Details

Time bar (total: 2.7s)

analyze3.0ms (0.1%)

Algorithm
1×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)

sample641.0ms (23.9%)

Results
630.0ms8256×body128valid

preprocess15.0ms (0.6%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1108
011
Stop Event
1×saturated
1×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)

simplify6.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1108
Stop Event
1×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))

eval1.0ms (0%)

Compiler

Compiled 14 to 8 computations (42.9% saved)

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
14.7b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶14.7b
(/.f64 x (fma.f64 x x 1))
Compiler

Compiled 14 to 8 computations (42.9% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓14.7b
(/.f64 x (fma.f64 x x 1))

series2.0ms (0.1%)

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))

rewrite33.0ms (1.2%)

Algorithm
1×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
1×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 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))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (fma.f64 x x 1))))))))

simplify32.0ms (1.2%)

Algorithm
1×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
1×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)))))

eval13.0ms (0.5%)

Compiler

Compiled 513 to 345 computations (32.7% saved)

prune26.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New42345
Fresh000
Picked101
Done000
Total43346
Error
0b
Counts
46 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
14.8b
(*.f64 x (/.f64 1 (fma.f64 x x 1)))
▶14.7b
(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x 1))) (/.f64 x (sqrt.f64 (fma.f64 x x 1))))
32.4b
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))
Compiler

Compiled 82 to 60 computations (26.8% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 1 (sqrt.f64 (fma.f64 x x 1)))
✓0.0b
(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x 1))) (/.f64 x (sqrt.f64 (fma.f64 x x 1))))
✓0.0b
(/.f64 x (sqrt.f64 (fma.f64 x x 1)))
✓14.7b
(sqrt.f64 (fma.f64 x x 1))

series5.0ms (0.2%)

Counts
4 → 48
Calls

12 calls:

TimeVariablePointExpression
1.0ms
x
@0
(/.f64 x (sqrt.f64 (fma.f64 x x 1)))
1.0ms
x
@0
(sqrt.f64 (fma.f64 x x 1))
1.0ms
x
@-inf
(/.f64 x (sqrt.f64 (fma.f64 x x 1)))
1.0ms
x
@inf
(/.f64 x (sqrt.f64 (fma.f64 x x 1)))
0.0ms
x
@inf
(sqrt.f64 (fma.f64 x x 1))

