Details

Time bar (total: 4.4s)

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)

sample1.0s (23.5%)

Results
1.0s8253×body256valid
1.0ms3×body2048valid

preprocess15.0ms (0.3%)

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)

simplify6.0ms (0.1%)

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))))

eval0.0ms (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)

localize11.0ms (0.2%)

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

rewrite53.0ms (1.2%)

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 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 hypot.f64 1 (sqrt.f64 x))))))
((#(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 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)))))))) (#(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)))))

simplify86.0ms (1.9%)

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))

eval33.0ms (0.7%)

Compiler

Compiled 1387 to 1085 computations (21.8% saved)

prune23.0ms (0.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1007107
Fresh000
Picked011
Done000
Total1008108
Error
0b
Counts
108 → 8
Alt Table
Click to see full alt table
StatusErrorProgram
▶21.0b
(/.f64 x (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
38.5b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
▶21.0b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
▶0.3b
(pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)
▶21.4b
(/.f64 x 2)
▶22.5b
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
7.7b
(*.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (+.f64 1 (+.f64 1 (-.f64 x (sqrt.f64 (+.f64 x 1))))))
Compiler

Compiled 159 to 125 computations (21.4% saved)

localize15.0ms (0.3%)

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)

series4.0ms (0.1%)

Counts
2 → 8
Calls

6 calls:

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

rewrite53.0ms (1.2%)

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
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(+.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)))))))

simplify42.0ms (1%)

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)))

localize3.0ms (0.1%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize8.0ms (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)

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite51.0ms (1.2%)

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))))))))

simplify35.0ms (0.8%)

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)))))

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiled 28 to 22 computations (21.4% saved)

series3.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(/.f64 x (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
0.0ms
x
@inf
(+.f64 1 (+.f64 (*.f64 1/2 x) 1))
0.0ms
x
@0
(+.f64 1 (+.f64 (*.f64 1/2 x) 1))
0.0ms
x
@0
(/.f64 x (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
0.0ms
x
@-inf
(+.f64 1 (+.f64 (*.f64 1/2 x) 1))

rewrite49.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
968×pow1_binary64
904×log1p-expm1-u_binary64
904×expm1-log1p-u_binary64
903×add-log-exp_binary64
91×add-sqr-sqrt_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0819
118017
2244017
Stop Event
1×node limit
Counts
2 → 65
Calls
Call 1
Inputs
(+.f64 1 (+.f64 (*.f64 1/2 x) 1))
(/.f64 x (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (*.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 (+.f64 (*.f64 1/2 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 1/2 x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2) (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (*.f64 1/2 x) 2)) (sqrt.f64 (+.f64 (*.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 (+.f64 1 (*.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x)))))))) (#(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 (+.f64 1 (*.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x))) (+.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 (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3)) (+.f64 1 (*.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x))))))) (#(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 (+.f64 1 (*.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x)))))))) (#(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 (+.f64 (*.f64 1/2 x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (*.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 expm1.f64 (log1p.f64 (+.f64 (*.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 (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 (sqrt.f64 (fma.f64 1/2 x 1)) (sqrt.f64 (fma.f64 1/2 x 1)) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))) 2) (cbrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))) (sqrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (*.f64 1/2 x) 2)) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2)) (/.f64 x (cbrt.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2)) (cbrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 1/2 x) 2))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (+.f64 (*.f64 1/2 x) 2))) (/.f64 (cbrt.f64 x) (sqrt.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3))) (+.f64 1 (*.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (-.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 (/.f64 x (+.f64 (*.f64 1/2 x) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (*.f64 1/2 x) 2) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 (*.f64 1/2 x) 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 x) (log1p.f64 (fma.f64 1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))))))))

simplify40.0ms (0.9%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
039210
1102210
2243208
3689199
42136199
55913199
Stop Event
1×node limit
Counts
89 → 82
Calls
Call 1
Inputs
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))
(*.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
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)
(*.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 1/2 x (fma.f64 1/32 (pow.f64 x 3) (*.f64 -1/128 (pow.f64 x 4)))))
(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 (+.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 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 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 -128 (pow.f64 x 3)) (+.f64 2 (/.f64 -8 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 (/.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 (+.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 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 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 -128 (pow.f64 x 3)) (+.f64 2 (/.f64 -8 x))))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 2 (+.f64 (/.f64 -8 x) (/.f64 -128 (pow.f64 x 3)))))

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 -1/8 (pow.f64 x 2))
0.0b
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
✓0.0b
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
✓0.2b
(*.f64 -1/8 (pow.f64 x 2))
Compiler

Compiled 25 to 19 computations (24% saved)

series2.0ms (0.1%)

Counts
2 → 3
Calls

6 calls:

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

rewrite58.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
900×pow1_binary64
843×add-log-exp_binary64
842×log1p-expm1-u_binary64
842×expm1-log1p-u_binary64
827×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0918
119718
2235718
Stop Event
1×node limit
Counts
2 → 48
Calls
Call 1
Inputs
(*.f64 -1/8 (pow.f64 x 2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 -1/8 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/8 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 -1/8 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 -1/8)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 x x) 3) -1/512) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 4) 1/64))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/8) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 x x) 3) -1/512))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/8 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 -1/8 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/8 (*.f64 x x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 x 4) 1/64) (+.f64 (*.f64 -1/8 (*.f64 x x)) (*.f64 -1/2 x))) (/.f64 (*.f64 (*.f64 x x) 1/4) (+.f64 (*.f64 -1/8 (*.f64 x x)) (*.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))) (pow.f64 (cbrt.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))) 2) (cbrt.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))) (sqrt.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (pow.f64 (*.f64 x x) 3) -1/512) (*.f64 (pow.f64 x 3) 1/8)) (/.f64 1 (+.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 x 1/2) (-.f64 (*.f64 x 1/2) (*.f64 -1/8 (*.f64 x x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 x x) 1/4)) (/.f64 1 (+.f64 (*.f64 -1/8 (*.f64 x x)) (*.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 x 1/2) (-.f64 (*.f64 x 1/2) (*.f64 -1/8 (*.f64 x x))))) (+.f64 (*.f64 (pow.f64 (*.f64 x x) 3) -1/512) (*.f64 (pow.f64 x 3) 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 -1/8 (*.f64 x x)) (*.f64 -1/2 x)) (-.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 x x) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 (*.f64 x x) 3) -1/512) (*.f64 (pow.f64 x 3) 1/8)) (+.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 x 1/2) (-.f64 (*.f64 x 1/2) (*.f64 -1/8 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 (*.f64 x x) 3) -1/512) (*.f64 (pow.f64 x 3) 1/8)) (+.f64 (*.f64 (*.f64 x x) 1/4) (-.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 x x) (*.f64 -1/8 (*.f64 x 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 x x) 1/4)) (+.f64 (*.f64 -1/8 (*.f64 x x)) (*.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (*.f64 (pow.f64 (*.f64 x x) 3) -1/512) (*.f64 (pow.f64 x 3) 1/8))) (neg.f64 (+.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 x 1/2) (-.f64 (*.f64 x 1/2) (*.f64 -1/8 (*.f64 x x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 x x) 1/4))) (neg.f64 (+.f64 (*.f64 -1/8 (*.f64 x x)) (*.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (pow.f64 x 4) 1/64)) (-.f64 (*.f64 x 1/2) (*.f64 -1/8 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/2 (*.f64 -1/8 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) -1/8 (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 x (*.f64 -1/8 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 -1/8 (*.f64 x x)) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 1/2) (*.f64 -1/8 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 1/2)) 2) (cbrt.f64 (*.f64 x 1/2)) (*.f64 -1/8 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 1/64)) (cbrt.f64 (*.f64 -1/8 (*.f64 x x))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/2)) (sqrt.f64 (*.f64 x 1/2)) (*.f64 -1/8 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 -1/8)) (*.f64 x (sqrt.f64 -1/8)) (*.f64 x 1/2))))))

simplify117.0ms (2.7%)

Algorithm
1×egg-herbie
Rules
1124×sqr-pow_binary64
565×cube-prod_binary64
560×fabs-mul_binary64
541×pow-sqr_binary64
511×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0818
11518
22518
35118
412218
535818
6137018
7225718
8242118
9263418
10285418
11315418
12355418
13404018
14459918
15528918
16612618
17652018
18681018
19708818
20715618
21719218
Stop Event
1×node limit
Counts
51 → 51
Calls
Call 1
Inputs
(*.f64 1/2 x)
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (pow.f64 x 2))
Outputs
(*.f64 1/2 x)
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (*.f64 x x))
(*.f64 x (*.f64 x -1/8))
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (*.f64 x x))
(*.f64 x (*.f64 x -1/8))

eval165.0ms (3.8%)

Compiler

Compiled 5086 to 3909 computations (23.1% saved)

prune44.0ms (1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New3613364
Fresh022
Picked101
Done235
Total3648372
Error
0b
Counts
372 → 8
Alt Table
Click to see full alt table
StatusErrorProgram
60.8b
2
✓21.4b
(/.f64 x 2)
▶21.1b
(pow.f64 (+.f64 1/2 (/.f64 2 x)) -1)
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
▶38.5b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
✓21.0b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
▶0.3b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))
▶7.7b
(*.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (+.f64 1 (+.f64 1 (-.f64 x (sqrt.f64 (+.f64 x 1))))))
Compiler

Compiled 74 to 59 computations (20.3% saved)

localize37.0ms (0.8%)

Local error

Found 8 expressions with local error:

NewErrorProgram
0.0b
(-.f64 x (sqrt.f64 (+.f64 x 1)))
0.0b
(pow.f64 (+.f64 x 1) 3/2)
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(+.f64 1 (pow.f64 (+.f64 x 1) 3/2))
✓0.0b
(-.f64 x (sqrt.f64 (+.f64 x 1)))
✓0.1b
(*.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (+.f64 1 (+.f64 1 (-.f64 x (sqrt.f64 (+.f64 x 1))))))
✓4.1b
(+.f64 1 (-.f64 x (sqrt.f64 (+.f64 x 1))))
✓7.5b
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))
Compiler

Compiled 76 to 59 computations (22.4% saved)

series17.0ms (0.4%)

Counts
4 → 30
Calls

12 calls:

TimeVariablePointExpression
3.0ms
x
@-inf
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))
3.0ms
x
@-inf
(*.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (+.f64 1 (+.f64 1 (-.f64 x (sqrt.f64 (+.f64 x 1))))))
3.0ms
x
@inf
(+.f64 1 (-.f64 x (sqrt.f64 (+.f64 x 1))))
3.0ms
x
@inf
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))
2.0ms
x
@inf
(*.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (+.f64 1 (+.f64 1 (-.f64 x (sqrt.f64 (+.f64 x 1))))))

rewrite100.0ms (2.3%)

