Details

Time bar (total: 3.8s)

analyze3.0ms (0.1%)

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
Compiler

Compiled 10 to 8 computations (20% saved)

sample939.0ms (24.8%)

Results
920.0ms8247×body256valid
3.0ms9×body2048valid
0.0ms1×body256invalid

preprocess18.0ms (0.5%)

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 10 to 8 computations (20% saved)

simplify7.0ms (0.2%)

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))))

eval1.0ms (0%)

Compiler

Compiled 9 to 7 computations (22.2% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Compiled 9 to 7 computations (22.2% saved)

localize42.0ms (1.1%)

Local error

Found 6 expressions with local error:

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

Compiled 24 to 18 computations (25% saved)

series8.0ms (0.2%)

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
(sqrt.f64 (+.f64 x 1))
1.0ms
x
@inf
(sqrt.f64 (+.f64 x 1))

rewrite66.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
859×pow1_binary64
804×log1p-expm1-u_binary64
804×expm1-log1p-u_binary64
803×add-log-exp_binary64
786×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0727
115727
2225827
Stop Event
1×node limit
Counts
3 → 86
Calls
Call 1
Inputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(sqrt.f64 (+.f64 x 1))
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.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 (neg.f64 (+.f64 1 (sqrt.f64 (+.f64 x 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 1 (+.f64 1 (-.f64 x (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 (neg.f64 (+.f64 1 (sqrt.f64 (+.f64 x 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 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 exp.f64 (-.f64 (log.f64 x) (log1p.f64 (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 -.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 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 exp.f64 (*.f64 (log1p.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.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 1 (+.f64 1 (-.f64 x (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 1 (+.f64 1 (-.f64 x (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 1 (+.f64 1 (-.f64 x (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 1 (+.f64 1 (-.f64 x (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 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 exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))

simplify92.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
803×unswap-sqr_binary64
633×*-commutative_binary64
601×distribute-lft-out_binary64
506×sqr-pow_binary64
504×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
033136
192132
2210130
3601109
41607109
52610109
64589109
74732109
84996109
95367109
106108109
117118109
127661109
Stop Event
1×node limit
Counts
98 → 107
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)))))
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)))))
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)))))
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 1/2 x (fma.f64 x (*.f64 x -1/8) (fma.f64 1/16 (pow.f64 x 3) (*.f64 -5/128 (pow.f64 x 4)))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (+.f64 (*.f64 x -5/128) 1/16)))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (+.f64 1/16 (*.f64 x -5/128))))
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 -1/8 (*.f64 x x) 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 x (*.f64 x -1/8) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 x (fma.f64 x -1/8 1/2) (fma.f64 1/16 (pow.f64 x 3) 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)) 1))
(fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) (fma.f64 1/2 x 1))
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 x (fma.f64 x -1/8 1/2) (fma.f64 1/16 (pow.f64 x 3) 2))
(fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) (fma.f64 1/2 x 2))
(fma.f64 1/2 x (fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) 2))

eval36.0ms (1%)

Compiler

Compiled 1387 to 1085 computations (21.8% saved)

prune21.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1025107
Fresh000
Picked011
Done000
Total1026108
Error
0b
Counts
108 → 6
Alt Table
Click to see full alt table
StatusErrorProgram
▶20.6b
(*.f64 1/2 x)
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
▶39.1b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
▶20.2b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
▶0.2b
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)
▶0.3b
(pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)
Compiler

Compiled 99 to 77 computations (22.2% saved)

localize17.0ms (0.4%)

Local error

Found 8 expressions with local error:

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

Compiled 34 to 27 computations (20.6% saved)

series4.0ms (0.1%)

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

rewrite88.0ms (2.3%)

Algorithm
1×batch-egg-rewrite
Rules
914×pow1_binary64
853×log1p-expm1-u_binary64
853×expm1-log1p-u_binary64
852×add-log-exp_binary64
834×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0824
117824
2243224
Stop Event
1×node limit
Counts
2 → 46
Calls
Call 1
Inputs
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)
(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.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 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 exp.f64 (-.f64 (log.f64 x) (log1p.f64 (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 -.f64 (+.f64 1 (/.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 (cbrt.f64 (/.f64 1 (+.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)) (cbrt.f64 (/.f64 1 (+.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 x (-.f64 1 (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 (cbrt.f64 (/.f64 1 (+.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 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 exp.f64 (neg.f64 (log1p.f64 (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))))))))))

simplify92.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
803×unswap-sqr_binary64
639×*-commutative_binary64
549×distribute-lft-out_binary64
505×sqr-pow_binary64
459×associate-+l+_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03099
18195
219688
356974
4150974
5241574
6443574
7458374
8487774
9526774
10614674
11705474
12764174
Stop Event
1×node limit
Counts
54 → 60
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)))))
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)))))
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 (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 1/16 (pow.f64 x 3) (*.f64 x (fma.f64 x -1/8 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 1/16 (pow.f64 x 3) (*.f64 -5/128 (pow.f64 x 4))) (*.f64 x (fma.f64 x -1/8 1/2)))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (fma.f64 x -5/128 1/16)))
(*.f64 x (fma.f64 x -1/8 (fma.f64 (*.f64 x x) (fma.f64 x -5/128 1/16) 1/2)))
1/2
(+.f64 (*.f64 -1/8 x) 1/2)
(fma.f64 -1/8 x 1/2)
(fma.f64 x -1/8 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 (*.f64 x x) 1/16))
(fma.f64 x -1/8 (fma.f64 (*.f64 x x) 1/16 1/2))
(fma.f64 x -1/8 (fma.f64 x (*.f64 x 1/16) 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 (*.f64 x x) 1/16))))
(fma.f64 x -1/8 (fma.f64 (pow.f64 x 3) -5/128 (fma.f64 (*.f64 x x) 1/16 1/2)))
(fma.f64 x -1/8 (fma.f64 x (*.f64 x 1/16) (fma.f64 (pow.f64 x 3) -5/128 1/2)))
(fma.f64 x -1/8 (fma.f64 (*.f64 x x) (fma.f64 x -5/128 1/16) 1/2))

localize3.0ms (0.1%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
✓0.0b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
Compiler

Compiled 19 to 14 computations (26.3% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
0.0ms
x
@inf
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
0.0ms
x
@-inf
(/.f64 x (+.f64 (*.f64 1/2 x) 2))

rewrite60.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
831×pow1_binary64
780×add-log-exp_binary64
779×log1p-expm1-u_binary64
779×expm1-log1p-u_binary64
767×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
11598
220688
Stop Event
1×node limit
Counts
1 → 33
Calls
Call 1
Inputs
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 x (fma.f64 x 1/2 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (fma.f64 x 1/2 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (fma.f64 x 1/2 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (fma.f64 x 1/2 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (fma.f64 x 1/2 2))) (pow.f64 (cbrt.f64 (/.f64 x (fma.f64 x 1/2 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (fma.f64 x 1/2 2))) 2) (cbrt.f64 (/.f64 x (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (fma.f64 x 1/2 2))) (sqrt.f64 (/.f64 x (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 x 1/2 2)) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (fma.f64 x 1/2 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (fma.f64 x 1/2 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 2)) 2)) (/.f64 x (cbrt.f64 (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (fma.f64 x 1/2 2)) 2)) (cbrt.f64 (/.f64 x (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (fma.f64 x 1/2 2)) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (fma.f64 x 1/2 2))) (/.f64 x (sqrt.f64 (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (fma.f64 x 1/2 2))) (/.f64 (cbrt.f64 x) (sqrt.f64 (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 8 (*.f64 1/8 (pow.f64 x 3)))) (+.f64 (*.f64 1/4 (*.f64 x x)) (-.f64 4 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 (*.f64 1/4 (*.f64 x x)) -4)) (fma.f64 x 1/2 -2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (fma.f64 x 1/2 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (fma.f64 x 1/2 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (fma.f64 x 1/2 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (fma.f64 x 1/2 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 x 1/2 2) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (fma.f64 x 1/2 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (fma.f64 x 1/2 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x 1/2 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (fma.f64 x 1/2 2))))))))

simplify39.0ms (1%)

Algorithm
1×egg-herbie
Rules
805×unswap-sqr_binary64
711×distribute-neg-frac_binary64
516×associate-/r*_binary64
369×fma-def_binary64
334×times-frac_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
037156
199156
2239154
3683145
42126145
55892145
Stop Event
1×node limit
Counts
45 → 47
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 1/32 (pow.f64 x 3)) (*.f64 1/2 x)))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/32 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (*.f64 -1/128 (pow.f64 x 4)))))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (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 x (*.f64 x -1/8)))
(*.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 1/32 (pow.f64 x 3)) (*.f64 1/2 x)))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/32 (pow.f64 x 3) (*.f64 1/2 x)))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/32 (pow.f64 x 3))))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x 1/32))))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/32 -1/8))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/32 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (*.f64 -1/128 (pow.f64 x 4)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/32 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 -1/128 (pow.f64 x 4)))))
(fma.f64 x (*.f64 x -1/8) (fma.f64 1/32 (pow.f64 x 3) (fma.f64 -1/128 (pow.f64 x 4) (*.f64 1/2 x))))
(fma.f64 -1/128 (pow.f64 x 4) (*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/32 -1/8)))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (+.f64 1/32 (*.f64 x -1/128))))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 2 (/.f64 8 x))
(+.f64 2 (/.f64 -8 x))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x)))
(+.f64 2 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)))
(+.f64 2 (+.f64 (/.f64 (/.f64 32 x) x) (/.f64 -8 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 2 (/.f64 32 (*.f64 x x))) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3))))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)) (/.f64 128 (pow.f64 x 3))))
(+.f64 (+.f64 2 (/.f64 -8 x)) (+.f64 (/.f64 (/.f64 32 x) x) (/.f64 -128 (pow.f64 x 3))))
(+.f64 (+.f64 2 (/.f64 -8 x)) (*.f64 (/.f64 1 (*.f64 x x)) (-.f64 32 (/.f64 128 x))))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 2 (+.f64 (/.f64 -8 x) (/.f64 -128 (pow.f64 x 3)))))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 2 (/.f64 8 x))
(+.f64 2 (/.f64 -8 x))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x)))
(+.f64 2 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)))
(+.f64 2 (+.f64 (/.f64 (/.f64 32 x) x) (/.f64 -8 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 2 (/.f64 32 (*.f64 x x))) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3))))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)) (/.f64 128 (pow.f64 x 3))))
(+.f64 (+.f64 2 (/.f64 -8 x)) (+.f64 (/.f64 (/.f64 32 x) x) (/.f64 -128 (pow.f64 x 3))))
(+.f64 (+.f64 2 (/.f64 -8 x)) (*.f64 (/.f64 1 (*.f64 x x)) (-.f64 32 (/.f64 128 x))))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 2 (+.f64 (/.f64 -8 x) (/.f64 -128 (pow.f64 x 3)))))

localize17.0ms (0.4%)