rewrite51.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
814×pow1_binary64
757×log1p-expm1-u_binary64
757×expm1-log1p-u_binary64
79×add-sqr-sqrt_binary64
76×*-un-lft-identity_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0835
116633
2216833
Stop Event
1×node limit
Counts
4 → 143
Calls
Call 1
Inputs
(sqrt.f64 (fma.f64 x x 1))
(/.f64 x (sqrt.f64 (fma.f64 x x 1)))
(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x 1))) (/.f64 x (sqrt.f64 (fma.f64 x x 1))))
(/.f64 1 (sqrt.f64 (fma.f64 x x 1)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x 1))) (cbrt.f64 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x 1)) (cbrt.f64 (sqrt.f64 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x x 1) 1/4) (pow.f64 (fma.f64 x x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x x 1)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x 1)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 x x 1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (pow.f64 (fma.f64 x x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (fma.f64 x x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (fma.f64 x x 1)) (cbrt.f64 (pow.f64 (fma.f64 x x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (fma.f64 x x 1) 1/4) (pow.f64 (sqrt.f64 (fma.f64 x x 1)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (fma.f64 x x 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x 1) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x 1) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (fma.f64 x x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x x 1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 x x 1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x 1))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (sqrt.f64 (fma.f64 x x 1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (pow.f64 (fma.f64 x x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (sqrt.f64 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (sqrt.f64 (fma.f64 x x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x x 1) -1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (pow.f64 (fma.f64 x x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (sqrt.f64 (fma.f64 x x 1)))) (cbrt.f64 (*.f64 x (/.f64 x (fma.f64 x x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (/.f64 x (fma.f64 x x 1)))) (cbrt.f64 (/.f64 x (sqrt.f64 (fma.f64 x x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 (fma.f64 x x 1))) (*.f64 (cbrt.f64 (pow.f64 (fma.f64 x x 1) -1/2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (pow.f64 (fma.f64 x x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (sqrt.f64 (fma.f64 x x 1)))) (sqrt.f64 (/.f64 x (sqrt.f64 (fma.f64 x x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (fma.f64 x x 1)) -1/2) (/.f64 x (pow.f64 (fma.f64 x x 1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (fma.f64 x x 1)) -1/2) (*.f64 (pow.f64 (sqrt.f64 (fma.f64 x x 1)) -1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (sqrt.f64 (fma.f64 x x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (sqrt.f64 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (sqrt.f64 (/.f64 x (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x 1))) (/.f64 x 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simplify37.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
460×associate-/r*_binary64
457×fma-def_binary64
311×fma-neg_binary64
276×sub-neg_binary64
239×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0106696
1326683
2907676
32617676
Stop Event
1×node limit
Counts
191 → 216
Calls
Call 1
Inputs
1
(+.f64 1 (*.f64 1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 4))))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
x
(+.f64 (*.f64 1/2 (/.f64 1 x)) x)
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) x) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(*.f64 -1 x)
(-.f64 (*.f64 -1 x) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 5)))))
x
(+.f64 (*.f64 -1/2 (pow.f64 x 3)) x)
(+.f64 (*.f64 -1/2 (pow.f64 x 3)) (+.f64 (*.f64 3/8 (pow.f64 x 5)) x))
(+.f64 (*.f64 -1/2 (pow.f64 x 3)) (+.f64 (*.f64 3/8 (pow.f64 x 5)) (+.f64 (*.f64 -5/16 (pow.f64 x 7)) x)))
1
(-.f64 1 (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 1 (*.f64 3/8 (/.f64 1 (pow.f64 x 4)))) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 1 (*.f64 3/8 (/.f64 1 (pow.f64 x 4)))) (+.f64 (*.f64 5/16 (/.f64 1 (pow.f64 x 6))) (*.f64 1/2 (/.f64 1 (pow.f64 x 2)))))
-1
(-.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 2))) 1)
(-.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 2))) (+.f64 1 (*.f64 3/8 (/.f64 1 (pow.f64 x 4)))))
(-.f64 (+.f64 (*.f64 5/16 (/.f64 1 (pow.f64 x 6))) (*.f64 1/2 (/.f64 1 (pow.f64 x 2)))) (+.f64 1 (*.f64 3/8 (/.f64 1 (pow.f64 x 4)))))
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))))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 3/8 (pow.f64 x 4))))