Algorithm
1×batch-egg-rewrite
Rules
721×log-prod_binary64
440×fma-neg_binary64
279×log-div_binary64
266×log1p-udef_binary64
265×expm1-udef_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01361
132161
2501060
Stop Event
1×node limit
Counts
4 → 237
Calls
Call 1
Inputs
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))
(+.f64 1 (-.f64 x (sqrt.f64 (+.f64 x 1))))
(*.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (+.f64 1 (+.f64 1 (-.f64 x (sqrt.f64 (+.f64 x 1))))))
(-.f64 x (sqrt.f64 (+.f64 x 1)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))))) (cbrt.f64 (exp.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 (/.f64 1 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))) 2) (cbrt.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))) 2) (*.f64 (cbrt.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 x 1) 3/4))) (/.f64 (sqrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 x 1) 3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 x 1) 3/4))) (*.f64 (/.f64 (sqrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 x 1) 3/4))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (+.f64 (neg.f64 (pow.f64 (+.f64 x 1) 3/2)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) 2))) (/.f64 x (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) 2))) (cbrt.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) 2))) (/.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 1 (pow.f64 (+.f64 x 1) 3/4))) (/.f64 x (hypot.f64 1 (pow.f64 (+.f64 x 1) 3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (hypot.f64 1 (pow.f64 (+.f64 x 1) 3/4))) (/.f64 (cbrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 x 1) 3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 9/2))) (+.f64 1 (-.f64 (pow.f64 (+.f64 x 1) 3) (pow.f64 (+.f64 x 1) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (-.f64 1 (pow.f64 (+.f64 x 1) 3))) (-.f64 1 (pow.f64 (+.f64 x 1) 3/2)))))) (#(struct:change #<rule egg-rr> (2) 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(+.f64 x 1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 x (sqrt.f64 (+.f64 x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 x (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 x (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 x)) (exp.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (exp.f64 x) (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 x)) (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 x)) (exp.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 x) (/.f64 1 (exp.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 x)) (/.f64 1 (exp.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (neg.f64 (sqrt.f64 (+.f64 x 1)))) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (/.f64 1 (exp.f64 (sqrt.f64 (+.f64 x 1)))) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (neg.f64 (sqrt.f64 (+.f64 x 1)))) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (/.f64 1 (exp.f64 (sqrt.f64 (+.f64 x 1)))) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 x (sqrt.f64 (+.f64 x 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 x (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 x (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 x (sqrt.f64 (+.f64 x 1)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 x (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 (log1p.f64 (-.f64 x (sqrt.f64 (+.f64 x 1)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1 (neg.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (neg.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x 1)) (expm1.f64 (*.f64 1/2 (log1p.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (-.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))) (cbrt.f64 (pow.f64 (-.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (-.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2)) (cbrt.f64 (-.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 2) (neg.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1) (neg.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))) (sqrt.f64 (-.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1) (neg.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (pow.f64 (-.f64 x (sqrt.f64 (+.f64 x 1))) 3)) (/.f64 1 (+.f64 1 (-.f64 (pow.f64 (-.f64 x (sqrt.f64 (+.f64 x 1))) 2) (-.f64 x (sqrt.f64 (+.f64 x 1)))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (pow.f64 (-.f64 x (sqrt.f64 (+.f64 x 1))) 2)) (/.f64 1 (+.f64 (-.f64 1 x) (sqrt.f64 (+.f64 x 1)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (pow.f64 (+.f64 x 1) 1/4)) (-.f64 (sqrt.f64 (+.f64 x 1)) (pow.f64 (+.f64 x 1) 1/4)) -1)))))

