Details

Time bar (total: 1.6s)

analyze3.0ms (0.2%)

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

Compiled 10 to 8 computations (20% saved)

sample733.0ms (47.2%)

Results
719.0ms8253×body128valid
1.0ms3×body2048valid
Compiler

Compiled 20 to 16 computations (20% saved)

preprocess13.0ms (0.8%)

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

Useful iterations: 0 (0.0ms)

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

Compiled 9 to 7 computations (22.2% saved)

simplify8.0ms (0.5%)

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))))

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series10.0ms (0.6%)

Counts
3 → 12
Calls

9 calls:

TimeVariablePointExpression
4.0ms
x
@inf
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
2.0ms
x
@-inf
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
1.0ms
x
@0
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
1.0ms
x
@inf
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
1.0ms
x
@-inf
(+.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite50.0ms (3.2%)

Algorithm
1×batch-egg-rewrite
Rules
804×log1p-expm1-u_binary64
804×expm1-log1p-u_binary64
81×add-sqr-sqrt_binary64
78×*-un-lft-identity_binary64
78×pow1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0727
115727
2225827
Stop Event
1×node limit
Counts
3 → 93
Calls
Call 1
Inputs
(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
(sqrt.f64 (+.f64 x 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (+.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (/.f64 x (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))) (/.f64 x (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))) (/.f64 (cbrt.f64 x) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (neg.f64 x)) (-.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (+.f64 (neg.f64 (sqrt.f64 (+.f64 x 1))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))) (/.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 x 1))) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 (+.f64 x 1) (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 x) (-.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2))) (neg.f64 (-.f64 (+.f64 1 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 x)) (neg.f64 (-.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 x 1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (fma.f64 x x -1)) (sqrt.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/2 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 1))))))

simplify28.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
591×fma-def_binary64
363×distribute-rgt-neg-in_binary64
306×distribute-lft-neg-in_binary64
251×distribute-lft-out--_binary64
235×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
031158
191142
2232130
3810109
42935109
Stop Event
1×node limit
Counts
105 → 114
Calls
Call 1
Inputs
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (+.f64 (*.f64 5/128 (pow.f64 x 4)) (*.f64 1/8 (pow.f64 x 2))))
2
(+.f64 2 (*.f64 1/2 x))
(-.f64 (+.f64 2 (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 2 (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3)))) (*.f64 1/8 (pow.f64 x 2)))
1
(+.f64 1 (*.f64 1/2 x))
(-.f64 (+.f64 1 (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3)))) (*.f64 1/8 (pow.f64 x 2)))
Outputs
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (*.f64 x x)))
(fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8))
(*.f64 x (-.f64 1/2 (*.f64 x 1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (*.f64 -1/8 (*.f64 x x)))
(fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8)))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (-.f64 (*.f64 x 1/16) 1/8)))
(*.f64 x (+.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 1/2))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (+.f64 (*.f64 5/128 (pow.f64 x 4)) (*.f64 1/8 (pow.f64 x 2))))
(-.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (fma.f64 5/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x))))
(-.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (fma.f64 1/8 (*.f64 x x) (*.f64 5/128 (pow.f64 x 4))))
(fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x (fma.f64 (*.f64 x x) -1/8 (*.f64 (pow.f64 x 4) -5/128))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (-.f64 1/16 (*.f64 x 5/128))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (+.f64 (*.f64 x -5/128) 1/16)))
2
(+.f64 2 (*.f64 1/2 x))
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 2)
(-.f64 (+.f64 2 (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 2 (-.f64 (*.f64 1/2 x) (*.f64 1/8 (*.f64 x x))))
(+.f64 2 (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8)))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/2 x 2))
(fma.f64 x (fma.f64 x -1/8 1/2) 2)
(-.f64 (+.f64 2 (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3)))) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 2 (+.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (*.f64 -1/8 (*.f64 x x))))
(+.f64 2 (fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8))))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 2)))
(fma.f64 1/2 x (fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) 2))
(fma.f64 1/16 (pow.f64 x 3) (fma.f64 x (fma.f64 x -1/8 1/2) 2))
1
(+.f64 1 (*.f64 1/2 x))
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(-.f64 (+.f64 1 (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 1 (-.f64 (*.f64 1/2 x) (*.f64 1/8 (*.f64 x x))))
(+.f64 1 (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8)))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/2 x 1))
(fma.f64 x (fma.f64 x -1/8 1/2) 1)
(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3)))) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 1 (+.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (*.f64 -1/8 (*.f64 x x))))
(+.f64 1 (fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8))))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x 1)))
(fma.f64 1/2 x (fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) 1))
(fma.f64 1/16 (pow.f64 x 3) (fma.f64 x (fma.f64 x -1/8 1/2) 1))

