Details

Time bar (total: 3.1s)

analyze3.0ms (0.1%)

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

Compiled 10 to 8 computations (20% saved)

sample1.0s (33.1%)

Results
1.0s8254×body256valid
1.0ms2×body2048valid
0.0ms1×body256invalid

preprocess16.0ms (0.5%)

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

Useful iterations: 0 (0.0ms)

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

Compiled 10 to 8 computations (20% saved)

simplify7.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

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

eval0.0ms (0%)

Compiler

Compiled 9 to 7 computations (22.2% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Compiled 9 to 7 computations (22.2% saved)

localize6.0ms (0.2%)

Local error

Found 6 expressions with local error:

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

series7.0ms (0.2%)

Counts
3 → 12
Calls

9 calls:

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

rewrite64.0ms (2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0727
115727
2225827
Stop Event
1×node limit
Counts
3 → 86
Calls
Call 1
Inputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(sqrt.f64 (+.f64 x 1))
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (/.f64 x (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))) (/.f64 x (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))) (/.f64 (cbrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (+.f64 1 (+.f64 1 (-.f64 x (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (neg.f64 x)) (-.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x 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 log1p.f64 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 x 1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (fma.f64 x x -1)) (sqrt.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (+.f64 1 (+.f64 1 (-.f64 x (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (+.f64 1 (-.f64 x (sqrt.f64 (+.f64 x 1))))) (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 x 1))) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 1 (+.f64 1 (-.f64 x (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) (-.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (neg.f64 (+.f64 1 (+.f64 1 (-.f64 x (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 x)) (neg.f64 (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x 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 log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))

simplify94.0ms (3%)

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

Useful iterations: 3 (0.0ms)

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

eval35.0ms (1.1%)

Compiler

Compiled 1387 to 1085 computations (21.8% saved)

prune46.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1016107
Fresh000
Picked011
Done000
Total1017108
Error
0b
Counts
108 → 7
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.2b
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)
▶22.8b
(/.f64 x 2)
▶22.4b
(/.f64 x (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
36.9b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
▶23.5b
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
▶22.4b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
Compiler

Compiled 119 to 91 computations (23.5% saved)

localize6.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

series9.0ms (0.3%)

Counts
2 → 8
Calls

6 calls:

TimeVariablePointExpression
6.0ms
x
@-inf
(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
1.0ms
x
@inf
(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
1.0ms
x
@inf
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)
1.0ms
x
@-inf
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)
0.0ms
x
@0
(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite56.0ms (1.8%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0824
117824
2243224
Stop Event
1×node limit
Counts
2 → 46
Calls
Call 1
Inputs
(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))) (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -2)) (cbrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -1/2) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2) -1) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) -1) (pow.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (pow.f64 (+.f64 1 x) 3/2))) (+.f64 1 (+.f64 x (-.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 0 x)) (-.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 x) 2) (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 x) (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4))) (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2)) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 x) (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x -1) (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))))

simplify95.0ms (3%)