Local error

Found 8 expressions with local error:

NewErrorProgram
4.0b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
0.2b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
0.2b
(/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.2b
(/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
✓0.2b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
✓4.0b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
Compiler

Compiled 34 to 25 computations (26.5% saved)

series6.0ms (0.2%)

Counts
3 → 12
Calls

9 calls:

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

rewrite62.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
925×pow1_binary64
870×log1p-expm1-u_binary64
870×expm1-log1p-u_binary64
869×add-log-exp_binary64
97×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0830
118725
2279725
Stop Event
1×node limit
Counts
3 → 146
Calls
Call 1
Inputs
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
(/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (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 x (/.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) 2) (cbrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) (sqrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) -1) (/.f64 1 (+.f64 x (+.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) x) x)))) (#(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 x) (/.f64 x (/.f64 1 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) x) (/.f64 (cbrt.f64 x) (/.f64 1 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) x) (/.f64 (sqrt.f64 x) (/.f64 1 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))))))) (#(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 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))))))) (#(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 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 (cbrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x 1) (/.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 x 1) 1/4) 1) (-.f64 (pow.f64 (+.f64 x 1) 1/4) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (neg.f64 x)) (neg.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (+.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 1 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 1 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 x (+.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (+.f64 (pow.f64 (+.f64 x 1) 3/2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x x) (*.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 x) 2) (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 x) (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) (neg.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) -1) (+.f64 x (+.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) -1) (+.f64 (+.f64 x 1) (-.f64 1 (*.f64 (sqrt.f64 (+.f64 x 1)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (/.f64 1 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) -1)) (neg.f64 (+.f64 x (+.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 (pow.f64 (+.f64 x 1) 3/2) -1)) (*.f64 x (+.f64 x (+.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (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 pow.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) 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 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 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 (log1p.f64 x) 1/2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (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 (/.f64 (pow.f64 (+.f64 x 1) 3/2) (+.f64 x (+.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))) (/.f64 1 (+.f64 x (+.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) 2) (cbrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) (sqrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) -1) (/.f64 1 (+.f64 x (+.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) x) x)))) (#(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 x) (/.f64 x (/.f64 1 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) x) (/.f64 (cbrt.f64 x) (/.f64 1 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) x) (/.f64 (sqrt.f64 x) (/.f64 1 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))))))) (#(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 (expm1.f64 (*.f64 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1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) 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 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 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 (log1p.f64 x) 1/2))))))
((#(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 (exp.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))))))) (#(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 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))))))) (#(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 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (expm1.f64 (*.f64 (log1p.f64 x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (expm1.f64 (*.f64 (log1p.f64 x) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) 2)) (/.f64 x (cbrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) 2)) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))) (/.f64 x (sqrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))) (/.f64 (cbrt.f64 x) (sqrt.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 x 1) 3/2) -1)) (+.f64 x (+.f64 1 (+.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 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)))))))) (#(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 cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (expm1.f64 (*.f64 (log1p.f64 x) 1/2)) 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 exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))

simplify100.0ms (2.6%)

Algorithm
1×egg-herbie
Rules
803×unswap-sqr_binary64
615×*-commutative_binary64
601×distribute-lft-out_binary64
506×sqr-pow_binary64
396×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
027155
173153
2169149
3492125
41416125
52412125
64391125
74534125
84798125
95162125
105865125
116839125
127325125
137876125
Stop Event
1×node limit
Counts
158 → 117
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)))))
(*.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)))))
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 1/16 (pow.f64 x 3) (*.f64 x (+.f64 1/2 (*.f64 x -1/8))))
(*.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 1/16 (pow.f64 x 3) (fma.f64 -5/128 (pow.f64 x 4) (*.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))))
(*.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 1/16 (pow.f64 x 3) (*.f64 x (+.f64 1/2 (*.f64 x -1/8))))
(*.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 1/16 (pow.f64 x 3) (fma.f64 -5/128 (pow.f64 x 4) (*.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 x (*.f64 x (fma.f64 x 1/16 -1/8)) (fma.f64 1/2 x 2))

localize17.0ms (0.4%)

Local error

Found 8 expressions with local error:

NewErrorProgram
0.2b
(pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)
0.1b
(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0b
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.1b
(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
✓0.2b
(pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)
Compiler

Compiled 35 to 27 computations (22.9% saved)

series6.0ms (0.2%)

Counts
2 → 8
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
1.0ms
x
@-inf
(pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)
1.0ms
x
@-inf
(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
1.0ms
x
@inf
(pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)
0.0ms
x
@0
(pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)

rewrite82.0ms (2.2%)

Algorithm
1×batch-egg-rewrite
Rules
424×prod-diff_binary64
416×log-prod_binary64
312×exp-prod_binary64
279×fma-def_binary64
264×pow-prod-down_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0927
119924
2272024
Stop Event
1×node limit
Counts
2 → 103
Calls
Call 1
Inputs
(pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)
(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))))) (#(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 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)) -2) (cbrt.f64 (/.f64 x (+.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) (/.f64 x (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 x x)) 1) (/.f64 (cbrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) -2) (/.f64 x (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 x x)) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2)) (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 x x)) (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4))) (/.f64 (cbrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4))) (/.f64 (sqrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 x))))) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 1 x) 3/2))) (+.f64 1 (-.f64 (+.f64 1 x) (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (neg.f64 x)) (-.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(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 1 (/.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 x x)) (/.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 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)) -2) (cbrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 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 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) (/.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 sqrt.f64 (pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 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 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 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 log1p.f64 (expm1.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))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 1 x))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x))) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 1 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x)) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 1 x)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x)) -1/2) 2))))) (#(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 +.f64 0 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 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 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2) (*.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)) 2) (cbrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) (*.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)) (sqrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 x)))) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2) 1) (/.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) 1) (/.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) 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 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2) (cbrt.f64 (*.f64 x x))) (cbrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) (cbrt.f64 (*.f64 x x))) (/.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x) 1)))) (#(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 (E.f64) (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x) -3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 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 (cbrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)) 2)))) (#(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 pow.f64 (/.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 3) (pow.f64 x 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x))) 2)) (cbrt.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x)))) (sqrt.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 1 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 1 x)))) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))))

simplify47.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
991×fma-def_binary64
803×unswap-sqr_binary64
674×associate-/l*_binary64
501×associate-/r/_binary64
445×distribute-lft-out_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
03398
18598
218691
347086
4136579
5315579
6514579
7624579
Stop Event
1×node limit
Counts
111 → 117
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)))))
(/.f64 2 x)
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x))))
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (+.f64 (*.f64 1/16 (pow.f64 x 2)) (*.f64 2 (/.f64 1 x)))))
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 (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 1/16 (pow.f64 x 3) (*.f64 x (fma.f64 x -1/8 1/2)))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
(*.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 (*.f64 -5/128 (pow.f64 x 4)) (fma.f64 1/16 (pow.f64 x 3) (*.f64 x (fma.f64 x -1/8 1/2))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (+.f64 (*.f64 x -5/128) 1/16)))
(*.f64 x (+.f64 (*.f64 x (fma.f64 x (fma.f64 x -5/128 1/16) -1/8)) 1/2))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x (fma.f64 x -5/128 1/16) -1/8))))
(/.f64 2 x)
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 2 x))
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x))))
(fma.f64 -1/8 x (+.f64 1/2 (/.f64 2 x)))
(+.f64 (/.f64 2 x) (fma.f64 x -1/8 1/2))
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (+.f64 (*.f64 1/16 (pow.f64 x 2)) (*.f64 2 (/.f64 1 x)))))
(fma.f64 -1/8 x (+.f64 1/2 (fma.f64 1/16 (*.f64 x x) (/.f64 2 x))))
(+.f64 (fma.f64 (*.f64 x x) 1/16 (/.f64 2 x)) (fma.f64 x -1/8 1/2))
(+.f64 (/.f64 2 x) (fma.f64 x -1/8 (fma.f64 (*.f64 x x) 1/16 1/2)))
(+.f64 (/.f64 2 x) (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
(+.f64 1/2 (fma.f64 x (fma.f64 x 1/16 -1/8) (/.f64 2 x)))

eval276.0ms (7.3%)

Compiler

Compiled 7176 to 5514 computations (23.2% saved)

prune68.0ms (1.8%)

Pruning

9 alts after pruning (5 fresh and 4 done)

