Details

Time bar (total: 1.5s)

analyze4.0ms (0.3%)

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

Compiled 10 to 8 computations (20% saved)

sample795.0ms (53.9%)

Results
774.0ms8253×body128valid
1.0ms3×body2048valid
Compiler

Compiled 20 to 16 computations (20% saved)

preprocess15.0ms (1%)

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

Useful iterations: 0 (0.0ms)

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

Compiled 9 to 7 computations (22.2% saved)

simplify6.0ms (0.4%)

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))))

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓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))))

series8.0ms (0.5%)

Counts
3 → 12
Calls

9 calls:

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

rewrite47.0ms (3.2%)

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

Useful iterations: 0 (0.0ms)

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

simplify46.0ms (3.1%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
033136
192132
2210130
3601109
41607109
52610109
64589109
74732109
84996109
Stop Event
1×node limit
Counts
105 → 114
Calls
Call 1
Inputs
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -5/128 (pow.f64 x 4)) (*.f64 1/16 (pow.f64 x 3)))))
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))
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))

prune68.0ms (4.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1122114
Fresh000
Picked101
Done000
Total1132115
Error
0b
Counts
115 → 2
Alt Table
StatusErrorProgram
41.5b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
▶0.2b
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 1/2)))
Compiler

Compiled 1506 to 1178 computations (21.8% saved)

localize6.0ms (0.4%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1 (pow.f64 (+.f64 x 1) 1/2))
✓0.0b
(pow.f64 (+.f64 x 1) 1/2)
✓0.2b
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 1/2)))

series4.0ms (0.3%)

Counts
3 → 12
Calls

9 calls:

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

rewrite51.0ms (3.4%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0827
118627
2248727
Stop Event
1×node limit
Counts
3 → 88
Calls
Call 1
Inputs
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 1/2)))
(pow.f64 (+.f64 x 1) 1/2)
(+.f64 1 (pow.f64 (+.f64 x 1) 1/2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (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 (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 (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 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (+.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (/.f64 x (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))) (/.f64 x (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))) (/.f64 (cbrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (+.f64 1 (-.f64 (+.f64 x 1) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (neg.f64 x)) (-.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (+.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(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 -.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 sqrt.f64 (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/2 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (+.f64 1 (-.f64 (+.f64 x 1) (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (-.f64 (+.f64 x 1) (sqrt.f64 (+.f64 x 1)))) (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 x 1))) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 1 (-.f64 (+.f64 x 1) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) (-.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (neg.f64 (+.f64 1 (-.f64 (+.f64 x 1) (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 x)) (neg.f64 (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x 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 expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))

simplify46.0ms (3.1%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
033136
192132
2210130
3601109
41607109
52610109
64589109
74732109
84996109
Stop Event
1×node limit
Counts
100 → 109
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))
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))

prune52.0ms (3.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1090109
Fresh011
Picked011
Done000
Total1092111
Error
0b
Counts
111 → 2
Alt Table
StatusErrorProgram
▶41.5b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
✓0.2b
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 1/2)))
Compiler

Compiled 1443 to 1128 computations (21.8% saved)

localize6.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 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))
✓2.8b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)

series5.0ms (0.4%)

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))
0.0ms
x
@0
(-.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)

rewrite57.0ms (3.9%)

Algorithm
1×batch-egg-rewrite
Rules
870×log1p-expm1-u_binary64
870×expm1-log1p-u_binary64
97×add-sqr-sqrt_binary64
93×*-un-lft-identity_binary64
93×pow1_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0830
118725
2279725
Stop Event
1×node limit
Counts
3 → 149
Calls
Call 1
Inputs
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
(/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
(/.f64 x (/.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 1/2 (log1p.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2) (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 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 (+.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 1/2 (log1p.f64 x))) 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 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) x) (/.f64 (cbrt.f64 x) (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) x) (/.f64 (sqrt.f64 x) (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (/.f64 x (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 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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 1/2 (log1p.f64 x))))))))) (#(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 1/2 (log1p.f64 x)))) 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 1/2 (log1p.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 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 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 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 exp.f64 (log.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (expm1.f64 (*.f64 1/2 (log1p.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)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 1/2 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))))
((#(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 1/2 (log1p.f64 x)))))))) (#(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 1/2 (log1p.f64 x))))))))) (#(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 1/2 (log1p.f64 x))))))))) (#(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 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2)) (/.f64 x (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 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 1/2 (log1p.f64 x)))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))) (/.f64 x (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))) (/.f64 (cbrt.f64 x) (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))))) (#(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 1/2 (log1p.f64 x))) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))))) (#(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 1/2 (log1p.f64 x))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x 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 expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.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 1/2 (log1p.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2) (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 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 (+.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 1/2 (log1p.f64 x))) 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 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) x) (/.f64 (cbrt.f64 x) (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) x) (/.f64 (sqrt.f64 x) (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (/.f64 x (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 (cbrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x 1) (/.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 x 1) 1/4) 1) (-.f64 (pow.f64 (+.f64 x 1) 1/4) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (neg.f64 x)) (neg.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 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 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 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 exp.f64 (log.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (expm1.f64 (*.f64 1/2 (log1p.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)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 1/2 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))))

simplify51.0ms (3.5%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
027155
173153
2169149
3492125
41416125
52412125
64391125
74534125
84798125
Stop Event
1×node limit
Counts
161 → 119
Calls
Call 1
Inputs
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -5/128 (pow.f64 x 4)) (*.f64 1/16 (pow.f64 x 3)))))
2
(+.f64 (*.f64 1/2 x) 2)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 2 (*.f64 1/16 (pow.f64 x 3)))))
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -5/128 (pow.f64 x 4)) (*.f64 1/16 (pow.f64 x 3)))))
Outputs
(*.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))
(*.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))))

prune93.0ms (6.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New1520152
Fresh000
Picked011
Done011
Total1522154
Error
0b
Counts
154 → 2
Alt Table
StatusErrorProgram
✓41.5b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
✓0.2b
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 1/2)))
Compiler

Compiled 2273 to 1615 computations (28.9% saved)

regimes61.0ms (4.2%)

Accuracy

Total 0.2b remaining (94.2%)

Threshold costs 0.2b (94.2%)

Counts
32 → 1
Compiler

Compiled 344 to 258 computations (25% saved)

simplify2.0ms (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
Calls
Call 1
Inputs
(/.f64 x (+.f64 (sqrt.f64 (+.f64 x 1)) 1))
Outputs
(/.f64 x (+.f64 (sqrt.f64 (+.f64 x 1)) 1))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

end46.0ms (3.1%)

Stop Event
1×done
Compiler

Compiled 39 to 30 computations (23.1% saved)

Profiling

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