Details

Time bar (total: 6.8s)

analyze29.0ms (0.4%)

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)

sample23.0ms (0.3%)

Algorithm
1×intervals
Results
6.0ms154×body128valid
5.0ms54×body512valid
2.0ms18×body1024valid
2.0ms30×body256valid
Compiler

Compiled 22 to 18 computations (18.2% saved)

simplify15.0ms (0.2%)

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

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
13.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶13.8b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
Compiler

Compiled 39 to 31 computations (20.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series6.0ms (0.1%)

Counts
2 → 24
Calls

2 calls:

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

rewrite95.0ms (1.4%)

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:

20.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
3.0ms
(/.f64 1 (+.f64 x 1))

simplify427.0ms (6.3%)

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 → 324
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
018311806
13806831
210405351
337265350
441765350
544255342
648035342

prune357.0ms (5.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New3231324
Fresh000
Picked011
Done000
Total3232325
Error
0.1b
Counts
325 → 2
Alt Table
StatusErrorProgram
▶0.1b
(/.f64 -1 (fma.f64 x x x))
✓13.8b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
Compiler

Compiled 11272 to 8581 computations (23.9% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.1%)

Counts
1 → 12
Calls

1 calls:

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

rewrite4.0ms (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:

3.0ms
(/.f64 -1 (fma.f64 x x x))

simplify111.0ms (1.6%)

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 → 52
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
078654
1148618
2308611
3680611
42297611
54211603
64978603
74914603

prune31.0ms (0.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New48452
Fresh000
Picked011
Done011
Total48654
Error
0.0b
Counts
54 → 6
Alt Table
StatusErrorProgram
✓0.1b
(/.f64 -1 (fma.f64 x x x))
17.1b
(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
▶0.6b
(/.f64 (/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x)))
31.3b
(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))
✓13.8b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
0.6b
(*.f64 (*.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))
Compiler

Compiled 806 to 424 computations (47.4% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 (/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x)))
✓0.4b
(*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))
✓0.7b
(/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))
✓15.8b
(cbrt.f64 (fma.f64 x x x))

series30.0ms (0.4%)

Counts
4 → 48
Calls

4 calls:

14.0ms
(/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))
6.0ms
(*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))
6.0ms
(cbrt.f64 (fma.f64 x x x))
4.0ms
(/.f64 (/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x)))

rewrite61.0ms (0.9%)

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:

13.0ms
(/.f64 (/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (cbrt.f64 (fma.f64 x x x)))
6.0ms
(*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))
5.0ms
(/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))
1.0ms
(cbrt.f64 (fma.f64 x x x))

simplify187.0ms (2.8%)

Algorithm
1×egg-herbie
Rules
641×fma-def_binary64
574×times-frac_binary64
403×associate-*l*_binary64
354×associate-/l/_binary64
292×associate-/r/_binary64
Counts
200 → 298
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02715328
16134956
216284414
346044414
450544414

prune274.0ms (4.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New3602362
Fresh033
Picked101
Done022
Total3617368
Error
0.0b
Counts
368 → 7
Alt Table
StatusErrorProgram
✓0.1b
(/.f64 -1 (fma.f64 x x x))
17.1b
(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
31.3b
(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))
✓13.8b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
▶0.6b
(/.f64 (/.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) (cbrt.f64 (fma.f64 x x x))) (cbrt.f64 (fma.f64 x x x)))
0.6b
(*.f64 (*.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))
17.2b
(/.f64 (/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x x))) (cbrt.f64 (sqrt.f64 (fma.f64 x x x)))))
Compiler

Compiled 9905 to 3387 computations (65.8% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 (/.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) (cbrt.f64 (fma.f64 x x x))) (cbrt.f64 (fma.f64 x x x)))
✓0.2b
(/.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) (cbrt.f64 (fma.f64 x x x)))
✓0.3b
(/.f64 -1 (cbrt.f64 (fma.f64 x x x)))
15.8b
(cbrt.f64 (fma.f64 x x x))

series21.0ms (0.3%)

Counts
3 → 36
Calls

3 calls:

9.0ms
(/.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) (cbrt.f64 (fma.f64 x x x)))
9.0ms
(/.f64 -1 (cbrt.f64 (fma.f64 x x x)))
3.0ms
(/.f64 (/.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) (cbrt.f64 (fma.f64 x x x))) (cbrt.f64 (fma.f64 x x x)))

rewrite416.0ms (6.2%)

Algorithm
1×rewrite-expression-head
Rules
2772×times-frac_binary64
1395×cbrt-prod_binary64
1290×*-un-lft-identity_binary64
1290×add-sqr-sqrt_binary64
1290×add-cube-cbrt_binary64
Counts
3 → 1195
Calls

3 calls:

29.0ms
(/.f64 (/.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) (cbrt.f64 (fma.f64 x x x))) (cbrt.f64 (fma.f64 x x x)))
7.0ms
(/.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) (cbrt.f64 (fma.f64 x x x)))
3.0ms
(/.f64 -1 (cbrt.f64 (fma.f64 x x x)))

simplify2.4s (35.6%)

Algorithm
1×egg-herbie
Rules
753×associate-/l/_binary64
558×associate-/r/_binary64
441×associate-/r*_binary64
414×associate-*l/_binary64
336×fma-def_binary64
Counts
1231 → 1637
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0106970466
1213169139
2257563011
3447860200
4498360200
5491560200

prune1.3s (19.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New173301733
Fresh044
Picked011
Done022
Total173371740
Error
0.0b
Counts
1740 → 7
Alt Table
StatusErrorProgram
✓0.1b
(/.f64 -1 (fma.f64 x x x))
17.1b
(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
31.3b
(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))
✓13.8b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
✓0.6b
(/.f64 (/.f64 (/.f64 -1 (cbrt.f64 (fma.f64 x x x))) (cbrt.f64 (fma.f64 x x x))) (cbrt.f64 (fma.f64 x x x)))
0.6b
(*.f64 (*.f64 (cbrt.f64 (/.f64 -1 (fma.f64 x x x))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x)))) (cbrt.f64 (/.f64 -1 (fma.f64 x x x))))
17.2b
(/.f64 (/.f64 -1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x x))) (cbrt.f64 (sqrt.f64 (fma.f64 x x x)))))
Compiler

Compiled 70267 to 20084 computations (71.4% saved)

regimes231.0ms (3.4%)

Accuracy

Total 0.2b remaining (54.5%)

Threshold costs 0.2b (54.5%)

Counts
103 → 1
Compiler

Compiled 4230 to 2174 computations (48.6% saved)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058
158

end0.0ms (0%)

Compiler

Compiled 7 to 4 computations (42.9% saved)

sample704.0ms (10.4%)

Algorithm
1×intervals
Results
181.0ms1960×body512valid
153.0ms4606×body128valid
62.0ms996×body256valid
54.0ms438×body1024valid
Compiler

Compiled 136 to 70 computations (48.5% saved)

Profiling

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