Details

Time bar (total: 12.4s)

analyze2.0ms (0%)

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

Compiled 10 to 7 computations (30% saved)

sample7.3s (58.7%)

Results
3.5s3581×body1024valid
2.4s1257×body2048valid
799.0ms1450×body512valid
272.0ms1358×body128valid
216.0ms608×body256valid
12.0msbody4096valid
Compiler

Compiled 29 to 20 computations (31% saved)

simplify29.0ms (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

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
41.3b
Counts
2 → 1
Alt Table
StatusErrorProgram
41.3b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 27 to 18 computations (33.3% saved)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.6b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.6b
(sin.f64 (+.f64 x eps))

series35.0ms (0.3%)

Counts
2 → 48
Calls

2 calls:

27.0ms
(sin.f64 (+.f64 x eps))
8.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

rewrite24.0ms (0.2%)

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:

13.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms
(sin.f64 (+.f64 x eps))

simplify156.0ms (1.3%)

Algorithm
egg-herbie
Rules
639×fma-neg_binary64
483×fma-def_binary64
351×cancel-sign-sub-inv_binary64
291×sub-neg_binary64
284×associate-+l-_binary64
Counts
90 → 92
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01281256
12971180
29601116
324261108
447761108
549531108
648391108

prune134.0ms (1.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New89392
Fresh000
Picked101
Done000
Total90393
Error
0.3b
Counts
93 → 3
Alt Table
StatusErrorProgram
25.1b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
30.6b
(fma.f64 (cos.f64 x) (+.f64 eps (*.f64 (pow.f64 eps 3) -1/6)) (*.f64 (sin.f64 x) (*.f64 (*.f64 eps eps) -1/2)))
25.1b
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
Compiler

Compiled 1657 to 503 computations (69.6% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))
0.1b
(*.f64 (cos.f64 x) (sin.f64 eps))
0.2b
(*.f64 (sin.f64 x) (cos.f64 eps))
2.5b
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))

series94.0ms (0.8%)

Counts
4 → 72
Calls

4 calls:

31.0ms
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))
31.0ms
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
16.0ms
(*.f64 (cos.f64 x) (sin.f64 eps))
16.0ms
(*.f64 (sin.f64 x) (cos.f64 eps))

rewrite48.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt_binary64
18×*-un-lft-identity_binary64
16×add-cube-cbrt_binary64
11×add-log-exp_binary64
prod-diff_binary64
Counts
4 → 87
Calls

4 calls:

27.0ms
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))
8.0ms
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
4.0ms
(*.f64 (cos.f64 x) (sin.f64 eps))
4.0ms
(*.f64 (sin.f64 x) (cos.f64 eps))

simplify195.0ms (1.6%)

Algorithm
egg-herbie
Rules
418×fma-neg_binary64
276×distribute-rgt-in_binary64
249×distribute-rgt-neg-in_binary64
245×distribute-lft-in_binary64
226×associate-*r*_binary64
Counts
159 → 189
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02403009
16162802
221902695
347982695
449722695
549112695

prune299.0ms (2.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1809189
Fresh022
Picked101
Done000
Total18111192
Error
0.1b
Counts
192 → 11
Alt Table
StatusErrorProgram
30.6b
(fma.f64 (cos.f64 x) (+.f64 eps (*.f64 (pow.f64 eps 3) -1/6)) (*.f64 (sin.f64 x) (*.f64 (*.f64 eps eps) -1/2)))
1.7b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
25.1b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
39.6b
(-.f64 (+.f64 (*.f64 (*.f64 (sin.f64 x) (sqrt.f64 (cos.f64 eps))) (sqrt.f64 (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
25.7b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))) (cbrt.f64 (-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)))) (cbrt.f64 (-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))))
0.4b
(*.f64 1 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
52.6b
(*.f64 (+.f64 (sqrt.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (sqrt.f64 (sin.f64 x))) (-.f64 (sqrt.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (sqrt.f64 (sin.f64 x))))
27.1b
(/.f64 (-.f64 (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (*.f64 (sin.f64 x) (sin.f64 x))) (+.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)))
28.0b
(/.f64 (-.f64 (pow.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) 3) (pow.f64 (sin.f64 x) 3)) (+.f64 (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (+.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)))))
32.4b
(*.f64 (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
21.7b
(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) 3))
Compiler

Compiled 5045 to 1428 computations (71.7% saved)

localize24.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
0.2b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
1.9b
(+.f64 (cos.f64 eps) -1)

series56.0ms (0.4%)

Counts
3 → 60
Calls

3 calls:

31.0ms
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
20.0ms
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
4.0ms
(+.f64 (cos.f64 eps) -1)

rewrite20.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
add-cube-cbrt_binary64
associate-*r*_binary64
add-cbrt-cube_binary64
Counts
3 → 54
Calls

3 calls:

11.0ms
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
5.0ms
(+.f64 (cos.f64 eps) -1)
1.0ms
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))

simplify139.0ms (1.1%)

