Details

Time bar (total: 3.2s)

analyze49.0ms (1.6%)

Algorithm
1×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
25%74.9%0.1%4
37.5%62.4%0.1%5
59.3%40.6%0.1%6
76.5%23.4%0.1%7
82%18%0.1%8
87.8%12.1%0.1%9
90.7%9.2%0.1%10
93.8%6.1%0.1%11
95.3%4.6%0.1%12
96.8%3.1%0.1%13
97.6%2.3%0.1%14
Compiler

Compiled 10 to 6 computations (40% saved)

sample113.0ms (3.6%)

Algorithm
1×intervals
Results
7.0ms256×body128valid
Compiler

Compiled 21 to 13 computations (38.1% saved)

simplify75.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
801×fma-def_binary64
511×fma-neg_binary64
365×times-frac_binary64
331×div-sub_binary64
156×associate-/l*_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0610
11210
21910
33010
45210
58110
612410
719110
830010
964110
1082210
11129910
12132810
13134310
14135710
15137710
16137710
17127610

prune9.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.0b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶0.0b
(/.f64 (-.f64 x y) (+.f64 x y))
Compiler

Compiled 27 to 15 computations (44.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series8.0ms (0.3%)

Counts
1 → 24
Calls

1 calls:

8.0ms
(/.f64 (-.f64 x y) (+.f64 x y))

rewrite9.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
34×*-un-lft-identity_binary64
22×add-sqr-sqrt_binary64
20×times-frac_binary64
12×add-cube-cbrt_binary64
6×distribute-lft-out_binary64
Counts
1 → 48
Calls

1 calls:

6.0ms
(/.f64 (-.f64 x y) (+.f64 x y))

simplify97.0ms (3.1%)

Algorithm
1×egg-herbie
Rules
610×div-sub_binary64
586×fma-neg_binary64
530×cancel-sign-sub-inv_binary64
194×distribute-neg-frac_binary64
184×fma-def_binary64
Counts
72 → 59
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01061287
12831239
27481195
324881183
443831183
554851183

prune44.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New56359
Fresh000
Picked011
Done000
Total56460
Error
0b
Counts
60 → 4
Alt Table
StatusErrorProgram
30.2b
(fma.f64 2 (-.f64 (/.f64 x y) (*.f64 (/.f64 x y) (/.f64 x y))) -1)
✓0.0b
(/.f64 (-.f64 x y) (+.f64 x y))
▶0.0b
(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
1.4b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y)))) (/.f64 (-.f64 x y) (cbrt.f64 (+.f64 x y))))
Compiler

Compiled 995 to 316 computations (68.2% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series30.0ms (0.9%)

Counts
3 → 72
Calls

3 calls:

11.0ms
(/.f64 y (+.f64 x y))
11.0ms
(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
8.0ms
(/.f64 x (+.f64 x y))

rewrite110.0ms (3.5%)

Algorithm
1×rewrite-expression-head
Rules
595×*-un-lft-identity_binary64
496×times-frac_binary64
339×add-sqr-sqrt_binary64
327×add-cube-cbrt_binary64
324×prod-diff_binary64
Counts
3 → 459
Calls

3 calls:

26.0ms
(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
3.0ms
(/.f64 x (+.f64 x y))
3.0ms
(/.f64 y (+.f64 x y))

simplify414.0ms (13.1%)

Algorithm
1×egg-herbie
Rules
764×fma-neg_binary64
542×times-frac_binary64
251×unsub-neg_binary64
239×sub-neg_binary64
210×fma-udef_binary64
Counts
531 → 449
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
046325191
1107716096
2249811283
3463411271
4489611271

prune249.0ms (7.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New4472449
Fresh202
Picked011
Done011
Total4494453
Error
0b
Counts
453 → 4
Alt Table
StatusErrorProgram
▶1.0b
(expm1.f64 (log1p.f64 (-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))))
30.2b
(fma.f64 2 (*.f64 (/.f64 x y) (-.f64 1 (/.f64 x y))) -1)
✓0.0b
(/.f64 (-.f64 x y) (+.f64 x y))
✓0.0b
(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
Compiler

