Details

Time bar (total: 8.1s)

analyze1.4s (17.3%)

Algorithm
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)

sample95.0ms (1.2%)

Algorithm
intervals
Results
41.0ms40×body2048valid
17.0ms50×body1024valid
11.0msbody4096valid
9.0ms132×body128valid
5.0ms23×body512valid
1.0msbody256valid
0.0msbody128invalid
Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify23.0ms (0.3%)

Algorithm
egg-herbie
Rules
50×cancel-sign-sub-inv_binary64
37×associate-/l*_binary64
36×sub-neg_binary64
30×div-sub_binary64
30×times-frac_binary64
Counts
1 → 1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01123
12420
24820
311420
416120
520720
624620
728520
834820
934220
1034620
1129920

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
20.8b
Counts
2 → 2
Alt Table
StatusErrorProgram
20.8b
(-.f64 (*.f64 PI.f64 l) (/.f64 (tan.f64 (*.f64 PI.f64 l)) (*.f64 F F)))
20.8b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 1 (*.f64 F F)) (tan.f64 (*.f64 PI.f64 l))))
Compiler

Compiled 74 to 44 computations (40.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 PI.f64 l)
0.7b
(/.f64 1 (*.f64 F F))
4.9b
(*.f64 (/.f64 1 (*.f64 F F)) (tan.f64 (*.f64 PI.f64 l)))
31.1b
(tan.f64 (*.f64 PI.f64 l))

rewrite152.0ms (1.9%)

Algorithm
rewrite-expression-head
Error
15.7b
Rules
36×add-exp-log_binary64
20×add-cbrt-cube_binary64
18×add-sqr-sqrt_binary64
16×pow1_binary64
14×prod-exp_binary64
Counts
4 → 93
Calls

4 calls:

8.0ms
(/.f64 1 (*.f64 F F))
8.0ms
(*.f64 (/.f64 1 (*.f64 F F)) (tan.f64 (*.f64 PI.f64 l)))
3.0ms
(*.f64 PI.f64 l)
1.0ms
(tan.f64 (*.f64 PI.f64 l))
Compiler

Compiled 1680 to 608 computations (63.8% saved)

series75.0ms (0.9%)

Error
20.8b
Counts
4 → 21
Calls

4 calls:

38.0ms
(*.f64 (/.f64 1 (*.f64 F F)) (tan.f64 (*.f64 PI.f64 l)))
13.0ms
(tan.f64 (*.f64 PI.f64 l))
6.0ms
(/.f64 1 (*.f64 F F))
5.0ms
(*.f64 PI.f64 l)
Compiler

Compiled 1064 to 664 computations (37.6% saved)

simplify98.0ms (1.2%)

Algorithm
egg-herbie
Rules
922×times-frac_binary64
480×associate-/l*_binary64
397×distribute-neg-frac_binary64
190×cancel-sign-sub-inv_binary64
158×associate-/r/_binary64
Counts
114 → 84
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01801886
13961625
214311590
341951590
450901590

prune55.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New75984
Fresh101
Picked101
Done000
Total77986
Error
15.8b
Counts
86 → 9
Alt Table
StatusErrorProgram
15.8b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 PI.f64 l)) F)))
32.6b
(-.f64 (*.f64 PI.f64 l) (exp.f64 (log.f64 (/.f64 (tan.f64 (*.f64 PI.f64 l)) (*.f64 F F)))))
20.9b
(-.f64 (*.f64 PI.f64 l) (*.f64 (*.f64 (cbrt.f64 (/.f64 1 (*.f64 F F))) (cbrt.f64 (/.f64 1 (*.f64 F F)))) (*.f64 (tan.f64 (*.f64 PI.f64 l)) (cbrt.f64 (/.f64 1 (*.f64 F F))))))
38.3b
(-.f64 (*.f64 PI.f64 l) (*.f64 (*.f64 (sqrt.f64 (tan.f64 (*.f64 PI.f64 l))) (/.f64 1 (fabs.f64 F))) (*.f64 (sqrt.f64 (tan.f64 (*.f64 PI.f64 l))) (/.f64 1 (fabs.f64 F)))))
39.6b
(-.f64 (*.f64 PI.f64 l) (*.f64 (exp.f64 (*.f64 (log.f64 F) -2)) (tan.f64 (*.f64 PI.f64 l))))
20.8b
(-.f64 (*.f64 PI.f64 l) (*.f64 (pow.f64 F -2) (tan.f64 (*.f64 PI.f64 l))))
44.0b
(-.f64 (cbrt.f64 (pow.f64 (*.f64 PI.f64 l) 3)) (*.f64 (/.f64 1 (*.f64 F F)) (tan.f64 (*.f64 PI.f64 l))))
20.9b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 (*.f64 (cbrt.f64 (tan.f64 (*.f64 PI.f64 l))) (cbrt.f64 (tan.f64 (*.f64 PI.f64 l)))) (*.f64 F F)) (cbrt.f64 (tan.f64 (*.f64 PI.f64 l)))))
20.9b
(-.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)))))
Compiler

