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)

sample783.0ms (51.1%)

Results
770.0ms8253×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)

localize6.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series10.0ms (0.6%)

Counts
3 → 12
Calls

9 calls:

TimeVariablePointExpression
4.0ms
x
@inf
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
2.0ms
x
@-inf
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
1.0ms
x
@0
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
1.0ms
x
@inf
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
1.0ms
x
@-inf
(+.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite49.0ms (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))))
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
(sqrt.f64 (+.f64 x 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (+.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (/.f64 x (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))) (/.f64 x (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))) (/.f64 (cbrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (neg.f64 x)) (-.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (+.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x 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 log1p.f64 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.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 log1p.f64 (expm1.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)))) (#(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 -.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 log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))))

simplify30.0ms (2%)

Algorithm
1×egg-herbie
Rules
591×fma-def_binary64
363×distribute-rgt-neg-in_binary64
306×distribute-lft-neg-in_binary64
251×distribute-lft-out--_binary64
235×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
031158
191142
2232130
3810109
42935109
Stop Event
1×node limit
Counts
105 → 114
Calls
Call 1
Inputs
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (+.f64 (*.f64 5/128 (pow.f64 x 4)) (*.f64 1/8 (pow.f64 x 2))))
2
(+.f64 2 (*.f64 1/2 x))
(-.f64 (+.f64 2 (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 2 (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3)))) (*.f64 1/8 (pow.f64 x 2)))
1
(+.f64 1 (*.f64 1/2 x))
(-.f64 (+.f64 1 (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3)))) (*.f64 1/8 (pow.f64 x 2)))
Outputs
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (*.f64 x x)))
(fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8))
(*.f64 x (-.f64 1/2 (*.f64 x 1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (*.f64 -1/8 (*.f64 x x)))
(fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8)))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (-.f64 (*.f64 x 1/16) 1/8)))
(*.f64 x (+.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 1/2))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (+.f64 (*.f64 5/128 (pow.f64 x 4)) (*.f64 1/8 (pow.f64 x 2))))
(-.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (fma.f64 5/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x))))
(-.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (fma.f64 1/8 (*.f64 x x) (*.f64 5/128 (pow.f64 x 4))))
(fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x (fma.f64 (*.f64 x x) -1/8 (*.f64 (pow.f64 x 4) -5/128))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (-.f64 1/16 (*.f64 x 5/128))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (+.f64 (*.f64 x -5/128) 1/16)))
2
(+.f64 2 (*.f64 1/2 x))
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 2)
(-.f64 (+.f64 2 (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 2 (-.f64 (*.f64 1/2 x) (*.f64 1/8 (*.f64 x x))))
(+.f64 2 (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8)))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/2 x 2))
(fma.f64 x (fma.f64 x -1/8 1/2) 2)
(-.f64 (+.f64 2 (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3)))) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 2 (+.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (*.f64 -1/8 (*.f64 x x))))
(+.f64 2 (fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8))))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 2)))
(fma.f64 1/2 x (fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) 2))
(fma.f64 1/16 (pow.f64 x 3) (fma.f64 x (fma.f64 x -1/8 1/2) 2))
1
(+.f64 1 (*.f64 1/2 x))
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(-.f64 (+.f64 1 (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 1 (-.f64 (*.f64 1/2 x) (*.f64 1/8 (*.f64 x x))))
(+.f64 1 (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8)))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/2 x 1))
(fma.f64 x (fma.f64 x -1/8 1/2) 1)
(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3)))) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 1 (+.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (*.f64 -1/8 (*.f64 x x))))
(+.f64 1 (fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8))))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/16 (pow.f64 x 3) (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 1/16 (pow.f64 x 3) (fma.f64 x (fma.f64 x -1/8 1/2) 1))

prune90.0ms (5.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1122114
Fresh000
Picked011
Done000
Total1123115
Error
0b
Counts
115 → 3
Alt Table
StatusErrorProgram
▶0.3b
(/.f64 x (fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 1))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
23.2b
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
Compiler