simplify78.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
683×fma-def_binary64
529×fma-neg_binary64
411×unswap-sqr_binary64
399×times-frac_binary64
285×associate-/l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01371275
14001213
21293995
36150877
Stop Event
1×node limit
Counts
267 → 284
Calls
Call 1
Inputs
(*.f64 1/2 x)
(+.f64 (*.f64 1/2 x) (*.f64 -3/8 (pow.f64 x 2)))
(+.f64 (*.f64 3/16 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (*.f64 -3/8 (pow.f64 x 2))))
(+.f64 (*.f64 3/16 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -3/8 (pow.f64 x 2)) (*.f64 -7/128 (pow.f64 x 4)))))
(/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1))
(+.f64 (*.f64 -3/2 (*.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 2)) (sqrt.f64 (pow.f64 x 3)))) (/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1)))
(-.f64 (+.f64 (*.f64 -3/2 (*.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 2)) (sqrt.f64 (pow.f64 x 3)))) (+.f64 (*.f64 9/4 (/.f64 (pow.f64 x 2) (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 3))) (/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1)))) (*.f64 3/8 (*.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 2)) (sqrt.f64 x))))
(-.f64 (+.f64 (*.f64 -3/2 (*.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 2)) (sqrt.f64 (pow.f64 x 3)))) (+.f64 (*.f64 9/4 (/.f64 (pow.f64 x 2) (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 3))) (+.f64 (*.f64 9/16 (/.f64 x (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 3))) (/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1))))) (+.f64 (*.f64 3/8 (*.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 2)) (sqrt.f64 x))) (+.f64 (*.f64 -1/16 (*.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 2)) (sqrt.f64 (/.f64 1 x)))) (*.f64 3/2 (*.f64 (/.f64 (-.f64 (*.f64 9/4 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 3))) (*.f64 3/8 (*.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 2)) (sqrt.f64 (pow.f64 x 3))))) (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1)) (sqrt.f64 (/.f64 1 x)))))))
(/.f64 x (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
(+.f64 (*.f64 -3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 2))) (/.f64 x (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))
(+.f64 (*.f64 -3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 2) x))) (+.f64 (*.f64 9/4 (/.f64 (pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (*.f64 (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 3) x))) (+.f64 (*.f64 -3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 2))) (/.f64 x (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))))
(+.f64 (*.f64 9/4 (/.f64 (pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (*.f64 (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 3) x))) (+.f64 (*.f64 -3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 2) x))) (+.f64 (*.f64 -3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 2))) (+.f64 (/.f64 x (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 -1 (/.f64 (+.f64 (*.f64 -9/16 (/.f64 (pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 3))) (+.f64 (*.f64 -1/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 2))) (*.f64 3/2 (/.f64 (*.f64 (+.f64 (*.f64 -3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 2))) (*.f64 9/4 (/.f64 (pow.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) 3)))) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))))) (pow.f64 x 2)))))))
(*.f64 1/2 x)
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 -1/16 (pow.f64 x 3)) (*.f64 1/2 x)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 -1/16 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (*.f64 5/128 (pow.f64 x 4)))))
x
x
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -5/128 (pow.f64 x 4)) (*.f64 1/16 (pow.f64 x 3)))))
(/.f64 (pow.f64 x 2) (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1))
(/.f64 (pow.f64 x 2) (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
-1
(-.f64 (*.f64 1/2 x) 1)
(-.f64 (+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 1/2 x)) 1)
(-.f64 (+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 -1/16 (pow.f64 x 3)))) 1)
x
x
Outputs
(*.f64 1/2 x)
(+.f64 (*.f64 1/2 x) (*.f64 -3/8 (pow.f64 x 2)))
(fma.f64 1/2 x (*.f64 -3/8 (*.f64 x x)))
(fma.f64 -3/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 1/2 (*.f64 x -3/8)))
(+.f64 (*.f64 3/16 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (*.f64 -3/8 (pow.f64 x 2))))
(fma.f64 3/16 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 -3/8 (*.f64 x x))))
(fma.f64 3/16 (pow.f64 x 3) (fma.f64 -3/8 (*.f64 x x) (*.f64 1/2 x)))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 -3/8 (*.f64 x 3/16))))
(+.f64 (*.f64 3/16 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -3/8 (pow.f64 x 2)) (*.f64 -7/128 (pow.f64 x 4)))))
(fma.f64 3/16 (pow.f64 x 3) (fma.f64 1/2 x (fma.f64 -3/8 (*.f64 x x) (*.f64 -7/128 (pow.f64 x 4)))))
(fma.f64 3/16 (pow.f64 x 3) (fma.f64 1/2 x (fma.f64 -7/128 (pow.f64 x 4) (*.f64 x (*.f64 x -3/8)))))
(fma.f64 3/16 (pow.f64 x 3) (fma.f64 -7/128 (pow.f64 x 4) (*.f64 x (+.f64 1/2 (*.f64 x -3/8)))))
(/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1))
(/.f64 x (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)))
(+.f64 (*.f64 -3/2 (*.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1) 2)) (sqrt.f64 (pow.f64 x 3)))) (/.f64 x (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1)))
(fma.f64 -3/2 (*.f64 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)) 2)) (sqrt.f64 (pow.f64 x 3))) (/.f64 x (+.f64 1 (pow.f64 (/.f64 1 x) -3/2))))
(fma.f64 -3/2 (/.f64 (sqrt.f64 (pow.f64 x 3)) (pow.f64 (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)) 2)) (/.f64 x (+.f64 1 (pow.f64 (/.f64 1 x) -3/2))))
(fma.f64 -3/2 (/.f64 (pow.f64 x 3/2) (pow.f64 (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)) 2)) (/.f64 x (+.f64 1 (pow.f64 (/.f64 1 x) -3/2))))
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(fma.f64 9/4 (/.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 3)) (fma.f64 -3/8 (/.f64 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)) (-.f64 (fma.f64 -3/2 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)) (/.f64 x (+.f64 1 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))) (/.f64 (fma.f64 -9/16 (/.f64 (pow.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 3)) (fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (/.f64 (+.f64 1 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (fma.f64 -3/8 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)) (/.f64 (*.f64 9/4 (pow.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 3))))) (*.f64 -1/16 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2))))) (*.f64 x x)))))
(+.f64 (-.f64 (/.f64 x (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) 1)) (/.f64 (fma.f64 -1/16 (/.f64 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2)) (pow.f64 (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) 1) 2)) (fma.f64 3/2 (*.f64 (/.f64 (pow.f64 (/.f64 -1 x) -3/2) (/.f64 (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) 1) (pow.f64 -1 3/2))) (fma.f64 9/4 (/.f64 (pow.f64 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2)) 2) (pow.f64 (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) 1) 3)) (*.f64 -3/8 (/.f64 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2)) (pow.f64 (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) 1) 2))))) (*.f64 -9/16 (/.f64 (pow.f64 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2)) 2) (pow.f64 (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) 1) 3))))) (*.f64 x x))) (fma.f64 (/.f64 9/4 x) (/.f64 (pow.f64 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2)) 2) (pow.f64 (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) 1) 3)) (*.f64 (/.f64 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2)) (pow.f64 (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) 1) 2)) (+.f64 -3/2 (/.f64 -3/8 x)))))
(+.f64 (-.f64 (/.f64 x (+.f64 1 (pow.f64 (exp.f64 (log.f64 x)) 3/2))) (/.f64 (fma.f64 -1/16 (/.f64 (pow.f64 (exp.f64 (log.f64 x)) 3/2) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (log.f64 x)) 3/2)) 2)) (fma.f64 3/2 (*.f64 (/.f64 (pow.f64 (exp.f64 (log.f64 x)) 3/2) (+.f64 1 (pow.f64 (exp.f64 (log.f64 x)) 3/2))) (fma.f64 -3/8 (/.f64 (pow.f64 (exp.f64 (log.f64 x)) 3/2) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (log.f64 x)) 3/2)) 2)) (*.f64 (/.f64 9/4 (pow.f64 (hypot.f64 1 (pow.f64 (exp.f64 (log.f64 x)) 3/4)) 6)) (pow.f64 (exp.f64 (log.f64 x)) 3)))) (/.f64 (pow.f64 (exp.f64 (log.f64 x)) 3) (/.f64 (pow.f64 (hypot.f64 1 (pow.f64 (exp.f64 (log.f64 x)) 3/4)) 6) -9/16)))) (*.f64 x x))) (fma.f64 9/4 (/.f64 (/.f64 (pow.f64 (exp.f64 (log.f64 x)) 3) x) (pow.f64 (hypot.f64 1 (pow.f64 (exp.f64 (log.f64 x)) 3/4)) 6)) (*.f64 (/.f64 (pow.f64 (exp.f64 (log.f64 x)) 3/2) (pow.f64 (+.f64 1 (pow.f64 (exp.f64 (log.f64 x)) 3/2)) 2)) (+.f64 -3/2 (/.f64 -3/8 x)))))
(*.f64 1/2 x)
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 1/8 (*.f64 x x) (*.f64 1/2 x))
(fma.f64 (*.f64 x x) 1/8 (*.f64 1/2 x))
(*.f64 x (+.f64 1/2 (*.f64 x 1/8)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 -1/16 (pow.f64 x 3)) (*.f64 1/2 x)))
(fma.f64 1/8 (*.f64 x x) (fma.f64 -1/16 (pow.f64 x 3) (*.f64 1/2 x)))
(fma.f64 (*.f64 x x) 1/8 (fma.f64 (pow.f64 x 3) -1/16 (*.f64 1/2 x)))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 1/8 (*.f64 x -1/16))))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 -1/16 (pow.f64 x 3)) (+.f64 (*.f64 1/2 x) (*.f64 5/128 (pow.f64 x 4)))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 -1/16 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 (pow.f64 x 4) 5/128))))
(fma.f64 (*.f64 x x) 1/8 (fma.f64 (pow.f64 x 3) -1/16 (fma.f64 1/2 x (*.f64 (pow.f64 x 4) 5/128))))
(fma.f64 x (*.f64 x 1/8) (fma.f64 (pow.f64 x 4) 5/128 (fma.f64 (pow.f64 x 3) -1/16 (*.f64 1/2 x))))
x
x
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(fma.f64 1/2 x (*.f64 x (*.f64 x -1/8)))
(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 (pow.f64 x 3) 1/16)))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 (pow.f64 x 3) 1/16 (*.f64 1/2 x)))
(fma.f64 (pow.f64 x 3) 1/16 (*.f64 x (+.f64 1/2 (*.f64 x -1/8))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -5/128 (pow.f64 x 4)) (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 -5/128 (pow.f64 x 4) (*.f64 (pow.f64 x 3) 1/16))))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/2 x (fma.f64 (pow.f64 x 3) 1/16 (*.f64 (pow.f64 x 4) -5/128))))
(fma.f64 x (*.f64 x -1/8) (fma.f64 (pow.f64 x 4) -5/128 (fma.f64 (pow.f64 x 3) 1/16 (*.f64 1/2 x))))
(/.f64 (pow.f64 x 2) (+.f64 (pow.f64 (/.f64 1 x) -3/2) 1))
(/.f64 (*.f64 x x) (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)))
(/.f64 x (/.f64 (+.f64 1 (pow.f64 (/.f64 1 x) -3/2)) x))
(/.f64 (pow.f64 x 2) (+.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
(/.f64 (*.f64 x x) (+.f64 1 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))
(/.f64 x (/.f64 (+.f64 1 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x))
(/.f64 (*.f64 x x) (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) 1))
(/.f64 (*.f64 x x) (+.f64 1 (pow.f64 (exp.f64 (log.f64 x)) 3/2)))
-1
(-.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x -1)
(-.f64 (+.f64 (*.f64 1/8 (pow.f64 x 2)) (*.f64 1/2 x)) 1)
(+.f64 (*.f64 (*.f64 x x) 1/8) (fma.f64 1/2 x -1))
(fma.f64 (*.f64 x x) 1/8 (fma.f64 1/2 x -1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/8) -1))
(fma.f64 x (+.f64 (*.f64 x 1/8) 1/2) -1)
(-.f64 (+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 -1/16 (pow.f64 x 3)))) 1)
(+.f64 (fma.f64 1/8 (*.f64 x x) (fma.f64 -1/16 (pow.f64 x 3) (*.f64 1/2 x))) -1)
(+.f64 -1 (fma.f64 (*.f64 x x) 1/8 (fma.f64 (pow.f64 x 3) -1/16 (*.f64 1/2 x))))
(fma.f64 x (*.f64 x 1/8) (fma.f64 1/2 x (fma.f64 (pow.f64 x 3) -1/16 -1)))
x
x

