Details

Time bar (total: 3.8s)

analyze7.0ms (0.2%)

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)

sample1.1s (29.4%)

Results
446.0ms2120×body512valid
392.0ms4680×body128valid
144.0ms1038×body256valid
107.0ms418×body1024valid
Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify10.0ms (0.3%)

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 (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
11.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶11.8b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
Compiler

Compiled 39 to 31 computations (20.5% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 1 (+.f64 x 1))
✓1.5b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

series5.0ms (0.1%)

Counts
2 → 24
Calls

2 calls:

3.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
2.0ms
(/.f64 1 (+.f64 x 1))

rewrite66.0ms (1.7%)

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:

17.0ms
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
3.0ms
(/.f64 1 (+.f64 x 1))

simplify278.0ms (7.3%)

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

prune268.0ms (7.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New3231324
Fresh000
Picked011
Done000
Total3232325
Error
0.6b
Counts
325 → 2
Alt Table
StatusErrorProgram
✓11.8b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
▶0.6b
(/.f64 -1 (fma.f64 x x x))
Compiler

Compiled 11272 to 8581 computations (23.9% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.6b
(/.f64 -1 (fma.f64 x x x))

series3.0ms (0.1%)

Counts
1 → 12
Calls

1 calls:

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

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 -1 (fma.f64 x x x))

simplify77.0ms (2%)

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

prune33.0ms (0.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New49352
Fresh000
Picked011
Done011
Total49554
Error
0.2b
Counts
54 → 5
Alt Table
StatusErrorProgram
17.5b
(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
✓0.6b
(/.f64 -1 (fma.f64 x x x))
✓11.8b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
31.7b
(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))
▶1.5b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))
Compiler

Compiled 762 to 402 computations (47.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))
✓0.4b
(*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))
✓1.0b
(/.f64 1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))
✓15.7b
(cbrt.f64 (fma.f64 x x x))

series22.0ms (0.6%)

Counts
4 → 48
Calls

4 calls:

8.0ms
(/.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))
3.0ms
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))

rewrite35.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
62×add-exp-log_binary64
59×add-sqr-sqrt_binary64
36×times-frac_binary64
33×*-un-lft-identity_binary64
31×cbrt-prod_binary64
Counts
4 → 164
Calls

4 calls:

11.0ms
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))
4.0ms
(/.f64 1 (*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x))))
4.0ms
(*.f64 (cbrt.f64 (fma.f64 x x x)) (cbrt.f64 (fma.f64 x x x)))
1.0ms
(cbrt.f64 (fma.f64 x x x))

simplify205.0ms (5.4%)

Algorithm
1×egg-herbie
Rules
477×associate-/l/_binary64
353×fma-neg_binary64
343×fma-def_binary64
269×*-commutative_binary64
251×associate-/r/_binary64
Counts
212 → 292
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02645549
16644253
219003652
341943401
449393401
549393401

prune244.0ms (6.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New3551356
Fresh022
Picked101
Done022
Total3565361
Error
0.2b
Counts
361 → 5
Alt Table
StatusErrorProgram
17.5b
(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
✓0.6b
(/.f64 -1 (fma.f64 x x x))
✓11.8b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
31.7b
(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))
▶1.5b
(*.f64 (*.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x x))) (/.f64 1 (cbrt.f64 (fma.f64 x x x)))) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))
Compiler

Compiled 9735 to 3753 computations (61.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 -1 (cbrt.f64 (fma.f64 x x x)))
✓0.3b
(*.f64 (*.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x x))) (/.f64 1 (cbrt.f64 (fma.f64 x x x)))) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))
✓0.4b
(*.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x x))) (/.f64 1 (cbrt.f64 (fma.f64 x x x))))
15.7b
(cbrt.f64 (fma.f64 x x x))

series18.0ms (0.5%)

Counts
3 → 36
Calls

3 calls:

8.0ms
(/.f64 -1 (cbrt.f64 (fma.f64 x x x)))
7.0ms
(*.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x x))) (/.f64 1 (cbrt.f64 (fma.f64 x x x))))
3.0ms
(*.f64 (*.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x x))) (/.f64 1 (cbrt.f64 (fma.f64 x x x)))) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))

rewrite71.0ms (1.9%)

Algorithm
1×rewrite-expression-head
Rules
178×add-exp-log_binary64
158×add-sqr-sqrt_binary64
150×times-frac_binary64
105×*-un-lft-identity_binary64
83×add-cube-cbrt_binary64
Counts
3 → 275
Calls

3 calls:

15.0ms
(*.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x x))) (/.f64 1 (cbrt.f64 (fma.f64 x x x))))
14.0ms
(*.f64 (*.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x x))) (/.f64 1 (cbrt.f64 (fma.f64 x x x)))) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))
5.0ms
(/.f64 -1 (cbrt.f64 (fma.f64 x x x)))

simplify191.0ms (5%)

Algorithm
1×egg-herbie
Rules
707×fma-def_binary64
404×associate-/l/_binary64
395×times-frac_binary64
297×fma-neg_binary64
260×associate-/r*_binary64
Counts
311 → 406
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03049128
17016701
219216341
344846335
450876335

prune306.0ms (8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New5020502
Fresh022
Picked011
Done022
Total5025507
Error
0.2b
Counts
507 → 5
Alt Table
StatusErrorProgram
17.5b
(/.f64 (/.f64 -1 (sqrt.f64 (fma.f64 x x x))) (sqrt.f64 (fma.f64 x x x)))
✓0.6b
(/.f64 -1 (fma.f64 x x x))
✓11.8b
(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))
31.7b
(*.f64 (/.f64 1 (hypot.f64 x (sqrt.f64 x))) (/.f64 -1 (hypot.f64 x (sqrt.f64 x))))
✓1.5b
(*.f64 (*.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x x))) (/.f64 1 (cbrt.f64 (fma.f64 x x x)))) (/.f64 -1 (cbrt.f64 (fma.f64 x x x))))
Compiler

Compiled 15814 to 6608 computations (58.2% saved)

regimes749.0ms (19.7%)

Accuracy

Total 0.2b remaining (51.5%)

Threshold costs 0.2b (51.5%)

Counts
85 → 1
Compiler

Compiled 3630 to 2096 computations (42.3% saved)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058
158

end60.0ms (1.6%)

Compiler

Compiled 83 to 45 computations (45.8% saved)

Profiling

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