Details

Time bar (total: 2.1s)

analyze4.0ms (0.2%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
25%50%25%3
50%25%25%4
62.5%12.5%25%5
68.7%6.2%25%6
71.8%3.1%25%7
73.4%1.6%25%8
74.2%0.8%25%9
74.6%0.4%25%10
74.8%0.2%25%11
74.9%0.1%25%12
74.9%0%25%13
74.9%0%25%14
Compiler

Compiled 10 to 8 computations (20% saved)

sample811.0ms (39.4%)

Results
780.0ms8255×body128valid
0.0ms1×body2048valid

preprocess16.0ms (0.8%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0712
11112
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Outputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify12.0ms (0.6%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0712
11112
Stop Event
1×saturated
Counts
1 → 1
Calls
Call 1
Inputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Outputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.2b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (+.f64 x 1))
✓0.0b
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series8.0ms (0.4%)

Counts
3 → 12
Calls

9 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
2.0ms
x
@-inf
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
1.0ms
x
@0
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
1.0ms
x
@inf
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
1.0ms
x
@-inf
(+.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite67.0ms (3.3%)

Algorithm
1×batch-egg-rewrite
Rules
804×log1p-expm1-u_binary64
804×expm1-log1p-u_binary64
81×add-sqr-sqrt_binary64
78×*-un-lft-identity_binary64
78×pow1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0727
115727
2225827
Stop Event
1×node limit
Counts
3 → 93
Calls
Call 1
Inputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
(sqrt.f64 (+.f64 x 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (+.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (/.f64 x (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))) (/.f64 x (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))) (/.f64 (cbrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (neg.f64 x)) (-.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (+.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 x 1))) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) (-.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (neg.f64 (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 x)) (neg.f64 (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 x 1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (fma.f64 x x -1)) (sqrt.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/2 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 1))))))

simplify65.0ms (3.2%)

Algorithm
1×egg-herbie
Rules
803×unswap-sqr_binary64
571×distribute-lft-out_binary64
504×fma-def_binary64
342×*-commutative_binary64
197×distribute-rgt-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
033136
192132
2210130
3600109
41607109
52603109
64582109
74725109
84989109
Stop Event
1×node limit
Counts
105 → 114
Calls
Call 1
Inputs
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -5/128 (pow.f64 x 4)) (*.f64 1/16 (pow.f64 x 3)))))
2
(+.f64 (*.f64 1/2 x) 2)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 2 (*.f64 1/16 (pow.f64 x 3)))))
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
Outputs
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(fma.f64 1/2 x (*.f64 -1/8 (*.f64 x x)))
(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x 1/16))))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -5/128 (pow.f64 x 4)) (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 -5/128 (pow.f64 x 4) (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) (*.f64 -5/128 (pow.f64 x 4)))))
(fma.f64 x (*.f64 x -1/8) (fma.f64 -5/128 (pow.f64 x 4) (fma.f64 1/16 (pow.f64 x 3) (*.f64 1/2 x))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (+.f64 1/16 (*.f64 x -5/128))))
2
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 2)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 2))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x 2))
(fma.f64 1/2 x (fma.f64 x (*.f64 x -1/8) 2))
(fma.f64 x (fma.f64 x -1/8 1/2) 2)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 2 (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (+.f64 (fma.f64 1/2 x 2) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 2)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x -1/8) (fma.f64 1/16 (pow.f64 x 3) 2)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)) 2))
(fma.f64 1/2 x (fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) 2))
(fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) (fma.f64 1/2 x 2))
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x -1/8) 1))
(fma.f64 x (fma.f64 x -1/8 1/2) 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (+.f64 (fma.f64 1/2 x 1) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x -1/8) (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) 1))

prune129.0ms (6.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1104114
Fresh000
Picked101
Done000
Total1114115
Error
0b
Counts
115 → 4
Alt Table
StatusErrorProgram
6.2b
(*.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))))
22.7b
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
▶0.2b
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
19.2b
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
Compiler

Compiled 1578 to 1235 computations (21.7% saved)

localize6.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
✓0.1b
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓0.1b
(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series4.0ms (0.2%)