Compiled 1531 to 1199 computations (21.7% saved)

localize9.0ms (0.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.1b
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 1)
✓0.2b
(cbrt.f64 (sqrt.f64 (+.f64 x 1)))
✓0.2b
(cbrt.f64 (+.f64 x 1))
✓0.2b
(/.f64 x (fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 1))

series11.0ms (0.7%)

Counts
4 → 28
Calls

12 calls:

TimeVariablePointExpression
3.0ms
x
@inf
(/.f64 x (fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 1))
2.0ms
x
@-inf
(/.f64 x (fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 1))
1.0ms
x
@-inf
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 1)
1.0ms
x
@0
(/.f64 x (fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 1))
1.0ms
x
@inf
(cbrt.f64 (sqrt.f64 (+.f64 x 1)))

rewrite51.0ms (3.3%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
0951
118534
2232534
Stop Event
1×node limit
Counts
4 → 106
Calls
Call 1
Inputs
(/.f64 x (fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 1))
(cbrt.f64 (+.f64 x 1))
(cbrt.f64 (sqrt.f64 (+.f64 x 1)))
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 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 (neg.f64 x) (/.f64 1 (+.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -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 (/.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 (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 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 log1p.f64 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/6) (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (*.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)) (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 2) (cbrt.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6) (*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6) (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 1/3) (cbrt.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (+.f64 x 1) 1/6) (cbrt.f64 (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (+.f64 1 (pow.f64 x 3))) (cbrt.f64 (fma.f64 x x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1)) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/3 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (+.f64 x 1))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 x 1) 1/6))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)) (cbrt.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6) (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 2)) (sqrt.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 1/3) (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x 1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 x 1) 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/3 (*.f64 1/2 (log1p.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (*.f64 1/2 (log1p.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (+.f64 x 1) 1/6)))))))
((#(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 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 (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 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) 1) (+.f64 (+.f64 x 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 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 log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))

simplify30.0ms (2%)

