Details

Time bar (total: 7.7s)

analyze1.0ms (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)

sample5.3s (68.5%)

Results
2.5s3626×body1024valid
1.6s1184×body2048valid
696.0ms1431×body512valid
216.0ms1409×body128valid
173.0ms601×body256valid
13.0msbody4096valid
Compiler

Compiled 29 to 20 computations (31% saved)

simplify11.0ms (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
36.5b
Counts
2 → 1
Alt Table
StatusErrorProgram
36.5b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 27 to 18 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
1.4b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.8b
(sin.f64 (+.f64 x eps))

series11.0ms (0.1%)

Counts
2 → 48
Calls

2 calls:

6.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms
(sin.f64 (+.f64 x eps))

rewrite13.0ms (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:

8.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms
(sin.f64 (+.f64 x eps))

simplify99.0ms (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

prune88.0ms (1.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New89392
Fresh000
Picked101
Done000
Total90393
Error
0.2b
Counts
93 → 3
Alt Table
StatusErrorProgram
21.4b
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
21.4b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
31.2b
(fma.f64 (cos.f64 x) (+.f64 eps (*.f64 (pow.f64 eps 3) -1/6)) (*.f64 (sin.f64 x) (*.f64 (*.f64 eps eps) -1/2)))
Compiler

Compiled 1657 to 503 computations (69.6% saved)

localize13.0ms (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))
3.1b
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))

series89.0ms (1.2%)

Counts
4 → 72
Calls

4 calls:

54.0ms
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
14.0ms
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))
10.0ms
(*.f64 (cos.f64 x) (sin.f64 eps))
10.0ms
(*.f64 (sin.f64 x) (cos.f64 eps))

rewrite24.0ms (0.3%)

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:

9.0ms
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
4.0ms
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))
3.0ms
(*.f64 (cos.f64 x) (sin.f64 eps))
3.0ms
(*.f64 (sin.f64 x) (cos.f64 eps))

simplify143.0ms (1.9%)

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

prune193.0ms (2.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1818189
Fresh022
Picked101
Done000
Total18210192
Error
0.1b
Counts
192 → 10
Alt Table
StatusErrorProgram
30.1b
(log.f64 (exp.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
23.2b
(/.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)))
21.8b
(+.f64 (fma.f64 1 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (neg.f64 (*.f64 (cbrt.f64 (sin.f64 x)) (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (sin.f64 x))) (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))) (*.f64 (cbrt.f64 (sin.f64 x)) (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))))))
0.5b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
31.2b
(fma.f64 (cos.f64 x) (+.f64 eps (*.f64 (pow.f64 eps 3) -1/6)) (*.f64 (sin.f64 x) (*.f64 (*.f64 eps eps) -1/2)))
30.1b
(log.f64 (/.f64 (exp.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (exp.f64 (sin.f64 x))))
25.5b
(/.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)))))
42.8b
(+.f64 (fma.f64 (sqrt.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (sqrt.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (neg.f64 (*.f64 (cbrt.f64 (sin.f64 x)) (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (sin.f64 x))) (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))) (*.f64 (cbrt.f64 (sin.f64 x)) (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))))))
20.1b
(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) 3))
21.4b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
Compiler

Compiled 4985 to 1388 computations (72.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(cos.f64 eps)
0.1b
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
0.1b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
2.1b
(+.f64 (cos.f64 eps) -1)

series33.0ms (0.4%)

Counts
4 → 64
Calls

4 calls:

18.0ms
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
11.0ms
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
2.0ms
(+.f64 (cos.f64 eps) -1)
2.0ms
(cos.f64 eps)

rewrite13.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
4 → 63
Calls

4 calls:

6.0ms
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
4.0ms
(+.f64 (cos.f64 eps) -1)
1.0ms
(cos.f64 eps)
0.0ms
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))

simplify88.0ms (1.1%)