Compiled 1157 to 484 computations (58.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 (tan.f64 (*.f64 PI.f64 l)) F)
0.2b
(*.f64 PI.f64 l)
0.2b
(*.f64 PI.f64 l)
31.1b
(tan.f64 (*.f64 PI.f64 l))

rewrite146.0ms (1.8%)

Algorithm
rewrite-expression-head
Error
15.6b
Rules
20×add-sqr-sqrt_binary64
16×*-un-lft-identity_binary64
16×add-cube-cbrt_binary64
10×add-cbrt-cube_binary64
10×add-exp-log_binary64
Counts
4 → 72
Calls

4 calls:

3.0ms
(/.f64 (tan.f64 (*.f64 PI.f64 l)) F)
3.0ms
(*.f64 PI.f64 l)
3.0ms
(*.f64 PI.f64 l)
1.0ms
(tan.f64 (*.f64 PI.f64 l))
Compiler

Compiled 1356 to 464 computations (65.8% saved)

series77.0ms (0.9%)

Error
15.8b
Counts
4 → 21
Calls

4 calls:

35.0ms
(/.f64 (tan.f64 (*.f64 PI.f64 l)) F)
13.0ms
(tan.f64 (*.f64 PI.f64 l))
6.0ms
(*.f64 PI.f64 l)
5.0ms
(*.f64 PI.f64 l)
Compiler

Compiled 1066 to 653 computations (38.7% saved)

simplify108.0ms (1.3%)

Algorithm
egg-herbie
Rules
415×associate-*l*_binary64
367×associate-*r*_binary64
334×neg-mul-1_binary64
329×neg-sub0_binary64
305×distribute-neg-frac_binary64
Counts
93 → 41
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01641665
13691483
210721483
332181483
444781483
551071483

prune40.0ms (0.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New37441
Fresh178
Picked011
Done000
Total381250
Error
15.7b
Counts
50 → 12
Alt Table
StatusErrorProgram
32.6b
(-.f64 (*.f64 PI.f64 l) (exp.f64 (log.f64 (/.f64 (tan.f64 (*.f64 PI.f64 l)) (*.f64 F F)))))
16.0b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (sqrt.f64 PI.f64) (*.f64 l (sqrt.f64 PI.f64)))) F)))
15.8b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 PI.f64 l)) F)))
38.3b
(-.f64 (*.f64 PI.f64 l) (*.f64 (*.f64 (sqrt.f64 (tan.f64 (*.f64 PI.f64 l))) (/.f64 1 (fabs.f64 F))) (*.f64 (sqrt.f64 (tan.f64 (*.f64 PI.f64 l))) (/.f64 1 (fabs.f64 F)))))
39.6b
(-.f64 (*.f64 PI.f64 l) (*.f64 (exp.f64 (*.f64 (log.f64 F) -2)) (tan.f64 (*.f64 PI.f64 l))))
20.8b
(-.f64 (*.f64 PI.f64 l) (*.f64 (pow.f64 F -2) (tan.f64 (*.f64 PI.f64 l))))
44.0b
(-.f64 (cbrt.f64 (pow.f64 (*.f64 PI.f64 l) 3)) (*.f64 (/.f64 1 (*.f64 F F)) (tan.f64 (*.f64 PI.f64 l))))
20.9b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 (*.f64 (cbrt.f64 (tan.f64 (*.f64 PI.f64 l))) (cbrt.f64 (tan.f64 (*.f64 PI.f64 l)))) (*.f64 F F)) (cbrt.f64 (tan.f64 (*.f64 PI.f64 l)))))
20.9b
(-.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)))))
34.8b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 1 F) (exp.f64 (log.f64 (/.f64 (tan.f64 (*.f64 PI.f64 l)) F)))))
16.1b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)) (*.f64 l (cbrt.f64 PI.f64)))) F)))
38.5b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 1 F) (/.f64 (tan.f64 (cbrt.f64 (pow.f64 (*.f64 PI.f64 l) 3))) F)))
Compiler