Counts
2 → 8
Calls

6 calls:

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

rewrite47.0ms (2.3%)

Algorithm
1×batch-egg-rewrite
Rules
853×log1p-expm1-u_binary64
853×expm1-log1p-u_binary64
90×add-sqr-sqrt_binary64
86×*-un-lft-identity_binary64
86×pow1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0824
117924
2244824
Stop Event
1×node limit
Counts
2 → 51
Calls
Call 1
Inputs
(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))) (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -2)) (/.f64 1 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -1/2) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2) -1) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) -1) (pow.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (pow.f64 (+.f64 1 x) 3/2))) (+.f64 1 (+.f64 1 (-.f64 x (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 0 x)) (-.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 x) 2) (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 x) (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4))) (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2)) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 x) (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x -1) (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 1 x)))) 1))))))

simplify50.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
803×unswap-sqr_binary64
504×distribute-lft-out_binary64
434×fma-def_binary64
369×*-commutative_binary64
209×distribute-rgt-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03099
18195
219688
357074
4151674
5243774
6445374
7460174
8489574
Stop Event
1×node limit
Counts
59 → 65
Calls
Call 1
Inputs
1/2
(+.f64 (*.f64 -1/8 x) 1/2)
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 1/16 (pow.f64 x 2))))
(+.f64 (*.f64 -1/8 x) (+.f64 (*.f64 -5/128 (pow.f64 x 3)) (+.f64 1/2 (*.f64 1/16 (pow.f64 x 2)))))
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -5/128 (pow.f64 x 4)) (*.f64 1/16 (pow.f64 x 3)))))
Outputs
1/2
(+.f64 (*.f64 -1/8 x) 1/2)
(fma.f64 -1/8 x 1/2)
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 1/16 (pow.f64 x 2))))
(+.f64 (fma.f64 -1/8 x 1/2) (*.f64 1/16 (*.f64 x x)))
(fma.f64 -1/8 x (fma.f64 1/16 (*.f64 x x) 1/2))
(fma.f64 x (*.f64 x 1/16) (fma.f64 -1/8 x 1/2))
(fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)
(+.f64 (*.f64 -1/8 x) (+.f64 (*.f64 -5/128 (pow.f64 x 3)) (+.f64 1/2 (*.f64 1/16 (pow.f64 x 2)))))
(fma.f64 -1/8 x (fma.f64 -5/128 (pow.f64 x 3) (+.f64 1/2 (*.f64 1/16 (*.f64 x x)))))
(fma.f64 -1/8 x (fma.f64 -5/128 (pow.f64 x 3) (fma.f64 1/16 (*.f64 x x) 1/2)))
(fma.f64 -1/8 x (fma.f64 x (*.f64 x 1/16) (fma.f64 -5/128 (pow.f64 x 3) 1/2)))
(fma.f64 -1/8 x (fma.f64 x (*.f64 x (fma.f64 x -5/128 1/16)) 1/2))
(fma.f64 x (fma.f64 x 1/16 -1/8) (fma.f64 -5/128 (pow.f64 x 3) 1/2))
(fma.f64 -1/8 x (fma.f64 (*.f64 x x) (fma.f64 x -5/128 1/16) 1/2))
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(fma.f64 1/2 x (*.f64 x (*.f64 -1/8 x)))
(*.f64 x (fma.f64 -1/8 x 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 1/16 (pow.f64 x 3) (*.f64 x (fma.f64 -1/8 x 1/2)))
(*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -5/128 (pow.f64 x 4)) (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 -5/128 (pow.f64 x 4) (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) (*.f64 -5/128 (pow.f64 x 4)))))
(+.f64 (fma.f64 -5/128 (pow.f64 x 4) (*.f64 1/16 (pow.f64 x 3))) (*.f64 x (fma.f64 -1/8 x 1/2)))
(fma.f64 x (fma.f64 -1/8 x 1/2) (*.f64 (pow.f64 x 3) (fma.f64 x -5/128 1/16)))
(*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) (fma.f64 -5/128 (pow.f64 x 3) 1/2)))
(*.f64 x (fma.f64 -1/8 x (fma.f64 (*.f64 x x) (fma.f64 x -5/128 1/16) 1/2)))

prune184.0ms (9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1361137
Fresh123
Picked011
Done000
Total1374141
Error
0b
Counts
141 → 4
Alt Table
StatusErrorProgram
▶6.2b
(*.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))))
22.7b
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
18.9b
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
✓0.2b
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
Compiler

