Details

Time bar (total: 4.0s)

analyze4.0ms (0.1%)

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

Compiled 10 to 8 computations (20% saved)

sample752.0ms (18.8%)

Results
739.0ms8256×body128valid
Compiler

Compiled 20 to 16 computations (20% saved)

preprocess15.0ms (0.4%)

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 (0.2%)

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

Useful iterations: 0 (0.0ms)

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

prune3.0ms (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 (0.1%)

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

series10.0ms (0.3%)

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 (1.2%)

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

simplify26.0ms (0.7%)

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))

prune80.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1113114
Fresh000
Picked011
Done000
Total1114115
Error
0b
Counts
115 → 4
Alt Table
StatusErrorProgram
40.0b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
▶0.2b
(/.f64 x (+.f64 1 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)))
1.8b
(*.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))))))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 1569 to 1233 computations (21.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2))
✓0.1b
(/.f64 x (+.f64 1 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)))
✓0.2b
(pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)

series7.0ms (0.2%)

Counts
3 → 20
Calls

9 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)
1.0ms
x
@inf
(pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)
1.0ms
x
@0
(pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)
1.0ms
x
@-inf
(/.f64 x (+.f64 1 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)))
1.0ms
x
@inf
(/.f64 x (+.f64 1 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)))

rewrite50.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
477×prod-diff_binary64
284×fma-def_binary64
172×log1p-udef_binary64
171×expm1-udef_binary64
156×fma-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01030
123027
2289127
Stop Event
1×node limit
Counts
3 → 110
Calls
Call 1
Inputs
(pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)
(/.f64 x (+.f64 1 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)))
(+.f64 1 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2))
Outputs
((#(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 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4))))) (#(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 (sqrt.f64 (+.f64 x 1))) (*.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 1/4)) (pow.f64 (+.f64 x 1) 1/4)))))) (#(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) 1/8) (*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/8)) (pow.f64 (+.f64 x 1) 1/8))))) (#(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 (*.f64 (pow.f64 (+.f64 x 1) 1/4) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (+.f64 x 1) 1/4)))))) (#(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 (hypot.f64 1 (pow.f64 x 3/2)) (hypot.f64 x (sqrt.f64 (-.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 log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (*.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/2 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.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 x)) (*.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 (cbrt.f64 (*.f64 x x)) 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 (cbrt.f64 (*.f64 x x)) (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 (cbrt.f64 (*.f64 x x)) (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 (-.f64 1 (+.f64 x 1))) (-.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (+.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 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))) (-.f64 1 (+.f64 x 1))))))) (#(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 (-.f64 1 (+.f64 x 1)) (-.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 (-.f64 1 (+.f64 x 1))) (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 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 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x 1)) 1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (*.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 1/4)) (pow.f64 (+.f64 x 1) 1/4)) 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) 1/8) (*.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/8)) (pow.f64 (+.f64 x 1) 1/8) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 x 1)) 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (pow.f64 (+.f64 x 1) 1/4) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (cbrt.f64 (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 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))))))