(+.f64 (*.f64 -5/16 (pow.f64 x 6)) (+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 3/8 (pow.f64 x 4)))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1 x) (*.f64 3/8 (/.f64 1 (pow.f64 x 5)))) (*.f64 1/2 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1 x) (*.f64 3/8 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 5/16 (/.f64 1 (pow.f64 x 7))) (*.f64 1/2 (/.f64 1 (pow.f64 x 3)))))
(/.f64 -1 x)
(-.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x))
(-.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (*.f64 3/8 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 (*.f64 5/16 (/.f64 1 (pow.f64 x 7))) (*.f64 1/2 (/.f64 1 (pow.f64 x 3)))) (+.f64 (/.f64 1 x) (*.f64 3/8 (/.f64 1 (pow.f64 x 5)))))
Outputs
1
(+.f64 1 (*.f64 1/2 (pow.f64 x 2)))
(+.f64 1 (*.f64 1/2 (*.f64 x x)))
(fma.f64 1/2 (*.f64 x x) 1)
(fma.f64 x (*.f64 1/2 x) 1)
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 -1/8 (pow.f64 x 4))))
(+.f64 1 (fma.f64 1/2 (*.f64 x x) (*.f64 -1/8 (pow.f64 x 4))))
(fma.f64 -1/8 (pow.f64 x 4) (fma.f64 1/2 (*.f64 x x) 1))
(fma.f64 1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) 1))
(+.f64 1 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/16 (pow.f64 x 6)) (*.f64 -1/8 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 1/2 (*.f64 x x) (fma.f64 1/16 (pow.f64 x 6) (*.f64 -1/8 (pow.f64 x 4)))))
(+.f64 1 (fma.f64 1/2 (*.f64 x x) (fma.f64 -1/8 (pow.f64 x 4) (*.f64 1/16 (pow.f64 x 6)))))
(+.f64 (*.f64 1/16 (pow.f64 x 6)) (fma.f64 -1/8 (pow.f64 x 4) (fma.f64 1/2 (*.f64 x x) 1)))
x
(+.f64 (*.f64 1/2 (/.f64 1 x)) x)
(+.f64 x (/.f64 1/2 x))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) x) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (-.f64 x (/.f64 1/8 (pow.f64 x 3))))
(+.f64 x (-.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 -1/8 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1/2 x) (-.f64 (+.f64 x (/.f64 1/16 (pow.f64 x 5))) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 (+.f64 x (/.f64 1/16 (pow.f64 x 5))) (-.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 x (-.f64 (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))) (/.f64 1/8 (pow.f64 x 3))))
(+.f64 x (+.f64 (-.f64 (/.f64 1/2 x) (/.f64 -1/16 (pow.f64 x 5))) (/.f64 -1/8 (pow.f64 x 3))))
(*.f64 -1 x)
(neg.f64 x)
(-.f64 (*.f64 -1 x) (*.f64 1/2 (/.f64 1 x)))
(-.f64 (neg.f64 x) (/.f64 1/2 x))
(fma.f64 x -1 (/.f64 -1/2 x))
(-.f64 (/.f64 -1/2 x) x)
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)) (*.f64 1/2 (/.f64 1 x)))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (neg.f64 x) (/.f64 1/2 x)))
(+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) x) (/.f64 -1/2 x))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (/.f64 -1/2 x) x))
(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 x (/.f64 1/2 x)))
(-.f64 (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)) (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (neg.f64 x) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
(+.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) x) (-.f64 (/.f64 -1/2 x) (/.f64 1/16 (pow.f64 x 5))))
(-.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))) x)
(+.f64 (/.f64 1/8 (pow.f64 x 3)) (-.f64 (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5))) x))
x
(+.f64 (*.f64 -1/2 (pow.f64 x 3)) x)
(fma.f64 -1/2 (pow.f64 x 3) x)
(fma.f64 (pow.f64 x 3) -1/2 x)
(+.f64 (*.f64 -1/2 (pow.f64 x 3)) (+.f64 (*.f64 3/8 (pow.f64 x 5)) x))
(fma.f64 -1/2 (pow.f64 x 3) (fma.f64 3/8 (pow.f64 x 5) x))
(fma.f64 (pow.f64 x 3) -1/2 (fma.f64 (pow.f64 x 5) 3/8 x))
(+.f64 (*.f64 -1/2 (pow.f64 x 3)) (+.f64 (*.f64 3/8 (pow.f64 x 5)) (+.f64 (*.f64 -5/16 (pow.f64 x 7)) x)))
(fma.f64 -1/2 (pow.f64 x 3) (fma.f64 3/8 (pow.f64 x 5) (fma.f64 -5/16 (pow.f64 x 7) x)))
(fma.f64 (pow.f64 x 3) -1/2 (fma.f64 (pow.f64 x 5) 3/8 (fma.f64 -5/16 (pow.f64 x 7) x)))
1
(-.f64 1 (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(-.f64 1 (/.f64 1/2 (*.f64 x x)))
(+.f64 1 (/.f64 -1/2 (*.f64 x x)))
(-.f64 (+.f64 1 (*.f64 3/8 (/.f64 1 (pow.f64 x 4)))) (*.f64 1/2 (/.f64 1 (pow.f64 x 2))))
(+.f64 1 (-.f64 (/.f64 3/8 (pow.f64 x 4)) (/.f64 1/2 (*.f64 x x))))
(+.f64 (+.f64 1 (/.f64 3/8 (pow.f64 x 4))) (/.f64 -1/2 (*.f64 x x)))
(+.f64 (/.f64 3/8 (pow.f64 x 4)) (+.f64 1 (/.f64 -1/2 (*.f64 x x))))
(+.f64 1 (+.f64 (/.f64 3/8 (pow.f64 x 4)) (/.f64 -1/2 (*.f64 x x))))
(-.f64 (+.f64 1 (*.f64 3/8 (/.f64 1 (pow.f64 x 4)))) (+.f64 (*.f64 5/16 (/.f64 1 (pow.f64 x 6))) (*.f64 1/2 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 1 (/.f64 3/8 (pow.f64 x 4))) (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 5/16 (pow.f64 x 6))))
(+.f64 1 (-.f64 (/.f64 3/8 (pow.f64 x 4)) (+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 5/16 (pow.f64 x 6)))))