Compiled 1967 to 1588 computations (19.3% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.1b
(*.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))))
✓6.0b
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))

series20.0ms (1%)

Counts
3 → 24
Calls

9 calls:

TimeVariablePointExpression
7.0ms
x
@-inf
(*.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))))
4.0ms
x
@inf
(*.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))))
3.0ms
x
@-inf
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))
3.0ms
x
@inf
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))
1.0ms
x
@0
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))

rewrite72.0ms (3.5%)

Algorithm
1×batch-egg-rewrite
Rules
236×expm1-udef_binary64
236×log1p-udef_binary64
150×add-sqr-sqrt_binary64
144×pow1_binary64
143×*-un-lft-identity_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01258
128852
2436052
Stop Event
1×node limit
Counts
3 → 124
Calls
Call 1
Inputs
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))
(*.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))))
(-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))
Outputs
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(+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (+.f64 x 2) 3) (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (+.f64 (pow.f64 (+.f64 x 2) 2) (+.f64 x (+.f64 1 (*.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1))))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (+.f64 x 2) 2) (+.f64 x 1)) (/.f64 1 (+.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 x 2)) (pow.f64 (+.f64 x 1) 1/4)) (-.f64 (sqrt.f64 (+.f64 x 2)) (pow.f64 (+.f64 x 1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 x 2) 2) (+.f64 x (+.f64 1 (*.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1)))))) (-.f64 (pow.f64 (+.f64 x 2) 3) (pow.f64 (+.f64 x 1) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1))) (-.f64 (pow.f64 (+.f64 x 2) 2) (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x 2) 3) (pow.f64 (+.f64 x 1) 3/2)) (+.f64 (pow.f64 (+.f64 x 2) 2) (+.f64 x (+.f64 1 (*.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x 2) 2) (+.f64 x 1)) (+.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 x 2) 3) (pow.f64 (+.f64 x 1) 3/2))) (neg.f64 (+.f64 (pow.f64 (+.f64 x 2) 2) (+.f64 x (+.f64 1 (*.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 x 2) 2) (+.f64 x 1))) (neg.f64 (+.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (-.f64 (+.f64 x 1) (sqrt.f64 (+.f64 x 1))) 3)) (+.f64 1 (-.f64 (*.f64 (-.f64 (+.f64 x 1) (sqrt.f64 (+.f64 x 1))) (-.f64 (+.f64 x 1) (sqrt.f64 (+.f64 x 1)))) (-.f64 (+.f64 x 1) (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x 2) 3) (pow.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) 3)) (+.f64 (pow.f64 (+.f64 x 2) 2) (-.f64 (*.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 (+.f64 x 1)))) (*.f64 (+.f64 x 2) (neg.f64 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (-.f64 (+.f64 x 1) (sqrt.f64 (+.f64 x 1))) (-.f64 (+.f64 x 1) (sqrt.f64 (+.f64 x 1))))) (-.f64 1 (-.f64 (+.f64 x 1) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x 2) 2) (*.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 (+.f64 x 1))))) (-.f64 (+.f64 x 2) (neg.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 x 2) (neg.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x 2)) 2) (cbrt.f64 (+.f64 x 2)) (neg.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x 2)) (sqrt.f64 (+.f64 x 2)) (neg.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 (+.f64 x 2) (sqrt.f64 (+.f64 x 1)))) 1))))))