Algorithm
1×egg-herbie
Rules
803×unswap-sqr_binary64
650×*-commutative_binary64
546×distribute-lft-out_binary64
505×sqr-pow_binary64
460×associate-+l+_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
03099
18195
219688
357074
4151674
5243774
6445374
7460174
8489574
9528574
10616674
11707474
12764974
Stop Event
1×node limit
Counts
54 → 60
Calls
Call 1
Inputs
1/2
(+.f64 (*.f64 -1/8 x) 1/2)
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 1/16 (pow.f64 x 2))))
(+.f64 (*.f64 -1/8 x) (+.f64 (*.f64 -5/128 (pow.f64 x 3)) (+.f64 1/2 (*.f64 1/16 (pow.f64 x 2)))))
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -5/128 (pow.f64 x 4)) (*.f64 1/16 (pow.f64 x 3)))))
Outputs
1/2
(+.f64 (*.f64 -1/8 x) 1/2)
(fma.f64 -1/8 x 1/2)
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 1/16 (pow.f64 x 2))))
(+.f64 (fma.f64 -1/8 x 1/2) (*.f64 1/16 (*.f64 x x)))
(fma.f64 -1/8 x (fma.f64 1/16 (*.f64 x x) 1/2))
(fma.f64 x (*.f64 x 1/16) (fma.f64 -1/8 x 1/2))
(fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)
(+.f64 (*.f64 -1/8 x) (+.f64 (*.f64 -5/128 (pow.f64 x 3)) (+.f64 1/2 (*.f64 1/16 (pow.f64 x 2)))))
(fma.f64 -1/8 x (fma.f64 -5/128 (pow.f64 x 3) (+.f64 1/2 (*.f64 1/16 (*.f64 x x)))))
(fma.f64 -1/8 x (fma.f64 -5/128 (pow.f64 x 3) (fma.f64 1/16 (*.f64 x x) 1/2)))
(fma.f64 -1/8 x (fma.f64 x (*.f64 x 1/16) (fma.f64 -5/128 (pow.f64 x 3) 1/2)))
(fma.f64 -1/8 x (fma.f64 x (*.f64 x (fma.f64 x -5/128 1/16)) 1/2))
(fma.f64 x (fma.f64 x 1/16 -1/8) (fma.f64 -5/128 (pow.f64 x 3) 1/2))
(fma.f64 -1/8 x (fma.f64 (*.f64 x x) (fma.f64 x -5/128 1/16) 1/2))
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(fma.f64 1/2 x (*.f64 x (*.f64 -1/8 x)))
(*.f64 x (fma.f64 -1/8 x 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 1/16 (pow.f64 x 3) (*.f64 x (fma.f64 -1/8 x 1/2)))
(*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -5/128 (pow.f64 x 4)) (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 -5/128 (pow.f64 x 4) (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) (*.f64 -5/128 (pow.f64 x 4)))))
(+.f64 (fma.f64 -5/128 (pow.f64 x 4) (*.f64 1/16 (pow.f64 x 3))) (*.f64 x (fma.f64 -1/8 x 1/2)))
(fma.f64 x (fma.f64 -1/8 x 1/2) (*.f64 (pow.f64 x 3) (fma.f64 x -5/128 1/16)))
(*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) (fma.f64 -5/128 (pow.f64 x 3) 1/2)))
(*.f64 x (fma.f64 -1/8 x (fma.f64 (*.f64 x x) (fma.f64 x -5/128 1/16) 1/2)))

localize2.0ms (0.1%)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite60.0ms (1.9%)

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

Useful iterations: 0 (0.0ms)

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

simplify41.0ms (1.3%)

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

Useful iterations: 3 (0.0ms)

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

localize5.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series3.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

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

rewrite54.0ms (1.7%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
0819
118017
2244017
Stop Event
1×node limit
Counts
2 → 65
Calls
Call 1
Inputs
(+.f64 1 (+.f64 (*.f64 1/2 x) 1))
(/.f64 x (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (*.f64 1/2 x) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 0 (*.f64 1/2 x))) (/.f64 (pow.f64 (fma.f64 1/2 x 1) 2) (-.f64 0 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (*.f64 1/2 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 1/2 x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2) (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (*.f64 1/2 x) 2)) (sqrt.f64 (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3)) (/.f64 1 (+.f64 1 (*.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2)) (/.f64 1 (-.f64 0 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (*.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x))) (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 0 (*.f64 1/2 x)) (-.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3)) (+.f64 1 (*.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3)) (+.f64 (pow.f64 (fma.f64 1/2 x 1) 2) (-.f64 0 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2)) (-.f64 0 (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3))) (neg.f64 (+.f64 1 (*.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2))) (neg.f64 (-.f64 0 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 1/2 x 1) 2) 1) (*.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (*.f64 1/2 x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 1/2 x 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x 1)) 2) (cbrt.f64 (fma.f64 1/2 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 1/2 x 1)) (sqrt.f64 (fma.f64 1/2 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (fma.f64 1/2 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (*.f64 1/2 x) 2)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))) 2) (cbrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))) (sqrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (*.f64 1/2 x) 2)) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2)) (/.f64 x (cbrt.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2)) (cbrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 1/2 x) 2))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (+.f64 (*.f64 1/2 x) 2))) (/.f64 (cbrt.f64 x) (sqrt.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3))) (+.f64 1 (*.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (-.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2))) (-.f64 0 (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (*.f64 1/2 x) 2) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 (*.f64 1/2 x) 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 x) (log1p.f64 (fma.f64 1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))))))))

simplify60.0ms (1.9%)

