Details

Time bar (total: 3.6s)

analyze1.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%0%50%2
Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.6s (46%)

Results
802.0ms2299×body1024valid
459.0ms4447×body128valid
282.0ms1024×body512valid
88.0ms486×body256valid
Compiler

Compiled 26 to 22 computations (15.4% saved)

preprocess19.0ms (0.5%)

Algorithm
2×egg-herbie
Rules
39×fma-def_binary64
32×fma-neg_binary64
15×cancel-sign-sub-inv_binary64
12×sub-neg_binary64
10×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0917
11417
22017
32817
43817
55617
69317
712717
817417
921017
1023617
1123817
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Outputs
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))
Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify9.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
39×fma-def_binary64
32×fma-neg_binary64
15×cancel-sign-sub-inv_binary64
12×sub-neg_binary64
10×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0917
11417
22017
32817
43817
55617
69317
712717
817417
921017
1023617
1123817
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Outputs
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 -1 (sqrt.f64 (+.f64 1 x))))

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
20.7b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶20.7b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
Compiler

Compiled 47 to 38 computations (19.1% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (+.f64 x 1))
✓0.1b
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
✓0.3b
(/.f64 1 (sqrt.f64 x))
✓2.4b
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

series12.0ms (0.3%)

Counts
4 → 8
Calls

12 calls:

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

rewrite60.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
776×prod-diff_binary64
170×log1p-udef_binary64
169×expm1-udef_binary64
106×add-sqr-sqrt_binary64
102×*-un-lft-identity_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0938
120730
2296530
Stop Event
1×node limit
Counts
4 → 173
Calls
Call 1
Inputs
(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
(/.f64 1 (sqrt.f64 x))
(/.f64 1 (sqrt.f64 (+.f64 x 1)))
(sqrt.f64 (+.f64 x 1))
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 1 x) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2)) (cbrt.f64 (/.f64 1 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 (+.f64 1 x))) (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -1) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 x) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 1 x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (*.f64 1/2 (log1p.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (*.f64 1/2 (log1p.f64 x))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x)))) 1)))) (#(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 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (pow.f64 (+.f64 1 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (+.f64 1 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 /.f64 (sqrt.f64 (fma.f64 x x -1)) (sqrt.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))))))) (#(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))))))

simplify23.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
914×fma-neg_binary64
744×cancel-sign-sub-inv_binary64
439×fma-def_binary64
222×distribute-rgt-neg-in_binary64
202×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02794
18086
222076
375764
4243164
Stop Event
1×node limit
Counts
181 → 186
Calls
Call 1
Inputs
1
(-.f64 1 (*.f64 1/2 x))
(-.f64 (+.f64 1 (*.f64 3/8 (pow.f64 x 2))) (*.f64 1/2 x))
(-.f64 (+.f64 1 (*.f64 3/8 (pow.f64 x 2))) (+.f64 (*.f64 1/2 x) (*.f64 5/16 (pow.f64 x 3))))
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
1
(-.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 -1/2 x))
(+.f64 1 (*.f64 x -1/2))
(fma.f64 x -1/2 1)
(-.f64 (+.f64 1 (*.f64 3/8 (pow.f64 x 2))) (*.f64 1/2 x))
(+.f64 1 (-.f64 (*.f64 3/8 (*.f64 x x)) (*.f64 1/2 x)))
(+.f64 1 (fma.f64 3/8 (*.f64 x x) (*.f64 x -1/2)))
(fma.f64 x -1/2 (fma.f64 x (*.f64 x 3/8) 1))
(fma.f64 x (fma.f64 x 3/8 -1/2) 1)
(-.f64 (+.f64 1 (*.f64 3/8 (pow.f64 x 2))) (+.f64 (*.f64 1/2 x) (*.f64 5/16 (pow.f64 x 3))))
(+.f64 1 (-.f64 (*.f64 3/8 (*.f64 x x)) (fma.f64 1/2 x (*.f64 5/16 (pow.f64 x 3)))))
(-.f64 (fma.f64 3/8 (*.f64 x x) 1) (fma.f64 1/2 x (*.f64 5/16 (pow.f64 x 3))))
(+.f64 1 (fma.f64 x (*.f64 x 3/8) (fma.f64 x -1/2 (*.f64 (pow.f64 x 3) -5/16))))
(fma.f64 (pow.f64 x 3) -5/16 (fma.f64 x (fma.f64 x 3/8 -1/2) 1))
1
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(-.f64 (+.f64 1 (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 (+.f64 1 (*.f64 1/2 x)) (*.f64 -1/8 (*.f64 x x)))
(-.f64 (fma.f64 1/2 x 1) (*.f64 x (*.f64 x 1/8)))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/2 x 1))
(fma.f64 x (-.f64 1/2 (*.f64 x 1/8)) 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 (pow.f64 x 3) 1/16)) (*.f64 (*.f64 x x) 1/8)))
(+.f64 (fma.f64 1/2 x (*.f64 (pow.f64 x 3) 1/16)) (-.f64 1 (*.f64 x (*.f64 x 1/8))))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 (pow.f64 x 3) 1/16 (fma.f64 1/2 x 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)) 1))

