Details

Time bar (total: 4.0s)

analyze6.0ms (0.2%)

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)

sample1.1s (28.6%)

Results
1.1s8251×body256valid
1.0ms5×body2048valid
0.0ms4×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)

simplify7.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

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

eval0.0ms (0%)

Compiler

Compiled 9 to 7 computations (22.2% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Compiled 9 to 7 computations (22.2% saved)

localize13.0ms (0.3%)

Local error

Found 6 expressions with local error:

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

Compiled 24 to 18 computations (25% saved)

series8.0ms (0.2%)

Counts
3 → 12
Calls

9 calls:

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

rewrite66.0ms (1.6%)

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

Useful iterations: 0 (0.0ms)

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

simplify93.0ms (2.3%)

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

Useful iterations: 3 (0.0ms)

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

eval70.0ms (1.7%)

Compiler

Compiled 1387 to 1085 computations (21.8% saved)

prune40.0ms (1%)

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
2.5b
(/.f64 x (expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
▶20.6b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
38.8b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
▶21.0b
(/.f64 x 2)
▶0.2b
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
▶22.0b
(*.f64 x (fma.f64 x -1/8 1/2))
▶22.0b
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
Compiler

Compiled 133 to 103 computations (22.6% saved)

localize30.0ms (0.7%)

Local error

Found 8 expressions with local error:

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

Compiled 34 to 27 computations (20.6% saved)

series7.0ms (0.2%)

Counts
2 → 8
Calls

6 calls:

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

rewrite69.0ms (1.7%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0824
117924
2244824
Stop Event
1×node limit
Counts
2 → 46
Calls
Call 1
Inputs
(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))) (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -2)) (cbrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -1/2) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2) -1) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) -1) (pow.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (pow.f64 (+.f64 1 x) 3/2))) (+.f64 1 (-.f64 (+.f64 1 x) (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 0 x)) (-.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 x) 2) (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 x) (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4))) (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x 1) (+.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2)) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 x) (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x -1) (+.f64 -1 (neg.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))))

simplify104.0ms (2.6%)

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

Useful iterations: 3 (0.0ms)

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

localize3.0ms (0.1%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

rewrite47.0ms (1.2%)

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

Useful iterations: 0 (0.0ms)

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

simplify41.0ms (1%)

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

Useful iterations: 3 (0.0ms)

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

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(*.f64 x (fma.f64 x -1/8 1/2))
✓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
@0
(*.f64 x (fma.f64 x -1/8 1/2))
1.0ms
x
@-inf
(*.f64 x (fma.f64 x -1/8 1/2))
1.0ms
x
@inf
(*.f64 x (fma.f64 x -1/8 1/2))

rewrite41.0ms (1%)

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

simplify152.0ms (3.8%)

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

Useful iterations: 3 (0.0ms)

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

localize13.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiled 25 to 19 computations (24% saved)

series1.0ms (0%)

Counts
1 → 3
Calls

3 calls:

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

rewrite49.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
900×pow1_binary64
843×add-log-exp_binary64
842×log1p-expm1-u_binary64
842×expm1-log1p-u_binary64
827×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
119711
2235711
Stop Event
1×node limit
Counts
1 → 37
Calls
Call 1
Inputs
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 (pow.f64 x 4) 1/64) (+.f64 (*.f64 -1/8 (*.f64 x x)) (*.f64 -1/2 x))) (/.f64 (*.f64 (*.f64 x x) 1/4) (+.f64 (*.f64 -1/8 (*.f64 x x)) (*.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))) (pow.f64 (cbrt.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))) 2) (cbrt.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))) (sqrt.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (pow.f64 (*.f64 x x) 3) -1/512) (*.f64 (pow.f64 x 3) 1/8)) (/.f64 1 (+.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 x 1/2) (-.f64 (*.f64 x 1/2) (*.f64 -1/8 (*.f64 x x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 x x) 1/4)) (/.f64 1 (+.f64 (*.f64 -1/8 (*.f64 x x)) (*.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 x 1/2) (-.f64 (*.f64 x 1/2) (*.f64 -1/8 (*.f64 x x))))) (+.f64 (*.f64 (pow.f64 (*.f64 x x) 3) -1/512) (*.f64 (pow.f64 x 3) 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 -1/8 (*.f64 x x)) (*.f64 -1/2 x)) (-.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 x x) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 (*.f64 x x) 3) -1/512) (*.f64 (pow.f64 x 3) 1/8)) (+.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 x 1/2) (-.f64 (*.f64 x 1/2) (*.f64 -1/8 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 (*.f64 x x) 3) -1/512) (*.f64 (pow.f64 x 3) 1/8)) (+.f64 (*.f64 (*.f64 x x) 1/4) (-.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 x x) (*.f64 -1/8 (*.f64 x 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 x x) 1/4)) (+.f64 (*.f64 -1/8 (*.f64 x x)) (*.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (*.f64 (pow.f64 (*.f64 x x) 3) -1/512) (*.f64 (pow.f64 x 3) 1/8))) (neg.f64 (+.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 x 1/2) (-.f64 (*.f64 x 1/2) (*.f64 -1/8 (*.f64 x x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (pow.f64 x 4) 1/64) (*.f64 (*.f64 x x) 1/4))) (neg.f64 (+.f64 (*.f64 -1/8 (*.f64 x x)) (*.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (pow.f64 x 4) 1/64)) (-.f64 (*.f64 x 1/2) (*.f64 -1/8 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/8 (*.f64 x x) (*.f64 x 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 (*.f64 x x) -1/8 (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 x (*.f64 -1/8 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 -1/8 (*.f64 x x)) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 1/2) (*.f64 -1/8 (*.f64 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 -1/8 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 1/64)) (cbrt.f64 (*.f64 -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 -1/8 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 -1/8)) (*.f64 x (sqrt.f64 -1/8)) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 -1/8 (*.f64 x x) (*.f64 x 1/2))))))))

simplify127.0ms (3.1%)