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

Useful iterations: 3 (0.0ms)

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

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
0.0b
(*.f64 x (fma.f64 x 1/16 -1/8))
✓0.0b
(*.f64 x (fma.f64 x 1/16 -1/8))
✓0.0b
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))

series3.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
1.0ms
x
@inf
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
1.0ms
x
@0
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
1.0ms
x
@-inf
(*.f64 x (fma.f64 x 1/16 -1/8))
0.0ms
x
@0
(*.f64 x (fma.f64 x 1/16 -1/8))

rewrite84.0ms (2.7%)

Algorithm
1×batch-egg-rewrite
Rules
566×unpow-prod-down_binary64
421×log-prod_binary64
313×exp-prod_binary64
275×prod-diff_binary64
271×pow-prod-down_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0922
120020
2249420
Stop Event
1×node limit
Counts
2 → 87
Calls
Call 1
Inputs
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
(*.f64 x (fma.f64 x 1/16 -1/8))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x 1/2) (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 1/2) 1) (*.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/8) (*.f64 (pow.f64 (fma.f64 x 1/16 -1/8) 3) (pow.f64 x 6))) (+.f64 (pow.f64 (*.f64 x 1/2) 2) (-.f64 (pow.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))) 2) (*.f64 (*.f64 x 1/2) (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 x 1/2) 2) (pow.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))) 2)) (-.f64 (*.f64 x 1/2) (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1/8 (pow.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 3)) x) (fma.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) (fma.f64 x (fma.f64 x 1/16 -1/8) -1/2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/4 (pow.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 2)) x) (-.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 1/8 (pow.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 3))) (fma.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) (fma.f64 x (fma.f64 x 1/16 -1/8) -1/2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (-.f64 1/4 (pow.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 2))) (-.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)))) 2)) (cbrt.f64 (log.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))))) (sqrt.f64 (log.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/2 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 x (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 x 1/16 -1/8) (*.f64 x x) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) x (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 1/2) (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (*.f64 x (fma.f64 x 1/16 -1/8))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/2) (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x 1/16 -1/8))) 2) (*.f64 (cbrt.f64 (*.f64 x (fma.f64 x 1/16 -1/8))) x) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (*.f64 x (fma.f64 x 1/16 -1/8))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/2) (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x (fma.f64 x 1/16 -1/8))) (*.f64 (sqrt.f64 (*.f64 x (fma.f64 x 1/16 -1/8))) x) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x 1/2) 1 (*.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))) 2) (cbrt.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 1/2)) 2) (cbrt.f64 (*.f64 x 1/2)) (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))) (sqrt.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/2)) (sqrt.f64 (*.f64 x 1/2)) (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x 1/16 -1/8))) 2)) (cbrt.f64 (*.f64 x (fma.f64 x 1/16 -1/8))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 (*.f64 x (fma.f64 x 1/16 -1/8)))) (sqrt.f64 (*.f64 x (fma.f64 x 1/16 -1/8))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 1/2) (fma.f64 x 1/16 -1/8)) (*.f64 (*.f64 x 1/2) (fma.f64 x 1/16 -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x (fma.f64 x 1/16 -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 1/16) x) (*.f64 -1/8 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x 1/16 -1/8))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x 1/16 -1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (fma.f64 x 1/16 -1/8)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x 1/16 -1/8))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x 1/16 -1/8))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 x (fma.f64 x 1/16 -1/8)))) 2)) (cbrt.f64 (log.f64 (*.f64 x (fma.f64 x 1/16 -1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 x (fma.f64 x 1/16 -1/8))))) (sqrt.f64 (log.f64 (*.f64 x (fma.f64 x 1/16 -1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (fma.f64 x 1/16 -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (fma.f64 x 1/16 -1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 x 1/16) (*.f64 x -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x 1/16) x (*.f64 -1/8 x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (fma.f64 x 1/16 -1/8))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 x (fma.f64 x 1/16 -1/8)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 x (fma.f64 x 1/16 -1/8)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 x (fma.f64 x 1/16 -1/8)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 x (fma.f64 x 1/16 -1/8))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 x (fma.f64 x 1/16 -1/8))) 3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (fma.f64 x 1/16 -1/8))))))))

