Details

Time bar (total: 5.8s)

analyze3.0ms (0.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
25%50%25%3
37.5%25%37.5%4
43.7%12.5%43.8%5
46.9%6.2%46.9%6
48.4%3.1%48.5%7
49.2%1.6%49.2%8
49.6%0.8%49.6%9
49.8%0.4%49.8%10
49.9%0.2%49.9%11
49.9%0.1%50%12
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.5s (26.1%)

Results
626.0ms2046×body1024valid
600.0ms4917×body256valid
186.0ms1051×body512valid
87.0ms242×body2048valid
1.0ms7×body256invalid

preprocess22.0ms (0.4%)

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
0711
11211
21611
32311
43211
54911
68611
712211
816811
920411
1023011
1123211
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Outputs
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify14.0ms (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
0711
11211
21611
32311
43211
54911
68611
712211
816811
920411
1023011
1123211
Stop Event
1×saturated
Counts
1 → 1
Calls
Call 1
Inputs
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Outputs
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

eval1.0ms (0%)

Compiler

Compiled 8 to 6 computations (25% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
30.8b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶30.8b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 8 to 6 computations (25% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiled 19 to 12 computations (36.8% saved)

series6.0ms (0.1%)

Counts
2 → 5
Calls

6 calls:

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

rewrite80.0ms (1.4%)

Algorithm
1×batch-egg-rewrite
Rules
794×pow1_binary64
742×log1p-expm1-u_binary64
742×expm1-log1p-u_binary64
741×add-log-exp_binary64
723×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0717
115317
2211117
Stop Event
1×node limit
Counts
2 → 58
Calls
Call 1
Inputs
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
(sqrt.f64 (+.f64 x 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 x 1)) (*.f64 (neg.f64 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) (/.f64 1 (+.f64 (+.f64 (+.f64 x 1) x) (sqrt.f64 (*.f64 (+.f64 x 1) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (-.f64 1 x)) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4)) (-.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 (+.f64 x 1) x) (sqrt.f64 (*.f64 (+.f64 x 1) x))) (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 (+.f64 x 1) x) (sqrt.f64 (*.f64 (+.f64 x 1) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (neg.f64 (+.f64 (+.f64 (+.f64 x 1) x) (sqrt.f64 (*.f64 (+.f64 x 1) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 x (-.f64 1 x))) (neg.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 (neg.f64 (sqrt.f64 x)) 3)) (+.f64 (+.f64 x 1) (-.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (+.f64 x 1) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 x 1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (fma.f64 x x -1)) (sqrt.f64 (-.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) 1/2))))))

simplify122.0ms (2.1%)

Algorithm
1×egg-herbie
Rules
660×distribute-rgt-in_binary64
606×distribute-lft-in_binary64
536×unswap-sqr_binary64
516×associate-*l*_binary64
445×*-commutative_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01840
14738
210538
330032
474431
5241431
6405931
7428731
8458631
9512531
10612231
Stop Event
1×node limit
Counts
63 → 65
Calls
Call 1
Inputs
1
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
Outputs
1
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x -1/8) 1))
(fma.f64 x (fma.f64 x -1/8 1/2) 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (+.f64 (fma.f64 1/2 x 1) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 x (*.f64 x -1/8) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 x (fma.f64 x -1/8 1/2) (fma.f64 1/16 (pow.f64 x 3) 1))
(fma.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))) 1)

eval19.0ms (0.3%)

Compiler

Compiled 829 to 549 computations (33.8% saved)

prune27.0ms (0.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New501565
Fresh000
Picked011
Done000
Total501666
Error
29.2b
Counts
66 → 16
Alt Table
Click to see full alt table
StatusErrorProgram
31.3b
(-.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x))
30.4b
(/.f64 (-.f64 (+.f64 x 1) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))
31.3b
(/.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 (neg.f64 (sqrt.f64 x)) 3)) (+.f64 (+.f64 x 1) (-.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))))
30.9b
(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))
31.2b
(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))
✓30.8b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
▶30.8b
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
▶30.1b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
31.1b
(-.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x))
31.9b
1
31.1b
(-.f64 (expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 x))
31.0b
(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))
▶30.8b
(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
▶62.5b
(-.f64 (/.f64 (sqrt.f64 (fma.f64 x x -1)) (sqrt.f64 (-.f64 x 1))) (sqrt.f64 x))
30.8b
(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
▶31.6b
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
Compiler

Compiled 422 to 298 computations (29.4% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.0b
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓0.0b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
✓1.7b
(+.f64 x (-.f64 1 x))
Compiler

Compiled 40 to 25 computations (37.5% saved)

series9.0ms (0.2%)

Counts
3 → 14
Calls

9 calls:

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

rewrite109.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
689×fma-def_binary64
545×log-prod_binary64
347×fma-neg_binary64
300×pow2_binary64
206×pow1/3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01038
123629
2362829
Stop Event
1×node limit
Counts
3 → 303
Calls
Call 1
Inputs
(+.f64 x (-.f64 1 x))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (-.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 x 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 x (-.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (+.f64 (+.f64 x -1) x)) (/.f64 (pow.f64 (-.f64 1 x) 2) (+.f64 (+.f64 x -1) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (-.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) (cbrt.f64 (pow.f64 (+.f64 x (-.f64 1 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x (-.f64 1 x)) 2)) (cbrt.f64 (+.f64 x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) 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(#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))) (exp.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))) (+.f64 1 (expm1.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))) (+.f64 1 (expm1.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 x))) (exp.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (sqrt.f64 x)) (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 x))) (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x 1)) 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) 1 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 2))) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (*.f64 x x))) (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))))

simplify15.0ms (0.3%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0114
1414
Stop Event
1×saturated
Counts
317 → 304
Calls
Call 1
Inputs
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Outputs
1
1
1
1
1
1
1
1
1
1
1
1
1
1

localize12.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiled 22 to 15 computations (31.8% saved)

series2.0ms (0%)

Counts
1 → 3
Calls

3 calls:

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

rewrite63.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
931×pow1_binary64
870×log1p-expm1-u_binary64
870×expm1-log1p-u_binary64
869×add-log-exp_binary64
852×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
117710
2237810
Stop Event
1×node limit
Counts
1 → 47
Calls
Call 1
Inputs
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 x) (-.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 x) (*.f64 (-.f64 1 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (*.f64 1/2 x) (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1/2 x 1) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1/2 x 1) (*.f64 (neg.f64 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x))) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x))) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 x)) (fma.f64 1/2 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x)))) (pow.f64 (cbrt.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x)))) 2) (cbrt.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x)))) (sqrt.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (fma.f64 1/2 x 1) 3) (pow.f64 x 3/2)) (/.f64 1 (+.f64 (pow.f64 (fma.f64 1/2 x 1) 2) (+.f64 x (*.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (fma.f64 1/2 x 1) 2) x) (/.f64 1 (+.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (fma.f64 1/2 x 1)) (pow.f64 x 1/4)) (-.f64 (sqrt.f64 (fma.f64 1/2 x 1)) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 1) 2) (+.f64 x (*.f64 (fma.f64 1/2 x 1) (sqrt.f64 x)))) (-.f64 (pow.f64 (fma.f64 1/2 x 1) 3) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (fma.f64 1/2 x 1) (sqrt.f64 x)) (-.f64 (pow.f64 (fma.f64 1/2 x 1) 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 1/2 x 1) 3) (pow.f64 x 3/2)) (+.f64 (pow.f64 (fma.f64 1/2 x 1) 2) (+.f64 x (*.f64 (fma.f64 1/2 x 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 1/2 x 1) 2) x) (+.f64 (fma.f64 1/2 x 1) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 1/2 x 1) 3) (pow.f64 x 3/2))) (neg.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 1) 2) (+.f64 x (*.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 1/2 x 1) 2) x)) (neg.f64 (+.f64 (fma.f64 1/2 x 1) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 1/2 x) 3) (pow.f64 (-.f64 1 (sqrt.f64 x)) 3)) (+.f64 (pow.f64 (*.f64 1/2 x) 2) (-.f64 (*.f64 (-.f64 1 (sqrt.f64 x)) (-.f64 1 (sqrt.f64 x))) (*.f64 (*.f64 1/2 x) (-.f64 1 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 1/2 x 1) 3) (pow.f64 (neg.f64 (sqrt.f64 x)) 3)) (+.f64 (pow.f64 (fma.f64 1/2 x 1) 2) (-.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (*.f64 (fma.f64 1/2 x 1) (neg.f64 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 1/2 x) 2) (*.f64 (-.f64 1 (sqrt.f64 x)) (-.f64 1 (sqrt.f64 x)))) (-.f64 (*.f64 1/2 x) (-.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 1/2 x 1) 2) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) (-.f64 (fma.f64 1/2 x 1) (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 1/2 x (-.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 x (-.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/2 x) (-.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 1/2 x 1) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x 1)) 2) (cbrt.f64 (fma.f64 1/2 x 1)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 x)) 2) (cbrt.f64 (*.f64 1/2 x)) (-.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 1/2 x 1)) (sqrt.f64 (fma.f64 1/2 x 1)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/2 x)) (sqrt.f64 (*.f64 1/2 x)) (-.f64 1 (sqrt.f64 x)))))))

simplify9.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
059
189
Stop Event
1×saturated
Counts
50 → 49
Calls
Call 1
Inputs
1
(*.f64 1/2 x)
(*.f64 1/2 x)
Outputs
1
(*.f64 1/2 x)
(*.f64 1/2 x)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.0b
(log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
✓0.0b
(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
2.5b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 36 to 23 computations (36.1% saved)

series11.0ms (0.2%)

Counts
2 → 2
Calls

6 calls:

TimeVariablePointExpression
6.0ms
x
@inf
(log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
2.0ms
x
@-inf
(log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
1.0ms
x
@0
(log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
1.0ms
x
@inf
(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
1.0ms
x
@-inf
(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

rewrite67.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
875×pow1_binary64
817×expm1-log1p-u_binary64
816×log1p-expm1-u_binary64
815×add-log-exp_binary64
795×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0924
117424
2231924
Stop Event
1×node limit
Counts
2 → 56
Calls
Call 1
Inputs
(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
(log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 x 1)) (*.f64 (neg.f64 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (+.f64 x 1) 3/2) (+.f64 (+.f64 x 1) (+.f64 x (sqrt.f64 (*.f64 (+.f64 x 1) x))))) (/.f64 (pow.f64 x 3/2) (+.f64 (+.f64 x 1) (+.f64 x (sqrt.f64 (*.f64 (+.f64 x 1) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (+.f64 x 1) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (/.f64 x (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) (/.f64 1 (+.f64 (+.f64 x 1) (+.f64 x (sqrt.f64 (*.f64 (+.f64 x 1) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (-.f64 1 x)) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4)) (-.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 x 1) (+.f64 x (sqrt.f64 (*.f64 (+.f64 x 1) x)))) (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 x 1) (+.f64 x (sqrt.f64 (*.f64 (+.f64 x 1) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (neg.f64 (+.f64 (+.f64 x 1) (+.f64 x (sqrt.f64 (*.f64 (+.f64 x 1) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 x (-.f64 1 x))) (neg.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3) 1) (+.f64 (*.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (+.f64 1 (*.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 (neg.f64 (sqrt.f64 x)) 3)) (+.f64 (+.f64 x 1) (-.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 1) (+.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (+.f64 x 1) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (pow.f64 (cbrt.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 2) (cbrt.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (sqrt.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))))

simplify13.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
044
164
Stop Event
1×saturated
Counts
58 → 58
Calls
Call 1
Inputs
1
(log.f64 2)
Outputs
1
(log.f64 2)

localize26.0ms (0.4%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.2b
(/.f64 (sqrt.f64 (fma.f64 x x -1)) (sqrt.f64 (-.f64 x 1)))
✓16.0b
(sqrt.f64 (fma.f64 x x -1))
✓18.5b
(-.f64 (/.f64 (sqrt.f64 (fma.f64 x x -1)) (sqrt.f64 (-.f64 x 1))) (sqrt.f64 x))
Compiler