prune73.0ms (4.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1113114
Fresh000
Picked101
Done000
Total1123115
Error
0b
Counts
115 → 3
Alt Table
StatusErrorProgram
▶1.6b
(/.f64 x (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))
38.3b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
22.4b
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
Compiler

Compiled 1524 to 1194 computations (21.7% saved)

localize8.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(log1p.f64 (sqrt.f64 (+.f64 x 1)))
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.1b
(/.f64 x (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))
✓1.6b
(exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))

series24.0ms (1.6%)

Counts
3 → 12
Calls

9 calls:

TimeVariablePointExpression
11.0ms
x
@inf
(/.f64 x (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))
4.0ms
x
@-inf
(/.f64 x (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))
4.0ms
x
@inf
(exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))
2.0ms
x
@inf
(log1p.f64 (sqrt.f64 (+.f64 x 1)))
1.0ms
x
@-inf
(log1p.f64 (sqrt.f64 (+.f64 x 1)))

rewrite49.0ms (3.1%)

Algorithm
1×batch-egg-rewrite
Rules
809×pow1_binary64
752×expm1-log1p-u_binary64
751×log1p-expm1-u_binary64
81×add-sqr-sqrt_binary64
78×*-un-lft-identity_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0831
116329
2207929
Stop Event
1×node limit
Counts
3 → 75
Calls
Call 1
Inputs
(exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))
(/.f64 x (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))
(log1p.f64 (sqrt.f64 (+.f64 x 1)))
Outputs
((#(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 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 (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 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (+.f64 1 (-.f64 (+.f64 x 1) (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (+.f64 x 1)) (-.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log1p.f64 (sqrt.f64 (+.f64 x 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 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 2)) (cbrt.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 2) (cbrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (+.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 (/.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 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 (cbrt.f64 x) (sqrt.f64 (+.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 log.f64 (+.f64 1 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log.f64 x) (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (log.f64 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)) (log.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) (pow.f64 (cbrt.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 2) (cbrt.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 1))))))