Algorithm
1×egg-herbie
Rules
510×associate-*l*_binary64
398×cancel-sign-sub-inv_binary64
359×fma-neg_binary64
328×fma-def_binary64
253×times-frac_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
087506
1249486
2672389
32256323
Stop Event
1×node limit
Counts
134 → 148
Calls
Call 1
Inputs
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (+.f64 (*.f64 5/128 (pow.f64 x 4)) (*.f64 1/8 (pow.f64 x 2))))
x
x
1
(+.f64 1 (*.f64 1/3 x))
(-.f64 (+.f64 1 (*.f64 1/3 x)) (*.f64 1/9 (pow.f64 x 2)))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/3 x) (*.f64 5/81 (pow.f64 x 3)))) (*.f64 1/9 (pow.f64 x 2)))
1
(+.f64 1 (*.f64 1/6 x))
(-.f64 (+.f64 1 (*.f64 1/6 x)) (*.f64 5/72 (pow.f64 x 2)))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/6 x) (*.f64 55/1296 (pow.f64 x 3)))) (*.f64 5/72 (pow.f64 x 2)))
(pow.f64 x 1/6)
(+.f64 (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6))
(-.f64 (+.f64 (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6)) (*.f64 5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)))
(-.f64 (+.f64 (*.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6)) (+.f64 (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6))) (*.f64 5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(+.f64 (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)) (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))
(-.f64 (+.f64 (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)) (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) (*.f64 5/72 (/.f64 (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)) (+.f64 (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 55/1296 (/.f64 (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3))))) (*.f64 5/72 (/.f64 (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2))))
2
(+.f64 2 (*.f64 1/2 x))
(-.f64 (+.f64 2 (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 2 (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3)))) (*.f64 1/8 (pow.f64 x 2)))
1
1
Outputs
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 (*.f64 1/2 x) (*.f64 -1/8 (*.f64 x x)))
(fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8))
(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))
(*.f64 x (+.f64 (*.f64 x -1/8) 1/2))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 (fma.f64 1/16 (pow.f64 x 3) (*.f64 1/2 x)) (*.f64 -1/8 (*.f64 x x)))
(fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8)))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 (*.f64 x 1/16) -1/8)))
(*.f64 x (+.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 1/2))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (+.f64 (*.f64 5/128 (pow.f64 x 4)) (*.f64 1/8 (pow.f64 x 2))))
(-.f64 (fma.f64 1/16 (pow.f64 x 3) (*.f64 1/2 x)) (fma.f64 5/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x))))
(-.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (fma.f64 1/8 (*.f64 x x) (*.f64 5/128 (pow.f64 x 4))))
(fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) (fma.f64 (*.f64 x x) -1/8 (*.f64 (pow.f64 x 4) -5/128))))
(fma.f64 1/2 x (fma.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)) (*.f64 (pow.f64 x 4) -5/128)))
x
x
1
(+.f64 1 (*.f64 1/3 x))
(+.f64 1 (*.f64 x 1/3))
(fma.f64 x 1/3 1)
(-.f64 (+.f64 1 (*.f64 1/3 x)) (*.f64 1/9 (pow.f64 x 2)))
(+.f64 1 (-.f64 (*.f64 x 1/3) (*.f64 (*.f64 x x) 1/9)))
(+.f64 1 (fma.f64 x 1/3 (*.f64 (*.f64 x x) -1/9)))
(fma.f64 (*.f64 x x) -1/9 (fma.f64 x 1/3 1))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/3 x) (*.f64 5/81 (pow.f64 x 3)))) (*.f64 1/9 (pow.f64 x 2)))
(+.f64 1 (-.f64 (fma.f64 1/3 x (*.f64 (pow.f64 x 3) 5/81)) (*.f64 (*.f64 x x) 1/9)))
(+.f64 1 (+.f64 (*.f64 (pow.f64 x 3) 5/81) (fma.f64 x 1/3 (*.f64 (*.f64 x x) -1/9))))
(fma.f64 (*.f64 x x) -1/9 (fma.f64 x 1/3 (fma.f64 (pow.f64 x 3) 5/81 1)))
(+.f64 1 (*.f64 x (+.f64 1/3 (*.f64 x (fma.f64 x 5/81 -1/9)))))
1
(+.f64 1 (*.f64 1/6 x))
(+.f64 1 (*.f64 x 1/6))
(fma.f64 x 1/6 1)
(-.f64 (+.f64 1 (*.f64 1/6 x)) (*.f64 5/72 (pow.f64 x 2)))
(+.f64 1 (-.f64 (*.f64 x 1/6) (*.f64 (*.f64 x x) 5/72)))
(+.f64 1 (fma.f64 x 1/6 (*.f64 (*.f64 x x) -5/72)))
(fma.f64 (*.f64 x x) -5/72 (fma.f64 x 1/6 1))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/6 x) (*.f64 55/1296 (pow.f64 x 3)))) (*.f64 5/72 (pow.f64 x 2)))
(+.f64 1 (-.f64 (fma.f64 1/6 x (*.f64 (pow.f64 x 3) 55/1296)) (*.f64 (*.f64 x x) 5/72)))
(+.f64 1 (+.f64 (*.f64 (pow.f64 x 3) 55/1296) (fma.f64 x 1/6 (*.f64 (*.f64 x x) -5/72))))