prune215.0ms (6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New17016186
Fresh000
Picked101
Done000
Total17116187
Error
20.1b
Counts
187 → 16
Alt Table
StatusErrorProgram
25.3b
(/.f64 (-.f64 (/.f64 1 x) (*.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))) (-.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 1 x) -1/2))))
31.1b
(+.f64 (fma.f64 (pow.f64 (pow.f64 x 1/4) -1) (pow.f64 (pow.f64 x 1/4) -1) (neg.f64 (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1))))
32.0b
(/.f64 (+.f64 (pow.f64 (sqrt.f64 x) -3) (pow.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) 3)) (+.f64 (/.f64 1 x) (-.f64 (*.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2))) (*.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 1 x) -1/2))))))
31.0b
(+.f64 (fma.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 x))) (neg.f64 (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1))))
31.3b
(fma.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (pow.f64 x -1/2)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
31.1b
(+.f64 (fma.f64 (pow.f64 (pow.f64 x 1/4) -1) (pow.f64 (pow.f64 x 1/4) -1) (neg.f64 (pow.f64 (+.f64 1 x) -1/2))) (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 (+.f64 1 x) -1/2)))
30.7b
(+.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2))) (cbrt.f64 (/.f64 1 (+.f64 1 x))) (pow.f64 (+.f64 1 x) -1/2)))
▶21.1b
(pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) 3)
29.9b
(+.f64 (fma.f64 (pow.f64 (cbrt.f64 x) -1) (pow.f64 (cbrt.f64 (sqrt.f64 x)) -1) (neg.f64 (pow.f64 (+.f64 1 x) -1/2))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2))) (cbrt.f64 (/.f64 1 (+.f64 1 x))) (pow.f64 (+.f64 1 x) -1/2)))
31.4b
(+.f64 (fma.f64 (cbrt.f64 (pow.f64 x -1/2)) (cbrt.f64 (/.f64 1 x)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2))) (fma.f64 (neg.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) (pow.f64 (+.f64 1 x) -1/2)))
30.1b
(+.f64 (fma.f64 (cbrt.f64 (pow.f64 x -1/2)) (cbrt.f64 (/.f64 1 x)) (neg.f64 (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1)))) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1)) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1) (*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) -1) (pow.f64 (cbrt.f64 (+.f64 1 x)) -1))))
31.0b
(fma.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))
31.0b
(+.f64 (fma.f64 (pow.f64 (pow.f64 x 1/4) -1) (pow.f64 (pow.f64 x 1/4) -1) (neg.f64 (pow.f64 (+.f64 1 x) -1/2))) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (+.f64 1 x) -1/2))) (cbrt.f64 (/.f64 1 (+.f64 1 x))) (pow.f64 (+.f64 1 x) -1/2)))
31.4b
(+.f64 (fma.f64 (pow.f64 (cbrt.f64 x) -1) (pow.f64 (cbrt.f64 (sqrt.f64 x)) -1) (neg.f64 (pow.f64 (+.f64 1 x) -1/2))) (fma.f64 (neg.f64 (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -1)) (pow.f64 (pow.f64 (+.f64 1 x) 1/4) -1) (pow.f64 (+.f64 1 x) -1/2)))
31.3b
(+.f64 (fma.f64 (pow.f64 (cbrt.f64 x) -1) (pow.f64 (cbrt.f64 (sqrt.f64 x)) -1) (neg.f64 (pow.f64 (+.f64 1 x) -1/2))) (fma.f64 -1 (pow.f64 (+.f64 1 x) -1/2) (pow.f64 (+.f64 1 x) -1/2)))
31.0b
(+.f64 (fma.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 x))) (neg.f64 (pow.f64 (+.f64 1 x) -1/2))) (fma.f64 (neg.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2)) (pow.f64 (sqrt.f64 (+.f64 1 x)) -1/2) (pow.f64 (+.f64 1 x) -1/2)))
Compiler

Compiled 5001 to 4025 computations (19.5% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(pow.f64 (+.f64 1 x) -1/2)
✓0.2b
(cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
✓0.4b
(pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) 3)
✓2.4b
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))

series17.0ms (0.5%)

Counts
4 → 32
Calls

12 calls:

TimeVariablePointExpression
4.0ms
x
@-inf
(pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) 3)
3.0ms
x
@inf
(pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) 3)
2.0ms
x
@0
(pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) 3)
2.0ms
x
@-inf
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
1.0ms
x
@inf
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))

rewrite90.0ms (2.5%)

Algorithm
1×batch-egg-rewrite
Rules
553×prod-diff_binary64
326×fma-def_binary64
182×expm1-udef_binary64
182×log1p-udef_binary64
138×fma-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01148
124948
2287148
Stop Event
1×node limit
Counts
4 → 300
Calls
Call 1
Inputs
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))
(pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2))) 3)
(cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 1 x) -1/2)))
(pow.f64 (+.f64 1 x) -1/2)
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))) (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))) (pow.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 2) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 2)) (cbrt.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) 1/6) (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 2) 1/3) (cbrt.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 1/3) (pow.f64 (sqrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (-.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1))) (cbrt.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 x 1) -3/2))) (cbrt.f64 (+.f64 (+.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1)) (pow.f64 (*.f64 x (+.f64 x 1)) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 x 1) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (+.f64 x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)) (cbrt.f64 (pow.f64 (+.f64 x 1) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) -1)) (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(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 (pow.f64 1 -1/2) (pow.f64 (+.f64 x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2)) -1/2) (pow.f64 (cbrt.f64 (+.f64 x 1)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) -1/2) (pow.f64 (sqrt.f64 (+.f64 x 1)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1) -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(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 (*.f64 -1/2 (log1p.f64 x)) 1))))))