PrunedKeptTotal
New5005505
Fresh000
Picked101
Done145
Total5029511
Error
0b
Counts
511 → 9
Alt Table
Click to see full alt table
StatusErrorProgram
60.8b
2
▶0.3b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))
✓20.6b
(*.f64 1/2 x)
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
▶39.1b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
▶20.2b
(*.f64 (/.f64 1 (+.f64 1 (+.f64 (*.f64 1/2 x) 1))) x)
✓20.2b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
✓0.2b
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)
▶20.2b
(*.f64 (/.f64 1 (+.f64 (*.f64 1/2 x) 2)) x)
Compiler

Compiled 74 to 60 computations (18.9% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (/.f64 1 (+.f64 (*.f64 1/2 x) 2)) x)
0.0b
(/.f64 1 (+.f64 (*.f64 1/2 x) 2))
✓0.0b
(/.f64 1 (+.f64 (*.f64 1/2 x) 2))
✓0.1b
(*.f64 (/.f64 1 (+.f64 (*.f64 1/2 x) 2)) x)
Compiler

Compiled 29 to 23 computations (20.7% saved)

series5.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
3.0ms
x
@0
(/.f64 1 (+.f64 (*.f64 1/2 x) 2))
0.0ms
x
@inf
(/.f64 1 (+.f64 (*.f64 1/2 x) 2))
0.0ms
x
@0
(*.f64 (/.f64 1 (+.f64 (*.f64 1/2 x) 2)) x)
0.0ms
x
@-inf
(/.f64 1 (+.f64 (*.f64 1/2 x) 2))
0.0ms
x
@inf
(*.f64 (/.f64 1 (+.f64 (*.f64 1/2 x) 2)) x)

rewrite63.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
894×pow1_binary64
835×add-log-exp_binary64
834×log1p-expm1-u_binary64
834×expm1-log1p-u_binary64
821×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0916
119316
2232316
Stop Event
1×node limit
Counts
2 → 46
Calls
Call 1
Inputs
(*.f64 (/.f64 1 (+.f64 (*.f64 1/2 x) 2)) x)
(/.f64 1 (+.f64 (*.f64 1/2 x) 2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 x (fma.f64 1/2 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 1/2 x 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (fma.f64 1/2 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 x x)) (/.f64 (fma.f64 1/2 x 2) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 x) (/.f64 (fma.f64 1/2 x 2) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) (neg.f64 (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (sqrt.f64 (fma.f64 1/2 x 2))) (sqrt.f64 (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x 1) (fma.f64 1/2 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (cbrt.f64 (pow.f64 (fma.f64 1/2 x 2) 2))) (cbrt.f64 (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 x) (neg.f64 (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x -1) (neg.f64 (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (fma.f64 1/2 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (fma.f64 1/2 x 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (fma.f64 1/2 x 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (fma.f64 1/2 x 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (fma.f64 1/2 x 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (fma.f64 1/2 x 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (fma.f64 1/2 x 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 1 (fma.f64 1/2 x 2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 1 (fma.f64 1/2 x 2)) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (fma.f64 1/2 x 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1 (fma.f64 1/2 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 1/2 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (fma.f64 1/2 x 2))) (cbrt.f64 (pow.f64 (fma.f64 1/2 x 2) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 1/2 x 2) -2)) (/.f64 1 (cbrt.f64 (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 1/2 x 2) -1/2) (pow.f64 (fma.f64 1/2 x 2) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (fma.f64 1/2 x 2) 2)) -1) (pow.f64 (cbrt.f64 (fma.f64 1/2 x 2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (fma.f64 1/2 x 2)) -1) (pow.f64 (sqrt.f64 (fma.f64 1/2 x 2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 8 (*.f64 1/8 (pow.f64 x 3)))) (+.f64 (*.f64 1/4 (*.f64 x x)) (-.f64 4 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (*.f64 1/4 (*.f64 x x)) -4)) (fma.f64 1/2 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/2 x 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (fma.f64 1/2 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (fma.f64 1/2 x 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 1/2 x 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 x 2) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/2 x 2) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (fma.f64 1/2 x 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (fma.f64 1/2 x 2))))))))

simplify53.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
624×fma-def_binary64
508×associate-/l/_binary64
444×fma-neg_binary64
383×associate-*l/_binary64
375×associate-*r/_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
057337
1160335
2403326
31107312
43264312
57952312
Stop Event
1×node limit
Counts
70 → 74
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 1/32 (pow.f64 x 3)) (*.f64 1/2 x)))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/32 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (*.f64 -1/128 (pow.f64 x 4)))))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
1/2
(+.f64 (*.f64 -1/8 x) 1/2)
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 1/32 (pow.f64 x 2))))
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (+.f64 (*.f64 1/32 (pow.f64 x 2)) (*.f64 -1/128 (pow.f64 x 3)))))
(/.f64 2 x)
(-.f64 (*.f64 2 (/.f64 1 x)) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 2))) (*.f64 128 (/.f64 1 (pow.f64 x 4)))))
(/.f64 2 x)
(-.f64 (*.f64 2 (/.f64 1 x)) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 2))) (*.f64 128 (/.f64 1 (pow.f64 x 4)))))
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 x (*.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/32 (pow.f64 x 3)) (*.f64 1/2 x)))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/32 (pow.f64 x 3) (*.f64 1/2 x)))
(fma.f64 1/32 (pow.f64 x 3) (*.f64 x (fma.f64 x -1/8 1/2)))
(*.f64 x (fma.f64 x (fma.f64 x 1/32 -1/8) 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/32 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (*.f64 -1/128 (pow.f64 x 4)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/32 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 -1/128 (pow.f64 x 4)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/32 (pow.f64 x 3) (fma.f64 -1/128 (pow.f64 x 4) (*.f64 1/2 x))))
(+.f64 (*.f64 -1/128 (pow.f64 x 4)) (fma.f64 1/32 (pow.f64 x 3) (*.f64 x (fma.f64 x -1/8 1/2))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (fma.f64 x -1/128 1/32)))
(*.f64 x (fma.f64 x -1/8 (fma.f64 (*.f64 x x) (fma.f64 x -1/128 1/32) 1/2)))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 2 (/.f64 8 x))
(+.f64 2 (/.f64 -8 x))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x)))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 2 (/.f64 -8 x)))
(+.f64 2 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)))
(+.f64 (/.f64 32 (*.f64 x x)) (-.f64 2 (/.f64 8 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(-.f64 (+.f64 2 (/.f64 32 (*.f64 x x))) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3))))
(+.f64 2 (+.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)) (/.f64 -128 (pow.f64 x 3))))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 -8 x) (+.f64 2 (/.f64 -128 (pow.f64 x 3)))))
(+.f64 (-.f64 2 (/.f64 8 x)) (*.f64 (/.f64 1 (*.f64 x x)) (-.f64 32 (/.f64 128 x))))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 2 (/.f64 8 x))
(+.f64 2 (/.f64 -8 x))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x)))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 2 (/.f64 -8 x)))
(+.f64 2 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)))
(+.f64 (/.f64 32 (*.f64 x x)) (-.f64 2 (/.f64 8 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(-.f64 (+.f64 2 (/.f64 32 (*.f64 x x))) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3))))
(+.f64 2 (+.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)) (/.f64 -128 (pow.f64 x 3))))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 -8 x) (+.f64 2 (/.f64 -128 (pow.f64 x 3)))))
(+.f64 (-.f64 2 (/.f64 8 x)) (*.f64 (/.f64 1 (*.f64 x x)) (-.f64 32 (/.f64 128 x))))
1/2
(+.f64 (*.f64 -1/8 x) 1/2)
(fma.f64 -1/8 x 1/2)
(fma.f64 x -1/8 1/2)
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 1/32 (pow.f64 x 2))))
(+.f64 (fma.f64 -1/8 x 1/2) (*.f64 (*.f64 x x) 1/32))
(fma.f64 x -1/8 (fma.f64 (*.f64 x x) 1/32 1/2))
(fma.f64 x -1/8 (fma.f64 x (*.f64 x 1/32) 1/2))
(fma.f64 x (fma.f64 x 1/32 -1/8) 1/2)
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (+.f64 (*.f64 1/32 (pow.f64 x 2)) (*.f64 -1/128 (pow.f64 x 3)))))
(+.f64 (fma.f64 -1/8 x 1/2) (fma.f64 1/32 (*.f64 x x) (*.f64 (pow.f64 x 3) -1/128)))
(+.f64 (fma.f64 x -1/8 (fma.f64 (*.f64 x x) 1/32 1/2)) (*.f64 (pow.f64 x 3) -1/128))
(fma.f64 x -1/8 (fma.f64 x (*.f64 x 1/32) (fma.f64 (pow.f64 x 3) -1/128 1/2)))
(fma.f64 x (fma.f64 x 1/32 -1/8) (fma.f64 (pow.f64 x 3) -1/128 1/2))
(fma.f64 x -1/8 (fma.f64 (*.f64 x x) (fma.f64 x -1/128 1/32) 1/2))
(/.f64 2 x)
(-.f64 (*.f64 2 (/.f64 1 x)) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 2 x) (/.f64 8 (*.f64 x x)))
(+.f64 (/.f64 2 x) (/.f64 -8 (*.f64 x x)))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -8 x) x))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (/.f64 2 x) (/.f64 8 (*.f64 x x))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 32 (pow.f64 x 3)) (/.f64 8 (*.f64 x x))))
(-.f64 (/.f64 2 x) (-.f64 (/.f64 8 (*.f64 x x)) (/.f64 32 (pow.f64 x 3))))
(+.f64 (/.f64 2 x) (*.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 32 x) -8)))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 2))) (*.f64 128 (/.f64 1 (pow.f64 x 4)))))
(+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (/.f64 2 x) (+.f64 (/.f64 8 (*.f64 x x)) (/.f64 128 (pow.f64 x 4)))))
(+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (+.f64 (/.f64 2 x) (/.f64 -8 (*.f64 x x))) (/.f64 128 (pow.f64 x 4))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (/.f64 -128 (pow.f64 x 4)) (/.f64 8 (*.f64 x x)))))
(+.f64 (-.f64 (/.f64 2 x) (-.f64 (/.f64 8 (*.f64 x x)) (/.f64 32 (pow.f64 x 3)))) (/.f64 -128 (pow.f64 x 4)))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 -8 (*.f64 x x)) (*.f64 (/.f64 1 (pow.f64 x 3)) (-.f64 (/.f64 128 x) 32))))
(/.f64 2 x)
(-.f64 (*.f64 2 (/.f64 1 x)) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 2 x) (/.f64 8 (*.f64 x x)))
(+.f64 (/.f64 2 x) (/.f64 -8 (*.f64 x x)))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -8 x) x))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (/.f64 2 x) (/.f64 8 (*.f64 x x))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 32 (pow.f64 x 3)) (/.f64 8 (*.f64 x x))))
(-.f64 (/.f64 2 x) (-.f64 (/.f64 8 (*.f64 x x)) (/.f64 32 (pow.f64 x 3))))
(+.f64 (/.f64 2 x) (*.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 32 x) -8)))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 2))) (*.f64 128 (/.f64 1 (pow.f64 x 4)))))
(+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (/.f64 2 x) (+.f64 (/.f64 8 (*.f64 x x)) (/.f64 128 (pow.f64 x 4)))))
(+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (+.f64 (/.f64 2 x) (/.f64 -8 (*.f64 x x))) (/.f64 128 (pow.f64 x 4))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (/.f64 -128 (pow.f64 x 4)) (/.f64 8 (*.f64 x x)))))
(+.f64 (-.f64 (/.f64 2 x) (-.f64 (/.f64 8 (*.f64 x x)) (/.f64 32 (pow.f64 x 3)))) (/.f64 -128 (pow.f64 x 4)))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 -8 (*.f64 x x)) (*.f64 (/.f64 1 (pow.f64 x 3)) (-.f64 (/.f64 128 x) 32))))