simplify65.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
917×fma-def_binary64
841×associate-+l+_binary64
536×unswap-sqr_binary64
534×associate-*l*_binary64
482×distribute-rgt-in_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
019282
147282
289264
3216222
4575210
52012210
64011210
74536210
86485210
Stop Event
1×node limit
Counts
111 → 101
Calls
Call 1
Inputs
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(*.f64 1/16 (pow.f64 x 3))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(*.f64 1/16 (pow.f64 x 3))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(*.f64 -1/8 x)
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(*.f64 1/16 (pow.f64 x 2))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(*.f64 1/16 (pow.f64 x 2))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
Outputs
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x 1/16))))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
(*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x 1/16))))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
(*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))
(*.f64 1/16 (pow.f64 x 3))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/16 (pow.f64 x 3)))
(*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x 1/16))))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
(*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x 1/16))))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
(*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))
(*.f64 1/16 (pow.f64 x 3))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/16 (pow.f64 x 3)))
(*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x 1/16))))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
(*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x 1/16))))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
(*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))
(*.f64 -1/8 x)
(*.f64 x -1/8)
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(fma.f64 -1/8 x (*.f64 (*.f64 x x) 1/16))
(fma.f64 x -1/8 (*.f64 (*.f64 x x) 1/16))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(fma.f64 -1/8 x (*.f64 (*.f64 x x) 1/16))
(fma.f64 x -1/8 (*.f64 (*.f64 x x) 1/16))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(fma.f64 -1/8 x (*.f64 (*.f64 x x) 1/16))
(fma.f64 x -1/8 (*.f64 (*.f64 x x) 1/16))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))
(*.f64 1/16 (pow.f64 x 2))
(*.f64 (*.f64 x x) 1/16)
(*.f64 x (*.f64 x 1/16))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(fma.f64 -1/8 x (*.f64 (*.f64 x x) 1/16))
(fma.f64 x -1/8 (*.f64 (*.f64 x x) 1/16))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(fma.f64 -1/8 x (*.f64 (*.f64 x x) 1/16))
(fma.f64 x -1/8 (*.f64 (*.f64 x x) 1/16))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(fma.f64 -1/8 x (*.f64 (*.f64 x x) 1/16))
(fma.f64 x -1/8 (*.f64 (*.f64 x x) 1/16))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))
(*.f64 1/16 (pow.f64 x 2))
(*.f64 (*.f64 x x) 1/16)
(*.f64 x (*.f64 x 1/16))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(fma.f64 -1/8 x (*.f64 (*.f64 x x) 1/16))
(fma.f64 x -1/8 (*.f64 (*.f64 x x) 1/16))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(fma.f64 -1/8 x (*.f64 (*.f64 x x) 1/16))
(fma.f64 x -1/8 (*.f64 (*.f64 x x) 1/16))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(fma.f64 -1/8 x (*.f64 (*.f64 x x) 1/16))
(fma.f64 x -1/8 (*.f64 (*.f64 x x) 1/16))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))

eval190.0ms (6.1%)

Compiler

Compiled 4859 to 3737 computations (23.1% saved)

prune61.0ms (2%)

Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New3543357
Fresh011
Picked101
Done145
Total3568364
Error
0b
Counts
364 → 8
Alt Table
Click to see full alt table
StatusErrorProgram
▶23.5b
(*.f64 x (+.f64 1/2 (+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8))))
▶36.9b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
60.9b
2
✓0.2b
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)
✓22.8b
(/.f64 x 2)
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
▶23.9b
(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))
✓22.4b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
Compiler

Compiled 67 to 51 computations (23.9% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite72.0ms (2.3%)

