Details

Time bar (total: 3.8s)

analyze6.0ms (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)

sample1.6s (41.4%)

Results
1.5s8254×body256valid
1.0ms2×body2048valid
0.0ms2×body256invalid

preprocess93.0ms (2.4%)

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)

simplify13.0ms (0.3%)

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))))

eval2.0ms (0.1%)

Compiler

Compiled 9 to 7 computations (22.2% saved)

prune2.0ms (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)

localize25.0ms (0.7%)

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)

series14.0ms (0.4%)

Counts
3 → 12
Calls

9 calls:

TimeVariablePointExpression
4.0ms
x
@inf
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
3.0ms
x
@-inf
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
1.0ms
x
@0
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
1.0ms
x
@inf
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
1.0ms
x
@-inf
(+.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite121.0ms (3.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0727
115727
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))))))

simplify146.0ms (3.9%)

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))

eval87.0ms (2.3%)

Compiler

Compiled 1387 to 1086 computations (21.7% saved)

prune40.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1016107
Fresh000
Picked011
Done000
Total1017108
Error
0b
Counts
108 → 7
Alt Table
Click to see full alt table
StatusErrorProgram
▶22.0b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
▶37.3b
(*.f64 (/.f64 x (neg.f64 x)) (-.f64 1 (sqrt.f64 (+.f64 x 1))))
▶22.4b
(/.f64 x 2)
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
▶0.3b
(pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)
▶37.3b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
23.1b
(/.f64 x (+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 2)))
Compiler

Compiled 129 to 99 computations (23.3% saved)

localize34.0ms (0.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
✓0.1b
(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
✓0.2b
(pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)
Compiler

Compiled 35 to 27 computations (22.9% saved)

series6.0ms (0.2%)

Counts
2 → 8
Calls

6 calls:

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

rewrite73.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
424×prod-diff_binary64
416×log-prod_binary64
312×exp-prod_binary64
279×fma-def_binary64
267×pow-prod-down_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0927
119924
2274324
Stop Event
1×node limit
Counts
2 → 103
Calls
Call 1
Inputs
(pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)
(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) -2) (/.f64 x (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2)) (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -1/2) (/.f64 x (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4))) (/.f64 (cbrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4))) (/.f64 (sqrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 x))))) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 1 x) 3/2))) (-.f64 (+.f64 1 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (neg.f64 x)) (-.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)) -2) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 x) 2) (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 x) (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4))) (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) (pow.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)) -2) (cbrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2)) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x) -3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 1 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 1 x))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x))) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 1 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x)) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 1 x)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x)) -1/2) 2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (pow.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2) (*.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)) 2) (cbrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) (*.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) (pow.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)) (sqrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 x)))) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1) (+.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2) 1) (/.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) 1) (/.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) -2) (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x) -3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 3) (pow.f64 x 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x))) 2)) (cbrt.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x)))) (sqrt.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 1 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) (log.f64 x)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 1 x)))) 1) -1))))))

simplify63.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
991×fma-def_binary64
803×unswap-sqr_binary64
686×associate-/l*_binary64
506×associate-/r/_binary64
445×distribute-lft-out_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
03398
18598
218691
347086
4140879
5319979
6518979
7628479
Stop Event
1×node limit
Counts
111 → 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 2 x)
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x))))
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (+.f64 (*.f64 1/16 (pow.f64 x 2)) (*.f64 2 (/.f64 1 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))
(fma.f64 1/2 x (*.f64 -1/8 (*.f64 x x)))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 1/16 (pow.f64 x 3) (*.f64 x (fma.f64 x -1/8 1/2)))
(*.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 (*.f64 -5/128 (pow.f64 x 4)) (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 -5/128 (pow.f64 x 4) (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) (*.f64 -5/128 (pow.f64 x 4)))))
(+.f64 (*.f64 x (fma.f64 x -1/8 1/2)) (fma.f64 1/16 (pow.f64 x 3) (*.f64 -5/128 (pow.f64 x 4))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (+.f64 1/16 (*.f64 x -5/128))))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x (fma.f64 x -5/128 1/16) -1/8))))
(/.f64 2 x)
(+.f64 1/2 (*.f64 2 (/.f64 1 x)))
(+.f64 1/2 (/.f64 2 x))
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 2 (/.f64 1 x))))
(fma.f64 -1/8 x (+.f64 1/2 (/.f64 2 x)))
(+.f64 (/.f64 2 x) (fma.f64 x -1/8 1/2))
(+.f64 1/2 (fma.f64 x -1/8 (/.f64 2 x)))
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (+.f64 (*.f64 1/16 (pow.f64 x 2)) (*.f64 2 (/.f64 1 x)))))
(fma.f64 -1/8 x (+.f64 1/2 (fma.f64 1/16 (*.f64 x x) (/.f64 2 x))))
(+.f64 (fma.f64 (*.f64 x x) 1/16 (/.f64 2 x)) (fma.f64 x -1/8 1/2))
(+.f64 (/.f64 2 x) (fma.f64 x -1/8 (fma.f64 (*.f64 x x) 1/16 1/2)))
(+.f64 1/2 (+.f64 (/.f64 2 x) (*.f64 x (fma.f64 x 1/16 -1/8))))
(+.f64 (/.f64 2 x) (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2))

