Details

Time bar (total: 3.5s)

analyze184.0ms (5.3%)

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
0%99.9%0.1%4
25%74.9%0.1%5
25%68.7%6.3%6
25%56.2%18.8%7
25%48.4%26.6%8
25%35.1%39.9%9
28.1%18.3%53.6%10
31.6%12.3%56.1%11
33.4%5.9%60.8%12
35.2%3.8%61%13
36.1%2.9%61%14
Compiler

Compiled 34 to 22 computations (35.3% saved)

sample1.2s (35.2%)

Results
1.2s8256×body128valid
1.0ms5×body128invalid
Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify62.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
725×fma-def_binary64
669×unsub-neg_binary64
596×cancel-sign-sub-inv_binary64
340×+-commutative_binary64
277×fma-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02042
16340
217036
354236
4186732
5328132
6488132
7495832

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶0.0b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
Compiler

Compiled 106 to 66 computations (37.7% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(fma.f64 a -3 1)
✓0.0b
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
✓0.1b
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
✓0.3b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

series50.0ms (1.4%)

Counts
4 → 84
Calls

4 calls:

28.0ms
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
10.0ms
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
10.0ms
(*.f64 (*.f64 b b) (fma.f64 a -3 1))
1.0ms
(fma.f64 a -3 1)

rewrite118.0ms (3.4%)

Algorithm
1×batch-egg-rewrite
Rules
440×prod-diff_binary64
320×fma-udef_binary64
233×expm1-udef_binary64
233×log1p-udef_binary64
209×log-pow_binary64
Counts
4 → 98
Calls

4 calls:

116.0ms
(fma.f64 a -3 1)
116.0ms
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
116.0ms
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
116.0ms
(*.f64 (*.f64 b b) (fma.f64 a -3 1))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01464
128364
2297264
3489764
4499364
5494464

simplify77.0ms (2.2%)

Algorithm
1×egg-herbie
Rules
645×fma-def_binary64
541×+-commutative_binary64
524×sub-neg_binary64
420×associate--l+_binary64
415×fma-neg_binary64
Counts
182 → 142
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0591651
11951531
25881259
323201236
442661236
550791236

prune191.0ms (5.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1402142
Fresh000
Picked011
Done000
Total1403143
Error
0b
Counts
143 → 3
Alt Table
StatusErrorProgram
▶11.9b
(+.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 a 4)) (+.f64 4 (*.f64 2 (*.f64 b b))))) -1)
✓0.0b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
23.3b
(+.f64 (/.f64 (-.f64 (*.f64 (*.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) 4) (*.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) 4)) (pow.f64 (hypot.f64 b a) 8)) (-.f64 (*.f64 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) 4) (pow.f64 (hypot.f64 b a) 4))) -1)
Compiler

Compiled 4001 to 2239 computations (44% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 2 (*.f64 b b))
✓0.0b
(*.f64 a (+.f64 a 4))
✓3.0b
(*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 a 4)) (+.f64 4 (*.f64 2 (*.f64 b b)))))

series37.0ms (1%)

Counts
3 → 48
Calls

3 calls:

32.0ms
(*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 a 4)) (+.f64 4 (*.f64 2 (*.f64 b b)))))
2.0ms
(*.f64 2 (*.f64 b b))
2.0ms
(*.f64 a (+.f64 a 4))

rewrite67.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
368×fma-neg_binary64
259×expm1-udef_binary64
259×log1p-udef_binary64
147×add-sqr-sqrt_binary64
145×log1p-expm1-u_binary64
Counts
3 → 69
Calls

3 calls:

65.0ms
(*.f64 2 (*.f64 b b))
65.0ms
(*.f64 a (+.f64 a 4))
65.0ms
(*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 a 4)) (+.f64 4 (*.f64 2 (*.f64 b b)))))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01337
130235
2390635
3497935

simplify119.0ms (3.4%)

