Details

Time bar (total: 7.1s)

analyze2.0ms (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)

sample138.0ms (2%)

Algorithm
1×intervals
Results
49.0ms112×body1024valid
39.0ms41×body2048valid
12.0ms46×body512valid
3.0ms38×body128valid
3.0ms19×body256valid
Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify10.0ms (0.1%)

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
36.7b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶36.7b
(-.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
✓2.1b
(sin.f64 (+.f64 x eps))
✓2.3b
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

series14.0ms (0.2%)

Counts
2 → 48
Calls

2 calls:

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

rewrite10.0ms (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:

5.0ms
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms
(sin.f64 (+.f64 x eps))

simplify100.0ms (1.4%)

Algorithm
1×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

prune75.0ms (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
20.6b
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
▶15.9b
(*.f64 2 (*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
20.7b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
Compiler

Compiled 1648 to 498 computations (69.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 x (+.f64 eps x))
✓0.3b
(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
✓1.8b
(cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

series21.0ms (0.3%)

Counts
3 → 72
Calls

3 calls:

13.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
5.0ms
(cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
3.0ms
(+.f64 x (+.f64 eps x))

rewrite16.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
11×*-un-lft-identity_binary64
8×add-sqr-sqrt_binary64
8×add-log-exp_binary64
6×add-cube-cbrt_binary64
5×add-cbrt-cube_binary64
Counts
3 → 50
Calls

3 calls:

5.0ms
(+.f64 x (+.f64 eps x))
5.0ms
(cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))
4.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))

simplify130.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
934×fma-neg_binary64
401×fma-def_binary64
390×associate-*l*_binary64
359×associate-*r*_binary64
313×distribute-rgt-neg-in_binary64
Counts
122 → 116
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01422063
13751829
210371598
331171591
447051591
549571591

prune119.0ms (1.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1115116
Fresh022
Picked101
Done000
Total1127119
Error
0.2b
Counts
119 → 7
Alt Table
StatusErrorProgram
20.6b
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
16.3b
(*.f64 2 (*.f64 (sin.f64 (/.f64 eps 2)) (*.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))) (cbrt.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))) (cbrt.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
▶16.0b
(*.f64 2 (*.f64 (sin.f64 (/.f64 eps 2)) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
20.7b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
16.2b
(*.f64 2 (*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
37.4b
(*.f64 2 (*.f64 (sqrt.f64 (sin.f64 (/.f64 eps 2))) (*.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sqrt.f64 (sin.f64 (/.f64 eps 2))))))
37.2b
(*.f64 2 (*.f64 (sqrt.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))) (sqrt.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))))
Compiler

Compiled 2873 to 2005 computations (30.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(expm1.f64 (log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))
✓0.3b
(*.f64 (sin.f64 (/.f64 eps 2)) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))))
✓0.4b
(log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))
✓2.1b
(cos.f64 (/.f64 (fma.f64 x 2 eps) 2))

series574.0ms (8.1%)

Counts
4 → 96
Calls

4 calls:

551.0ms
(log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))
13.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))))
5.0ms
(expm1.f64 (log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))
5.0ms
(cos.f64 (/.f64 (fma.f64 x 2 eps) 2))

rewrite14.0ms (0.2%)

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 → 51
Calls

4 calls:

8.0ms
(cos.f64 (/.f64 (fma.f64 x 2 eps) 2))
4.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))))
0.0ms
(log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))
0.0ms
(expm1.f64 (log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))

simplify105.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
928×times-frac_binary64
504×fma-def_binary64
295×cancel-sign-sub-inv_binary64
274×fma-neg_binary64
153×neg-mul-1_binary64
Counts
147 → 115
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01953021
15242821
217552726
347352704
450022704

prune127.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1150115
Fresh066
Picked011
Done000
Total1157122
Error
0.2b
Counts
122 → 7
Alt Table
StatusErrorProgram
20.6b
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
16.3b
(*.f64 2 (*.f64 (sin.f64 (/.f64 eps 2)) (*.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))) (cbrt.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))) (cbrt.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
✓16.0b
(*.f64 2 (*.f64 (sin.f64 (/.f64 eps 2)) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
20.7b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
▶16.2b
(*.f64 2 (*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
37.4b
(*.f64 2 (*.f64 (sqrt.f64 (sin.f64 (/.f64 eps 2))) (*.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sqrt.f64 (sin.f64 (/.f64 eps 2))))))
37.2b
(*.f64 2 (*.f64 (sqrt.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))) (sqrt.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))))
Compiler

