Details

Time bar (total: 4.2s)

analyze4.0ms (0.1%)

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

Compiled 10 to 8 computations (20% saved)

sample1.3s (31.2%)

Results
1.3s8256×body256valid
0.0ms1×body256invalid

preprocess17.0ms (0.4%)

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

Useful iterations: 0 (0.0ms)

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

Compiled 10 to 8 computations (20% saved)

simplify6.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

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

eval0.0ms (0%)

Compiler

Compiled 9 to 7 computations (22.2% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Compiled 9 to 7 computations (22.2% saved)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiled 24 to 18 computations (25% saved)

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

rewrite73.0ms (1.7%)

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
2228227
Stop Event
1×node limit
Counts
3 → 86
Calls
Call 1
Inputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
(sqrt.f64 (+.f64 x 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.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 (+.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (/.f64 x (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))) (/.f64 x (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))) (/.f64 (cbrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (+.f64 1 (+.f64 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 (+.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x 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 log1p.f64 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 x 1)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.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 expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x -.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 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x (-.f64 1 x))))))) (#(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 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 hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) 1/2))))))

simplify122.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
803×unswap-sqr_binary64
601×distribute-lft-out_binary64
598×*-commutative_binary64
504×fma-def_binary64
407×associate-+l+_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
033136
192132
2210130
3601109
41652109
52656109
64635109
74778109
85042109
95411109
106152109
117162109
127707109
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)))))
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)))))
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)))))
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 1/2 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 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 (*.f64 x x) (fma.f64 x 1/16 -1/8) (fma.f64 1/2 x 2))
(fma.f64 1/2 x (fma.f64 x (*.f64 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))
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 x (*.f64 x -1/8) 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 1/2 x (fma.f64 x (*.f64 x -1/8) (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))

eval39.0ms (0.9%)

Compiler

Compiled 1387 to 1086 computations (21.7% saved)

prune20.0ms (0.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1007107
Fresh000
Picked011
Done000
Total1008108
Error
0b
Counts
108 → 8
Alt Table
Click to see full alt table
StatusErrorProgram
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
39.6b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
▶0.2b
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 1/2)))
▶21.1b
(*.f64 x (fma.f64 x -1/8 1/2))
20.8b
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
▶19.7b
(/.f64 x (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
▶19.7b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
▶20.1b
(/.f64 x 2)
Compiler

Compiled 131 to 99 computations (24.4% saved)

localize17.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

Compiled 28 to 22 computations (21.4% saved)

series4.0ms (0.1%)

Counts
3 → 12
Calls

9 calls:

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

rewrite65.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
935×pow1_binary64
876×add-log-exp_binary64
876×log1p-expm1-u_binary64
876×expm1-log1p-u_binary64
91×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0827
118627
2250627
Stop Event
1×node limit
Counts
3 → 85
Calls
Call 1
Inputs
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 1/2)))
(+.f64 1 (pow.f64 (+.f64 x 1) 1/2))
(pow.f64 (+.f64 x 1) 1/2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (+.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (/.f64 x (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))) (/.f64 x (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))) (/.f64 (cbrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (+.f64 1 (+.f64 x (-.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (neg.f64 x)) (-.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (+.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 x 1)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (+.f64 1 (+.f64 x (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (+.f64 x (-.f64 1 (sqrt.f64 (+.f64 x 1))))) (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 x 1))) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 1 (+.f64 x (-.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) (-.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (neg.f64 (+.f64 1 (+.f64 x (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 x)) (neg.f64 (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 x 1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (fma.f64 x x -1)) (sqrt.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/2 (log1p.f64 x)))))))

simplify120.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
803×unswap-sqr_binary64
601×distribute-lft-out_binary64
598×*-commutative_binary64
504×fma-def_binary64
407×associate-+l+_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
033136
192132
2210130
3601109
41652109
52656109
64635109
74778109
85042109
95411109
106152109
117162109
127707109
Stop Event
1×node limit
Counts
97 → 106
Calls
Call 1
Inputs
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 -5/128 (pow.f64 x 4)) (*.f64 1/16 (pow.f64 x 3)))))
2
(+.f64 (*.f64 1/2 x) 2)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 2 (*.f64 1/16 (pow.f64 x 3)))))
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)))))
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 1/2 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 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 (*.f64 x x) (fma.f64 x 1/16 -1/8) (fma.f64 1/2 x 2))
(fma.f64 1/2 x (fma.f64 x (*.f64 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))
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 x (*.f64 x -1/8) 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 1/2 x (fma.f64 x (*.f64 x -1/8) (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))

localize3.0ms (0.1%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiled 19 to 14 computations (26.3% saved)

