Details

Time bar (total: 1.1s)

analyze4.0ms (0.3%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%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 9 to 6 computations (33.3% saved)

sample917.0ms (80.9%)

Results
905.0ms8256×body128valid

preprocess17.0ms (1.5%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
1-exp_binary64
fma-def_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1108
011
Stop Event
saturated
saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(/.f64 x (+.f64 (*.f64 x x) 1))
Outputs
(/.f64 x (+.f64 (*.f64 x x) 1))
(/.f64 x (fma.f64 x x 1))
Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify8.0ms (0.7%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
1-exp_binary64
fma-def_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1108
Stop Event
saturated
Counts
1 → 2
Calls
Call 1
Inputs
(/.f64 x (+.f64 (*.f64 x x) 1))
Outputs
(/.f64 x (+.f64 (*.f64 x x) 1))
(/.f64 x (fma.f64 x x 1))

prune3.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
13.6b
Counts
3 → 1
Alt Table
StatusErrorProgram
13.6b
(/.f64 x (fma.f64 x x 1))
Compiler

Compiled 28 to 16 computations (42.9% saved)

localize3.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
13.6b
(/.f64 x (fma.f64 x x 1))

series2.0ms (0.2%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
(/.f64 x (fma.f64 x x 1))
1.0ms
x
@inf
(/.f64 x (fma.f64 x x 1))
1.0ms
x
@-inf
(/.f64 x (fma.f64 x x 1))

rewrite35.0ms (3.1%)

Algorithm
batch-egg-rewrite
Rules
499×pow1_binary64
462×add-log-exp_binary64
462×log1p-expm1-u_binary64
462×expm1-log1p-u_binary64
452×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
058
1988
212148
Stop Event
node limit
Counts
1 → 31
Calls
Call 1
Inputs
(/.f64 x (fma.f64 x x 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 x (fma.f64 x x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (fma.f64 x x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (fma.f64 x x 1))) (pow.f64 (cbrt.f64 (/.f64 x (fma.f64 x x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (fma.f64 x x 1))) 2) (cbrt.f64 (/.f64 x (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (fma.f64 x x 1))) (sqrt.f64 (/.f64 x (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 x x 1)) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 (fma.f64 x x 1) 2))) (/.f64 x (cbrt.f64 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 (fma.f64 x x 1) 2))) (cbrt.f64 (/.f64 x (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (fma.f64 x x 1) 2))) (/.f64 (sqrt.f64 x) (cbrt.f64 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x 1))) (/.f64 x (sqrt.f64 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (fma.f64 x x 1))) (/.f64 (cbrt.f64 x) (sqrt.f64 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (fma.f64 x x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (fma.f64 x x 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (fma.f64 x x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (fma.f64 x x 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 x x 1) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (fma.f64 x x 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (fma.f64 x x 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x x 1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (fma.f64 x x 1))))))))

simplify31.0ms (2.7%)

