Details

Time bar (total: 4.8s)

analyze1.2s (24.5%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%48.6%51.4%0
0%48.6%51.4%1
24.3%24.3%51.4%2
24.3%24.3%51.4%3
30.4%18.2%51.4%4
30.4%18.2%51.4%5
33.4%15.2%51.4%6
33.4%15.2%51.4%7
34.6%14.1%51.4%8
34.8%13.9%51.4%9
35.4%13.2%51.4%10
35.6%13.1%51.4%11
35.9%12.7%51.4%12
36%12.6%51.4%13
36.2%12.4%51.4%14
Compiler

Compiled 28 to 20 computations (28.6% saved)

sample2.1s (42.9%)

Results
923.0ms6309×body128valid
489.0ms774×body2048valid
268.0ms531×body1024valid
214.0ms278×body4096valid
102.0ms252×body512valid
30.0ms112×body256valid
Compiler

Compiled 75 to 54 computations (28% saved)

simplify7.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
9×fma-def_binary64
6×*-commutative_binary64
2×+-commutative_binary64
2×associate-/l*_binary64
2×distribute-lft-in_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01524
13124
24122
34822
45022
55222
65322
Stop Event
1×saturated
Counts
1 → 2

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
13.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶13.8b
(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 4 (*.f64 p p))))) 1/2))
Compiler

Compiled 68 to 48 computations (29.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 4 (*.f64 p p))))) 1/2))
✓0.0b
(*.f64 4 (*.f64 p p))
✓0.5b
(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 4 (*.f64 p p))))) 1/2)
✓17.2b
(sqrt.f64 (fma.f64 x x (*.f64 4 (*.f64 p p))))

series60.0ms (1.3%)

Counts
4 → 84
Calls

4 calls:

25.0ms
(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 4 (*.f64 p p))))) 1/2))
23.0ms
(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 4 (*.f64 p p))))) 1/2)
10.0ms
(sqrt.f64 (fma.f64 x x (*.f64 4 (*.f64 p p))))
2.0ms
(*.f64 4 (*.f64 p p))

rewrite69.0ms (1.4%)

Algorithm
1×batch-egg-rewrite
Rules
544×log-prod_binary64
204×expm1-udef_binary64
204×log1p-udef_binary64
190×log-pow_binary64
154×prod-diff_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01262
124744
2289244
Stop Event
1×node limit
Counts
4 → 101
Calls

4 calls:

65.0ms
(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 4 (*.f64 p p))))) 1/2))
65.0ms
(*.f64 4 (*.f64 p p))
65.0ms
(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 4 (*.f64 p p))))) 1/2)
65.0ms
(sqrt.f64 (fma.f64 x x (*.f64 4 (*.f64 p p))))

simplify44.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
580×associate-/l*_binary64
515×associate-/r*_binary64
431×fma-def_binary64
304×cancel-sign-sub-inv_binary64
210×fma-neg_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01541801
14971749
217471656
Stop Event
1×node limit
Counts
185 → 188

prune163.0ms (3.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1853188
Fresh000
Picked011
Done000
Total1854189
Error
3.0b
Counts
189 → 4
Alt Table
StatusErrorProgram
52.4b
(/.f64 (neg.f64 p) x)
✓13.8b
(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 4 (*.f64 p p))))) 1/2))
51.1b
(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))
▶13.8b
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))))
Compiler

Compiled 3734 to 2745 computations (26.5% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))
✓0.4b
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))))
✓0.5b
(fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)

series62.0ms (1.3%)

Counts
3 → 72
Calls

3 calls:

21.0ms
(fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)
20.0ms
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))))
20.0ms
(sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))

rewrite56.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
497×log-prod_binary64
193×expm1-udef_binary64
193×log1p-udef_binary64
192×pow1/3_binary64
178×pow3_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01246
122846
2263746
Stop Event
1×node limit
Counts
3 → 92
Calls

3 calls:

54.0ms
(sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))
54.0ms
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))))
54.0ms
(fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)

simplify51.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
972×times-frac_binary64
469×associate-/l*_binary64
428×associate-/r*_binary64
319×fma-def_binary64
222×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01201914
13761846
213301716
Stop Event
1×node limit
Counts
164 → 118

prune96.0ms (2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1180118
Fresh022
Picked011
Done011
Total1184122
Error
3.0b
Counts
122 → 4
Alt Table
StatusErrorProgram
52.4b
(/.f64 (neg.f64 p) x)
✓13.8b
(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 4 (*.f64 p p))))) 1/2))
▶51.1b
(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))
✓13.8b
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))))
Compiler

Compiled 2463 to 1507 computations (38.8% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.3b
(*.f64 (/.f64 p x) (/.f64 p x))
✓19.1b
(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))

series30.0ms (0.6%)

Counts
2 → 48
Calls

2 calls:

24.0ms
(*.f64 (/.f64 p x) (/.f64 p x))
5.0ms
(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))

rewrite36.0ms (0.7%)

Algorithm
1×batch-egg-rewrite
Rules
567×log1p-expm1-u_binary64
567×expm1-log1p-u_binary64
286×log-prod_binary64
142×pow2_binary64
103×egg-rr
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0611
112911
2159911
Stop Event
1×node limit
Counts
2 → 103
Calls

2 calls:

35.0ms
(*.f64 (/.f64 p x) (/.f64 p x))
35.0ms
(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))

simplify41.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
671×times-frac_binary64
650×unswap-sqr_binary64
326×associate-/l*_binary64
213×associate-/r*_binary64
150×associate-/l/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
010352
122352
242352
3106352
4434352
53292352
64926352
Stop Event
1×node limit
Counts
151 → 107

prune36.0ms (0.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1061107
Fresh011
Picked101
Done022
Total1074111
Error
0b
Counts
111 → 4
Alt Table
StatusErrorProgram
▶52.4b
(/.f64 (neg.f64 p) x)
✓13.8b
(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 4 (*.f64 p p))))) 1/2))
✓13.8b
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))))
53.2b
(/.f64 p x)
Compiler

Compiled 953 to 458 computations (51.9% saved)

localize3.0ms (0.1%)

prune3.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New000
Fresh011
Picked011
Done022
Total044
Error
0b
Counts
4 → 4
Alt Table
StatusErrorProgram
✓52.4b
(/.f64 (neg.f64 p) x)
✓13.8b
(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 4 (*.f64 p p))))) 1/2))
✓13.8b
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))))
53.2b
(/.f64 p x)
Compiler

Compiled 43 to 31 computations (27.9% saved)

regimes719.0ms (14.9%)

Accuracy

Total 5.5b remaining (98.9%)

Threshold costs 0b (0%)

Counts
98 → 2
Compiler

Compiled 9773 to 7634 computations (21.9% saved)

bsearch2.0ms (0%)

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Rules
2×*-commutative_binary64
1×+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02555
12855
Stop Event
1×saturated

end69.0ms (1.4%)

Compiler

Compiled 119 to 79 computations (33.6% saved)

Profiling

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