Details

Time bar (total: 3.0s)

analyze5.0ms (0.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%50%0%2
50%50%0%3
75%25%0%4
87.5%12.5%0%5
93.7%6.2%0%6
96.8%3.1%0%7
98.4%1.6%0%8
99.2%0.8%0%9
99.6%0.4%0%10
99.8%0.2%0%11
99.9%0.1%0%12
99.9%0%0%13
99.9%0%0%14
Compiler

Compiled 21 to 17 computations (19% saved)

sample961.0ms (32%)

Results
948.0ms8256×body128valid
Compiler

Compiled 42 to 34 computations (19% saved)

preprocess44.0ms (1.5%)

Algorithm
egg-herbie
Rules
677×fma-def_binary64
646×fma-neg_binary64
298×distribute-rgt-in_binary64
239×div-sub_binary64
214×distribute-lft-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01728
13422
26722
310722
415322
519520
629220
752920
8115220
9227720
10473520
011
Stop Event
saturated
node limit
Compiler

Compiled 20 to 16 computations (20% saved)

simplify33.0ms (1.1%)

Algorithm
egg-herbie
Rules
677×fma-def_binary64
646×fma-neg_binary64
298×distribute-rgt-in_binary64
239×div-sub_binary64
214×distribute-lft-in_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01728
13422
26722
310722
415322
519520
629220
752920
8115220
9227720
10473520
Stop Event
node limit
Counts
1 → 2

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.1b
(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
Compiler

Compiled 67 to 51 computations (23.9% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
0.2b
(fma.f64 x 4481/100000 99229/100000)
0.2b
(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
16.7b
(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series8.0ms (0.3%)

Counts
4 → 48
Calls

12 calls:

1.0ms
(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
x
-inf
1.0ms
(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
x
inf
1.0ms
(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
x
0
1.0ms
(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
x
-inf
1.0ms
(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
x
inf

rewrite64.0ms (2.1%)

Algorithm
batch-egg-rewrite
Rules
488×log-prod_binary64
223×expm1-udef_binary64
223×log1p-udef_binary64
176×log-pow_binary64
157×prod-diff_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01346
126746
2296546
Stop Event
node limit
Counts
4 → 117

simplify42.0ms (1.4%)

Algorithm
egg-herbie
Rules
485×fma-def_binary64
417×times-frac_binary64
342×sub-neg_binary64
309×cancel-sign-sub-inv_binary64
245×fma-neg_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
060500
1167448
2421436
31168420
43782420
Stop Event
node limit
Counts
165 → 154

prune127.0ms (4.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1495154
Fresh000
Picked011
Done000
Total1496155
Error
0.0b
Counts
155 → 6
Alt Table
StatusErrorProgram
18.5b
(fma.f64 x -70711/100000 (/.f64 (/.f64 (fma.f64 (*.f64 x 1913510371/10000000000) (*.f64 x 1913510371/10000000000) -266237158899274796689/100000000000000000000) (fma.f64 x 1913510371/10000000000 -16316775383/10000000000)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
0.1b
(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
30.8b
(fma.f64 x (fma.f64 x 134362287316698645903/100000000000000000000 -2134856267379707/1000000000000000) 16316775383/10000000000)
22.3b
(cbrt.f64 (pow.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) 3))
15.1b
(pow.f64 (sqrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) 2)
1.4b
(pow.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) 3)
Compiler

Compiled 3241 to 2517 computations (22.3% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(fma.f64 x 1913510371/10000000000 16316775383/10000000000)
0.3b
(cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
1.1b
(pow.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) 3)
16.7b
(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series36.0ms (1.2%)

Counts
2 → 8
Calls

6 calls:

13.0ms
(cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
x
0
11.0ms
(pow.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) 3)
x
0
4.0ms
(pow.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) 3)
x
-inf
4.0ms
(pow.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) 3)
x
inf
2.0ms
(cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
x
-inf

rewrite59.0ms (2%)

Algorithm
batch-egg-rewrite
Rules
253×expm1-udef_binary64
253×log1p-udef_binary64
203×log-pow_binary64
157×prod-diff_binary64
146×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01642
132842
2346342
Stop Event
node limit
Counts
2 → 76

simplify35.0ms (1.2%)

Algorithm
egg-herbie
Rules
806×times-frac_binary64
330×sub-neg_binary64
321×fma-def_binary64
236×associate-*r*_binary64
209×associate-*l*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
071293
1208287
2715272
33450272
Stop Event
node limit
Counts
84 → 90

prune154.0ms (5.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1664170
Fresh134
Picked011
Done011
Total1679176
Error
0.0b
Counts
176 → 9
Alt Table
StatusErrorProgram
22.3b
(cbrt.f64 (pow.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) 3))
32.1b
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) -70711/100000) (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
15.1b
(pow.f64 (sqrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) 2)
0.6b
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) -70711/100000) (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
1.4b
(pow.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) 3)
1.4b
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))) 2)) (cbrt.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))))
30.8b
(fma.f64 x (fma.f64 x 134362287316698645903/100000000000000000000 -2134856267379707/1000000000000000) 16316775383/10000000000)
2.0b
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))) 2) 3) (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
0.1b
(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
Compiler