simplify37.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
622×fma-def_binary64
399×times-frac_binary64
284×associate-/l*_binary64
260×associate-*r*_binary64
247×associate-/r*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01291211
13791151
21242967
Stop Event
1×node limit
Counts
148 → 165
Calls
Call 1
Inputs
(*.f64 1/2 x)
(+.f64 (*.f64 1/2 x) (*.f64 -3/8 (pow.f64 x 2)))
(+.f64 (*.f64 3/16 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (*.f64 -3/8 (pow.f64 x 2))))
(+.f64 (*.f64 3/16 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -3/8 (pow.f64 x 2)) (*.f64 -7/128 (pow.f64 x 4)))))
(/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1))
(+.f64 (*.f64 -3/2 (*.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 2)) (sqrt.f64 (pow.f64 x 3)))) (/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1)))
(-.f64 (+.f64 (*.f64 -3/2 (*.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 2)) (sqrt.f64 (pow.f64 x 3)))) (+.f64 (*.f64 9/4 (/.f64 (pow.f64 x 2) (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 3))) (/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1)))) (*.f64 3/8 (*.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 2)) (sqrt.f64 x))))
(-.f64 (+.f64 (*.f64 -3/2 (*.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 2)) (sqrt.f64 (pow.f64 x 3)))) (+.f64 (*.f64 9/4 (/.f64 (pow.f64 x 2) (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 3))) (+.f64 (*.f64 9/16 (/.f64 x (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 3))) (/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1))))) (+.f64 (*.f64 3/8 (*.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 2)) (sqrt.f64 x))) (+.f64 (*.f64 -1/16 (*.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 2)) (sqrt.f64 (/.f64 1 x)))) (*.f64 3/2 (*.f64 (/.f64 (-.f64 (*.f64 9/4 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 3))) (*.f64 3/8 (*.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 2)) (sqrt.f64 (pow.f64 x 3))))) (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1)) (sqrt.f64 (/.f64 1 x)))))))
(/.f64 x (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
(+.f64 (*.f64 -3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 2))) (/.f64 x (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))
(+.f64 (*.f64 -3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 2) x))) (+.f64 (*.f64 9/4 (/.f64 (pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (*.f64 (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 3) x))) (+.f64 (*.f64 -3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 2))) (/.f64 x (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))))
(+.f64 (*.f64 9/4 (/.f64 (pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (*.f64 (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 3) x))) (+.f64 (*.f64 -3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 2) x))) (+.f64 (*.f64 -3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 2))) (+.f64 (/.f64 x (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 -1 (/.f64 (+.f64 (*.f64 -9/16 (/.f64 (pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 3))) (+.f64 (*.f64 -1/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 2))) (*.f64 3/2 (/.f64 (*.f64 (+.f64 (*.f64 -3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 2))) (*.f64 9/4 (/.f64 (pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 3)))) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))))) (pow.f64 x 2)))))))
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -5/128 (pow.f64 x 4)) (*.f64 1/16 (pow.f64 x 3)))))
(/.f64 (pow.f64 x 2) (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1))
(/.f64 (pow.f64 x 2) (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -1/16 (pow.f64 x 3)) 1)))
x
x
Outputs
(*.f64 1/2 x)
(+.f64 (*.f64 1/2 x) (*.f64 -3/8 (pow.f64 x 2)))
(fma.f64 1/2 x (*.f64 -3/8 (*.f64 x x)))
(fma.f64 -3/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 (*.f64 x -3/8) 1/2))
(+.f64 (*.f64 3/16 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (*.f64 -3/8 (pow.f64 x 2))))
(fma.f64 3/16 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 -3/8 (*.f64 x x))))
(fma.f64 3/16 (pow.f64 x 3) (fma.f64 -3/8 (*.f64 x x) (*.f64 1/2 x)))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 -3/8 (*.f64 3/16 x))))
(+.f64 (*.f64 3/16 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -3/8 (pow.f64 x 2)) (*.f64 -7/128 (pow.f64 x 4)))))
(fma.f64 3/16 (pow.f64 x 3) (fma.f64 1/2 x (fma.f64 -3/8 (*.f64 x x) (*.f64 -7/128 (pow.f64 x 4)))))
(fma.f64 3/16 (pow.f64 x 3) (fma.f64 1/2 x (fma.f64 -7/128 (pow.f64 x 4) (*.f64 x (*.f64 x -3/8)))))
(fma.f64 3/16 (pow.f64 x 3) (fma.f64 -7/128 (pow.f64 x 4) (*.f64 x (+.f64 (*.f64 x -3/8) 1/2))))
(/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1))
(/.f64 x (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)))
(+.f64 (*.f64 -3/2 (*.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 2)) (sqrt.f64 (pow.f64 x 3)))) (/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1)))