localize27.0ms (0.7%)

Local error

Found 6 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (/.f64 1 (+.f64 1 (+.f64 (*.f64 1/2 x) 1))) x)
0.0b
(/.f64 1 (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
0.0b
(+.f64 1 (+.f64 (*.f64 1/2 x) 1))
✓0.0b
(+.f64 1 (+.f64 (*.f64 1/2 x) 1))
✓0.0b
(/.f64 1 (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
✓0.1b
(*.f64 (/.f64 1 (+.f64 1 (+.f64 (*.f64 1/2 x) 1))) x)
Compiler

Compiled 39 to 32 computations (17.9% saved)

series3.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
0.0ms
x
@0
(*.f64 (/.f64 1 (+.f64 1 (+.f64 (*.f64 1/2 x) 1))) x)
0.0ms
x
@inf
(+.f64 1 (+.f64 (*.f64 1/2 x) 1))
0.0ms
x
@inf
(*.f64 (/.f64 1 (+.f64 1 (+.f64 (*.f64 1/2 x) 1))) x)
0.0ms
x
@0
(/.f64 1 (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
0.0ms
x
@0
(+.f64 1 (+.f64 (*.f64 1/2 x) 1))

rewrite66.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
438×log-prod_binary64
410×prod-diff_binary64
339×exp-prod_binary64
282×fma-def_binary64
265×pow-prod-down_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0930
120127
2263021
Stop Event
1×node limit
Counts
3 → 148
Calls
Call 1
Inputs
(*.f64 (/.f64 1 (+.f64 1 (+.f64 (*.f64 1/2 x) 1))) x)
(/.f64 1 (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(+.f64 1 (+.f64 (*.f64 1/2 x) 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 x (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 x (fma.f64 1/2 x 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 x (fma.f64 1/2 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (fma.f64 1/2 x 2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (fma.f64 1/2 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (fma.f64 1/2 x 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 1/2 x 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (fma.f64 1/2 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 x) 2) (/.f64 (fma.f64 1/2 x 2) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 x) (/.f64 (fma.f64 1/2 x 2) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) (neg.f64 (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (sqrt.f64 (fma.f64 1/2 x 2))) (sqrt.f64 (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x 1) (fma.f64 1/2 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (pow.f64 (cbrt.f64 (fma.f64 1/2 x 2)) 2)) (cbrt.f64 (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 x) (neg.f64 (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x -1) (neg.f64 (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (fma.f64 1/2 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (/.f64 x (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (fma.f64 1/2 x 2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (fma.f64 1/2 x 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (fma.f64 1/2 x 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (fma.f64 1/2 x 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 x 3) (pow.f64 (fma.f64 1/2 x 2) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 1/2 x 2) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 x (fma.f64 1/2 x 2)))) 2)) (cbrt.f64 (log.f64 (/.f64 x (fma.f64 1/2 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 x (fma.f64 1/2 x 2))))) (sqrt.f64 (log.f64 (/.f64 x (fma.f64 1/2 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (fma.f64 1/2 x 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (fma.f64 1/2 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (fma.f64 1/2 x 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (fma.f64 1/2 x 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 x (fma.f64 1/2 x 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (/.f64 x (fma.f64 1/2 x 2)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 x (fma.f64 1/2 x 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 x (fma.f64 1/2 x 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 x (fma.f64 1/2 x 2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (fma.f64 1/2 x 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (fma.f64 1/2 x 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (fma.f64 1/2 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (fma.f64 1/2 x 2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (fma.f64 1/2 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (fma.f64 1/2 x 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 1/2 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (fma.f64 1/2 x 2))) (cbrt.f64 (pow.f64 (fma.f64 1/2 x 2) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 1/2 x 2) -2)) (/.f64 1 (cbrt.f64 (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 1/2 x 2) -1/2) (pow.f64 (fma.f64 1/2 x 2) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x 2)) -2) (/.f64 1 (cbrt.f64 (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3))) (fma.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2))) (-.f64 0 (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/2 x 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (fma.f64 1/2 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (neg.f64 (log1p.f64 (fma.f64 1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 x 2) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 x 2) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 x 2) 2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 x 2) 3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 1/2 x 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/2 x 2)) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 x 2) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/2 x 2)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 -1) (log1p.f64 (fma.f64 1/2 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (fma.f64 1/2 x 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (neg.f64 (log1p.f64 (fma.f64 1/2 x 1)))) 2)) (cbrt.f64 (neg.f64 (log1p.f64 (fma.f64 1/2 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (neg.f64 (log1p.f64 (fma.f64 1/2 x 1))))) (sqrt.f64 (neg.f64 (log1p.f64 (fma.f64 1/2 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/2 x 2) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (fma.f64 1/2 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/2 x 2) -3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log1p.f64 (fma.f64 1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (fma.f64 1/2 x 1)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log1p.f64 (fma.f64 1/2 x 1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 1/2 x 2) -3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (cbrt.f64 (fma.f64 1/2 x 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (log1p.f64 (fma.f64 1/2 x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 (fma.f64 1/2 x 1)) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 (fma.f64 1/2 x 1)) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (neg.f64 (log1p.f64 (fma.f64 1/2 x 1))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (fma.f64 1/2 x 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 1/2 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 0 (*.f64 1/2 x))) (/.f64 (pow.f64 (fma.f64 1/2 x 1) 2) (-.f64 0 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/2 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/2 x 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/2 x 2)) (pow.f64 (cbrt.f64 (fma.f64 1/2 x 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x 2)) 2) (cbrt.f64 (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/2 x 2)) (sqrt.f64 (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3)) (/.f64 1 (fma.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2)) (/.f64 1 (-.f64 0 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1 (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x) 1) (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 0 (*.f64 1/2 x)) (-.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/2 x 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x 2)) 2) (/.f64 1 (cbrt.f64 (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (fma.f64 1/2 x 2)) (pow.f64 (fma.f64 1/2 x 2) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 1/2 x 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3)) (fma.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3)) (+.f64 (pow.f64 (fma.f64 1/2 x 1) 2) (-.f64 0 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2)) (-.f64 0 (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3))) (neg.f64 (fma.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2))) (neg.f64 (-.f64 0 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 1/2 x 1) 2) 1) (*.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/2 x 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (fma.f64 1/2 x 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log1p.f64 (fma.f64 1/2 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 x 2) -3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 x 2) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 x 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 1/2 x 2))) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/2 x 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 x 2) -1/2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/2 x 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x) 1) (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 0 (*.f64 1/2 x)) (-.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (fma.f64 1/2 x 1))) 2)) (cbrt.f64 (log1p.f64 (fma.f64 1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (fma.f64 1/2 x 1)))) (sqrt.f64 (log1p.f64 (fma.f64 1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/2 x 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/2 x 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/2 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 1/2 x 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 x 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/2 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 x) 1 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 1/2 x 1) 1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 1/2 x)) (pow.f64 (cbrt.f64 (*.f64 1/2 x)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 x)) 2) (cbrt.f64 (*.f64 1/2 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 x)) 2) (*.f64 (cbrt.f64 (*.f64 1/2 x)) 1) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 1/2 x 1)) (pow.f64 (cbrt.f64 (fma.f64 1/2 x 1)) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x 1)) 2) (cbrt.f64 (fma.f64 1/2 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/2 x)) (sqrt.f64 (*.f64 1/2 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/2 x)) (*.f64 (sqrt.f64 (*.f64 1/2 x)) 1) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 1/2 x 1)) (sqrt.f64 (fma.f64 1/2 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 1/8 (pow.f64 x 3) 1) (/.f64 1 (-.f64 (fma.f64 1/4 (*.f64 x x) 1) (*.f64 1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 1/4 (*.f64 x x) -1) (/.f64 1 (fma.f64 1/2 x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (fma.f64 1/2 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (fma.f64 1/2 x 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log1p.f64 (fma.f64 1/2 x 1))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (fma.f64 1/2 x 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 1/2 x 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 (fma.f64 1/2 x 1)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/2 x 2)))))))