Compiled 45 to 29 computations (35.6% saved)

series7.0ms (0.1%)

Counts
3 → 17
Calls

9 calls:

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

rewrite95.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
506×log-prod_binary64
448×fma-def_binary64
367×pow-prod-down_binary64
275×pow2_binary64
275×fma-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01138
123624
2318724
Stop Event
1×node limit
Counts
3 → 189
Calls
Call 1
Inputs
(-.f64 (/.f64 (sqrt.f64 (fma.f64 x x -1)) (sqrt.f64 (-.f64 x 1))) (sqrt.f64 x))
(sqrt.f64 (fma.f64 x x -1))
(/.f64 (sqrt.f64 (fma.f64 x x -1)) (sqrt.f64 (-.f64 x 1)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (hypot.f64 1 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (hypot.f64 1 (sqrt.f64 x)) (*.f64 (neg.f64 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/6)) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (+.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 x)) (hypot.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 2) (cbrt.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (sqrt.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) (/.f64 1 (+.f64 (+.f64 x 1) (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (+.f64 x 1) x) (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4)) (-.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 x 1) (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)) (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (-.f64 (+.f64 x 1) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 x 1) (fma.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x x -1) 1/6) (cbrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x -1)) (pow.f64 (fma.f64 x x -1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x x -1) 1/4) (pow.f64 (fma.f64 x x -1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x -1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x x -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x -1) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x -1) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x -1) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x -1) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x -1)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x -1) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (fma.f64 x x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x -1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x x -1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/2 (log.f64 (fma.f64 x x -1))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x -1) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/4 (log.f64 (fma.f64 x x -1))) 2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (hypot.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x x -1)) (pow.f64 (+.f64 x -1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (hypot.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/6) (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x -1)) (*.f64 (pow.f64 (fma.f64 x x -1) 1/6) (pow.f64 (+.f64 x -1) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 x x -1) 1/4) (*.f64 (pow.f64 (fma.f64 x x -1) 1/4) (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 (neg.f64 (sqrt.f64 (fma.f64 x x -1))) (/.f64 1 (neg.f64 (sqrt.f64 (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x -1) -1/2) (sqrt.f64 (fma.f64 x x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (fma.f64 x x -1)) 1) (/.f64 (pow.f64 (fma.f64 x x -1) 1/6) (sqrt.f64 (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (fma.f64 x x -1) 1/4) 1) (/.f64 (pow.f64 (fma.f64 x x -1) 1/4) (sqrt.f64 (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 x -1))) (/.f64 (sqrt.f64 (fma.f64 x x -1)) (pow.f64 (+.f64 x -1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (+.f64 x -1))) (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (fma.f64 x x -1) 1/4) (cbrt.f64 (+.f64 x -1))) (/.f64 (pow.f64 (fma.f64 x x -1) 1/4) (pow.f64 (+.f64 x -1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x -1) -1/4) (/.f64 (sqrt.f64 (fma.f64 x x -1)) (pow.f64 (+.f64 x -1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (fma.f64 x x -1)) (pow.f64 (+.f64 x -1) 1/4)) (/.f64 (pow.f64 (fma.f64 x x -1) 1/6) (pow.f64 (+.f64 x -1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 1/6) 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 pow.f64 (pow.f64 (+.f64 x 1) -1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (+.f64 x 1) -1/2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 (fma.f64 x x -1)) (neg.f64 (sqrt.f64 (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (hypot.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (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 (*.f64 1/2 (log1p.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 x 1) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (*.f64 1/2 (log1p.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/2 (log1p.f64 x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (*.f64 1/2 (log1p.f64 x))) -1))))))

simplify55.0ms (1%)

Algorithm
1×egg-herbie
Rules
740×associate-/l*_binary64
581×fma-def_binary64
564×unswap-sqr_binary64
481×associate-*l*_binary64
456×associate-/r*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
058244
1167231
2447225
31452217
46724217
Stop Event
1×node limit
Counts
206 → 218
Calls
Call 1
Inputs
1
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(*.f64 -1 x)
(+.f64 (*.f64 -1 x) (*.f64 1/2 (/.f64 1 x)))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x))))
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
Outputs
1
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 -1))))
(fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1))
(fma.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 -1)) (sqrt.f64 -1))
(fma.f64 1/2 (*.f64 x (/.f64 x (sqrt.f64 -1))) (sqrt.f64 -1))
(+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 -1)))))
(+.f64 (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (sqrt.f64 -1)) (*.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))))
(fma.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 -1)) (fma.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)) (sqrt.f64 -1)))
(+.f64 (sqrt.f64 -1) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 -1))) (+.f64 1/2 (/.f64 (*.f64 x x) 8))))
(+.f64 (*.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
(fma.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3)) (+.f64 (sqrt.f64 -1) (fma.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 -1)) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
(+.f64 (sqrt.f64 -1) (+.f64 (fma.f64 1/2 (/.f64 x (/.f64 (sqrt.f64 -1) x)) (/.f64 (*.f64 1/16 (pow.f64 x 6)) (pow.f64 (sqrt.f64 -1) 5))) (*.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(fma.f64 1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)) (fma.f64 1/2 (/.f64 (*.f64 x x) (sqrt.f64 -1)) (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)) (sqrt.f64 -1))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)) (sqrt.f64 -1)) (*.f64 (*.f64 x (/.f64 x (sqrt.f64 -1))) (+.f64 1/2 (/.f64 (*.f64 x x) 8))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (/.f64 1/2 x))
(+.f64 x (/.f64 -1/2 x))
(-.f64 x (+.f64 (*.f64 1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (/.f64 1/2 x) (/.f64 1/8 (pow.f64 x 3))))
(-.f64 (-.f64 x (/.f64 1/8 (pow.f64 x 3))) (/.f64 1/2 x))
(+.f64 x (-.f64 (/.f64 -1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
(-.f64 x (+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(-.f64 x (+.f64 (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))) (/.f64 1/8 (pow.f64 x 3))))
(-.f64 (-.f64 (-.f64 x (/.f64 1/8 (pow.f64 x 3))) (/.f64 1/2 x)) (/.f64 1/16 (pow.f64 x 5)))
(+.f64 x (-.f64 (-.f64 (/.f64 -1/8 (pow.f64 x 3)) (/.f64 1/2 x)) (/.f64 1/16 (pow.f64 x 5))))
(+.f64 (+.f64 x (-.f64 (/.f64 -1/8 (pow.f64 x 3)) (/.f64 1/2 x))) (/.f64 -1/16 (pow.f64 x 5)))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (*.f64 -1 x) (*.f64 1/2 (/.f64 1 x)))
(fma.f64 -1 x (/.f64 1/2 x))
(-.f64 (/.f64 1/2 x) x)
(+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (neg.f64 x)))
(+.f64 (/.f64 1/2 x) (-.f64 (/.f64 1/8 (pow.f64 x 3)) x))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x))))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/16 (pow.f64 x 5)) (+.f64 (/.f64 1/8 (pow.f64 x 3)) (neg.f64 x))))
(+.f64 (/.f64 1/2 x) (+.f64 (/.f64 1/16 (pow.f64 x 5)) (-.f64 (/.f64 1/8 (pow.f64 x 3)) x)))
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x 1))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/2 x 1))
(fma.f64 x (*.f64 x -1/8) (fma.f64 1/2 x 1))
(fma.f64 x (fma.f64 x -1/8 1/2) 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (+.f64 (fma.f64 1/2 x 1) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 x (*.f64 x -1/8) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 x (fma.f64 x -1/8 1/2) (fma.f64 1/16 (pow.f64 x 3) 1))

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.3b
(cbrt.f64 (+.f64 x 1))
✓0.3b
(cbrt.f64 (sqrt.f64 (+.f64 x 1)))
✓31.1b
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
Compiler

Compiled 37 to 24 computations (35.1% saved)

series15.0ms (0.3%)

Counts
3 → 17
Calls

9 calls:

TimeVariablePointExpression
7.0ms
x
@-inf
(cbrt.f64 (sqrt.f64 (+.f64 x 1)))
3.0ms
x
@inf
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
2.0ms
x
@-inf
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
1.0ms
x
@0
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
1.0ms
x
@inf
(cbrt.f64 (sqrt.f64 (+.f64 x 1)))

rewrite91.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
767×pow1_binary64
714×log1p-expm1-u_binary64
714×expm1-log1p-u_binary64
713×add-log-exp_binary64
693×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01035
120024
2239724
Stop Event
1×node limit
Counts
3 → 67
Calls
Call 1
Inputs
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
(cbrt.f64 (sqrt.f64 (+.f64 x 1)))
(cbrt.f64 (+.f64 x 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) 0) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 x 1) (-.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (+.f64 x 1) x) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 1/6)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)) (cbrt.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6) (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 2)) (sqrt.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 1/3) (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x 1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 x) 1/2) 1/3))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cbrt.f64 (+.f64 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/6) (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (*.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)) (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 2) (cbrt.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6) (*.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 1/6) (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 1/3) (cbrt.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (+.f64 x 1) 1/6) (cbrt.f64 (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (pow.f64 (+.f64 x 1) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (+.f64 1 (pow.f64 x 3))) (cbrt.f64 (fma.f64 x x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (fma.f64 x x -1)) (cbrt.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1)) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) 1/3))))))