Algorithm
1×batch-egg-rewrite
Rules
807×pow1_binary64
758×add-log-exp_binary64
758×log1p-expm1-u_binary64
758×expm1-log1p-u_binary64
745×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0710
11588
220598
Stop Event
1×node limit
Counts
1 → 24
Calls
Call 1
Inputs
(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x 1/2) (*.f64 x (*.f64 x -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x -1/8)) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 1/2) 1) (*.f64 (*.f64 x (*.f64 x -1/8)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (fma.f64 x -1/8 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x 1/2) 3) (pow.f64 (*.f64 x (*.f64 x -1/8)) 3)) (+.f64 (*.f64 (*.f64 x 1/2) (*.f64 x 1/2)) (-.f64 (*.f64 (*.f64 x (*.f64 x -1/8)) (*.f64 x (*.f64 x -1/8))) (*.f64 (*.f64 x 1/2) (*.f64 x (*.f64 x -1/8))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x 1/2) (*.f64 x 1/2)) (*.f64 (*.f64 x (*.f64 x -1/8)) (*.f64 x (*.f64 x -1/8)))) (-.f64 (*.f64 x 1/2) (*.f64 x (*.f64 x -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1/8 (*.f64 (pow.f64 x 3) -1/512)) x) (+.f64 1/4 (-.f64 (*.f64 (*.f64 x x) 1/64) (*.f64 -1/16 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/4 (*.f64 (*.f64 x x) 1/64)) x) (+.f64 1/2 (*.f64 1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 1/8 (*.f64 (pow.f64 x 3) -1/512))) (+.f64 1/4 (-.f64 (*.f64 (*.f64 x x) 1/64) (*.f64 -1/16 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (-.f64 1/4 (*.f64 (*.f64 x x) 1/64))) (+.f64 1/2 (*.f64 1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (fma.f64 x -1/8 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (fma.f64 x -1/8 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x -1/8 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x -1/8 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (fma.f64 x -1/8 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (fma.f64 x -1/8 1/2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x -1/8 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (fma.f64 x -1/8 1/2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (fma.f64 x -1/8 1/2) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/2 (*.f64 x (*.f64 x -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 x (*.f64 x (*.f64 x -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x -1/8 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (fma.f64 x -1/8 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (fma.f64 x -1/8 1/2))))))))

simplify149.0ms (4.8%)

Algorithm
1×egg-herbie
Rules
802×sqr-pow_binary64
565×cube-prod_binary64
554×fabs-mul_binary64
541×pow-sqr_binary64
533×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
09117
118117
231108
36790
416790
546690
6164290
7289890
8310290
9331590
10353590
11384290
12424290
13475290
14531190
15599790
16682890
17722090
18750690
19778090
20785490
21789090
Stop Event
1×node limit
Counts
36 → 29
Calls
Call 1
Inputs
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(*.f64 -1/8 (pow.f64 x 2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(*.f64 -1/8 (pow.f64 x 2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
Outputs
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 (*.f64 x -1/8) 1/2))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 (*.f64 x -1/8) 1/2))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 (*.f64 x -1/8) 1/2))
(*.f64 x (fma.f64 x -1/8 1/2))
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (*.f64 x x))
(*.f64 x (*.f64 x -1/8))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 (*.f64 x -1/8) 1/2))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 (*.f64 x -1/8) 1/2))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 (*.f64 x -1/8) 1/2))
(*.f64 x (fma.f64 x -1/8 1/2))
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (*.f64 x x))
(*.f64 x (*.f64 x -1/8))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 (*.f64 x -1/8) 1/2))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 (*.f64 x -1/8) 1/2))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 (*.f64 x -1/8) 1/2))
(*.f64 x (fma.f64 x -1/8 1/2))

localize7.0ms (0.2%)

Local error

Found 8 expressions with local error:

NewErrorProgram
3.4b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
0.2b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
0.2b
(/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.2b
(/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
✓0.2b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
✓3.4b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)

series7.0ms (0.2%)

Counts
3 → 12
Calls

9 calls:

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

rewrite73.0ms (2.3%)

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

Useful iterations: 1 (0.0ms)

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

simplify101.0ms (3.2%)

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

Useful iterations: 3 (0.0ms)

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

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 x (+.f64 1/2 (+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8))))
0.0b
(+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8))
✓0.0b
(+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8))
✓0.0b
(*.f64 x (+.f64 1/2 (+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8))))

series3.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@0
(*.f64 x (+.f64 1/2 (+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8))))
0.0ms
x
@inf
(*.f64 x (+.f64 1/2 (+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8))))
0.0ms
x
@-inf
(*.f64 x (+.f64 1/2 (+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8))))
0.0ms
x
@inf
(+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8))
0.0ms
x
@0
(+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8))

rewrite83.0ms (2.7%)