(fma.f64 -3/2 (/.f64 (*.f64 1 (sqrt.f64 (pow.f64 x 3))) (pow.f64 (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)) 2)) (/.f64 x (+.f64 1 (pow.f64 (/.f64 1 x) -3/2))))
(fma.f64 -3/2 (/.f64 (sqrt.f64 (pow.f64 x 3)) (pow.f64 (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)) 2)) (/.f64 x (+.f64 1 (pow.f64 (/.f64 1 x) -3/2))))
(fma.f64 -3/2 (/.f64 (pow.f64 x 3/2) (pow.f64 (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)) 2)) (/.f64 x (+.f64 1 (pow.f64 (/.f64 1 x) -3/2))))
(-.f64 (+.f64 (*.f64 -3/2 (*.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 2)) (sqrt.f64 (pow.f64 x 3)))) (+.f64 (*.f64 9/4 (/.f64 (pow.f64 x 2) (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 3))) (/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1)))) (*.f64 3/8 (*.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 2)) (sqrt.f64 x))))
(+.f64 (fma.f64 -3/2 (/.f64 (*.f64 1 (sqrt.f64 (pow.f64 x 3))) (pow.f64 (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)) 2)) (fma.f64 9/4 (/.f64 (*.f64 x x) (pow.f64 (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)) 3)) (/.f64 x (+.f64 1 (pow.f64 (/.f64 1 x) -3/2))))) (*.f64 -3/8 (/.f64 (*.f64 1 (sqrt.f64 x)) (pow.f64 (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)) 2))))
(+.f64 (fma.f64 -3/2 (/.f64 (sqrt.f64 (pow.f64 x 3)) (pow.f64 (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)) 2)) (fma.f64 9/4 (/.f64 x (/.f64 (pow.f64 (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)) 3) x)) (/.f64 x (+.f64 1 (pow.f64 (/.f64 1 x) -3/2))))) (*.f64 -3/8 (/.f64 (sqrt.f64 x) (pow.f64 (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)) 2))))
(+.f64 (fma.f64 9/4 (/.f64 x (/.f64 (pow.f64 (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)) 3) x)) (/.f64 x (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)))) (*.f64 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)) 2)) (-.f64 (*.f64 -3/2 (pow.f64 x 3/2)) (*.f64 3/8 (sqrt.f64 x)))))
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(+.f64 (fma.f64 9/4 (/.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) 2) (*.f64 x (pow.f64 (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) 1) 3))) (*.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) (pow.f64 (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) 1) 2)) (+.f64 -3/2 (/.f64 -3/8 x)))) (-.f64 (/.f64 x (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) 1)) (/.f64 (fma.f64 -1/16 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) (pow.f64 (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) 1) 2)) (fma.f64 3/2 (*.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) 1)) (fma.f64 -3/8 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) (pow.f64 (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) 1) 2)) (*.f64 9/4 (/.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) 2) (pow.f64 (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) 1) 3))))) (*.f64 -9/16 (/.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) 2) (pow.f64 (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) 1) 3))))) (*.f64 x x))))
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(fma.f64 1/2 x (*.f64 (*.f64 -1/8 x) x))
(*.f64 x (+.f64 1/2 (*.f64 -1/8 x)))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 (pow.f64 x 3) 1/16)))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 (pow.f64 x 3) 1/16 (*.f64 1/2 x)))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 (*.f64 1/16 x) -1/8)))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -5/128 (pow.f64 x 4)) (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 -5/128 (pow.f64 x 4) (*.f64 (pow.f64 x 3) 1/16))))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/2 x (fma.f64 (pow.f64 x 4) -5/128 (*.f64 (pow.f64 x 3) 1/16))))
(fma.f64 1/2 x (fma.f64 x (*.f64 x -1/8) (fma.f64 (pow.f64 x 3) 1/16 (*.f64 (pow.f64 x 4) -5/128))))
(/.f64 (pow.f64 x 2) (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1))
(/.f64 (*.f64 x x) (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)))
(/.f64 x (/.f64 (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)) x))
(*.f64 (/.f64 x (+.f64 1 (pow.f64 (/.f64 1 x) -3/2))) x)
(/.f64 (pow.f64 x 2) (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
(/.f64 (*.f64 x x) (+.f64 1 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))
(/.f64 x (/.f64 (+.f64 1 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x))
(*.f64 (/.f64 x (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) 1)) x)
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x 1))
(fma.f64 (*.f64 x x) 1/8 (fma.f64 1/2 x 1))
(fma.f64 x (*.f64 x 1/8) (fma.f64 1/2 x 1))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -1/16 (pow.f64 x 3)) 1)))
(fma.f64 1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 -1/16 (pow.f64 x 3) 1)))
(fma.f64 (*.f64 x x) 1/8 (fma.f64 1/2 x (fma.f64 (pow.f64 x 3) -1/16 1)))
(fma.f64 x (*.f64 x 1/8) (fma.f64 1/2 x (fma.f64 (pow.f64 x 3) -1/16 1)))
x
x

