Details

Time bar (total: 2.9s)

analyze25.0ms (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)

sample22.0ms (0.7%)

Algorithm
1×intervals
Results
5.0ms150×body128valid
5.0ms55×body512valid
3.0ms39×body256valid
2.0ms12×body1024valid
Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify14.0ms (0.5%)

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

prune6.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
12.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶12.8b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
Compiler

Compiled 47 to 39 computations (17% saved)

localize6.0ms (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))
✓3.7b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

rewrite120.0ms (4.1%)

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:

38.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
7.0ms
(/.f64 1 (+.f64 x 1))
4.0ms
(/.f64 1 (-.f64 x 1))

series12.0ms (0.4%)

Counts
3 → 36
Calls

3 calls:

8.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
2.0ms
(/.f64 1 (+.f64 x 1))
2.0ms
(/.f64 1 (-.f64 x 1))

simplify673.0ms (22.8%)

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 → 1368
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
027227782
163218403
2177213759
3394512706
4497212706
5498912706
6490912706

prune565.0ms (19.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New136621368
Fresh000
Picked101
Done000
Total136721369
Error
0.4b
Counts
1369 → 2
Alt Table
StatusErrorProgram
32.9b
(+.f64 (-.f64 (/.f64 -2 (*.f64 x x)) (/.f64 2 (pow.f64 x 4))) (/.f64 -2 (pow.f64 x 6)))
▶11.7b
(/.f64 (-.f64 x (+.f64 2 x)) (fma.f64 x x -1))
Compiler

Compiled 23077 to 19158 computations (17% saved)

localize6.0ms (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))

rewrite16.0ms (0.5%)

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:

7.0ms
(/.f64 (-.f64 x (+.f64 2 x)) (fma.f64 x x -1))
5.0ms
(-.f64 x (+.f64 2 x))

series5.0ms (0.2%)

Counts
2 → 24
Calls

2 calls:

5.0ms
(/.f64 (-.f64 x (+.f64 2 x)) (fma.f64 x x -1))
1.0ms
(-.f64 x (+.f64 2 x))

simplify84.0ms (2.8%)

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 → 190
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01561716
13711547
211431129
344081129
448771129

prune77.0ms (2.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1864190
Fresh101
Picked101
Done000
Total1884192
Error
0.3b
Counts
192 → 4
Alt Table
StatusErrorProgram
33.0b
(/.f64 (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
0.6b
(/.f64 (/.f64 -2 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))) (cbrt.f64 (fma.f64 x x -1)))
1.4b
(*.f64 (*.f64 (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))) (cbrt.f64 (/.f64 -2 (fma.f64 x x -1)))) (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))))
▶0.4b
(/.f64 -2 (fma.f64 x x -1))
Compiler

Compiled 2455 to 1691 computations (31.1% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.4b
(/.f64 -2 (fma.f64 x x -1))

rewrite3.0ms (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:

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

series4.0ms (0.1%)

Counts
1 → 12
Calls

1 calls:

4.0ms
(/.f64 -2 (fma.f64 x x -1))

simplify67.0ms (2.3%)

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 → 60
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
089680
1194628
2483625
31288622
44089622
55299622

prune30.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New60060
Fresh033
Picked011
Done000
Total60464
Error
0.3b
Counts
64 → 4
Alt Table
StatusErrorProgram
33.0b
(/.f64 (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
▶0.6b
(/.f64 (/.f64 -2 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))) (cbrt.f64 (fma.f64 x x -1)))
1.4b
(*.f64 (*.f64 (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))) (cbrt.f64 (/.f64 -2 (fma.f64 x x -1)))) (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))))
✓0.4b
(/.f64 -2 (fma.f64 x x -1))
Compiler

Compiled 753 to 571 computations (24.2% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.5b
(/.f64 -2 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1))))
16.4b
(cbrt.f64 (fma.f64 x x -1))
16.4b
(cbrt.f64 (fma.f64 x x -1))
✓16.4b
(cbrt.f64 (fma.f64 x x -1))

rewrite6.0ms (0.2%)

Algorithm
1×rewrite-expression-head
Rules
7×add-exp-log_binary64
5×*-un-lft-identity_binary64
5×add-sqr-sqrt_binary64
5×add-cube-cbrt_binary64
5×add-cbrt-cube_binary64
Counts
2 → 36
Calls

2 calls:

4.0ms
(/.f64 -2 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1))))
1.0ms
(cbrt.f64 (fma.f64 x x -1))

series24.0ms (0.8%)

Counts
2 → 24
Calls

2 calls:

14.0ms
(/.f64 -2 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1))))
10.0ms
(cbrt.f64 (fma.f64 x x -1))

simplify109.0ms (3.7%)

Algorithm
1×egg-herbie
Rules
360×distribute-rgt-neg-in_binary64
343×distribute-lft-neg-in_binary64
325×fma-def_binary64
283×neg-mul-1_binary64
227×unswap-sqr_binary64
Counts
60 → 103
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01301350
13251229
29001170
327101165
447501075
549651075

prune136.0ms (4.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2221223
Fresh112
Picked101
Done011
Total2243227
Error
0.3b
Counts
227 → 3
Alt Table
StatusErrorProgram
0.6b
(/.f64 (/.f64 -2 (*.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1)) 2)) (cbrt.f64 (cbrt.f64 (fma.f64 x x -1)))) (cbrt.f64 (fma.f64 x x -1)))) (cbrt.f64 (fma.f64 x x -1)))
33.0b
(/.f64 (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
✓0.4b
(/.f64 -2 (fma.f64 x x -1))
Compiler

Compiled 3762 to 2814 computations (25.2% saved)

regimes154.0ms (5.2%)

Accuracy

Total 0.0b remaining (12%)

Threshold costs 0.0b (12%)

Compiler

Compiled 3222 to 2468 computations (23.4% saved)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
168

end0.0ms (0%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

sample769.0ms (26.1%)

Algorithm
1×intervals
Results
237.0ms1996×body512valid
170.0ms4595×body128valid
69.0ms1007×body256valid
54.0ms402×body1024valid
Compiler

Compiled 72 to 54 computations (25% saved)

Profiling

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