Details

Time bar (total: 5.7s)

analyze51.0ms (0.9%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
62.5%37.5%0%4
81.2%18.7%0%5
90.6%9.4%0%6
95.3%4.7%0%7
97.6%2.3%0%8
98.8%1.2%0%9
99.4%0.6%0%10
99.7%0.3%0%11
99.8%0.1%0%12
99.9%0.1%0%13
99.9%0%0%14
Compiler

Compiled 11 to 9 computations (18.2% saved)

sample39.0ms (0.7%)

Algorithm
1×intervals
Results
13.0ms66×body512valid
8.0ms141×body128valid
4.0ms38×body256valid
2.0ms11×body1024valid
Compiler

Compiled 22 to 18 computations (18.2% saved)

simplify26.0ms (0.4%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0713
11213
21813
32613
43413
55213
67713
79413
811113
912113
1012513
1112713
1211313

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
14.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶14.8b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
Compiler

Compiled 39 to 31 computations (20.5% saved)

localize16.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 1 (+.f64 x 1))
✓2.5b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

rewrite135.0ms (2.4%)

Algorithm
1×rewrite-expression-head
Rules
377×*-un-lft-identity_binary64
375×times-frac_binary64
284×add-sqr-sqrt_binary64
260×add-cube-cbrt_binary64
234×prod-diff_binary64
Counts
2 → 337
Calls

2 calls:

43.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
11.0ms
(/.f64 1 (+.f64 x 1))

series8.0ms (0.1%)

Counts
2 → 24
Calls

2 calls:

5.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
3.0ms
(/.f64 1 (+.f64 x 1))

simplify625.0ms (10.9%)

Algorithm
1×egg-herbie
Rules
781×fma-def_binary64
395×sub-neg_binary64
340×times-frac_binary64
306×div-sub_binary64
297×associate-*l*_binary64
Counts
361 → 703
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
018311806
13806831
210405351
337265350
441765350
544255342
648035342

prune501.0ms (8.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New7021703
Fresh000
Picked101
Done000
Total7031704
Error
0.3b
Counts
704 → 1
Alt Table
StatusErrorProgram
▶0.3b
(/.f64 -1 (fma.f64 x x x))
Compiler

Compiled 11257 to 8569 computations (23.9% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.3b
(/.f64 -1 (fma.f64 x x x))

rewrite6.0ms (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:

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

series6.0ms (0.1%)

Counts
1 → 12
Calls

1 calls:

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

simplify130.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
888×fma-neg_binary64
327×distribute-rgt-out_binary64
306×unswap-sqr_binary64
201×sub-neg_binary64
188×cancel-sign-sub-inv_binary64
Counts
41 → 64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
078654
1148618
2308611
3680611
42297611
54211603
64978603
74914603

prune75.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New62264
Fresh000
Picked011
Done000
Total62365
Error
0.2b
Counts
65 → 3
Alt Table
StatusErrorProgram
✓0.3b
(/.f64 -1 (fma.f64 x x x))
▶15.7b
(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
31.2b
(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))
Compiler

Compiled 708 to 376 computations (46.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 -1 (sqrt.f64 (fma.f64 x x x)))
✓0.2b
(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
14.8b
(sqrt.f64 (fma.f64 x x x))
✓14.8b
(sqrt.f64 (fma.f64 x x x))

rewrite65.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Rules
276×times-frac_binary64
157×add-sqr-sqrt_binary64
156×*-un-lft-identity_binary64
156×add-cube-cbrt_binary64
147×sqrt-prod_binary64
Counts
3 → 233
Calls

3 calls:

17.0ms
(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
6.0ms
(/.f64 -1 (sqrt.f64 (fma.f64 x x x)))
2.0ms
(sqrt.f64 (fma.f64 x x x))

series27.0ms (0.5%)

Counts
3 → 28
Calls

3 calls:

11.0ms
(/.f64 -1 (sqrt.f64 (fma.f64 x x x)))
10.0ms
(sqrt.f64 (fma.f64 x x x))
5.0ms
(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))

simplify585.0ms (10.2%)

Algorithm
1×egg-herbie
Rules
462×associate-/l/_binary64
429×fma-def_binary64
311×times-frac_binary64
294×associate-/r*_binary64
230×fma-neg_binary64
Counts
261 → 510
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02648068
15907401
211636523
328596418
446966408
549976408
649076408

prune361.0ms (6.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New5492551
Fresh101
Picked011
Done011
Total5504554
Error
0.2b
Counts
554 → 4
Alt Table
StatusErrorProgram
▶15.8b
(/.f64 (/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (sqrt.f64 (fma.f64 x x x))))
31.1b
(/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (neg.f64 (hypot.f64 x (sqrt.f64 x))))
✓0.3b
(/.f64 -1 (fma.f64 x x x))
✓15.7b
(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
Compiler

Compiled 8843 to 3098 computations (65% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (sqrt.f64 (fma.f64 x x x))))
14.8b
(sqrt.f64 (fma.f64 x x x))
14.8b
(sqrt.f64 (fma.f64 x x x))
14.8b
(sqrt.f64 (fma.f64 x x x))

rewrite114.0ms (2%)

Algorithm
1×rewrite-expression-head
Rules
378×times-frac_binary64
297×sqrt-prod_binary64
200×*-un-lft-identity_binary64
200×add-sqr-sqrt_binary64
200×add-cube-cbrt_binary64
Counts
1 → 246
Calls

1 calls:

21.0ms
(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (sqrt.f64 (fma.f64 x x x))))

series17.0ms (0.3%)

Counts
1 → 12
Calls

1 calls:

17.0ms
(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (sqrt.f64 (fma.f64 x x x))))

simplify761.0ms (13.3%)

Algorithm
1×egg-herbie
Rules
758×fma-def_binary64
432×times-frac_binary64
312×associate-/l*_binary64
299×associate-/l/_binary64
263×fma-neg_binary64
Counts
258 → 512
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
030610733
167810234
216299561
332659558
445099549
549609549
649049549

prune483.0ms (8.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New108601086
Fresh011
Picked011
Done022
Total108641090
Error
0.2b
Counts
1090 → 4
Alt Table
StatusErrorProgram
✓15.8b
(/.f64 (/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (sqrt.f64 (fma.f64 x x x)))) (sqrt.f64 (sqrt.f64 (fma.f64 x x x))))
31.1b
(/.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (neg.f64 (hypot.f64 x (sqrt.f64 x))))
✓0.3b
(/.f64 -1 (fma.f64 x x x))
✓15.7b
(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
Compiler

Compiled 14127 to 4180 computations (70.4% saved)

regimes244.0ms (4.3%)

Accuracy

Total 0.2b remaining (49.3%)

Threshold costs 0.2b (49.3%)

Compiler

Compiled 2226 to 1294 computations (41.9% saved)

simplify5.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058
158

end1.0ms (0%)

Compiler

Compiled 7 to 4 computations (42.9% saved)

sample1.4s (24.7%)

Algorithm
1×intervals
Results
423.0ms1967×body512valid
338.0ms4570×body128valid
135.0ms1005×body256valid
112.0ms458×body1024valid
Compiler

Compiled 75 to 39 computations (48% saved)

Profiling

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