Details

Time bar (total: 7.0s)

analyze22.0ms (0.3%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
99.9%0%0.1%1
Compiler

Compiled 10 to 7 computations (30% saved)

sample162.0ms (2.3%)

Algorithm
intervals
Results
95.0ms140×body1024valid
49.0ms58×body2048valid
8.0ms41×body512valid
1.0ms11×body256valid
0.0msbody128valid
Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify12.0ms (0.2%)

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
0711
11011
21511
32111
42711
54211
66511
77811
89011
99211
108611
117211

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done000
Total011
Error
39.9b
Counts
1 → 1
Alt Table
StatusErrorProgram
39.9b
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 18 to 12 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.9b
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
2.1b
(cos.f64 (+.f64 x eps))

rewrite30.0ms (0.4%)

Algorithm
rewrite-expression-head
Error
17.9b
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-log-exp_binary64
cancel-sign-sub-inv_binary64
add-cube-cbrt_binary64
Counts
2 → 26
Calls

2 calls:

5.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
3.0ms
(cos.f64 (+.f64 x eps))
Compiler

Compiled 375 to 99 computations (73.6% saved)

series77.0ms (1.1%)

Error
13.6b
Counts
2 → 24
Calls

2 calls:

16.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
12.0ms
(cos.f64 (+.f64 x eps))
Compiler

Compiled 719 to 440 computations (38.8% saved)

simplify77.0ms (1.1%)

Algorithm
egg-herbie
Rules
319×distribute-rgt-in_binary64
299×sub-neg_binary64
296×associate-+l-_binary64
261×distribute-lft-in_binary64
232×associate--l+_binary64
Counts
50 → 31
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0111854
1273829
2635789
31955765
44830765
54967765

prune34.0ms (0.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New24731
Fresh000
Picked101
Done000
Total25732
Error
0.2b
Counts
32 → 7
Alt Table
StatusErrorProgram
32.2b
(+.f64 (*.f64 (cos.f64 x) (+.f64 (*.f64 1/24 (pow.f64 eps 4)) (*.f64 (*.f64 eps eps) -1/2))) (*.f64 (sin.f64 x) (-.f64 (*.f64 1/6 (pow.f64 eps 3)) eps)))
40.2b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (cbrt.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))) (cbrt.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
14.8b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
40.0b
(cbrt.f64 (pow.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) 3))
50.3b
(*.f64 (+.f64 (sqrt.f64 (cos.f64 (+.f64 eps x))) (sqrt.f64 (cos.f64 x))) (-.f64 (sqrt.f64 (cos.f64 (+.f64 eps x))) (sqrt.f64 (cos.f64 x))))
25.0b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (cos.f64 x) (*.f64 (sin.f64 eps) (sin.f64 x))))
24.9b
(-.f64 (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))) (cos.f64 x))
Compiler

Compiled 729 to 339 computations (53.5% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 x (+.f64 eps x))
0.3b
(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
2.0b
(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

rewrite55.0ms (0.8%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
10×*-un-lft-identity_binary64
add-log-exp_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
3 → 41
Calls

3 calls:

8.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
5.0ms
(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
5.0ms
(+.f64 x (+.f64 eps x))
Compiler

Compiled 903 to 542 computations (40% saved)

series125.0ms (1.8%)

Error
0.2b
Counts
3 → 36
Calls

3 calls:

75.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
16.0ms
(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
14.0ms
(+.f64 x (+.f64 eps x))
Compiler

Compiled 1419 to 1121 computations (21% saved)

simplify69.0ms (1%)

Algorithm
egg-herbie
Rules
551×distribute-rgt-neg-in_binary64
531×distribute-lft-neg-in_binary64
408×associate-*l*_binary64
400×associate-*r*_binary64
295×cancel-sign-sub-inv_binary64
Counts
77 → 61
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01311521
13501380
29531302
328941285
449471285

prune57.0ms (0.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New55661
Fresh246
Picked101
Done000
Total581068
Error
0.2b
Counts
68 → 10
Alt Table
StatusErrorProgram
44.3b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 eps (+.f64 x x)) 3)) 2))))
40.2b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (cbrt.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))) (cbrt.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
40.0b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (*.f64 (sqrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))) (sqrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))))))
32.2b
(+.f64 (*.f64 (cos.f64 x) (+.f64 (*.f64 1/24 (pow.f64 eps 4)) (*.f64 (*.f64 eps eps) -1/2))) (*.f64 (sin.f64 x) (-.f64 (*.f64 1/6 (pow.f64 eps 3)) eps)))
24.5b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))))))
34.0b
(*.f64 -2 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))) 3)))
15.5b
(*.f64 -2 (*.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))) (cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))) (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))))
38.7b
(*.f64 -2 (*.f64 (sqrt.f64 (sin.f64 (/.f64 eps 2))) (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sqrt.f64 (sin.f64 (/.f64 eps 2))))))
25.0b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (cos.f64 x) (*.f64 (sin.f64 eps) (sin.f64 x))))
24.9b
(-.f64 (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))) (cos.f64 x))
Compiler

Compiled 1458 to 960 computations (34.2% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b
(cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))
2.0b
(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
2.0b
(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
2.0b
(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

rewrite63.0ms (0.9%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
4 → 32
Calls

4 calls:

7.0ms
(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
7.0ms
(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
6.0ms
(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
6.0ms
(cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))
Compiler

Compiled 1376 to 779 computations (43.4% saved)

series192.0ms (2.7%)

Error
0.2b
Counts
4 → 46
Calls

4 calls:

56.0ms
(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
56.0ms
(cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))
21.0ms
(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
20.0ms
(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
Compiler

Compiled 4451 to 3179 computations (28.6% saved)

simplify69.0ms (1%)