simplify38.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
550×fma-def_binary64
352×cancel-sign-sub-inv_binary64
304×associate-*l*_binary64
300×associate-*r*_binary64
219×associate--l+_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01341355
13981309
213051106
Stop Event
1×node limit
Counts
332 → 234
Calls
Call 1
Inputs
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (+.f64 (pow.f64 x -1/2) (*.f64 1/2 x)) 1)
(-.f64 (+.f64 (pow.f64 x -1/2) (*.f64 1/2 x)) (+.f64 1 (*.f64 3/8 (pow.f64 x 2))))
(-.f64 (+.f64 (pow.f64 x -1/2) (+.f64 (*.f64 1/2 x) (*.f64 5/16 (pow.f64 x 3)))) (+.f64 1 (*.f64 3/8 (pow.f64 x 2))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (*.f64 35/128 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))
(*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x))
(-.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)) (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)) (*.f64 5/16 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3)))) (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)) (*.f64 5/16 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3)))) (+.f64 (*.f64 35/128 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 4))) (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2)))))
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (+.f64 (pow.f64 x -1/2) (*.f64 1/2 (*.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 4) 1/9) x))) 1)
(-.f64 (+.f64 (pow.f64 x -1/2) (*.f64 1/2 (*.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 4) 1/9) x))) (+.f64 1 (*.f64 3/8 (pow.f64 x 2))))
(-.f64 (+.f64 (pow.f64 x -1/2) (+.f64 (*.f64 1/2 (*.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 4) 1/9) x)) (*.f64 5/16 (pow.f64 x 3)))) (+.f64 1 (*.f64 3/8 (pow.f64 x 2))))
(pow.f64 (-.f64 (pow.f64 x -1/2) 1) 1/3)
(+.f64 (*.f64 1/6 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 1/9) x)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 1/3))
(-.f64 (+.f64 (*.f64 1/6 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 1/9) x)) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 1/3)) (+.f64 (*.f64 1/36 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 7)) 1/9) (pow.f64 x 2))) (*.f64 1/8 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 1/3) (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 1/6 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 1/9) x)) (+.f64 (*.f64 1/24 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 11)) 1/9) (pow.f64 x 3))) (+.f64 (*.f64 5/48 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 1/3) (pow.f64 x 3))) (+.f64 (*.f64 5/648 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 4)) 1/3) (pow.f64 x 3))) (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 1/3))))) (+.f64 (*.f64 1/36 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 7)) 1/9) (pow.f64 x 2))) (*.f64 1/8 (*.f64 (pow.f64 (/.f64 1 (pow.f64 (-.f64 (pow.f64 x -1/2) 1) 2)) 1/3) (pow.f64 x 2)))))
1
(-.f64 1 (*.f64 1/2 x))
(-.f64 (+.f64 1 (*.f64 3/8 (pow.f64 x 2))) (*.f64 1/2 x))
(-.f64 (+.f64 1 (*.f64 3/8 (pow.f64 x 2))) (+.f64 (*.f64 1/2 x) (*.f64 5/16 (pow.f64 x 3))))
(sqrt.f64 (/.f64 1 x))
(-.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(-.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)))
(-.f64 (+.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)))
(-.f64 (+.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2)))) (+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)) (*.f64 5/16 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3)))))
Outputs
(-.f64 (pow.f64 x -1/2) 1)
(+.f64 (pow.f64 x -1/2) -1)
(-.f64 (+.f64 (pow.f64 x -1/2) (*.f64 1/2 x)) 1)
(+.f64 (pow.f64 x -1/2) (-.f64 (*.f64 x 1/2) 1))
(+.f64 (pow.f64 x -1/2) (fma.f64 x 1/2 -1))
(-.f64 (+.f64 (pow.f64 x -1/2) (*.f64 1/2 x)) (+.f64 1 (*.f64 3/8 (pow.f64 x 2))))
(-.f64 (+.f64 (pow.f64 x -1/2) (-.f64 (*.f64 x 1/2) 1)) (*.f64 3/8 (*.f64 x x)))
(-.f64 (fma.f64 x 1/2 (pow.f64 x -1/2)) (fma.f64 3/8 (*.f64 x x) 1))
(-.f64 (fma.f64 x 1/2 (pow.f64 x -1/2)) (fma.f64 x (*.f64 x 3/8) 1))
(-.f64 (+.f64 (pow.f64 x -1/2) (+.f64 (*.f64 1/2 x) (*.f64 5/16 (pow.f64 x 3)))) (+.f64 1 (*.f64 3/8 (pow.f64 x 2))))
(+.f64 (pow.f64 x -1/2) (-.f64 (fma.f64 1/2 x (*.f64 5/16 (pow.f64 x 3))) (+.f64 1 (*.f64 3/8 (*.f64 x x)))))
(+.f64 (fma.f64 5/16 (pow.f64 x 3) (*.f64 x 1/2)) (-.f64 (pow.f64 x -1/2) (fma.f64 3/8 (*.f64 x x) 1)))
(-.f64 (fma.f64 5/16 (pow.f64 x 3) (fma.f64 x 1/2 (pow.f64 x -1/2))) (fma.f64 x (*.f64 x 3/8) 1))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8))
(-.f64 (+.f64 (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))))))
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1
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(+.f64 (sqrt.f64 (/.f64 1 x)) (-.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (sqrt.f64 (/.f64 1 x))) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (sqrt.f64 (/.f64 1 x))))
(-.f64 (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(-.f64 (+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (sqrt.f64 (/.f64 1 x))) (fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(-.f64 (fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (sqrt.f64 (/.f64 1 x))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))))))
(+.f64 (sqrt.f64 (/.f64 1 x)) (fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) -5/16))))
(exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0))
(-.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)))
(+.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x)))
(fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)) x) (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)))
(-.f64 (+.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)))
(+.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (-.f64 (*.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x))) (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x))))
(+.f64 (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x)))
(+.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)) (*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)) x) (-.f64 (/.f64 3/8 x) 1/2)))
(-.f64 (+.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2)))) (+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)) (*.f64 5/16 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3)))))
(+.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (-.f64 (*.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x))) (fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (/.f64 (*.f64 5/16 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3)))))
(-.f64 (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (/.f64 5/16 (/.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))))
(+.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)) (-.f64 (*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)) x) (-.f64 (/.f64 3/8 x) 1/2)) (*.f64 (/.f64 5/16 (pow.f64 x 3)) (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)))))