simplify57.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
630×fma-def_binary64
504×associate-/l/_binary64
444×fma-neg_binary64
384×associate-*l/_binary64
377×associate-*r/_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
059391
1163389
2407380
31110366
43274366
57926366
Stop Event
1×node limit
Counts
184 → 178
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 1/32 (pow.f64 x 3)) (*.f64 1/2 x)))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/32 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (*.f64 -1/128 (pow.f64 x 4)))))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
1/2
(+.f64 (*.f64 -1/8 x) 1/2)
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 1/32 (pow.f64 x 2))))
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (+.f64 (*.f64 1/32 (pow.f64 x 2)) (*.f64 -1/128 (pow.f64 x 3)))))
(/.f64 2 x)
(-.f64 (*.f64 2 (/.f64 1 x)) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 2))) (*.f64 128 (/.f64 1 (pow.f64 x 4)))))
(/.f64 2 x)
(-.f64 (*.f64 2 (/.f64 1 x)) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 2))) (*.f64 128 (/.f64 1 (pow.f64 x 4)))))
2
(+.f64 (*.f64 1/2 x) 2)
(+.f64 (*.f64 1/2 x) 2)
(+.f64 (*.f64 1/2 x) 2)
(*.f64 1/2 x)
(+.f64 2 (*.f64 1/2 x))
(+.f64 2 (*.f64 1/2 x))
(+.f64 2 (*.f64 1/2 x))
(*.f64 1/2 x)
(+.f64 2 (*.f64 1/2 x))
(+.f64 2 (*.f64 1/2 x))
(+.f64 2 (*.f64 1/2 x))
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 x (*.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/32 (pow.f64 x 3)) (*.f64 1/2 x)))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/32 (pow.f64 x 3) (*.f64 1/2 x)))
(fma.f64 1/32 (pow.f64 x 3) (*.f64 x (fma.f64 x -1/8 1/2)))
(*.f64 x (fma.f64 x (fma.f64 x 1/32 -1/8) 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/32 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (*.f64 -1/128 (pow.f64 x 4)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/32 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 -1/128 (pow.f64 x 4)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/32 (pow.f64 x 3) (fma.f64 -1/128 (pow.f64 x 4) (*.f64 1/2 x))))
(+.f64 (*.f64 -1/128 (pow.f64 x 4)) (fma.f64 1/32 (pow.f64 x 3) (*.f64 x (fma.f64 x -1/8 1/2))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (fma.f64 x -1/128 1/32)))
(*.f64 x (fma.f64 x -1/8 (fma.f64 (*.f64 x x) (fma.f64 x -1/128 1/32) 1/2)))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 2 (/.f64 8 x))
(+.f64 2 (/.f64 -8 x))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x)))
(+.f64 2 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 2 (/.f64 -8 x)))
(-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) -2))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)) (/.f64 128 (pow.f64 x 3))))
(+.f64 2 (+.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -128 (pow.f64 x 3))) (/.f64 -8 x)))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (-.f64 (/.f64 8 x) (/.f64 -128 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (/.f64 -8 x) (*.f64 (/.f64 1 (*.f64 x x)) (-.f64 (/.f64 128 x) 32))))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 2 (/.f64 8 x))
(+.f64 2 (/.f64 -8 x))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x)))
(+.f64 2 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 2 (/.f64 -8 x)))
(-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) -2))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)) (/.f64 128 (pow.f64 x 3))))
(+.f64 2 (+.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -128 (pow.f64 x 3))) (/.f64 -8 x)))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (-.f64 (/.f64 8 x) (/.f64 -128 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (/.f64 -8 x) (*.f64 (/.f64 1 (*.f64 x x)) (-.f64 (/.f64 128 x) 32))))
1/2
(+.f64 (*.f64 -1/8 x) 1/2)
(fma.f64 -1/8 x 1/2)
(fma.f64 x -1/8 1/2)
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 1/32 (pow.f64 x 2))))
(+.f64 (fma.f64 -1/8 x 1/2) (*.f64 (*.f64 x x) 1/32))
(fma.f64 x -1/8 (fma.f64 (*.f64 x x) 1/32 1/2))
(fma.f64 x -1/8 (fma.f64 x (*.f64 x 1/32) 1/2))
(fma.f64 x (fma.f64 x 1/32 -1/8) 1/2)
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (+.f64 (*.f64 1/32 (pow.f64 x 2)) (*.f64 -1/128 (pow.f64 x 3)))))
(+.f64 (fma.f64 -1/8 x 1/2) (fma.f64 1/32 (*.f64 x x) (*.f64 (pow.f64 x 3) -1/128)))
(+.f64 (fma.f64 (*.f64 x x) 1/32 (*.f64 (pow.f64 x 3) -1/128)) (fma.f64 x -1/8 1/2))
(fma.f64 x -1/8 (fma.f64 x (*.f64 x 1/32) (fma.f64 (pow.f64 x 3) -1/128 1/2)))
(fma.f64 (*.f64 x x) (fma.f64 x -1/128 1/32) (fma.f64 x -1/8 1/2))
(fma.f64 x -1/8 (fma.f64 (*.f64 x x) (fma.f64 x -1/128 1/32) 1/2))
(/.f64 2 x)
(-.f64 (*.f64 2 (/.f64 1 x)) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 2 x) (/.f64 8 (*.f64 x x)))
(+.f64 (/.f64 2 x) (/.f64 -8 (*.f64 x x)))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -8 x) x))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (/.f64 2 x) (/.f64 8 (*.f64 x x))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 32 (pow.f64 x 3)) (/.f64 8 (*.f64 x x))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 32 (pow.f64 x 3)) (/.f64 (/.f64 -8 x) x)))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 32 (pow.f64 x 3)) (/.f64 -8 (*.f64 x x))))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 2))) (*.f64 128 (/.f64 1 (pow.f64 x 4)))))
(+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (/.f64 2 x) (+.f64 (/.f64 8 (*.f64 x x)) (/.f64 128 (pow.f64 x 4)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 32 (pow.f64 x 3)) (+.f64 (/.f64 (/.f64 -8 x) x) (/.f64 -128 (pow.f64 x 4)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 -128 (pow.f64 x 4)) (+.f64 (/.f64 32 (pow.f64 x 3)) (/.f64 (/.f64 -8 x) x))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 -128 (pow.f64 x 4)) (+.f64 (/.f64 32 (pow.f64 x 3)) (/.f64 -8 (*.f64 x x)))))
(/.f64 2 x)
(-.f64 (*.f64 2 (/.f64 1 x)) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 2 x) (/.f64 8 (*.f64 x x)))
(+.f64 (/.f64 2 x) (/.f64 -8 (*.f64 x x)))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -8 x) x))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (/.f64 2 x) (/.f64 8 (*.f64 x x))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 32 (pow.f64 x 3)) (/.f64 8 (*.f64 x x))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 32 (pow.f64 x 3)) (/.f64 (/.f64 -8 x) x)))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 32 (pow.f64 x 3)) (/.f64 -8 (*.f64 x x))))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 2))) (*.f64 128 (/.f64 1 (pow.f64 x 4)))))
(+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (/.f64 2 x) (+.f64 (/.f64 8 (*.f64 x x)) (/.f64 128 (pow.f64 x 4)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 32 (pow.f64 x 3)) (+.f64 (/.f64 (/.f64 -8 x) x) (/.f64 -128 (pow.f64 x 4)))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 -128 (pow.f64 x 4)) (+.f64 (/.f64 32 (pow.f64 x 3)) (/.f64 (/.f64 -8 x) x))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 -128 (pow.f64 x 4)) (+.f64 (/.f64 32 (pow.f64 x 3)) (/.f64 -8 (*.f64 x x)))))
2
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 2)
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 2)
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 2)
(*.f64 1/2 x)
(+.f64 2 (*.f64 1/2 x))
(fma.f64 1/2 x 2)
(+.f64 2 (*.f64 1/2 x))
(fma.f64 1/2 x 2)
(+.f64 2 (*.f64 1/2 x))
(fma.f64 1/2 x 2)
(*.f64 1/2 x)
(+.f64 2 (*.f64 1/2 x))
(fma.f64 1/2 x 2)
(+.f64 2 (*.f64 1/2 x))
(fma.f64 1/2 x 2)
(+.f64 2 (*.f64 1/2 x))
(fma.f64 1/2 x 2)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
4.0b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(sqrt.f64 (+.f64 x 1))
4.0b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
Compiler

Compiled 16 to 12 computations (25% saved)

rewrite0.0ms (0%)

Counts
0 → 0

simplify7.0ms (0.2%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
0 → 0
Calls
Call 1
Inputs
Outputs

localize19.0ms (0.5%)

Local error

Found 8 expressions with local error:

NewErrorProgram
0.2b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))
0.1b
(/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)
0.0b
(sqrt.f64 (+.f64 1 x))
0.0b
(+.f64 1 (sqrt.f64 (+.f64 1 x)))
✓0.0b
(+.f64 1 (sqrt.f64 (+.f64 1 x)))
✓0.0b
(sqrt.f64 (+.f64 1 x))
✓0.1b
(/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)
✓0.2b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))
Compiler

Compiled 34 to 26 computations (23.5% saved)

series4.0ms (0.1%)

Counts
4 → 16
Calls

12 calls:

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

rewrite85.0ms (2.2%)