(fma.f64 (*.f64 x x) -5/72 (fma.f64 (pow.f64 x 3) 55/1296 (fma.f64 x 1/6 1)))
(+.f64 1 (*.f64 x (+.f64 1/6 (*.f64 x (fma.f64 x 55/1296 -5/72)))))
(pow.f64 x 1/6)
(+.f64 (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6))
(fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (pow.f64 x 1/6))
(-.f64 (+.f64 (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6)) (*.f64 5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)))
(+.f64 (fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (pow.f64 x 1/6)) (*.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)))
(fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (-.f64 (pow.f64 x 1/6) (*.f64 5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6))))
(fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) -5/72 (fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (pow.f64 x 1/6)))
(-.f64 (+.f64 (*.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6)) (+.f64 (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)) (pow.f64 x 1/6))) (*.f64 5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)))
(+.f64 (fma.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (pow.f64 x 1/6))) (*.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)))
(+.f64 (fma.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (pow.f64 x 1/6))) (*.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) -5/72))
(fma.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (fma.f64 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) -5/72 (fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (pow.f64 x 1/6))))
(exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(pow.f64 x 1/6)
(+.f64 (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)) (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))
(fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 x) 0)) x) (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 x) 0)))
(*.f64 (+.f64 (/.f64 1/6 x) 1) (pow.f64 x 1/6))
(-.f64 (+.f64 (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)) (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) (*.f64 5/72 (/.f64 (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2))))
(+.f64 (fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 -5/72 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x))))
(+.f64 (fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) -5/72))
(+.f64 (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 x) 0)) (*.f64 (/.f64 (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 x) 0)) x) (-.f64 1/6 (/.f64 5/72 x))))
(+.f64 (pow.f64 x 1/6) (*.f64 (/.f64 (pow.f64 x 1/6) x) (+.f64 1/6 (/.f64 -5/72 x))))
(-.f64 (+.f64 (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)) (+.f64 (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 55/1296 (/.f64 (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3))))) (*.f64 5/72 (/.f64 (exp.f64 (*.f64 1/6 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2))))
(+.f64 (+.f64 (fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 55/1296 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)))) (*.f64 -5/72 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x))))
(+.f64 (fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (fma.f64 55/1296 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) (*.f64 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) -5/72))
(+.f64 (fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 x) 0)) x) (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 x) 0))) (*.f64 (/.f64 (pow.f64 (exp.f64 1/6) (+.f64 (log.f64 x) 0)) (*.f64 x x)) (-.f64 (/.f64 55/1296 x) 5/72)))
(+.f64 (pow.f64 x 1/6) (*.f64 (/.f64 (pow.f64 x 1/6) x) (-.f64 (+.f64 1/6 (/.f64 55/1296 (*.f64 x x))) (/.f64 5/72 x))))
2
(+.f64 2 (*.f64 1/2 x))
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 2)
(-.f64 (+.f64 2 (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 2 (+.f64 (*.f64 1/2 x) (*.f64 -1/8 (*.f64 x x))))
(+.f64 2 (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8)))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/2 x 2))
(-.f64 (+.f64 2 (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3)))) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 2 (+.f64 (fma.f64 1/16 (pow.f64 x 3) (*.f64 1/2 x)) (*.f64 -1/8 (*.f64 x x))))
(+.f64 2 (fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8))))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x 2)))
(+.f64 2 (*.f64 x (+.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 1/2)))
1
1