prune248.0ms (6.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New2304234
Fresh14115
Picked101
Done000
Total2455250
Error
1.2b
Counts
250 → 5
Alt Table
StatusErrorProgram
32.1b
(pow.f64 (cbrt.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)) x) (+.f64 1/2 (/.f64 5/16 (*.f64 x x)))) (*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)) (*.f64 x x)) (+.f64 3/8 (/.f64 35/128 (*.f64 x x)))))) 3)
25.3b
(/.f64 (-.f64 (/.f64 1 x) (*.f64 (neg.f64 (pow.f64 (+.f64 1 x) -1/2)) (neg.f64 (pow.f64 (+.f64 1 x) -1/2)))) (-.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 1 x) -1/2))))
31.8b
(pow.f64 (cbrt.f64 (fma.f64 5/16 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)) (pow.f64 x 3)) (*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)) x) (-.f64 1/2 (/.f64 3/8 x))))) 3)
42.2b
(pow.f64 (cbrt.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))))))) 3)
▶20.5b
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
Compiler

Compiled 7127 to 6031 computations (15.4% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(pow.f64 (+.f64 x 1) -1/2)
✓2.4b
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))

series3.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@0
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
0.0ms
x
@-inf
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
0.0ms
x
@-inf
(pow.f64 (+.f64 x 1) -1/2)
0.0ms
x
@inf
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
0.0ms
x
@inf
(pow.f64 (+.f64 x 1) -1/2)

rewrite42.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
875×log1p-expm1-u_binary64
875×expm1-log1p-u_binary64
94×add-sqr-sqrt_binary64
90×add-log-exp_binary64
90×pow1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0820
118420
2241220
Stop Event
1×node limit
Counts
2 → 54
Calls
Call 1
Inputs
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
(pow.f64 (+.f64 x 1) -1/2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x -1/2) (*.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 1 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (fma.f64 (neg.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2))) (cbrt.f64 (pow.f64 (+.f64 x 1) -1)) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (fma.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/4)) (pow.f64 (+.f64 x 1) -1/4) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 2) (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) (sqrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 x 1) -3/2)) (/.f64 1 (+.f64 (pow.f64 x -1) (+.f64 (pow.f64 (+.f64 x 1) -1) (pow.f64 (*.f64 x (+.f64 x 1)) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1)) (/.f64 1 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 x 1) -1/4)) (-.f64 (pow.f64 x -1/4) (pow.f64 (+.f64 x 1) -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x -1) (+.f64 (pow.f64 (+.f64 x 1) -1) (pow.f64 (*.f64 x (+.f64 x 1)) -1/2))) (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 x 1) -3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (-.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 x 1) -3/2)) (+.f64 (pow.f64 x -1) (+.f64 (pow.f64 (+.f64 x 1) -1) (pow.f64 (*.f64 x (+.f64 x 1)) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x -3/2) (pow.f64 (+.f64 x 1) -3/2))) (neg.f64 (+.f64 (pow.f64 x -1) (+.f64 (pow.f64 (+.f64 x 1) -1) (pow.f64 (*.f64 x (+.f64 x 1)) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1))) (neg.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x -3/2) (pow.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) 3)) (+.f64 (pow.f64 x -1) (-.f64 (*.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (neg.f64 (pow.f64 (+.f64 x 1) -1/2))) (*.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -1) (*.f64 (neg.f64 (pow.f64 (+.f64 x 1) -1/2)) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))) (-.f64 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x -1)) (cbrt.f64 (pow.f64 x -1/2)) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 x 1) -1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (+.f64 x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)) (cbrt.f64 (pow.f64 (+.f64 x 1) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) -1)) (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(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 (pow.f64 1 -1/2) (pow.f64 (+.f64 x 1) -1/2))))) (#(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 (pow.f64 (sqrt.f64 (+.f64 x 1)) -1/2) (pow.f64 (sqrt.f64 (+.f64 x 1)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1) -3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(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 (*.f64 -1/2 (log1p.f64 x)) 1))))))