Algorithm
egg-herbie
Rules
833×distribute-rgt-neg-in_binary64
626×unswap-sqr_binary64
509×associate-*r*_binary64
478×associate-*l*_binary64
284×cancel-sign-sub-inv_binary64
Counts
78 → 46
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01151674
12821599
28141473
329001473
451511473

prune50.0ms (0.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New45146
Fresh099
Picked011
Done000
Total451156
Error
0.2b
Counts
56 → 11
Alt Table
StatusErrorProgram
44.3b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 eps (+.f64 x x)) 3)) 2))))
40.2b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (cbrt.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))) (cbrt.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
40.0b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (*.f64 (sqrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))) (sqrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))))))
32.2b
(+.f64 (*.f64 (cos.f64 x) (+.f64 (*.f64 1/24 (pow.f64 eps 4)) (*.f64 (*.f64 eps eps) -1/2))) (*.f64 (sin.f64 x) (-.f64 (*.f64 1/6 (pow.f64 eps 3)) eps)))
24.5b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))))))
34.0b
(*.f64 -2 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))) 3)))
24.9b
(-.f64 (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))) (cos.f64 x))
24.7b
(*.f64 -2 (*.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))) (cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))) (sin.f64 (/.f64 eps 2))) (cbrt.f64 (log.f64 (exp.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))))))
15.5b
(*.f64 -2 (*.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))) (cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))) (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))))
38.7b
(*.f64 -2 (*.f64 (sqrt.f64 (sin.f64 (/.f64 eps 2))) (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sqrt.f64 (sin.f64 (/.f64 eps 2))))))
25.0b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (cos.f64 x) (*.f64 (sin.f64 eps) (sin.f64 x))))
Compiler

Compiled 2007 to 1260 computations (37.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(exp.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))
0.3b
(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))))
2.0b
(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
2.9b
(log.f64 (exp.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))))

rewrite89.0ms (1.3%)

Algorithm
rewrite-expression-head
Error
0.2b
Rules
14×add-sqr-sqrt_binary64
12×*-un-lft-identity_binary64
12×add-cube-cbrt_binary64
log-prod_binary64
exp-prod_binary64
Counts
4 → 61
Calls

4 calls:

13.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))))
7.0ms
(log.f64 (exp.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))))
7.0ms
(exp.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))
6.0ms
(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
Compiler

Compiled 1585 to 1020 computations (35.6% saved)

series177.0ms (2.5%)

Error
0.2b
Counts
4 → 47
Calls

4 calls:

61.0ms
(log.f64 (exp.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))))
44.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))))
25.0ms
(exp.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))
16.0ms
(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
Compiler

Compiled 2646 to 2044 computations (22.8% saved)

simplify124.0ms (1.8%)

Algorithm
egg-herbie
Rules
579×cancel-sign-sub-inv_binary64
511×distribute-rgt-neg-in_binary64
493×distribute-lft-neg-in_binary64
427×*-commutative_binary64
409×sub-neg_binary64
Counts
108 → 82
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01932814
14582546
213632347
331162338
448392338
549692338

prune70.0ms (1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New79382
Fresh189
Picked011
Done011
Total801393
Error
0.2b
Counts
93 → 13
Alt Table
StatusErrorProgram
44.3b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 eps (+.f64 x x)) 3)) 2))))
40.2b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))) (cbrt.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)))) (cbrt.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
40.0b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (*.f64 (sqrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))) (sqrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))))))
31.9b
(*.f64 -2 (+.f64 (*.f64 (sin.f64 x) (*.f64 1/2 eps)) (*.f64 1/4 (*.f64 eps (*.f64 eps (cos.f64 x))))))
15.5b
(*.f64 -2 (*.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))) (cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))) (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))))
24.5b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))))))
34.0b
(*.f64 -2 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2))) 3)))
24.9b
(-.f64 (-.f64 (*.f64 (cos.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 eps) (sin.f64 x))) (cos.f64 x))
24.7b
(*.f64 -2 (*.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))) (cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))) (sin.f64 (/.f64 eps 2))) (cbrt.f64 (log.f64 (exp.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))))))
44.8b
(*.f64 -2 (*.f64 (*.f64 (sqrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))) (sin.f64 (/.f64 eps 2))) (sqrt.f64 (log.f64 (exp.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)))))))
24.4b
(*.f64 -2 (*.f64 (*.f64 (cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))) (sin.f64 (/.f64 eps 2))) (log.f64 (exp.f64 (*.f64 (cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))) (cbrt.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))))))))
38.7b
(*.f64 -2 (*.f64 (sqrt.f64 (sin.f64 (/.f64 eps 2))) (*.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sqrt.f64 (sin.f64 (/.f64 eps 2))))))
25.0b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (cos.f64 x) (*.f64 (sin.f64 eps) (sin.f64 x))))
Compiler

Compiled 1862 to 1258 computations (32.4% saved)

regimes1.1s (15.8%)

Accuracy

Total 0.4b remaining (60.9%)

Threshold costs 0.4b (60.9%)

Compiler

Compiled 10675 to 7611 computations (28.7% saved)

bsearch144.0ms (2%)

Steps
ItersRangePoint
9
0.07553734523160144
4092500.798751867
0.07710856464853962
10
-46.098525850605434
-5.16978352494913e-9
-3.718011094065103e-5
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify5.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03266
15166
26366
37166
47666
57766
67666

end1.0ms (0%)

Compiler

Compiled 43 to 31 computations (27.9% saved)

sample4.2s (59.2%)

Algorithm
intervals
Results
1.8s2079×body2048valid
1.5s3819×body1024valid
272.0ms1335×body512valid
71.0ms522×body256valid
18.0ms244×body128valid
3.0msbody4096valid
Compiler

Compiled 393 to 267 computations (32.1% saved)

Profiling

Loading profile data...