Compiled 885 to 440 computations (50.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b
(*.f64 (sqrt.f64 PI.f64) (*.f64 l (sqrt.f64 PI.f64)))
1.0b
(sqrt.f64 PI.f64)
1.0b
(sqrt.f64 PI.f64)
30.9b
(tan.f64 (*.f64 (sqrt.f64 PI.f64) (*.f64 l (sqrt.f64 PI.f64))))

rewrite112.0ms (1.4%)

Algorithm
rewrite-expression-head
Error
15.6b
Rules
11×pow1_binary64
10×add-sqr-sqrt_binary64
sqrt-prod_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
4 → 55
Calls

4 calls:

6.0ms
(*.f64 (sqrt.f64 PI.f64) (*.f64 l (sqrt.f64 PI.f64)))
2.0ms
(tan.f64 (*.f64 (sqrt.f64 PI.f64) (*.f64 l (sqrt.f64 PI.f64))))
1.0ms
(sqrt.f64 PI.f64)
1.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 1162 to 437 computations (62.4% saved)

series75.0ms (0.9%)

Error
15.7b
Counts
4 → 9
Calls

4 calls:

60.0ms
(tan.f64 (*.f64 (sqrt.f64 PI.f64) (*.f64 l (sqrt.f64 PI.f64))))
5.0ms
(*.f64 (sqrt.f64 PI.f64) (*.f64 l (sqrt.f64 PI.f64)))
0.0ms
(sqrt.f64 PI.f64)
0.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 466 to 292 computations (37.3% saved)

simplify102.0ms (1.3%)

Algorithm
egg-herbie
Rules
559×unswap-sqr_binary64
510×associate-*l*_binary64
357×associate-*r*_binary64
265×times-frac_binary64
207×sub-neg_binary64
Counts
64 → 41
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01091014
1252704
2669704
32036700
43464700
54717700
64974700

prune49.0ms (0.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New39241
Fresh2810
Picked011
Done101
Total421153
Error
15.6b
Counts
53 → 11
Alt Table
StatusErrorProgram
44.0b
(-.f64 (cbrt.f64 (pow.f64 (*.f64 PI.f64 l) 3)) (*.f64 (/.f64 1 (*.f64 F F)) (tan.f64 (*.f64 PI.f64 l))))
16.2b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 PI.f64)) (cbrt.f64 (sqrt.f64 PI.f64))) (*.f64 (*.f64 l (sqrt.f64 PI.f64)) (cbrt.f64 (sqrt.f64 PI.f64))))) F)))
32.6b
(-.f64 (*.f64 PI.f64 l) (exp.f64 (log.f64 (/.f64 (tan.f64 (*.f64 PI.f64 l)) (*.f64 F F)))))
16.0b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (sqrt.f64 PI.f64) (*.f64 l (sqrt.f64 PI.f64)))) F)))
38.3b
(-.f64 (*.f64 PI.f64 l) (*.f64 (*.f64 (sqrt.f64 (tan.f64 (*.f64 PI.f64 l))) (/.f64 1 (fabs.f64 F))) (*.f64 (sqrt.f64 (tan.f64 (*.f64 PI.f64 l))) (/.f64 1 (fabs.f64 F)))))
39.6b
(-.f64 (*.f64 PI.f64 l) (*.f64 (exp.f64 (*.f64 (log.f64 F) -2)) (tan.f64 (*.f64 PI.f64 l))))
15.8b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (*.f64 (*.f64 l (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))))) F)))
20.9b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 (*.f64 (cbrt.f64 (tan.f64 (*.f64 PI.f64 l))) (cbrt.f64 (tan.f64 (*.f64 PI.f64 l)))) (*.f64 F F)) (cbrt.f64 (tan.f64 (*.f64 PI.f64 l)))))
20.9b
(-.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)))))
34.8b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 1 F) (exp.f64 (log.f64 (/.f64 (tan.f64 (*.f64 PI.f64 l)) F)))))
16.1b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)) (*.f64 l (cbrt.f64 PI.f64)))) F)))
Compiler

Compiled 1136 to 559 computations (50.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b
(sqrt.f64 PI.f64)
1.0b
(sqrt.f64 PI.f64)
1.0b
(sqrt.f64 PI.f64)
30.7b
(tan.f64 (*.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (*.f64 (*.f64 l (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64)))))

rewrite216.0ms (2.7%)

