Details

Time bar (total: 3.7s)

analyze5.0ms (0.1%)

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)

sample1.2s (32.3%)

Results
464.0ms2079×body512valid
411.0ms4690×body128valid
161.0ms1024×body256valid
135.0ms463×body1024valid
Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify13.0ms (0.3%)

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

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
16.9b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶16.9b
(-.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 2 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 1 (+.f64 x 1))
✓4.7b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

series6.0ms (0.2%)

Counts
2 → 24
Calls

2 calls:

4.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
2.0ms
(/.f64 1 (+.f64 x 1))

rewrite161.0ms (4.3%)

Algorithm
1×rewrite-expression-head
Rules
845×*-un-lft-identity_binary64
783×times-frac_binary64
704×add-sqr-sqrt_binary64
486×prod-diff_binary64
452×add-cube-cbrt_binary64
Counts
2 → 610
Calls

2 calls:

42.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
4.0ms
(/.f64 1 (+.f64 x 1))

simplify514.0ms (13.8%)

Algorithm
1×egg-herbie
Rules
372×div-sub_binary64
293×times-frac_binary64
259×unsub-neg_binary64
206×exp-prod_binary64
201×distribute-rgt-in_binary64
Counts
634 → 449
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
024827037
158117682
2162213025
3395611972
4479411972
5479811972

prune669.0ms (17.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New4463449
Fresh000
Picked101
Done000
Total4473450
Error
0.4b
Counts
450 → 3
Alt Table
StatusErrorProgram
▶15.8b
(/.f64 (+.f64 x (-.f64 -2 x)) (fma.f64 x x -1))
16.9b
(+.f64 (/.f64 1 (+.f64 x 1)) (/.f64 -1 (-.f64 x 1)))
28.7b
(-.f64 (-.f64 (/.f64 -2 (*.f64 x x)) (/.f64 2 (pow.f64 x 4))) (/.f64 2 (pow.f64 x 6)))
Compiler

Compiled 21691 to 18038 computations (16.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (+.f64 x (-.f64 -2 x)) (fma.f64 x x -1))
✓3.6b
(+.f64 x (-.f64 -2 x))

series5.0ms (0.1%)

Counts
2 → 24
Calls

2 calls:

3.0ms
(/.f64 (+.f64 x (-.f64 -2 x)) (fma.f64 x x -1))
1.0ms
(+.f64 x (-.f64 -2 x))

rewrite16.0ms (0.4%)

Algorithm
1×rewrite-expression-head
Rules
45×*-un-lft-identity_binary64
20×add-sqr-sqrt_binary64
20×add-cube-cbrt_binary64
15×times-frac_binary64
13×associate-+r+_binary64
Counts
2 → 73
Calls

2 calls:

6.0ms
(/.f64 (+.f64 x (-.f64 -2 x)) (fma.f64 x x -1))
5.0ms
(+.f64 x (-.f64 -2 x))

simplify88.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
654×fma-neg_binary64
560×fma-def_binary64
470×div-sub_binary64
338×unswap-sqr_binary64
282×distribute-rgt-in_binary64
Counts
97 → 122
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01451379
13211288
21042940
33433934
44530934
54940934

prune78.0ms (2.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1193122
Fresh202
Picked101
Done000
Total1223125
Error
0.3b
Counts
125 → 3
Alt Table
StatusErrorProgram
▶0.4b
(/.f64 -2 (fma.f64 x x -1))
28.6b
(/.f64 (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
0.7b
(/.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)))
Compiler

Compiled 2169 to 1392 computations (35.8% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series49.0ms (1.3%)

Counts
1 → 12
Calls

1 calls:

49.0ms
(/.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))

simplify59.0ms (1.6%)

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

prune30.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New48048
Fresh022
Picked011
Done000
Total48351
Error
0.3b
Counts
51 → 3
Alt Table
StatusErrorProgram
✓0.4b
(/.f64 -2 (fma.f64 x x -1))
28.6b
(/.f64 (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
▶0.7b
(/.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)))
Compiler

Compiled 705 to 535 computations (24.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(/.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)))
✓0.2b
(*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))
✓0.7b
(/.f64 -2 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1))))
✓16.1b
(cbrt.f64 (fma.f64 x x -1))

series31.0ms (0.8%)

Counts
4 → 48
Calls

4 calls:

9.0ms
(/.f64 -2 (*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1))))
9.0ms
(cbrt.f64 (fma.f64 x x -1))
8.0ms
(*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))
4.0ms
(/.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)))

rewrite31.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
66×times-frac_binary64
53×add-sqr-sqrt_binary64
45×*-un-lft-identity_binary64
45×add-cube-cbrt_binary64
43×cbrt-prod_binary64
Counts
4 → 152
Calls

4 calls:

7.0ms
(/.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)))
6.0ms
(*.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (fma.f64 x x -1)))
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))

simplify175.0ms (4.7%)

Algorithm
1×egg-herbie
Rules
582×fma-def_binary64
504×times-frac_binary64
334×fma-neg_binary64
329×associate-/l/_binary64
231×cancel-sign-sub-inv_binary64
Counts
200 → 295
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02935397
17035006
220704484
347194484
449854484
549234484

prune324.0ms (8.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New3570357
Fresh011
Picked011
Done011
Total3573360
Error
0.3b
Counts
360 → 3
Alt Table
StatusErrorProgram
✓0.4b
(/.f64 -2 (fma.f64 x x -1))
28.6b
(/.f64 (/.f64 -2 (sqrt.f64 (fma.f64 x x -1))) (sqrt.f64 (fma.f64 x x -1)))
✓0.7b
(/.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)))
Compiler

Compiled 9703 to 7239 computations (25.4% saved)

regimes186.0ms (5%)

Accuracy

Total 0.0b remaining (12.3%)

Threshold costs 0.0b (12.3%)

Counts
78 → 1
Compiler

Compiled 2814 to 2200 computations (21.8% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
168

end56.0ms (1.5%)

Compiler

Compiled 55 to 39 computations (29.1% saved)

Profiling

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