Algorithm
1×egg-herbie
Rules
676×fma-def_binary64
466×distribute-rgt-out_binary64
452×unswap-sqr_binary64
449×associate-*l*_binary64
369×associate-+l+_binary64
Counts
117 → 88
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
028799
179672
2205651
3590589
41947589
53498589
63881589
74300589
84512589
94747589
104864589

prune98.0ms (2.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New87188
Fresh101
Picked101
Done011
Total89291
Error
0b
Counts
91 → 2
Alt Table
StatusErrorProgram
✓0.0b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
▶17.4b
(+.f64 (sqrt.f64 (*.f64 (pow.f64 a 4) (pow.f64 (fma.f64 a (+.f64 a 4) (fma.f64 2 (*.f64 b b) 4)) 2))) -1)
Compiler

Compiled 2061 to 1289 computations (37.5% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.2b
(pow.f64 (fma.f64 a (+.f64 a 4) (fma.f64 2 (*.f64 b b) 4)) 2)
✓1.2b
(*.f64 (pow.f64 a 4) (pow.f64 (fma.f64 a (+.f64 a 4) (fma.f64 2 (*.f64 b b) 4)) 2))
✓21.5b
(sqrt.f64 (*.f64 (pow.f64 a 4) (pow.f64 (fma.f64 a (+.f64 a 4) (fma.f64 2 (*.f64 b b) 4)) 2)))

series150.0ms (4.3%)

Counts
3 → 72
Calls

3 calls:

67.0ms
(sqrt.f64 (*.f64 (pow.f64 a 4) (pow.f64 (fma.f64 a (+.f64 a 4) (fma.f64 2 (*.f64 b b) 4)) 2)))
66.0ms
(*.f64 (pow.f64 a 4) (pow.f64 (fma.f64 a (+.f64 a 4) (fma.f64 2 (*.f64 b b) 4)) 2))
16.0ms
(pow.f64 (fma.f64 a (+.f64 a 4) (fma.f64 2 (*.f64 b b) 4)) 2)

rewrite66.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
569×log-prod_binary64
222×expm1-udef_binary64
222×log1p-udef_binary64
210×fma-def_binary64
205×log-pow_binary64
Counts
3 → 74
Calls

3 calls:

64.0ms
(pow.f64 (fma.f64 a (+.f64 a 4) (fma.f64 2 (*.f64 b b) 4)) 2)
64.0ms
(*.f64 (pow.f64 a 4) (pow.f64 (fma.f64 a (+.f64 a 4) (fma.f64 2 (*.f64 b b) 4)) 2))
64.0ms
(sqrt.f64 (*.f64 (pow.f64 a 4) (pow.f64 (fma.f64 a (+.f64 a 4) (fma.f64 2 (*.f64 b b) 4)) 2)))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01368
127663
2293963
3527263

simplify152.0ms (4.3%)

Algorithm
1×egg-herbie
Rules
606×unswap-sqr_binary64
564×distribute-rgt-out_binary64
407×associate-*l*_binary64
339×associate-*r*_binary64
332×associate-+r+_binary64
Counts
146 → 136
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01412649
14752430
217022300
332242270
449212270
549672231
649732231

prune148.0ms (4.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1360136
Fresh000
Picked011
Done011
Total1362138
Error
0b
Counts
138 → 2
Alt Table
StatusErrorProgram
✓0.0b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
✓17.4b
(+.f64 (sqrt.f64 (*.f64 (pow.f64 a 4) (pow.f64 (fma.f64 a (+.f64 a 4) (fma.f64 2 (*.f64 b b) 4)) 2))) -1)
Compiler

Compiled 3942 to 2823 computations (28.4% saved)

regimes634.0ms (18.1%)

Accuracy

Total 0.0b remaining (61.6%)

Threshold costs 0.0b (61.6%)

Counts
106 → 1
Compiler

Compiled 12702 to 9167 computations (27.8% saved)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
1×+-commutative_binary64
1×*-commutative_binary64
1×*-rgt-identity_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01425
11825
21725

end72.0ms (2.1%)

Compiler

Compiled 87 to 57 computations (34.5% saved)

Profiling

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