Algorithm
rewrite-expression-head
Error
15.6b
Rules
10×add-sqr-sqrt_binary64
sqrt-prod_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
pow1_binary64
Counts
4 → 47
Calls

4 calls:

3.0ms
(tan.f64 (*.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (*.f64 (*.f64 l (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64)))))
1.0ms
(sqrt.f64 PI.f64)
1.0ms
(sqrt.f64 PI.f64)
1.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 1247 to 430 computations (65.5% saved)

series23.0ms (0.3%)

Error
15.6b
Counts
4 → 6
Calls

4 calls:

14.0ms
(tan.f64 (*.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (*.f64 (*.f64 l (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64)))))
0.0ms
(sqrt.f64 PI.f64)
0.0ms
(sqrt.f64 PI.f64)
0.0ms
(sqrt.f64 PI.f64)
Compiler

Compiled 356 to 226 computations (36.5% saved)

simplify90.0ms (1.1%)

Algorithm
egg-herbie
Rules
692×unswap-sqr_binary64
459×times-frac_binary64
260×associate-*l*_binary64
245×associate-*r*_binary64
194×associate-/l*_binary64
Counts
53 → 24
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
083810
1184738
2482558
31711554
43234554
54737554
65012554

prune37.0ms (0.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New24024
Fresh099
Picked011
Done011
Total241135
Error
15.6b
Counts
35 → 11
Alt Table
StatusErrorProgram
44.0b
(-.f64 (cbrt.f64 (pow.f64 (*.f64 PI.f64 l) 3)) (*.f64 (/.f64 1 (*.f64 F F)) (tan.f64 (*.f64 PI.f64 l))))
16.2b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 PI.f64)) (cbrt.f64 (sqrt.f64 PI.f64))) (*.f64 (*.f64 l (sqrt.f64 PI.f64)) (cbrt.f64 (sqrt.f64 PI.f64))))) F)))
32.6b
(-.f64 (*.f64 PI.f64 l) (exp.f64 (log.f64 (/.f64 (tan.f64 (*.f64 PI.f64 l)) (*.f64 F F)))))
16.0b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (sqrt.f64 PI.f64) (*.f64 l (sqrt.f64 PI.f64)))) F)))
38.3b
(-.f64 (*.f64 PI.f64 l) (*.f64 (*.f64 (sqrt.f64 (tan.f64 (*.f64 PI.f64 l))) (/.f64 1 (fabs.f64 F))) (*.f64 (sqrt.f64 (tan.f64 (*.f64 PI.f64 l))) (/.f64 1 (fabs.f64 F)))))
39.6b
(-.f64 (*.f64 PI.f64 l) (*.f64 (exp.f64 (*.f64 (log.f64 F) -2)) (tan.f64 (*.f64 PI.f64 l))))
15.8b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (*.f64 (*.f64 l (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))))) F)))
20.9b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 (*.f64 (cbrt.f64 (tan.f64 (*.f64 PI.f64 l))) (cbrt.f64 (tan.f64 (*.f64 PI.f64 l)))) (*.f64 F F)) (cbrt.f64 (tan.f64 (*.f64 PI.f64 l)))))
20.9b
(-.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)))))
34.8b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 1 F) (exp.f64 (log.f64 (/.f64 (tan.f64 (*.f64 PI.f64 l)) F)))))
16.1b
(-.f64 (*.f64 PI.f64 l) (*.f64 (/.f64 1 F) (/.f64 (tan.f64 (*.f64 (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64)) (*.f64 l (cbrt.f64 PI.f64)))) F)))
Compiler

Compiled 801 to 386 computations (51.8% saved)

regimes1.9s (23.6%)

Accuracy

Total 0.2b remaining (1.5%)

Threshold costs 0.2b (1.5%)

Compiler

Compiled 35906 to 21767 computations (39.4% saved)

simplify6.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01868
13068
24168
34968
45768
56268
66568
76668
86468

end1.0ms (0%)

Compiler

Compiled 39 to 17 computations (56.4% saved)

sample3.2s (39%)

Algorithm
intervals
Results
1.2s1008×body2048valid
659.0ms1843×body1024valid
376.0ms4076×body128valid
223.0ms63×body4096valid
207.0ms716×body512valid
42.0ms294×body256valid
14.0ms188×body128invalid
4.0msbody2048invalid
2.0msbody8192exit
Compiler

Compiled 313 to 171 computations (45.4% saved)

Profiling

Loading profile data...