Details

Time bar (total: 2.5s)

analyze1.0ms (0.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
100%0%0%2
Compiler

Compiled 8 to 6 computations (25% saved)

sample10.0ms (0.4%)

Algorithm
1×intervals
Results
5.0ms256×body128valid
Compiler

Compiled 15 to 12 computations (20% saved)

simplify123.0ms (4.9%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0810
1810

prune9.0ms (0.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
14.8b
Counts
2 → 1
Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 (*.f64 x x) 1)
14.8b
(/.f64 x (+.f64 (*.f64 x x) 1))

rewrite13.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
10×*-un-lft-identity_binary64_760 add-cube-cbrt_binary64_795 add-sqr-sqrt_binary64_782
9×times-frac_binary64_766
4×add-exp-log_binary64_798 add-log-exp_binary64_799 add-cbrt-cube_binary64_796
3×associate-/r*_binary64_704 associate-/l*_binary64_705
2×associate-/r/_binary64_706 flip3-+_binary64_763 flip-+_binary64_734 pow1_binary64_821
1×frac-2neg_binary64_771 cbrt-undiv_binary64_794 div-inv_binary64_757 +-commutative_binary64_690 sum-log_binary64_851 div-exp_binary64_811 clear-num_binary64_759
Counts
2 → 40
Calls

2 calls:

6.0ms
(/.f64 x (+.f64 (*.f64 x x) 1))
4.0ms
(+.f64 (*.f64 x x) 1)

series68.0ms (2.7%)

Counts
2 → 6
Calls

2 calls:

35.0ms
(+.f64 (*.f64 x x) 1)
33.0ms
(/.f64 x (+.f64 (*.f64 x x) 1))

simplify101.0ms (4.1%)

Algorithm
1×egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 0 (79.0ms)

IterNodesCost
05596689

prune60.0ms (2.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New42446
Fresh000
Picked101
Done000
Total43447
Error
0b
Counts
47 → 4
Compiler

Compiled 662 to 369 computations (44.3% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.0b
(/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) 1)))
14.8b
(sqrt.f64 (+.f64 (*.f64 x x) 1))
14.8b
(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite47.0ms (1.9%)

Algorithm
1×rewrite-expression-head
Rules
38×add-sqr-sqrt_binary64_782
36×*-un-lft-identity_binary64_760 add-cube-cbrt_binary64_795 times-frac_binary64_766
30×sqrt-prod_binary64_776
12×associate-/r*_binary64_704
10×add-exp-log_binary64_798
8×sqrt-div_binary64_777 add-cbrt-cube_binary64_796 pow1_binary64_821
6×associate-/l*_binary64_705
4×associate-/r/_binary64_706 flip3-+_binary64_763 add-log-exp_binary64_799 flip-+_binary64_734
3×sqrt-pow1_binary64_778 pow1/2_binary64_840 div-exp_binary64_811 pow-flip_binary64_834
2×rem-sqrt-square_binary64_773 frac-2neg_binary64_771 cbrt-undiv_binary64_794 div-inv_binary64_757 clear-num_binary64_759
1×inv-pow_binary64_845 rec-exp_binary64_810 1-exp_binary64_804
Counts
4 → 118
Calls

4 calls:

7.0ms
(/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) 1)))
7.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))
4.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))

series134.0ms (5.4%)

Counts
4 → 12
Calls

4 calls:

40.0ms
(/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) 1)))
31.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
31.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))
31.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify71.0ms (2.9%)

Algorithm
1×egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049892284
149892284

prune203.0ms (8.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1300130
Fresh033
Picked011
Done000
Total1304134
Error
0b
Counts
134 → 4
Compiler

Compiled 3141 to 1969 computations (37.3% saved)

localize12.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.0b
(+.f64 (*.f64 x x) 1)
0.1b
(/.f64 1 (/.f64 (+.f64 (*.f64 x x) 1) x))
14.8b
(/.f64 (+.f64 (*.f64 x x) 1) x)

rewrite29.0ms (1.2%)