Algorithm
1×batch-egg-rewrite
Rules
421×log-prod_binary64
414×prod-diff_binary64
321×exp-prod_binary64
284×fma-def_binary64
269×pow-prod-down_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0842
118439
2267639
Stop Event
1×node limit
Counts
4 → 204
Calls
Call 1
Inputs
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))
(/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)
(sqrt.f64 (+.f64 1 x))
(+.f64 1 (sqrt.f64 (+.f64 1 x)))
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 x))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) 1/6) (cbrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 x)) (pow.f64 (+.f64 1 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (hypot.f64 1 (pow.f64 x 3/2)) (sqrt.f64 (fma.f64 x (-.f64 x 1) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (*.f64 1/2 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 x)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/2) (log1p.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 (log1p.f64 x))) 2)) (cbrt.f64 (*.f64 1/2 (log1p.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (*.f64 1/2 (log1p.f64 x)))) (sqrt.f64 (*.f64 1/2 (log1p.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 x) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (pow.f64 (+.f64 1 x) 3/2)) (/.f64 1 (-.f64 (+.f64 1 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 x))))))) (#(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))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (*.f64 1/2 (log1p.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/4 (log1p.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/2 (log1p.f64 x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 x) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 x) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1 x)))) (/.f64 (+.f64 1 x) (-.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (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 (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 (neg.f64 x) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (+.f64 1 x) 3/2)) (/.f64 1 (-.f64 (+.f64 1 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (+.f64 1 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (+.f64 1 (pow.f64 (+.f64 1 x) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x))) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) (-.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 1 x) 3/2)) (-.f64 (+.f64 1 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 1 x) 3/2)) (+.f64 (+.f64 1 x) (-.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 1 x) 3/2))) (neg.f64 (-.f64 (+.f64 1 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 x)) (neg.f64 (-.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 (E.f64) (log1p.f64 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (+.f64 1 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (+.f64 1 (pow.f64 (+.f64 1 x) 3/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x))) (neg.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x)))) 2)) (cbrt.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(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 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 x)) 1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1 x) 1/6) (cbrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1 x)) (pow.f64 (+.f64 1 x) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.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 (*.f64 3 (log1p.f64 (sqrt.f64 (+.f64 1 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (sqrt.f64 (+.f64 1 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (sqrt.f64 (+.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))))

simplify67.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
803×unswap-sqr_binary64
672×associate-/l*_binary64
557×fma-def_binary64
511×associate-/r/_binary64
445×distribute-lft-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
043176
1119172
2268161
3669148
41712148
52663148
64653148
75742148
87534148
Stop Event
1×node limit
Counts
220 → 232
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)))))
(/.f64 2 x)
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x))))
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (+.f64 (*.f64 1/16 (pow.f64 x 2)) (*.f64 2 (/.f64 1 x)))))
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)))))
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)))))
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))
(*.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 1/16 (pow.f64 x 3) (*.f64 x (fma.f64 x -1/8 1/2)))
(*.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)))))
(+.f64 (*.f64 -5/128 (pow.f64 x 4)) (fma.f64 1/16 (pow.f64 x 3) (*.f64 x (fma.f64 x -1/8 1/2))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (+.f64 (*.f64 x -5/128) 1/16)))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (+.f64 1/16 (*.f64 x -5/128))))
(/.f64 2 x)
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 2 x))
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x))))
(fma.f64 -1/8 x (+.f64 1/2 (/.f64 2 x)))
(+.f64 (/.f64 2 x) (fma.f64 x -1/8 1/2))
(+.f64 1/2 (fma.f64 x -1/8 (/.f64 2 x)))
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (+.f64 (*.f64 1/16 (pow.f64 x 2)) (*.f64 2 (/.f64 1 x)))))
(fma.f64 -1/8 x (+.f64 1/2 (fma.f64 1/16 (*.f64 x x) (/.f64 2 x))))
(+.f64 (fma.f64 (*.f64 x x) 1/16 (/.f64 2 x)) (fma.f64 x -1/8 1/2))
(+.f64 (/.f64 2 x) (fma.f64 x -1/8 (fma.f64 x (*.f64 x 1/16) 1/2)))
(+.f64 (+.f64 1/2 (/.f64 2 x)) (*.f64 x (fma.f64 x 1/16 -1/8)))
(+.f64 1/2 (+.f64 (/.f64 2 x) (*.f64 x (fma.f64 x 1/16 -1/8))))
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))
(+.f64 1 (*.f64 x (fma.f64 x -1/8 1/2)))
(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)))
(+.f64 1 (fma.f64 1/16 (pow.f64 x 3) (*.f64 x (fma.f64 x -1/8 1/2))))
(fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) (fma.f64 1/2 x 1))
(fma.f64 1/2 x (fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)) 1))
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))
(+.f64 2 (*.f64 x (fma.f64 x -1/8 1/2)))
(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)))
(+.f64 2 (fma.f64 1/16 (pow.f64 x 3) (*.f64 x (fma.f64 x -1/8 1/2))))
(fma.f64 1/16 (pow.f64 x 3) (fma.f64 x (fma.f64 x -1/8 1/2) 2))
(fma.f64 1/2 x (fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) 2))

eval255.0ms (6.7%)

Compiler

Compiled 7736 to 6123 computations (20.9% saved)

prune89.0ms (2.3%)

Pruning

12 alts after pruning (4 fresh and 8 done)

PrunedKeptTotal
New5803583
Fresh011
Picked011
Done077
Total58012592
Error
0b
Counts
592 → 12
Alt Table
Click to see full alt table
StatusErrorProgram
60.8b
2
✓0.3b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))
✓20.6b
(*.f64 1/2 x)
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓20.2b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
▶20.7b
(/.f64 1 (/.f64 2 x))
✓39.1b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
✓20.2b
(*.f64 (/.f64 1 (+.f64 1 (+.f64 (*.f64 1/2 x) 1))) x)
▶21.1b
(/.f64 1 (+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x)))))
▶20.3b
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
✓0.2b
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)
✓20.2b
(*.f64 (/.f64 1 (+.f64 (*.f64 1/2 x) 2)) x)
Compiler

Compiled 102 to 84 computations (17.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
0.0b
(+.f64 1/2 (/.f64 2 x))
✓0.0b
(+.f64 1/2 (/.f64 2 x))
✓0.1b
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
Compiler

Compiled 20 to 16 computations (20% saved)

series2.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@0
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
0.0ms
x
@inf
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
0.0ms
x
@-inf
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
0.0ms
x
@0
(+.f64 1/2 (/.f64 2 x))
0.0ms
x
@-inf
(+.f64 1/2 (/.f64 2 x))

rewrite75.0ms (2%)

Algorithm
1×batch-egg-rewrite
Rules
836×pow1_binary64
783×add-log-exp_binary64
782×log1p-expm1-u_binary64
782×expm1-log1p-u_binary64
770×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0817
117817
2217517
Stop Event
1×node limit
Counts
2 → 58
Calls
Call 1
Inputs
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
(+.f64 1/2 (/.f64 2 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 1/2 (/.f64 2 x)))) (cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -2)) (/.f64 1 (cbrt.f64 (+.f64 1/2 (/.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -1/2) (pow.f64 (+.f64 1/2 (/.f64 2 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (+.f64 1/2 (/.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 2 x))) 2) -1) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 2 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 2 x))) -1) (pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 2 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1/8 (/.f64 8 (pow.f64 x 3)))) (+.f64 1/4 (-.f64 (/.f64 4 (*.f64 x x)) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 1/4 (/.f64 4 (*.f64 x x)))) (-.f64 1/2 (/.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/2 (/.f64 2 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1/2 (/.f64 2 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (+.f64 1/2 (/.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 1/2 (/.f64 2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/4 (-.f64 1/2 (/.f64 2 x))) (/.f64 (/.f64 4 (*.f64 x x)) (-.f64 1/2 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1/2 (/.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/2 (/.f64 2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1/2 (/.f64 2 x))) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 2 x))) 2) (cbrt.f64 (+.f64 1/2 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1/2 (/.f64 2 x))) (sqrt.f64 (+.f64 1/2 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/8 (/.f64 8 (pow.f64 x 3))) (/.f64 1 (+.f64 1/4 (-.f64 (/.f64 4 (*.f64 x x)) (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/4 (/.f64 4 (*.f64 x x))) (/.f64 1 (-.f64 1/2 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1/4 (-.f64 (/.f64 4 (*.f64 x x)) (/.f64 1 x))) (+.f64 1/8 (/.f64 8 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1/2 (/.f64 2 x)) (-.f64 1/4 (/.f64 4 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/2 (/.f64 2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 2 x))) 2) (/.f64 1 (cbrt.f64 (+.f64 1/2 (/.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1/2 (/.f64 2 x))) (pow.f64 (+.f64 1/2 (/.f64 2 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/2 (/.f64 2 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (/.f64 8 (pow.f64 x 3))) (+.f64 1/4 (-.f64 (/.f64 4 (*.f64 x x)) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/8 (/.f64 8 (pow.f64 x 3))) (+.f64 (/.f64 4 (*.f64 x x)) (-.f64 1/4 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (/.f64 4 (*.f64 x x))) (-.f64 1/2 (/.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/8 (/.f64 8 (pow.f64 x 3)))) (neg.f64 (+.f64 1/4 (-.f64 (/.f64 4 (*.f64 x x)) (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/4 (/.f64 4 (*.f64 x x)))) (neg.f64 (-.f64 1/2 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (/.f64 4 (*.f64 x x)) 1/4) (-.f64 (/.f64 2 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/2 (/.f64 2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 2 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 2 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1/2 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 2 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 (/.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) (cbrt.f64 (/.f64 2 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 2 x)) (sqrt.f64 (/.f64 2 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1/2 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 1/2 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1/2 (/.f64 2 x))))))))

