Details

Time bar (total: 1.8s)

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)

sample13.0ms (0.7%)

Algorithm
1×intervals
Results
8.0ms256×body128valid
Compiler

Compiled 15 to 12 computations (20% saved)

simplify97.0ms (5.3%)

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
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))

rewrite14.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
10×add-sqr-sqrt_binary64_1805 add-cube-cbrt_binary64_1818 *-un-lft-identity_binary64_1783
9×times-frac_binary64_1789
4×add-cbrt-cube_binary64_1819 add-exp-log_binary64_1821 add-log-exp_binary64_1822
3×associate-/l*_binary64_1728 associate-/r*_binary64_1727
2×associate-/r/_binary64_1729 flip-+_binary64_1757 flip3-+_binary64_1786 pow1_binary64_1844
1×+-commutative_binary64_1713 div-inv_binary64_1780 cbrt-undiv_binary64_1817 frac-2neg_binary64_1794 sum-log_binary64_1874 div-exp_binary64_1834 clear-num_binary64_1782
Counts
2 → 40
Calls

2 calls:

7.0ms
(/.f64 x (+.f64 (*.f64 x x) 1))
5.0ms
(+.f64 (*.f64 x x) 1)

series53.0ms (2.9%)

Counts
2 → 6
Calls

2 calls:

27.0ms
(+.f64 (*.f64 x x) 1)
25.0ms
(/.f64 x (+.f64 (*.f64 x x) 1))

simplify56.0ms (3.1%)

Algorithm
1×egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
05596689

prune47.0ms (2.6%)

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)

localize8.0ms (0.5%)

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))

rewrite32.0ms (1.7%)

Algorithm
1×rewrite-expression-head
Rules
38×add-sqr-sqrt_binary64_1805
36×add-cube-cbrt_binary64_1818 *-un-lft-identity_binary64_1783 times-frac_binary64_1789
30×sqrt-prod_binary64_1799
12×associate-/r*_binary64_1727
10×add-exp-log_binary64_1821
8×add-cbrt-cube_binary64_1819 sqrt-div_binary64_1800 pow1_binary64_1844
6×associate-/l*_binary64_1728
4×associate-/r/_binary64_1729 flip-+_binary64_1757 flip3-+_binary64_1786 add-log-exp_binary64_1822
3×pow-flip_binary64_1857 pow1/2_binary64_1863 div-exp_binary64_1834 sqrt-pow1_binary64_1801
2×div-inv_binary64_1780 cbrt-undiv_binary64_1817 frac-2neg_binary64_1794 clear-num_binary64_1782 rem-sqrt-square_binary64_1796
1×inv-pow_binary64_1868 1-exp_binary64_1827 rec-exp_binary64_1833
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))

series91.0ms (5%)

Counts
4 → 12
Calls

4 calls:

34.0ms
(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
22.0ms
(/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) 1)))
17.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))
16.0ms
(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify70.0ms (3.8%)

Algorithm
1×egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049892284
149892284

prune149.0ms (8.2%)

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)

localize10.0ms (0.6%)

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)

rewrite31.0ms (1.7%)

Algorithm
1×rewrite-expression-head
Rules
84×times-frac_binary64_1789
53×add-sqr-sqrt_binary64_1805 add-cube-cbrt_binary64_1818 *-un-lft-identity_binary64_1783
16×add-exp-log_binary64_1821 associate-/r*_binary64_1727
10×add-cbrt-cube_binary64_1819
8×div-exp_binary64_1834
6×associate-/l*_binary64_1728 div-inv_binary64_1780
5×add-log-exp_binary64_1822
4×cbrt-undiv_binary64_1817 pow1_binary64_1844
2×associate-/l/_binary64_1730 1-exp_binary64_1827 flip-+_binary64_1757 frac-2neg_binary64_1794 flip3-+_binary64_1786 clear-num_binary64_1782 rec-exp_binary64_1833
1×associate-/r/_binary64_1729 +-commutative_binary64_1713 inv-pow_binary64_1868 pow-flip_binary64_1857 sum-log_binary64_1874
Counts
3 → 116
Calls

3 calls:

10.0ms
(/.f64 1 (/.f64 (+.f64 (*.f64 x x) 1) x))
6.0ms
(/.f64 (+.f64 (*.f64 x x) 1) x)
5.0ms
(+.f64 (*.f64 x x) 1)

series89.0ms (4.9%)

Counts
3 → 9
Calls

3 calls:

43.0ms
(/.f64 (+.f64 (*.f64 x x) 1) x)
25.0ms
(/.f64 1 (/.f64 (+.f64 (*.f64 x x) 1) x))
21.0ms
(+.f64 (*.f64 x x) 1)

simplify98.0ms (5.4%)

Algorithm
1×egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 0 (70.0ms)

IterNodesCost
049092371
149092371

prune100.0ms (5.5%)

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)))

rewrite18.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
28×*-un-lft-identity_binary64_1783
18×times-frac_binary64_1789
16×add-exp-log_binary64_1821
13×add-sqr-sqrt_binary64_1805 add-cube-cbrt_binary64_1818
10×distribute-lft-out_binary64_1734
6×div-inv_binary64_1780 associate-/r*_binary64_1727 rec-exp_binary64_1833
5×cosh-undef_binary64_1977
4×add-cbrt-cube_binary64_1819 add-log-exp_binary64_1822
3×associate-/l*_binary64_1728 pow1_binary64_1844
2×associate-/r/_binary64_1729 flip-+_binary64_1757 div-exp_binary64_1834 flip3-+_binary64_1786
1×+-commutative_binary64_1713 inv-pow_binary64_1868 1-exp_binary64_1827 pow-flip_binary64_1857 cbrt-undiv_binary64_1817 frac-2neg_binary64_1794 sum-log_binary64_1874 clear-num_binary64_1782
Counts
2 → 59
Calls

2 calls:

9.0ms
(/.f64 1 (+.f64 x (/.f64 1 x)))
6.0ms
(+.f64 x (/.f64 1 x))

series36.0ms (2%)

Counts
2 → 6
Calls

2 calls:

19.0ms
(/.f64 1 (+.f64 x (/.f64 1 x)))
17.0ms
(+.f64 x (/.f64 1 x))

simplify64.0ms (3.5%)

Algorithm
1×egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
05042836

prune47.0ms (2.6%)

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)

regimes74.0ms (4%)

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%)

sample618.0ms (33.8%)

Algorithm
1×intervals
Results
191.0ms8000×body128valid
Compiler

Compiled 289 to 202 computations (30.1% saved)

Profiling

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