Details

Time bar (total: 8.3s)

analyze1.0ms (0%)

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

Compiled 10 to 7 computations (30% saved)

sample4.6s (55%)

Results
2.0s4063×body1024valid
2.0s2074×body2048valid
381.0ms1345×body512valid
97.0ms490×body256valid
32.0ms283×body128valid
3.0ms1×body4096valid
Compiler

Compiled 29 to 20 computations (31% saved)

simplify27.0ms (0.3%)

Algorithm
1×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
37.5b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶37.5b
(-.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
✓0.8b
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
✓2.4b
(cos.f64 (+.f64 x eps))

series12.0ms (0.1%)

Counts
2 → 48
Calls

2 calls:

7.0ms
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0ms
(cos.f64 (+.f64 x eps))

rewrite12.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
12×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
9×prod-diff_binary64
4×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))

simplify82.0ms (1%)

Algorithm
1×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

prune99.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New84892
Fresh000
Picked101
Done000
Total85893
Error
0.2b
Counts
93 → 8
Alt Table
StatusErrorProgram
37.6b
(log.f64 (/.f64 (exp.f64 (cos.f64 (+.f64 x eps))) (exp.f64 (cos.f64 x))))
23.6b
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
37.6b
(cbrt.f64 (pow.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x)) 3))
37.5b
(log.f64 (exp.f64 (-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))))
▶14.0b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
34.3b
(+.f64 (*.f64 (cos.f64 x) (fma.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)))
23.6b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
23.6b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 x)))
Compiler

Compiled 1805 to 640 computations (64.5% saved)

localize11.0ms (0.1%)

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))
✓0.3b
(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
✓2.5b
(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

series42.0ms (0.5%)

Counts
4 → 96
Calls

4 calls:

19.0ms
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
14.0ms
(*.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))
3.0ms
(+.f64 x (+.f64 eps x))

rewrite31.0ms (0.4%)

Algorithm
1×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:

10.0ms
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
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))
4.0ms
(+.f64 x (+.f64 eps x))

simplify145.0ms (1.7%)

Algorithm
1×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

prune174.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1577164
Fresh347
Picked101
Done000
Total16111172
Error
0.2b
Counts
172 → 11
Alt Table
StatusErrorProgram
30.6b
(*.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))))))
14.1b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (log1p.f64 (expm1.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
23.6b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
23.9b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
14.7b
(*.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))))))
23.6b
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
34.3b
(+.f64 (*.f64 (cos.f64 x) (fma.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)))
▶14.0b
(*.f64 -2 (expm1.f64 (log1p.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))))
28.0b
(*.f64 (sin.f64 (*.f64 1/2 eps)) (+.f64 (*.f64 (sin.f64 (*.f64 1/2 eps)) (fma.f64 x x -2)) (*.f64 (*.f64 (cos.f64 (*.f64 1/2 eps)) x) -2)))
16.4b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) 3))))
23.6b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 x)))
Compiler

Compiled 4115 to 2861 computations (30.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(log1p.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))
✓0.2b
(expm1.f64 (log1p.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))))
✓0.3b
(*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))
✓2.5b
(sin.f64 (/.f64 (fma.f64 x 2 eps) 2))

series938.0ms (11.3%)

Counts
4 → 96
Calls

4 calls:

859.0ms
(log1p.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))
61.0ms
(*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))
13.0ms
(expm1.f64 (log1p.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))))
5.0ms
(sin.f64 (/.f64 (fma.f64 x 2 eps) 2))

rewrite10.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
8×add-sqr-sqrt_binary64
6×*-un-lft-identity_binary64
6×add-cube-cbrt_binary64
6×add-cbrt-cube_binary64
6×add-exp-log_binary64
Counts
4 → 52
Calls

4 calls:

