Details

Time bar (total: 5.8s)

analyze46.0ms (0.8%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
75%25%0%4
87.5%12.5%0%5
93.7%6.2%0%6
96.8%3.1%0%7
98.4%1.6%0%8
99.2%0.8%0%9
99.6%0.4%0%10
99.8%0.2%0%11
99.9%0.1%0%12
99.9%0%0%13
99.9%0%0%14
Compiler

Compiled 13 to 11 computations (15.4% saved)

sample45.0ms (0.8%)

Algorithm
1×intervals
Results
13.0ms62×body512valid
10.0ms145×body128valid
5.0ms37×body256valid
3.0ms12×body1024valid
Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify24.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
39×fma-def_binary64
32×fma-neg_binary64
14×cancel-sign-sub-inv_binary64
13×sub-neg_binary64
10×distribute-rgt-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0816
11616
22116
32916
43716
55516
68016
79716
811416
912416
1012816
1113016
1211616

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
13.7b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶13.7b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
Compiler

Compiled 47 to 39 computations (17% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 1 (-.f64 x 1))
✓0.0b
(/.f64 1 (+.f64 x 1))
✓3.5b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

series17.0ms (0.3%)

Counts
3 → 36
Calls

3 calls:

7.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
5.0ms
(/.f64 1 (+.f64 x 1))
4.0ms
(/.f64 1 (-.f64 x 1))

rewrite321.0ms (5.5%)

Algorithm
1×rewrite-expression-head
Rules
870×*-un-lft-identity_binary64
804×times-frac_binary64
733×add-sqr-sqrt_binary64
486×prod-diff_binary64
465×add-cube-cbrt_binary64
Counts
3 → 661
Calls

3 calls:

70.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
14.0ms
(/.f64 1 (-.f64 x 1))
7.0ms
(/.f64 1 (+.f64 x 1))

simplify1.2s (19.8%)

Algorithm
1×egg-herbie
Rules
947×fma-neg_binary64
335×times-frac_binary64
236×distribute-rgt-in_binary64
231×div-sub_binary64
202×associate-/l*_binary64
Counts
697 → 531
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
027227782
163218403
2177213759
3394512706
4497212706
5498912706
6490912706

prune1.3s (21.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New5292531
Fresh000
Picked011
Done000
Total5293532
Error
0.2b
Counts
532 → 3
Alt Table
StatusErrorProgram
29.6b
(-.f64 (/.f64 -2 (*.f64 x x)) (/.f64 2 (pow.f64 x 4)))
▶12.8b
(/.f64 (-.f64 x (+.f64 2 x)) (fma.f64 x x -1))
✓13.7b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
Compiler

Compiled 23079 to 19160 computations (17% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (-.f64 x (+.f64 2 x)) (fma.f64 x x -1))
✓2.7b
(-.f64 x (+.f64 2 x))

series8.0ms (0.1%)

Counts
2 → 24
Calls

2 calls:

6.0ms
(/.f64 (-.f64 x (+.f64 2 x)) (fma.f64 x x -1))
2.0ms
(-.f64 x (+.f64 2 x))

rewrite36.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
55×*-un-lft-identity_binary64
32×add-sqr-sqrt_binary64
22×add-cube-cbrt_binary64
18×times-frac_binary64
12×prod-diff_binary64
Counts
2 → 81
Calls

2 calls:

13.0ms
(/.f64 (-.f64 x (+.f64 2 x)) (fma.f64 x x -1))
10.0ms
(-.f64 x (+.f64 2 x))

simplify124.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
512×fma-def_binary64
468×associate-*r*_binary64
325×distribute-rgt-in_binary64
280×distribute-lft-in_binary64
260×div-sub_binary64
Counts
105 → 127
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01561716
13711547
211431129
344081129
448771129

prune158.0ms (2.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1234127
Fresh101
Picked101
Done101
Total1264130
Error
0.2b
Counts
130 → 4
Alt Table
StatusErrorProgram
8.7b
(cbrt.f64 (pow.f64 (/.f64 -2 (fma.f64 x x -1)) 3))
▶0.2b
(/.f64 -2 (fma.f64 x x -1))
29.1b
(/.f64 (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
29.2b
(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x -1))) (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))))
Compiler