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))

rewrite80.0ms (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
220698
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 log1p.f64 (expm1.f64 (/.f64 x (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (fma.f64 x 1/2 2))))))))

simplify51.0ms (1.2%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
037156
199156
2239154
3680145
42199145
56016145
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 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 (+.f64 2 (/.f64 32 (*.f64 x x))) (/.f64 8 x))
(+.f64 (/.f64 32 (*.f64 x x)) (-.f64 2 (/.f64 8 x)))
(+.f64 2 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)))
(+.f64 (+.f64 2 (/.f64 -8 x)) (/.f64 32 (*.f64 x x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 (/.f64 -8 x) (+.f64 (+.f64 2 (/.f64 32 (*.f64 x x))) (/.f64 -128 (pow.f64 x 3))))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 (+.f64 2 (/.f64 -8 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 2 (+.f64 (/.f64 8 x) (+.f64 (/.f64 128 (pow.f64 x 3)) (/.f64 -32 (*.f64 x x)))))
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 (+.f64 2 (/.f64 32 (*.f64 x x))) (/.f64 8 x))
(+.f64 (/.f64 32 (*.f64 x x)) (-.f64 2 (/.f64 8 x)))
(+.f64 2 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)))
(+.f64 (+.f64 2 (/.f64 -8 x)) (/.f64 32 (*.f64 x x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 (/.f64 -8 x) (+.f64 (+.f64 2 (/.f64 32 (*.f64 x x))) (/.f64 -128 (pow.f64 x 3))))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 (+.f64 2 (/.f64 -8 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 2 (+.f64 (/.f64 8 x) (+.f64 (/.f64 128 (pow.f64 x 3)) (/.f64 -32 (*.f64 x x)))))

localize14.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiled 28 to 22 computations (21.4% saved)

series2.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

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

rewrite74.0ms (1.8%)

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
2245717
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 expm1.f64 (log1p.f64 (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (fma.f64 1/2 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 1/2 x 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x 1)) 2) (cbrt.f64 (fma.f64 1/2 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 1/2 x 1)) (sqrt.f64 (fma.f64 1/2 x 1)) 1)))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))) 2) (cbrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))) (sqrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (*.f64 1/2 x) 2)) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2)) (/.f64 x (cbrt.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2)) (cbrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 1/2 x) 2))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (+.f64 (*.f64 1/2 x) 2))) (/.f64 (cbrt.f64 x) (sqrt.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3))) (+.f64 1 (*.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (-.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2))) (-.f64 0 (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (*.f64 1/2 x) 2) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 (*.f64 1/2 x) 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (+.f64 (*.f64 1/2 x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 x) (log1p.f64 (fma.f64 1/2 x 1))))))))

simplify54.0ms (1.3%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
039210
1102210
2243208
3693199
42220199
56011199
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 -1/128 (pow.f64 x 4) (fma.f64 1/32 (pow.f64 x 3) (*.f64 1/2 x))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (+.f64 1/32 (*.f64 x -1/128))))
2
(-.f64 2 (*.f64 8 (/.f64 1 x)))
(-.f64 2 (/.f64 8 x))
(+.f64 2 (/.f64 -8 x))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (*.f64 8 (/.f64 1 x)))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x)))
(+.f64 2 (+.f64 (/.f64 (/.f64 32 x) x) (/.f64 -8 x)))
(+.f64 (+.f64 2 (/.f64 -8 x)) (/.f64 32 (*.f64 x x)))
(+.f64 2 (+.f64 (/.f64 32 (*.f64 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 2 (-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (/.f64 (/.f64 32 x) x) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 2 (-.f64 (/.f64 -8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 (+.f64 2 (/.f64 -8 x)) (+.f64 (/.f64 32 (*.f64 x 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))))
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 (/.f64 32 x) x) (/.f64 -8 x)))
(+.f64 (+.f64 2 (/.f64 -8 x)) (/.f64 32 (*.f64 x x)))
(+.f64 2 (+.f64 (/.f64 32 (*.f64 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 2 (-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (/.f64 (/.f64 32 x) x) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 2 (-.f64 (/.f64 -8 x) (/.f64 128 (pow.f64 x 3)))))
(+.f64 (+.f64 2 (/.f64 -8 x)) (+.f64 (/.f64 32 (*.f64 x 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))))