Algorithm
1×batch-egg-rewrite
Rules
605×log-prod_binary64
575×fma-def_binary64
434×pow-prod-down_binary64
318×pow2_binary64
269×fma-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01126
125520
2351820
Stop Event
1×node limit
Counts
2 → 125
Calls
Call 1
Inputs
(*.f64 x (+.f64 1/2 (+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8))))
(+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x 1/2) (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (fma.f64 1/16 (*.f64 x x) 1/2) x) (*.f64 (*.f64 x -1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 1/2) 1) (*.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (fma.f64 1/16 (*.f64 x x) 1/2)) (*.f64 x (*.f64 x -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (fma.f64 x (fma.f64 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(*.f64 x -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (*.f64 1/4 (sqrt.f64 x))) (*.f64 1/4 (sqrt.f64 x)) (*.f64 x -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x 1/16) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 x -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 x 1/16) (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (fma.f64 x 1/16 -1/8))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (fma.f64 x 1/16 -1/8))))))))

simplify64.0ms (2%)

Algorithm
1×egg-herbie
Rules
917×fma-def_binary64
841×associate-+l+_binary64
536×unswap-sqr_binary64
534×associate-*l*_binary64
482×distribute-rgt-in_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
019282
147282
289264
3216222
4575210
52012210
64011210
74536210
86485210
Stop Event
1×node limit
Counts
149 → 138
Calls
Call 1
Inputs
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(*.f64 1/16 (pow.f64 x 3))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(*.f64 1/16 (pow.f64 x 3))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(*.f64 -1/8 x)
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(*.f64 1/16 (pow.f64 x 2))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(*.f64 1/16 (pow.f64 x 2))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
Outputs
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x 1/16))))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
(*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x 1/16))))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
(*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))
(*.f64 1/16 (pow.f64 x 3))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/16 (pow.f64 x 3)))
(*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x 1/16))))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
(*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x 1/16))))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
(*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))
(*.f64 1/16 (pow.f64 x 3))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/16 (pow.f64 x 3)))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/16 (pow.f64 x 3)))
(*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x 1/16))))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
(*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x 1/16))))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
(*.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))
(*.f64 -1/8 x)
(*.f64 x -1/8)
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(fma.f64 -1/8 x (*.f64 (*.f64 x x) 1/16))
(fma.f64 x -1/8 (*.f64 (*.f64 x x) 1/16))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(fma.f64 -1/8 x (*.f64 (*.f64 x x) 1/16))
(fma.f64 x -1/8 (*.f64 (*.f64 x x) 1/16))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(fma.f64 -1/8 x (*.f64 (*.f64 x x) 1/16))
(fma.f64 x -1/8 (*.f64 (*.f64 x x) 1/16))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))
(*.f64 1/16 (pow.f64 x 2))
(*.f64 (*.f64 x x) 1/16)
(*.f64 x (*.f64 x 1/16))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(fma.f64 -1/8 x (*.f64 (*.f64 x x) 1/16))
(fma.f64 x -1/8 (*.f64 (*.f64 x x) 1/16))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(fma.f64 -1/8 x (*.f64 (*.f64 x x) 1/16))
(fma.f64 x -1/8 (*.f64 (*.f64 x x) 1/16))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(fma.f64 -1/8 x (*.f64 (*.f64 x x) 1/16))
(fma.f64 x -1/8 (*.f64 (*.f64 x x) 1/16))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))
(*.f64 1/16 (pow.f64 x 2))
(*.f64 (*.f64 x x) 1/16)
(*.f64 x (*.f64 x 1/16))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(fma.f64 -1/8 x (*.f64 (*.f64 x x) 1/16))
(fma.f64 x -1/8 (*.f64 (*.f64 x x) 1/16))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(fma.f64 -1/8 x (*.f64 (*.f64 x x) 1/16))
(fma.f64 x -1/8 (*.f64 (*.f64 x x) 1/16))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))
(+.f64 (*.f64 -1/8 x) (*.f64 1/16 (pow.f64 x 2)))
(fma.f64 -1/8 x (*.f64 (*.f64 x x) 1/16))
(fma.f64 x -1/8 (*.f64 (*.f64 x x) 1/16))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))

eval155.0ms (5%)

Compiler

Compiled 4803 to 3417 computations (28.9% saved)

prune54.0ms (1.7%)