(+.f64 1 (+.f64 (+.f64 (/.f64 3/8 (pow.f64 x 4)) (/.f64 -5/16 (pow.f64 x 6))) (/.f64 -1/2 (*.f64 x x))))
-1
(-.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 2))) 1)
(+.f64 (/.f64 1/2 (*.f64 x x)) -1)
(+.f64 -1 (/.f64 1/2 (*.f64 x x)))
(-.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 2))) (+.f64 1 (*.f64 3/8 (/.f64 1 (pow.f64 x 4)))))
(-.f64 (/.f64 1/2 (*.f64 x x)) (+.f64 1 (/.f64 3/8 (pow.f64 x 4))))
(+.f64 (/.f64 1/2 (*.f64 x x)) (-.f64 -1 (/.f64 3/8 (pow.f64 x 4))))
(+.f64 -1 (+.f64 (/.f64 -3/8 (pow.f64 x 4)) (/.f64 1/2 (*.f64 x x))))
(-.f64 (+.f64 (*.f64 5/16 (/.f64 1 (pow.f64 x 6))) (*.f64 1/2 (/.f64 1 (pow.f64 x 2)))) (+.f64 1 (*.f64 3/8 (/.f64 1 (pow.f64 x 4)))))
(+.f64 (/.f64 5/16 (pow.f64 x 6)) (-.f64 (/.f64 1/2 (*.f64 x x)) (+.f64 1 (/.f64 3/8 (pow.f64 x 4)))))
(+.f64 (/.f64 1/2 (*.f64 x x)) (-.f64 (/.f64 5/16 (pow.f64 x 6)) (+.f64 1 (/.f64 3/8 (pow.f64 x 4)))))
(+.f64 (/.f64 1/2 (*.f64 x x)) (+.f64 (/.f64 5/16 (pow.f64 x 6)) (+.f64 -1 (/.f64 -3/8 (pow.f64 x 4)))))
(+.f64 (/.f64 1/2 (*.f64 x x)) (+.f64 (+.f64 (/.f64 5/16 (pow.f64 x 6)) -1) (/.f64 -3/8 (pow.f64 x 4))))
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 (pow.f64 x 5) (-.f64 x (pow.f64 x 3)))
(-.f64 (+.f64 x (pow.f64 x 5)) (pow.f64 x 3))
(-.f64 x (-.f64 (pow.f64 x 3) (pow.f64 x 5)))
(+.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 (-.f64 (+.f64 x (pow.f64 x 5)) (pow.f64 x 3)) (pow.f64 x 7))
(+.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 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 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 (/.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 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 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 (/.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)))))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 x 2)))
(+.f64 1 (*.f64 (*.f64 x x) -1/2))
(fma.f64 (*.f64 x x) -1/2 1)
(fma.f64 x (*.f64 x -1/2) 1)
(+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 3/8 (pow.f64 x 4))))
(+.f64 1 (fma.f64 -1/2 (*.f64 x x) (*.f64 (pow.f64 x 4) 3/8)))
(+.f64 1 (fma.f64 (*.f64 x x) -1/2 (*.f64 (pow.f64 x 4) 3/8)))
(fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 3/8 1))
(+.f64 (*.f64 -5/16 (pow.f64 x 6)) (+.f64 1 (+.f64 (*.f64 -1/2 (pow.f64 x 2)) (*.f64 3/8 (pow.f64 x 4)))))
(fma.f64 -5/16 (pow.f64 x 6) (+.f64 1 (fma.f64 -1/2 (*.f64 x x) (*.f64 (pow.f64 x 4) 3/8))))
(+.f64 (fma.f64 (*.f64 x x) -1/2 (*.f64 (pow.f64 x 4) 3/8)) (fma.f64 (pow.f64 x 6) -5/16 1))
(fma.f64 (pow.f64 x 6) -5/16 (fma.f64 x (*.f64 x -1/2) (fma.f64 (pow.f64 x 4) 3/8 1)))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 1 (pow.f64 x 3))))
(-.f64 (/.f64 1 x) (/.f64 1/2 (pow.f64 x 3)))
(+.f64 (/.f64 1 x) (/.f64 -1/2 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 x) (*.f64 3/8 (/.f64 1 (pow.f64 x 5)))) (*.f64 1/2 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1 x) (-.f64 (/.f64 3/8 (pow.f64 x 5)) (/.f64 1/2 (pow.f64 x 3))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 3/8 (pow.f64 x 5)) (/.f64 -1/2 (pow.f64 x 3))))
(+.f64 (/.f64 3/8 (pow.f64 x 5)) (+.f64 (/.f64 1 x) (/.f64 -1/2 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1 x) (*.f64 3/8 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 5/16 (/.f64 1 (pow.f64 x 7))) (*.f64 1/2 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (/.f64 1 x) (-.f64 (/.f64 3/8 (pow.f64 x 5)) (+.f64 (/.f64 1/2 (pow.f64 x 3)) (/.f64 5/16 (pow.f64 x 7)))))
(+.f64 (+.f64 (/.f64 1 x) (-.f64 (/.f64 3/8 (pow.f64 x 5)) (/.f64 5/16 (pow.f64 x 7)))) (/.f64 -1/2 (pow.f64 x 3)))
(+.f64 (/.f64 -1/2 (pow.f64 x 3)) (+.f64 (/.f64 3/8 (pow.f64 x 5)) (+.f64 (/.f64 1 x) (/.f64 -5/16 (pow.f64 x 7)))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 3/8 (pow.f64 x 5)) (+.f64 (/.f64 -1/2 (pow.f64 x 3)) (/.f64 -5/16 (pow.f64 x 7)))))
(/.f64 -1 x)
(-.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x))
(-.f64 (/.f64 1/2 (pow.f64 x 3)) (/.f64 1 x))
(+.f64 (/.f64 1/2 (pow.f64 x 3)) (/.f64 -1 x))
(-.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (*.f64 3/8 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (/.f64 1/2 (pow.f64 x 3)) (+.f64 (/.f64 1 x) (/.f64 3/8 (pow.f64 x 5))))
(+.f64 (/.f64 1/2 (pow.f64 x 3)) (-.f64 (/.f64 -1 x) (/.f64 3/8 (pow.f64 x 5))))
(+.f64 (/.f64 1/2 (pow.f64 x 3)) (+.f64 (/.f64 -1 x) (/.f64 -3/8 (pow.f64 x 5))))
(-.f64 (+.f64 (*.f64 5/16 (/.f64 1 (pow.f64 x 7))) (*.f64 1/2 (/.f64 1 (pow.f64 x 3)))) (+.f64 (/.f64 1 x) (*.f64 3/8 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 (/.f64 1/2 (pow.f64 x 3)) (/.f64 5/16 (pow.f64 x 7))) (+.f64 (/.f64 1 x) (/.f64 3/8 (pow.f64 x 5))))
(+.f64 (/.f64 1/2 (pow.f64 x 3)) (-.f64 (/.f64 5/16 (pow.f64 x 7)) (+.f64 (/.f64 1 x) (/.f64 3/8 (pow.f64 x 5)))))
(+.f64 (/.f64 1/2 (pow.f64 x 3)) (+.f64 (/.f64 5/16 (pow.f64 x 7)) (+.f64 (/.f64 -1 x) (/.f64 -3/8 (pow.f64 x 5)))))