simplify36.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
808×times-frac_binary64
464×associate-/l*_binary64
319×cancel-sign-sub-inv_binary64
283×fma-neg_binary64
240×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
068466
1188446
2513328
31780259
Stop Event
1×node limit
Counts
130 → 145
Calls
Call 1
Inputs
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)))
(sqrt.f64 x)
(+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x)) (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (sqrt.f64 x))) (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)
(+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) x)))
(-.f64 (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) x))) (*.f64 1/8 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) (pow.f64 x 2))))
(-.f64 (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) x)) (*.f64 1/16 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) (pow.f64 x 3))))) (*.f64 1/8 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) (pow.f64 x 2))))
(*.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)))
Outputs
1
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(-.f64 (+.f64 1 (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 (+.f64 1 (*.f64 1/2 x)) (*.f64 -1/8 (*.f64 x x)))
(+.f64 1 (fma.f64 1/2 x (*.f64 (*.f64 -1/8 x) x)))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/2 x 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 1/16 (pow.f64 x 3) (*.f64 1/2 x)) (*.f64 1/8 (*.f64 x x))))
(+.f64 1 (fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 (*.f64 -1/8 x) x))))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 1)))
(+.f64 1 (*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8)))))
(sqrt.f64 x)
(+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x))
(-.f64 (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (sqrt.f64 x)) (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)) (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)) (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)))
(-.f64 (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (sqrt.f64 x))) (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (sqrt.f64 x))) (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (sqrt.f64 x))))
(pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2)
(sqrt.f64 x)
(+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) x)))
(+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (*.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x)))
(fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))
(fma.f64 1/2 (/.f64 (pow.f64 (*.f64 1 (exp.f64 (log.f64 x))) 1/2) x) (pow.f64 (*.f64 1 (exp.f64 (log.f64 x))) 1/2))
(*.f64 (+.f64 (/.f64 1/2 x) 1) (sqrt.f64 x))
(-.f64 (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) x))) (*.f64 1/8 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) (pow.f64 x 2))))
(+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (-.f64 (*.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x)) (*.f64 1/8 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (*.f64 x x)))))
(+.f64 (fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (*.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (*.f64 x x)) -1/8))
(+.f64 (pow.f64 (*.f64 1 (exp.f64 (log.f64 x))) 1/2) (*.f64 (/.f64 (pow.f64 (*.f64 1 (exp.f64 (log.f64 x))) 1/2) x) (-.f64 1/2 (/.f64 1/8 x))))
(+.f64 (sqrt.f64 x) (*.f64 (/.f64 (sqrt.f64 x) x) (+.f64 1/2 (/.f64 -1/8 x))))
(-.f64 (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) x)) (*.f64 1/16 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) (pow.f64 x 3))))) (*.f64 1/8 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 2) (pow.f64 x 2))))
(+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x) (*.f64 1/16 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (pow.f64 x 3)))) (*.f64 1/8 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (*.f64 x x)))))
(+.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (+.f64 (fma.f64 1/16 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (pow.f64 x 3)) (/.f64 (*.f64 1/2 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) x)) (*.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (*.f64 x x)) -1/8)))
(+.f64 (pow.f64 (*.f64 1 (exp.f64 (log.f64 x))) 1/2) (fma.f64 1/2 (/.f64 (pow.f64 (*.f64 1 (exp.f64 (log.f64 x))) 1/2) x) (*.f64 (/.f64 (pow.f64 (*.f64 1 (exp.f64 (log.f64 x))) 1/2) (*.f64 x x)) (-.f64 (/.f64 1/16 x) 1/8))))
(+.f64 (sqrt.f64 x) (*.f64 (/.f64 (sqrt.f64 x) x) (+.f64 (/.f64 1/16 (*.f64 x x)) (+.f64 1/2 (/.f64 -1/8 x)))))
(*.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 -1/8 x) x))
(*.f64 x (-.f64 1/2 (*.f64 x 1/8)))
(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))
(-.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 -1/8 x) x)))
(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 1/16 (pow.f64 x 3) (*.f64 1/2 x)) (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)))
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 (+.f64 (*.f64 1/2 x) 2) (*.f64 1/8 (*.f64 x x)))
(+.f64 2 (fma.f64 1/2 x (*.f64 (*.f64 -1/8 x) x)))
(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 -1/8 x) x))))
(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 1/2 (*.f64 x (fma.f64 x 1/16 -1/8)))))

prune93.0ms (2.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1450145
Fresh022
Picked011
Done011
Total1454149
Error
0b
Counts
149 → 4
Alt Table
StatusErrorProgram
40.0b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
✓0.2b
(/.f64 x (+.f64 1 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)))
▶1.8b
(*.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))))))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 2268 to 1794 computations (20.9% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.5b
(/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))
✓0.5b
(cbrt.f64 x)
✓0.7b
(cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓0.8b
(cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series2.2s (55.9%)

Counts
4 → 4
Calls

12 calls:

TimeVariablePointExpression
1.1s
x
@inf
(/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))
1.0s
x
@-inf
(/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))
76.0ms
x
@-inf
(cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
56.0ms
x
@inf
(cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
6.0ms
x
@0
(/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))

rewrite70.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
556×prod-diff_binary64
219×log1p-udef_binary64
144×add-sqr-sqrt_binary64
140×pow1_binary64
138×*-un-lft-identity_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01450
130245
2388545
Stop Event
1×node limit
Counts
4 → 130
Calls
Call 1
Inputs
(cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(cbrt.f64 x)
(/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2) (cbrt.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))) (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 1/6) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) 1/3) (pow.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (+.f64 1 (pow.f64 (+.f64 1 x) 3/2))) (cbrt.f64 (-.f64 (+.f64 1 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (neg.f64 x)) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/3 (log1p.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (sqrt.f64 (+.f64 1 x)))) 1))))))
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x)))) 1/6) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (cbrt.f64 x) 2)) (/.f64 1 (neg.f64 (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) -2) (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 x) 1) (/.f64 (cbrt.f64 x) (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 x (cbrt.f64 x))) 1) (/.f64 (pow.f64 (cbrt.f64 (cbrt.f64 x)) 2) (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))) (/.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 x (cbrt.f64 x))) (cbrt.f64 (+.f64 1 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(cbrt.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))))) 2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 2) (*.f64 x x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (neg.f64 (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2)) 1))))))