Algorithm
egg-herbie
Rules
821×fma-def_binary64
696×sub-neg_binary64
466×cancel-sign-sub-inv_binary64
294×distribute-rgt-in_binary64
256×distribute-lft-in_binary64
Counts
127 → 148
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01822031
14921858
215451811
344471811
452591811

prune252.0ms (3.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1444148
Fresh549
Picked011
Done000
Total1499158
Error
0.1b
Counts
158 → 9
Alt Table
StatusErrorProgram
23.2b
(/.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)))
0.6b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (log.f64 (*.f64 (exp.f64 (cos.f64 eps)) (exp.f64 -1)))))
0.5b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 eps) 1) 3))))
25.5b
(/.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)))))
0.5b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
42.8b
(+.f64 (fma.f64 (sqrt.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (sqrt.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (neg.f64 (*.f64 (cbrt.f64 (sin.f64 x)) (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (sin.f64 x))) (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))) (*.f64 (cbrt.f64 (sin.f64 x)) (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))))))
20.1b
(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) 3))
0.5b
(fma.f64 (sin.f64 eps) (cos.f64 x) (log.f64 (exp.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
27.8b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 -1/2 (pow.f64 eps 2))))
Compiler

Compiled 3375 to 1527 computations (54.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
0.1b
(fma.f64 (sin.f64 eps) (cos.f64 x) (log.f64 (exp.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
2.1b
(+.f64 (cos.f64 eps) -1)
3.1b
(log.f64 (exp.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))

series29.0ms (0.4%)

Counts
2 → 48
Calls

2 calls:

17.0ms
(fma.f64 (sin.f64 eps) (cos.f64 x) (log.f64 (exp.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
12.0ms
(log.f64 (exp.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))

rewrite3.0ms (0%)

Algorithm
rewrite-expression-head
Rules
log-prod_binary64
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
pow1_binary64
Counts
2 → 28
Calls

2 calls:

2.0ms
(log.f64 (exp.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
0.0ms
(fma.f64 (sin.f64 eps) (cos.f64 x) (log.f64 (exp.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))

simplify113.0ms (1.5%)

Algorithm
egg-herbie
Rules
599×fma-def_binary64
546×sub-neg_binary64
373×cancel-sign-sub-inv_binary64
316×associate-*r*_binary64
308×associate-*l*_binary64
Counts
76 → 80
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01411534
13421398
210641352
340231346
447681346
549821346
649421346

prune235.0ms (3.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1751176
Fresh077
Picked101
Done011
Total1769185
Error
0.1b
Counts
185 → 9
Alt Table
StatusErrorProgram
23.2b
(/.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)))
0.6b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (log.f64 (*.f64 (exp.f64 (cos.f64 eps)) (exp.f64 -1)))))
0.5b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (cbrt.f64 (pow.f64 (-.f64 (cos.f64 eps) 1) 3))))
25.5b
(/.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)))))
0.5b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
42.8b
(+.f64 (fma.f64 (sqrt.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (sqrt.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps)))) (neg.f64 (*.f64 (cbrt.f64 (sin.f64 x)) (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (sin.f64 x))) (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))) (*.f64 (cbrt.f64 (sin.f64 x)) (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x))))))
20.1b
(cbrt.f64 (pow.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))) 3))
0.5b
(+.f64 (*.f64 (sin.f64 eps) (cos.f64 x)) (log.f64 (exp.f64 (*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))))
27.8b
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (sin.f64 x) (*.f64 -1/2 (pow.f64 eps 2))))
Compiler

Compiled 4043 to 2009 computations (50.3% saved)

regimes769.0ms (10%)

Accuracy

Total 0.3b remaining (63.6%)

Threshold costs 0.3b (63.6%)

Counts
208 → 1
Compiler

Compiled 13014 to 8111 computations (37.7% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01119
11719
21819
31619

end169.0ms (2.2%)

Compiler

Compiled 299 to 145 computations (51.5% saved)

Profiling

Loading profile data...