simplify93.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
717×fma-def_binary64
327×distribute-rgt-out_binary64
309×times-frac_binary64
295×associate-*l*_binary64
260×associate-*r*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
066395
1179372
2464303
31337245
44754225
57031225
Stop Event
1×node limit
Counts
84 → 94
Calls
Call 1
Inputs
1
1
(+.f64 1 (*.f64 1/6 x))
(+.f64 1 (+.f64 (*.f64 1/6 x) (*.f64 -5/72 (pow.f64 x 2))))
(+.f64 (*.f64 55/1296 (pow.f64 x 3)) (+.f64 1 (+.f64 (*.f64 1/6 x) (*.f64 -5/72 (pow.f64 x 2)))))
(pow.f64 x 1/6)
(+.f64 (pow.f64 x 1/6) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)))
(+.f64 (pow.f64 x 1/6) (+.f64 (*.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))))
(+.f64 (*.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6)) (+.f64 (pow.f64 x 1/6) (+.f64 (*.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)))))
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (*.f64 -5/72 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(+.f64 (*.f64 -5/72 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (*.f64 55/1296 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
1
(+.f64 1 (*.f64 1/3 x))
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (*.f64 1/3 x)))
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 5/81 (pow.f64 x 3)) (*.f64 1/3 x))))
Outputs
1
1
(+.f64 1 (*.f64 1/6 x))
(fma.f64 1/6 x 1)
(+.f64 1 (+.f64 (*.f64 1/6 x) (*.f64 -5/72 (pow.f64 x 2))))
(+.f64 1 (fma.f64 1/6 x (*.f64 -5/72 (*.f64 x x))))
(+.f64 (fma.f64 1/6 x 1) (*.f64 (*.f64 -5/72 x) x))
(fma.f64 1/6 x (fma.f64 x (*.f64 x -5/72) 1))
(fma.f64 x (fma.f64 x -5/72 1/6) 1)
(+.f64 (*.f64 55/1296 (pow.f64 x 3)) (+.f64 1 (+.f64 (*.f64 1/6 x) (*.f64 -5/72 (pow.f64 x 2)))))
(fma.f64 55/1296 (pow.f64 x 3) (+.f64 1 (fma.f64 1/6 x (*.f64 -5/72 (*.f64 x x)))))
(+.f64 (fma.f64 1/6 x (*.f64 (*.f64 -5/72 x) x)) (fma.f64 55/1296 (pow.f64 x 3) 1))
(fma.f64 55/1296 (pow.f64 x 3) (fma.f64 1/6 x (fma.f64 x (*.f64 x -5/72) 1)))
(fma.f64 x (fma.f64 x -5/72 1/6) (fma.f64 55/1296 (pow.f64 x 3) 1))
(pow.f64 x 1/6)
(+.f64 (pow.f64 x 1/6) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)))
(fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (pow.f64 x 1/6))
(+.f64 (pow.f64 x 1/6) (+.f64 (*.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))))
(+.f64 (pow.f64 x 1/6) (fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))))
(fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (pow.f64 x 1/6)))
(fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (pow.f64 x 1/6)))
(+.f64 (*.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6)) (+.f64 (pow.f64 x 1/6) (+.f64 (*.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6)) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)))))
(fma.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (+.f64 (pow.f64 x 1/6) (fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6)))))
(+.f64 (fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (*.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6))) (fma.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (pow.f64 x 1/6)))
(fma.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (pow.f64 x 1/6))))
(fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/6) (fma.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 1/6) (pow.f64 x 1/6))))
(exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 x 1/6)
(+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))
(fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(fma.f64 1/6 (/.f64 (*.f64 (pow.f64 -1 1/6) (pow.f64 (/.f64 -1 x) -1/6)) x) (*.f64 (pow.f64 -1 1/6) (pow.f64 (/.f64 -1 x) -1/6)))
(*.f64 (+.f64 (/.f64 1/6 x) 1) (pow.f64 (exp.f64 1/6) (log.f64 x)))
(*.f64 (+.f64 1 (/.f64 1/6 x)) (pow.f64 x 1/6))
(+.f64 (*.f64 -5/72 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(fma.f64 -5/72 (/.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (+.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x))))
(fma.f64 -5/72 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))
(fma.f64 (pow.f64 (/.f64 -1 x) -1/6) (pow.f64 -1 1/6) (*.f64 (/.f64 (*.f64 (pow.f64 -1 1/6) (pow.f64 (/.f64 -1 x) -1/6)) x) (+.f64 1/6 (/.f64 -5/72 x))))
(fma.f64 (/.f64 (pow.f64 (exp.f64 1/6) (log.f64 x)) x) (+.f64 1/6 (/.f64 -5/72 x)) (pow.f64 (exp.f64 1/6) (log.f64 x)))
(fma.f64 (/.f64 (pow.f64 x 1/6) x) (+.f64 1/6 (/.f64 -5/72 x)) (pow.f64 x 1/6))
(+.f64 (*.f64 -5/72 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (+.f64 (*.f64 55/1296 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/6 (/.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
(fma.f64 -5/72 (/.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (fma.f64 55/1296 (/.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (+.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))))
(fma.f64 -5/72 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (fma.f64 55/1296 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (fma.f64 1/6 (/.f64 (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 1/6) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))
(fma.f64 55/1296 (/.f64 (*.f64 (pow.f64 -1 1/6) (pow.f64 (/.f64 -1 x) -1/6)) (pow.f64 x 3)) (fma.f64 (pow.f64 (/.f64 -1 x) -1/6) (pow.f64 -1 1/6) (*.f64 (/.f64 (*.f64 (pow.f64 -1 1/6) (pow.f64 (/.f64 -1 x) -1/6)) x) (+.f64 1/6 (/.f64 -5/72 x)))))
(+.f64 (pow.f64 (exp.f64 1/6) (log.f64 x)) (*.f64 (/.f64 (pow.f64 (exp.f64 1/6) (log.f64 x)) x) (+.f64 (+.f64 1/6 (/.f64 55/1296 (*.f64 x x))) (/.f64 -5/72 x))))
(+.f64 (pow.f64 x 1/6) (*.f64 (/.f64 (pow.f64 x 1/6) x) (+.f64 1/6 (+.f64 (/.f64 -5/72 x) (/.f64 55/1296 (*.f64 x x))))))
1
(+.f64 1 (*.f64 1/3 x))
(+.f64 1 (*.f64 x 1/3))
(fma.f64 x 1/3 1)
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (*.f64 1/3 x)))
(fma.f64 -1/9 (*.f64 x x) (+.f64 1 (*.f64 x 1/3)))
(fma.f64 (*.f64 x x) -1/9 (fma.f64 x 1/3 1))
(fma.f64 x 1/3 (fma.f64 (*.f64 x x) -1/9 1))
(fma.f64 x (fma.f64 x -1/9 1/3) 1)
(+.f64 (*.f64 -1/9 (pow.f64 x 2)) (+.f64 1 (+.f64 (*.f64 5/81 (pow.f64 x 3)) (*.f64 1/3 x))))
(fma.f64 -1/9 (*.f64 x x) (+.f64 1 (fma.f64 5/81 (pow.f64 x 3) (*.f64 x 1/3))))
(+.f64 (fma.f64 (*.f64 x x) -1/9 (fma.f64 x 1/3 1)) (*.f64 (pow.f64 x 3) 5/81))
(fma.f64 x (*.f64 x -1/9) (fma.f64 x 1/3 (fma.f64 (pow.f64 x 3) 5/81 1)))
(fma.f64 x (fma.f64 x -1/9 1/3) (fma.f64 (pow.f64 x 3) 5/81 1))

eval407.0ms (7%)

Compiler

Compiled 15369 to 9980 computations (35.1% saved)

prune105.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New8406846
Fresh10010
Picked101
Done415
Total8557862
Error
0.1b
Counts
862 → 7
Alt Table
Click to see full alt table
StatusErrorProgram
31.9b
1
✓30.8b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
▶30.0b
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))))
▶30.1b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x)))
▶0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
▶31.6b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
▶31.6b
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
Compiler

Compiled 162 to 120 computations (25.9% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiled 28 to 18 computations (35.7% saved)

series2.0ms (0%)

Counts
1 → 1
Calls

3 calls:

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

rewrite58.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
905×pow1_binary64
845×log1p-expm1-u_binary64
845×expm1-log1p-u_binary64
844×add-log-exp_binary64
823×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0814
117814
2246614
Stop Event
1×node limit
Counts
1 → 22
Calls
Call 1
Inputs
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1) (pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 1 (+.f64 x (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (-.f64 x x))) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))))

simplify7.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
011
141
Stop Event
1×saturated
Counts
23 → 23
Calls
Call 1
Inputs
1
Outputs
1

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiled 23 to 14 computations (39.1% saved)

series1.0ms (0%)

Counts
1 → 2
Calls

3 calls:

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

rewrite54.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
676×pow1_binary64
631×add-log-exp_binary64
631×log1p-expm1-u_binary64
631×expm1-log1p-u_binary64
617×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
11329
217479
Stop Event
1×node limit
Counts
1 → 37
Calls
Call 1
Inputs
(-.f64 (*.f64 1/2 x) (sqrt.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 x) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 x) (*.f64 (neg.f64 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 x)) (*.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) 2) (cbrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) (sqrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 (pow.f64 x 3) 1/8) (pow.f64 x 3/2)) (/.f64 1 (+.f64 (pow.f64 (*.f64 1/2 x) 2) (+.f64 x (*.f64 1/2 (pow.f64 x 3/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (*.f64 1/2 x) 2) x) (/.f64 1 (fma.f64 1/2 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (*.f64 1/2 x)) (pow.f64 x 1/4)) (-.f64 (sqrt.f64 (*.f64 1/2 x)) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (*.f64 1/2 x) 2) (+.f64 x (*.f64 1/2 (pow.f64 x 3/2)))) (-.f64 (*.f64 (pow.f64 x 3) 1/8) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 1/2 x (sqrt.f64 x)) (-.f64 (pow.f64 (*.f64 1/2 x) 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 x 3) 1/8) (pow.f64 x 3/2)) (+.f64 (pow.f64 (*.f64 1/2 x) 2) (+.f64 x (*.f64 1/2 (pow.f64 x 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 1/2 x) 2) x) (fma.f64 1/2 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 (pow.f64 x 3) 1/8) (pow.f64 x 3/2))) (neg.f64 (+.f64 (pow.f64 (*.f64 1/2 x) 2) (+.f64 x (*.f64 1/2 (pow.f64 x 3/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 1/2 x) 2) x)) (neg.f64 (fma.f64 1/2 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 x 3) 1/8) (pow.f64 (neg.f64 (sqrt.f64 x)) 3)) (+.f64 (pow.f64 (*.f64 1/2 x) 2) (-.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (*.f64 (*.f64 1/2 x) (neg.f64 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 1/2 x) 2) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) (-.f64 (*.f64 1/2 x) (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 x (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/2 (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/2 x) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 x)) 2) (cbrt.f64 (*.f64 1/2 x)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/2 x)) (sqrt.f64 (*.f64 1/2 x)) (neg.f64 (sqrt.f64 x)))))))

simplify7.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
048
158
Stop Event
1×saturated
Counts
39 → 38
Calls
Call 1
Inputs
(*.f64 1/2 x)
(*.f64 1/2 x)
Outputs
(*.f64 1/2 x)
(*.f64 1/2 x)

localize20.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
✓0.1b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
1.7b
(+.f64 x (-.f64 1 x))
Compiler