simplify26.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
723×times-frac_binary64
682×cancel-sign-sub-inv_binary64
364×fma-neg_binary64
181×unswap-sqr_binary64
163×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
048189
1133187
2452185
32122171
Stop Event
1×node limit
Counts
134 → 137
Calls
Call 1
Inputs
(cbrt.f64 2)
(+.f64 (*.f64 1/6 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 2)) 1/3) x)) (cbrt.f64 2))
(-.f64 (+.f64 (*.f64 1/6 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 2)) 1/3) x)) (cbrt.f64 2)) (+.f64 (*.f64 1/36 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 7)) 1/3) (pow.f64 x 2))) (*.f64 1/24 (/.f64 (pow.f64 x 2) (pow.f64 (cbrt.f64 2) 2)))))
(-.f64 (+.f64 (*.f64 1/6 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 2)) 1/3) x)) (+.f64 (*.f64 1/72 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 11)) 1/3) (pow.f64 x 3))) (+.f64 (*.f64 1/48 (/.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 2) 2))) (+.f64 (cbrt.f64 2) (*.f64 5/648 (/.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 2) 4))))))) (+.f64 (*.f64 1/36 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 7)) 1/3) (pow.f64 x 2))) (*.f64 1/24 (/.f64 (pow.f64 x 2) (pow.f64 (cbrt.f64 2) 2)))))
Outputs
(cbrt.f64 2)
(+.f64 (*.f64 1/6 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 2)) 1/3) x)) (cbrt.f64 2))
(fma.f64 1/6 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 2))) x) (cbrt.f64 2))
(fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 2))) (*.f64 1/6 x) (cbrt.f64 2))
(-.f64 (+.f64 (*.f64 1/6 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 2)) 1/3) x)) (cbrt.f64 2)) (+.f64 (*.f64 1/36 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 7)) 1/3) (pow.f64 x 2))) (*.f64 1/24 (/.f64 (pow.f64 x 2) (pow.f64 (cbrt.f64 2) 2)))))
(-.f64 (fma.f64 1/6 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 2))) x) (cbrt.f64 2)) (fma.f64 1/36 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 7))) (*.f64 x x)) (*.f64 1/24 (/.f64 (*.f64 x x) (pow.f64 (cbrt.f64 2) 2)))))
(-.f64 (fma.f64 1/6 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 2))) x) (cbrt.f64 2)) (fma.f64 1/36 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 7))) (*.f64 x x)) (/.f64 1/24 (/.f64 (pow.f64 (cbrt.f64 2) 2) (*.f64 x x)))))
(+.f64 (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 2))) (*.f64 1/6 x) (cbrt.f64 2)) (*.f64 (*.f64 x x) (-.f64 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 7))) -1/36) (/.f64 1/24 (pow.f64 (cbrt.f64 2) 2)))))
(-.f64 (+.f64 (*.f64 1/6 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 2)) 1/3) x)) (+.f64 (*.f64 1/72 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 11)) 1/3) (pow.f64 x 3))) (+.f64 (*.f64 1/48 (/.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 2) 2))) (+.f64 (cbrt.f64 2) (*.f64 5/648 (/.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 2) 4))))))) (+.f64 (*.f64 1/36 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 7)) 1/3) (pow.f64 x 2))) (*.f64 1/24 (/.f64 (pow.f64 x 2) (pow.f64 (cbrt.f64 2) 2)))))
(-.f64 (fma.f64 1/6 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 2))) x) (fma.f64 1/72 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 11))) (pow.f64 x 3)) (fma.f64 1/48 (/.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 2) 2)) (+.f64 (cbrt.f64 2) (*.f64 5/648 (/.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 2) 4))))))) (fma.f64 1/36 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 7))) (*.f64 x x)) (*.f64 1/24 (/.f64 (*.f64 x x) (pow.f64 (cbrt.f64 2) 2)))))
(-.f64 (fma.f64 1/6 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 2))) x) (fma.f64 (*.f64 1/72 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 11)))) (pow.f64 x 3) (fma.f64 1/48 (/.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 2) 2)) (fma.f64 5/648 (/.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 2) 4)) (cbrt.f64 2))))) (fma.f64 1/36 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 7))) (*.f64 x x)) (/.f64 1/24 (/.f64 (pow.f64 (cbrt.f64 2) 2) (*.f64 x x)))))
(fma.f64 1/6 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 2))) x) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 11))) (*.f64 1/72 (pow.f64 x 3)) (-.f64 (+.f64 (cbrt.f64 2) (*.f64 (/.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 2) 2)) (+.f64 (/.f64 5/648 (pow.f64 (cbrt.f64 2) 2)) 1/48))) (fma.f64 1/36 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 7))) (*.f64 x x)) (/.f64 1/24 (/.f64 (pow.f64 (cbrt.f64 2) 2) (*.f64 x x)))))))
(+.f64 (fma.f64 1/72 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 11))) (pow.f64 x 3)) (+.f64 (cbrt.f64 2) (*.f64 (/.f64 (pow.f64 x 3) (cbrt.f64 2)) (+.f64 (/.f64 1/48 (cbrt.f64 2)) 5/1296)))) (fma.f64 1/6 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 2))) x) (*.f64 (*.f64 x x) (-.f64 (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 2) 7))) -1/36) (/.f64 1/24 (pow.f64 (cbrt.f64 2) 2))))))