simplify42.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
805×unswap-sqr_binary64
728×distribute-neg-frac_binary64
526×associate-/r*_binary64
371×fma-def_binary64
336×times-frac_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
040225
1105225
2247223
3692214
42140214
55936214
Stop Event
1×node limit
Counts
82 → 76
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 1/32 (pow.f64 x 3)) (*.f64 1/2 x)))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/32 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (*.f64 -1/128 (pow.f64 x 4)))))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
(/.f64 2 x)
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
1/2
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
1/2
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
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 1/32 (pow.f64 x 3)) (*.f64 1/2 x)))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/32 (pow.f64 x 3) (*.f64 1/2 x)))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/32 (pow.f64 x 3))))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x 1/32))))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/32 -1/8))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/32 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (*.f64 -1/128 (pow.f64 x 4)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/32 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 -1/128 (pow.f64 x 4)))))
(fma.f64 x (*.f64 x -1/8) (fma.f64 1/32 (pow.f64 x 3) (fma.f64 -1/128 (pow.f64 x 4) (*.f64 1/2 x))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (+.f64 1/32 (*.f64 x -1/128))))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 2 (/.f64 8 x))
(+.f64 2 (/.f64 -8 x))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x)))
(+.f64 2 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 2 (/.f64 -8 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 (/.f64 32 (*.f64 x x)) (-.f64 2 (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)) (/.f64 128 (pow.f64 x 3))))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 -8 x) (+.f64 2 (/.f64 -128 (pow.f64 x 3)))))
(+.f64 2 (+.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)) (/.f64 -128 (pow.f64 x 3))))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 2 (/.f64 8 x))
(+.f64 2 (/.f64 -8 x))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x)))
(+.f64 2 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 2 (/.f64 -8 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 (/.f64 32 (*.f64 x x)) (-.f64 2 (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)) (/.f64 128 (pow.f64 x 3))))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 -8 x) (+.f64 2 (/.f64 -128 (pow.f64 x 3)))))
(+.f64 2 (+.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)) (/.f64 -128 (pow.f64 x 3))))
(/.f64 2 x)
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 2 x))
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 2 x))
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 2 x))
1/2
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 2 x))
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 2 x))
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 2 x))
1/2
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 2 x))
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 2 x))
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 2 x))

localize38.0ms (1%)

Local error

Found 6 expressions with local error:

NewErrorProgram
0.1b
(/.f64 1 (+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x)))))
0.0b
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x))))
0.0b
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
✓0.0b
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
✓0.0b
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x))))
✓0.1b
(/.f64 1 (+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x)))))
Compiler

Compiled 48 to 39 computations (18.8% saved)

series3.0ms (0.1%)

Counts
3 → 21
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(/.f64 1 (+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x)))))
1.0ms
x
@0
(/.f64 1 (+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x)))))
0.0ms
x
@-inf
(/.f64 1 (+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x)))))
0.0ms
x
@inf
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x))))
0.0ms
x
@0
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x))))

rewrite80.0ms (2.1%)

Algorithm
1×batch-egg-rewrite
Rules
542×log-prod_binary64
408×fma-def_binary64
342×pow-prod-down_binary64
317×pow2_binary64
235×fma-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01232
127132
2350532
Stop Event
1×node limit
Counts
3 → 161
Calls
Call 1
Inputs
(/.f64 1 (+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x)))))
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x))))
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
Outputs
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(-.f64 1/2 (/.f64 2 x))) (*.f64 -1/8 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 -1/8 x 1/2) 1 (/.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/8 x 1/2)) 2) (cbrt.f64 (fma.f64 -1/8 x 1/2)) (/.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 -1/8 x 1/2)) (sqrt.f64 (fma.f64 -1/8 x 1/2)) (/.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/8 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (+.f64 1/2 (/.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/8 (sqrt.f64 x)) (sqrt.f64 x) (+.f64 1/2 (/.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 2 (cbrt.f64 (pow.f64 x -2))) (/.f64 1 (cbrt.f64 x)) (fma.f64 -1/8 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 2 (pow.f64 x -1/2)) (pow.f64 x -1/2) (fma.f64 -1/8 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (/.f64 2 x) (fma.f64 -1/8 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (/.f64 2 x) (fma.f64 -1/8 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (/.f64 2 x) (fma.f64 -1/8 x 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (/.f64 2 x) (fma.f64 -1/8 x 1/2))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1/2 (/.f64 2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/4 (-.f64 1/2 (/.f64 2 x))) (/.f64 (*.f64 (pow.f64 x -2) 4) (-.f64 1/2 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1/2 (/.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/2 (/.f64 2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1/2 (/.f64 2 x))) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 2 x))) 2) (cbrt.f64 (+.f64 1/2 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1/2 (/.f64 2 x))) (sqrt.f64 (+.f64 1/2 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 x -3) 8 1/8) (/.f64 1 (fma.f64 (/.f64 2 x) (-.f64 (/.f64 2 x) 1/2) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/4 (*.f64 (pow.f64 x -2) 4)) (/.f64 1 (-.f64 1/2 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (/.f64 2 x) (-.f64 (/.f64 2 x) 1/2) 1/4) (fma.f64 (pow.f64 x -3) 8 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1/2 (/.f64 2 x)) (-.f64 1/4 (*.f64 (pow.f64 x -2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x -3) 8 1/8) (fma.f64 (/.f64 2 x) (-.f64 (/.f64 2 x) 1/2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x -3) 8 1/8) (fma.f64 (pow.f64 x -2) 4 (-.f64 1/4 (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (*.f64 (pow.f64 x -2) 4)) (-.f64 1/2 (/.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (pow.f64 x -3) 8 1/8)) (neg.f64 (fma.f64 (/.f64 2 x) (-.f64 (/.f64 2 x) 1/2) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/4 (*.f64 (pow.f64 x -2) 4))) (neg.f64 (-.f64 1/2 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x -2) 4 -1/4) (-.f64 (/.f64 2 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/2 (/.f64 2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 2 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/2 (/.f64 2 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (/.f64 2 x) (-.f64 (/.f64 2 x) 1/2) 1/4) (fma.f64 (pow.f64 x -3) 8 1/8)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1/2 (/.f64 2 x)) (-.f64 1/4 (*.f64 (pow.f64 x -2) 4))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1/2 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1/2 (/.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 2 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 (/.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) 2 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 2 x) 1 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (*.f64 (/.f64 1 (cbrt.f64 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 2 x)) (cbrt.f64 (*.f64 (pow.f64 x -2) 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) 4)) (cbrt.f64 (/.f64 2 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (*.f64 (pow.f64 x -1/2) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 2 x)) (sqrt.f64 (/.f64 2 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 2 (cbrt.f64 (pow.f64 x -2))) (/.f64 1 (cbrt.f64 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 2 (pow.f64 x -1/2)) (pow.f64 x -1/2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1/2 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 1/2 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 1/2 (/.f64 2 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1/2 (/.f64 2 x))))))))