localize16.0ms (0.4%)

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

rewrite64.0ms (1.4%)

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 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 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 hypot.f64 1 (sqrt.f64 x))))))
((#(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 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)))))))) (#(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)))))

simplify64.0ms (1.5%)

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))

localize15.0ms (0.3%)

Local error

Found 8 expressions with local error:

NewErrorProgram
3.9b
(-.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)))
✓3.9b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
Compiler

Compiled 34 to 25 computations (26.5% saved)

series6.0ms (0.1%)

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

rewrite54.0ms (1.2%)

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 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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 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 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 +.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 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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 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 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 +.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 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)))))))) (#(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)))))

simplify90.0ms (2.1%)

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))

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiled 20 to 16 computations (20% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite39.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
851×pow1_binary64
798×add-log-exp_binary64
797×log1p-expm1-u_binary64
797×expm1-log1p-u_binary64
784×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
118010
2216510
Stop Event
1×node limit
Counts
1 → 21
Calls
Call 1
Inputs
(pow.f64 (+.f64 1/2 (/.f64 2 x)) -1)
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 (/.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 (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 (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 /.f64 -1 (neg.f64 (+.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 1 (/.f64 (+.f64 1/2 (/.f64 2 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -1/2) (sqrt.f64 (+.f64 1/2 (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (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 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)))))))))

simplify34.0ms (0.8%)