Compiled 3463 to 2676 computations (22.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(exp.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))
✓0.3b
(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))))
✓0.6b
(log.f64 (exp.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))
2.1b
(cos.f64 (/.f64 (fma.f64 x 2 eps) 2))

series29.0ms (0.4%)

Counts
3 → 72
Calls

3 calls:

13.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))))
11.0ms
(exp.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))
5.0ms
(log.f64 (exp.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))

rewrite15.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
13×add-sqr-sqrt_binary64
11×*-un-lft-identity_binary64
11×add-cube-cbrt_binary64
9×log-prod_binary64
9×exp-prod_binary64
Counts
3 → 60
Calls

3 calls:

7.0ms
(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))))
2.0ms
(log.f64 (exp.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))
2.0ms
(exp.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))

simplify100.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
895×fma-def_binary64
571×cancel-sign-sub-inv_binary64
520×sub-neg_binary64
242×associate-*r*_binary64
207×associate--l+_binary64
Counts
132 → 136
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02022928
15252749
216972633
343972633
449842633

prune184.0ms (2.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1591160
Fresh055
Picked011
Done011
Total1598167
Error
0.2b
Counts
167 → 8
Alt Table
StatusErrorProgram
20.7b
(+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
16.4b
(*.f64 2 (*.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))) (*.f64 (cbrt.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))) (sin.f64 (/.f64 eps 2)))) (cbrt.f64 (log.f64 (exp.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))))))
20.6b
(-.f64 (+.f64 (*.f64 (sin.f64 x) (cos.f64 eps)) (*.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
16.3b
(*.f64 2 (*.f64 (sin.f64 (/.f64 eps 2)) (*.f64 (*.f64 (cbrt.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))) (cbrt.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)))) (cbrt.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
✓16.0b
(*.f64 2 (*.f64 (sin.f64 (/.f64 eps 2)) (expm1.f64 (log1p.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
✓16.2b
(*.f64 2 (*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2))))))
37.4b
(*.f64 2 (*.f64 (sqrt.f64 (sin.f64 (/.f64 eps 2))) (*.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sqrt.f64 (sin.f64 (/.f64 eps 2))))))
37.2b
(*.f64 2 (*.f64 (sqrt.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2)))) (sqrt.f64 (*.f64 (cos.f64 (/.f64 (fma.f64 x 2 eps) 2)) (sin.f64 (/.f64 eps 2))))))
Compiler

Compiled 4435 to 3412 computations (23.1% saved)

regimes1.1s (15.5%)

Accuracy

Total 0.1b remaining (19.9%)

Threshold costs 0.1b (19.9%)

Counts
154 → 3
Compiler

Compiled 9691 to 6888 computations (28.9% saved)

bsearch108.0ms (1.5%)

Steps
ItersRangePoint
9
5.222965166042814e-18
3.7032754848993736e-13
3.667474565851914e-13
9
-0.19252867143018362
-2.0323615053218694e-10
-1.144346946787095e-8
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify9.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
6×*-commutative_binary64
3×+-commutative_binary64
2×sub-neg_binary64
1×*-rgt-identity_binary64
1×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02858
14158
24558
34758
44858
54758

end1.0ms (0%)

Compiler

Compiled 39 to 28 computations (28.2% saved)

sample4.0s (56.9%)

Algorithm
1×intervals
Results
1.8s3510×body1024valid
1.2s1211×body2048valid
333.0ms1377×body512valid
109.0ms1306×body128valid
101.0ms592×body256valid
9.0ms4×body4096valid
Compiler

Compiled 245 to 189 computations (22.9% saved)

Profiling

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