Details

Time bar (total: 8.2s)

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)

sample5.7s (70%)

Results
2.9s3657×body1024valid
1.6s1178×body2048valid
589.0ms1421×body512valid
306.0ms1401×body128valid
242.0ms596×body256valid
9.0msbody4096valid
Compiler

Compiled 29 to 20 computations (31% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Rules
rules-21_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
1811
2811

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
37.3b
Counts
2 → 1
Alt Table
StatusErrorProgram
37.3b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
Compiler

Compiled 27 to 18 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
1.6b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.1b
(sin.f64 (+.f64 x eps))

series12.0ms (0.1%)

Counts
2 → 48
Calls

2 calls:

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

rewrite67.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
818×fma-neg_binary64
440×log-prod_binary64
170×expm1-udef_binary64
170×log1p-udef_binary64
147×log-div_binary64
Counts
2 → 117
Calls

2 calls:

65.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
65.0ms
(sin.f64 (+.f64 x eps))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0717
118717
2275617
3556117
000
100

simplify56.0ms (0.7%)

Algorithm
egg-herbie
Rules
510×rules-4_binary64
432×rules-11_binary64
402×fma-neg_binary64
293×rules-21_binary64
236×fma-def_binary64
Counts
165 → 146
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
053602
1169591
2815581
34816573
45040573

prune111.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1388146
Fresh000
Picked101
Done000
Total1398147
Error
0.1b
Counts
147 → 8
Alt Table
StatusErrorProgram
20.2b
(-.f64 (fma.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (neg.f64 (-.f64 0 (*.f64 (sin.f64 x) (cos.f64 eps))))) (sin.f64 x))
19.6b
(-.f64 (*.f64 (cos.f64 x) (+.f64 (sin.f64 eps) (/.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (cos.f64 x)))) (sin.f64 x))
19.5b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
1.6b
(fma.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))))
25.8b
(-.f64 (log.f64 (*.f64 (exp.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (exp.f64 (*.f64 (sin.f64 x) (cos.f64 eps))))) (sin.f64 x))
19.6b
(fma.f64 (cos.f64 x) (+.f64 (sin.f64 eps) (/.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (cos.f64 x))) (neg.f64 (sin.f64 x)))
0.5b
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))))
35.7b
(-.f64 (*.f64 eps (cos.f64 x)) (*.f64 1/2 (*.f64 (pow.f64 eps 2) (sin.f64 x))))
Compiler

Compiled 2658 to 939 computations (64.7% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (sin.f64 x) (cos.f64 eps))
0.2b
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))))
2.0b
(-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))

series40.0ms (0.5%)

Counts
3 → 52
Calls

3 calls:

18.0ms
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))))
12.0ms
(-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))
10.0ms
(*.f64 (sin.f64 x) (cos.f64 eps))

rewrite75.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
226×expm1-udef_binary64
226×log1p-udef_binary64
199×log-pow_binary64
195×log-div_binary64
125×add-sqr-sqrt_binary64
Counts
3 → 115
Calls

3 calls:

73.0ms
(*.f64 (sin.f64 x) (cos.f64 eps))
73.0ms
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))))
73.0ms
(-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01144
126544
2364344
3506644
000
100

simplify46.0ms (0.6%)

Algorithm
egg-herbie
Rules
926×fma-neg_binary64
800×fma-def_binary64
496×rules-13_binary64
412×rules-20_binary64
225×rules-21_binary64
Counts
167 → 164
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01061150
13461077
217771053
349901053

