Details

Time bar (total: 2.6s)

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
6.0ms256×body128valid
Compiler

Compiled 15 to 12 computations (20% saved)

simplify159.0ms (6.1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0810
1810

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 13.1b

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)
13.1b
(/.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)

series98.0ms (3.8%)

Counts
2 → 6
Calls

2 calls:

51.0ms
(/.f64 x (+.f64 (*.f64 x x) 1))
47.0ms
(+.f64 (*.f64 x x) 1)

simplify68.0ms (2.6%)

Algorithm
1×egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
04989689
14989689

prune43.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New43346
Fresh000
Picked101
Done000
Total44347

Merged error: 0b

Counts
47 → 3
Compiler

Compiled 656 to 364 computations (44.5% saved)

localize6.0ms (0.2%)

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))
13.1b
(/.f64 (+.f64 (*.f64 x x) 1) x)

rewrite30.0ms (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:

9.0ms
(/.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)

series203.0ms (7.8%)

Counts
3 → 9
Calls

3 calls:

103.0ms
(/.f64 (+.f64 (*.f64 x x) 1) x)
53.0ms
(/.f64 1 (/.f64 (+.f64 (*.f64 x x) 1) x))
46.0ms
(+.f64 (*.f64 x x) 1)

simplify100.0ms (3.8%)

Algorithm
1×egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
048712371
148712371

prune101.0ms (3.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1250125
Fresh022
Picked011
Done000
Total1253128

Merged error: 0b

Counts
128 → 3
Compiler

Compiled 2065 to 1194 computations (42.2% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

6.1b
(/.f64 x (*.f64 (cbrt.f64 (+.f64 (*.f64 x x) 1)) (cbrt.f64 (+.f64 (*.f64 x x) 1))))
13.5b
(cbrt.f64 (+.f64 (*.f64 x x) 1))
13.5b
(cbrt.f64 (+.f64 (*.f64 x x) 1))
13.5b
(cbrt.f64 (+.f64 (*.f64 x x) 1))

rewrite35.0ms (1.4%)

Algorithm
1×rewrite-expression-head
Rules
18×cbrt-div_binary64_792
9×*-un-lft-identity_binary64_760 flip3-+_binary64_763 add-exp-log_binary64_798 add-cube-cbrt_binary64_795 flip-+_binary64_734 cbrt-prod_binary64_791 add-sqr-sqrt_binary64_782
8×associate-/r/_binary64_706
7×add-cbrt-cube_binary64_796
4×add-log-exp_binary64_799 frac-times_binary64_770 pow1_binary64_821
3×pow1/3_binary64_842 associate-/l*_binary64_705 times-frac_binary64_766
2×cbrt-undiv_binary64_794 associate-*l/_binary64_703 associate-*r/_binary64_702 div-exp_binary64_811
1×frac-2neg_binary64_771 prod-exp_binary64_809 associate-/r*_binary64_704 div-inv_binary64_757 cbrt-unprod_binary64_793 clear-num_binary64_759
Counts
4 → 68
Calls

4 calls:

14.0ms
(/.f64 x (*.f64 (cbrt.f64 (+.f64 (*.f64 x x) 1)) (cbrt.f64 (+.f64 (*.f64 x x) 1))))
5.0ms
(cbrt.f64 (+.f64 (*.f64 x x) 1))
5.0ms
(cbrt.f64 (+.f64 (*.f64 x x) 1))
4.0ms
(cbrt.f64 (+.f64 (*.f64 x x) 1))

series400.0ms (15.3%)

Counts
4 → 12
Calls

4 calls:

151.0ms
(/.f64 x (*.f64 (cbrt.f64 (+.f64 (*.f64 x x) 1)) (cbrt.f64 (+.f64 (*.f64 x x) 1))))
85.0ms
(cbrt.f64 (+.f64 (*.f64 x x) 1))
83.0ms
(cbrt.f64 (+.f64 (*.f64 x x) 1))
80.0ms
(cbrt.f64 (+.f64 (*.f64 x x) 1))

simplify75.0ms (2.9%)

Algorithm
1×egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
048721501
148721501

prune104.0ms (4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New80080
Fresh011
Picked011
Done011
Total80383

Merged error: 0b

Counts
83 → 3
Compiler

Compiled 2310 to 1430 computations (38.1% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.1b
(/.f64 1 (pow.f64 x 5))
0.2b
(pow.f64 (/.f64 1 x) 3)
21.5b
(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (pow.f64 (/.f64 1 x) 3))

rewrite75.0ms (2.9%)

Algorithm
1×rewrite-expression-head
Rules
66×add-sqr-sqrt_binary64_782
61×*-un-lft-identity_binary64_760 times-frac_binary64_766
49×add-cube-cbrt_binary64_795
41×unpow-prod-down_binary64_839
32×cancel-sign-sub-inv_binary64_726
29×cube-prod_binary64_788
17×add-exp-log_binary64_798
9×div-inv_binary64_757
8×add-log-exp_binary64_799 difference-of-squares_binary64_729 add-cbrt-cube_binary64_796 div-exp_binary64_811
7×associate-/r*_binary64_704 pow-exp_binary64_828 sqr-pow_binary64_732
5×distribute-lft-out--_binary64_712 pow1_binary64_821
4×distribute-lft-out_binary64_711 pow-to-exp_binary64_829 cube-div_binary64_789 rec-exp_binary64_810 1-exp_binary64_804
3×associate-/l*_binary64_705 frac-sub_binary64_769 pow-unpow_binary64_837 pow-pow_binary64_832
2×cube-mult_binary64_790 diff-log_binary64_852 cbrt-undiv_binary64_794 unpow3_binary64_826 inv-pow_binary64_845 rem-cube-cbrt_binary64_783 pow-flip_binary64_834
1×frac-2neg_binary64_771 flip3-+_binary64_763 frac-add_binary64_768 flip-+_binary64_734 sum-log_binary64_851 associate--l+_binary64_697 clear-num_binary64_759 sub-neg_binary64_753 flip--_binary64_735 flip3--_binary64_764
Counts
3 → 164
Calls

3 calls:

48.0ms
(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (pow.f64 (/.f64 1 x) 3))
6.0ms
(pow.f64 (/.f64 1 x) 3)
5.0ms
(/.f64 1 (pow.f64 x 5))

series142.0ms (5.5%)

Counts
3 → 9
Calls

3 calls:

59.0ms
(/.f64 1 (pow.f64 x 5))
42.0ms
(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (pow.f64 (/.f64 1 x) 3))
41.0ms
(pow.f64 (/.f64 1 x) 3)

simplify93.0ms (3.6%)

Algorithm
1×egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
048552535
148552535

prune204.0ms (7.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1730173
Fresh000
Picked011
Done022
Total1733176

Merged error: 0b

Counts
176 → 3
Compiler

Compiled 3412 to 2701 computations (20.8% saved)

regimes66.0ms (2.5%)

Compiler

Compiled 576 to 404 computations (29.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
1810

end0.0ms (0%)

sample552.0ms (21.2%)

Algorithm
1×intervals
Results
182.0ms8000×body128valid
Compiler

Compiled 265 to 190 computations (28.3% saved)

Profiling

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