prune260.0ms (12.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1971198
Fresh112
Picked011
Done011
Total1984202
Error
0b
Counts
202 → 4
Alt Table
StatusErrorProgram
✓6.2b
(*.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))))
22.7b
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓0.2b
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
▶18.9b
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 (*.f64 1/16 x) -1/8)))
Compiler

Compiled 6052 to 4953 computations (18.2% saved)

localize7.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(*.f64 (*.f64 x x) (+.f64 (*.f64 1/16 x) -1/8))

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
(*.f64 (*.f64 x x) (+.f64 (*.f64 1/16 x) -1/8))
1.0ms
x
@inf
(*.f64 (*.f64 x x) (+.f64 (*.f64 1/16 x) -1/8))
1.0ms
x
@-inf
(*.f64 (*.f64 x x) (+.f64 (*.f64 1/16 x) -1/8))

rewrite43.0ms (2.1%)

Algorithm
1×batch-egg-rewrite
Rules
834×log1p-expm1-u_binary64
834×expm1-log1p-u_binary64
88×add-sqr-sqrt_binary64
86×add-exp-log_binary64
86×add-log-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
118211
2233111
Stop Event
1×node limit
Counts
1 → 26
Calls
Call 1
Inputs
(*.f64 (*.f64 x x) (+.f64 (*.f64 1/16 x) -1/8))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 x (*.f64 x -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x -1/8)) (*.f64 1/16 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 1/16 (pow.f64 x 3)) 1) (*.f64 (*.f64 x (*.f64 x -1/8)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 1/16 (pow.f64 x 3)) 3) (pow.f64 (*.f64 x (*.f64 x -1/8)) 3)) (+.f64 (*.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/16 (pow.f64 x 3))) (-.f64 (*.f64 (*.f64 x (*.f64 x -1/8)) (*.f64 x (*.f64 x -1/8))) (*.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 x (*.f64 x -1/8))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/16 (pow.f64 x 3))) (*.f64 (*.f64 x (*.f64 x -1/8)) (*.f64 x (*.f64 x -1/8)))) (-.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 x (*.f64 x -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 -1/512 (*.f64 (pow.f64 x 3) 1/4096)) (*.f64 x x)) (+.f64 (*.f64 (*.f64 x x) 1/256) (-.f64 1/64 (*.f64 x -1/128))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (*.f64 (*.f64 x x) 1/256) -1/64) (*.f64 x x)) (fma.f64 x 1/16 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 x x) (+.f64 -1/512 (*.f64 (pow.f64 x 3) 1/4096))) (+.f64 (*.f64 (*.f64 x x) 1/256) (-.f64 1/64 (*.f64 x -1/128))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 x x) 1/256) -1/64)) (fma.f64 x 1/16 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 (fma.f64 x 1/16 -1/8))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 4) (pow.f64 (fma.f64 x 1/16 -1/8) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 x x) 3) (pow.f64 (fma.f64 x 1/16 -1/8) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (fma.f64 x 1/16 -1/8) 3) (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) (*.f64 x 1/16) (*.f64 x (*.f64 x -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x 1/16) (*.f64 x x) (*.f64 x (*.f64 x -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))) 1))))))

simplify57.0ms (2.8%)