eval105.0ms (3.9%)

Compiler

Compiled 4960 to 3541 computations (28.6% saved)

prune857.0ms (32%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2651266
Fresh112
Picked011
Done000
Total2663269
Error
0b
Counts
269 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
▶14.8b
(*.f64 x (/.f64 1 (fma.f64 x x 1)))
✓14.7b
(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x 1))) (/.f64 x (sqrt.f64 (fma.f64 x x 1))))
32.4b
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))
Compiler

Compiled 66 to 49 computations (25.8% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.4b
(/.f64 1 (fma.f64 x x 1))
✓14.3b
(*.f64 x (/.f64 1 (fma.f64 x x 1)))

series2.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
0.0ms
x
@inf
(/.f64 1 (fma.f64 x x 1))
0.0ms
x
@-inf
(/.f64 1 (fma.f64 x x 1))
0.0ms
x
@0
(*.f64 x (/.f64 1 (fma.f64 x x 1)))
0.0ms
x
@0
(/.f64 1 (fma.f64 x x 1))
0.0ms
x
@inf
(*.f64 x (/.f64 1 (fma.f64 x x 1)))

rewrite51.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
548×pow1_binary64
506×add-log-exp_binary64
506×log1p-expm1-u_binary64
506×expm1-log1p-u_binary64
495×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0616
112116
2144716
Stop Event
1×node limit
Counts
2 → 44
Calls
Call 1
Inputs
(*.f64 x (/.f64 1 (fma.f64 x x 1)))
(/.f64 1 (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 (fma.f64 x x 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x 1) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 x) 2) (/.f64 (fma.f64 x x 1) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 x) (/.f64 (fma.f64 x x 1) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) (neg.f64 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (sqrt.f64 (fma.f64 x x 1))) (sqrt.f64 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x 1) (fma.f64 x x 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (pow.f64 (cbrt.f64 (fma.f64 x x 1)) 2)) (cbrt.f64 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 x) (neg.f64 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x -1) (neg.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 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 cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 1 (fma.f64 x x 1)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 1 (fma.f64 x x 1)) 3) (pow.f64 x 3)))))) (#(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))))))) (#(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 -.f64 (+.f64 1 (/.f64 1 (fma.f64 x x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (fma.f64 x x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 x x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x 1))) (cbrt.f64 (pow.f64 (fma.f64 x x 1) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 x x 1) -2)) (/.f64 1 (cbrt.f64 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x x 1) -1/2) (pow.f64 (fma.f64 x x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x x 1)) 2) -1) (pow.f64 (cbrt.f64 (fma.f64 x x 1)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (fma.f64 x x 1)) -1) (pow.f64 (sqrt.f64 (fma.f64 x x 1)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (fma.f64 x x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (fma.f64 x x 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 x x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x 1) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x 1) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (fma.f64 x x 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (fma.f64 x x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (fma.f64 x x 1))))))))

simplify94.0ms (3.5%)