Algorithm
1×rewrite-expression-head
Rules
84×times-frac_binary64_766
53×*-un-lft-identity_binary64_760 add-cube-cbrt_binary64_795 add-sqr-sqrt_binary64_782
16×add-exp-log_binary64_798 associate-/r*_binary64_704
10×add-cbrt-cube_binary64_796
8×div-exp_binary64_811
6×div-inv_binary64_757 associate-/l*_binary64_705
5×add-log-exp_binary64_799
4×cbrt-undiv_binary64_794 pow1_binary64_821
2×frac-2neg_binary64_771 flip3-+_binary64_763 associate-/l/_binary64_707 flip-+_binary64_734 rec-exp_binary64_810 clear-num_binary64_759 1-exp_binary64_804
1×associate-/r/_binary64_706 inv-pow_binary64_845 +-commutative_binary64_690 sum-log_binary64_851 pow-flip_binary64_834
Counts
3 → 116
Calls

3 calls:

8.0ms
(/.f64 1 (/.f64 (+.f64 (*.f64 x x) 1) x))
7.0ms
(/.f64 (+.f64 (*.f64 x x) 1) x)
4.0ms
(+.f64 (*.f64 x x) 1)

series138.0ms (5.5%)

Counts
3 → 9
Calls

3 calls:

61.0ms
(/.f64 (+.f64 (*.f64 x x) 1) x)
48.0ms
(/.f64 1 (/.f64 (+.f64 (*.f64 x x) 1) x))
29.0ms
(+.f64 (*.f64 x x) 1)

simplify108.0ms (4.3%)

Algorithm
1×egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
049092371
149092371

prune117.0ms (4.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1241125
Fresh112
Picked011
Done011
Total1254129
Error
0b
Counts
129 → 4
Compiler

Compiled 2046 to 1180 computations (42.3% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(+.f64 x (/.f64 1 x))
0.1b
(/.f64 1 (+.f64 x (/.f64 1 x)))

rewrite21.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
28×*-un-lft-identity_binary64_760
18×times-frac_binary64_766
16×add-exp-log_binary64_798
13×add-cube-cbrt_binary64_795 add-sqr-sqrt_binary64_782
10×distribute-lft-out_binary64_711
6×associate-/r*_binary64_704 div-inv_binary64_757 rec-exp_binary64_810
5×cosh-undef_binary64_954
4×add-log-exp_binary64_799 add-cbrt-cube_binary64_796
3×associate-/l*_binary64_705 pow1_binary64_821
2×associate-/r/_binary64_706 flip3-+_binary64_763 flip-+_binary64_734 div-exp_binary64_811
1×frac-2neg_binary64_771 cbrt-undiv_binary64_794 inv-pow_binary64_845 +-commutative_binary64_690 sum-log_binary64_851 clear-num_binary64_759 1-exp_binary64_804 pow-flip_binary64_834
Counts
2 → 59
Calls

2 calls:

8.0ms
(/.f64 1 (+.f64 x (/.f64 1 x)))
6.0ms
(+.f64 x (/.f64 1 x))

series60.0ms (2.4%)

Counts
2 → 6
Calls

2 calls:

32.0ms
(+.f64 x (/.f64 1 x))
28.0ms
(/.f64 1 (+.f64 x (/.f64 1 x)))

simplify97.0ms (3.9%)

Algorithm
1×egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 0 (77.0ms)

IterNodesCost
05042836

prune57.0ms (2.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New65065
Fresh011
Picked011
Done022
Total65469
Error
0b
Counts
69 → 4
Compiler

Compiled 764 to 575 computations (24.7% saved)

regimes88.0ms (3.5%)

Accuracy

Total 0.1b remaining (99.7%)

Threshold costs 0.1b (99.7%)

Compiler

Compiled 624 to 428 computations (31.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0810
1810

end0.0ms (0%)

sample906.0ms (36.3%)

Algorithm
1×intervals
Results
286.0ms8000×body128valid
Compiler

Compiled 289 to 202 computations (30.1% saved)

Profiling

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