localize3.0ms (0.1%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize10.0ms (0.3%)

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)

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite62.0ms (1.6%)

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))))))))

simplify53.0ms (1.4%)

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)))))

localize19.0ms (0.5%)

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)))
✓3.1b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
Compiler

Compiled 34 to 25 computations (26.5% saved)

series5.0ms (0.1%)

Counts
3 → 12
Calls

9 calls:

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

rewrite80.0ms (2.1%)

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

simplify139.0ms (3.7%)

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))

localize15.0ms (0.4%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
✓3.1b
(-.f64 1 (sqrt.f64 (+.f64 x 1)))
Compiler

Compiled 33 to 20 computations (39.4% saved)

series2.0ms (0.1%)

Counts
1 → 4
Calls

3 calls:

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

rewrite50.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
683×pow1_binary64
639×log1p-expm1-u_binary64
639×expm1-log1p-u_binary64
638×add-log-exp_binary64
625×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
11329
217689
Stop Event
1×node limit
Counts
1 → 28
Calls
Call 1
Inputs
(-.f64 1 (sqrt.f64 (+.f64 x 1)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (neg.f64 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (neg.f64 (sqrt.f64 (+.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 (+.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x)))) (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x)))) 2) (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (+.f64 1 x) 3/2)) (/.f64 1 (+.f64 1 (+.f64 (+.f64 1 x) (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 0 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (+.f64 (+.f64 1 x) (sqrt.f64 (+.f64 1 x)))) (-.f64 1 (pow.f64 (+.f64 1 x) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (-.f64 0 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 1 x) 3/2)) (+.f64 1 (+.f64 (+.f64 1 x) (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 x) (+.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (+.f64 1 x) 3/2))) (neg.f64 (+.f64 1 (+.f64 (+.f64 1 x) (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 0 x)) (neg.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (neg.f64 (sqrt.f64 (+.f64 1 x))) 3)) (+.f64 1 (-.f64 (*.f64 (neg.f64 (sqrt.f64 (+.f64 1 x))) (neg.f64 (sqrt.f64 (+.f64 1 x)))) (neg.f64 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (neg.f64 (sqrt.f64 (+.f64 1 x))) (neg.f64 (sqrt.f64 (+.f64 1 x))))) (-.f64 1 (neg.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (neg.f64 (sqrt.f64 (+.f64 1 x)))))))))

simplify118.0ms (3.1%)

Algorithm
1×egg-herbie
Rules
937×fma-def_binary64
803×unswap-sqr_binary64
577×distribute-lft-out_binary64
539×*-commutative_binary64
371×sqr-pow_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02258
15658
212856
340047
4129342
5311842
6507842
7521542
8545542
9573942
10628742
11710542
12772942
Stop Event
1×node limit
Counts
32 → 35
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 -1/16 (pow.f64 x 3)) (*.f64 -1/2 x)))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 -1/16 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 x) (*.f64 5/128 (pow.f64 x 4)))))
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 -1/16 (pow.f64 x 3)) (*.f64 -1/2 x)))
(fma.f64 1/8 (*.f64 x x) (fma.f64 -1/16 (pow.f64 x 3) (*.f64 -1/2 x)))
(fma.f64 1/8 (*.f64 x x) (fma.f64 -1/2 x (*.f64 -1/16 (pow.f64 x 3))))
(fma.f64 -1/2 x (*.f64 (*.f64 x x) (+.f64 1/8 (*.f64 x -1/16))))
(*.f64 x (+.f64 -1/2 (*.f64 x (fma.f64 x -1/16 1/8))))
(*.f64 x (fma.f64 x (fma.f64 x -1/16 1/8) -1/2))
(+.f64 (*.f64 1/8 (pow.f64 x 2)) (+.f64 (*.f64 -1/16 (pow.f64 x 3)) (+.f64 (*.f64 -1/2 x) (*.f64 5/128 (pow.f64 x 4)))))
(fma.f64 1/8 (*.f64 x x) (fma.f64 -1/16 (pow.f64 x 3) (fma.f64 -1/2 x (*.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 5/128 (pow.f64 x 4) (*.f64 x (+.f64 -1/2 (*.f64 x (fma.f64 x -1/16 1/8)))))
(*.f64 x (+.f64 -1/2 (*.f64 x (fma.f64 x (fma.f64 x 5/128 -1/16) 1/8))))

