13×associate-*r*_binary64
Counts
4 → 94
Calls

4 calls:

10.0ms
(cbrt.f64 (+.f64 (+.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/27) (*.f64 (pow.f64 x 5) 1/135)) (*.f64 17/14175 (pow.f64 x 7))) (*.f64 16/91125 (pow.f64 x 9))))
7.0ms
(*.f64 (pow.f64 x 5) 1/135)
6.0ms
(*.f64 (pow.f64 x 3) 1/27)
5.0ms
(*.f64 17/14175 (pow.f64 x 7))
Compiler

Compiled 2825 to 2358 computations (16.5% saved)

series83.0ms (0.8%)

Error
22.0b
Counts
4 → 16
Calls

4 calls:

35.0ms
(cbrt.f64 (+.f64 (+.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/27) (*.f64 (pow.f64 x 5) 1/135)) (*.f64 17/14175 (pow.f64 x 7))) (*.f64 16/91125 (pow.f64 x 9))))
14.0ms
(*.f64 17/14175 (pow.f64 x 7))
11.0ms
(*.f64 (pow.f64 x 5) 1/135)
10.0ms
(*.f64 (pow.f64 x 3) 1/27)
Compiler

Compiled 1055 to 909 computations (13.8% saved)

simplify119.0ms (1.1%)

Algorithm
egg-herbie
Rules
500×*-commutative_binary64
289×distribute-rgt-in_binary64
283×log-prod_binary64
277×distribute-lft-in_binary64
203×sqr-pow_binary64
Counts
110 → 76
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02191978
14691884
214451799
339231728
448571728
548911728

prune107.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New68876
Fresh000
Picked101
Done000
Total69877
Error
0.2b
Counts
77 → 8
Alt Table
StatusErrorProgram
57.1b
(/.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 (*.f64 17/14175 (pow.f64 x 7)) (+.f64 (*.f64 1/27 (pow.f64 x 3)) (*.f64 1/135 (pow.f64 x 5)))) 3) (pow.f64 (*.f64 16/91125 (pow.f64 x 9)) 3))) (cbrt.f64 (+.f64 (*.f64 256/8303765625 (pow.f64 x 18)) (*.f64 (+.f64 (*.f64 17/14175 (pow.f64 x 7)) (+.f64 (*.f64 1/27 (pow.f64 x 3)) (*.f64 1/135 (pow.f64 x 5)))) (-.f64 (+.f64 (*.f64 17/14175 (pow.f64 x 7)) (+.f64 (*.f64 1/27 (pow.f64 x 3)) (*.f64 1/135 (pow.f64 x 5)))) (*.f64 16/91125 (pow.f64 x 9)))))))
41.0b
(*.f64 (*.f64 (cbrt.f64 (cbrt.f64 (+.f64 (+.f64 (*.f64 17/14175 (pow.f64 x 7)) (+.f64 (*.f64 1/27 (pow.f64 x 3)) (*.f64 1/135 (pow.f64 x 5)))) (*.f64 16/91125 (pow.f64 x 9))))) (cbrt.f64 (cbrt.f64 (+.f64 (+.f64 (*.f64 17/14175 (pow.f64 x 7)) (+.f64 (*.f64 1/27 (pow.f64 x 3)) (*.f64 1/135 (pow.f64 x 5)))) (*.f64 16/91125 (pow.f64 x 9)))))) (cbrt.f64 (cbrt.f64 (+.f64 (+.f64 (*.f64 17/14175 (pow.f64 x 7)) (+.f64 (*.f64 1/27 (pow.f64 x 3)) (*.f64 1/135 (pow.f64 x 5)))) (*.f64 16/91125 (pow.f64 x 9))))))
0.3b
(*.f64 (*.f64 x (cbrt.f64 1/27)) (+.f64 (*.f64 1/15 (*.f64 x x)) (+.f64 1 (*.f64 2/315 (pow.f64 x 4)))))
40.7b
(cbrt.f64 (+.f64 (+.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 1/27 x)) (*.f64 (pow.f64 x 5) 1/135)) (*.f64 17/14175 (pow.f64 x 7))) (*.f64 16/91125 (pow.f64 x 9))))
53.2b
(cbrt.f64 (+.f64 (+.f64 (+.f64 (*.f64 (pow.f64 (sqrt.f64 x) 3) (*.f64 1/27 (pow.f64 x 3/2))) (*.f64 (pow.f64 x 5) 1/135)) (*.f64 17/14175 (pow.f64 x 7))) (*.f64 16/91125 (pow.f64 x 9))))
40.9b
(cbrt.f64 (+.f64 (+.f64 (+.f64 (*.f64 (pow.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) 3) (*.f64 1/27 x)) (*.f64 (pow.f64 x 5) 1/135)) (*.f64 17/14175 (pow.f64 x 7))) (*.f64 16/91125 (pow.f64 x 9))))
53.2b
(cbrt.f64 (+.f64 (+.f64 (+.f64 (*.f64 (*.f64 (pow.f64 x 3/2) (sqrt.f64 1/27)) (*.f64 (pow.f64 x 3/2) (sqrt.f64 1/27))) (*.f64 (pow.f64 x 5) 1/135)) (*.f64 17/14175 (pow.f64 x 7))) (*.f64 16/91125 (pow.f64 x 9))))
52.4b
(/.f64 (cbrt.f64 (-.f64 (*.f64 (+.f64 (*.f64 17/14175 (pow.f64 x 7)) (+.f64 (*.f64 1/27 (pow.f64 x 3)) (*.f64 1/135 (pow.f64 x 5)))) (+.f64 (*.f64 17/14175 (pow.f64 x 7)) (+.f64 (*.f64 1/27 (pow.f64 x 3)) (*.f64 1/135 (pow.f64 x 5))))) (*.f64 256/8303765625 (pow.f64 x 18)))) (cbrt.f64 (-.f64 (+.f64 (*.f64 17/14175 (pow.f64 x 7)) (+.f64 (*.f64 1/27 (pow.f64 x 3)) (*.f64 1/135 (pow.f64 x 5)))) (*.f64 16/91125 (pow.f64 x 9)))))
Compiler