prune94.0ms (6.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1480148
Fresh011
Picked011
Done011
Total1483151
Error
0b
Counts
151 → 3
Alt Table
StatusErrorProgram
✓0.3b
(/.f64 x (fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 1))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
▶23.2b
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
Compiler

Compiled 2469 to 1960 computations (20.6% saved)

localize8.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series15.0ms (1%)

Counts
2 → 4
Calls

6 calls:

TimeVariablePointExpression
5.0ms
x
@inf
(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
4.0ms
x
@-inf
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
2.0ms
x
@-inf
(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
2.0ms
x
@0
(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
1.0ms
x
@inf
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite53.0ms (3.4%)

Algorithm
1×batch-egg-rewrite
Rules
484×prod-diff_binary64
301×fma-def_binary64
175×fma-neg_binary64
166×log1p-udef_binary64
165×expm1-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01026
122826
2290226
Stop Event
1×node limit
Counts
2 → 81
Calls
Call 1
Inputs
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(/.f64 (sqrt.f64 x) (+.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 (sqrt.f64 (+.f64 x 1))))))) (#(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 (sqrt.f64 x) (*.f64 (pow.f64 x -1/2) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (pow.f64 x -1/2) (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (*.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x)) (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (pow.f64 x -1/2))))) (#(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 (+.f64 1 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2) (/.f64 1 (cbrt.f64 (/.f64 x (+.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))))) (/.f64 1 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 x)) (*.f64 -1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 x)) (*.f64 (pow.f64 x -1/2) (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 x)) (*.f64 (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 x 1)))) (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 x)) (*.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (*.f64 -1 (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (*.f64 (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 x 1)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)) (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)) (*.f64 (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 x 1)))) 1))))) (#(struct:change #<rule 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cbrt.f64 (*.f64 (pow.f64 (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3) (pow.f64 x 3/2)))))) (#(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 log1p.f64 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (*.f64 (cbrt.f64 (sqrt.f64 x)) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (cbrt.f64 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2))) (cbrt.f64 (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 x 1/4) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))) (/.f64 (pow.f64 x 1/4) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 1/4) (/.f64 (pow.f64 x 1/4) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 1/4) (*.f64 (pow.f64 x 1/4) (/.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))))) (/.f64 1 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 x)) (/.f64 1 (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 x) 1) (/.f64 (cbrt.f64 (sqrt.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 1 (cbrt.f64 (+.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 (sqrt.f64 x) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (cbrt.f64 (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 x 1/4) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (/.f64 (pow.f64 x 1/4) (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))) (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))) (/.f64 (cbrt.f64 (sqrt.f64 x)) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.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 (sqrt.f64 x) (-.f64 0 x)) (-.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 x 1/4) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 x) (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3/2) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (sqrt.f64 x)) (log1p.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log.f64 (sqrt.f64 x)) (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))))

simplify21.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
362×distribute-rgt-neg-in_binary64
306×distribute-lft-neg-in_binary64
287×*-commutative_binary64
272×fma-def_binary64
251×distribute-lft-out--_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02164
15960
215756
355747
4222447
Stop Event
1×node limit
Counts
85 → 88
Calls
Call 1
Inputs
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (+.f64 (*.f64 5/128 (pow.f64 x 4)) (*.f64 1/8 (pow.f64 x 2))))
Outputs
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 (*.f64 1/2 x) (*.f64 -1/8 (*.f64 x x)))
(fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8))
(*.f64 x (-.f64 1/2 (*.f64 x 1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 (fma.f64 1/16 (pow.f64 x 3) (*.f64 1/2 x)) (*.f64 -1/8 (*.f64 x x)))
(fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8)))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (-.f64 (*.f64 x 1/16) 1/8)))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (+.f64 (*.f64 5/128 (pow.f64 x 4)) (*.f64 1/8 (pow.f64 x 2))))
(-.f64 (fma.f64 1/16 (pow.f64 x 3) (*.f64 1/2 x)) (fma.f64 5/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x))))
(-.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (fma.f64 1/8 (*.f64 x x) (*.f64 5/128 (pow.f64 x 4))))
(fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) (fma.f64 (*.f64 x x) -1/8 (*.f64 (pow.f64 x 4) -5/128))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (-.f64 1/16 (*.f64 x 5/128))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (+.f64 1/16 (*.f64 x -5/128))))

prune83.0ms (5.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1600160
Fresh000
Picked011
Done022
Total1603163
Error
0b
Counts
163 → 3
Alt Table
StatusErrorProgram
✓0.3b
(/.f64 x (fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 1))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓23.2b
(*.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
Compiler

Compiled 2781 to 1976 computations (28.9% saved)

regimes107.0ms (7%)

Accuracy

Total 0.2b remaining (93.4%)

Threshold costs 0.2b (93.4%)

Counts
59 → 1
Compiler

Compiled 681 to 515 computations (24.4% saved)

simplify2.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01016
11416
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 x (+.f64 1 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)))
Outputs
(/.f64 x (+.f64 1 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)))

end55.0ms (3.6%)

Stop Event
1×done
Compiler

Compiled 62 to 49 computations (21% saved)

Profiling

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