Algorithm
egg-herbie
Rules
786×fma-def_binary64
629×sub-neg_binary64
442×cancel-sign-sub-inv_binary64
294×distribute-rgt-in_binary64
256×distribute-lft-in_binary64
Counts
114 → 131
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01721922
14731753
215081707
345791707
452931707

prune349.0ms (2.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1238131
Fresh6410
Picked101
Done000
Total13012142
Error
0.1b
Counts
142 → 12
Alt Table
StatusErrorProgram
0.4b
(*.f64 1 (+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
29.4b
(*.f64 1 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (fma.f64 1/24 (pow.f64 eps 4) (fma.f64 -1/2 (*.f64 eps eps) (*.f64 (pow.f64 eps 6) -1/720))))))
0.4b
(*.f64 1 (fma.f64 (sin.f64 eps) (cos.f64 x) (/.f64 (*.f64 (sin.f64 x) (+.f64 -1 (pow.f64 (cos.f64 eps) 3))) (+.f64 (*.f64 (cos.f64 eps) (cos.f64 eps)) (-.f64 (*.f64 -1 -1) (*.f64 (cos.f64 eps) -1))))))
21.7b
(*.f64 1 (cbrt.f64 (pow.f64 (fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps))) 3)))
21.7b
(*.f64 1 (cbrt.f64 (*.f64 (*.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))))
0.6b
(*.f64 1 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (fma.f64 (*.f64 (cbrt.f64 (cos.f64 eps)) (cbrt.f64 (cos.f64 eps))) (cbrt.f64 (cos.f64 eps)) -1))))
0.4b
(*.f64 1 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (log1p.f64 (expm1.f64 (+.f64 (cos.f64 eps) -1))))))
27.1b
(/.f64 (-.f64 (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (*.f64 (sin.f64 x) (sin.f64 x))) (+.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)))
32.4b
(*.f64 (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
1.7b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))) (cbrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
39.6b
(-.f64 (+.f64 (*.f64 (*.f64 (sin.f64 x) (sqrt.f64 (cos.f64 eps))) (sqrt.f64 (cos.f64 eps))) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
0.4b
(*.f64 1 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (log.f64 (exp.f64 (-.f64 (cos.f64 eps) 1))))))
Compiler

Compiled 3485 to 1813 computations (48% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
0.1b
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
0.1b
(*.f64 (sin.f64 eps) (cos.f64 x))
1.9b
(+.f64 (cos.f64 eps) -1)

series61.0ms (0.5%)

Counts
2 → 40
Calls

2 calls:

40.0ms
(+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
21.0ms
(*.f64 (sin.f64 eps) (cos.f64 x))

rewrite20.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-log-exp_binary64
Counts
2 → 39
Calls

2 calls:

9.0ms
(+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
6.0ms
(*.f64 (sin.f64 eps) (cos.f64 x))

simplify152.0ms (1.2%)

Algorithm
egg-herbie
Rules
747×fma-def_binary64
433×distribute-rgt-in_binary64
422×sub-neg_binary64
383×distribute-lft-in_binary64
358×cancel-sign-sub-inv_binary64
Counts
79 → 91
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01601575
14741472
215581438
345251434
451831434

prune545.0ms (4.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1816187
Fresh4711
Picked101
Done000
Total18613199
Error
0.0b
Counts
199 → 13
Alt Table
StatusErrorProgram
0.6b
(*.f64 1 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (fma.f64 (*.f64 (cbrt.f64 (cos.f64 eps)) (cbrt.f64 (cos.f64 eps))) (cbrt.f64 (cos.f64 eps)) -1))))
1.6b
(*.f64 1 (+.f64 (*.f64 (*.f64 (cbrt.f64 (sin.f64 eps)) (cbrt.f64 (sin.f64 eps))) (*.f64 (cbrt.f64 (sin.f64 eps)) (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
16.8b
(*.f64 1 (+.f64 (*.f64 (*.f64 (sin.f64 eps) (sqrt.f64 (cos.f64 x))) (sqrt.f64 (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
30.5b
(*.f64 1 (+.f64 (log.f64 (exp.f64 (*.f64 (sin.f64 eps) (cos.f64 x)))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
0.4b
(*.f64 1 (fma.f64 (sin.f64 eps) (cos.f64 x) (/.f64 (*.f64 (sin.f64 x) (+.f64 -1 (pow.f64 (cos.f64 eps) 3))) (+.f64 (*.f64 (cos.f64 eps) (cos.f64 eps)) (-.f64 (*.f64 -1 -1) (*.f64 (cos.f64 eps) -1))))))
21.7b
(*.f64 1 (cbrt.f64 (pow.f64 (fma.f64 (-.f64 (cos.f64 eps) 1) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps))) 3)))
30.9b
(*.f64 1 (+.f64 (*.f64 (sqrt.f64 (sin.f64 eps)) (*.f64 (sqrt.f64 (sin.f64 eps)) (cos.f64 x))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
0.4b
(*.f64 1 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (log1p.f64 (expm1.f64 (+.f64 (cos.f64 eps) -1))))))
29.4b
(*.f64 1 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (fma.f64 1/24 (pow.f64 eps 4) (fma.f64 -1/2 (*.f64 eps eps) (*.f64 (pow.f64 eps 6) -1/720))))))
27.1b
(/.f64 (-.f64 (*.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (*.f64 (sin.f64 x) (sin.f64 x))) (+.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x)))
32.4b
(*.f64 (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))) (sqrt.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
21.8b
(*.f64 1 (+.f64 (cbrt.f64 (*.f64 (*.f64 (*.f64 (sin.f64 eps) (sin.f64 eps)) (sin.f64 eps)) (*.f64 (*.f64 (cos.f64 x) (cos.f64 x)) (cos.f64 x)))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
1.6b
(*.f64 1 (+.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (sin.f64 eps) (cos.f64 x))) (cbrt.f64 (*.f64 (sin.f64 eps) (cos.f64 x)))) (cbrt.f64 (*.f64 (sin.f64 eps) (cos.f64 x)))) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
Compiler

Compiled 4709 to 2295 computations (51.3% saved)

regimes2.2s (18.1%)

Accuracy

Total 0.3b remaining (79.4%)

Threshold costs 0.3b (79.4%)

Counts
302 → 1
Compiler

Compiled 19746 to 12350 computations (37.5% saved)

simplify17.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
*-lft-identity_binary64
sub-neg_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01219
11919
22019
31819

end414.0ms (3.3%)

Compiler

Compiled 375 to 232 computations (38.1% saved)

Profiling

Loading profile data...