Algorithm
1×egg-herbie
Rules
1124×sqr-pow_binary64
565×cube-prod_binary64
560×fabs-mul_binary64
541×pow-sqr_binary64
511×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0818
11518
22518
35118
412218
535818
6137018
7225718
8242118
9263418
10285418
11315418
12355418
13404018
14459918
15528918
16612618
17652018
18681018
19708818
20715618
21719218
Stop Event
1×node limit
Counts
40 → 40
Calls
Call 1
Inputs
(*.f64 1/2 x)
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (pow.f64 x 2))
Outputs
(*.f64 1/2 x)
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (*.f64 x x))
(*.f64 x (*.f64 x -1/8))
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (*.f64 x x))
(*.f64 x (*.f64 x -1/8))

eval120.0ms (3%)

Compiler

Compiled 3056 to 2323 computations (24% saved)

prune37.0ms (0.9%)

Pruning

10 alts after pruning (6 fresh and 4 done)

PrunedKeptTotal
New2284232
Fresh022
Picked101
Done145
Total23010240
Error
0b
Counts
240 → 10
Alt Table
Click to see full alt table
StatusErrorProgram
▶2.5b
(/.f64 x (expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
✓20.6b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
▶38.8b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
✓21.0b
(/.f64 x 2)
60.9b
2
▶22.0b
(+.f64 (*.f64 (*.f64 x -1/8) x) (*.f64 1/2 x))
✓0.2b
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
▶22.0b
(*.f64 x (+.f64 (*.f64 -1/8 x) 1/2))
▶20.7b
(*.f64 x (/.f64 1 (+.f64 (*.f64 1/2 x) 2)))
Compiler

Compiled 134 to 103 computations (23.1% saved)

localize27.0ms (0.7%)

Local error

Found 8 expressions with local error:

NewErrorProgram
0.6b
(log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.2b
(/.f64 x (expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.2b
(/.f64 x (expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
✓0.6b
(log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
✓1.6b
(expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
Compiler

Compiled 41 to 33 computations (19.5% saved)

series27.0ms (0.7%)

Counts
3 → 12
Calls

9 calls:

TimeVariablePointExpression
21.0ms
x
@-inf
(log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
2.0ms
x
@inf
(log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
1.0ms
x
@0
(log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
1.0ms
x
@inf
(/.f64 x (expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
1.0ms
x
@-inf
(/.f64 x (expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))

rewrite60.0ms (1.5%)

Algorithm
1×batch-egg-rewrite
Rules
941×pow1_binary64
880×expm1-log1p-u_binary64
879×log1p-expm1-u_binary64
878×add-log-exp_binary64
89×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0932
117832
2246732
Stop Event
1×node limit
Counts
3 → 84
Calls
Call 1
Inputs
(expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 x (expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1 x)))) (/.f64 (+.f64 1 x) (-.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(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 (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 1 (pow.f64 (+.f64 1 x) 3/2)) (/.f64 1 (+.f64 1 (+.f64 1 (-.f64 x (sqrt.f64 (+.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (+.f64 1 (-.f64 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))) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (-.f64 (sqrt.f64 (+.f64 1 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 1 x) 3/2)) (+.f64 1 (+.f64 1 (-.f64 x (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 1 x) 3/2)) (+.f64 (+.f64 1 x) (-.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 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 1 (-.f64 x (sqrt.f64 (+.f64 1 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 x)) (neg.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) 3) 1) (+.f64 (*.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) (+.f64 2 (sqrt.f64 (+.f64 1 x)))) (+.f64 1 (*.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) (+.f64 2 (sqrt.f64 (+.f64 1 x)))) 1) (+.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))) 1))))) (#(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 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) 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 log.f64 (+.f64 1 (expm1.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 exp.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (sqrt.f64 (+.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4) 1)))) (#(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 -.f64 (exp.f64 (log1p.f64 (log.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))))) (pow.f64 (cbrt.f64 (log.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))))) 2) (cbrt.f64 (log.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))))) (sqrt.f64 (log.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log.f64 (+.f64 2 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log.f64 (+.f64 2 (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 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (+.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 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (+.f64 (neg.f64 (sqrt.f64 (+.f64 1 x))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 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 (/.f64 1 (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)) (cbrt.f64 (/.f64 x (+.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 (/.f64 1 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4))) (/.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 x (+.f64 1 (pow.f64 (+.f64 1 x) 3/2))) (+.f64 1 (+.f64 1 (-.f64 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 pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (+.f64 (neg.f64 (sqrt.f64 (+.f64 1 x))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x 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 x (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))))

simplify101.0ms (2.5%)

