Details

Time bar (total: 7.7s)

analyze26.0ms (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)

sample127.0ms (1.7%)

Algorithm
intervals
Results
59.0ms72×body2048valid
48.0ms127×body1024valid
7.0ms33×body512valid
3.0ms20×body256valid
0.0msbody128valid
Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify15.0ms (0.2%)

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
0711
11011
21511
32211
42911
54611
67211
79311
811011
912011
1012411
1112611
1211211

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
39.9b
Counts
2 → 1
Alt Table
StatusErrorProgram
39.9b
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
Compiler

Compiled 27 to 18 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.5b
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
3.1b
(cos.f64 (+.f64 x eps))

rewrite10.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
prod-diff_binary64
add-log-exp_binary64
Counts
2 → 42
Calls

2 calls:

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

series18.0ms (0.2%)

Counts
2 → 48
Calls

2 calls:

14.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0ms
(cos.f64 (+.f64 x eps))

simplify92.0ms (1.2%)

Algorithm
egg-herbie
Rules
757×fma-neg_binary64
498×cancel-sign-sub-inv_binary64
477×fma-def_binary64
311×sub-neg_binary64
244×distribute-rgt-in_binary64
Counts
90 → 135
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01341274
13091207
29651144
323731120
445221120
548381120

prune81.0ms (1.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New12510135
Fresh000
Picked101
Done000
Total12610136
Error
0.2b
Counts
136 → 10
Alt Table
StatusErrorProgram
25.4b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
30.4b
(-.f64 (*.f64 1/6 (*.f64 (pow.f64 eps 3) (sin.f64 x))) (+.f64 (*.f64 1/2 (*.f64 (pow.f64 eps 2) (cos.f64 x))) (*.f64 eps (sin.f64 x))))
25.4b
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
25.4b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 x)))
39.9b
(log.f64 (exp.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
41.4b
(-.f64 (*.f64 (*.f64 x x) (-.f64 (+.f64 (*.f64 x (*.f64 (sin.f64 eps) 1/6)) 1/2) (*.f64 (cos.f64 eps) 1/2))) (-.f64 (fma.f64 (sin.f64 eps) x 1) (cos.f64 eps)))
14.2b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
48.6b
(fma.f64 (sqrt.f64 (cos.f64 (+.f64 x eps))) (sqrt.f64 (cos.f64 (+.f64 x eps))) (neg.f64 (cos.f64 x)))
40.0b
(-.f64 (log.f64 (exp.f64 (cos.f64 (+.f64 x eps)))) (cos.f64 x))
39.9b
(log1p.f64 (expm1.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
Compiler

Compiled 1878 to 684 computations (63.6% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(+.f64 x (+.f64 eps x))
0.3b
(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
2.8b
(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

rewrite20.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-log-exp_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
3 → 50
Calls

3 calls:

8.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
6.0ms
(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
4.0ms
(+.f64 x (+.f64 eps x))

series47.0ms (0.6%)

Counts
3 → 72
Calls

3 calls:

31.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
10.0ms
(+.f64 x (+.f64 eps x))
5.0ms
(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

simplify114.0ms (1.5%)

Algorithm
egg-herbie
Rules
551×distribute-rgt-neg-in_binary64
531×distribute-lft-neg-in_binary64
408×associate-*l*_binary64
400×associate-*r*_binary64
396×fma-def_binary64
Counts
122 → 226
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01372057
13651802
210511564
333251563
447461563
549951563

