Details

Time bar (total: 10.8s)

analyze21.0ms (0.2%)

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

Compiled 10 to 7 computations (30% saved)

sample131.0ms (1.2%)

Algorithm
intervals
Results
61.0ms80×body2048valid
50.0ms119×body1024valid
8.0ms36×body512valid
3.0ms16×body256valid
0.0msbody128valid
Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify10.0ms (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
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
40.2b
Counts
2 → 1
Alt Table
StatusErrorProgram
40.2b
(-.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
0.6b
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
1.7b
(cos.f64 (+.f64 x eps))

series15.0ms (0.1%)

Counts
2 → 48
Calls

2 calls:

8.0ms
(cos.f64 (+.f64 x eps))
7.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

rewrite12.0ms (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:

7.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
3.0ms
(cos.f64 (+.f64 x eps))

simplify96.0ms (0.9%)

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 → 92
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01341274
13091207
29651144
323731120
445221120
548381120

prune143.0ms (1.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New85792
Fresh000
Picked101
Done000
Total86793
Error
0.2b
Counts
93 → 7
Alt Table
StatusErrorProgram
28.7b
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
40.2b
(/.f64 (-.f64 (pow.f64 (cos.f64 (+.f64 x eps)) 3) (pow.f64 (cos.f64 x) 3)) (+.f64 (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (+.f64 x eps))) (+.f64 (*.f64 (cos.f64 x) (cos.f64 x)) (*.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))
26.2b
(neg.f64 (fma.f64 eps (sin.f64 x) (*.f64 1/2 (*.f64 (cos.f64 x) (*.f64 eps eps)))))
40.2b
(cbrt.f64 (*.f64 (*.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
11.7b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
28.7b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
28.8b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 x)))
Compiler

Compiled 1839 to 620 computations (66.3% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
0.0b
(+.f64 x (+.f64 eps x))
0.2b
(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
1.8b
(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

series74.0ms (0.7%)

Counts
4 → 96
Calls

4 calls:

33.0ms
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
24.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
9.0ms
(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
8.0ms
(+.f64 x (+.f64 eps x))

rewrite66.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity_binary64
11×add-cbrt-cube_binary64
11×add-exp-log_binary64
11×pow1_binary64
10×add-sqr-sqrt_binary64
Counts
4 → 71
Calls

4 calls:

20.0ms
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
18.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
13.0ms
(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
8.0ms
(+.f64 x (+.f64 eps x))

simplify218.0ms (2%)

Algorithm
egg-herbie
Rules
549×fma-def_binary64
428×*-commutative_binary64
417×cancel-sign-sub-inv_binary64
354×sub-neg_binary64
330×distribute-rgt-neg-in_binary64
Counts
167 → 164
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01843349
15002908
215282564
336862549
447102549
549852549
649252549

prune303.0ms (2.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1577164
Fresh156
Picked101
Done000
Total15912171
Error
0.2b
Counts
171 → 12
Alt Table
StatusErrorProgram
28.7b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
35.5b
(*.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))))))
28.7b
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
32.6b
(*.f64 -2 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))) 3)))
28.8b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 x)))
22.2b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
26.2b
(neg.f64 (fma.f64 eps (sin.f64 x) (*.f64 1/2 (*.f64 (cos.f64 x) (*.f64 eps eps)))))
11.8b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (expm1.f64 (log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
43.9b
(*.f64 -2 (exp.f64 (+.f64 (log.f64 (sin.f64 (/.f64 eps 2))) (log.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))))
40.2b
(cbrt.f64 (*.f64 (*.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
14.3b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) 3))))
23.8b
(*.f64 -2 (*.f64 (sqrt.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))) (sqrt.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))))
Compiler

Compiled 4095 to 2837 computations (30.7% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (sin.f64 (/.f64 eps 2)) (expm1.f64 (log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)))))
0.3b
(expm1.f64 (log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))
0.3b
(log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)))
1.8b
(sin.f64 (/.f64 (fma.f64 x 2 eps) 2))

series521.0ms (4.8%)

Counts
4 → 96
Calls

4 calls:

495.0ms
(log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)))
12.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (expm1.f64 (log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)))))
9.0ms
(sin.f64 (/.f64 (fma.f64 x 2 eps) 2))
5.0ms
(expm1.f64 (log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))

rewrite8.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
4 → 51
Calls

4 calls:

4.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (expm1.f64 (log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)))))
2.0ms
(sin.f64 (/.f64 (fma.f64 x 2 eps) 2))
0.0ms
(log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)))
0.0ms
(expm1.f64 (log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))

simplify97.0ms (0.9%)