localize11.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiled 14 to 10 computations (28.6% saved)

series3.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite61.0ms (1.5%)

Algorithm
1×batch-egg-rewrite
Rules
533×pow1_binary64
521×add-sqr-sqrt_binary64
496×add-log-exp_binary64
496×log1p-expm1-u_binary64
496×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
11228
213338
Stop Event
1×node limit
Counts
1 → 13
Calls
Call 1
Inputs
(*.f64 x (fma.f64 x -1/8 1/2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x -1/8) x) (*.f64 1/2 x))))) (#(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 1 (*.f64 x (fma.f64 x -1/8 1/2))) 1)))) (#(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 x) (fma.f64 x -1/8 1/2)))))) (#(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 expm1.f64 (log1p.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))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (fma.f64 x -1/8 1/2))))))))

simplify195.0ms (4.7%)

Algorithm
1×egg-herbie
Rules
778×sqr-pow_binary64
565×cube-prod_binary64
563×fabs-mul_binary64
540×associate-*l*_binary64
434×unswap-sqr_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
09117
118117
231108
36790
416690
547390
6171190
7296090
8316490
9337790
10359790
11390890
12431090
13481990
14538590
15607590
16691290
17730290
18759490
19787490
20794890
21798490
Stop Event
1×node limit
Counts
25 → 18
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 1/2 (*.f64 x -1/8)))
(*.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 1/2 (*.f64 x -1/8)))
(*.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 1/2 (*.f64 x -1/8)))
(*.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 1/2 (*.f64 x -1/8)))
(*.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 1/2 (*.f64 x -1/8)))
(*.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 1/2 (*.f64 x -1/8)))
(*.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 1/2 (*.f64 x -1/8)))
(*.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 1/2 (*.f64 x -1/8)))
(*.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 1/2 (*.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))

eval131.0ms (3.1%)

Compiler

Compiled 3135 to 2430 computations (22.5% saved)

prune36.0ms (0.9%)

Pruning

9 alts after pruning (4 fresh and 5 done)

PrunedKeptTotal
New2503253
Fresh112
Picked101
Done055
Total2529261
Error
0b
Counts
261 → 9
Alt Table
Click to see full alt table
StatusErrorProgram
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
▶20.8b
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
✓19.7b
(/.f64 x (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
✓0.2b
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 1/2)))
▶21.1b
(+.f64 (*.f64 (*.f64 x -1/8) x) (*.f64 1/2 x))
60.9b
2
▶39.6b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
✓19.7b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
✓20.1b
(/.f64 x 2)
Compiler

Compiled 75 to 57 computations (24% saved)

localize15.0ms (0.4%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓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))))
Compiler

Compiled 33 to 24 computations (27.3% saved)