prune140.0ms (1.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New2188226
Fresh459
Picked101
Done000
Total22313236
Error
0.2b
Counts
236 → 13
Alt Table
StatusErrorProgram
25.4b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
14.9b
(*.f64 -2 (*.f64 (*.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 eps 2)))) (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (cbrt.f64 (sin.f64 (/.f64 eps 2))))))
33.1b
(*.f64 -2 (-.f64 (+.f64 (pow.f64 (sin.f64 (*.f64 1/2 eps)) 2) (*.f64 (sin.f64 (*.f64 1/2 eps)) (*.f64 (cos.f64 (*.f64 1/2 eps)) x))) (+.f64 (*.f64 1/2 (*.f64 (pow.f64 (sin.f64 (*.f64 1/2 eps)) 2) (pow.f64 x 2))) (*.f64 1/6 (*.f64 (sin.f64 (*.f64 1/2 eps)) (*.f64 (cos.f64 (*.f64 1/2 eps)) (pow.f64 x 3)))))))
30.0b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (fma.f64 1/2 (*.f64 eps (cos.f64 x)) (sin.f64 x))))
39.9b
(log1p.f64 (expm1.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
37.5b
(*.f64 -2 (*.f64 (*.f64 (sqrt.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))) (sin.f64 (/.f64 eps 2))) (sqrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))))
25.4b
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
41.0b
(*.f64 -2 (*.f64 (sqrt.f64 (sin.f64 (/.f64 eps 2))) (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sqrt.f64 (sin.f64 (/.f64 eps 2))))))
25.4b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 x)))
39.9b
(log.f64 (exp.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
32.3b
(*.f64 -2 (cbrt.f64 (*.f64 (*.f64 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 eps 2))) (sin.f64 (/.f64 eps 2))) (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))))
14.8b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (*.f64 (*.f64 (cbrt.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))) (cbrt.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)))) (cbrt.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
17.0b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) 3))))
Compiler

Compiled 3178 to 2223 computations (30.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(cbrt.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)))
2.9b
(sin.f64 (/.f64 (fma.f64 x 2 eps) 2))
2.9b
(sin.f64 (/.f64 (fma.f64 x 2 eps) 2))
2.9b
(sin.f64 (/.f64 (fma.f64 x 2 eps) 2))

rewrite4.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
cbrt-prod_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
2 → 22
Calls

2 calls:

2.0ms
(sin.f64 (/.f64 (fma.f64 x 2 eps) 2))
1.0ms
(cbrt.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)))

series620.0ms (8.1%)

Counts
2 → 48
Calls

2 calls:

613.0ms
(cbrt.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)))
7.0ms
(sin.f64 (/.f64 (fma.f64 x 2 eps) 2))

simplify72.0ms (0.9%)

Algorithm
egg-herbie
Rules
656×fma-neg_binary64
634×unswap-sqr_binary64
485×fma-def_binary64
440×cancel-sign-sub-inv_binary64
427×*-commutative_binary64
Counts
70 → 103
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01361424
13791393
212931355
332951351
450611351

prune157.0ms (2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New2230223
Fresh01212
Picked011
Done000
Total22313236
Error
0.2b
Counts
236 → 13
Alt Table
StatusErrorProgram
25.4b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
14.9b
(*.f64 -2 (*.f64 (*.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 eps 2)))) (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (cbrt.f64 (sin.f64 (/.f64 eps 2))))))
33.1b
(*.f64 -2 (-.f64 (+.f64 (pow.f64 (sin.f64 (*.f64 1/2 eps)) 2) (*.f64 (sin.f64 (*.f64 1/2 eps)) (*.f64 (cos.f64 (*.f64 1/2 eps)) x))) (+.f64 (*.f64 1/2 (*.f64 (pow.f64 (sin.f64 (*.f64 1/2 eps)) 2) (pow.f64 x 2))) (*.f64 1/6 (*.f64 (sin.f64 (*.f64 1/2 eps)) (*.f64 (cos.f64 (*.f64 1/2 eps)) (pow.f64 x 3)))))))
30.0b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (fma.f64 1/2 (*.f64 eps (cos.f64 x)) (sin.f64 x))))
39.9b
(log1p.f64 (expm1.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
37.5b
(*.f64 -2 (*.f64 (*.f64 (sqrt.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))) (sin.f64 (/.f64 eps 2))) (sqrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))))
25.4b
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
41.0b
(*.f64 -2 (*.f64 (sqrt.f64 (sin.f64 (/.f64 eps 2))) (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sqrt.f64 (sin.f64 (/.f64 eps 2))))))
25.4b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 x)))
39.9b
(log.f64 (exp.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
32.3b
(*.f64 -2 (cbrt.f64 (*.f64 (*.f64 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 eps 2))) (sin.f64 (/.f64 eps 2))) (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))))
14.8b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (*.f64 (*.f64 (cbrt.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))) (cbrt.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)))) (cbrt.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
17.0b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) 3))))
Compiler