Algorithm
1×egg-herbie
Rules
643×fma-def_binary64
412×associate-*l*_binary64
264×associate-*r*_binary64
243×fma-neg_binary64
210×associate-/r*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
050393
1132384
2347382
31144380
44906380
Stop Event
1×node limit
Counts
68 → 73
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))))
1
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 -1 (pow.f64 x 2)) (pow.f64 x 4)))
(+.f64 (*.f64 -1 (pow.f64 x 6)) (+.f64 1 (+.f64 (*.f64 -1 (pow.f64 x 2)) (pow.f64 x 4))))
(/.f64 1 (pow.f64 x 2))
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 4)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6))) (/.f64 1 (pow.f64 x 4)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 8))))
(/.f64 1 (pow.f64 x 2))
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 4)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6))) (/.f64 1 (pow.f64 x 4)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 8))))
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 (*.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 3)) (pow.f64 x 7)))
(-.f64 x (+.f64 (-.f64 (pow.f64 x 7) (pow.f64 x 5)) (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 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 1 (pow.f64 x 5)) (+.f64 (/.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 (/.f64 1 (pow.f64 x 5)) (-.f64 (/.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 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 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 1 (pow.f64 x 5)) (+.f64 (/.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 (/.f64 1 (pow.f64 x 5)) (-.f64 (/.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))))
1
(+.f64 1 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1 (neg.f64 (*.f64 x x)))
(-.f64 1 (*.f64 x x))
(neg.f64 (fma.f64 x x -1))
(+.f64 1 (+.f64 (*.f64 -1 (pow.f64 x 2)) (pow.f64 x 4)))
(+.f64 1 (fma.f64 -1 (*.f64 x x) (pow.f64 x 4)))
(+.f64 (-.f64 1 (*.f64 x x)) (pow.f64 x 4))
(fma.f64 (*.f64 x x) (fma.f64 x x -1) 1)
(-.f64 (pow.f64 x 4) (fma.f64 x x -1))
(+.f64 (*.f64 -1 (pow.f64 x 6)) (+.f64 1 (+.f64 (*.f64 -1 (pow.f64 x 2)) (pow.f64 x 4))))
(fma.f64 -1 (pow.f64 x 6) (+.f64 1 (fma.f64 -1 (*.f64 x x) (pow.f64 x 4))))
(-.f64 (+.f64 (-.f64 1 (*.f64 x x)) (pow.f64 x 4)) (pow.f64 x 6))
(fma.f64 (*.f64 x x) (fma.f64 x x -1) (-.f64 1 (pow.f64 x 6)))
(-.f64 (-.f64 (pow.f64 x 4) (fma.f64 x x -1)) (pow.f64 x 6))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 4)))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 4)))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 4)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6))) (/.f64 1 (pow.f64 x 4)))
(+.f64 (/.f64 1 (*.f64 x x)) (-.f64 (/.f64 1 (pow.f64 x 6)) (/.f64 1 (pow.f64 x 4))))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1 (pow.f64 x 6)) (/.f64 -1 (pow.f64 x 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 8))))
(-.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 6))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 8))))
(+.f64 (/.f64 1 (*.f64 x x)) (-.f64 (+.f64 (/.f64 1 (pow.f64 x 6)) (/.f64 -1 (pow.f64 x 4))) (/.f64 1 (pow.f64 x 8))))
(+.f64 (/.f64 1 (pow.f64 x 6)) (+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 -1 (pow.f64 x 4)) (/.f64 -1 (pow.f64 x 8)))))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1 (pow.f64 x 6)) (+.f64 (/.f64 -1 (pow.f64 x 4)) (/.f64 -1 (pow.f64 x 8)))))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 4)))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 4)))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 -1 (pow.f64 x 4)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6))) (/.f64 1 (pow.f64 x 4)))
(+.f64 (/.f64 1 (*.f64 x x)) (-.f64 (/.f64 1 (pow.f64 x 6)) (/.f64 1 (pow.f64 x 4))))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1 (pow.f64 x 6)) (/.f64 -1 (pow.f64 x 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 8))))
(-.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 6))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 8))))
(+.f64 (/.f64 1 (*.f64 x x)) (-.f64 (+.f64 (/.f64 1 (pow.f64 x 6)) (/.f64 -1 (pow.f64 x 4))) (/.f64 1 (pow.f64 x 8))))
(+.f64 (/.f64 1 (pow.f64 x 6)) (+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 -1 (pow.f64 x 4)) (/.f64 -1 (pow.f64 x 8)))))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1 (pow.f64 x 6)) (+.f64 (/.f64 -1 (pow.f64 x 4)) (/.f64 -1 (pow.f64 x 8)))))

eval21.0ms (0.8%)