prune193.0ms (2.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1559164
Fresh347
Picked101
Done000
Total15913172
Error
0.1b
Counts
172 → 13
Alt Table
StatusErrorProgram
25.7b
(log.f64 (exp.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))))))
19.6b
(-.f64 (*.f64 (cos.f64 x) (+.f64 (sin.f64 eps) (/.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (cos.f64 x)))) (sin.f64 x))
3.6b
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (log.f64 (/.f64 (exp.f64 (sin.f64 x)) (+.f64 1 (expm1.f64 (*.f64 (sin.f64 x) (cos.f64 eps))))))))
1.6b
(fma.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))))
0.5b
(+.f64 (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))) (*.f64 (cos.f64 x) (sin.f64 eps)))
35.7b
(-.f64 (*.f64 eps (cos.f64 x)) (*.f64 1/2 (*.f64 (pow.f64 eps 2) (sin.f64 x))))
15.0b
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) 3)) (+.f64 (pow.f64 (sin.f64 x) 2) (+.f64 (pow.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) 2) (*.f64 (cos.f64 eps) (pow.f64 (sin.f64 x) 2)))))))
0.4b
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (*.f64 (-.f64 1 (cos.f64 eps)) (sin.f64 x))))
3.2b
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (expm1.f64 (log1p.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))))))
16.4b
(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps))))) 3))
19.5b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
0.5b
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (/.f64 1 (cos.f64 eps))))))
27.5b
(*.f64 (pow.f64 (cbrt.f64 (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps))))) 2) (+.f64 (cbrt.f64 (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps))))) (/.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (pow.f64 (cbrt.f64 (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps))))) 2))))
Compiler

Compiled 4197 to 1522 computations (63.7% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series39.0ms (0.5%)

Counts
3 → 36
Calls

3 calls:

21.0ms
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (*.f64 (-.f64 1 (cos.f64 eps)) (sin.f64 x))))
15.0ms
(*.f64 (-.f64 1 (cos.f64 eps)) (sin.f64 x))
2.0ms
(-.f64 1 (cos.f64 eps))

rewrite95.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
922×fma-neg_binary64
414×prod-diff_binary64
213×expm1-udef_binary64
213×log1p-udef_binary64
182×egg-rr
Counts
3 → 182
Calls

3 calls:

90.0ms
(*.f64 (-.f64 1 (cos.f64 eps)) (sin.f64 x))
90.0ms
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (*.f64 (-.f64 1 (cos.f64 eps)) (sin.f64 x))))
90.0ms
(-.f64 1 (cos.f64 eps))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01238
127038
2331738
3563338
000
100

simplify42.0ms (0.5%)

Algorithm
egg-herbie
Rules
805×fma-neg_binary64
700×rules-11_binary64
697×fma-def_binary64
453×rules-13_binary64
365×rules-20_binary64
Counts
218 → 223
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0102878
1330844
21602836
36134836

prune327.0ms (4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New2185223
Fresh3912
Picked101
Done000
Total22214236
Error
0.1b
Counts
236 → 14
Alt Table
StatusErrorProgram
3.2b
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (expm1.f64 (log1p.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))))))
1.6b
(pow.f64 (cbrt.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (*.f64 (-.f64 1 (cos.f64 eps)) (sin.f64 x))))) 3)
3.6b
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (log.f64 (/.f64 (exp.f64 (sin.f64 x)) (+.f64 1 (expm1.f64 (*.f64 (sin.f64 x) (cos.f64 eps))))))))
1.6b
(fma.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))))
0.5b
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (/.f64 (-.f64 1 (pow.f64 (cos.f64 eps) 3)) (/.f64 (+.f64 1 (fma.f64 (cos.f64 eps) (cos.f64 eps) (cos.f64 eps))) (sin.f64 x)))))
0.5b
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 x) (/.f64 1 (cos.f64 eps))))))
0.5b
(+.f64 (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))) (*.f64 (cos.f64 x) (sin.f64 eps)))
35.7b
(-.f64 (*.f64 eps (cos.f64 x)) (*.f64 1/2 (*.f64 (pow.f64 eps 2) (sin.f64 x))))
19.5b
(-.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x))) (sin.f64 x))
16.4b
(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps))))) 3))
27.5b
(*.f64 (pow.f64 (cbrt.f64 (neg.f64 (*.f64 (-.f64 1 (cos.f64 eps)) (sin.f64 x)))) 2) (+.f64 (cbrt.f64 (neg.f64 (*.f64 (-.f64 1 (cos.f64 eps)) (sin.f64 x)))) (/.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (pow.f64 (cbrt.f64 (neg.f64 (*.f64 (-.f64 1 (cos.f64 eps)) (sin.f64 x)))) 2))))
25.7b
(log.f64 (exp.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))))))
19.5b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
0.5b
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (*.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 eps)))) (sin.f64 x))))
Compiler