Algorithm
1×egg-herbie
Rules
803×unswap-sqr_binary64
659×distribute-lft-out_binary64
588×fma-def_binary64
457×*-commutative_binary64
413×associate-+l+_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
037142
196140
2237138
3729117
42020117
53169117
65195117
75340117
85622117
96022117
106833117
117915117
Stop Event
1×node limit
Counts
96 → 105
Calls
Call 1
Inputs
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)))))
(log.f64 3)
(+.f64 (*.f64 1/6 x) (log.f64 3))
(+.f64 (*.f64 -1/18 (pow.f64 x 2)) (+.f64 (*.f64 1/6 x) (log.f64 3)))
(+.f64 (*.f64 19/648 (pow.f64 x 3)) (+.f64 (*.f64 -1/18 (pow.f64 x 2)) (+.f64 (*.f64 1/6 x) (log.f64 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)))))
Outputs
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 x (*.f64 x -1/8) (fma.f64 1/2 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 (*.f64 x x) (fma.f64 x 1/16 -1/8) 2))
(log.f64 3)
(+.f64 (*.f64 1/6 x) (log.f64 3))
(fma.f64 1/6 x (log.f64 3))
(fma.f64 x 1/6 (log.f64 3))
(+.f64 (*.f64 -1/18 (pow.f64 x 2)) (+.f64 (*.f64 1/6 x) (log.f64 3)))
(fma.f64 -1/18 (*.f64 x x) (fma.f64 1/6 x (log.f64 3)))
(fma.f64 (*.f64 x x) -1/18 (fma.f64 x 1/6 (log.f64 3)))
(fma.f64 x 1/6 (fma.f64 x (*.f64 x -1/18) (log.f64 3)))
(fma.f64 x (fma.f64 x -1/18 1/6) (log.f64 3))
(+.f64 (*.f64 19/648 (pow.f64 x 3)) (+.f64 (*.f64 -1/18 (pow.f64 x 2)) (+.f64 (*.f64 1/6 x) (log.f64 3))))
(fma.f64 19/648 (pow.f64 x 3) (fma.f64 -1/18 (*.f64 x x) (fma.f64 1/6 x (log.f64 3))))
(fma.f64 (pow.f64 x 3) 19/648 (fma.f64 (*.f64 x x) -1/18 (fma.f64 x 1/6 (log.f64 3))))
(fma.f64 x (*.f64 x -1/18) (fma.f64 (pow.f64 x 3) 19/648 (fma.f64 x 1/6 (log.f64 3))))
(fma.f64 x 1/6 (fma.f64 (*.f64 x x) (fma.f64 x 19/648 -1/18) (log.f64 3)))
(fma.f64 x 1/6 (fma.f64 x (*.f64 x (fma.f64 x 19/648 -1/18)) (log.f64 3)))
(fma.f64 x (fma.f64 x -1/18 1/6) (fma.f64 (pow.f64 x 3) 19/648 (log.f64 3)))
(*.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 (*.f64 x 1/16) -1/8)))
(*.f64 x (+.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 1/2))
(*.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 -5/128 (pow.f64 x 4) (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (+.f64 1/16 (*.f64 x -5/128))))

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite43.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
796×pow1_binary64
747×add-log-exp_binary64
747×log1p-expm1-u_binary64
747×expm1-log1p-u_binary64
734×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
11598
220378
Stop Event
1×node limit
Counts
1 → 24
Calls
Call 1
Inputs
(*.f64 x (+.f64 (*.f64 -1/8 x) 1/2))
Outputs
((#(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 x 1/2) (*.f64 x (*.f64 x -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x (*.f64 x -1/8)) 1) (*.f64 (*.f64 x 1/2) 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 (*.f64 x -1/8)) 3) (pow.f64 (*.f64 x 1/2) 3)) (+.f64 (*.f64 (*.f64 x (*.f64 x -1/8)) (*.f64 x (*.f64 x -1/8))) (-.f64 (*.f64 (*.f64 x 1/2) (*.f64 x 1/2)) (*.f64 (*.f64 x (*.f64 x -1/8)) (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x (*.f64 x -1/8)) (*.f64 x (*.f64 x -1/8))) (*.f64 (*.f64 x 1/2) (*.f64 x 1/2))) (-.f64 (*.f64 x (*.f64 x -1/8)) (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1/8 (*.f64 -1/512 (pow.f64 x 3))) x) (+.f64 (pow.f64 (*.f64 x -1/8) 2) (-.f64 1/4 (*.f64 x -1/16))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (*.f64 x -1/8) 2) -1/4) x) (fma.f64 x -1/8 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 1/8 (*.f64 -1/512 (pow.f64 x 3)))) (+.f64 (pow.f64 (*.f64 x -1/8) 2) (-.f64 1/4 (*.f64 x -1/16))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 (pow.f64 (*.f64 x -1/8) 2) -1/4)) (fma.f64 x -1/8 -1/2))))) (#(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 exp.f64 (log.f64 (*.f64 x (fma.f64 x -1/8 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 x -1/8) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x -1/8) x (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (fma.f64 x -1/8 1/2))))))))

simplify144.0ms (3.6%)

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

Useful iterations: 3 (0.0ms)

