Details

Time bar (total: 5.1s)

analyze1.0s (20.3%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
14%85.8%0.1%7
22.6%77.2%0.1%8
23.8%74.5%1.7%9
40%56.4%3.7%10
46.9%48.7%4.4%11
48%45.8%6.2%12
58.1%32.2%9.7%13
62.1%27.2%10.6%14
Compiler

Compiled 13 to 9 computations (30.8% saved)

sample36.0ms (0.7%)

Algorithm
intervals
Results
18.0ms256×body128valid
2.0ms33×body128invalid
Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify74.0ms (1.4%)

Algorithm
egg-herbie
Rules
823×div-sub_binary64
529×fma-neg_binary64
475×distribute-rgt-in_binary64
409×fma-def_binary64
380×distribute-lft-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0913
12511
25011
315611
433111
566611
6174411
7398811
8495311

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
11.2b
Counts
3 → 1
Alt Table
StatusErrorProgram
11.2b
(/.f64 (fma.f64 x (-.f64 y z) x) z)
Compiler

Compiled 42 to 22 computations (47.6% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 x (-.f64 y z) x)
10.5b
(/.f64 (fma.f64 x (-.f64 y z) x) z)

series45.0ms (0.9%)

Counts
2 → 72
Calls

2 calls:

31.0ms
(/.f64 (fma.f64 x (-.f64 y z) x) z)
13.0ms
(fma.f64 x (-.f64 y z) x)

rewrite8.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
times-frac_binary64
add-cbrt-cube_binary64
Counts
2 → 39
Calls

2 calls:

4.0ms
(/.f64 (fma.f64 x (-.f64 y z) x) z)
1.0ms
(fma.f64 x (-.f64 y z) x)

simplify118.0ms (2.3%)

Algorithm
egg-herbie
Rules
672×associate-/l*_binary64
629×fma-def_binary64
448×associate-/l/_binary64
308×associate-/r*_binary64
291×associate-/r/_binary64
Counts
111 → 73
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0821522
11601371
23741332
312271332
443581332
550421332

prune82.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New66773
Fresh000
Picked101
Done000
Total67774
Error
0.0b
Counts
74 → 7
Alt Table
StatusErrorProgram
3.2b
(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
11.2b
(/.f64 (+.f64 (*.f64 x (-.f64 y z)) x) z)
52.6b
(*.f64 (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (sqrt.f64 z)) (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (sqrt.f64 z)))
12.3b
(/.f64 (/.f64 (fma.f64 x (-.f64 y z) x) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 z))
32.6b
(/.f64 (fma.f64 y x x) z)
38.2b
(*.f64 (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)) (sqrt.f64 (/.f64 (fma.f64 x (-.f64 y z) x) z)))
11.3b
(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
Compiler

Compiled 1177 to 301 computations (74.4% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
5.1b
(fma.f64 (/.f64 x z) y (/.f64 x z))

series70.0ms (1.4%)

Counts
2 → 72
Calls

2 calls:

36.0ms
(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
34.0ms
(fma.f64 (/.f64 x z) y (/.f64 x z))

rewrite11.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
prod-diff_binary64
add-log-exp_binary64
Counts
2 → 41
Calls

2 calls:

6.0ms
(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
1.0ms
(fma.f64 (/.f64 x z) y (/.f64 x z))

simplify144.0ms (2.8%)

Algorithm
egg-herbie
Rules
663×fma-neg_binary64
438×associate-*l*_binary64
352×associate-*r*_binary64
336×fma-def_binary64
307×distribute-rgt-out_binary64
Counts
113 → 74
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0871698
11601621
26071157
327301152
444681152
549611152

prune80.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New73174
Fresh336
Picked011
Done000
Total76581
Error
0.0b
Counts
81 → 5
Alt Table
StatusErrorProgram
3.2b
(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
3.9b
(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
52.6b
(*.f64 (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (sqrt.f64 z)) (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (sqrt.f64 z)))
32.6b
(/.f64 (fma.f64 y x x) z)
11.3b
(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
Compiler

Compiled 1465 to 311 computations (78.8% saved)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
0.0b
(+.f64 (/.f64 y z) (/.f64 1 z))
3.7b
(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)

series95.0ms (1.9%)

Counts
3 → 75
Calls

3 calls:

45.0ms
(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)
37.0ms
(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
13.0ms
(+.f64 (/.f64 y z) (/.f64 1 z))

rewrite88.0ms (1.7%)

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity_binary64
23×times-frac_binary64
20×add-sqr-sqrt_binary64
18×add-cube-cbrt_binary64
13×fma-def_binary64
Counts
3 → 89
Calls

3 calls:

26.0ms
(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)
25.0ms
(+.f64 (/.f64 y z) (/.f64 1 z))
25.0ms
(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)

simplify171.0ms (3.3%)