Pruning

8 alts after pruning (2 fresh and 6 done)

PrunedKeptTotal
New3131314
Fresh011
Picked011
Done156
Total3148322
Error
0b
Counts
322 → 8
Alt Table
Click to see full alt table
StatusErrorProgram
▶36.9b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
✓23.9b
(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))
60.9b
2
✓0.2b
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)
✓22.8b
(/.f64 x 2)
✓23.5b
(*.f64 x (+.f64 1/2 (+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8))))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓22.4b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
Compiler

Compiled 63 to 49 computations (22.2% saved)

localize4.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
3.4b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(sqrt.f64 (+.f64 x 1))
3.4b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)

rewrite0.0ms (0%)

Counts
0 → 0

simplify9.0ms (0.3%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

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

eval31.0ms (1%)

Compiler

Compiled 1150 to 886 computations (23% saved)

prune40.0ms (1.3%)

Pruning

8 alts after pruning (1 fresh and 7 done)

PrunedKeptTotal
New99099
Fresh011
Picked011
Done066
Total998107
Error
0b
Counts
107 → 8
Alt Table
Click to see full alt table
StatusErrorProgram
✓36.9b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
✓23.9b
(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))
60.9b
2
✓0.2b
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)
✓22.8b
(/.f64 x 2)
✓23.5b
(*.f64 x (+.f64 1/2 (+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8))))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓22.4b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
Compiler

Compiled 63 to 49 computations (22.2% saved)

regimes27.0ms (0.9%)

Counts
11 → 1
Calls
Call 1
Inputs
2
(/.f64 x 2)
(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(/.f64 x (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 x (+.f64 1/2 (+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8))))
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
Outputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Calls

2 calls:

15.0ms
x
7.0ms
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Results
ErrorSegmentsBranch
0.2b1x
0.2b1(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 96 to 71 computations (26% saved)

regimes13.0ms (0.4%)

Counts
7 → 2
Calls
Call 1
Inputs
2
(/.f64 x 2)
(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(/.f64 x (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 x (+.f64 1/2 (+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8))))
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
Outputs
(*.f64 x (+.f64 1/2 (+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8))))
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
Calls

1 calls:

11.0ms
x
Results
ErrorSegmentsBranch
0.2b2x
Compiler

Compiled 49 to 36 computations (26.5% saved)

bsearch18.0ms (0.6%)

Algorithm
1×binary-search
Steps
TimeLeftRight
18.0ms
2.6903770676420974e-8
12035017.219109325
Compiler

Compiled 13 to 10 computations (23.1% saved)

regimes7.0ms (0.2%)

Counts
6 → 1
Calls
Call 1
Inputs
2
(/.f64 x 2)
(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(/.f64 x (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 x (+.f64 1/2 (+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8))))
Outputs
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
Calls

1 calls:

5.0ms
x
Results
ErrorSegmentsBranch
22.4b1x
Compiler

Compiled 43 to 31 computations (27.9% saved)

regimes32.0ms (1%)

Accuracy

Total -39.6b remaining (-174%)

Threshold costs -39.6b (-174%)

Counts
3 → 1
Calls
Call 1
Inputs
2
(/.f64 x 2)
(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))
Outputs
(/.f64 x 2)
Calls

1 calls:

31.0ms
x
Results
ErrorSegmentsBranch
22.8b1x
Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
6×+-commutative_binary64
5×*-commutative_binary64
1×sub-neg_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02661
14161
24261
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(if (<=.f64 x 8131165753929063/302231454903657293676544) (*.f64 x (+.f64 1/2 (+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8)))) (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(/.f64 x 2)
2
Outputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(if (<=.f64 x 8131165753929063/302231454903657293676544) (*.f64 x (+.f64 1/2 (+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8)))) (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
(if (<=.f64 x 8131165753929063/302231454903657293676544) (*.f64 x (+.f64 1/2 (+.f64 (*.f64 x (*.f64 x 1/16)) (*.f64 x -1/8)))) (+.f64 (sqrt.f64 (+.f64 x 1)) -1))
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(/.f64 x (+.f64 (*.f64 x 1/2) 2))
(/.f64 x 2)
2

end41.0ms (1.3%)

Stop Event
1×fuel
Compiler

Compiled 90 to 68 computations (24.4% saved)

Profiling

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