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

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiled 29 to 23 computations (20.7% saved)

series2.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

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

rewrite51.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
897×pow1_binary64
838×add-log-exp_binary64
837×log1p-expm1-u_binary64
837×expm1-log1p-u_binary64
824×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0916
119516
2236016
Stop Event
1×node limit
Counts
2 → 46
Calls
Call 1
Inputs
(*.f64 x (/.f64 1 (+.f64 (*.f64 1/2 x) 2)))
(/.f64 1 (+.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 (fma.f64 x 1/2 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x 1/2 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 x) 2) (/.f64 (fma.f64 x 1/2 2) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 x) (/.f64 (fma.f64 x 1/2 2) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) (neg.f64 (fma.f64 x 1/2 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (sqrt.f64 (fma.f64 x 1/2 2))) (sqrt.f64 (fma.f64 x 1/2 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x 1) (fma.f64 x 1/2 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 x (pow.f64 (cbrt.f64 (fma.f64 x 1/2 2)) 2)) (cbrt.f64 (fma.f64 x 1/2 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 x) (neg.f64 (fma.f64 x 1/2 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x -1) (neg.f64 (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 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 cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (/.f64 1 (fma.f64 x 1/2 2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 1 (fma.f64 x 1/2 2)) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (fma.f64 x 1/2 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1 (fma.f64 x 1/2 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (fma.f64 x 1/2 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 x 1/2 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (fma.f64 x 1/2 2))) (cbrt.f64 (pow.f64 (fma.f64 x 1/2 2) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 x 1/2 2) -2)) (/.f64 1 (cbrt.f64 (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x 1/2 2) -1/2) (pow.f64 (fma.f64 x 1/2 2) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 2)) 2) -1) (pow.f64 (cbrt.f64 (fma.f64 x 1/2 2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (fma.f64 x 1/2 2)) -1) (pow.f64 (sqrt.f64 (fma.f64 x 1/2 2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 8 (*.f64 (pow.f64 x 3) 1/8))) (+.f64 (*.f64 (*.f64 x x) 1/4) (-.f64 4 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (*.f64 (*.f64 x x) 1/4) -4)) (fma.f64 x 1/2 -2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x 1/2 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (fma.f64 x 1/2 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (fma.f64 x 1/2 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 x 1/2 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 1/2 2) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x 1/2 2) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (fma.f64 x 1/2 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (fma.f64 x 1/2 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (fma.f64 x 1/2 2))))))))