simplify28.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
700×fma-def_binary64
387×distribute-rgt-neg-in_binary64
326×distribute-lft-neg-in_binary64
281×associate-*l*_binary64
263×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
038166
1107152
2287138
31021119
43566119
Stop Event
1×node limit
Counts
87 → 96
Calls
Call 1
Inputs
2
(+.f64 2 (*.f64 1/2 x))
(-.f64 (+.f64 2 (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 2 (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3)))) (*.f64 1/8 (pow.f64 x 2)))
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (+.f64 (*.f64 5/128 (pow.f64 x 4)) (*.f64 1/8 (pow.f64 x 2))))
(log.f64 2)
(+.f64 (log.f64 2) (*.f64 1/4 x))
(-.f64 (+.f64 (log.f64 2) (*.f64 1/4 x)) (*.f64 3/32 (pow.f64 x 2)))
(-.f64 (+.f64 (log.f64 2) (+.f64 (*.f64 1/4 x) (*.f64 5/96 (pow.f64 x 3)))) (*.f64 3/32 (pow.f64 x 2)))
Outputs
2
(+.f64 2 (*.f64 1/2 x))
(fma.f64 1/2 x 2)
(-.f64 (+.f64 2 (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 2 (+.f64 (*.f64 1/2 x) (*.f64 -1/8 (*.f64 x x))))
(+.f64 2 (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8)))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/2 x 2))
(fma.f64 x (fma.f64 x -1/8 1/2) 2)
(-.f64 (+.f64 2 (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3)))) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 2 (+.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (*.f64 -1/8 (*.f64 x x))))
(+.f64 2 (fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8))))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x 2)))
(fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) (fma.f64 1/2 x 2))
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 (*.f64 1/2 x) (*.f64 -1/8 (*.f64 x x)))
(fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8))
(*.f64 x (+.f64 1/2 (*.f64 x -1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (*.f64 -1/8 (*.f64 x x)))
(fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8)))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (-.f64 (*.f64 x 1/16) 1/8)))
(*.f64 x (+.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 1/2))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (+.f64 (*.f64 5/128 (pow.f64 x 4)) (*.f64 1/8 (pow.f64 x 2))))
(-.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (fma.f64 5/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x))))
(-.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (fma.f64 1/8 (*.f64 x x) (*.f64 5/128 (pow.f64 x 4))))
(fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) (fma.f64 (*.f64 x x) -1/8 (*.f64 (pow.f64 x 4) -5/128))))
(fma.f64 (pow.f64 x 4) -5/128 (*.f64 x (+.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 1/2)))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (+.f64 1/16 (*.f64 x -5/128))))
(log.f64 2)
(+.f64 (log.f64 2) (*.f64 1/4 x))
(+.f64 (log.f64 2) (*.f64 x 1/4))
(fma.f64 x 1/4 (log.f64 2))
(-.f64 (+.f64 (log.f64 2) (*.f64 1/4 x)) (*.f64 3/32 (pow.f64 x 2)))
(+.f64 (log.f64 2) (-.f64 (*.f64 x 1/4) (*.f64 (*.f64 x x) 3/32)))
(+.f64 (log.f64 2) (fma.f64 x 1/4 (*.f64 (*.f64 x x) -3/32)))
(fma.f64 (*.f64 x x) -3/32 (fma.f64 x 1/4 (log.f64 2)))
(fma.f64 x (+.f64 1/4 (*.f64 x -3/32)) (log.f64 2))
(-.f64 (+.f64 (log.f64 2) (+.f64 (*.f64 1/4 x) (*.f64 5/96 (pow.f64 x 3)))) (*.f64 3/32 (pow.f64 x 2)))
(+.f64 (log.f64 2) (-.f64 (fma.f64 1/4 x (*.f64 (pow.f64 x 3) 5/96)) (*.f64 (*.f64 x x) 3/32)))
(+.f64 (fma.f64 x 1/4 (*.f64 (pow.f64 x 3) 5/96)) (+.f64 (log.f64 2) (*.f64 (*.f64 x x) -3/32)))
(fma.f64 (*.f64 x x) -3/32 (fma.f64 x 1/4 (fma.f64 (pow.f64 x 3) 5/96 (log.f64 2))))
(fma.f64 x 1/4 (fma.f64 x (*.f64 x (fma.f64 x 5/96 -3/32)) (log.f64 2)))

prune73.0ms (4.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1290129
Fresh022
Picked011
Done000
Total1293132
Error
0b
Counts
132 → 3
Alt Table
StatusErrorProgram
✓1.6b
(/.f64 x (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))
38.3b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
▶22.4b
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
Compiler

Compiled 1666 to 1318 computations (20.9% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
✓0.2b
(*.f64 1/8 (pow.f64 x 2))

series5.0ms (0.3%)