Compiled 44 to 29 computations (34.1% saved)

series4.0ms (0.1%)

Counts
2 → 6
Calls

6 calls:

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

rewrite79.0ms (1.4%)

Algorithm
1×batch-egg-rewrite
Rules
715×fma-def_binary64
609×log-prod_binary64
404×fma-neg_binary64
229×expm1-udef_binary64
229×log1p-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01129
126229
2398429
Stop Event
1×node limit
Counts
2 → 126
Calls
Call 1
Inputs
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
Outputs
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1/2)) (pow.f64 (cbrt.f64 (*.f64 x 1/2)) 2) (+.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x 1/2)) (pow.f64 (cbrt.f64 (*.f64 x 1/2)) 2) (*.f64 (+.f64 1 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 1/2)) 2) (cbrt.f64 (*.f64 x 1/2)) (+.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 1/2)) 2) (cbrt.f64 (*.f64 x 1/2)) (*.f64 (+.f64 1 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 1/2)) 2) (*.f64 (cbrt.f64 (*.f64 x 1/2)) 1) (+.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 1/2)) 2) (*.f64 (cbrt.f64 (*.f64 x 1/2)) 1) (*.f64 (+.f64 1 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x 1/2 1)) (sqrt.f64 (fma.f64 x 1/2 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (fma.f64 x 1/2 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/2)) (sqrt.f64 (*.f64 x 1/2)) (+.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/2)) (sqrt.f64 (*.f64 x 1/2)) (*.f64 (+.f64 1 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/2)) (*.f64 (sqrt.f64 (*.f64 x 1/2)) 1) (+.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/2)) (*.f64 (sqrt.f64 (*.f64 x 1/2)) 1) (*.f64 (+.f64 1 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 1/8 (pow.f64 x 3) 1) (/.f64 1 (-.f64 (fma.f64 (*.f64 x x) 1/4 1) (*.f64 x 1/2))) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 (*.f64 x x) 1/4 -1) (/.f64 1 (fma.f64 x 1/2 -1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 x))) (cbrt.f64 (+.f64 1 (sqrt.f64 x)))) (cbrt.f64 (+.f64 1 (sqrt.f64 x))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 x 1/4)) (hypot.f64 1 (pow.f64 x 1/4)) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (sqrt.f64 (cbrt.f64 x)) (fma.f64 x 1/2 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (sqrt.f64 x) (fma.f64 x 1/2 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) 1/2) (pow.f64 (cbrt.f64 x) 1/2) (fma.f64 x 1/2 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) (+.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (sqrt.f64 x)) (sqrt.f64 x) (*.f64 (+.f64 1 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (+.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 1/2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 (+.f64 1 (sqrt.f64 x)) 1))))))

simplify10.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0718
11018
Stop Event
1×saturated
Counts
132 → 130
Calls
Call 1
Inputs
1
(/.f64 2 x)
(/.f64 2 x)
1
(*.f64 1/2 x)
(*.f64 1/2 x)
Outputs
1
(/.f64 2 x)
(/.f64 2 x)
1
(*.f64 1/2 x)
(*.f64 x 1/2)
(*.f64 1/2 x)
(*.f64 x 1/2)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x))
✓0.0b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x)))
1.7b
(+.f64 x (-.f64 1 x))
✓2.6b
(exp.f64 (*.f64 (log1p.f64 x) 1/2))
Compiler

Compiled 47 to 27 computations (42.6% saved)

series17.0ms (0.3%)

Counts
3 → 14
Calls

9 calls:

TimeVariablePointExpression
4.0ms
x
@inf
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x)))
4.0ms
x
@inf
(+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x))
4.0ms
x
@-inf
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x)))
2.0ms
x
@-inf
(+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x))
1.0ms
x
@-inf
(exp.f64 (*.f64 (log1p.f64 x) 1/2))

rewrite134.0ms (2.3%)

Algorithm
1×batch-egg-rewrite
Rules
603×log-prod_binary64
554×fma-def_binary64
330×pow2_binary64
268×fma-neg_binary64
227×pow1/3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01243
126428
2381228
Stop Event
1×node limit
Counts
3 → 210
Calls
Call 1
Inputs
(exp.f64 (*.f64 (log1p.f64 x) 1/2))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x)))
(+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (hypot.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (hypot.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 x))) (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x))))))) (#(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 pow.f64 (hypot.f64 1 (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (*.f64 (log1p.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/2) (log1p.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 1 (sqrt.f64 x))) 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 (+.f64 x 1) 1/2)))) (#(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 pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (*.f64 (log1p.f64 x) 1/2)) 2)) (cbrt.f64 (*.f64 (log1p.f64 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (*.f64 (log1p.f64 x) 1/2))) (sqrt.f64 (*.f64 (log1p.f64 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (hypot.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 1 (sqrt.f64 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (hypot.f64 1 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (hypot.f64 1 (sqrt.f64 x)) (*.f64 -1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (hypot.f64 1 (sqrt.f64 x)) (*.f64 (neg.f64 (cbrt.f64 x)) (cbrt.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (hypot.f64 1 (sqrt.f64 x)) (*.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (+.f64 x 1) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (/.f64 x (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (-.f64 x x)) (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (cbrt.f64 (pow.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 2)) (cbrt.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1 (-.f64 x x))) 2) (*.f64 (cbrt.f64 (-.f64 1 (-.f64 x x))) (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (sqrt.f64 (-.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (-.f64 x x))) (*.f64 (sqrt.f64 (-.f64 1 (-.f64 x x))) (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (-.f64 1 (-.f64 x x))) (/.f64 1 (neg.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (-.f64 1 (-.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 1 (-.f64 x x))) 2) 1) (/.f64 (cbrt.f64 (-.f64 1 (-.f64 x x))) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (-.f64 x x))) 1) (/.f64 (sqrt.f64 (-.f64 1 (-.f64 x x))) (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 2)) (/.f64 (-.f64 1 (-.f64 x x)) (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule 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simplify65.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
450×fma-def_binary64
309×times-frac_binary64
290×distribute-rgt-out_binary64
236×associate-/l*_binary64
217×fma-neg_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
052301
1135280
2336227
3987186
43711170
56057156
Stop Event
1×node limit
Counts
224 → 230
Calls
Call 1
Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(+.f64 (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))
(+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))))
(exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (+.f64 (exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 -1/8 (/.f64 (exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (+.f64 (*.f64 1/16 (/.f64 (exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 -1/8 (/.f64 (exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))))
1
1
Outputs
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x -1/8) 1))
(fma.f64 x (fma.f64 x -1/8 1/2) 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (+.f64 (fma.f64 1/2 x 1) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x -1/8) (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 (*.f64 x x) (fma.f64 x 1/16 -1/8) 1))
(fma.f64 x (fma.f64 x -1/8 1/2) (fma.f64 1/16 (pow.f64 x 3) 1))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x))
(fma.f64 1/2 (pow.f64 x -1/2) (sqrt.f64 x))
(+.f64 (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))
(fma.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))
(fma.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (fma.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 x)))
(fma.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/2 (pow.f64 x -1/2) (sqrt.f64 x)))
(+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))))
(fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))))
(fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x))))
(fma.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (fma.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (sqrt.f64 x))))
(fma.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 1/2 (pow.f64 x -1/2) (sqrt.f64 x))))
(exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(sqrt.f64 x)
(+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x))
(fma.f64 1/2 (pow.f64 x -1/2) (sqrt.f64 x))
(+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (+.f64 (exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 -1/8 (/.f64 (exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (pow.f64 (exp.f64 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (*.f64 -1/8 (/.f64 (pow.f64 (exp.f64 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.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 -1/8 (/.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 (pow.f64 (/.f64 -1 x) -1/2) (pow.f64 -1 1/2) (*.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/2) (pow.f64 -1 1/2)) x) (+.f64 (/.f64 -1/8 x) 1/2)))
(fma.f64 (/.f64 (sqrt.f64 (exp.f64 (log.f64 x))) x) (+.f64 1/2 (/.f64 -1/8 x)) (sqrt.f64 (exp.f64 (log.f64 x))))
(fma.f64 (/.f64 (sqrt.f64 x) x) (+.f64 1/2 (/.f64 -1/8 x)) (sqrt.f64 x))
(fma.f64 (pow.f64 x -1/2) (+.f64 1/2 (/.f64 -1/8 x)) (sqrt.f64 x))
(+.f64 (*.f64 1/2 (/.f64 (exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (+.f64 (*.f64 1/16 (/.f64 (exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 -1/8 (/.f64 (exp.f64 (*.f64 1/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))))
(fma.f64 1/2 (/.f64 (pow.f64 (exp.f64 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (fma.f64 1/16 (/.f64 (pow.f64 (exp.f64 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (+.f64 (pow.f64 (exp.f64 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 -1/8 (/.f64 (pow.f64 (exp.f64 1/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.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 1/16 (/.f64 (pow.f64 (exp.f64 1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (fma.f64 -1/8 (/.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 (*.f64 (pow.f64 (/.f64 -1 x) -1/2) (pow.f64 -1 1/2)) x) (fma.f64 (pow.f64 (/.f64 -1 x) -1/2) (pow.f64 -1 1/2) (*.f64 (*.f64 (/.f64 (pow.f64 (/.f64 -1 x) -1/2) x) (/.f64 (pow.f64 -1 1/2) x)) (+.f64 -1/8 (/.f64 1/16 x)))))
(+.f64 (sqrt.f64 (exp.f64 (log.f64 x))) (*.f64 (/.f64 (sqrt.f64 (exp.f64 (log.f64 x))) x) (+.f64 (+.f64 1/2 (/.f64 -1/8 x)) (/.f64 1/16 (*.f64 x x)))))
(+.f64 (sqrt.f64 x) (*.f64 (/.f64 (sqrt.f64 x) x) (+.f64 1/2 (+.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x))))))
(+.f64 (sqrt.f64 x) (fma.f64 (pow.f64 x -1/2) (+.f64 1/2 (/.f64 -1/8 x)) (/.f64 1/16 (pow.f64 x 5/2))))
1
1

localize55.0ms (0.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))
✓0.0b
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))))
✓0.0b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))
1.7b
(+.f64 x (-.f64 1 x))
Compiler

Compiled 94 to 59 computations (37.2% saved)

series14.0ms (0.2%)

Counts
3 → 29
Calls

9 calls:

TimeVariablePointExpression
5.0ms
x
@inf
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))))
2.0ms
x
@0
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))))
2.0ms
x
@-inf
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))))
1.0ms
x
@0
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))
1.0ms
x
@inf
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))

rewrite101.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
527×fma-neg_binary64
326×expm1-udef_binary64
326×log1p-udef_binary64
205×add-sqr-sqrt_binary64
200×pow1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01674
139274
2613174
Stop Event
1×node limit
Counts
3 → 116
Calls
Call 1
Inputs
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))))
(+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (+.f64 x 1) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (/.f64 x (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (-.f64 1 x)) (/.f64 1 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))) (pow.f64 (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))) 2) (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) 2) (*.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) (hypot.f64 (pow.f64 x 3/4) (pow.f64 (+.f64 x 1) 3/4))) (/.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) (hypot.f64 (pow.f64 x 3/4) (pow.f64 (+.f64 x 1) 3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) (*.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) (/.f64 1 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (+.f64 x (-.f64 1 x))) (/.f64 1 (neg.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (+.f64 x (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) 2) 1) (/.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) 1) (/.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) 2)) (/.f64 (+.f64 x (-.f64 1 x)) (cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) 2) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) 2)) (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (+.f64 x 1) 3) (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (/.f64 (pow.f64 x 3) (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) 2) (cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 (pow.f64 x 3/4) (pow.f64 (+.f64 x 1) 3/4)) (hypot.f64 (pow.f64 x 3/4) (pow.f64 (+.f64 x 1) 3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 x 1) 9/2) (pow.f64 x 9/2)) (/.f64 1 (-.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x 1) 3)) (pow.f64 (fma.f64 x x x) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (+.f64 x 1) 3) (pow.f64 x 3)) (/.f64 1 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x 1) 3)) (pow.f64 (fma.f64 x x x) 3/2)) (+.f64 (pow.f64 (+.f64 x 1) 9/2) (pow.f64 x 9/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) (-.f64 (pow.f64 (+.f64 x 1) 3) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x 1) 9/2) (pow.f64 x 9/2)) (-.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x 1) 3)) (pow.f64 (fma.f64 x x x) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x 1) 9/2) (pow.f64 x 9/2)) (+.f64 (pow.f64 x 3) (-.f64 (pow.f64 (+.f64 x 1) 3) (pow.f64 (fma.f64 x x x) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x 1) 3) (pow.f64 x 3)) (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 x 1) 9/2) (pow.f64 x 9/2))) (neg.f64 (-.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x 1) 3)) (pow.f64 (fma.f64 x x x) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 x 1) 3) (pow.f64 x 3))) (neg.f64 (-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 3) (pow.f64 (+.f64 x 1) 3)) (-.f64 (pow.f64 x 3/2) (pow.f64 (+.f64 x 1) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 (pow.f64 x 3/4) (pow.f64 (+.f64 x 1) 3/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (sqrt.f64 x) (pow.f64 (+.f64 x 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 x 3/2) (pow.f64 (+.f64 x 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x 1) (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (pow.f64 x 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/4) (pow.f64 x 3/4) (pow.f64 (+.f64 x 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 3/4) (pow.f64 (+.f64 x 1) 3/4) (pow.f64 x 3/2))))))

simplify71.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
683×associate-/l*_binary64
496×fma-def_binary64
369×associate-/l/_binary64
343×distribute-rgt-in_binary64
325×distribute-lft-in_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01401138
14031087
21156955
34103792
Stop Event
1×node limit
Counts
145 → 168
Calls
Call 1
Inputs
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))))
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (+.f64 (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (*.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (pow.f64 x 2))))
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (+.f64 (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (+.f64 (*.f64 (-.f64 (+.f64 (*.f64 9/16 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 1/16 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (*.f64 3/2 (/.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (+.f64 1 (pow.f64 x 3/2))))) (pow.f64 x 3)) (*.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (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 -1 (/.f64 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2))) (+.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 (/.f64 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -3/4 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (+.f64 (*.f64 -1/64 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -9/128 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (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 1/2 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(-.f64 (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(-.f64 (+.f64 (*.f64 3/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(-.f64 (+.f64 (*.f64 3/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (+.f64 (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))) (*.f64 7/128 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))))))
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(*.f64 3/2 (/.f64 x (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
(-.f64 (*.f64 3/2 (/.f64 x (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 5/8 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))
(+.f64 1 (pow.f64 x 3/2))
(+.f64 1 (+.f64 (pow.f64 x 3/2) (*.f64 3/2 x)))
(+.f64 1 (+.f64 (*.f64 3/8 (pow.f64 x 2)) (+.f64 (pow.f64 x 3/2) (*.f64 3/2 x))))
(+.f64 (*.f64 -1/16 (pow.f64 x 3)) (+.f64 1 (+.f64 (*.f64 3/8 (pow.f64 x 2)) (+.f64 (pow.f64 x 3/2) (*.f64 3/2 x)))))
(*.f64 2 (sqrt.f64 (pow.f64 x 3)))
(+.f64 (*.f64 2 (sqrt.f64 (pow.f64 x 3))) (*.f64 3/2 (sqrt.f64 x)))
(+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (*.f64 2 (sqrt.f64 (pow.f64 x 3))) (*.f64 3/2 (sqrt.f64 x))))
(+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (*.f64 2 (sqrt.f64 (pow.f64 x 3))) (+.f64 (*.f64 3/2 (sqrt.f64 x)) (*.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(*.f64 2 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(+.f64 (*.f64 2 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (*.f64 2 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(+.f64 (*.f64 2 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (+.f64 (*.f64 -1/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
Outputs
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))))
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (/.f64 (*.f64 -3/2 x) (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))
(fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (/.f64 1 (+.f64 1 (pow.f64 x 3/2))))
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (+.f64 (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (*.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (pow.f64 x 2))))
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (*.f64 (-.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (*.f64 x x))))
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (*.f64 x (*.f64 x (+.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 -3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))))))
(fma.f64 x (*.f64 x (+.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 -3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (/.f64 1 (+.f64 1 (pow.f64 x 3/2)))))
(fma.f64 x (*.f64 x (+.f64 (/.f64 9/4 (pow.f64 (hypot.f64 1 (pow.f64 x 3/4)) 6)) (/.f64 -3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (/.f64 1 (+.f64 1 (pow.f64 x 3/2)))))
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (+.f64 (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (+.f64 (*.f64 (-.f64 (+.f64 (*.f64 9/16 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 1/16 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (*.f64 3/2 (/.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (+.f64 1 (pow.f64 x 3/2))))) (pow.f64 x 3)) (*.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (pow.f64 x 2)))))
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (fma.f64 (+.f64 (/.f64 9/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (-.f64 (/.f64 1/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (*.f64 3/2 (/.f64 (-.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (+.f64 1 (pow.f64 x 3/2)))))) (pow.f64 x 3) (*.f64 (-.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (*.f64 x x)))))
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(fma.f64 3/8 (sqrt.f64 (/.f64 1 x)) (fma.f64 3/2 (sqrt.f64 x) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/16 (*.f64 (pow.f64 x 3/2) 2))))
(*.f64 2 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(*.f64 2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))
(*.f64 2 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(*.f64 (*.f64 2 (pow.f64 (/.f64 -1 x) -3/2)) (pow.f64 -1 3/2))
(*.f64 2 (pow.f64 (exp.f64 3/2) (log.f64 x)))
(+.f64 (*.f64 2 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(fma.f64 2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))
(fma.f64 2 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x)))
(fma.f64 3/2 (/.f64 (pow.f64 (/.f64 -1 x) -3/2) (/.f64 x (pow.f64 -1 3/2))) (*.f64 (*.f64 2 (pow.f64 (/.f64 -1 x) -3/2)) (pow.f64 -1 3/2)))
(*.f64 (pow.f64 (exp.f64 3/2) (log.f64 x)) (+.f64 2 (/.f64 3/2 x)))
(+.f64 (*.f64 2 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(fma.f64 2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (*.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x))))
(fma.f64 2 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)))))
(fma.f64 2 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) (*.f64 (/.f64 (pow.f64 (/.f64 -1 x) -3/2) (/.f64 x (pow.f64 -1 3/2))) (+.f64 (/.f64 3/8 x) 3/2)))
(fma.f64 2 (pow.f64 (exp.f64 3/2) (log.f64 x)) (*.f64 (/.f64 (pow.f64 (exp.f64 3/2) (log.f64 x)) x) (+.f64 3/2 (/.f64 3/8 x))))
(+.f64 (*.f64 2 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))) (+.f64 (*.f64 -1/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
(fma.f64 2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 -1/16 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (*.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))))
(fma.f64 2 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 -1/16 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x))))))
(fma.f64 2 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) (fma.f64 -1/16 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) (pow.f64 x 3)) (*.f64 (/.f64 (pow.f64 (/.f64 -1 x) -3/2) (/.f64 x (pow.f64 -1 3/2))) (+.f64 (/.f64 3/8 x) 3/2))))
(fma.f64 2 (pow.f64 (exp.f64 3/2) (log.f64 x)) (*.f64 (/.f64 (pow.f64 (exp.f64 3/2) (log.f64 x)) x) (+.f64 3/2 (+.f64 (/.f64 3/8 x) (/.f64 -1/16 (*.f64 x x))))))

eval458.0ms (7.9%)

Compiler

Compiled 24149 to 15292 computations (36.7% saved)

prune132.0ms (2.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New9827989
Fresh011
Picked101
Done235
Total98511996
Error
0.0b
Counts
996 → 11
Alt Table
Click to see full alt table
StatusErrorProgram
▶60.1b
(/.f64 2 x)
31.9b
1
✓30.8b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
▶2.1b
(/.f64 1 (+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x)))
✓31.6b
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
✓0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
▶17.4b
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 1 (+.f64 x (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x))))))
▶0.2b
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))
▶29.5b
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
0.3b
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)
0.8b
(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)
Compiler

Compiled 199 to 161 computations (19.1% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(pow.f64 (+.f64 x 1) 1/4)
✓0.0b
(+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x))
✓0.2b
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))
✓0.3b
(pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)
Compiler

Compiled 44 to 33 computations (25% saved)

series16.0ms (0.3%)

Counts
4 → 26
Calls

12 calls:

TimeVariablePointExpression
5.0ms
x
@-inf
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))
3.0ms
x
@inf
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))
1.0ms
x
@-inf
(pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)
1.0ms
x
@inf
(pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)
1.0ms
x
@-inf
(+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x))

rewrite80.0ms (1.4%)