simplify49.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
624×fma-def_binary64
508×associate-/l/_binary64
444×fma-neg_binary64
383×associate-*l/_binary64
375×associate-*r/_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
057337
1160335
2403326
31107312
43264312
57952312
Stop Event
1×node limit
Counts
70 → 74
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)))))
1/2
(+.f64 (*.f64 -1/8 x) 1/2)
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 1/32 (pow.f64 x 2))))
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (+.f64 (*.f64 1/32 (pow.f64 x 2)) (*.f64 -1/128 (pow.f64 x 3)))))
(/.f64 2 x)
(-.f64 (*.f64 2 (/.f64 1 x)) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 2))) (*.f64 128 (/.f64 1 (pow.f64 x 4)))))
(/.f64 2 x)
(-.f64 (*.f64 2 (/.f64 1 x)) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 2))) (*.f64 128 (/.f64 1 (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 (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 1/32 (pow.f64 x 3) (*.f64 x (fma.f64 x -1/8 1/2)))
(*.f64 x (fma.f64 x (fma.f64 x 1/32 -1/8) 1/2))
(+.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 -1/8 (*.f64 x x) (fma.f64 1/32 (pow.f64 x 3) (fma.f64 -1/128 (pow.f64 x 4) (*.f64 1/2 x))))
(+.f64 (*.f64 -1/128 (pow.f64 x 4)) (fma.f64 1/32 (pow.f64 x 3) (*.f64 x (fma.f64 x -1/8 1/2))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (fma.f64 x -1/128 1/32)))
(*.f64 x (fma.f64 x -1/8 (fma.f64 (*.f64 x x) (fma.f64 x -1/128 1/32) 1/2)))
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 (/.f64 32 (*.f64 x x)) (+.f64 2 (/.f64 -8 x)))
(+.f64 2 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)))
(+.f64 (/.f64 32 (*.f64 x x)) (-.f64 2 (/.f64 8 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(-.f64 (+.f64 2 (/.f64 32 (*.f64 x x))) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3))))
(+.f64 2 (+.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)) (/.f64 -128 (pow.f64 x 3))))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 -8 x) (+.f64 2 (/.f64 -128 (pow.f64 x 3)))))
(+.f64 (-.f64 2 (/.f64 8 x)) (*.f64 (/.f64 1 (*.f64 x x)) (-.f64 32 (/.f64 128 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 2 (-.f64 (/.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 32 (*.f64 x x)) (-.f64 2 (/.f64 8 x)))
(-.f64 (+.f64 2 (*.f64 32 (/.f64 1 (pow.f64 x 2)))) (+.f64 (*.f64 8 (/.f64 1 x)) (*.f64 128 (/.f64 1 (pow.f64 x 3)))))
(+.f64 2 (-.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3)))))
(-.f64 (+.f64 2 (/.f64 32 (*.f64 x x))) (+.f64 (/.f64 8 x) (/.f64 128 (pow.f64 x 3))))
(+.f64 2 (+.f64 (+.f64 (/.f64 32 (*.f64 x x)) (/.f64 -8 x)) (/.f64 -128 (pow.f64 x 3))))
(+.f64 (/.f64 32 (*.f64 x x)) (+.f64 (/.f64 -8 x) (+.f64 2 (/.f64 -128 (pow.f64 x 3)))))
(+.f64 (-.f64 2 (/.f64 8 x)) (*.f64 (/.f64 1 (*.f64 x x)) (-.f64 32 (/.f64 128 x))))
1/2
(+.f64 (*.f64 -1/8 x) 1/2)
(fma.f64 -1/8 x 1/2)
(fma.f64 x -1/8 1/2)
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (*.f64 1/32 (pow.f64 x 2))))
(+.f64 (fma.f64 -1/8 x 1/2) (*.f64 (*.f64 x x) 1/32))
(fma.f64 x -1/8 (fma.f64 (*.f64 x x) 1/32 1/2))
(fma.f64 x -1/8 (fma.f64 x (*.f64 x 1/32) 1/2))
(fma.f64 x (fma.f64 x 1/32 -1/8) 1/2)
(+.f64 (*.f64 -1/8 x) (+.f64 1/2 (+.f64 (*.f64 1/32 (pow.f64 x 2)) (*.f64 -1/128 (pow.f64 x 3)))))
(+.f64 (fma.f64 -1/8 x 1/2) (fma.f64 1/32 (*.f64 x x) (*.f64 (pow.f64 x 3) -1/128)))
(+.f64 (fma.f64 x -1/8 (fma.f64 (*.f64 x x) 1/32 1/2)) (*.f64 (pow.f64 x 3) -1/128))
(fma.f64 x -1/8 (fma.f64 x (*.f64 x 1/32) (fma.f64 (pow.f64 x 3) -1/128 1/2)))
(fma.f64 x (fma.f64 x 1/32 -1/8) (fma.f64 (pow.f64 x 3) -1/128 1/2))
(fma.f64 x -1/8 (fma.f64 (*.f64 x x) (fma.f64 x -1/128 1/32) 1/2))
(/.f64 2 x)
(-.f64 (*.f64 2 (/.f64 1 x)) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 2 x) (/.f64 8 (*.f64 x x)))
(+.f64 (/.f64 2 x) (/.f64 -8 (*.f64 x x)))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -8 x) x))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (/.f64 2 x) (/.f64 8 (*.f64 x x))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 32 (pow.f64 x 3)) (/.f64 8 (*.f64 x x))))
(-.f64 (/.f64 2 x) (-.f64 (/.f64 8 (*.f64 x x)) (/.f64 32 (pow.f64 x 3))))
(+.f64 (/.f64 2 x) (*.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 32 x) -8)))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 2))) (*.f64 128 (/.f64 1 (pow.f64 x 4)))))
(+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (/.f64 2 x) (+.f64 (/.f64 8 (*.f64 x x)) (/.f64 128 (pow.f64 x 4)))))
(+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (+.f64 (/.f64 2 x) (/.f64 -8 (*.f64 x x))) (/.f64 128 (pow.f64 x 4))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (/.f64 -128 (pow.f64 x 4)) (/.f64 8 (*.f64 x x)))))
(+.f64 (-.f64 (/.f64 2 x) (-.f64 (/.f64 8 (*.f64 x x)) (/.f64 32 (pow.f64 x 3)))) (/.f64 -128 (pow.f64 x 4)))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 -8 (*.f64 x x)) (*.f64 (/.f64 1 (pow.f64 x 3)) (-.f64 (/.f64 128 x) 32))))
(/.f64 2 x)
(-.f64 (*.f64 2 (/.f64 1 x)) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(-.f64 (/.f64 2 x) (/.f64 8 (*.f64 x x)))
(+.f64 (/.f64 2 x) (/.f64 -8 (*.f64 x x)))
(+.f64 (/.f64 2 x) (/.f64 (/.f64 -8 x) x))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (*.f64 8 (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (/.f64 2 x) (/.f64 8 (*.f64 x x))))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 32 (pow.f64 x 3)) (/.f64 8 (*.f64 x x))))
(-.f64 (/.f64 2 x) (-.f64 (/.f64 8 (*.f64 x x)) (/.f64 32 (pow.f64 x 3))))
(+.f64 (/.f64 2 x) (*.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 32 x) -8)))
(-.f64 (+.f64 (*.f64 32 (/.f64 1 (pow.f64 x 3))) (*.f64 2 (/.f64 1 x))) (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 2))) (*.f64 128 (/.f64 1 (pow.f64 x 4)))))
(+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (/.f64 2 x) (+.f64 (/.f64 8 (*.f64 x x)) (/.f64 128 (pow.f64 x 4)))))
(+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (+.f64 (/.f64 2 x) (/.f64 -8 (*.f64 x x))) (/.f64 128 (pow.f64 x 4))))
(+.f64 (/.f64 2 x) (+.f64 (/.f64 32 (pow.f64 x 3)) (-.f64 (/.f64 -128 (pow.f64 x 4)) (/.f64 8 (*.f64 x x)))))
(+.f64 (-.f64 (/.f64 2 x) (-.f64 (/.f64 8 (*.f64 x x)) (/.f64 32 (pow.f64 x 3)))) (/.f64 -128 (pow.f64 x 4)))
(+.f64 (/.f64 2 x) (-.f64 (/.f64 -8 (*.f64 x x)) (*.f64 (/.f64 1 (pow.f64 x 3)) (-.f64 (/.f64 128 x) 32))))