Compiled 2425 to 1671 computations (31.1% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 -2 (fma.f64 x x -1))

series6.0ms (0.1%)

Counts
1 → 12
Calls

1 calls:

6.0ms
(/.f64 -2 (fma.f64 x x -1))

rewrite8.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
9×*-un-lft-identity_binary64
9×times-frac_binary64
9×add-sqr-sqrt_binary64
9×add-cube-cbrt_binary64
3×associate-/r*_binary64
Counts
1 → 29
Calls

1 calls:

6.0ms
(/.f64 -2 (fma.f64 x x -1))

simplify104.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
741×fma-def_binary64
662×fma-neg_binary64
373×unswap-sqr_binary64
363×associate-*l*_binary64
341×associate-/r*_binary64
Counts
41 → 48
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
089680
1194628
2483625
31288622
44089622
55299622

prune58.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New48048
Fresh033
Picked011
Done000
Total48452
Error
0.2b
Counts
52 → 4
Alt Table
StatusErrorProgram
▶8.7b
(cbrt.f64 (pow.f64 (/.f64 -2 (fma.f64 x x -1)) 3))
✓0.2b
(/.f64 -2 (fma.f64 x x -1))
29.1b
(/.f64 (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
29.2b
(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x -1))) (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))))
Compiler

Compiled 717 to 547 computations (23.7% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.1b
(pow.f64 (/.f64 -2 (fma.f64 x x -1)) 3)
0.2b
(/.f64 -2 (fma.f64 x x -1))
✓8.8b
(cbrt.f64 (pow.f64 (/.f64 -2 (fma.f64 x x -1)) 3))

series28.0ms (0.5%)

Counts
2 → 24
Calls

2 calls:

21.0ms
(cbrt.f64 (pow.f64 (/.f64 -2 (fma.f64 x x -1)) 3))
7.0ms
(pow.f64 (/.f64 -2 (fma.f64 x x -1)) 3)

rewrite26.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
36×times-frac_binary64
32×*-un-lft-identity_binary64
32×add-sqr-sqrt_binary64
32×cbrt-prod_binary64
32×add-cube-cbrt_binary64
Counts
2 → 92
Calls

2 calls:

7.0ms
(cbrt.f64 (pow.f64 (/.f64 -2 (fma.f64 x x -1)) 3))
7.0ms
(pow.f64 (/.f64 -2 (fma.f64 x x -1)) 3)

simplify174.0ms (3%)

Algorithm
1×egg-herbie
Rules
599×associate-*l/_binary64
556×fma-def_binary64
344×times-frac_binary64
335×associate-/r*_binary64
241×associate-/l*_binary64
Counts
116 → 125
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01772232
14361992
213291949
348641948
451391948

prune243.0ms (4.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1721173
Fresh022
Picked011
Done011
Total1725177
Error
0.2b
Counts
177 → 5
Alt Table
StatusErrorProgram
✓8.7b
(cbrt.f64 (pow.f64 (/.f64 -2 (fma.f64 x x -1)) 3))
6.1b
(*.f64 (cbrt.f64 (pow.f64 (/.f64 -2 (fma.f64 x x -1)) 2)) (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))))
✓0.2b
(/.f64 -2 (fma.f64 x x -1))
29.1b
(/.f64 (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
29.2b
(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x -1))) (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))))
Compiler

Compiled 2883 to 2321 computations (19.5% saved)

regimes441.0ms (7.6%)

Accuracy

Total 0.0b remaining (11.2%)

Threshold costs 0.0b (11.2%)

Counts
88 → 1
Compiler

Compiled 6453 to 5455 computations (15.5% saved)

simplify4.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
168

end1.0ms (0%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

sample1.5s (25.7%)

Algorithm
1×intervals
Results
403.0ms1981×body512valid
356.0ms4584×body128valid
138.0ms994×body256valid
122.0ms441×body1024valid
Compiler

Compiled 86 to 66 computations (23.3% saved)

Profiling

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