Compiled 5208 to 3973 computations (23.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.7b
(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.7b
(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.7b
(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.9b
(sin.f64 (/.f64 (fma.f64 x 2 eps) 2))

rewrite2.0ms (0%)

Algorithm
rewrite-expression-head
Rules
cbrt-prod_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
1 → 13
Calls

1 calls:

2.0ms
(cbrt.f64 (sin.f64 (/.f64 eps 2)))

series282.0ms (3.7%)

Counts
1 → 12
Calls

1 calls:

282.0ms
(cbrt.f64 (sin.f64 (/.f64 eps 2)))

simplify75.0ms (1%)

Algorithm
egg-herbie
Rules
747×unswap-sqr_binary64
712×distribute-rgt-neg-in_binary64
643×fma-def_binary64
449×cancel-sign-sub-inv_binary64
320×neg-mul-1_binary64
Counts
25 → 39
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
050411
1110385
2251338
3885300
42633300
54799300
65026300

prune130.0ms (1.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New3151316
Fresh01111
Picked101
Done011
Total31613329
Error
0.1b
Counts
329 → 13
Alt Table
StatusErrorProgram
23.0b
(*.f64 -2 (*.f64 (*.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 eps 2)))) (*.f64 (log.f64 (exp.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)))) (cbrt.f64 (sin.f64 (/.f64 eps 2))))))
33.1b
(*.f64 -2 (-.f64 (+.f64 (pow.f64 (sin.f64 (*.f64 1/2 eps)) 2) (*.f64 (sin.f64 (*.f64 1/2 eps)) (*.f64 (cos.f64 (*.f64 1/2 eps)) x))) (+.f64 (*.f64 1/2 (*.f64 (pow.f64 (sin.f64 (*.f64 1/2 eps)) 2) (pow.f64 x 2))) (*.f64 1/6 (*.f64 (sin.f64 (*.f64 1/2 eps)) (*.f64 (cos.f64 (*.f64 1/2 eps)) (pow.f64 x 3)))))))
30.0b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (fma.f64 1/2 (*.f64 eps (cos.f64 x)) (sin.f64 x))))
39.9b
(log1p.f64 (expm1.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
37.5b
(*.f64 -2 (*.f64 (*.f64 (sqrt.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))) (sin.f64 (/.f64 eps 2))) (sqrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))))
25.4b
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
41.0b
(*.f64 -2 (*.f64 (sqrt.f64 (sin.f64 (/.f64 eps 2))) (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sqrt.f64 (sin.f64 (/.f64 eps 2))))))
25.4b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
25.4b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 x)))
39.9b
(log.f64 (exp.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
32.3b
(*.f64 -2 (cbrt.f64 (*.f64 (*.f64 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 eps 2))) (sin.f64 (/.f64 eps 2))) (*.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))))
14.8b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (*.f64 (*.f64 (cbrt.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))) (cbrt.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)))) (cbrt.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
17.0b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) 3))))
Compiler

Compiled 3708 to 2963 computations (20.1% saved)

regimes1.3s (17%)

Accuracy

Total 0.3b remaining (59.1%)

Threshold costs 0.3b (59.1%)

Compiler

Compiled 13132 to 9792 computations (25.4% saved)

bsearch104.0ms (1.3%)

Steps
ItersRangePoint
10
2.279471233196332e-10
59223.63505175613
5.874348258429151e-5
11
-1.492493056834911
-1.9800664678178108e-28
-3.519909493265526e-5
Compiler

Compiled 3 to 2 computations (33.3% 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
02979
14379
25979
36979
47579
57679
67679

end1.0ms (0%)

Compiler

Compiled 52 to 27 computations (48.1% saved)

sample4.2s (54.6%)

Algorithm
intervals
Results
1.7s2080×body2048valid
1.6s3880×body1024valid
278.0ms1297×body512valid
74.0ms478×body256valid
20.0ms262×body128valid
7.0msbody4096valid
Compiler

Compiled 382 to 276 computations (27.7% saved)

Profiling

Loading profile data...