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiled 24 to 16 computations (33.3% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite48.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
885×pow1_binary64
827×add-log-exp_binary64
827×log1p-expm1-u_binary64
827×expm1-log1p-u_binary64
812×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0810
11768
222698
Stop Event
1×node limit
Counts
1 → 41
Calls
Call 1
Inputs
(+.f64 (*.f64 (*.f64 x -1/8) x) (*.f64 1/2 x))
Outputs
((#(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 (*.f64 x -1/8)) 2) (*.f64 x (-.f64 (*.f64 x -1/8) 1/2))) (/.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 x (-.f64 (*.f64 x -1/8) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (fma.f64 x -1/8 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (fma.f64 x -1/8 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (fma.f64 x -1/8 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (fma.f64 x -1/8 1/2))) (pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x -1/8 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x -1/8 1/2))) 2) (cbrt.f64 (*.f64 x (fma.f64 x -1/8 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (fma.f64 x -1/8 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (fma.f64 x -1/8 1/2))) (sqrt.f64 (*.f64 x (fma.f64 x -1/8 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (fma.f64 x -1/8 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (*.f64 x (*.f64 x -1/8)) 3) (*.f64 (pow.f64 x 3) 1/8)) (/.f64 1 (+.f64 (pow.f64 (*.f64 x (*.f64 x -1/8)) 2) (*.f64 (*.f64 x 1/2) (-.f64 (*.f64 x 1/2) (*.f64 x (*.f64 x -1/8)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (*.f64 x (*.f64 x -1/8)) 2) (*.f64 (*.f64 x x) 1/4)) (/.f64 1 (*.f64 x (-.f64 (*.f64 x -1/8) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x -1/8 1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (*.f64 x (*.f64 x -1/8)) 2) (*.f64 (*.f64 x 1/2) (-.f64 (*.f64 x 1/2) (*.f64 x (*.f64 x -1/8))))) (+.f64 (pow.f64 (*.f64 x (*.f64 x -1/8)) 3) (*.f64 (pow.f64 x 3) 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (*.f64 x (-.f64 (*.f64 x -1/8) 1/2)) (-.f64 (pow.f64 (*.f64 x (*.f64 x -1/8)) 2) (*.f64 (*.f64 x x) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (*.f64 x -1/8)) 3) (*.f64 (pow.f64 x 3) 1/8)) (+.f64 (pow.f64 (*.f64 x (*.f64 x -1/8)) 2) (*.f64 (*.f64 x 1/2) (-.f64 (*.f64 x 1/2) (*.f64 x (*.f64 x -1/8))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (*.f64 x -1/8)) 3) (*.f64 (pow.f64 x 3) 1/8)) (+.f64 (*.f64 (*.f64 x x) 1/4) (-.f64 (pow.f64 (*.f64 x (*.f64 x -1/8)) 2) (*.f64 x (*.f64 (*.f64 x -1/8) (*.f64 x 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 x (*.f64 x -1/8)) 2) (*.f64 (*.f64 x x) 1/4)) (*.f64 x (-.f64 (*.f64 x -1/8) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 x (*.f64 x -1/8)) 3) (*.f64 (pow.f64 x 3) 1/8))) (neg.f64 (+.f64 (pow.f64 (*.f64 x (*.f64 x -1/8)) 2) (*.f64 (*.f64 x 1/2) (-.f64 (*.f64 x 1/2) (*.f64 x (*.f64 x -1/8)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 x (*.f64 x -1/8)) 2) (*.f64 (*.f64 x x) 1/4))) (neg.f64 (*.f64 x (-.f64 (*.f64 x -1/8) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) 1/4) (pow.f64 (*.f64 x (*.f64 x -1/8)) 2)) (-.f64 (*.f64 x 1/2) (*.f64 x (*.f64 x -1/8))))))) (#(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 exp.f64 (log.f64 (*.f64 x (fma.f64 x -1/8 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (*.f64 x -1/8) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/2 (*.f64 x (*.f64 x -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x -1/8) x (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 x (*.f64 x (*.f64 x -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x (*.f64 x -1/8)) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 1/2) (*.f64 x (*.f64 x -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 x -1/8))) 2) (cbrt.f64 (*.f64 x (*.f64 x -1/8))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 1/2)) 2) (cbrt.f64 (*.f64 x 1/2)) (*.f64 x (*.f64 x -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x (*.f64 x -1/8))) (sqrt.f64 (*.f64 x (*.f64 x -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 -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (fma.f64 x -1/8 1/2))))))))

simplify145.0ms (3.6%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
09117
118117
231108
36790
416790
546690
6164290
7289890
8310290
9331590
10353590
11384290
12424290
13475290
14531190
15599790
16682890
17722090
18750690
19778090
20785490
21789090
Stop Event
1×node limit
Counts
53 → 45
Calls
Call 1
Inputs
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(*.f64 -1/8 (pow.f64 x 2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(*.f64 -1/8 (pow.f64 x 2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
Outputs
(*.f64 1/2 x)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 (*.f64 x -1/8) 1/2))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 (*.f64 x -1/8) 1/2))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 (*.f64 x -1/8) 1/2))
(*.f64 x (fma.f64 x -1/8 1/2))
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (*.f64 x x))
(*.f64 x (*.f64 x -1/8))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 (*.f64 x -1/8) 1/2))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 (*.f64 x -1/8) 1/2))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 (*.f64 x -1/8) 1/2))
(*.f64 x (fma.f64 x -1/8 1/2))
(*.f64 -1/8 (pow.f64 x 2))
(*.f64 -1/8 (*.f64 x x))
(*.f64 x (*.f64 x -1/8))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 (*.f64 x -1/8) 1/2))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 (*.f64 x -1/8) 1/2))
(*.f64 x (fma.f64 x -1/8 1/2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(fma.f64 -1/8 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (+.f64 (*.f64 x -1/8) 1/2))
(*.f64 x (fma.f64 x -1/8 1/2))

localize16.0ms (0.4%)