Counts
2 → 3
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@0
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
1.0ms
x
@-inf
(*.f64 1/8 (pow.f64 x 2))
1.0ms
x
@0
(*.f64 1/8 (pow.f64 x 2))
1.0ms
x
@inf
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
1.0ms
x
@inf
(*.f64 1/8 (pow.f64 x 2))

rewrite44.0ms (2.9%)

Algorithm
1×batch-egg-rewrite
Rules
878×log1p-expm1-u_binary64
878×expm1-log1p-u_binary64
97×add-sqr-sqrt_binary64
93×add-log-exp_binary64
92×add-cbrt-cube_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0920
120518
2245118
Stop Event
1×node limit
Counts
2 → 63
Calls
Call 1
Inputs
(*.f64 1/8 (pow.f64 x 2))
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 1/8 (*.f64 x x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/8 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 1/8)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 x x) 3) 1/512) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 4) 1/64))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 1/8 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 x x) 3) 1/512))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/8 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/8 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/8 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 1/8 (*.f64 x x))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x 1/2) (*.f64 (*.f64 x x) -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x 1/2) (*.f64 (*.f64 (*.f64 x x) -1/8) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x 1/2) (+.f64 (*.f64 (*.f64 x x) -1/8) (+.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 1/8 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)) (+.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 1/8 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)) (fma.f64 -1/8 (*.f64 x x) (*.f64 1/8 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)) (fma.f64 (*.f64 (*.f64 x x) -1/8) 1 (*.f64 1/8 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)) (fma.f64 (neg.f64 (*.f64 1/2 (pow.f64 (cbrt.f64 x) 2))) (cbrt.f64 (*.f64 (pow.f64 x 4) 1/64)) (*.f64 1/8 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)) (fma.f64 (neg.f64 (*.f64 x (sqrt.f64 1/8))) (*.f64 x (sqrt.f64 1/8)) (*.f64 1/8 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)) (*.f64 (+.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 1/8 (*.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)) (+.f64 (+.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 1/8 (*.f64 x x))) (+.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 1/8 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 1/8 (*.f64 x x))) (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8))) (pow.f64 (cbrt.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8))) 2) (cbrt.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8))) (sqrt.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 1/8 (pow.f64 x 3)) (*.f64 (pow.f64 (*.f64 x x) 3) 1/512)) (/.f64 1 (+.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (*.f64 1/8 (*.f64 x x)) (fma.f64 x 1/2 (*.f64 1/8 (*.f64 x x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (pow.f64 x 4) 1/64)) (/.f64 1 (fma.f64 x 1/2 (*.f64 1/8 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (*.f64 x 1/2)) (*.f64 x (sqrt.f64 1/8))) (-.f64 (sqrt.f64 (*.f64 x 1/2)) (*.f64 x (sqrt.f64 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (*.f64 1/8 (*.f64 x x)) (fma.f64 x 1/2 (*.f64 1/8 (*.f64 x x))))) (-.f64 (*.f64 1/8 (pow.f64 x 3)) (*.f64 (pow.f64 (*.f64 x x) 3) 1/512))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x 1/2 (*.f64 1/8 (*.f64 x x))) (-.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (pow.f64 x 4) 1/64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 1/8 (pow.f64 x 3)) (*.f64 (pow.f64 (*.f64 x x) 3) 1/512)) (+.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (*.f64 1/8 (*.f64 x x)) (fma.f64 x 1/2 (*.f64 1/8 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (pow.f64 x 4) 1/64)) (fma.f64 x 1/2 (*.f64 1/8 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 1/8 (pow.f64 x 3)) (*.f64 (pow.f64 (*.f64 x x) 3) 1/512))) (neg.f64 (+.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (*.f64 1/8 (*.f64 x x)) (fma.f64 x 1/2 (*.f64 1/8 (*.f64 x x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (pow.f64 x 4) 1/64))) (neg.f64 (fma.f64 x 1/2 (*.f64 1/8 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 1/8 (pow.f64 x 3)) (pow.f64 (*.f64 (*.f64 x x) -1/8) 3)) (+.f64 (*.f64 (*.f64 x x) 1/4) (-.f64 (*.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 (*.f64 x x) -1/8)) (*.f64 (*.f64 x 1/2) (*.f64 (*.f64 x x) -1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)) 3) (pow.f64 (+.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 1/8 (*.f64 x x))) 3)) (+.f64 (pow.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)) 2) (-.f64 (*.f64 (+.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 1/8 (*.f64 x x))) (+.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 1/8 (*.f64 x x)))) (*.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)) (+.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 1/8 (*.f64 x x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 (*.f64 x x) -1/8))) (-.f64 (*.f64 x 1/2) (*.f64 (*.f64 x x) -1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)) 2) (*.f64 (+.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 1/8 (*.f64 x x))) (+.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 1/8 (*.f64 x x))))) (-.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)) (+.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 1/8 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 1/2) (*.f64 (*.f64 x x) -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8)) (+.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 1/8 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (*.f64 x x) 1/4)) (cbrt.f64 (*.f64 x 1/2)) (*.f64 (*.f64 x x) -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8))) 2) (cbrt.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8))) (+.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 1/8 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/2)) (sqrt.f64 (*.f64 x 1/2)) (*.f64 (*.f64 x x) -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8))) (sqrt.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8))) (+.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 1/8 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x 1/2 (*.f64 (*.f64 x x) -1/8))) 1))))))