Compiled 18689 to 3307 computations (82.3% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 x (+.f64 x y))
✓0.0b
(expm1.f64 (log1p.f64 (-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))))
0.0b
(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
✓2.9b
(log1p.f64 (-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y))))

series29.0ms (0.9%)

Counts
2 → 48
Calls

2 calls:

19.0ms
(log1p.f64 (-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y))))
10.0ms
(expm1.f64 (log1p.f64 (-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))))

rewrite2.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
3×expm1-log1p-u_binary64
2×*-un-lft-identity_binary64
2×add-sqr-sqrt_binary64
2×add-cube-cbrt_binary64
2×add-cbrt-cube_binary64
Counts
2 → 22
Calls

2 calls:

1.0ms
(log1p.f64 (-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y))))
0.0ms
(expm1.f64 (log1p.f64 (-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))))

simplify64.0ms (2%)

Algorithm
1×egg-herbie
Rules
719×fma-neg_binary64
392×sub-neg_binary64
355×distribute-neg-frac_binary64
204×times-frac_binary64
182×associate-+l+_binary64
Counts
70 → 76
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0991451
12641351
28181291
333941279
450921279

prune766.0ms (24.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New4760476
Fresh011
Picked011
Done022
Total4764480
Error
0b
Counts
480 → 4
Alt Table
StatusErrorProgram
✓1.0b
(expm1.f64 (log1p.f64 (-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))))
▶30.2b
(fma.f64 2 (*.f64 (/.f64 x y) (-.f64 1 (/.f64 x y))) -1)
✓0.0b
(/.f64 (-.f64 x y) (+.f64 x y))
✓0.0b
(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
Compiler

Compiled 19963 to 4369 computations (78.1% saved)

localize12.0ms (0.4%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 1 (/.f64 x y))
✓0.1b
(*.f64 (/.f64 x y) (-.f64 1 (/.f64 x y)))

series18.0ms (0.6%)

Counts
2 → 30
Calls

2 calls:

14.0ms
(*.f64 (/.f64 x y) (-.f64 1 (/.f64 x y)))
4.0ms
(-.f64 1 (/.f64 x y))

rewrite52.0ms (1.7%)

Algorithm
1×rewrite-expression-head
Rules
155×add-sqr-sqrt_binary64
142×*-un-lft-identity_binary64
134×add-cube-cbrt_binary64
122×times-frac_binary64
117×prod-diff_binary64
Counts
2 → 222
Calls

2 calls:

19.0ms
(*.f64 (/.f64 x y) (-.f64 1 (/.f64 x y)))
7.0ms
(-.f64 1 (/.f64 x y))

simplify166.0ms (5.2%)

Algorithm
1×egg-herbie
Rules
491×distribute-rgt-in_binary64
461×associate-*l*_binary64
427×associate-*r*_binary64
281×fma-neg_binary64
246×exp-prod_binary64
Counts
252 → 269
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02727018
17255080
225563592
344643591
448023591

prune180.0ms (5.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New2690269
Fresh000
Picked011
Done033
Total2694273
Error
0b
Counts
273 → 4
Alt Table
StatusErrorProgram
✓1.0b
(expm1.f64 (log1p.f64 (-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))))
✓30.2b
(fma.f64 2 (*.f64 (/.f64 x y) (-.f64 1 (/.f64 x y))) -1)
✓0.0b
(/.f64 (-.f64 x y) (+.f64 x y))
✓0.0b
(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
Compiler

Compiled 8961 to 3412 computations (61.9% saved)

regimes117.0ms (3.7%)

Accuracy

Total 0.0b remaining (66.3%)

Threshold costs 0.0b (66.3%)

Counts
45 → 1
Compiler

Compiled 1857 to 1180 computations (36.5% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0716
11016
21716
32116
42416
52516
62516

end0.0ms (0%)

Compiler

Compiled 13 to 6 computations (53.8% saved)

sample530.0ms (16.7%)

Algorithm
1×intervals
Results
227.0ms8000×body128valid
Compiler

Compiled 76 to 42 computations (44.7% saved)

Profiling

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