simplify32.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
537×cancel-sign-sub-inv_binary64
484×times-frac_binary64
431×fma-neg_binary64
270×sub-neg_binary64
261×associate-/l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
082809
1242781
2715590
32261471
Stop Event
1×node limit
Counts
78 → 99
Calls
Call 1
Inputs
(-.f64 (pow.f64 x -1/2) 1)
(-.f64 (+.f64 (pow.f64 x -1/2) (*.f64 1/2 x)) 1)
(-.f64 (+.f64 (pow.f64 x -1/2) (*.f64 1/2 x)) (+.f64 1 (*.f64 3/8 (pow.f64 x 2))))
(-.f64 (+.f64 (pow.f64 x -1/2) (+.f64 (*.f64 1/2 x) (*.f64 5/16 (pow.f64 x 3)))) (+.f64 1 (*.f64 3/8 (pow.f64 x 2))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (*.f64 35/128 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))
(*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x))
(-.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)) (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)) (*.f64 5/16 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3)))) (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)) (*.f64 5/16 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3)))) (+.f64 (*.f64 35/128 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 4))) (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2)))))
1
(-.f64 1 (*.f64 1/2 x))
(-.f64 (+.f64 1 (*.f64 3/8 (pow.f64 x 2))) (*.f64 1/2 x))
(-.f64 (+.f64 1 (*.f64 3/8 (pow.f64 x 2))) (+.f64 (*.f64 1/2 x) (*.f64 5/16 (pow.f64 x 3))))
(sqrt.f64 (/.f64 1 x))
(-.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(-.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)))
(-.f64 (+.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)))
(-.f64 (+.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2)))) (+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)) (*.f64 5/16 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3)))))
Outputs
(-.f64 (pow.f64 x -1/2) 1)
(+.f64 (pow.f64 x -1/2) -1)
(+.f64 -1 (pow.f64 x -1/2))
(-.f64 (+.f64 (pow.f64 x -1/2) (*.f64 1/2 x)) 1)
(+.f64 (pow.f64 x -1/2) (-.f64 (*.f64 x 1/2) 1))
(+.f64 (pow.f64 x -1/2) (fma.f64 x 1/2 -1))
(-.f64 (+.f64 (pow.f64 x -1/2) (*.f64 1/2 x)) (+.f64 1 (*.f64 3/8 (pow.f64 x 2))))
(+.f64 (pow.f64 x -1/2) (-.f64 (*.f64 x 1/2) (+.f64 1 (*.f64 3/8 (*.f64 x x)))))
(-.f64 (fma.f64 x 1/2 (pow.f64 x -1/2)) (fma.f64 3/8 (*.f64 x x) 1))
(+.f64 (pow.f64 x -1/2) (fma.f64 x (+.f64 1/2 (*.f64 x -3/8)) -1))
(-.f64 (+.f64 (pow.f64 x -1/2) (+.f64 (*.f64 1/2 x) (*.f64 5/16 (pow.f64 x 3)))) (+.f64 1 (*.f64 3/8 (pow.f64 x 2))))
(+.f64 (pow.f64 x -1/2) (-.f64 (fma.f64 1/2 x (*.f64 5/16 (pow.f64 x 3))) (+.f64 1 (*.f64 3/8 (*.f64 x x)))))
(+.f64 (fma.f64 x 1/2 (pow.f64 x -1/2)) (-.f64 (*.f64 5/16 (pow.f64 x 3)) (fma.f64 3/8 (*.f64 x x) 1)))
(-.f64 (fma.f64 x 1/2 (fma.f64 5/16 (pow.f64 x 3) (pow.f64 x -1/2))) (fma.f64 3/8 (*.f64 x x) 1))
(+.f64 (pow.f64 x -1/2) (fma.f64 5/16 (pow.f64 x 3) (fma.f64 x (+.f64 1/2 (*.f64 x -3/8)) -1)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)))
(fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)))
(-.f64 (+.f64 (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (*.f64 35/128 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))
(-.f64 (fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (fma.f64 35/128 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))
(-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))))) (fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (*.f64 35/128 (sqrt.f64 (/.f64 1 (pow.f64 x 9))))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) -35/128))))
(fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 9))) -35/128 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8))))
(*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x))
(*.f64 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x))
(*.f64 (/.f64 1/2 x) (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)))
(*.f64 1/2 (/.f64 (pow.f64 x -1/2) x))
(-.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)) (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2))))
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x)) (*.f64 -3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x))))
(fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) -3/8))
(*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)) x) (-.f64 1/2 (/.f64 3/8 x)))
(*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 1/2 (/.f64 -3/8 x)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)) (*.f64 5/16 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3)))) (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2))))
(+.f64 (fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 5/16 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)))) (*.f64 -3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x))))
(fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (fma.f64 5/16 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) -3/8)))
(fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)) x) (*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)) (*.f64 x x)) (-.f64 (/.f64 5/16 x) 3/8)))
(*.f64 (/.f64 (pow.f64 x -1/2) x) (-.f64 (/.f64 5/16 (*.f64 x x)) (+.f64 (/.f64 3/8 x) -1/2)))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)) (*.f64 5/16 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3)))) (+.f64 (*.f64 35/128 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 4))) (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2)))))
(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 5/16 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)))) (fma.f64 35/128 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 4)) (*.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)))))
(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 5/16 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)))) (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (*.f64 35/128 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 4)))))
(-.f64 (*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)) x) (+.f64 1/2 (/.f64 5/16 (*.f64 x x)))) (*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)) (*.f64 x x)) (+.f64 3/8 (/.f64 35/128 (*.f64 x x)))))
(-.f64 (*.f64 (/.f64 (pow.f64 x -1/2) (pow.f64 x 3)) (-.f64 5/16 (/.f64 35/128 x))) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 (/.f64 3/8 x) -1/2)))
1
(-.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 -1/2 x))
(+.f64 1 (*.f64 x -1/2))
(fma.f64 x -1/2 1)
(-.f64 (+.f64 1 (*.f64 3/8 (pow.f64 x 2))) (*.f64 1/2 x))
(+.f64 1 (-.f64 (*.f64 3/8 (*.f64 x x)) (*.f64 x 1/2)))
(+.f64 1 (fma.f64 3/8 (*.f64 x x) (*.f64 x -1/2)))
(fma.f64 x -1/2 (fma.f64 3/8 (*.f64 x x) 1))
(+.f64 1 (*.f64 x (fma.f64 x 3/8 -1/2)))
(-.f64 (+.f64 1 (*.f64 3/8 (pow.f64 x 2))) (+.f64 (*.f64 1/2 x) (*.f64 5/16 (pow.f64 x 3))))
(+.f64 1 (-.f64 (*.f64 3/8 (*.f64 x x)) (fma.f64 1/2 x (*.f64 5/16 (pow.f64 x 3)))))
(-.f64 (fma.f64 3/8 (*.f64 x x) 1) (fma.f64 x 1/2 (*.f64 5/16 (pow.f64 x 3))))
(-.f64 (*.f64 x (-.f64 (*.f64 x 3/8) 1/2)) (fma.f64 5/16 (pow.f64 x 3) -1))
(+.f64 1 (fma.f64 x (fma.f64 x 3/8 -1/2) (*.f64 (pow.f64 x 3) -5/16)))
(sqrt.f64 (/.f64 1 x))
(-.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x)))
(-.f64 (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (sqrt.f64 (/.f64 1 x))) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (sqrt.f64 (/.f64 1 x))) (*.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x))))
(fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (sqrt.f64 (/.f64 1 x))))
(-.f64 (+.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))) (+.f64 (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (sqrt.f64 (/.f64 1 x)) (-.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(-.f64 (fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (sqrt.f64 (/.f64 1 x))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))))))
(+.f64 (sqrt.f64 (/.f64 1 x)) (fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) -5/16))))
(exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))
(pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0))
(pow.f64 x -1/2)
(-.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)))
(+.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x)))
(+.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (/.f64 (*.f64 -1/2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x))
(fma.f64 -1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)) x) (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)))
(fma.f64 -1/2 (/.f64 (pow.f64 x -1/2) x) (pow.f64 x -1/2))
(-.f64 (+.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)))
(+.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (-.f64 (*.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x))) (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x))))
(+.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (/.f64 (*.f64 -1/2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)))
(+.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)) (*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)) x) (-.f64 (/.f64 3/8 x) 1/2)))
(+.f64 (pow.f64 x -1/2) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 (/.f64 3/8 x) -1/2)))
(-.f64 (+.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 3/8 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2)))) (+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)) (*.f64 5/16 (/.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3)))))
(+.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (-.f64 (*.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x))) (fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 5/16 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3))))))
(-.f64 (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 5/16 (/.f64 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)))))
(+.f64 (*.f64 (/.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)) x) (-.f64 (/.f64 3/8 x) 1/2)) (-.f64 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)) (/.f64 (*.f64 5/16 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0))) (pow.f64 x 3))))
(+.f64 (pow.f64 x -1/2) (*.f64 (/.f64 (pow.f64 x -1/2) x) (-.f64 (+.f64 (/.f64 3/8 x) -1/2) (/.f64 5/16 (*.f64 x x)))))