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

rewrite64.0ms (1.5%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
0922
120020
2249020
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 (fma.f64 x 1/16 -1/8) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (fma.f64 x 1/16 -1/8) (*.f64 x x)) (*.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 (fma.f64 x 1/16 -1/8) (*.f64 x x)) 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) (pow.f64 (*.f64 (fma.f64 x 1/16 -1/8) (*.f64 x x)) 3)) (+.f64 (pow.f64 (*.f64 x 1/2) 2) (-.f64 (pow.f64 (*.f64 (fma.f64 x 1/16 -1/8) (*.f64 x x)) 2) (*.f64 (*.f64 x 1/2) (*.f64 (fma.f64 x 1/16 -1/8) (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 x 1/2) 2) (pow.f64 (*.f64 (fma.f64 x 1/16 -1/8) (*.f64 x x)) 2)) (-.f64 (*.f64 x 1/2) (*.f64 (fma.f64 x 1/16 -1/8) (*.f64 x x))))))) (#(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 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 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 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 fma.f64 x 1/2 (*.f64 (fma.f64 x 1/16 -1/8) (*.f64 x x)))))) (#(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 (fma.f64 x 1/16 -1/8) (*.f64 x x)))))) (#(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 (fma.f64 x 1/16 -1/8) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.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 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 (fma.f64 x 1/16 -1/8) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.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 (fma.f64 x 1/16 -1/8) (*.f64 x x)))))) (#(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 (fma.f64 x 1/16 -1/8) (*.f64 x x)) 1))))) (#(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 (fma.f64 x 1/16 -1/8) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 (fma.f64 x 1/16 -1/8) (*.f64 x x))) 2) (cbrt.f64 (*.f64 (fma.f64 x 1/16 -1/8) (*.f64 x x))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/2)) (sqrt.f64 (*.f64 x 1/2)) (*.f64 (fma.f64 x 1/16 -1/8) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (fma.f64 x 1/16 -1/8) (*.f64 x x))) (sqrt.f64 (*.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 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 (fma.f64 x 1/16 -1/8) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) (*.f64 (fma.f64 x 1/16 -1/8) (*.f64 x x)))))) (#(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 (cbrt.f64 (pow.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 +.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 expm1.f64 (log1p.f64 (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.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 (log.f64 (pow.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 3)) 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 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))))))

simplify81.0ms (1.9%)

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

Useful iterations: 4 (0.0ms)

IterNodesCost
019282
147282
289264
3216222
4611210
52171210
64160210
74701210
86649210
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))
(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 1/2 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 (*.f64 x 1/16) -1/8)))
(*.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 (*.f64 x 1/16) -1/8)))
(*.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)))
(fma.f64 1/16 (pow.f64 x 3) (*.f64 x (*.f64 x -1/8)))
(*.f64 (*.f64 x x) (+.f64 (*.f64 x 1/16) -1/8))
(*.f64 x (*.f64 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 (*.f64 x 1/16) -1/8)))
(*.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 (*.f64 x 1/16) -1/8)))
(*.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)))
(fma.f64 1/16 (pow.f64 x 3) (*.f64 x (*.f64 x -1/8)))
(*.f64 (*.f64 x x) (+.f64 (*.f64 x 1/16) -1/8))
(*.f64 x (*.f64 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 (*.f64 x 1/16) -1/8)))
(*.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 (*.f64 x 1/16) -1/8)))
(*.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 x (*.f64 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 x (*.f64 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 x (*.f64 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 x (*.f64 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 x (*.f64 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 x (*.f64 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 x (*.f64 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 x (*.f64 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 x (*.f64 x 1/16)))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))

localize11.0ms (0.3%)

Compiler

Compiled 24 to 16 computations (33.3% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
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)
Compiler

Compiled 34 to 25 computations (26.5% saved)

series6.0ms (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)

rewrite71.0ms (1.7%)

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
2291125
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 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 (cbrt.f64 (pow.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) (cbrt.f64 (pow.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) (cbrt.f64 (pow.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 (+.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x 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 expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1)))))

simplify129.0ms (3.1%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
027155
173153
2169149
3496125
41476125
52481125
64460125
74603125
84867125
95236125
105939125
116913125
127409125
137961125
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 1/2 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 -5/128 (pow.f64 x 4) (*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8)))))
(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 1/2 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 -5/128 (pow.f64 x 4) (*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8)))))
(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 -1/8 (*.f64 x x) 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 x (fma.f64 x -1/8 1/2) (fma.f64 1/16 (pow.f64 x 3) 2))

eval89.0ms (2.1%)

Compiler

Compiled 3706 to 2629 computations (29.1% saved)

prune35.0ms (0.8%)

Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New2453248
Fresh011
Picked101
Done347
Total2498257
Error
0b
Counts
257 → 8
Alt Table
Click to see full alt table
StatusErrorProgram
▶21.1b
(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))
✓19.7b
(/.f64 x (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
▶20.8b
(*.f64 x (+.f64 1/2 (+.f64 (*.f64 (*.f64 x 1/16) x) (*.f64 -1/8 x))))
✓20.1b
(/.f64 x 2)
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
▶39.6b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
60.9b
2
✓19.7b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
Compiler

Compiled 62 to 48 computations (22.6% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiled 19 to 14 computations (26.3% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite49.0ms (1.2%)

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
220628
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 -1/8 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 -1/8 (*.f64 x x)) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 1/2) 1) (*.f64 (*.f64 -1/8 (*.f64 x x)) 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 -1/8 (*.f64 x x)) 3)) (+.f64 (*.f64 (*.f64 x 1/2) (*.f64 x 1/2)) (-.f64 (*.f64 (*.f64 -1/8 (*.f64 x x)) (*.f64 -1/8 (*.f64 x x))) (*.f64 (*.f64 x 1/2) (*.f64 -1/8 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x 1/2) (*.f64 x 1/2)) (*.f64 (*.f64 -1/8 (*.f64 x x)) (*.f64 -1/8 (*.f64 x x)))) (-.f64 (*.f64 x 1/2) (*.f64 -1/8 (*.f64 x x))))))) (#(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 expm1.f64 (log1p.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))))))) (#(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 fma.f64 x 1/2 (*.f64 -1/8 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 x (*.f64 -1/8 (*.f64 x x)))))))

simplify182.0ms (4.3%)

Algorithm
1×egg-herbie
Rules
778×sqr-pow_binary64
565×cube-prod_binary64
563×fabs-mul_binary64
540×associate-*l*_binary64
434×unswap-sqr_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
09117
118117
231108
36790
416690
547390
6171190
7296090
8316490
9337790
10359790
11390890
12431090
13481990
14538590
15607590
16691290
17730290
18759490
19787490
20794890
21798490
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 1/2 (*.f64 x -1/8)))
(*.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 1/2 (*.f64 x -1/8)))
(*.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 1/2 (*.f64 x -1/8)))
(*.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 1/2 (*.f64 x -1/8)))
(*.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 1/2 (*.f64 x -1/8)))
(*.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 1/2 (*.f64 x -1/8)))
(*.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 1/2 (*.f64 x -1/8)))
(*.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 1/2 (*.f64 x -1/8)))
(*.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 1/2 (*.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))

localize20.0ms (0.5%)

Local error

Found 2 expressions with local error:

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

Compiled 49 to 34 computations (30.6% saved)