Algorithm
egg-herbie
Rules
475×fma-def_binary64
420×times-frac_binary64
268×sub-neg_binary64
259×associate-*l*_binary64
219×fma-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
027184
175180
2197180
3552180
41468180
53917180
Stop Event
node limit
Counts
43 → 45
Calls
Call 1
Inputs
x
(+.f64 (*.f64 -1 (pow.f64 x 3)) x)
(+.f64 (*.f64 -1 (pow.f64 x 3)) (+.f64 (pow.f64 x 5) x))
(+.f64 (*.f64 -1 (pow.f64 x 3)) (+.f64 (pow.f64 x 5) (+.f64 (*.f64 -1 (pow.f64 x 7)) x)))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 7))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 7))))
Outputs
x
(+.f64 (*.f64 -1 (pow.f64 x 3)) x)
(fma.f64 -1 (pow.f64 x 3) x)
(-.f64 x (pow.f64 x 3))
(+.f64 (*.f64 -1 (pow.f64 x 3)) (+.f64 (pow.f64 x 5) x))
(fma.f64 -1 (pow.f64 x 3) (+.f64 x (pow.f64 x 5)))
(-.f64 (+.f64 x (pow.f64 x 5)) (pow.f64 x 3))
(+.f64 x (-.f64 (pow.f64 x 5) (pow.f64 x 3)))
(+.f64 (*.f64 -1 (pow.f64 x 3)) (+.f64 (pow.f64 x 5) (+.f64 (*.f64 -1 (pow.f64 x 7)) x)))
(fma.f64 -1 (pow.f64 x 3) (+.f64 (pow.f64 x 5) (fma.f64 -1 (pow.f64 x 7) x)))
(+.f64 (-.f64 (pow.f64 x 5) (pow.f64 x 7)) (-.f64 x (pow.f64 x 3)))
(+.f64 x (-.f64 (-.f64 (pow.f64 x 5) (pow.f64 x 7)) (pow.f64 x 3)))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 1 x) (/.f64 -1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 1 (pow.f64 x 5)) (+.f64 (/.f64 1 x) (/.f64 -1 (pow.f64 x 3))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 -1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 7))))
(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 7))))
(+.f64 (/.f64 1 x) (-.f64 (/.f64 1 (pow.f64 x 5)) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 7)))))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (+.f64 (/.f64 -1 (pow.f64 x 3)) (/.f64 -1 (pow.f64 x 7))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 5)) (+.f64 (/.f64 -1 (pow.f64 x 3)) (/.f64 -1 (pow.f64 x 7)))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 1 x) (/.f64 -1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 1 (pow.f64 x 5)) (+.f64 (/.f64 1 x) (/.f64 -1 (pow.f64 x 3))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 -1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 7))))
(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 7))))
(+.f64 (/.f64 1 x) (-.f64 (/.f64 1 (pow.f64 x 5)) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 7)))))
(+.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 5))) (+.f64 (/.f64 -1 (pow.f64 x 3)) (/.f64 -1 (pow.f64 x 7))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (pow.f64 x 5)) (+.f64 (/.f64 -1 (pow.f64 x 3)) (/.f64 -1 (pow.f64 x 7)))))

prune21.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New44145
Fresh000
Picked011
Done000
Total44246
Error
0b
Counts
46 → 2
Alt Table
StatusErrorProgram
13.6b
(/.f64 x (fma.f64 x x 1))
35.6b
(/.f64 1 x)
Compiler

Compiled 528 to 355 computations (32.8% saved)

localize2.0ms (0.1%)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done011
Total022
Error
0b
Counts
2 → 2
Alt Table
StatusErrorProgram
13.6b
(/.f64 x (fma.f64 x x 1))
35.6b
(/.f64 1 x)
Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes23.0ms (2%)

Accuracy

Total -46.5b remaining (-329085.9%)

Threshold costs -46.5b (-329085.9%)

Counts
4 → 3
Compiler

Compiled 28 to 16 computations (42.9% saved)

bsearch31.0ms (2.8%)

Algorithm
binary-search
Calls

2 calls:

16.0ms
x
15.0ms
x
Steps
ItersPointRange
57952138.18550921
∈ [
57952138.18550921
,
519112205963285.25
]
-1.2761356384804217e+29
∈ [
-1.2761356384804217e+29
,
-52472463437937640.0
]
Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify2.0ms (0.2%)

Algorithm
egg-herbie
Rules
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01328
11528
Stop Event
saturated
Calls
Call 1
Inputs
(if (<=.f64 x -127613563848042167934384078848) (/.f64 1 x) (if (<=.f64 x 248902538240034848/4294967296) (/.f64 x (fma.f64 x x 1)) (/.f64 1 x)))
Outputs
(if (<=.f64 x -127613563848042167934384078848) (/.f64 1 x) (if (<=.f64 x 248902538240034848/4294967296) (/.f64 x (fma.f64 x x 1)) (/.f64 1 x)))
(if (<=.f64 x -127613563848042167934384078848) (/.f64 1 x) (if (<=.f64 x 7778204320001089/134217728) (/.f64 x (fma.f64 x x 1)) (/.f64 1 x)))

end35.0ms (3.1%)

Stop Event
done
Compiler

Compiled 51 to 33 computations (35.3% saved)

Profiling

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