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
33 → 35
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)))))

eval802.0ms (18.2%)

Compiler

Compiled 14691 to 11546 computations (21.4% saved)

prune81.0ms (1.8%)

Pruning

11 alts after pruning (6 fresh and 5 done)

PrunedKeptTotal
New6926698
Fresh101
Picked101
Done156
Total69511706
Error
0b
Counts
706 → 11
Alt Table
Click to see full alt table
StatusErrorProgram
▶59.4b
(-.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))) 1)
✓0.3b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))
▶38.5b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
▶21.1b
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓21.0b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
✓21.4b
(/.f64 x 2)
▶22.1b
(/.f64 1 (+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x)))))
60.8b
2
▶21.1b
(/.f64 1 (/.f64 (+.f64 (*.f64 1/2 x) 2) x))
✓7.7b
(*.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (+.f64 1 (+.f64 1 (-.f64 x (sqrt.f64 (+.f64 x 1))))))
Compiler

Compiled 157 to 132 computations (15.9% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiled 20 to 16 computations (20% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite39.0ms (0.9%)

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
0810
117810
2217510
Stop Event
1×node limit
Counts
1 → 22
Calls
Call 1
Inputs
(/.f64 1 (+.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)))))))))

simplify36.0ms (0.8%)

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
34 → 36
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)))))

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiled 29 to 22 computations (24.1% saved)

series2.0ms (0%)

Counts
2 → 24
Calls

6 calls:

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

rewrite49.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
430×log-prod_binary64
336×exp-prod_binary64
280×prod-exp_binary64
236×pow-prod-down_binary64
235×pow2_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0919
120016
2255816
Stop Event
1×node limit
Counts
2 → 105
Calls
Call 1
Inputs
(/.f64 1 (/.f64 (+.f64 (*.f64 1/2 x) 2) x))
(/.f64 (+.f64 (*.f64 1/2 x) 2) x)
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 (+.f64 1 (/.f64 x (fma.f64 1/2 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (fma.f64 1/2 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (fma.f64 1/2 x 2))) (cbrt.f64 (pow.f64 (/.f64 x (fma.f64 1/2 x 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 x (fma.f64 1/2 x 2)) 2)) (cbrt.f64 (/.f64 x (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (fma.f64 1/2 x 2))) (sqrt.f64 (/.f64 x (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (/.f64 (neg.f64 (fma.f64 1/2 x 2)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 1/2 x 2)) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 1/2 x 2) x)) -2) (cbrt.f64 (/.f64 x (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 x x)) 1) (/.f64 (cbrt.f64 x) (fma.f64 1/2 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (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 x (cbrt.f64 (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 x x) (pow.f64 (fma.f64 1/2 x 2) 2))) (cbrt.f64 (/.f64 x (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 (pow.f64 (fma.f64 1/2 x 2) 2))) (/.f64 (sqrt.f64 x) (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) (/.f64 x (sqrt.f64 (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 x x)) (sqrt.f64 (fma.f64 1/2 x 2))) (/.f64 (cbrt.f64 x) (sqrt.f64 (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 (fma.f64 1/2 x 2))) (/.f64 (sqrt.f64 x) (sqrt.f64 (fma.f64 1/2 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (neg.f64 (fma.f64 1/2 x 2))) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (fma.f64 1/8 (pow.f64 x 3) 8)) (-.f64 (fma.f64 1/4 (*.f64 x x) 4) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (fma.f64 1/4 (*.f64 x x) -4)) (fma.f64 1/2 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 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2))))))) (#(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 expm1.f64 (log1p.f64 (/.f64 x (fma.f64 1/2 x 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (fma.f64 1/2 x 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (fma.f64 1/2 x 2) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (fma.f64 1/2 x 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 1/2 x 2) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (fma.f64 1/2 x 2) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (fma.f64 1/2 x 2) x)) 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 (fma.f64 1/2 x 2) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 1/2 x 2) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (fma.f64 1/2 x 2) x)) (pow.f64 (cbrt.f64 (/.f64 (fma.f64 1/2 x 2) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (fma.f64 1/2 x 2) x)) 2) 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(#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (fma.f64 1/2 x 2) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (fma.f64 1/2 x 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (fma.f64 1/2 x 2) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (fma.f64 1/2 x 2) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (/.f64 (fma.f64 1/2 x 2) x) 3/2) (pow.f64 (/.f64 (fma.f64 1/2 x 2) x) -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (neg.f64 (fma.f64 1/2 x 2)) 3) (pow.f64 (neg.f64 x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (fma.f64 1/2 x 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (fma.f64 1/2 x 2) x)))))) (#(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 (fma.f64 1/2 x 2) x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 (fma.f64 1/2 x 2) x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (fma.f64 1/2 x 2) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (fma.f64 1/2 x 2) x)))))))

simplify44.0ms (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
129 → 123
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))

localize16.0ms (0.4%)

Local error

Found 6 expressions with local error:

NewErrorProgram
3.9b
(-.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))) 1)
0.1b
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
0.0b
(+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))
✓0.0b
(+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))
0.1b
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
✓3.9b
(-.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))) 1)
Compiler

Compiled 40 to 34 computations (15% saved)

series3.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

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

rewrite60.0ms (1.4%)