Local error

Found 8 expressions with local error:

NewErrorProgram
2.5b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
0.2b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
0.2b
(/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.2b
(/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
✓0.2b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
✓2.5b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
Compiler

Compiled 34 to 25 computations (26.5% saved)

series7.0ms (0.2%)

Counts
3 → 12
Calls

9 calls:

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

rewrite66.0ms (1.6%)

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

Useful iterations: 1 (0.0ms)

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

simplify100.0ms (2.5%)

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

Useful iterations: 3 (0.0ms)

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

eval208.0ms (5.2%)

Compiler

Compiled 5888 to 4402 computations (25.2% saved)

prune124.0ms (3.1%)

Pruning

10 alts after pruning (4 fresh and 6 done)

PrunedKeptTotal
New4273430
Fresh011
Picked101
Done268
Total43010440
Error
0b
Counts
440 → 10
Alt Table
Click to see full alt table
StatusErrorProgram
▶60.9b
(*.f64 x (/.f64 2 x))
✓22.0b
(*.f64 x (+.f64 (*.f64 -1/8 x) 1/2))
✓20.6b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
60.9b
2
✓22.0b
(+.f64 (*.f64 (*.f64 x -1/8) x) (*.f64 1/2 x))
✓0.2b
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
▶38.8b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
▶21.9b
(/.f64 x (expm1.f64 (log1p.f64 (+.f64 1 1))))
✓21.0b
(/.f64 x 2)
Compiler

Compiled 73 to 57 computations (21.9% saved)

localize29.0ms (0.7%)

Local error

Found 2 expressions with local error:

NewErrorProgram
1.0b
(log1p.f64 (+.f64 1 1))
✓1.0b
(log1p.f64 (+.f64 1 1))
Compiler

Compiled 22 to 20 computations (9.1% saved)

series0.0ms (0%)

Counts
1 → 0

rewrite98.0ms (2.4%)

Algorithm
1×batch-egg-rewrite
Rules
544×fma-def_binary64
378×expm1-udef_binary64
378×log1p-udef_binary64
298×fma-neg_binary64
246×pow1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
053
1743
26603
362413
Stop Event
1×node limit
Counts
1 → 47
Calls
Call 1
Inputs
(log1p.f64 (+.f64 1 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (log.f64 3)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log.f64 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log.f64 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log.f64 3)) (pow.f64 (cbrt.f64 (log.f64 3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log.f64 3)) 2) (cbrt.f64 (log.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log.f64 3)) (sqrt.f64 (log.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (log.f64 3) 1/6) (*.f64 (pow.f64 (log.f64 3) 1/6) (pow.f64 (cbrt.f64 (log.f64 3)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (log.f64 3))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (log.f64 3))) (pow.f64 (cbrt.f64 (log.f64 3)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (log.f64 3)) 4)) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (log.f64 3))) 2) (cbrt.f64 (log.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (log.f64 3) 1/4) (sqrt.f64 (pow.f64 (log.f64 3) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (log.f64 3) 1/4) (*.f64 (pow.f64 (log.f64 3) 1/4) (sqrt.f64 (log.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (log.f64 3)) (pow.f64 (log.f64 3) 1/4)) (pow.f64 (log.f64 3) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (log.f64 3)) 4) 2)) (cbrt.f64 (cbrt.f64 (log.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (log.f64 3) 5/2)) (pow.f64 (log.f64 3) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (log.f64 3)) 5)) (pow.f64 (log.f64 3) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (log.f64 3) 3/2)) (pow.f64 (log.f64 3) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (log.f64 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (log.f64 3)) 4) 2) 1/3) (cbrt.f64 (cbrt.f64 (log.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (log.f64 3) 5/2) 1/3) (pow.f64 (log.f64 3) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (log.f64 3)) (cbrt.f64 (log.f64 3))) (pow.f64 (log.f64 3) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (log.f64 3)) (cbrt.f64 (pow.f64 (cbrt.f64 (log.f64 3)) 4))) (pow.f64 (cbrt.f64 (cbrt.f64 (log.f64 3))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (log.f64 3)) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (log.f64 3))) 2)) (cbrt.f64 (cbrt.f64 (log.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (log.f64 3)) 2) (pow.f64 (log.f64 3) 1/6)) (pow.f64 (log.f64 3) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1 (log.f64 3)) 3) 1) (fma.f64 (+.f64 1 (log.f64 3)) (+.f64 1 (log.f64 3)) (+.f64 1 (+.f64 1 (log.f64 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (+.f64 1 (log.f64 3)) (+.f64 1 (log.f64 3)) -1) (+.f64 (+.f64 1 (log.f64 3)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (log.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log.f64 3) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log.f64 3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log.f64 3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log.f64 3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (log.f64 3)))) (sqrt.f64 (log.f64 (log.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (log.f64 3))) 2)) (cbrt.f64 (log.f64 (log.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log.f64 3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (log.f64 3))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 3)))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log.f64 3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (log.f64 3))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (log.f64 3))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (log.f64 3))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (log.f64 3)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (log.f64 3)) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (+.f64 1 (log.f64 3))) (cbrt.f64 (+.f64 1 (log.f64 3)))) (cbrt.f64 (+.f64 1 (log.f64 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 (log.f64 3))) (sqrt.f64 (+.f64 1 (log.f64 3))) -1)))))

simplify6.0ms (0.2%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
47 → 47
Calls
Call 1
Inputs
Outputs