Algorithm
egg-herbie
Rules
919×times-frac_binary64
443×fma-def_binary64
391×cancel-sign-sub-inv_binary64
386×fma-neg_binary64
161×distribute-rgt-neg-in_binary64
Counts
147 → 115
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01862974
15012792
217412696
345602680
450222680

prune211.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1132115
Fresh11011
Picked101
Done000
Total11512127
Error
0.2b
Counts
127 → 12
Alt Table
StatusErrorProgram
28.7b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
35.5b
(*.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))))))
23.8b
(*.f64 -2 (*.f64 (sqrt.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))) (sqrt.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))))
43.9b
(*.f64 -2 (exp.f64 (+.f64 (log.f64 (sin.f64 (/.f64 eps 2))) (log.f64 (expm1.f64 (log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))))))
14.2b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (expm1.f64 (cbrt.f64 (pow.f64 (log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))) 3)))))
28.7b
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
32.6b
(*.f64 -2 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))) 3)))
28.8b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 x)))
22.2b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
26.2b
(neg.f64 (fma.f64 eps (sin.f64 x) (*.f64 1/2 (*.f64 (cos.f64 x) (*.f64 eps eps)))))
40.2b
(cbrt.f64 (*.f64 (*.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
14.3b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) 3))))
Compiler

Compiled 3647 to 2795 computations (23.4% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)))
0.5b
(pow.f64 (log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))) 3)
1.8b
(sin.f64 (/.f64 (fma.f64 x 2 eps) 2))
7.9b
(cbrt.f64 (pow.f64 (log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))) 3))

series1.8s (16.3%)

Counts
2 → 48
Calls

2 calls:

980.0ms
(pow.f64 (log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))) 3)
785.0ms
(cbrt.f64 (pow.f64 (log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))) 3))

rewrite10.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
cube-prod_binary64
Counts
2 → 48
Calls

2 calls:

3.0ms
(pow.f64 (log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))) 3)
3.0ms
(cbrt.f64 (pow.f64 (log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))) 3))

simplify156.0ms (1.4%)

Algorithm
egg-herbie
Rules
896×fma-def_binary64
368×unswap-sqr_binary64
252×associate-*r*_binary64
230×cancel-sign-sub-inv_binary64
174×associate-/l*_binary64
Counts
96 → 90
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02393188
17213037
230662962
348832962
450702962

prune368.0ms (3.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1441145
Fresh01111
Picked101
Done000
Total14512157
Error
0.2b
Counts
157 → 12
Alt Table
StatusErrorProgram
28.7b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
35.5b
(*.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))))))
23.8b
(*.f64 -2 (*.f64 (sqrt.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))) (sqrt.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))))
43.9b
(*.f64 -2 (exp.f64 (+.f64 (log.f64 (sin.f64 (/.f64 eps 2))) (log.f64 (expm1.f64 (log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))))))
28.7b
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
32.6b
(*.f64 -2 (cbrt.f64 (pow.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))) 3)))
28.8b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 x)))
22.2b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
26.2b
(neg.f64 (fma.f64 eps (sin.f64 x) (*.f64 1/2 (*.f64 (cos.f64 x) (*.f64 eps eps)))))
23.1b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (expm1.f64 (cbrt.f64 (log.f64 (exp.f64 (pow.f64 (log1p.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))) 3)))))))
40.2b
(cbrt.f64 (*.f64 (*.f64 (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
14.3b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) 3))))
Compiler

Compiled 6241 to 4862 computations (22.1% saved)

regimes1.3s (11.7%)

Accuracy

Total 0.3b remaining (52.4%)

Threshold costs 0.3b (52.4%)

Counts
144 → 3
Compiler

Compiled 8027 to 5906 computations (26.4% saved)

bsearch88.0ms (0.8%)

Steps
ItersRangePoint
9
1.4471309635938159e-8
0.6512744844284002
0.002642006392618735
10
-67351557194.80865
-1.7125811283861844e-7
-0.0032009189843879215
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify5.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03592
15392
27292
38492
49192
59292
69292

end1.0ms (0%)

Compiler

Compiled 61 to 33 computations (45.9% saved)

sample5.2s (47.7%)

Algorithm
intervals
Results
2.2s2044×body2048valid
2.0s3814×body1024valid
365.0ms1345×body512valid
103.0ms536×body256valid
25.0ms260×body128valid
2.0msbody4096valid
Compiler

Compiled 315 to 219 computations (30.5% saved)

Profiling

Loading profile data...