Algorithm
egg-herbie
Rules
757×times-frac_binary64
585×fma-def_binary64
393×fma-neg_binary64
381×distribute-rgt-in_binary64
362×distribute-lft-in_binary64
Counts
164 → 145
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01342112
13012041
212251572
338191517
449891517

prune185.0ms (3.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1432145
Fresh213
Picked011
Done011
Total1455150
Error
0.0b
Counts
150 → 5
Alt Table
StatusErrorProgram
3.2b
(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
3.9b
(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
34.7b
(-.f64 (*.f64 (fma.f64 (/.f64 1 (sqrt.f64 z)) (/.f64 y (sqrt.f64 z)) (/.f64 1 z)) x) x)
29.0b
(-.f64 (*.f64 (fma.f64 (sqrt.f64 (/.f64 y z)) (sqrt.f64 (/.f64 y z)) (/.f64 1 z)) x) x)
32.6b
(/.f64 (fma.f64 y x x) z)
Compiler

Compiled 2529 to 1183 computations (53.2% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 (fma.f64 (sqrt.f64 (/.f64 y z)) (sqrt.f64 (/.f64 y z)) (/.f64 1 z)) x) x)
0.1b
(fma.f64 (sqrt.f64 (/.f64 y z)) (sqrt.f64 (/.f64 y z)) (/.f64 1 z))
1.1b
(*.f64 (fma.f64 (sqrt.f64 (/.f64 y z)) (sqrt.f64 (/.f64 y z)) (/.f64 1 z)) x)
9.4b
(sqrt.f64 (/.f64 y z))

series399.0ms (7.8%)

Counts
4 → 38
Calls

4 calls:

147.0ms
(-.f64 (*.f64 (fma.f64 (sqrt.f64 (/.f64 y z)) (sqrt.f64 (/.f64 y z)) (/.f64 1 z)) x) x)
135.0ms
(*.f64 (fma.f64 (sqrt.f64 (/.f64 y z)) (sqrt.f64 (/.f64 y z)) (/.f64 1 z)) x)
83.0ms
(fma.f64 (sqrt.f64 (/.f64 y z)) (sqrt.f64 (/.f64 y z)) (/.f64 1 z))
33.0ms
(sqrt.f64 (/.f64 y z))

rewrite27.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt_binary64
16×*-un-lft-identity_binary64
15×add-cube-cbrt_binary64
13×sqrt-prod_binary64
10×times-frac_binary64
Counts
4 → 78
Calls

4 calls:

6.0ms
(-.f64 (*.f64 (fma.f64 (sqrt.f64 (/.f64 y z)) (sqrt.f64 (/.f64 y z)) (/.f64 1 z)) x) x)
5.0ms
(*.f64 (fma.f64 (sqrt.f64 (/.f64 y z)) (sqrt.f64 (/.f64 y z)) (/.f64 1 z)) x)
4.0ms
(sqrt.f64 (/.f64 y z))
1.0ms
(fma.f64 (sqrt.f64 (/.f64 y z)) (sqrt.f64 (/.f64 y z)) (/.f64 1 z))

simplify175.0ms (3.4%)

Algorithm
egg-herbie
Rules
696×fma-neg_binary64
339×fma-def_binary64
308×unswap-sqr_binary64
291×distribute-rgt-in_binary64
280×distribute-lft-in_binary64
Counts
116 → 123
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01491635
12481556
28491425
325261425
441911423
548961423
648921423

prune169.0ms (3.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1531154
Fresh022
Picked011
Done022
Total1536159
Error
0b
Counts
159 → 6
Alt Table
StatusErrorProgram
3.2b
(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
3.9b
(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
29.3b
(-.f64 (*.f64 (fma.f64 (sqrt.f64 (/.f64 y z)) (expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 y z)))) (/.f64 1 z)) x) x)
34.7b
(-.f64 (*.f64 (fma.f64 (/.f64 1 (sqrt.f64 z)) (/.f64 y (sqrt.f64 z)) (/.f64 1 z)) x) x)
29.0b
(-.f64 (*.f64 (fma.f64 (sqrt.f64 (/.f64 y z)) (sqrt.f64 (/.f64 y z)) (/.f64 1 z)) x) x)
32.6b
(/.f64 (fma.f64 y x x) z)
Compiler

Compiled 3469 to 1209 computations (65.1% saved)

regimes674.0ms (13.2%)

Accuracy

Total 0.1b remaining (86.3%)

Threshold costs 0.1b (86.3%)

Counts
60 → 3
Compiler

Compiled 3368 to 1962 computations (41.7% saved)

bsearch3.0ms (0.1%)

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify9.0ms (0.2%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
sub-neg_binary64
*-commutative_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02363
13563
24363
34763
44963
54863

end6.0ms (0.1%)

Compiler

Compiled 46 to 25 computations (45.7% saved)

sample1.3s (26.3%)

Algorithm
intervals
Results
569.0ms8000×body128valid
79.0ms1076×body128invalid
Compiler

Compiled 157 to 91 computations (42% saved)

Profiling

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