Compiler

Compiled 829 to 584 computations (29.6% saved)

prune130.0ms (4.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New73073
Fresh011
Picked011
Done011
Total73376
Error
0b
Counts
76 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
✓14.8b
(*.f64 x (/.f64 1 (fma.f64 x x 1)))
✓14.7b
(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x 1))) (/.f64 x (sqrt.f64 (fma.f64 x x 1))))
▶32.4b
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))
Compiler

Compiled 57 to 43 computations (24.6% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x))
✓0.1b
(/.f64 1 (pow.f64 x 5))
✓0.3b
(/.f64 1 (pow.f64 x 3))
✓19.4b
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))

series5.0ms (0.2%)

Counts
4 → 9
Calls

12 calls:

TimeVariablePointExpression
1.0ms
x
@0
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))
1.0ms
x
@0
(/.f64 1 (pow.f64 x 3))
1.0ms
x
@0
(/.f64 1 (pow.f64 x 5))
0.0ms
x
@-inf
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))
0.0ms
x
@-inf
(/.f64 1 (pow.f64 x 3))

rewrite68.0ms (2.5%)

Algorithm
1×batch-egg-rewrite
Rules
330×fma-neg_binary64
226×expm1-udef_binary64
226×log1p-udef_binary64
144×add-sqr-sqrt_binary64
137×add-log-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01234
129434
2426534
Stop Event
1×node limit
Counts
4 → 164
Calls
Call 1
Inputs
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))
(/.f64 1 (pow.f64 x 3))
(/.f64 1 (pow.f64 x 5))
(+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -5) (-.f64 (/.f64 1 x) (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -5) (*.f64 (-.f64 (/.f64 1 x) (pow.f64 x -3)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 x) (-.f64 (pow.f64 x -5) (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 x) (+.f64 (pow.f64 x -5) (neg.f64 (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 x -5) (/.f64 1 x)) (neg.f64 (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 x -5) (/.f64 1 x)) (*.f64 (neg.f64 (pow.f64 x -3)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 x -5) (-.f64 (/.f64 1 x) (pow.f64 x -3))) (fma.f64 (neg.f64 (pow.f64 x -3)) 1 (pow.f64 x -3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 x -5) (-.f64 (/.f64 1 x) (pow.f64 x -3))) (fma.f64 (neg.f64 (/.f64 1 x)) (pow.f64 x -2) (pow.f64 x -3)))))) (#(struct:change 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(#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x -3) (pow.f64 x -15)) (/.f64 1 (+.f64 (pow.f64 x -10) (-.f64 (pow.f64 x -2) (pow.f64 x -6)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x -10) (pow.f64 x -2)) (/.f64 1 (-.f64 (pow.f64 x -5) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 x 6) (+.f64 x (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x -10) (-.f64 (pow.f64 x -2) (pow.f64 x -6))) (+.f64 (pow.f64 x -3) (pow.f64 x -15))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (pow.f64 x -5) (/.f64 1 x)) (-.f64 (pow.f64 x -10) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 x (pow.f64 x 5)) (pow.f64 x 6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x -3) (pow.f64 x -15)) (+.f64 (pow.f64 x -10) (-.f64 (pow.f64 x -2) (pow.f64 x -6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x -3) (pow.f64 x -15)) (+.f64 (pow.f64 x -2) (-.f64 (pow.f64 x -10) (pow.f64 x -6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -10) (pow.f64 x -2)) (-.f64 (pow.f64 x -5) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 x (pow.f64 x 5))) (neg.f64 (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x -3) (pow.f64 x -15))) (neg.f64 (+.f64 (pow.f64 x -10) (-.f64 (pow.f64 x -2) (pow.f64 x -6)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x -10) (pow.f64 x -2))) (neg.f64 (-.f64 (pow.f64 x -5) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (neg.f64 x) (*.f64 (neg.f64 (pow.f64 x 5)) 1)) (*.f64 (neg.f64 (pow.f64 x 5)) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (neg.f64 x) (*.f64 (pow.f64 x 5) -1)) (*.f64 (pow.f64 x 5) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 -1 (neg.f64 x)) (*.f64 (neg.f64 (pow.f64 x 5)) -1)) (*.f64 (neg.f64 (pow.f64 x 5)) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (neg.f64 (pow.f64 x 5)) (*.f64 (neg.f64 x) 1)) (*.f64 (neg.f64 x) (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (neg.f64 (pow.f64 x 5)) (*.f64 x -1)) (*.f64 x (neg.f64 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 -1 (neg.f64 (pow.f64 x 5))) (*.f64 (neg.f64 x) -1)) (*.f64 (neg.f64 x) (neg.f64 (pow.f64 x 5))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -2) (pow.f64 x -10)) (-.f64 (/.f64 1 x) (pow.f64 x -5)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 x (pow.f64 x 5)) (pow.f64 x 5)) x)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (pow.f64 x -5) (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (pow.f64 x -5) (/.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 (pow.f64 x -5/2) (pow.f64 x -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (pow.f64 x -5) (/.f64 1 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (pow.f64 x -5) (/.f64 1 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (pow.f64 x -5) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (pow.f64 x -5) (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (pow.f64 x -5) (/.f64 1 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (pow.f64 x -5) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (pow.f64 x -5) (/.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 x -5) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 x) (pow.f64 x -5))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -10)) (cbrt.f64 (pow.f64 x -5)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (/.f64 1 (cbrt.f64 x)) (pow.f64 x -5))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -5/2) (pow.f64 x -5/2) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (pow.f64 x -1/2) (pow.f64 x -5))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (pow.f64 x -5) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (pow.f64 x -5) (/.f64 1 x))))))))