simplify57.0ms (3.7%)

Algorithm
1×egg-herbie
Rules
625×sqr-pow_binary64
511×associate-*l*_binary64
434×unswap-sqr_binary64
285×cube-prod_binary64
278×fabs-mul_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0818
11518
22518
35118
412218
535818
6137018
7225718
8242118
9263418
10285418
11315418
12355418
13404018
14459918
Stop Event
1×node limit
Counts
66 → 66
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))

prune39.0ms (2.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New66066
Fresh011
Picked011
Done011
Total66369
Error
0b
Counts
69 → 3
Alt Table
StatusErrorProgram
✓1.6b
(/.f64 x (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))
▶38.3b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
✓22.4b
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
Compiler

Compiled 1242 to 750 computations (39.6% saved)

localize8.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.1b
(/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
✓0.1b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
✓4.5b
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)

series8.0ms (0.5%)

Counts
3 → 12
Calls

9 calls:

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

rewrite56.0ms (3.6%)

Algorithm
1×batch-egg-rewrite
Rules
870×log1p-expm1-u_binary64
870×expm1-log1p-u_binary64
97×add-sqr-sqrt_binary64
93×*-un-lft-identity_binary64
93×pow1_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0830
118725
2279725
Stop Event
1×node limit
Counts
3 → 149
Calls
Call 1
Inputs
(-.f64 (sqrt.f64 (+.f64 x 1)) 1)
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
(/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1))
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (expm1.f64 (*.f64 1/2 (log1p.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2)) (/.f64 x (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2)) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x)))) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))) (/.f64 x (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))) (/.f64 (cbrt.f64 x) (sqrt.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 (pow.f64 (+.f64 x 1) 3/2) -1)) (+.f64 x (+.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 x 3) (pow.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))) 1))))))