Compiled 5826 to 2985 computations (48.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(exp.f64 (-.f64 1 (cos.f64 eps)))
0.2b
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (*.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 eps)))) (sin.f64 x))))
1.9b
(-.f64 1 (cos.f64 eps))
2.0b
(log.f64 (exp.f64 (-.f64 1 (cos.f64 eps))))

series24.0ms (0.3%)

Counts
3 → 40
Calls

3 calls:

17.0ms
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (*.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 eps)))) (sin.f64 x))))
4.0ms
(exp.f64 (-.f64 1 (cos.f64 eps)))
2.0ms
(log.f64 (exp.f64 (-.f64 1 (cos.f64 eps))))

rewrite75.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
434×prod-diff_binary64
227×expm1-udef_binary64
227×log1p-udef_binary64
128×add-sqr-sqrt_binary64
118×log1p-expm1-u_binary64
Counts
3 → 97
Calls

3 calls:

73.0ms
(exp.f64 (-.f64 1 (cos.f64 eps)))
73.0ms
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (*.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 eps)))) (sin.f64 x))))
73.0ms
(log.f64 (exp.f64 (-.f64 1 (cos.f64 eps))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01435
129035
2355135
3514035
000
100

simplify94.0ms (1.1%)

Algorithm
egg-herbie
Rules
461×rules-4_binary64
413×rules-21_binary64
354×fma-neg_binary64
320×rules-11_binary64
314×fma-def_binary64
Counts
137 → 129
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
074702
1224686
2936677
34678677
44990677
54984677
64961677

prune220.0ms (2.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1691170
Fresh31013
Picked101
Done000
Total17311184
Error
0.1b
Counts
184 → 11
Alt Table
StatusErrorProgram
3.6b
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (log.f64 (/.f64 (exp.f64 (sin.f64 x)) (+.f64 1 (expm1.f64 (*.f64 (sin.f64 x) (cos.f64 eps))))))))
1.6b
(fma.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps)))) (cbrt.f64 (*.f64 (cos.f64 x) (sin.f64 eps))) (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))))
0.5b
(+.f64 (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))) (*.f64 (cos.f64 x) (sin.f64 eps)))
35.7b
(-.f64 (*.f64 eps (cos.f64 x)) (*.f64 1/2 (*.f64 (pow.f64 eps 2) (sin.f64 x))))
1.6b
(pow.f64 (cbrt.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (*.f64 (-.f64 1 (cos.f64 eps)) (sin.f64 x))))) 3)
19.5b
(-.f64 (fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x))) (sin.f64 x))
16.4b
(cbrt.f64 (pow.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps))))) 3))
27.5b
(*.f64 (pow.f64 (cbrt.f64 (neg.f64 (*.f64 (-.f64 1 (cos.f64 eps)) (sin.f64 x)))) 2) (+.f64 (cbrt.f64 (neg.f64 (*.f64 (-.f64 1 (cos.f64 eps)) (sin.f64 x)))) (/.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (pow.f64 (cbrt.f64 (neg.f64 (*.f64 (-.f64 1 (cos.f64 eps)) (sin.f64 x)))) 2))))
25.7b
(log.f64 (exp.f64 (fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (-.f64 (sin.f64 x) (*.f64 (sin.f64 x) (cos.f64 eps)))))))
19.5b
(-.f64 (fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
0.5b
(fma.f64 (cos.f64 x) (sin.f64 eps) (neg.f64 (*.f64 (log.f64 (pow.f64 (exp.f64 (sqrt.f64 (-.f64 1 (cos.f64 eps)))) (sqrt.f64 (-.f64 1 (cos.f64 eps))))) (sin.f64 x))))
Compiler

Compiled 3724 to 1983 computations (46.8% saved)

regimes692.0ms (8.4%)

Accuracy

Total 0.2b remaining (62.2%)

Threshold costs 0.2b (62.2%)

Counts
210 → 1
Compiler

Compiled 12197 to 8197 computations (32.8% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01322
11422
21322

end190.0ms (2.3%)

Compiler

Compiled 266 to 178 computations (33.1% saved)

Profiling

Loading profile data...