series2.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

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

rewrite74.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
598×log-prod_binary64
564×fma-def_binary64
429×pow-prod-down_binary64
318×pow2_binary64
258×fma-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01126
125520
2350020
Stop Event
1×node limit
Counts
2 → 125
Calls
Call 1
Inputs
(*.f64 x (+.f64 1/2 (+.f64 (*.f64 (*.f64 x 1/16) x) (*.f64 -1/8 x))))
(+.f64 (*.f64 (*.f64 x 1/16) x) (*.f64 -1/8 x))
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 x (*.f64 x 1/16) 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 x (*.f64 x 1/16) 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 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 (pow.f64 (*.f64 x 1/2) 3) (pow.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))) 3)) (+.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 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 log.f64 (*.f64 (exp.f64 (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)))) (exp.f64 (*.f64 x 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 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 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 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 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 x (fma.f64 x (*.f64 x 1/16) 1/2) (*.f64 x (*.f64 x -1/8)))))) (#(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 (*.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) 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 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 (cbrt.f64 (pow.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) 1/2) (*.f64 x (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(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 (*.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 (fma.f64 x (*.f64 x 1/16) 1/2) x (*.f64 (*.f64 x -1/8) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 1/2)) 2) (cbrt.f64 (*.f64 x 1/2)) (*.f64 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 (*.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 (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 (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 (*.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 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 (cbrt.f64 (pow.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 -.f64 (exp.f64 (log1p.f64 (*.f64 x (fma.f64 x 1/16 -1/8)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 x (*.f64 x 1/16)) 2) (*.f64 x (fma.f64 x 1/16 1/8))) (/.f64 (*.f64 (*.f64 x x) 1/64) (*.f64 x (fma.f64 x 1/16 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (fma.f64 x 1/16 -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (fma.f64 x 1/16 -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (fma.f64 x 1/16 -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (fma.f64 x 1/16 -1/8))) (cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 2)) (cbrt.f64 (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (fma.f64 x 1/16 -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (fma.f64 x 1/16 -1/8))) (sqrt.f64 (*.f64 x (fma.f64 x 1/16 -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 x 3) -1/512 (pow.f64 (*.f64 x (*.f64 x 1/16)) 3)) (/.f64 1 (fma.f64 (*.f64 x -1/8) (-.f64 (*.f64 x -1/8) (*.f64 x (*.f64 x 1/16))) (pow.f64 (*.f64 x (*.f64 x 1/16)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) (*.f64 x (fma.f64 x 1/16 1/8))) (/.f64 1 (*.f64 x (fma.f64 x 1/16 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x 1/16 -1/8) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (*.f64 x -1/8) (-.f64 (*.f64 x -1/8) (*.f64 x (*.f64 x 1/16))) (pow.f64 (*.f64 x (*.f64 x 1/16)) 2)) (fma.f64 (pow.f64 x 3) -1/512 (pow.f64 (*.f64 x (*.f64 x 1/16)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 x (fma.f64 x 1/16 1/8)) (*.f64 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1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (*.f64 x 1/16)) (*.f64 x -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x (*.f64 x 1/16))) (sqrt.f64 (*.f64 x (*.f64 x 1/16))) (*.f64 x -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/8 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 x (*.f64 x 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/8 (sqrt.f64 x)) (sqrt.f64 x) (*.f64 x (*.f64 x 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (cbrt.f64 (*.f64 (*.f64 x x) 1/256))) (cbrt.f64 (*.f64 x 1/16)) (*.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))))))

simplify81.0ms (1.9%)

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

Useful iterations: 4 (0.0ms)

IterNodesCost
019282
147282
289264
3216222
4611210
52171210
64160210
74701210
86649210
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))
(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 1/2 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 (*.f64 x 1/16) -1/8)))
(*.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 (*.f64 x 1/16) -1/8)))
(*.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)))
(fma.f64 1/16 (pow.f64 x 3) (*.f64 x (*.f64 x -1/8)))
(*.f64 (*.f64 x x) (+.f64 (*.f64 x 1/16) -1/8))
(*.f64 x (*.f64 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 (*.f64 x 1/16) -1/8)))
(*.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 (*.f64 x 1/16) -1/8)))
(*.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)))
(fma.f64 1/16 (pow.f64 x 3) (*.f64 x (*.f64 x -1/8)))
(*.f64 (*.f64 x x) (+.f64 (*.f64 x 1/16) -1/8))
(*.f64 x (*.f64 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 (*.f64 x 1/16) -1/8)))
(*.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 (*.f64 x 1/16) -1/8)))
(*.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 x (*.f64 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 x (*.f64 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 x (*.f64 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 x (*.f64 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 x (*.f64 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 x (*.f64 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 x (*.f64 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 x (*.f64 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 x (*.f64 x 1/16)))
(*.f64 x (+.f64 -1/8 (*.f64 x 1/16)))
(*.f64 x (fma.f64 x 1/16 -1/8))

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiled 16 to 12 computations (25% saved)

eval148.0ms (3.5%)

Compiler

Compiled 3810 to 2747 computations (27.9% saved)

prune37.0ms (0.9%)

Pruning

8 alts after pruning (1 fresh and 7 done)