Algorithm
1×egg-herbie
Rules
536×unswap-sqr_binary64
490×fma-def_binary64
448×associate-*l*_binary64
378×sqr-pow_binary64
365×*-commutative_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
011147
127147
259138
3155120
4393120
51542120
63299120
73655120
83905120
94192120
104571120
Stop Event
1×node limit
Counts
38 → 31
Calls
Call 1
Inputs
(*.f64 -1/8 (pow.f64 x 2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(*.f64 1/16 (pow.f64 x 3))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(*.f64 1/16 (pow.f64 x 3))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
Outputs
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (*.f64 x x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 1/16 (pow.f64 x 3) (*.f64 -1/8 (*.f64 x x)))
(*.f64 (*.f64 x x) (+.f64 (*.f64 x 1/16) -1/8))
(*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))
(*.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 1/16 (pow.f64 x 3) (*.f64 -1/8 (*.f64 x x)))
(*.f64 (*.f64 x x) (+.f64 (*.f64 x 1/16) -1/8))
(*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))
(*.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 1/16 (pow.f64 x 3) (*.f64 -1/8 (*.f64 x x)))
(*.f64 (*.f64 x x) (+.f64 (*.f64 x 1/16) -1/8))
(*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))
(*.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8))
(*.f64 1/16 (pow.f64 x 3))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 1/16 (pow.f64 x 3) (*.f64 -1/8 (*.f64 x x)))
(*.f64 (*.f64 x x) (+.f64 (*.f64 x 1/16) -1/8))
(*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))
(*.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 1/16 (pow.f64 x 3) (*.f64 -1/8 (*.f64 x x)))
(*.f64 (*.f64 x x) (+.f64 (*.f64 x 1/16) -1/8))
(*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))
(*.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 1/16 (pow.f64 x 3) (*.f64 -1/8 (*.f64 x x)))
(*.f64 (*.f64 x x) (+.f64 (*.f64 x 1/16) -1/8))
(*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))
(*.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8))
(*.f64 1/16 (pow.f64 x 3))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 1/16 (pow.f64 x 3) (*.f64 -1/8 (*.f64 x x)))
(*.f64 (*.f64 x x) (+.f64 (*.f64 x 1/16) -1/8))
(*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))
(*.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 1/16 (pow.f64 x 3) (*.f64 -1/8 (*.f64 x x)))
(*.f64 (*.f64 x x) (+.f64 (*.f64 x 1/16) -1/8))
(*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))
(*.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 1/16 (pow.f64 x 3) (*.f64 -1/8 (*.f64 x x)))
(*.f64 (*.f64 x x) (+.f64 (*.f64 x 1/16) -1/8))
(*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))
(*.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8))

prune32.0ms (1.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New31031
Fresh011
Picked011
Done022
Total31435
Error
0b
Counts
35 → 4
Alt Table
StatusErrorProgram
✓6.2b
(*.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))))
22.7b
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓0.2b
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓18.9b
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 (*.f64 1/16 x) -1/8)))
Compiler

Compiled 579 to 407 computations (29.7% saved)

regimes87.0ms (4.2%)

Accuracy

Total -62.4b remaining (-39960.3%)

Threshold costs -62.4b (-39960.3%)

Counts
45 → 1
Compiler

Compiled 538 to 405 computations (24.7% saved)

simplify2.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0815
11315
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
Outputs
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

end17.0ms (0.8%)

Stop Event
1×fuel
Compiler

Compiled 22 to 18 computations (18.2% saved)

Profiling

Loading profile data...