Algorithm
1×batch-egg-rewrite
Rules
444×log-prod_binary64
406×fma-def_binary64
305×pow-prod-down_binary64
271×pow2_binary64
239×fma-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01141
125138
2311738
Stop Event
1×node limit
Counts
4 → 164
Calls
Call 1
Inputs
(pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))
(+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x))
(pow.f64 (+.f64 x 1) 1/4)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 1)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/6) (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 1)) (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 3/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 3/8) (pow.f64 (+.f64 x 1) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 x 1)) 5/6) (pow.f64 (+.f64 x 1) 1/12))))) (#(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 (hypot.f64 1 (pow.f64 x 3/2)) (hypot.f64 x (sqrt.f64 (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/2 (log1p.f64 x)))))) (#(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))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log1p.f64 x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (*.f64 1/2 (log1p.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/2 (log1p.f64 x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 x) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 1/4 (log1p.f64 x)) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 x) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 3) 1/3))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) -2)) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) -1/2) (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (sqrt.f64 (*.f64 x (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 (+.f64 x 1) x)) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) -2) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) -3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) -3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 1) 1))))))
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 x 1) 1/4))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (+.f64 x 1) 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 x 1) 1/4)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (+.f64 x 1) 1/4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (+.f64 x 1) 1/4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/6) (pow.f64 (+.f64 x 1) 1/12))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/12) (pow.f64 (+.f64 x 1) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/8) (pow.f64 (+.f64 x 1) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (+.f64 x 1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (+.f64 x 1) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (+.f64 x 1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (+.f64 x 1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/4 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/4 (log1p.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/4 (log1p.f64 x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log1p.f64 x)) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (*.f64 1/4 (log1p.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/8 (log1p.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 x) 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 1/4 (log1p.f64 x)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 x) 1/2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 x) 1/8) 2))))))

simplify70.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
600×associate-/r*_binary64
523×associate-*l/_binary64
430×fma-def_binary64
383×*-commutative_binary64
343×+-commutative_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0108744
1290703
2820558
32962426
47965386
Stop Event
1×node limit
Counts
190 → 205
Calls
Call 1
Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(+.f64 (*.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -3/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (*.f64 -3/16 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (*.f64 1/16 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))))))
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -7/64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (*.f64 3/64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (pow.f64 x 3))) (+.f64 (*.f64 -3/16 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (*.f64 1/16 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2)))))))
1
1
1
(+.f64 1 (*.f64 1/4 x))
(+.f64 1 (+.f64 (*.f64 -3/32 (pow.f64 x 2)) (*.f64 1/4 x)))
(+.f64 1 (+.f64 (*.f64 7/128 (pow.f64 x 3)) (+.f64 (*.f64 -3/32 (pow.f64 x 2)) (*.f64 1/4 x))))
(pow.f64 x 1/4)
(+.f64 (pow.f64 x 1/4) (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)))
(+.f64 (pow.f64 x 1/4) (+.f64 (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))))
(+.f64 (*.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4)) (+.f64 (pow.f64 x 1/4) (+.f64 (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(+.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/4 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 1/4 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (*.f64 -3/32 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 7/128 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (*.f64 1/4 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (*.f64 -3/32 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))))
Outputs
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 1))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x -1/8) 1))
(fma.f64 x (*.f64 x -1/8) (fma.f64 1/2 x 1))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (+.f64 (fma.f64 1/2 x 1) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x -1/8) (fma.f64 1/16 (pow.f64 x 3) 1)))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x))
(+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (+.f64 (sqrt.f64 x) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16))))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16 (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 x)))
(+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8))
(+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)) (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (*.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -3/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (sqrt.f64 x) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))))
(fma.f64 7/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -3/64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (+.f64 (sqrt.f64 x) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16))))))
(+.f64 (+.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 1/16) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 x))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16 (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 1/16 (+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8)))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 1/16 (+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)) (*.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)
(sqrt.f64 x)
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))
(fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) x) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))
(fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))
(fma.f64 1/2 (/.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) x) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2))
(*.f64 (+.f64 (/.f64 1/2 x) 1) (sqrt.f64 (exp.f64 (log.f64 x))))
(*.f64 (+.f64 (/.f64 1/2 x) 1) (sqrt.f64 x))
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (*.f64 -3/16 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (*.f64 1/16 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))))))
(+.f64 (fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) x) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)) (*.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (*.f64 x x)) -1/8))
(fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x) (fma.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (*.f64 x x)) -1/8 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)))
(fma.f64 1/2 (/.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) x) (fma.f64 -1/8 (/.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (*.f64 x x)) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)))
(+.f64 (sqrt.f64 (exp.f64 (log.f64 x))) (*.f64 (/.f64 (sqrt.f64 (exp.f64 (log.f64 x))) x) (+.f64 1/2 (/.f64 -1/8 x))))
(+.f64 (sqrt.f64 x) (*.f64 (/.f64 (sqrt.f64 x) x) (+.f64 1/2 (/.f64 -1/8 x))))
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x)) (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -7/64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) (*.f64 3/64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))) (pow.f64 x 3))) (+.f64 (*.f64 -3/16 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2))) (*.f64 1/16 (/.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 x 2)))))))
(+.f64 (fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) x) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)) (fma.f64 -1 (/.f64 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) -1/16) (pow.f64 x 3)) (*.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (*.f64 x x)) -1/8)))
(+.f64 (fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (fma.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (*.f64 x x)) -1/8 (neg.f64 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (/.f64 (pow.f64 x 3) -1/16)))))
(+.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (fma.f64 1/2 (/.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) x) (*.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (*.f64 x x)) (-.f64 -1/8 (/.f64 -1/16 x)))))
(+.f64 (*.f64 (+.f64 (/.f64 1/2 x) 1) (sqrt.f64 (exp.f64 (log.f64 x)))) (*.f64 (/.f64 (sqrt.f64 (exp.f64 (log.f64 x))) (*.f64 x x)) (+.f64 -1/8 (/.f64 1/16 x))))
(+.f64 (*.f64 (+.f64 (/.f64 1/2 x) 1) (sqrt.f64 x)) (/.f64 (*.f64 (sqrt.f64 x) (+.f64 -1/8 (/.f64 1/16 x))) (*.f64 x x)))
1
1
1
(+.f64 1 (*.f64 1/4 x))
(+.f64 1 (*.f64 x 1/4))
(fma.f64 x 1/4 1)
(+.f64 1 (+.f64 (*.f64 -3/32 (pow.f64 x 2)) (*.f64 1/4 x)))
(+.f64 1 (fma.f64 -3/32 (*.f64 x x) (*.f64 x 1/4)))
(+.f64 1 (fma.f64 (*.f64 x x) -3/32 (*.f64 x 1/4)))
(fma.f64 x 1/4 (fma.f64 x (*.f64 x -3/32) 1))
(+.f64 1 (+.f64 (*.f64 7/128 (pow.f64 x 3)) (+.f64 (*.f64 -3/32 (pow.f64 x 2)) (*.f64 1/4 x))))
(+.f64 1 (fma.f64 7/128 (pow.f64 x 3) (fma.f64 -3/32 (*.f64 x x) (*.f64 x 1/4))))
(+.f64 1 (fma.f64 (pow.f64 x 3) 7/128 (fma.f64 (*.f64 x x) -3/32 (*.f64 x 1/4))))
(fma.f64 (pow.f64 x 3) 7/128 (fma.f64 x 1/4 (fma.f64 x (*.f64 x -3/32) 1)))
(pow.f64 x 1/4)
(+.f64 (pow.f64 x 1/4) (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)))
(fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (pow.f64 x 1/4))
(+.f64 (pow.f64 x 1/4) (+.f64 (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))))
(+.f64 (pow.f64 x 1/4) (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))))
(fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (fma.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4) (pow.f64 x 1/4)))
(+.f64 (*.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4)) (+.f64 (pow.f64 x 1/4) (+.f64 (*.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)))))
(fma.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (+.f64 (pow.f64 x 1/4) (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4)))))
(+.f64 (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (*.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4))) (fma.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (pow.f64 x 1/4)))
(fma.f64 7/128 (pow.f64 (/.f64 1 (pow.f64 x 11)) 1/4) (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (fma.f64 -3/32 (pow.f64 (/.f64 1 (pow.f64 x 7)) 1/4) (pow.f64 x 1/4))))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 x 1/4)
(+.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 1/4 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (/.f64 (*.f64 1/4 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) x))
(fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(fma.f64 1/4 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) x) (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)))
(*.f64 (+.f64 (/.f64 1/4 x) 1) (pow.f64 (exp.f64 1/4) (log.f64 x)))
(*.f64 (+.f64 (/.f64 1/4 x) 1) (pow.f64 x 1/4))
(+.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 1/4 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (*.f64 -3/32 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))))
(+.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (*.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)))))
(+.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)))))
(fma.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4) (*.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) x) (+.f64 1/4 (/.f64 -3/32 x))))
(+.f64 (pow.f64 (exp.f64 1/4) (log.f64 x)) (*.f64 (/.f64 (pow.f64 (exp.f64 1/4) (log.f64 x)) x) (+.f64 1/4 (/.f64 -3/32 x))))
(+.f64 (pow.f64 x 1/4) (*.f64 (/.f64 (pow.f64 x 1/4) x) (+.f64 1/4 (/.f64 -3/32 x))))
(+.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 7/128 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (*.f64 1/4 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)) (*.f64 -3/32 (/.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))))))
(+.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 7/128 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x) (*.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x))))))
(+.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 7/128 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (fma.f64 1/4 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (*.f64 -3/32 (/.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x))))))
(fma.f64 7/128 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) (pow.f64 x 3)) (fma.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4) (*.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) x) (+.f64 1/4 (/.f64 -3/32 x)))))
(+.f64 (pow.f64 (exp.f64 1/4) (log.f64 x)) (*.f64 (/.f64 (pow.f64 (exp.f64 1/4) (log.f64 x)) x) (+.f64 1/4 (+.f64 (/.f64 -3/32 x) (/.f64 7/128 (*.f64 x x))))))
(+.f64 (pow.f64 x 1/4) (*.f64 (/.f64 (pow.f64 x 1/4) x) (+.f64 1/4 (+.f64 (/.f64 -3/32 x) (/.f64 7/128 (*.f64 x x))))))

localize3.0ms (0%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiled 17 to 13 computations (23.5% saved)

series2.0ms (0%)

Counts
1 → 0
Calls

3 calls:

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

rewrite53.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
399×pow1_binary64
386×add-sqr-sqrt_binary64
376×*-un-lft-identity_binary64
371×add-log-exp_binary64
371×log1p-expm1-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
056
1994
211014
Stop Event
1×node limit
Counts
1 → 46
Calls
Call 1
Inputs
(sqrt.f64 (/.f64 1 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 x -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (pow.f64 1 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (pow.f64 1 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 x)) (cbrt.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 x -1/2)) (sqrt.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (pow.f64 x -2))) (pow.f64 (*.f64 (/.f64 1 (cbrt.f64 x)) (pow.f64 x -1/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 -1) (pow.f64 (/.f64 1 (neg.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x -1/2)) (/.f64 1 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x -1/2)) (pow.f64 (*.f64 (cbrt.f64 (pow.f64 x -1/2)) (pow.f64 x -1/2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 (pow.f64 x -1/2))) (pow.f64 (*.f64 (sqrt.f64 (pow.f64 x -1/2)) (pow.f64 x -1/2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 -1/2) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) -1/2) (pow.f64 (pow.f64 (cbrt.f64 x) 2) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 x) 2) -1/2) (pow.f64 (cbrt.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (sqrt.f64 (pow.f64 x -1/2)) 3) 1/2) (sqrt.f64 (sqrt.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 x -1/2) (/.f64 1 (cbrt.f64 x))) 1/2) (sqrt.f64 (cbrt.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (/.f64 1 x) 3/2)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (/.f64 1 x) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 1 x) (/.f64 1 (cbrt.f64 x))) 1/3) (cbrt.f64 (cbrt.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (pow.f64 x -1/2))) 1/3) (sqrt.f64 (cbrt.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (pow.f64 x -1/2))) 2) 3) (cbrt.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) -1) (pow.f64 (sqrt.f64 (cbrt.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 -1) (sqrt.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/2) 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 (sqrt.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (pow.f64 x -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 x -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -1/2 (log.f64 x)))))))