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
2.5b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
0.0b
(sqrt.f64 (+.f64 x 1))
0.0b
(sqrt.f64 (+.f64 x 1))
2.5b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
Compiler

Compiled 16 to 12 computations (25% saved)

rewrite0.0ms (0%)

Counts
0 → 0

simplify7.0ms (0.2%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

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

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.1b
(*.f64 x (/.f64 2 x))
✓0.1b
(*.f64 x (/.f64 2 x))
Compiler

Compiled 11 to 7 computations (36.4% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite43.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
528×pow1_binary64
514×add-sqr-sqrt_binary64
492×add-log-exp_binary64
492×log1p-expm1-u_binary64
492×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11097
213397
Stop Event
1×node limit
Counts
1 → 20
Calls
Call 1
Inputs
(*.f64 x (/.f64 2 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (/.f64 2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (/.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 x (*.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 x 2)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 x 2) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 x 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 x 2) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -2 x) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x -2) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (/.f64 2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (/.f64 2 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (/.f64 2 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (/.f64 2 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (/.f64 2 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (/.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (/.f64 2 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (/.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (/.f64 2 x))))))))

simplify7.0ms (0.2%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0112
Stop Event
1×saturated
Counts
32 → 21
Calls
Call 1
Inputs
2
2
2
2
2
2
2
2
2
2
2
2
Outputs
2
2
2
2
2
2
2
2
2
2
2
2

eval76.0ms (1.9%)

Compiler

Compiled 1889 to 1529 computations (19.1% saved)

prune28.0ms (0.7%)

Pruning

10 alts after pruning (1 fresh and 9 done)

PrunedKeptTotal
New1670167
Fresh011
Picked011
Done088
Total16710177
Error
0b
Counts
177 → 10
Alt Table
Click to see full alt table
StatusErrorProgram
✓60.9b
(*.f64 x (/.f64 2 x))
✓22.0b
(*.f64 x (+.f64 (*.f64 -1/8 x) 1/2))
✓20.6b
(/.f64 x (+.f64 (*.f64 1/2 x) 2))
✓0.2b
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
60.9b
2
✓22.0b
(+.f64 (*.f64 (*.f64 x -1/8) x) (*.f64 1/2 x))
✓0.2b
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
✓38.8b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
✓21.9b
(/.f64 x (expm1.f64 (log1p.f64 (+.f64 1 1))))
✓21.0b
(/.f64 x 2)
Compiler

Compiled 73 to 57 computations (21.9% saved)

regimes23.0ms (0.6%)

Counts
15 → 1
Calls
Call 1
Inputs
2
(/.f64 x 2)
(*.f64 x (/.f64 2 x))
(*.f64 x (+.f64 (*.f64 -1/8 x) 1/2))
(/.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) 2)))
(-.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 (*.f64 -1/8 (pow.f64 x 2)) (*.f64 1/2 x))
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
(/.f64 x (expm1.f64 (log1p.f64 (+.f64 1 1))))
(/.f64 x (expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
Outputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
Calls

2 calls:

11.0ms
(/.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))))
Compiler

Compiled 119 to 89 computations (25.2% saved)

regimes16.0ms (0.4%)

Counts
9 → 2
Calls
Call 1
Inputs
2
(/.f64 x 2)
(*.f64 x (/.f64 2 x))
(*.f64 x (+.f64 (*.f64 -1/8 x) 1/2))
(/.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) 2)))
(-.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
0.1b2x
Compiler

Compiled 56 to 40 computations (28.6% saved)

bsearch28.0ms (0.7%)

Algorithm
1×binary-search
Steps
TimeLeftRight
28.0ms
1.654963891712827e-8
0.004028897698743788
Compiler

Compiled 13 to 10 computations (23.1% saved)

regimes7.0ms (0.2%)

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

1 calls:

5.0ms
x
Results
ErrorSegmentsBranch
20.6b1x
Compiler

Compiled 44 to 31 computations (29.5% saved)

regimes5.0ms (0.1%)

Accuracy

Total -41.2b remaining (-196%)

Threshold costs -41.2b (-196%)

Counts
4 → 1
Calls
Call 1
Inputs
2
(/.f64 x 2)
(*.f64 x (/.f64 2 x))
(*.f64 x (+.f64 (*.f64 -1/8 x) 1/2))
Outputs
(/.f64 x 2)
Calls

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
21.0b1x
Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02255
13455
23555
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(if (<=.f64 x 625227681006733/37778931862957161709568) (+.f64 (*.f64 (*.f64 x -1/8) x) (*.f64 1/2 x)) (-.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 625227681006733/37778931862957161709568) (+.f64 (*.f64 (*.f64 x -1/8) x) (*.f64 1/2 x)) (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
(if (<=.f64 x 625227681006733/37778931862957161709568) (+.f64 (*.f64 x (*.f64 x -1/8)) (*.f64 x 1/2)) (+.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

end39.0ms (1%)

Stop Event
1×fuel
Compiler

Compiled 82 to 62 computations (24.4% saved)

Profiling

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