PrunedKeptTotal
New2660266
Fresh011
Picked011
Done066
Total2668274
Error
0b
Counts
274 → 8
Alt Table
Click to see full alt table
StatusErrorProgram
✓21.1b
(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))
✓19.7b
(/.f64 x (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
✓20.8b
(*.f64 x (+.f64 1/2 (+.f64 (*.f64 (*.f64 x 1/16) x) (*.f64 -1/8 x))))
✓20.1b
(/.f64 x 2)
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓39.6b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
60.9b
2
✓19.7b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
Compiler

Compiled 62 to 48 computations (22.6% saved)

regimes49.0ms (1.2%)

Counts
14 → 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 (*.f64 (*.f64 x -1/8) x) (*.f64 1/2 x))
(/.f64 x (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(*.f64 x (+.f64 1/2 (+.f64 (*.f64 (*.f64 x 1/16) x) (*.f64 -1/8 x))))
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
(*.f64 x (fma.f64 x -1/8 1/2))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 1/2)))
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
(/.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 (pow.f64 (+.f64 x 1) 1/2)))
Calls

3 calls:

28.0ms
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
9.0ms
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
8.0ms
x
Results
ErrorSegmentsBranch
0.2b1x
0.2b1(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.2b1(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 129 to 94 computations (27.1% saved)

regimes17.0ms (0.4%)

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

2 calls:

9.0ms
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms
x
Results
ErrorSegmentsBranch
0.2b1x
0.2b1(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 81 to 59 computations (27.2% saved)

regimes14.0ms (0.3%)

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

1 calls:

11.0ms
x
Results
ErrorSegmentsBranch
0.0b2x
Compiler

Compiled 64 to 46 computations (28.1% saved)

bsearch20.0ms (0.5%)

Algorithm
1×binary-search
Steps
TimeLeftRight
20.0ms
2.7674244720436593e-8
0.10266196555053207
Compiler

Compiled 13 to 10 computations (23.1% saved)

regimes9.0ms (0.2%)

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

1 calls:

5.0ms
x
Results
ErrorSegmentsBranch
19.7b1x
Compiler

Compiled 52 to 37 computations (28.8% saved)

regimes43.0ms (1%)

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

1 calls:

42.0ms
x
Results
ErrorSegmentsBranch
19.7b1x
Compiler

Compiled 30 to 21 computations (30% saved)

regimes5.0ms (0.1%)

Accuracy

Total -42.1b remaining (-209.1%)

Threshold costs -42.1b (-209.1%)

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:

4.0ms
x
Results
ErrorSegmentsBranch
20.1b1x
Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify7.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02881
14381
24481
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 1/2)))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(if (<=.f64 x 65343962853261/2361183241434822606848) (+.f64 (*.f64 (*.f64 x -1/8) x) (*.f64 1/2 x)) (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
(/.f64 x (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(/.f64 x 2)
2
Outputs
(/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 1/2)))
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(if (<=.f64 x 65343962853261/2361183241434822606848) (+.f64 (*.f64 (*.f64 x -1/8) x) (*.f64 1/2 x)) (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
(if (<=.f64 x 65343962853261/2361183241434822606848) (+.f64 (*.f64 x (*.f64 x -1/8)) (*.f64 x 1/2)) (+.f64 (sqrt.f64 (+.f64 x 1)) -1))
(/.f64 x (+.f64 1 (+.f64 (*.f64 1/2 x) 1)))
(/.f64 x (+.f64 1 (+.f64 1 (*.f64 x 1/2))))
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(/.f64 x (+.f64 (*.f64 x 1/2) 2))
(/.f64 x 2)
2
Compiler

Compiled 63 to 49 computations (22.2% saved)

soundness175.0ms (4.2%)

Algorithm
1×egg-herbie
Rules
803×unswap-sqr_binary64
601×distribute-lft-out_binary64
598×*-commutative_binary64
504×fma-def_binary64
407×associate-+l+_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
033136
192132
2210130
3601109
41652109
52656109
64635109
74778109
85042109
95411109
106152109
117162109
127707109
Stop Event
1×node limit
Compiler

Compiled 53 to 39 computations (26.4% saved)

end173.0ms (4.1%)

Compiler

Compiled 57 to 43 computations (24.6% saved)

Profiling

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