eval161.0ms (4.2%)

Compiler

Compiled 6493 to 4809 computations (25.9% saved)

prune99.0ms (2.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New4394443
Fresh101
Picked101
Done235
Total4437450
Error
0b
Counts
450 → 7
Alt Table
Click to see full alt table
StatusErrorProgram
✓22.4b
(/.f64 x 2)
▶22.5b
(pow.f64 (/.f64 2 x) -1)
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
▶37.3b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
▶23.1b
(/.f64 x (+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 2)))
60.7b
2
✓22.0b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
Compiler

Compiled 50 to 40 computations (20% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
3.1b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
Compiler

Compiled 16 to 12 computations (25% saved)

localize19.0ms (0.5%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 2))
✓10.1b
(/.f64 x (+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 2)))
Compiler

Compiled 45 to 35 computations (22.2% saved)

series3.0ms (0.1%)

Counts
2 → 18
Calls

6 calls:

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

rewrite74.0ms (2%)

Algorithm
1×batch-egg-rewrite
Rules
557×log-prod_binary64
418×fma-def_binary64
350×pow-prod-down_binary64
311×pow2_binary64
263×fma-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01127
125627
2342127
Stop Event
1×node limit
Counts
2 → 114
Calls
Call 1
Inputs
(/.f64 x (+.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) 2))
Outputs
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-1/8)) (+.f64 1 (expm1.f64 (fma.f64 x 1/2 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 (*.f64 -1/8 x) x))) (+.f64 1 (expm1.f64 (fma.f64 x 1/2 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (fma.f64 x 1/2 2))) (pow.f64 (exp.f64 x) (*.f64 x -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (fma.f64 x 1/2 2)) (+.f64 1 (expm1.f64 (*.f64 (*.f64 -1/8 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (fma.f64 x 1/2 2))) (+.f64 1 (expm1.f64 (*.f64 (*.f64 -1/8 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (*.f64 x -1/8) (fma.f64 x 1/2 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (*.f64 x -1/8) (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (*.f64 x -1/8) (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (*.f64 x -1/8) (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x (*.f64 x -1/8) (fma.f64 x 1/2 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/2 (+.f64 2 (*.f64 (*.f64 -1/8 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 x -1/8) (fma.f64 x 1/2 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/8 (*.f64 x x) (fma.f64 x 1/2 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) -1/8 (fma.f64 x 1/2 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 -1/8 x) x) 1 (fma.f64 x 1/2 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 x (+.f64 2 (*.f64 (*.f64 -1/8 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x 1/2) 1 (+.f64 2 (*.f64 (*.f64 -1/8 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 x 1/2 2) 1 (*.f64 (*.f64 -1/8 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (*.f64 -1/8 x) x) (fma.f64 x 1/2 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 1/2) (+.f64 2 (*.f64 (*.f64 -1/8 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x 1/2 2) (*.f64 (*.f64 -1/8 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x 1/2 (*.f64 (*.f64 -1/8 x) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x 1/2)) (pow.f64 (cbrt.f64 (*.f64 x 1/2)) 2) (+.f64 2 (*.f64 (*.f64 -1/8 x) 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 2 (*.f64 (*.f64 -1/8 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 x) x) (*.f64 (pow.f64 (cbrt.f64 x) 2) -1/8) (fma.f64 x 1/2 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/2) (+.f64 2 (*.f64 (*.f64 -1/8 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 x 1/2 2)) (cbrt.f64 (pow.f64 (fma.f64 x 1/2 2) 2)) (*.f64 (*.f64 -1/8 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (fma.f64 x 1/2 2) 2)) (cbrt.f64 (fma.f64 x 1/2 2)) (*.f64 (*.f64 -1/8 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (*.f64 -1/8 x) x)) (cbrt.f64 (*.f64 (pow.f64 x 4) 1/64)) (fma.f64 x 1/2 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 1/64)) (cbrt.f64 (*.f64 (*.f64 -1/8 x) x)) (fma.f64 x 1/2 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/2)) (sqrt.f64 (*.f64 x 1/2)) (+.f64 2 (*.f64 (*.f64 -1/8 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/2) (+.f64 2 (*.f64 (*.f64 -1/8 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x 1/2 2)) (sqrt.f64 (fma.f64 x 1/2 2)) (*.f64 (*.f64 -1/8 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 -1/8)) (*.f64 x (sqrt.f64 -1/8)) (fma.f64 x 1/2 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (pow.f64 x 3) 1/8 8) (/.f64 1 (-.f64 (fma.f64 (*.f64 x x) 1/4 4) x)) (*.f64 (*.f64 -1/8 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (*.f64 x x) 1/4 -4) (/.f64 1 (fma.f64 x 1/2 -2)) (*.f64 (*.f64 -1/8 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 x 1/2 (*.f64 (*.f64 -1/8 x) x)) 1 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 (*.f64 (*.f64 -1/8 x) x))) 2) (cbrt.f64 (fma.f64 x 1/2 (*.f64 (*.f64 -1/8 x) x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x 1/2 (*.f64 (*.f64 -1/8 x) x))) (sqrt.f64 (fma.f64 x 1/2 (*.f64 (*.f64 -1/8 x) x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (+.f64 2 (*.f64 (*.f64 -1/8 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) (+.f64 2 (*.f64 (*.f64 -1/8 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/8 x) x (fma.f64 x 1/2 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/8 (*.f64 (cbrt.f64 x) x)) (pow.f64 (cbrt.f64 x) 2) (fma.f64 x 1/2 2))))))