simplify58.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
898×fma-neg_binary64
812×times-frac_binary64
459×fma-def_binary64
456×cancel-sign-sub-inv_binary64
406×associate-/l/_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
049245
1129233
2342226
31083222
43392222
Stop Event
1×node limit
Counts
182 → 183
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 -3/128 (pow.f64 x 4)) (*.f64 1/16 (pow.f64 x 3)))))
(/.f64 -8 x)
(neg.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 2))) (*.f64 8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 256 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 32 (/.f64 1 (pow.f64 x 2))))))
(neg.f64 (+.f64 (*.f64 1536 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 256 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 32 (/.f64 1 (pow.f64 x 2)))))))
(/.f64 -8 x)
(neg.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 2))) (*.f64 8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 256 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 32 (/.f64 1 (pow.f64 x 2))))))
(neg.f64 (+.f64 (*.f64 1536 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 256 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 32 (/.f64 1 (pow.f64 x 2)))))))
(/.f64 2 x)
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(*.f64 -1/8 x)
(+.f64 (*.f64 -1/8 x) 1/2)
(*.f64 -1/8 x)
(+.f64 (*.f64 -1/8 x) 1/2)
(/.f64 2 x)
1/2
1/2
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))
(*.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 -1/8 (*.f64 x x) (fma.f64 1/16 (pow.f64 x 3) (*.f64 1/2 x)))
(fma.f64 1/16 (pow.f64 x 3) (*.f64 x (fma.f64 x -1/8 1/2)))
(*.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 -3/128 (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 -3/128 (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 -3/128 (pow.f64 x 4)))))
(+.f64 (*.f64 -3/128 (pow.f64 x 4)) (fma.f64 1/16 (pow.f64 x 3) (*.f64 x (fma.f64 x -1/8 1/2))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (+.f64 1/16 (*.f64 x -3/128))))
(/.f64 -8 x)
(neg.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 2))) (*.f64 8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x)))
(-.f64 (/.f64 -32 (*.f64 x x)) (/.f64 8 x))
(+.f64 (/.f64 -32 (*.f64 x x)) (/.f64 -8 x))
(neg.f64 (+.f64 (*.f64 256 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 32 (/.f64 1 (pow.f64 x 2))))))
(neg.f64 (+.f64 (/.f64 256 (pow.f64 x 3)) (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x))))
(+.f64 (/.f64 -256 (pow.f64 x 3)) (-.f64 (/.f64 -32 (*.f64 x x)) (/.f64 8 x)))
(+.f64 (/.f64 -256 (pow.f64 x 3)) (+.f64 (/.f64 -32 (*.f64 x x)) (/.f64 -8 x)))
(-.f64 (/.f64 -32 (*.f64 x x)) (-.f64 (/.f64 8 x) (/.f64 -256 (pow.f64 x 3))))
(+.f64 (/.f64 -32 (*.f64 x x)) (+.f64 (/.f64 -8 x) (/.f64 -256 (pow.f64 x 3))))
(neg.f64 (+.f64 (*.f64 1536 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 256 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 32 (/.f64 1 (pow.f64 x 2)))))))
(neg.f64 (+.f64 (+.f64 (/.f64 256 (pow.f64 x 3)) (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x))) (/.f64 1536 (pow.f64 x 4))))
(+.f64 (+.f64 (/.f64 -256 (pow.f64 x 3)) (-.f64 (/.f64 -32 (*.f64 x x)) (/.f64 8 x))) (/.f64 -1536 (pow.f64 x 4)))
(+.f64 (/.f64 -256 (pow.f64 x 3)) (-.f64 (+.f64 (/.f64 -32 (*.f64 x x)) (/.f64 -8 x)) (/.f64 1536 (pow.f64 x 4))))
(+.f64 (/.f64 -32 (*.f64 x x)) (+.f64 (/.f64 -8 x) (+.f64 (/.f64 -256 (pow.f64 x 3)) (/.f64 -1536 (pow.f64 x 4)))))
(/.f64 -8 x)
(neg.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 2))) (*.f64 8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x)))
(-.f64 (/.f64 -32 (*.f64 x x)) (/.f64 8 x))
(+.f64 (/.f64 -32 (*.f64 x x)) (/.f64 -8 x))
(neg.f64 (+.f64 (*.f64 256 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 32 (/.f64 1 (pow.f64 x 2))))))
(neg.f64 (+.f64 (/.f64 256 (pow.f64 x 3)) (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x))))
(+.f64 (/.f64 -256 (pow.f64 x 3)) (-.f64 (/.f64 -32 (*.f64 x x)) (/.f64 8 x)))
(+.f64 (/.f64 -256 (pow.f64 x 3)) (+.f64 (/.f64 -32 (*.f64 x x)) (/.f64 -8 x)))
(-.f64 (/.f64 -32 (*.f64 x x)) (-.f64 (/.f64 8 x) (/.f64 -256 (pow.f64 x 3))))
(+.f64 (/.f64 -32 (*.f64 x x)) (+.f64 (/.f64 -8 x) (/.f64 -256 (pow.f64 x 3))))
(neg.f64 (+.f64 (*.f64 1536 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 256 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 32 (/.f64 1 (pow.f64 x 2)))))))
(neg.f64 (+.f64 (+.f64 (/.f64 256 (pow.f64 x 3)) (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x))) (/.f64 1536 (pow.f64 x 4))))
(+.f64 (+.f64 (/.f64 -256 (pow.f64 x 3)) (-.f64 (/.f64 -32 (*.f64 x x)) (/.f64 8 x))) (/.f64 -1536 (pow.f64 x 4)))
(+.f64 (/.f64 -256 (pow.f64 x 3)) (-.f64 (+.f64 (/.f64 -32 (*.f64 x x)) (/.f64 -8 x)) (/.f64 1536 (pow.f64 x 4))))
(+.f64 (/.f64 -32 (*.f64 x x)) (+.f64 (/.f64 -8 x) (+.f64 (/.f64 -256 (pow.f64 x 3)) (/.f64 -1536 (pow.f64 x 4)))))
(/.f64 2 x)
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 2 x))
(*.f64 -1/8 x)
(*.f64 x -1/8)
(+.f64 (*.f64 -1/8 x) 1/2)
(fma.f64 -1/8 x 1/2)
(fma.f64 x -1/8 1/2)
(*.f64 -1/8 x)
(*.f64 x -1/8)
(+.f64 (*.f64 -1/8 x) 1/2)
(fma.f64 -1/8 x 1/2)
(fma.f64 x -1/8 1/2)
(/.f64 2 x)
1/2
1/2

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.1b
(/.f64 1 (/.f64 2 x))
✓0.1b
(/.f64 1 (/.f64 2 x))
Compiler

Compiled 12 to 9 computations (25% saved)

series3.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
(/.f64 1 (/.f64 2 x))
0.0ms
x
@inf
(/.f64 1 (/.f64 2 x))
0.0ms
x
@-inf
(/.f64 1 (/.f64 2 x))

rewrite46.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
543×pow1_binary64
507×add-log-exp_binary64
507×log1p-expm1-u_binary64
507×expm1-log1p-u_binary64
497×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
064
11294
214954
Stop Event
1×node limit
Counts
1 → 26
Calls
Call 1
Inputs
(/.f64 1 (/.f64 2 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x 1/2)) (pow.f64 (cbrt.f64 (*.f64 x 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x 1/2)) 2) (cbrt.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x 1/2)) (sqrt.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (/.f64 -2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (pow.f64 (/.f64 1 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) -1) (pow.f64 (cbrt.f64 (/.f64 2 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 2 x)) -1) (pow.f64 (sqrt.f64 (/.f64 2 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/4 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x 1/2)))))))

simplify9.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0448
1548
Stop Event
1×saturated
Counts
38 → 26
Calls
Call 1
Inputs
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
Outputs
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)

eval168.0ms (4.5%)

Compiler

Compiled 4125 to 3393 computations (17.7% saved)

prune42.0ms (1.1%)

Pruning

12 alts after pruning (2 fresh and 10 done)

PrunedKeptTotal
New2841285
Fresh011
Picked011
Done1910
Total28512297
Error
0b
Counts
297 → 12
Alt Table
Click to see full alt table
StatusErrorProgram
59.1b
(-.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))) 1)
60.8b
2
✓0.3b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))
✓20.6b
(*.f64 1/2 x)
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓20.2b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
✓20.7b
(/.f64 1 (/.f64 2 x))
✓39.1b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
✓21.1b
(/.f64 1 (+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x)))))
✓20.3b
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
✓0.2b
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)
✓20.2b
(*.f64 (/.f64 1 (+.f64 (*.f64 1/2 x) 2)) x)
Compiler

Compiled 102 to 85 computations (16.7% saved)

regimes22.0ms (0.6%)

Counts
12 → 1
Calls
Call 1
Inputs
2
(*.f64 1/2 x)
(/.f64 1 (/.f64 2 x))
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(*.f64 (/.f64 1 (+.f64 (*.f64 1/2 x) 2)) x)
(-.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))) 1)
(/.f64 1 (+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x)))))
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))
Outputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Calls

2 calls:

11.0ms
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms
x
Results
ErrorSegmentsBranch
0.2b1x
0.2b1(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 102 to 82 computations (19.6% saved)

regimes15.0ms (0.4%)

Counts
9 → 2
Calls
Call 1
Inputs
2
(*.f64 1/2 x)
(/.f64 1 (/.f64 2 x))
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(*.f64 (/.f64 1 (+.f64 (*.f64 1/2 x) 2)) x)
(-.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))) 1)
(/.f64 1 (+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x)))))
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
Outputs
(/.f64 1 (+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x)))))
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
Calls

1 calls:

12.0ms
x
Results
ErrorSegmentsBranch
0.3b2x
Compiler

Compiled 65 to 53 computations (18.5% saved)

bsearch20.0ms (0.5%)

Algorithm
1×binary-search
Steps
TimeLeftRight
20.0ms
7.324045184595973e-6
0.020906970886639117
Compiler

Compiled 13 to 10 computations (23.1% saved)

regimes12.0ms (0.3%)

Counts
8 → 1
Calls
Call 1
Inputs
2
(*.f64 1/2 x)
(/.f64 1 (/.f64 2 x))
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(*.f64 (/.f64 1 (+.f64 (*.f64 1/2 x) 2)) x)
(-.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))) 1)
(/.f64 1 (+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x)))))
Outputs
(*.f64 (/.f64 1 (+.f64 (*.f64 1/2 x) 2)) x)
Calls

1 calls:

10.0ms
x
Results
ErrorSegmentsBranch
20.2b1x
Compiler

Compiled 59 to 48 computations (18.6% saved)

regimes6.0ms (0.2%)

Counts
5 → 1
Calls
Call 1
Inputs
2
(*.f64 1/2 x)
(/.f64 1 (/.f64 2 x))
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
Outputs
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
Calls

1 calls:

5.0ms
x
Results
ErrorSegmentsBranch
20.2b1x
Compiler

Compiled 26 to 20 computations (23.1% saved)

regimes10.0ms (0.3%)

Counts
4 → 1
Calls
Call 1
Inputs
2
(*.f64 1/2 x)
(/.f64 1 (/.f64 2 x))
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
Outputs
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
Calls

1 calls:

9.0ms
x
Results
ErrorSegmentsBranch
20.3b1x
Compiler

Compiled 19 to 15 computations (21.1% saved)

regimes5.0ms (0.1%)

Accuracy

Total -40.2b remaining (-195%)

Threshold costs -40.2b (-195%)

Counts
3 → 1
Calls
Call 1
Inputs
2
(*.f64 1/2 x)
(/.f64 1 (/.f64 2 x))
Outputs
(*.f64 1/2 x)
Calls

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
20.6b1x
Compiler

Compiled 12 to 9 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
7×+-commutative_binary64
4×*-commutative_binary64
1×sub-neg_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02984
14484
24584
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(if (<=.f64 x 540419148418107/73786976294838206464) (/.f64 1 (+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x))))) (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
(*.f64 (/.f64 1 (+.f64 (*.f64 1/2 x) 2)) x)
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
(*.f64 1/2 x)
2
Outputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(if (<=.f64 x 540419148418107/73786976294838206464) (/.f64 1 (+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x))))) (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
(if (<=.f64 x 540419148418107/73786976294838206464) (/.f64 1 (+.f64 (*.f64 x -1/8) (+.f64 1/2 (*.f64 2 (/.f64 1 x))))) (+.f64 (sqrt.f64 (+.f64 x 1)) -1))
(*.f64 (/.f64 1 (+.f64 (*.f64 1/2 x) 2)) x)
(*.f64 x (/.f64 1 (+.f64 2 (*.f64 x 1/2))))
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(/.f64 x (+.f64 2 (*.f64 x 1/2)))
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
(*.f64 1/2 x)
(*.f64 x 1/2)
2

end58.0ms (1.5%)

Stop Event
1×fuel
Compiler

Compiled 124 to 100 computations (19.4% saved)

Profiling

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