Details

Time bar (total: 5.6s)

analyze1.1s (18.8%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
6.2%93.6%0.2%9
12.5%87.3%0.2%10
25%74.9%0.2%11
31.2%63.9%4.9%12
39%50.9%10.1%13
44.8%44.4%10.7%14
Compiler

Compiled 12 to 8 computations (33.3% saved)

sample39.0ms (0.7%)

Algorithm
1×intervals
Results
8.0ms256×body128valid
1.0ms35×body128invalid
Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify18.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
171×fma-def_binary64
87×fma-neg_binary64
36×cancel-sign-sub-inv_binary64
23×distribute-rgt-neg-in_binary64
20×sub-neg_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
11610
22710
34410
46610
510010
615210
721310
825710
927910
1029910
1130510
1227410

prune1.0ms (0%)

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.re y.re) (*.f64 x.im y.im))
Compiler

Compiled 33 to 21 computations (36.4% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

series9.0ms (0.2%)

Counts
1 → 48
Calls

1 calls:

9.0ms
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

rewrite3.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
3×add-log-exp_binary64
1×cancel-sign-sub-inv_binary64
1×flip--_binary64
1×sub-neg_binary64
1×*-un-lft-identity_binary64
Counts
1 → 16
Calls

1 calls:

3.0ms
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

simplify114.0ms (2%)

Algorithm
1×egg-herbie
Rules
480×times-frac_binary64
463×fma-def_binary64
444×unsub-neg_binary64
265×sub-neg_binary64
232×distribute-rgt-neg-in_binary64
Counts
64 → 32
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
042682
1112658
2347652
3974652
42183652
53451652
64489652
74961652
84995652
94859652

prune27.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New29332
Fresh000
Picked101
Done000
Total30333
Error
0.0b
Counts
33 → 3
Alt Table
StatusErrorProgram
40.3b
(/.f64 (-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 x.im y.im) 3)) (+.f64 (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re)) (+.f64 (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im)) (*.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))))
1.4b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))) (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))
▶0.0b
(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))
Compiler

Compiled 573 to 160 computations (72.1% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))

series11.0ms (0.2%)

Counts
1 → 48
Calls

1 calls:

11.0ms
(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))

rewrite1.0ms (0%)

Algorithm
1×rewrite-expression-head
Rules
1×*-un-lft-identity_binary64
1×add-sqr-sqrt_binary64
1×add-cube-cbrt_binary64
1×add-cbrt-cube_binary64
1×add-exp-log_binary64
Counts
1 → 10
Calls

1 calls:

0.0ms
(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))

simplify85.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
967×unsub-neg_binary64
792×times-frac_binary64
422×fma-neg_binary64
384×neg-sub0_binary64
364×neg-mul-1_binary64
Counts
58 → 21
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
022568
136547
265547
3215547
4895547
51760547
63723547
74512547
85729547

prune9.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New21021
Fresh022
Picked011
Done000
Total21324
Error
0.0b
Counts
24 → 3
Alt Table
StatusErrorProgram
40.3b
(/.f64 (-.f64 (pow.f64 (*.f64 x.re y.re) 3) (pow.f64 (*.f64 x.im y.im) 3)) (+.f64 (*.f64 (*.f64 x.re y.re) (*.f64 x.re y.re)) (+.f64 (*.f64 (*.f64 x.im y.im) (*.f64 x.im y.im)) (*.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))))
▶1.4b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))) (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))
✓0.0b
(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))
Compiler

Compiled 390 to 111 computations (71.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
✓0.3b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))) (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))
✓0.5b
(*.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))
✓1.3b
(cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))

series269.0ms (4.8%)

Counts
3 → 144
Calls

3 calls:

121.0ms
(*.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))
116.0ms
(cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))
32.0ms
(*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))) (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))

rewrite51.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
68×cbrt-div_binary64
34×flip--_binary64
34×flip3--_binary64
32×frac-times_binary64
29×pow1_binary64
Counts
3 → 129
Calls

3 calls:

13.0ms
(*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))) (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))
9.0ms
(*.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))
2.0ms
(cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))

simplify183.0ms (3.3%)

Algorithm
1×egg-herbie
Rules
787×associate-/r*_binary64
684×associate-/l*_binary64
280×fma-def_binary64
246×*-commutative_binary64
147×cancel-sign-sub-inv_binary64
Counts
273 → 349
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
062712010
1208811381
2585911381

prune414.0ms (7.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New6501651
Fresh101
Picked101
Done011
Total6522654
Error
0b
Counts
654 → 2
Alt Table
StatusErrorProgram
▶1.7b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im))) (cbrt.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im))))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im)))) (cbrt.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im)))))) (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))
✓0.0b
(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))
Compiler

Compiled 32766 to 11033 computations (66.3% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.5b
(*.f64 (cbrt.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im)))) (cbrt.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im)))))
✓0.6b
(cbrt.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im))))
1.3b
(cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))
✓1.3b
(cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im)))

series311.0ms (5.6%)

Counts
3 → 144
Calls

3 calls:

123.0ms
(*.f64 (cbrt.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im)))) (cbrt.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im)))))
96.0ms
(cbrt.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im))))
91.0ms
(cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im)))

rewrite32.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
66×cbrt-prod_binary64
36×add-sqr-sqrt_binary64
30×cbrt-div_binary64
18×*-un-lft-identity_binary64
18×add-cube-cbrt_binary64
Counts
3 → 97
Calls

3 calls:

10.0ms
(*.f64 (cbrt.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im)))) (cbrt.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im)))))
3.0ms
(cbrt.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im))))
2.0ms
(cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im)))

simplify259.0ms (4.6%)

Algorithm
1×egg-herbie
Rules
424×fma-def_binary64
318×*-commutative_binary64
219×cancel-sign-sub-inv_binary64
206×fma-neg_binary64
199×sub-neg_binary64
Counts
241 → 344
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
082513649
1283912947
2492112945
3498312945

prune727.0ms (13%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New9230923
Fresh000
Picked011
Done011
Total9232925
Error
0b
Counts
925 → 2
Alt Table
StatusErrorProgram
✓1.7b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im))) (cbrt.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im))))) (*.f64 (cbrt.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im)))) (cbrt.f64 (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 y.im x.im)))))) (cbrt.f64 (-.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))))
✓0.0b
(fma.f64 x.re y.re (neg.f64 (*.f64 x.im y.im)))
Compiler

Compiled 72557 to 23392 computations (67.8% saved)

regimes1.1s (20.2%)

Accuracy

Total 0.0b remaining (14.6%)

Threshold costs 0.0b (14.6%)

Counts
112 → 1
Compiler

Compiled 32606 to 13410 computations (58.9% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01122
12222
23022
33422
43522
53522

end102.0ms (1.8%)

Remove

(sort x.im y.im)

(sort x.re y.re)

Compiler

Compiled 95 to 50 computations (47.4% saved)

sample703.0ms (12.6%)

Algorithm
1×intervals
Results
262.0ms8000×body128valid
41.0ms1326×body128invalid
Compiler

Compiled 97 to 45 computations (53.6% saved)

Profiling

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