simplify25.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
724×unswap-sqr_binary64
358×associate-/r*_binary64
319×associate-*l*_binary64
300×fma-def_binary64
265×distribute-neg-frac_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01272
12972
25372
311272
423572
567972
6270772
Stop Event
1×node limit
Counts
173 → 170
Calls
Call 1
Inputs
(/.f64 1 (pow.f64 x 5))
(-.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3)))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))
(/.f64 1 (pow.f64 x 5))
(/.f64 1 x)
(/.f64 1 x)
Outputs
(/.f64 1 (pow.f64 x 5))
(-.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 -1 (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 1 x)
(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 1 x) (/.f64 -1 (pow.f64 x 3)))
(/.f64 1 (pow.f64 x 5))
(/.f64 1 x)
(/.f64 1 x)

eval76.0ms (2.8%)

Compiler

Compiled 3214 to 2488 computations (22.6% saved)

prune258.0ms (9.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1700170
Fresh000
Picked011
Done022
Total1703173
Error
0b
Counts
173 → 3
Alt Table
Click to see full alt table
StatusErrorProgram
✓14.8b
(*.f64 x (/.f64 1 (fma.f64 x x 1)))
✓14.7b
(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x 1))) (/.f64 x (sqrt.f64 (fma.f64 x x 1))))
✓32.4b
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))
Compiler

Compiled 41 to 30 computations (26.8% saved)

regimes28.0ms (1.1%)

Accuracy

Total -47.2b remaining (-1208171.3%)

Threshold costs -47.2b (-1208171.3%)

Counts
6 → 3
Calls
Call 1
Inputs
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))
(*.f64 x (/.f64 1 (fma.f64 x x 1)))
(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x x 1))) (/.f64 x (sqrt.f64 (fma.f64 x x 1))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))
(/.f64 x (fma.f64 x x 1))
(/.f64 x (+.f64 (*.f64 x x) 1))
Outputs
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))
(*.f64 x (/.f64 1 (fma.f64 x x 1)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))
Results
TimeErrorSegmentsBranch
14.0ms0.0b3x
12.0ms0.0b3(/.f64 x (+.f64 (*.f64 x x) 1))
Compiler

Compiled 77 to 53 computations (31.2% saved)

bsearch31.0ms (1.2%)

Algorithm
2×binary-search
Steps
TimePointRange
16.0ms
1732693.7619002569
∈ [
1732693.7619002569
, 
5.0990461364359695e+23
]
15.0ms
-1.711991797943903e+38
∈ [
-1.711991797943903e+38
, 
-2.6673957442790206e+33
]
Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
3×+-commutative_binary64
2×*-commutative_binary64
2×sub-neg_binary64
1×distribute-neg-frac_binary64
1×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02267
12867
23467
33667
43767
Stop Event
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 x -171199179794390300770753655392142622720) (-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3))) (if (<=.f64 x 7441863041344814/4294967296) (*.f64 x (/.f64 1 (fma.f64 x x 1))) (-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))))
Outputs
(if (<=.f64 x -171199179794390300770753655392142622720) (-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3))) (if (<=.f64 x 7441863041344814/4294967296) (*.f64 x (/.f64 1 (fma.f64 x x 1))) (-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))))
(if (<=.f64 x -171199179794390300770753655392142622720) (-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3))) (if (<=.f64 x 3720931520672407/2147483648) (*.f64 x (/.f64 1 (fma.f64 x x 1))) (-.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 1 (pow.f64 x 3)))))
(if (<=.f64 x -171199179794390300770753655392142622720) (+.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 -1 (pow.f64 x 3))) (if (<=.f64 x 3720931520672407/2147483648) (*.f64 x (/.f64 1 (fma.f64 x x 1))) (+.f64 (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 x)) (/.f64 -1 (pow.f64 x 3)))))

end33.0ms (1.2%)

Stop Event
1×done
Compiler

Compiled 94 to 72 computations (23.4% saved)

Profiling

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