prune106.0ms (3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New95499
Fresh314
Picked011
Done000
Total986104
Error
0.1b
Counts
104 → 6
Alt Table
StatusErrorProgram
42.2b
(pow.f64 (cbrt.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))))))) 3)
42.0b
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)))
▶20.8b
(/.f64 (-.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))
✓20.5b
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
30.4b
(*.f64 (/.f64 (pow.f64 x -1/2) x) (-.f64 (/.f64 5/16 (*.f64 x x)) (+.f64 (/.f64 3/8 x) -1/2)))
21.1b
(pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 3)
Compiler

Compiled 2034 to 1675 computations (17.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(pow.f64 (+.f64 x 1) -1/2)
✓0.0b
(pow.f64 (+.f64 x 1) -1)
✓0.3b
(/.f64 (-.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))
✓2.4b
(-.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1))

series9.0ms (0.3%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
4.0ms
x
@0
(-.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1))
2.0ms
x
@0
(/.f64 (-.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))
1.0ms
x
@-inf
(/.f64 (-.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))
1.0ms
x
@inf
(/.f64 (-.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))
1.0ms
x
@inf
(-.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1))

rewrite64.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
242×log1p-udef_binary64
241×expm1-udef_binary64
151×add-sqr-sqrt_binary64
148×pow1_binary64
144×*-un-lft-identity_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01348
130833
2426833
Stop Event
1×node limit
Counts
3 → 115
Calls
Call 1
Inputs
(-.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1))
(/.f64 (-.f64 (pow.f64 x -1) (pow.f64 (+.f64 x 1) -1)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))
(pow.f64 (+.f64 x 1) -1)
Outputs
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(#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 (/.f64 1 x) (/.f64 -1 (+.f64 x 1))) (neg.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (exp.f64 (pow.f64 x -1/2)) (exp.f64 (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 (/.f64 1 x) (/.f64 -1 (+.f64 x 1))) 3) (pow.f64 (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 x -1/2) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -1/2)) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x -1/4) (pow.f64 x -1/4) (neg.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 (+.f64 x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 x 1))) (cbrt.f64 (pow.f64 (+.f64 x 1) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 x 1))) (*.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) -2)) (/.f64 1 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) -1/4) (*.f64 (pow.f64 (+.f64 x 1) -1/4) (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (+.f64 x 1) -1/2) (pow.f64 (+.f64 x 1) -1/4)) (pow.f64 (+.f64 x 1) -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) -1) (pow.f64 (cbrt.f64 (+.f64 x 1)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) -1) (pow.f64 (sqrt.f64 (+.f64 x 1)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3))) (fma.f64 x x (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 x x -1)) (+.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (+.f64 x 1) -1/2) (/.f64 1 (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (+.f64 x 1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 x 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (+.f64 x 1) -1/2) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x 1) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1) -3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log1p.f64 x)) 1))))))