simplify28.0ms (1.8%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
026175
176161
2196149
3685125
42574125
Stop Event
1×node limit
Counts
161 → 119
Calls
Call 1
Inputs
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (+.f64 (*.f64 5/128 (pow.f64 x 4)) (*.f64 1/8 (pow.f64 x 2))))
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (+.f64 (*.f64 5/128 (pow.f64 x 4)) (*.f64 1/8 (pow.f64 x 2))))
2
(+.f64 2 (*.f64 1/2 x))
(-.f64 (+.f64 2 (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 2 (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3)))) (*.f64 1/8 (pow.f64 x 2)))
Outputs
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (*.f64 x x)))
(fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8))
(*.f64 x (-.f64 1/2 (*.f64 x 1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (*.f64 -1/8 (*.f64 x x)))
(fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8)))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (-.f64 (*.f64 x 1/16) 1/8)))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
(*.f64 x (+.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 1/2))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (+.f64 (*.f64 5/128 (pow.f64 x 4)) (*.f64 1/8 (pow.f64 x 2))))
(-.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (fma.f64 5/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x))))
(-.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (fma.f64 1/8 (*.f64 x x) (*.f64 5/128 (pow.f64 x 4))))
(fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) (fma.f64 (*.f64 x x) -1/8 (*.f64 (pow.f64 x 4) -5/128))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (-.f64 1/16 (*.f64 x 5/128))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (+.f64 1/16 (*.f64 x -5/128))))
(*.f64 1/2 x)
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (*.f64 x x)))
(fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8))
(*.f64 x (-.f64 1/2 (*.f64 x 1/8)))
(*.f64 x (fma.f64 x -1/8 1/2))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (*.f64 -1/8 (*.f64 x x)))
(fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8)))
(fma.f64 1/2 x (*.f64 (*.f64 x x) (-.f64 (*.f64 x 1/16) 1/8)))
(*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))))
(*.f64 x (+.f64 (*.f64 x (fma.f64 x 1/16 -1/8)) 1/2))
(-.f64 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (*.f64 1/2 x)) (+.f64 (*.f64 5/128 (pow.f64 x 4)) (*.f64 1/8 (pow.f64 x 2))))
(-.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (fma.f64 5/128 (pow.f64 x 4) (*.f64 1/8 (*.f64 x x))))
(-.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (fma.f64 1/8 (*.f64 x x) (*.f64 5/128 (pow.f64 x 4))))
(fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) (fma.f64 (*.f64 x x) -1/8 (*.f64 (pow.f64 x 4) -5/128))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (-.f64 1/16 (*.f64 x 5/128))))
(fma.f64 x (fma.f64 x -1/8 1/2) (*.f64 (pow.f64 x 3) (+.f64 1/16 (*.f64 x -5/128))))
2
(+.f64 2 (*.f64 1/2 x))
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 2)
(-.f64 (+.f64 2 (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 2 (-.f64 (*.f64 1/2 x) (*.f64 1/8 (*.f64 x x))))
(+.f64 2 (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8)))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/2 x 2))
(fma.f64 x (fma.f64 x -1/8 1/2) 2)
(-.f64 (+.f64 2 (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3)))) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 2 (+.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (*.f64 -1/8 (*.f64 x x))))
(+.f64 2 (fma.f64 1/16 (pow.f64 x 3) (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8))))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 2)))
(fma.f64 1/16 (pow.f64 x 3) (fma.f64 x (fma.f64 x -1/8 1/2) 2))
(fma.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)) (fma.f64 1/2 x 2))

prune71.0ms (4.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1520152
Fresh000
Picked011
Done022
Total1523155
Error
0b
Counts
155 → 3
Alt Table
StatusErrorProgram
✓1.6b
(/.f64 x (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))))
✓38.3b
(/.f64 x (/.f64 x (-.f64 (sqrt.f64 (+.f64 x 1)) 1)))
✓22.4b
(-.f64 (*.f64 1/2 x) (*.f64 1/8 (pow.f64 x 2)))
Compiler

Compiled 2282 to 1624 computations (28.8% saved)

regimes74.0ms (4.8%)

Accuracy

Total 0.2b remaining (96.1%)

Threshold costs 0.2b (96.1%)

Counts
39 → 1
Compiler

Compiled 392 to 292 computations (25.5% saved)

simplify2.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0713
11013
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 x (fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1))
Outputs
(/.f64 x (fma.f64 1 (sqrt.f64 (+.f64 x 1)) 1))

end51.0ms (3.3%)

Stop Event
1×done
Compiler

Compiled 50 to 39 computations (22% saved)

Profiling

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