Algorithm
1×batch-egg-rewrite
Rules
416×log-prod_binary64
355×fma-def_binary64
345×prod-diff_binary64
264×pow2_binary64
238×pow-prod-down_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01029
123823
2320323
Stop Event
1×node limit
Counts
2 → 142
Calls
Call 1
Inputs
(-.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))) 1)
(+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x))) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))) (/.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -2) (-.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))))))) (#(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 (cbrt.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))) (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))) 2) (cbrt.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))) 2) (*.f64 (cbrt.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))) 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(/.f64 2 x)) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -3)) (+.f64 1 (-.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -2) (/.f64 1 (+.f64 1/2 (/.f64 2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -3)) (+.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -2) (-.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -2)) (-.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -3))) (neg.f64 (+.f64 1 (-.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -2) (/.f64 1 (+.f64 1/2 (/.f64 2 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -2))) (neg.f64 (-.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -2) 1) (+.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -3)) 1) (+.f64 1 (-.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -2) (/.f64 1 (+.f64 1/2 (/.f64 2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -2)) 1) (-.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (-.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -2) (/.f64 1 (+.f64 1/2 (/.f64 2 x))))) (+.f64 1 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))) (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log1p.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log.f64 (+.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x))) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x))) 1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 (+.f64 1/2 (/.f64 2 x)))) (cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -2)) (/.f64 1 (cbrt.f64 (+.f64 1/2 (/.f64 2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -1/2) (pow.f64 (+.f64 1/2 (/.f64 2 x)) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (/.f64 1 (+.f64 (neg.f64 (/.f64 2 x)) -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (expm1.f64 (*.f64 3 (log1p.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))))) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))) 2) (+.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x))) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (expm1.f64 (*.f64 2 (log1p.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))))) (/.f64 1 (+.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x))) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x))) 2) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x))) 2)) 2) (cbrt.f64 (+.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x))) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x))) 2)) (sqrt.f64 (+.f64 (/.f64 1 (+.f64 1/2 (/.f64 2 x))) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 2 x))) -2) (/.f64 1 (cbrt.f64 (+.f64 1/2 (/.f64 2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -1/2)) 1) (-.f64 (hypot.f64 1 (pow.f64 (+.f64 1/2 (/.f64 2 x)) -1/2)) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (fma.f64 8 (pow.f64 x -3) 1/8)) (fma.f64 (/.f64 2 x) (-.f64 (/.f64 2 x) 1/2) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (-.f64 1/4 (*.f64 4 (pow.f64 x -2)))) (-.f64 1/2 (/.f64 2 x)) 1)))))

simplify42.0ms (1%)

Algorithm
1×egg-herbie
Rules
805×unswap-sqr_binary64
525×fma-def_binary64
515×associate-/r*_binary64
334×times-frac_binary64
274×distribute-lft-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
046291
1131291
2315289
3881274
42549274
56579274
Stop Event
1×node limit
Counts
166 → 170
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
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/32 (pow.f64 x 3)) 1)))
3
(-.f64 3 (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 3 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 3 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
3
(-.f64 3 (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 3 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(-.f64 (+.f64 3 (*.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 1/2 x (fma.f64 1/32 (pow.f64 x 3) (*.f64 -1/128 (pow.f64 x 4)))))
(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 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 32 (*.f64 x 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 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 32 (*.f64 x x)) (/.f64 -128 (pow.f64 x 3)))))
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 x (*.f64 x -1/8) (fma.f64 1/2 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 (*.f64 1/32 (pow.f64 x 3)) 1)))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/32 (pow.f64 x 3) 1)))
(fma.f64 x (*.f64 x -1/8) (fma.f64 1/2 x (fma.f64 1/32 (pow.f64 x 3) 1)))
(fma.f64 x (fma.f64 x -1/8 1/2) (fma.f64 1/32 (pow.f64 x 3) 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x (fma.f64 x 1/32 -1/8)) 1))
3
(-.f64 3 (*.f64 8 (/.f64 1 x)))
(-.f64 3 (/.f64 8 x))
(+.f64 3 (/.f64 -8 x))
(-.f64 (+.f64 3 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(+.f64 3 (-.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x)))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 3 (/.f64 -8 x)))
(+.f64 3 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)))
(-.f64 (+.f64 3 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 3 (/.f64 32 (*.f64 x x))) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3))))
(+.f64 3 (-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 3 (+.f64 (/.f64 -8 x) (/.f64 -128 (pow.f64 x 3)))))
(+.f64 (+.f64 3 (/.f64 32 (*.f64 x x))) (+.f64 (/.f64 -8 x) (/.f64 -128 (pow.f64 x 3))))
(+.f64 3 (+.f64 (/.f64 -8 x) (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -128 (pow.f64 x 3)))))
3
(-.f64 3 (*.f64 8 (/.f64 1 x)))
(-.f64 3 (/.f64 8 x))
(+.f64 3 (/.f64 -8 x))
(-.f64 (+.f64 3 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(+.f64 3 (-.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x)))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 3 (/.f64 -8 x)))
(+.f64 3 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)))
(-.f64 (+.f64 3 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 3 (/.f64 32 (*.f64 x x))) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3))))
(+.f64 3 (-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 3 (+.f64 (/.f64 -8 x) (/.f64 -128 (pow.f64 x 3)))))
(+.f64 (+.f64 3 (/.f64 32 (*.f64 x x))) (+.f64 (/.f64 -8 x) (/.f64 -128 (pow.f64 x 3))))
(+.f64 3 (+.f64 (/.f64 -8 x) (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -128 (pow.f64 x 3)))))

localize26.0ms (0.6%)

Local error

Found 4 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 (*.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)

series2.0ms (0%)

Counts
2 → 18
Calls

6 calls:

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

rewrite57.0ms (1.3%)