simplify55.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
898×fma-neg_binary64
810×times-frac_binary64
472×fma-def_binary64
471×cancel-sign-sub-inv_binary64
408×associate-/l/_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
045252
1121240
2334236
31094223
43534223
Stop Event
1×node limit
Counts
132 → 133
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 -3/128 (pow.f64 x 4)) (*.f64 1/16 (pow.f64 x 3)))))
(/.f64 -8 x)
(neg.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 2))) (*.f64 8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 256 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 32 (/.f64 1 (pow.f64 x 2))))))
(neg.f64 (+.f64 (*.f64 1536 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 256 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 32 (/.f64 1 (pow.f64 x 2)))))))
(/.f64 -8 x)
(neg.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 2))) (*.f64 8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 256 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 32 (/.f64 1 (pow.f64 x 2))))))
(neg.f64 (+.f64 (*.f64 1536 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 256 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 32 (/.f64 1 (pow.f64 x 2)))))))
2
(+.f64 (*.f64 1/2 x) 2)
(*.f64 -1/8 (pow.f64 x 2))
(+.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))
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 -1/8 (*.f64 x x) (fma.f64 1/16 (pow.f64 x 3) (*.f64 1/2 x)))
(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 -3/128 (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 -3/128 (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 -3/128 (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 -3/128 (pow.f64 x 4)))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (+.f64 1/16 (*.f64 x -3/128))))
(/.f64 -8 x)
(neg.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 2))) (*.f64 8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x)))
(+.f64 (/.f64 -32 (*.f64 x x)) (/.f64 -8 x))
(-.f64 (/.f64 -32 (*.f64 x x)) (/.f64 8 x))
(neg.f64 (+.f64 (*.f64 256 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 32 (/.f64 1 (pow.f64 x 2))))))
(neg.f64 (+.f64 (/.f64 256 (pow.f64 x 3)) (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x))))
(+.f64 (/.f64 -256 (pow.f64 x 3)) (+.f64 (/.f64 -32 (*.f64 x x)) (/.f64 -8 x)))
(+.f64 (/.f64 -32 (*.f64 x x)) (+.f64 (/.f64 -8 x) (/.f64 -256 (pow.f64 x 3))))
(+.f64 (/.f64 -8 x) (*.f64 (/.f64 1 (*.f64 x x)) (-.f64 -32 (/.f64 256 x))))
(neg.f64 (+.f64 (*.f64 1536 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 256 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 32 (/.f64 1 (pow.f64 x 2)))))))
(neg.f64 (+.f64 (+.f64 (/.f64 256 (pow.f64 x 3)) (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x))) (/.f64 1536 (pow.f64 x 4))))
(+.f64 (+.f64 (/.f64 -1536 (pow.f64 x 4)) (/.f64 -256 (pow.f64 x 3))) (+.f64 (/.f64 -32 (*.f64 x x)) (/.f64 -8 x)))
(+.f64 (+.f64 (/.f64 -32 (*.f64 x x)) (+.f64 (/.f64 -8 x) (/.f64 -256 (pow.f64 x 3)))) (/.f64 -1536 (pow.f64 x 4)))
(+.f64 (+.f64 (/.f64 -8 x) (*.f64 (/.f64 1 (*.f64 x x)) (-.f64 -32 (/.f64 256 x)))) (/.f64 -1536 (pow.f64 x 4)))
(/.f64 -8 x)
(neg.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 2))) (*.f64 8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x)))
(+.f64 (/.f64 -32 (*.f64 x x)) (/.f64 -8 x))
(-.f64 (/.f64 -32 (*.f64 x x)) (/.f64 8 x))
(neg.f64 (+.f64 (*.f64 256 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 32 (/.f64 1 (pow.f64 x 2))))))
(neg.f64 (+.f64 (/.f64 256 (pow.f64 x 3)) (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x))))
(+.f64 (/.f64 -256 (pow.f64 x 3)) (+.f64 (/.f64 -32 (*.f64 x x)) (/.f64 -8 x)))
(+.f64 (/.f64 -32 (*.f64 x x)) (+.f64 (/.f64 -8 x) (/.f64 -256 (pow.f64 x 3))))
(+.f64 (/.f64 -8 x) (*.f64 (/.f64 1 (*.f64 x x)) (-.f64 -32 (/.f64 256 x))))
(neg.f64 (+.f64 (*.f64 1536 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 256 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 32 (/.f64 1 (pow.f64 x 2)))))))
(neg.f64 (+.f64 (+.f64 (/.f64 256 (pow.f64 x 3)) (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 8 x))) (/.f64 1536 (pow.f64 x 4))))
(+.f64 (+.f64 (/.f64 -1536 (pow.f64 x 4)) (/.f64 -256 (pow.f64 x 3))) (+.f64 (/.f64 -32 (*.f64 x x)) (/.f64 -8 x)))
(+.f64 (+.f64 (/.f64 -32 (*.f64 x x)) (+.f64 (/.f64 -8 x) (/.f64 -256 (pow.f64 x 3)))) (/.f64 -1536 (pow.f64 x 4)))
(+.f64 (+.f64 (/.f64 -8 x) (*.f64 (/.f64 1 (*.f64 x x)) (-.f64 -32 (/.f64 256 x)))) (/.f64 -1536 (pow.f64 x 4)))
2
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 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))
(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 -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))
(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))