simplify51.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
599×fma-neg_binary64
297×associate-+l+_binary64
282×fma-def_binary64
248×associate--l+_binary64
236×associate-/r*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01291096
13921043
21155962
34471962
Stop Event
1×node limit
Counts
151 → 165
Calls
Call 1
Inputs
(/.f64 1 x)
(-.f64 (/.f64 1 x) 1)
(-.f64 (+.f64 (/.f64 1 x) x) 1)
(-.f64 (+.f64 (/.f64 1 x) x) (+.f64 1 (pow.f64 x 2)))
(/.f64 1 (pow.f64 x 2))
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (/.f64 1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3))))
(/.f64 1 (pow.f64 x 2))
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (/.f64 1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3))))
(/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) (+.f64 1 (pow.f64 x -1/2))))) (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x))) (/.f64 1 (+.f64 1 (pow.f64 x -1/2))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) (+.f64 1 (pow.f64 x -1/2))))) (+.f64 (*.f64 1/4 (/.f64 x (*.f64 (+.f64 (pow.f64 x -1/2) 1) (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)))) (+.f64 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x)) (/.f64 x (+.f64 1 (pow.f64 x -1/2)))))) (+.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (*.f64 7/8 (/.f64 x (*.f64 (+.f64 (pow.f64 x -1/2) 1) (+.f64 1 (pow.f64 x -1/2)))))))
(-.f64 (+.f64 (*.f64 1/2 (/.f64 1 (*.f64 (+.f64 (pow.f64 x -1/2) 1) (+.f64 1 (pow.f64 x -1/2))))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 x 2) (*.f64 (pow.f64 (+.f64 (pow.f64 x -1/2) 1) 2) (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)))) (+.f64 (*.f64 1/4 (/.f64 x (*.f64 (+.f64 (pow.f64 x -1/2) 1) (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)))) (+.f64 (/.f64 1 (*.f64 (+.f64 1 (pow.f64 x -1/2)) x)) (+.f64 (/.f64 x (+.f64 1 (pow.f64 x -1/2))) (*.f64 19/16 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 (pow.f64 x -1/2) 1) (+.f64 1 (pow.f64 x -1/2)))))))))) (+.f64 (/.f64 1 (+.f64 1 (pow.f64 x -1/2))) (+.f64 (*.f64 5/8 (/.f64 (pow.f64 x 2) (*.f64 (+.f64 (pow.f64 x -1/2) 1) (pow.f64 (+.f64 1 (pow.f64 x -1/2)) 2)))) (+.f64 (*.f64 7/8 (/.f64 x (*.f64 (+.f64 (pow.f64 x -1/2) 1) (+.f64 1 (pow.f64 x -1/2))))) (/.f64 (pow.f64 x 2) (+.f64 1 (pow.f64 x -1/2)))))))
(*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 (*.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (*.f64 35/128 (sqrt.f64 (/.f64 1 (pow.f64 x 9)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))
(/.f64 1/2 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2)))
(-.f64 (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2)))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3)))))
(-.f64 (+.f64 (*.f64 5/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 4)))) (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2))))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3)))))
(-.f64 (+.f64 (*.f64 5/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 4)))) (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2))))) (+.f64 (*.f64 35/128 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 5)))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3))))))
1
(-.f64 1 x)
(-.f64 (+.f64 1 (pow.f64 x 2)) x)
(-.f64 (+.f64 1 (pow.f64 x 2)) (+.f64 x (pow.f64 x 3)))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 2)))
(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))
(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 2)))
(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))
(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))))
Outputs
(/.f64 1 x)
(-.f64 (/.f64 1 x) 1)
(+.f64 (/.f64 1 x) -1)
(-.f64 (+.f64 (/.f64 1 x) x) 1)
(+.f64 (/.f64 1 x) (-.f64 x 1))
(-.f64 (+.f64 (/.f64 1 x) x) (+.f64 1 (pow.f64 x 2)))
(+.f64 (/.f64 1 x) (-.f64 x (+.f64 1 (*.f64 x x))))
(+.f64 x (-.f64 (/.f64 1 x) (fma.f64 x x 1)))
(+.f64 (/.f64 1 x) (-.f64 x (fma.f64 x x 1)))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 (/.f64 1 x) x)
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 3)))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 (/.f64 1 x) x) (/.f64 -1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 1 (pow.f64 x 4)) (-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 (/.f64 1 x) x) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 -1 (pow.f64 x 3))))
(+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 (/.f64 1 x) x) (/.f64 -1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 4))) (+.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 5))))
(-.f64 (+.f64 (/.f64 (/.f64 1 x) x) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 -1 (pow.f64 x 3)))) (/.f64 1 (pow.f64 x 5)))
(+.f64 (/.f64 (/.f64 1 x) x) (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 -1 (pow.f64 x 3)) (/.f64 -1 (pow.f64 x 5)))))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 (/.f64 1 x) x)
(-.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 3)))
(-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 (/.f64 1 x) x) (/.f64 -1 (pow.f64 x 3)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (/.f64 1 (pow.f64 x 3)))
(+.f64 (/.f64 1 (pow.f64 x 4)) (-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 (/.f64 1 x) x) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 -1 (pow.f64 x 3))))
(+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 (/.f64 1 x) x) (/.f64 -1 (pow.f64 x 3))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))) (+.f64 (/.f64 1 (pow.f64 x 5)) (/.f64 1 (pow.f64 x 3))))
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(/.f64 1/2 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2)))
(/.f64 1/2 (*.f64 (*.f64 x x) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))
(/.f64 (/.f64 1/2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 x x))
(/.f64 (/.f64 1/2 (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0))) (*.f64 x x))
(-.f64 (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2)))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3)))))
(-.f64 (/.f64 1/2 (*.f64 (*.f64 x x) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) (/.f64 3/8 (*.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))
(+.f64 (/.f64 (/.f64 1/2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 x x)) (/.f64 -3/8 (*.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))
(fma.f64 1/2 (/.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 x) 0))) (*.f64 x x)) (/.f64 -3/8 (*.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)))))
(-.f64 (+.f64 (*.f64 5/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 4)))) (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2))))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3)))))
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(-.f64 (+.f64 (*.f64 5/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 4)))) (*.f64 1/2 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 2))))) (+.f64 (*.f64 35/128 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 5)))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 -1/2 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (pow.f64 x 3))))))
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(+.f64 (/.f64 (/.f64 1/2 (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (*.f64 x x)) (-.f64 (/.f64 (/.f64 5/16 (pow.f64 x 4)) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (+.f64 (/.f64 3/8 (*.f64 (pow.f64 x 3) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) (/.f64 35/128 (*.f64 (pow.f64 x 5) (pow.f64 (exp.f64 -1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))))
(fma.f64 5/16 (/.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 x) 0))) (pow.f64 x 4)) (fma.f64 1/2 (/.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 x) 0))) (*.f64 x x)) (fma.f64 (/.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 x) 0))) (pow.f64 x 3)) -3/8 (/.f64 -35/128 (*.f64 (pow.f64 x 5) (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)))))))
(fma.f64 1/2 (/.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 x) 0))) (*.f64 x x)) (fma.f64 5/16 (/.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 x) 0))) (pow.f64 x 4)) (fma.f64 (/.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 x) 0))) (pow.f64 x 3)) -3/8 (/.f64 -35/128 (*.f64 (pow.f64 x 5) (pow.f64 (exp.f64 -1/2) (+.f64 (log.f64 x) 0)))))))
1
(-.f64 1 x)
(-.f64 (+.f64 1 (pow.f64 x 2)) x)
(+.f64 1 (-.f64 (*.f64 x x) x))
(-.f64 (fma.f64 x x 1) x)
(-.f64 (+.f64 1 (pow.f64 x 2)) (+.f64 x (pow.f64 x 3)))
(-.f64 (+.f64 1 (*.f64 x x)) (+.f64 x (pow.f64 x 3)))
(-.f64 (fma.f64 x x 1) (+.f64 x (pow.f64 x 3)))
(-.f64 (-.f64 (fma.f64 x x 1) x) (pow.f64 x 3))
(+.f64 1 (*.f64 x (-.f64 x (fma.f64 x x 1))))
(/.f64 1 x)
(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 2)))
(-.f64 (/.f64 1 x) (/.f64 1 (*.f64 x x)))
(-.f64 (/.f64 1 x) (/.f64 (/.f64 1 x) x))
(+.f64 (/.f64 1 x) (/.f64 -1 (*.f64 x x)))
(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))
(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (/.f64 1 (*.f64 x x)))
(+.f64 (/.f64 1 (pow.f64 x 3)) (-.f64 (/.f64 1 x) (/.f64 (/.f64 1 x) x)))
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(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))))
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(+.f64 (+.f64 (/.f64 1 x) (-.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 4)))) (/.f64 -1 (*.f64 x x)))
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(/.f64 1 x)
(-.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 2)))
(-.f64 (/.f64 1 x) (/.f64 1 (*.f64 x x)))
(-.f64 (/.f64 1 x) (/.f64 (/.f64 1 x) x))
(+.f64 (/.f64 1 x) (/.f64 -1 (*.f64 x x)))
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(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (/.f64 1 (*.f64 x x)))
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(-.f64 (+.f64 (/.f64 1 x) (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2))))
(+.f64 (/.f64 1 x) (-.f64 (/.f64 1 (pow.f64 x 3)) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 4)))))
(+.f64 (+.f64 (/.f64 1 x) (-.f64 (/.f64 1 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 4)))) (/.f64 -1 (*.f64 x x)))
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prune208.0ms (5.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2013204
Fresh224
Picked101
Done011
Total2046210
Error
0.0b
Counts
210 → 6
Alt Table
StatusErrorProgram
42.0b
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 5/16 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)))
36.3b
(/.f64 (/.f64 (/.f64 1 x) x) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))
30.4b
(*.f64 (/.f64 (pow.f64 x -1/2) x) (-.f64 (/.f64 5/16 (*.f64 x x)) (+.f64 (/.f64 3/8 x) -1/2)))
36.5b
(/.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))
20.1b
(/.f64 (/.f64 (-.f64 (+.f64 x 1) x) (*.f64 x (+.f64 x 1))) (+.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)))
✓20.5b
(-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2))
Compiler