prune99.0ms (2.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1370137
Fresh011
Picked011
Done022
Total1374141
Error
0b
Counts
141 → 4
Alt Table
StatusErrorProgram
▶40.0b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
✓0.2b
(/.f64 x (+.f64 1 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)))
✓1.8b
(*.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))))))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 4212 to 3395 computations (19.4% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.1b
(/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
✓0.1b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
✓3.7b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)

series7.0ms (0.2%)

Counts
3 → 12
Calls

9 calls:

TimeVariablePointExpression
3.0ms
x
@inf
(/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
2.0ms
x
@-inf
(/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
1.0ms
x
@inf
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
0.0ms
x
@-inf
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
0.0ms
x
@0
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)

rewrite57.0ms (1.4%)

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 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
(/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 x 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 (expm1.f64 (*.f64 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 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((#(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 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 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))))))

simplify25.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
431×fma-def_binary64
363×distribute-rgt-neg-in_binary64
305×distribute-lft-neg-in_binary64
251×distribute-lft-out--_binary64
217×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
026175
176161
2196149
3685125
42574125
Stop Event
1×node limit
Counts
161 → 119
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))))
(*.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)))
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 1/2 (*.f64 x (fma.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 1/2 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))))
(*.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 1/2 (*.f64 x (fma.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 1/2 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))))
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 1/16 (pow.f64 x 3) (fma.f64 x (fma.f64 x -1/8 1/2) 2))
(fma.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)) (fma.f64 1/2 x 2))

prune90.0ms (2.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New1520152
Fresh000
Picked011
Done033
Total1524156
Error
0b
Counts
156 → 4
Alt Table
StatusErrorProgram
✓40.0b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
✓0.2b
(/.f64 x (+.f64 1 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)))
✓1.8b
(*.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))))))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 2309 to 1647 computations (28.7% saved)

regimes144.0ms (3.6%)

Accuracy

Total 0.2b remaining (95.5%)

Threshold costs 0.2b (95.5%)

Counts
79 → 1
Compiler

Compiled 1073 to 782 computations (27.1% saved)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
7×+-commutative_binary64
7×*-commutative_binary64
5×sub-neg_binary64
5×neg-sub0_binary64
5×neg-mul-1_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01225
12723
24121
35221
45621
55721
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 x (/.f64 x (*.f64 (neg.f64 x) (/.f64 1 (neg.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))
Outputs
(/.f64 x (/.f64 x (*.f64 (neg.f64 x) (/.f64 1 (neg.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))
(/.f64 x (/.f64 x (*.f64 (neg.f64 x) (/.f64 1 (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 x 1))))))))
(/.f64 x (/.f64 x (*.f64 x (neg.f64 (/.f64 1 (-.f64 -1 (sqrt.f64 (+.f64 x 1))))))))
(/.f64 x (/.f64 x (*.f64 x (/.f64 -1 (-.f64 -1 (sqrt.f64 (+.f64 x 1)))))))

end79.0ms (2%)

Stop Event
1×done
Compiler

Compiled 87 to 68 computations (21.8% saved)

Profiling

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