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiled 12 to 9 computations (25% saved)

series3.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite64.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
547×pow1_binary64
511×add-log-exp_binary64
511×log1p-expm1-u_binary64
511×expm1-log1p-u_binary64
500×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
067
11284
214534
Stop Event
1×node limit
Counts
1 → 28
Calls
Call 1
Inputs
(pow.f64 (/.f64 2 x) -1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x 1/2)) (cbrt.f64 (pow.f64 (/.f64 2 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 2 x) -2)) (cbrt.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x 1/2)) (sqrt.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (pow.f64 (/.f64 1 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) -1) (pow.f64 (cbrt.f64 (/.f64 2 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 2 x)) -1) (pow.f64 (sqrt.f64 (/.f64 2 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (/.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 2 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 x) 2) (/.f64 2 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 x) (/.f64 2 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 x 1/2)) (sqrt.f64 (/.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/2 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2)) (cbrt.f64 (/.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 2 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x 1/2)))))))

simplify7.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
1×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0448
1548
Stop Event
1×saturated
Counts
40 → 28
Calls
Call 1
Inputs
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
Outputs
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)

eval153.0ms (4%)

Compiler

Compiled 3731 to 2750 computations (26.3% saved)

prune34.0ms (0.9%)

Pruning

7 alts after pruning (2 fresh and 5 done)

PrunedKeptTotal
New2591260
Fresh011
Picked101
Done055
Total2607267
Error
0b
Counts
267 → 7
Alt Table
Click to see full alt table
StatusErrorProgram
✓23.1b
(/.f64 x (+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 2)))
▶22.5b
(/.f64 1 (/.f64 2 x))
✓22.4b
(/.f64 x 2)
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓37.3b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
60.7b
2
✓22.0b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
Compiler