Compiled 4658 to 3738 computations (19.8% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (cbrt.f64 x) -70711/100000)
0.5b
(pow.f64 (cbrt.f64 x) 2)
0.6b
(cbrt.f64 x)
16.7b
(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series49.0ms (1.6%)

Counts
3 → 0
Calls

9 calls:

19.0ms
(pow.f64 (cbrt.f64 x) 2)
x
-inf
11.0ms
(*.f64 (cbrt.f64 x) -70711/100000)
x
-inf
8.0ms
(cbrt.f64 x)
x
-inf
2.0ms
(pow.f64 (cbrt.f64 x) 2)
x
inf
2.0ms
(pow.f64 (cbrt.f64 x) 2)
x
0

rewrite41.0ms (1.4%)

Algorithm
batch-egg-rewrite
Rules
507×log1p-expm1-u_binary64
507×expm1-log1p-u_binary64
329×unpow-prod-down_binary64
253×log-prod_binary64
151×pow2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0715
114115
2147315
Stop Event
node limit
Counts
3 → 96

simplify7.0ms (0.2%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
saturated
Counts
96 → 96

prune196.0ms (6.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1851186
Fresh066
Picked011
Done022
Total18510195
Error
0.0b
Counts
195 → 10
Alt Table
StatusErrorProgram
22.3b
(cbrt.f64 (pow.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) 3))
32.1b
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) -70711/100000) (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
15.1b
(pow.f64 (sqrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) 2)
0.6b
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) -70711/100000) (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
0.7b
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (*.f64 (cbrt.f64 x) -70711/100000)) 3) (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
1.4b
(pow.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) 3)
1.4b
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))) 2)) (cbrt.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))))
30.8b
(fma.f64 x (fma.f64 x 134362287316698645903/100000000000000000000 -2134856267379707/1000000000000000) 16316775383/10000000000)
2.0b
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))) 2) 3) (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
0.1b
(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
Compiler

Compiled 5423 to 3743 computations (31% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(pow.f64 (cbrt.f64 x) 2)
0.6b
(cbrt.f64 x)
0.7b
(pow.f64 (cbrt.f64 (*.f64 (cbrt.f64 x) -70711/100000)) 3)
16.7b
(/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series362.0ms (12%)

Counts
1 → 12
Calls

3 calls:

207.0ms
(pow.f64 (cbrt.f64 (*.f64 (cbrt.f64 x) -70711/100000)) 3)
x
-inf
81.0ms
(pow.f64 (cbrt.f64 (*.f64 (cbrt.f64 x) -70711/100000)) 3)
x
0
74.0ms
(pow.f64 (cbrt.f64 (*.f64 (cbrt.f64 x) -70711/100000)) 3)
x
inf

rewrite40.0ms (1.3%)

Algorithm
batch-egg-rewrite
Rules
553×log1p-expm1-u_binary64
553×expm1-log1p-u_binary64
512×unpow-prod-down_binary64
280×log-prod_binary64
156×pow2_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
086
11596
215686
Stop Event
node limit
Counts
1 → 64

simplify65.0ms (2.2%)

Algorithm
egg-herbie
Rules
636×sqr-pow_binary64
416×unswap-sqr_binary64
337×associate-*l*_binary64
332×cube-prod_binary64
323×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
012100
128100
254100
3117100
4299100
5958100
61335100
71977100
82087100
92262100
102486100
112821100
123288100
133898100
144654100
Stop Event
node limit
Counts
76 → 67

prune260.0ms (8.6%)

Pruning

10 alts after pruning (6 fresh and 4 done)

PrunedKeptTotal
New2360236
Fresh066
Picked011
Done033
Total23610246
Error
0.0b
Counts
246 → 10
Alt Table
StatusErrorProgram
22.3b
(cbrt.f64 (pow.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) 3))
32.1b
(fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) -70711/100000) (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
15.1b
(pow.f64 (sqrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) 2)
0.6b
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) -70711/100000) (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
0.7b
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (*.f64 (cbrt.f64 x) -70711/100000)) 3) (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
1.4b
(pow.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) 3)
1.4b
(*.f64 (*.f64 (pow.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))) 2)) (cbrt.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))))
30.8b
(fma.f64 x (fma.f64 x 134362287316698645903/100000000000000000000 -2134856267379707/1000000000000000) 16316775383/10000000000)
2.0b
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))) 2) 3) (cbrt.f64 (fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
0.1b
(fma.f64 x -70711/100000 (/.f64 (fma.f64 x 1913510371/10000000000 16316775383/10000000000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
Compiler

Compiled 7339 to 5241 computations (28.6% saved)

regimes165.0ms (5.5%)

Accuracy

Total 0.1b remaining (63.4%)

Threshold costs 0.1b (63.4%)

Counts
51 → 1
Compiler

Compiled 2849 to 2174 computations (23.7% saved)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Rules
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01320
11520
Stop Event
saturated

end194.0ms (6.4%)

Stop Event
fuel
Compiler

Compiled 276 to 212 computations (23.2% saved)

Profiling

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