Compiled 2410 to 2000 computations (17% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (*.f64 x (cbrt.f64 1/27)) (+.f64 (*.f64 1/15 (*.f64 x x)) (+.f64 1 (*.f64 2/315 (pow.f64 x 4)))))
0.1b
(*.f64 2/315 (pow.f64 x 4))
0.1b
(*.f64 1/15 (*.f64 x x))
0.3b
(*.f64 x (cbrt.f64 1/27))

rewrite158.0ms (1.5%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
22×add-sqr-sqrt_binary64
21×add-exp-log_binary64
17×associate-*r*_binary64
16×pow1_binary64 add-cbrt-cube_binary64
12×add-cube-cbrt_binary64 *-un-lft-identity_binary64
Counts
4 → 88
Calls

4 calls:

11.0ms
(*.f64 (*.f64 x (cbrt.f64 1/27)) (+.f64 (*.f64 1/15 (*.f64 x x)) (+.f64 1 (*.f64 2/315 (pow.f64 x 4)))))
5.0ms
(*.f64 2/315 (pow.f64 x 4))
5.0ms
(*.f64 1/15 (*.f64 x x))
5.0ms
(*.f64 x (cbrt.f64 1/27))
Compiler

Compiled 2094 to 1545 computations (26.2% saved)

series55.0ms (0.5%)

Error
0.2b
Counts
4 → 14
Calls

4 calls:

17.0ms
(*.f64 (*.f64 x (cbrt.f64 1/27)) (+.f64 (*.f64 1/15 (*.f64 x x)) (+.f64 1 (*.f64 2/315 (pow.f64 x 4)))))
9.0ms
(*.f64 x (cbrt.f64 1/27))
8.0ms
(*.f64 2/315 (pow.f64 x 4))
8.0ms
(*.f64 1/15 (*.f64 x x))
Compiler

Compiled 563 to 463 computations (17.8% saved)

simplify86.0ms (0.8%)