Compiled 50 to 40 computations (20% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiled 12 to 9 computations (25% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite79.0ms (2.1%)

Algorithm
1×batch-egg-rewrite
Rules
543×pow1_binary64
507×add-log-exp_binary64
507×log1p-expm1-u_binary64
507×expm1-log1p-u_binary64
497×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
064
11294
214954
Stop Event
1×node limit
Counts
1 → 26
Calls
Call 1
Inputs
(/.f64 1 (/.f64 2 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x 1/2)) (pow.f64 (cbrt.f64 (*.f64 x 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x 1/2)) 2) (cbrt.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x 1/2)) (sqrt.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (/.f64 -2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (pow.f64 (/.f64 1 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) -1) (pow.f64 (cbrt.f64 (/.f64 2 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 2 x)) -1) (pow.f64 (sqrt.f64 (/.f64 2 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/4 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x 1/2)))))))

simplify7.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
1×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0448
1548
Stop Event
1×saturated
Counts
38 → 26
Calls
Call 1
Inputs
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
Outputs
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)

eval7.0ms (0.2%)

Compiler

Compiled 178 to 142 computations (20.2% saved)

prune6.0ms (0.2%)

Pruning

7 alts after pruning (1 fresh and 6 done)

PrunedKeptTotal
New26026
Fresh011
Picked011
Done055
Total26733
Error
0b
Counts
33 → 7
Alt Table
Click to see full alt table
StatusErrorProgram
✓23.1b
(/.f64 x (+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 2)))
✓22.5b
(/.f64 1 (/.f64 2 x))
✓22.4b
(/.f64 x 2)
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓37.3b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
60.7b
2
✓22.0b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
Compiler

Compiled 50 to 40 computations (20% saved)

regimes19.0ms (0.5%)

Counts
12 → 1
Calls
Call 1
Inputs
2
(/.f64 x 2)
(/.f64 1 (/.f64 2 x))
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(pow.f64 (/.f64 2 x) -1)
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
(*.f64 (/.f64 x (neg.f64 x)) (-.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 x (+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 2)))
(/.f64 x (+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 2)))
(pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)
Outputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Calls

2 calls:

8.0ms
x
7.0ms
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Results
ErrorSegmentsBranch
0.2b1x
0.2b1(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 104 to 79 computations (24% saved)

regimes12.0ms (0.3%)

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

1 calls:

10.0ms
x
Results
ErrorSegmentsBranch
0.1b2x
Compiler

Compiled 30 to 23 computations (23.3% saved)

bsearch18.0ms (0.5%)

Algorithm
1×binary-search
Steps
TimeLeftRight
17.0ms
5.1071620072706165e-8
0.0008121028484948965
Compiler

Compiled 13 to 10 computations (23.1% saved)

regimes51.0ms (1.4%)

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

1 calls:

50.0ms
x
Results
ErrorSegmentsBranch
22.0b1x
Compiler

Compiled 24 to 18 computations (25% saved)

regimes5.0ms (0.1%)

Accuracy

Total -38.4b remaining (-171.6%)

Threshold costs -38.4b (-171.6%)

Counts
3 → 1
Calls
Call 1
Inputs
2
(/.f64 x 2)
(/.f64 1 (/.f64 2 x))
Outputs
(/.f64 x 2)
Calls

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
22.4b1x
Compiler

Compiled 12 to 9 computations (25% saved)

simplify5.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01852
12752
22852
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(if (<=.f64 x 3858862509715203/75557863725914323419136) (/.f64 x (+.f64 (*.f64 1/2 x) 2)) (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(/.f64 x 2)
2
Outputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(if (<=.f64 x 3858862509715203/75557863725914323419136) (/.f64 x (+.f64 (*.f64 1/2 x) 2)) (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
(if (<=.f64 x 3858862509715203/75557863725914323419136) (/.f64 x (+.f64 (*.f64 x 1/2) 2)) (+.f64 (sqrt.f64 (+.f64 x 1)) -1))
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
(/.f64 x (+.f64 (*.f64 x 1/2) 2))
(/.f64 x 2)
2
Compiler

Compiled 41 to 32 computations (22% saved)

soundness0.0ms (0%)

end37.0ms (1%)

Compiler

Compiled 37 to 28 computations (24.3% saved)

Profiling

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