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
01225
127125
2350525
Stop Event
1×node limit
Counts
2 → 118
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))))
Outputs
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x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/8 x) 1 (+.f64 1/2 (/.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 (/.f64 1 x) (fma.f64 -1/8 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) 2 (fma.f64 -1/8 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 2 x) 1 (fma.f64 -1/8 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1/2 (/.f64 2 x)) 1 (*.f64 -1/8 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -2)) (*.f64 (/.f64 1 (cbrt.f64 x)) 2) (fma.f64 -1/8 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 -1/8 x)) (pow.f64 (cbrt.f64 (*.f64 -1/8 x)) 2) (+.f64 1/2 (/.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 -1/8 x)) 2) (cbrt.f64 (*.f64 -1/8 x)) (+.f64 1/2 (/.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 2 x)) (cbrt.f64 (*.f64 (pow.f64 x -2) 4)) (fma.f64 -1/8 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x -2) 4)) (cbrt.f64 (/.f64 2 x)) (fma.f64 -1/8 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1/2 (/.f64 2 x))) (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 2 x))) 2) (*.f64 -1/8 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1/2 (/.f64 2 x))) 2) (cbrt.f64 (+.f64 1/2 (/.f64 2 x))) (*.f64 -1/8 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) -1/8) (+.f64 1/2 (/.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/2) (*.f64 (pow.f64 x -1/2) 2) (fma.f64 -1/8 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 -1/8 x)) (sqrt.f64 (*.f64 -1/8 x)) (+.f64 1/2 (/.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 2 x)) (sqrt.f64 (/.f64 2 x)) (fma.f64 -1/8 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1/2 (/.f64 2 x))) (sqrt.f64 (+.f64 1/2 (/.f64 2 x))) (*.f64 -1/8 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) -1/8) (+.f64 1/2 (/.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.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)) (*.f64 -1/8 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1/4 (*.f64 (pow.f64 x -2) 4)) (/.f64 1 (-.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))))))

simplify31.0ms (0.7%)

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
049239
1129227
2342220
31083216
43392216
Stop Event
1×node limit
Counts
136 → 139
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)
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)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
3.9b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(sqrt.f64 (+.f64 x 1))
3.9b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
Compiler

Compiled 16 to 12 computations (25% saved)

rewrite0.0ms (0%)

Counts
0 → 0

simplify6.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

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

eval233.0ms (5.3%)

Compiler

Compiled 8802 to 7326 computations (16.8% saved)

prune75.0ms (1.7%)

Pruning

11 alts after pruning (2 fresh and 9 done)

PrunedKeptTotal
New6021603
Fresh011
Picked011
Done189
Total60311614
Error
0b
Counts
614 → 11
Alt Table
Click to see full alt table
StatusErrorProgram
1.6b
(expm1.f64 (*.f64 (log1p.f64 x) 1/2))
✓21.0b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
✓59.4b
(-.f64 (+.f64 1 (/.f64 1 (+.f64 1/2 (/.f64 2 x)))) 1)
✓0.3b
(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))
✓38.5b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
✓21.1b
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓21.4b
(/.f64 x 2)
✓22.1b
(/.f64 1 (+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x)))))
60.8b
2
✓21.1b
(/.f64 1 (/.f64 (+.f64 (*.f64 1/2 x) 2) x))
Compiler

Compiled 91 to 76 computations (16.5% saved)

regimes17.0ms (0.4%)

Counts
11 → 1
Calls
Call 1
Inputs
2
(/.f64 x 2)
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(/.f64 1 (/.f64 (+.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 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))
(expm1.f64 (*.f64 (log1p.f64 x) 1/2))
Outputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Calls

2 calls:

8.0ms
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms
x
Results
ErrorSegmentsBranch
0.2b1x
0.2b1(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 92 to 74 computations (19.6% saved)

regimes13.0ms (0.3%)

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

11.0ms
x
Results
ErrorSegmentsBranch
0.5b2x
Compiler

Compiled 60 to 49 computations (18.3% saved)

bsearch18.0ms (0.4%)

Algorithm
1×binary-search
Steps
TimeLeftRight
18.0ms
6.956487753070853e-7
0.0029421815227809534
Compiler

Compiled 13 to 10 computations (23.1% saved)

regimes10.0ms (0.2%)

Counts
7 → 1
Calls
Call 1
Inputs
2
(/.f64 x 2)
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(/.f64 1 (/.f64 (+.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 x (+.f64 (*.f64 1/2 x) 2))
Calls

1 calls:

5.0ms
x
Results
ErrorSegmentsBranch
21.0b1x
Compiler

Compiled 54 to 44 computations (18.5% saved)

regimes4.0ms (0.1%)

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

1 calls:

3.0ms
x
Results
ErrorSegmentsBranch
21.1b1x
Compiler

Compiled 14 to 11 computations (21.4% saved)

regimes5.0ms (0.1%)

Accuracy

Total -39.4b remaining (-183.7%)

Threshold costs -39.4b (-183.7%)

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

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
21.4b1x
Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02871
14271
24371
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(if (<=.f64 x 6570216920718993/9444732965739290427392) (/.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 (*.f64 1/2 x) 2))
(/.f64 1 (+.f64 1/2 (/.f64 2 x)))
(/.f64 x 2)
2
Outputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(if (<=.f64 x 6570216920718993/9444732965739290427392) (/.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 6570216920718993/9444732965739290427392) (/.f64 1 (+.f64 (*.f64 x -1/8) (+.f64 1/2 (*.f64 2 (/.f64 1 x))))) (+.f64 (sqrt.f64 (+.f64 x 1)) -1))
(/.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 x 2)
2

end83.0ms (1.9%)

Stop Event
1×fuel
Compiler

Compiled 105 to 85 computations (19% saved)

Profiling

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