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
46 → 46
Calls
Call 1
Inputs
Outputs

localize17.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x))
✓0.2b
(/.f64 1 (+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x)))
2.6b
(exp.f64 (*.f64 (log1p.f64 x) 1/2))
Compiler

Compiled 35 to 20 computations (42.9% saved)

series3.0ms (0%)

Counts
1 → 1
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(/.f64 1 (+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x)))
1.0ms
x
@inf
(/.f64 1 (+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x)))
0.0ms
x
@0
(/.f64 1 (+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x)))

rewrite57.0ms (1%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
01016
120414
2253014
Stop Event
1×node limit
Counts
1 → 23
Calls
Call 1
Inputs
(/.f64 1 (+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 (pow.f64 x 1/4) (pow.f64 (+.f64 1 x) 1/4)) -1) (pow.f64 (hypot.f64 (pow.f64 x 1/4) (pow.f64 (+.f64 1 x) 1/4)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 1 x) x) (pow.f64 (*.f64 (+.f64 1 x) x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 (+.f64 1 x) x)) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))))

simplify9.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
011
141
Stop Event
1×saturated
Counts
24 → 24
Calls
Call 1
Inputs
1
Outputs
1

localize55.0ms (1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.3b
(/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))
✓2.1b
(-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))
✓12.6b
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 1 (+.f64 x (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x))))))
✓16.0b
(sqrt.f64 (*.f64 (+.f64 1 x) x))
Compiler

Compiled 100 to 71 computations (29% saved)

series10.0ms (0.2%)

Counts
4 → 37
Calls

12 calls:

TimeVariablePointExpression
2.0ms
x
@-inf
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 1 (+.f64 x (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x))))))
2.0ms
x
@0
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 1 (+.f64 x (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x))))))
1.0ms
x
@inf
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 1 (+.f64 x (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x))))))
1.0ms
x
@-inf
(sqrt.f64 (*.f64 (+.f64 1 x) x))
1.0ms
x
@0
(sqrt.f64 (*.f64 (+.f64 1 x) x))

rewrite104.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
521×fma-neg_binary64
302×expm1-udef_binary64
302×log1p-udef_binary64
256×log-pow_binary64
189×add-sqr-sqrt_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01570
136570
2572461
Stop Event
1×node limit
Counts
4 → 160
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (+.f64 1 x) x))
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 1 (+.f64 x (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x))))))
(-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))
(/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))
Outputs
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simplify65.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
776×fma-def_binary64
425×associate-+l+_binary64
332×associate-+r+_binary64
307×associate-/r*_binary64
241×associate--r+_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02191886
16751579
222661297
Stop Event
1×node limit
Counts
197 → 220
Calls
Call 1
Inputs
x
(+.f64 1/2 x)
(-.f64 (+.f64 1/2 x) (*.f64 1/8 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) x)) (*.f64 1/8 (/.f64 1 x)))
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(+.f64 1/2 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))))
(+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 x 2)))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))))
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))) (+.f64 (*.f64 3/4 (/.f64 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) x)) (+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))))
(-.f64 (+.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -1/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))) (+.f64 (*.f64 -1/64 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 3/4 (/.f64 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) x)) (+.f64 (*.f64 3/4 (/.f64 (-.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/4 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))) (pow.f64 x 2))) (*.f64 3/16 (/.f64 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2)))))))))
(*.f64 1/2 (/.f64 (*.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) x) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 1/2 (/.f64 (*.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) x) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) x) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 -1 (/.f64 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (+.f64 (*.f64 -3/4 (-.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))) (*.f64 -3/32 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))) x)))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) x) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 3/16 (-.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))) (+.f64 (*.f64 -1/64 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (+.f64 (*.f64 1/32 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 4) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (*.f64 -3/4 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (+.f64 (*.f64 -3/4 (-.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))) (*.f64 -3/32 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))))))) (pow.f64 x 2))) (*.f64 -1 (/.f64 (-.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (+.f64 (*.f64 -3/4 (-.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))) (*.f64 -3/32 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))) x))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))
-1/2
(-.f64 (*.f64 1/8 (/.f64 1 x)) 1/2)
(-.f64 (*.f64 1/8 (/.f64 1 x)) (+.f64 1/2 (*.f64 1/16 (/.f64 1 (pow.f64 x 2)))))
(-.f64 (+.f64 (*.f64 5/128 (/.f64 1 (pow.f64 x 3))) (*.f64 1/8 (/.f64 1 x))) (+.f64 1/2 (*.f64 1/16 (/.f64 1 (pow.f64 x 2)))))
(*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x)
(-.f64 (*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) 1/2)
(-.f64 (*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) (+.f64 1/2 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))))
(-.f64 (*.f64 (+.f64 1 (pow.f64 (sqrt.f64 -1) 2)) x) (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 x 2)))) (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))))))
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))))
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (+.f64 (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (*.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (pow.f64 x 2))))
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (+.f64 (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (+.f64 (*.f64 (-.f64 (+.f64 (*.f64 9/16 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 1/16 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (*.f64 3/2 (/.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (+.f64 1 (pow.f64 x 3/2))))) (pow.f64 x 3)) (*.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (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 -1 (/.f64 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2))) (+.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 (/.f64 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -3/4 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (+.f64 (*.f64 -1/64 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -9/128 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (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 1/2 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(-.f64 (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(-.f64 (+.f64 (*.f64 3/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(-.f64 (+.f64 (*.f64 3/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (+.f64 (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))) (*.f64 7/128 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))))))
Outputs
x
(+.f64 1/2 x)
(+.f64 x 1/2)
(-.f64 (+.f64 1/2 x) (*.f64 1/8 (/.f64 1 x)))
(-.f64 (+.f64 x 1/2) (/.f64 1/8 x))
(+.f64 (+.f64 x 1/2) (/.f64 -1/8 x))
(-.f64 (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) x)) (*.f64 1/8 (/.f64 1 x)))
(-.f64 (+.f64 1/2 (+.f64 x (/.f64 1/16 (*.f64 x x)))) (/.f64 1/8 x))
(+.f64 (+.f64 1/2 (/.f64 1/16 (*.f64 x x))) (+.f64 x (/.f64 -1/8 x)))
(+.f64 x (+.f64 (/.f64 -1/8 x) (+.f64 1/2 (/.f64 1/16 (*.f64 x x)))))
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))
x
(+.f64 1/2 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(+.f64 x 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))))
(-.f64 (+.f64 x 1/2) (/.f64 1/8 x))
(+.f64 (+.f64 x 1/2) (/.f64 -1/8 x))
(+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 x 2)))) (+.f64 (*.f64 1/8 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))) (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))))
(-.f64 (+.f64 1/2 (+.f64 x (/.f64 1/16 (*.f64 x x)))) (/.f64 1/8 x))
(+.f64 (+.f64 1/2 (/.f64 1/16 (*.f64 x x))) (+.f64 x (/.f64 -1/8 x)))
(+.f64 x (+.f64 (/.f64 -1/8 x) (+.f64 1/2 (/.f64 1/16 (*.f64 x x)))))
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (fma.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8))
(-.f64 (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))) (+.f64 (*.f64 3/4 (/.f64 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) x)) (+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))))
(-.f64 (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))) (fma.f64 3/4 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8) x) (fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 3/32))))
(-.f64 (-.f64 (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) 3/8 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 3/32))) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/32) x))
(fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (-.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8)) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 3/32 (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 x -3/32)))))
(-.f64 (+.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -1/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))) (+.f64 (*.f64 -1/64 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 3/4 (/.f64 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) x)) (+.f64 (*.f64 3/4 (/.f64 (-.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/4 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))) (pow.f64 x 2))) (*.f64 3/16 (/.f64 (-.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2)))))))))
(-.f64 (fma.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))) (fma.f64 -1/64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (fma.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 3/4 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8) x) (fma.f64 3/4 (/.f64 (-.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (fma.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 3/4 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8)))) (*.f64 x x)) (*.f64 3/16 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8) (*.f64 x x)))))))))
(-.f64 (fma.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) -1/64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) 3/8 (+.f64 (fma.f64 3/4 (/.f64 (-.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/32) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/32)) (*.f64 x x)) (*.f64 (/.f64 3/16 x) (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 x -1/8)))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 3/32 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/32) x))))))
(+.f64 (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (fma.f64 -1/32 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))) (-.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/8) (+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 3/32 (+.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) 3/64) (*.f64 x x)) (*.f64 (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (/.f64 x -1/8)) (+.f64 (/.f64 3/16 x) 3/4)))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 7))) -1/64))))
(*.f64 1/2 (/.f64 (*.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) x) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
(*.f64 1/2 (/.f64 (*.f64 x (+.f64 2 (pow.f64 (sqrt.f64 -1) 2))) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))
(/.f64 (*.f64 1/2 x) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(*.f64 (/.f64 1/2 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))) x)
(-.f64 (+.f64 (*.f64 1/4 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 1/2 (/.f64 (*.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) x) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (*.f64 3/8 (/.f64 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2)) (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))
(+.f64 (/.f64 1/4 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (-.f64 (*.f64 1/2 (/.f64 (*.f64 x (+.f64 2 (pow.f64 (sqrt.f64 -1) 2))) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (/.f64 (*.f64 3/8 (+.f64 2 (pow.f64 (sqrt.f64 -1) 2))) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))))
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(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (+.f64 (*.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (+.f64 (*.f64 (-.f64 (+.f64 (*.f64 9/16 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 1/16 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (*.f64 3/2 (/.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (+.f64 1 (pow.f64 x 3/2))))) (pow.f64 x 3)) (*.f64 (-.f64 (*.f64 9/4 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (*.f64 3/8 (/.f64 1 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))) (pow.f64 x 2)))))
(+.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (fma.f64 (+.f64 (/.f64 9/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (-.f64 (/.f64 1/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (*.f64 3/2 (/.f64 (-.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (+.f64 1 (pow.f64 x 3/2)))))) (pow.f64 x 3) (*.f64 (*.f64 x x) (-.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))))))
(+.f64 (fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (/.f64 1 (+.f64 1 (pow.f64 x 3/2)))) (fma.f64 (pow.f64 x 3) (+.f64 (/.f64 9/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (+.f64 (/.f64 1/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (*.f64 -3/2 (-.f64 (/.f64 9/4 (*.f64 (+.f64 1 (pow.f64 x 3/2)) (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3))) (/.f64 3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)))))) (*.f64 x (*.f64 x (+.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 -3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)))))))
(+.f64 (fma.f64 -3/2 (/.f64 x (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (/.f64 1 (+.f64 1 (pow.f64 x 3/2)))) (*.f64 (*.f64 x x) (+.f64 (+.f64 (/.f64 9/4 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 -3/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (*.f64 (+.f64 (/.f64 9/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (-.f64 (/.f64 1/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2)) (/.f64 (+.f64 (/.f64 27/8 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 3)) (/.f64 -9/16 (pow.f64 (+.f64 1 (pow.f64 x 3/2)) 2))) (+.f64 1 (pow.f64 x 3/2))))) x))))
(*.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)))))
(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 -1 (/.f64 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2))) (+.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 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16) (*.f64 x x)) (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)))
(-.f64 (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 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) x) (/.f64 -3/16 x)))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) 3/16) (*.f64 x x))))
(+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (pow.f64 x 2))) (+.f64 (*.f64 -1 (/.f64 (+.f64 (*.f64 -3/4 (+.f64 (*.f64 -9/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (+.f64 (*.f64 -1/64 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 -9/128 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))) (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)))))))
(fma.f64 -1 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16) (*.f64 x x)) (fma.f64 -1 (/.f64 (fma.f64 -3/4 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -11/128)) (pow.f64 x 3)) (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 (fma.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) -3/8)) (/.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -11/128 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) 9/64)) (pow.f64 x 3))) (*.f64 (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) x) (/.f64 -3/16 x)))
(-.f64 (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 (/.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) x) (/.f64 -3/16 x) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) 7/128) (pow.f64 x 3))))
(/.f64 1/2 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))
(/.f64 1/2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))
(/.f64 1/2 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(/.f64 1/2 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)))
(-.f64 (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(-.f64 (/.f64 1/2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (/.f64 3/8 (*.f64 x (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))))
(fma.f64 1/2 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) (/.f64 -3/8 (*.f64 x (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))
(+.f64 (/.f64 1/2 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))) (/.f64 (/.f64 -3/8 x) (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))))
(-.f64 (+.f64 (*.f64 3/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(+.f64 (/.f64 3/16 (*.f64 (*.f64 x x) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (-.f64 (/.f64 1/2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (/.f64 3/8 (*.f64 x (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))))
(fma.f64 3/16 (/.f64 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) (*.f64 x x)) (fma.f64 1/2 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) (/.f64 -3/8 (*.f64 x (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))))
(+.f64 (+.f64 (/.f64 1/2 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))) (/.f64 (/.f64 -3/8 x) (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)))) (/.f64 3/16 (*.f64 (*.f64 x x) (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)))))
(-.f64 (+.f64 (*.f64 3/16 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2)))) (*.f64 1/2 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))) (+.f64 (*.f64 3/8 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))) (*.f64 7/128 (/.f64 1 (*.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))))))
(-.f64 (+.f64 (/.f64 1/2 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (/.f64 3/16 (*.f64 (*.f64 x x) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))) (+.f64 (/.f64 3/8 (*.f64 x (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (/.f64 7/128 (*.f64 (pow.f64 x 3) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))))
(-.f64 (fma.f64 1/2 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) (/.f64 (/.f64 3/16 (*.f64 x x)) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) (fma.f64 7/128 (/.f64 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) (pow.f64 x 3)) (/.f64 3/8 (*.f64 x (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))))
(+.f64 (+.f64 (/.f64 1/2 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))) (/.f64 (/.f64 -3/8 x) (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)))) (-.f64 (/.f64 3/16 (*.f64 (*.f64 x x) (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)))) (/.f64 7/128 (*.f64 (pow.f64 x 3) (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))))))