6.0ms
(*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))
2.0ms
(sin.f64 (/.f64 (fma.f64 x 2 eps) 2))
0.0ms
(log1p.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))
0.0ms
(expm1.f64 (log1p.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))))

simplify120.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
650×times-frac_binary64
464×cancel-sign-sub-inv_binary64
452×fma-neg_binary64
201×associate-*r*_binary64
179×distribute-rgt-neg-in_binary64
Counts
148 → 102
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02033713
15613476
219983375
345493361
450383361

prune135.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1011102
Fresh1910
Picked101
Done000
Total10310113
Error
0.2b
Counts
113 → 10
Alt Table
StatusErrorProgram
14.7b
(*.f64 -2 (expm1.f64 (log1p.f64 (*.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (*.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 eps 2))))) (cbrt.f64 (sin.f64 (/.f64 eps 2)))))))
23.6b
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
30.6b
(*.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))))))
▶14.1b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (log1p.f64 (expm1.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
23.6b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
23.9b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
34.3b
(+.f64 (*.f64 (cos.f64 x) (fma.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)))
28.0b
(*.f64 (sin.f64 (*.f64 1/2 eps)) (+.f64 (*.f64 (sin.f64 (*.f64 1/2 eps)) (fma.f64 x x -2)) (*.f64 (*.f64 (cos.f64 (*.f64 1/2 eps)) x) -2)))
16.4b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) 3))))
23.6b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 x)))
Compiler

Compiled 3546 to 2735 computations (22.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(expm1.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)))
✓0.3b
(log1p.f64 (expm1.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))
✓0.3b
(*.f64 (sin.f64 (/.f64 eps 2)) (log1p.f64 (expm1.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)))))
2.5b
(sin.f64 (/.f64 (fma.f64 x 2 eps) 2))

series32.0ms (0.4%)

Counts
3 → 72
Calls

3 calls:

15.0ms
(expm1.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)))
12.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (log1p.f64 (expm1.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)))))
5.0ms
(log1p.f64 (expm1.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))

rewrite6.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
7×add-sqr-sqrt_binary64
5×*-un-lft-identity_binary64
5×add-cube-cbrt_binary64
5×add-cbrt-cube_binary64
5×add-exp-log_binary64
Counts
3 → 42
Calls

3 calls:

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

simplify92.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
664×sub-neg_binary64
502×*-commutative_binary64
472×cancel-sign-sub-inv_binary64
261×associate--l+_binary64
258×associate--r+_binary64
Counts
114 → 111
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01812459
15112262
217092170
343862170
450942170

prune216.0ms (2.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1351136
Fresh099
Picked011
Done000
Total13511146
Error
0.2b
Counts
146 → 11
Alt Table
StatusErrorProgram
14.7b
(*.f64 -2 (expm1.f64 (log1p.f64 (*.f64 (*.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) (*.f64 (cbrt.f64 (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 eps 2))))) (cbrt.f64 (sin.f64 (/.f64 eps 2)))))))
23.6b
(-.f64 (-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x))
30.6b
(*.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))))))
✓14.1b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (log1p.f64 (expm1.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
34.3b
(+.f64 (*.f64 (cos.f64 x) (fma.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)))
37.5b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (log1p.f64 (-.f64 (+.f64 (exp.f64 (sin.f64 (*.f64 1/2 eps))) (*.f64 (exp.f64 (sin.f64 (*.f64 1/2 eps))) (*.f64 (cos.f64 (*.f64 1/2 eps)) x))) 1))))
23.6b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 eps) (sin.f64 x) (cos.f64 x)))
23.9b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
28.0b
(*.f64 (sin.f64 (*.f64 1/2 eps)) (+.f64 (*.f64 (sin.f64 (*.f64 1/2 eps)) (fma.f64 x x -2)) (*.f64 (*.f64 (cos.f64 (*.f64 1/2 eps)) x) -2)))
16.4b
(*.f64 -2 (*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (fma.f64 x 2 eps) 2)) 3))))
23.6b
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (+.f64 (*.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 x)))
Compiler

Compiled 3810 to 2879 computations (24.4% saved)

regimes1.2s (14.4%)

Accuracy

Total 0.3b remaining (56%)

Threshold costs 0.3b (56%)

Counts
176 → 3
Compiler

Compiled 10817 to 8116 computations (25% saved)

bsearch97.0ms (1.2%)

Steps
ItersRangePoint
8
9.521032825014926e-5
0.06466545111844321
0.0024976197326744567
10
-17158.231625865104
-7.790159968564277e-9
-0.0019177648911019745
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify6.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03592
15392
27292
38492
49192
59292
69292

end218.0ms (2.6%)

Compiler

Compiled 382 to 260 computations (31.9% saved)

Profiling

Loading profile data...