Compiled 5434 to 4383 computations (19.3% saved)

regimes524.0ms (14.7%)

Accuracy

Total 0.1b remaining (70.9%)

Threshold costs 0.1b (70.9%)

Counts
270 → 2
Compiler

Compiled 4939 to 3985 computations (19.3% saved)

bsearch15.0ms (0.4%)

Algorithm
1×binary-search
Calls

1 calls:

13.0ms
x
Steps
ItersPointRange
7800.0
∈ [
3782.5944671097827
, 
537187.9560378381
]
Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
7×+-commutative_binary64
5×sub-neg_binary64
4×*-commutative_binary64
3×neg-sub0_binary64
3×neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02144
13044
24244
35244
45644
55744
Stop Event
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 x 7800) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (*.f64 (/.f64 (pow.f64 x -1/2) x) (-.f64 (/.f64 5/16 (*.f64 x x)) (+.f64 (/.f64 3/8 x) -1/2))))
Outputs
(if (<=.f64 x 7800) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (*.f64 (/.f64 (pow.f64 x -1/2) x) (-.f64 (/.f64 5/16 (*.f64 x x)) (+.f64 (/.f64 3/8 x) -1/2))))
(if (<=.f64 x 7800) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (*.f64 (/.f64 (pow.f64 x -1/2) x) (-.f64 (/.f64 5/16 (*.f64 x x)) (+.f64 -1/2 (/.f64 3/8 x)))))
(if (<=.f64 x 7800) (-.f64 (pow.f64 x -1/2) (pow.f64 (+.f64 x 1) -1/2)) (*.f64 (/.f64 (pow.f64 x -1/2) x) (+.f64 (/.f64 5/16 (*.f64 x x)) (+.f64 1/2 (/.f64 -3/8 x)))))

end105.0ms (2.9%)

Stop Event
1×fuel
Compiler

Compiled 169 to 130 computations (23.1% saved)

Profiling

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