eval325.0ms (5.6%)

Compiler

Compiled 13647 to 9867 computations (27.7% saved)

prune146.0ms (2.5%)

Pruning

13 alts after pruning (8 fresh and 5 done)

PrunedKeptTotal
New5837590
Fresh213
Picked101
Done257
Total58813601
Error
0b
Counts
601 → 13
Alt Table
Click to see full alt table
StatusErrorProgram
29.4b
(*.f64 1/2 (pow.f64 x -1/2))
38.4b
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 1 (+.f64 x -1/2)))
✓60.1b
(/.f64 2 x)
31.9b
1
✓30.8b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓2.1b
(/.f64 1 (+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x)))
✓31.6b
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
58.8b
(*.f64 1/2 (-.f64 (+.f64 1 (pow.f64 x -1/2)) 1))
27.0b
(/.f64 1 (+.f64 1 (sqrt.f64 x)))
31.9b
(*.f64 1/2 (exp.f64 (*.f64 -1/2 (log.f64 x))))
29.6b
(*.f64 1/2 (/.f64 1 (sqrt.f64 x)))
42.6b
(*.f64 1/2 (cbrt.f64 (pow.f64 (/.f64 1 x) 3/2)))
✓0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Compiler

Compiled 109 to 91 computations (16.5% saved)

regimes41.0ms (0.7%)

Counts
36 → 1
Calls
Call 1
Inputs
1
1
(/.f64 2 x)
(*.f64 1/2 (pow.f64 x -1/2))
(/.f64 1 (+.f64 1 (sqrt.f64 x)))
(*.f64 1/2 (/.f64 1 (sqrt.f64 x)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
(*.f64 1/2 (-.f64 (+.f64 1 (pow.f64 x -1/2)) 1))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(*.f64 1/2 (exp.f64 (*.f64 -1/2 (log.f64 x))))
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
(*.f64 1/2 (cbrt.f64 (pow.f64 (/.f64 1 x) 3/2)))
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 1 (+.f64 x -1/2)))
(-.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x))
(-.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x))
(/.f64 1 (+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x)))
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x)))
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 1 (+.f64 x (-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x))))))
(-.f64 (expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 x))
(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)
(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)
(-.f64 (/.f64 (sqrt.f64 (fma.f64 x x -1)) (sqrt.f64 (-.f64 x 1))) (sqrt.f64 x))
(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))
(/.f64 (-.f64 (+.f64 x 1) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))))
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))
(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))
(/.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 (neg.f64 (sqrt.f64 x)) 3)) (+.f64 (+.f64 x 1) (-.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))))
Outputs
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Calls

3 calls:

17.0ms
x
6.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
5.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Results
ErrorSegmentsBranch
0.2b1x
0.2b1(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.2b1(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 427 to 283 computations (33.7% saved)

regimes71.0ms (1.2%)

Counts
14 → 2
Calls
Call 1
Inputs
1
1
(/.f64 2 x)
(*.f64 1/2 (pow.f64 x -1/2))
(/.f64 1 (+.f64 1 (sqrt.f64 x)))
(*.f64 1/2 (/.f64 1 (sqrt.f64 x)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
(*.f64 1/2 (-.f64 (+.f64 1 (pow.f64 x -1/2)) 1))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(*.f64 1/2 (exp.f64 (*.f64 -1/2 (log.f64 x))))
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
(*.f64 1/2 (cbrt.f64 (pow.f64 (/.f64 1 x) 3/2)))
Outputs
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
(*.f64 1/2 (pow.f64 x -1/2))
Calls

3 calls:

47.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
16.0ms
x
5.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Results
ErrorSegmentsBranch
0.4b2x
0.4b2(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.4b2(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 108 to 80 computations (25.9% saved)

bsearch20.0ms (0.3%)

Algorithm
1×binary-search
Steps
TimeLeftRight
20.0ms
643402.3745248648
267928395.73708117
Compiler

Compiled 12 to 9 computations (25% saved)

regimes18.0ms (0.3%)

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

1 calls:

15.0ms
x
Results
ErrorSegmentsBranch
0.6b2x
Compiler

Compiled 77 to 57 computations (26% saved)

bsearch18.0ms (0.3%)

Algorithm
1×binary-search
Steps
TimeLeftRight
18.0ms
6.352330830085446e-10
149235.42791003702
Compiler

Compiled 12 to 9 computations (25% saved)

regimes13.0ms (0.2%)

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

1 calls:

12.0ms
x
Results
ErrorSegmentsBranch
0.8b2x
Compiler

Compiled 31 to 24 computations (22.6% saved)

bsearch20.0ms (0.4%)

Algorithm
1×binary-search
Steps
TimeLeftRight
20.0ms
6.352330830085446e-10
149235.42791003702
Compiler

Compiled 12 to 9 computations (25% saved)

regimes9.0ms (0.1%)

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

1 calls:

7.0ms
x
Results
ErrorSegmentsBranch
1.7b2x
Compiler

Compiled 13 to 10 computations (23.1% saved)

bsearch19.0ms (0.3%)

Algorithm
1×binary-search
Steps
TimeLeftRight
19.0ms
6.352330830085446e-10
149235.42791003702
Compiler

Compiled 12 to 9 computations (25% saved)

regimes4.0ms (0.1%)

Accuracy

Total -28.3b remaining (-88.7%)

Threshold costs -28.3b (-88.7%)

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

1 calls:

3.0ms
x
Results
ErrorSegmentsBranch
31.9b1x
Compiler

Compiled 8 to 6 computations (25% saved)

simplify8.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
027100
138100
243100
345100
446100
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(if (<=.f64 x 2763392156753038/4294967296) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (*.f64 1/2 (pow.f64 x -1/2)))
(if (<=.f64 x 1535899351044865/2417851639229258349412352) (+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) (*.f64 1/2 (pow.f64 x -1/2)))
(if (<=.f64 x 1535899351044865/2417851639229258349412352) (/.f64 1 (+.f64 1 (sqrt.f64 x))) (*.f64 1/2 (pow.f64 x -1/2)))
(if (<=.f64 x 1535899351044865/2417851639229258349412352) 1 (*.f64 1/2 (pow.f64 x -1/2)))
1
Outputs
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(if (<=.f64 x 2763392156753038/4294967296) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (*.f64 1/2 (pow.f64 x -1/2)))
(if (<=.f64 x 1381696078376519/2147483648) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 1/2 (pow.f64 x -1/2)))
(if (<=.f64 x 1535899351044865/2417851639229258349412352) (+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) (*.f64 1/2 (pow.f64 x -1/2)))
(if (<=.f64 x 1535899351044865/2417851639229258349412352) (+.f64 1 (-.f64 (*.f64 x 1/2) (sqrt.f64 x))) (*.f64 1/2 (pow.f64 x -1/2)))
(if (<=.f64 x 1535899351044865/2417851639229258349412352) (/.f64 1 (+.f64 1 (sqrt.f64 x))) (*.f64 1/2 (pow.f64 x -1/2)))
(if (<=.f64 x 1535899351044865/2417851639229258349412352) 1 (*.f64 1/2 (pow.f64 x -1/2)))
1
Compiler

Compiled 74 to 59 computations (20.3% saved)

soundness0.0ms (0%)

end82.0ms (1.4%)

Compiler

Compiled 69 to 51 computations (26.1% saved)

Profiling

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