Algorithm
egg-herbie
Rules
793×distribute-rgt-in_binary64
770×distribute-lft-in_binary64
264×associate-*l*_binary64
235×associate-*r*_binary64
188×exp-prod_binary64
Counts
102 → 61
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01601602
13861410
214311376
349151376
450271376

prune74.0ms (0.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New56561
Fresh437
Picked011
Done000
Total60969
Error
0.2b
Counts
69 → 9
Alt Table
StatusErrorProgram
57.1b
(/.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 (*.f64 17/14175 (pow.f64 x 7)) (+.f64 (*.f64 1/27 (pow.f64 x 3)) (*.f64 1/135 (pow.f64 x 5)))) 3) (pow.f64 (*.f64 16/91125 (pow.f64 x 9)) 3))) (cbrt.f64 (+.f64 (*.f64 256/8303765625 (pow.f64 x 18)) (*.f64 (+.f64 (*.f64 17/14175 (pow.f64 x 7)) (+.f64 (*.f64 1/27 (pow.f64 x 3)) (*.f64 1/135 (pow.f64 x 5)))) (-.f64 (+.f64 (*.f64 17/14175 (pow.f64 x 7)) (+.f64 (*.f64 1/27 (pow.f64 x 3)) (*.f64 1/135 (pow.f64 x 5)))) (*.f64 16/91125 (pow.f64 x 9)))))))
31.9b
(*.f64 (*.f64 (sqrt.f64 (*.f64 (cbrt.f64 1/27) x)) (sqrt.f64 (*.f64 (cbrt.f64 1/27) x))) (+.f64 (*.f64 1/15 (*.f64 x x)) (+.f64 1 (*.f64 2/315 (pow.f64 x 4)))))
0.3b
(*.f64 (*.f64 x (cbrt.f64 1/27)) (+.f64 (*.f64 1/15 (*.f64 x x)) (+.f64 1 (*.f64 2/315 (pow.f64 x 4)))))
1.5b
(*.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 1/27) (cbrt.f64 x))) (+.f64 (*.f64 1/15 (*.f64 x x)) (+.f64 1 (*.f64 2/315 (pow.f64 x 4)))))
40.7b
(cbrt.f64 (+.f64 (+.f64 (+.f64 (*.f64 (*.f64 x x) (*.f64 1/27 x)) (*.f64 (pow.f64 x 5) 1/135)) (*.f64 17/14175 (pow.f64 x 7))) (*.f64 16/91125 (pow.f64 x 9))))
1.5b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 1/27) x)) (cbrt.f64 (*.f64 (cbrt.f64 1/27) x))) (cbrt.f64 (*.f64 (cbrt.f64 1/27) x))) (+.f64 (*.f64 1/15 (*.f64 x x)) (+.f64 1 (*.f64 2/315 (pow.f64 x 4)))))
31.9b
(*.f64 (*.f64 (sqrt.f64 x) (*.f64 (cbrt.f64 1/27) (sqrt.f64 x))) (+.f64 (*.f64 1/15 (*.f64 x x)) (+.f64 1 (*.f64 2/315 (pow.f64 x 4)))))
40.7b
(*.f64 (cbrt.f64 (pow.f64 (*.f64 (cbrt.f64 1/27) x) 3)) (+.f64 (*.f64 1/15 (*.f64 x x)) (+.f64 1 (*.f64 2/315 (pow.f64 x 4)))))
40.9b
(cbrt.f64 (+.f64 (+.f64 (+.f64 (*.f64 (pow.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) 3) (*.f64 1/27 x)) (*.f64 (pow.f64 x 5) 1/135)) (*.f64 17/14175 (pow.f64 x 7))) (*.f64 16/91125 (pow.f64 x 9))))
Compiler

Compiled 1307 to 993 computations (24% saved)

regimes775.0ms (7.4%)

Accuracy

Total 0.2b remaining (51.5%)

Threshold costs 0.2b (51.5%)

Compiler

Compiled 12970 to 10450 computations (19.4% saved)

simplify3.0ms (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)

sample7.5s (71.9%)

Algorithm
intervals
Results
5.8s4110×body2048valid
676.0ms1968×body1024valid
137.0ms8000×pre128true
126.0ms964×body512valid
107.0ms203×body4096valid
42.0ms517×body256valid
11.0ms238×body128valid
Compiler

Compiled 317 to 252 computations (20.5% saved)

Profiling

Loading profile data...