Details

Time bar (total: 7.3s)

analyze3.0ms (0%)

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)

sample1.6s (22.3%)

Results
684.0ms4944×body256valid
598.0ms2082×body1024valid
204.0ms1033×body512valid
119.0ms197×body2048valid
1.0ms6×body256invalid

preprocess20.0ms (0.3%)

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))

eval0.0ms (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
27.7b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶27.7b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 8 to 6 computations (25% saved)

localize8.0ms (0.1%)

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)

series5.0ms (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))

rewrite56.0ms (0.8%)

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))))))

simplify88.0ms (1.2%)

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)

eval18.0ms (0.2%)

Compiler

Compiled 829 to 549 computations (33.8% saved)

prune46.0ms (0.6%)

Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New481765
Fresh000
Picked011
Done000
Total481866
Error
26.4b
Counts
66 → 18
Alt Table
Click to see full alt table
StatusErrorProgram
27.8b
(-.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x))
27.7b
(pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2)
29.5b
1
27.9b
(-.f64 (expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 x))
▶27.6b
(-.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 x))
✓27.7b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
27.6b
(/.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))))
28.2b
(/.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))))))
27.9b
(+.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)))
▶27.7b
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
▶27.2b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
27.7b
(-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 3) (sqrt.f64 x))
28.2b
(/.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))))
62.8b
(-.f64 (/.f64 (sqrt.f64 (fma.f64 x x -1)) (sqrt.f64 (-.f64 x 1))) (sqrt.f64 x))
▶27.7b
(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
▶28.7b
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
27.7b
(-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x))
27.9b
(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))
Compiler

Compiled 488 to 356 computations (27% saved)

localize18.0ms (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)))
✓1.9b
(+.f64 x (-.f64 1 x))
Compiler

Compiled 40 to 25 computations (37.5% saved)

series8.0ms (0.1%)

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 (1.5%)

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)))))))

simplify12.0ms (0.2%)

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

localize11.0ms (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))

rewrite59.0ms (0.8%)

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)))))))

simplify7.0ms (0.1%)

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
(exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
✓1.8b
(log.f64 (exp.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)

series5.0ms (0.1%)

Counts
2 → 3
Calls

6 calls:

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

rewrite73.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
869×pow1_binary64
810×log1p-expm1-u_binary64
810×expm1-log1p-u_binary64
809×add-log-exp_binary64
789×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0924
117724
2230824
Stop Event
1×node limit
Counts
2 → 64
Calls
Call 1
Inputs
(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
(exp.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 0 (-.f64 (sqrt.f64 (+.f64 x 1)) (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 (log.f64 (sqrt.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (-.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 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))))) (#(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 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 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 1 (expm1.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))) (exp.f64 (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 2) (cbrt.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (sqrt.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (exp.f64 (sqrt.f64 x)) (exp.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))) (exp.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (exp.f64 (sqrt.f64 (+.f64 x 1)))) (neg.f64 (exp.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.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 pow.f64 (exp.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 sqrt.f64 (pow.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))))))

simplify8.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
1×exp-1-e_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
034
164
Stop Event
1×saturated
Counts
67 → 67
Calls
Call 1
Inputs
1
(exp.f64 1)
1
Outputs
1
(exp.f64 1)
(E.f64)
1

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))))
✓0.3b
(cbrt.f64 (sqrt.f64 (+.f64 x 1)))
✓0.3b
(cbrt.f64 (+.f64 x 1))
✓12.7b
(-.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 x))
Compiler

Compiled 44 to 32 computations (27.3% saved)

series7.0ms (0.1%)

Counts
4 → 21
Calls

12 calls:

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

rewrite87.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
915×pow1_binary64
856×log1p-expm1-u_binary64
856×expm1-log1p-u_binary64
855×add-log-exp_binary64
832×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01031
121530
2251730
Stop Event
1×node limit
Counts
4 → 97
Calls
Call 1
Inputs
(-.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 x))
(cbrt.f64 (+.f64 x 1))
(cbrt.f64 (sqrt.f64 (+.f64 x 1)))
(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (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 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 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)) (pow.f64 (+.f64 x 1) 1/6) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 x 1) 1/6) (cbrt.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 (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) (pow.f64 (+.f64 x 1) 1/4))))) (#(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 (fma.f64 x x -1)) (cbrt.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (+.f64 1 (pow.f64 x 3))) (cbrt.f64 (fma.f64 x x (-.f64 1 x))))))) (#(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 (pow.f64 (+.f64 x 1) 1/6) 2)))) (#(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 (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))))))
((#(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 (pow.f64 (+.f64 x 1) 1/6) 1)))) (#(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 (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 (log.f64 (pow.f64 (+.f64 x 1) 1/6)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)))) (#(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 (pow.f64 (+.f64 x 1) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(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 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 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))))))

simplify73.0ms (1%)

Algorithm
1×egg-herbie
Rules
903×fma-def_binary64
374×distribute-rgt-out_binary64
360×associate-*l*_binary64
309×times-frac_binary64
308×associate-*r*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
077434
1206409
2538340
31576276
45364256
57731256
Stop Event
1×node limit
Counts
118 → 130
Calls
Call 1
Inputs
1
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))))
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 (*.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 1 (*.f64 1/3 x))
(fma.f64 1/3 x 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 1/3 x)))
(fma.f64 -1/9 (*.f64 x x) (fma.f64 1/3 x 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 1/3 x))))
(+.f64 (fma.f64 -1/9 (*.f64 x x) (fma.f64 1/3 x 1)) (*.f64 5/81 (pow.f64 x 3)))
(fma.f64 x (*.f64 x -1/9) (fma.f64 1/3 x (fma.f64 5/81 (pow.f64 x 3) 1)))
(fma.f64 x (fma.f64 x -1/9 1/3) (fma.f64 5/81 (pow.f64 x 3) 1))
1
(+.f64 1 (*.f64 1/6 x))
(+.f64 1 (*.f64 x 1/6))
(fma.f64 x 1/6 1)
(+.f64 1 (+.f64 (*.f64 1/6 x) (*.f64 -5/72 (pow.f64 x 2))))
(+.f64 1 (fma.f64 1/6 x (*.f64 (*.f64 x x) -5/72)))
(+.f64 1 (fma.f64 x 1/6 (*.f64 (*.f64 x x) -5/72)))
(fma.f64 x 1/6 (fma.f64 (*.f64 x 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 (*.f64 x x) -5/72))))
(+.f64 (fma.f64 x 1/6 (*.f64 (*.f64 x x) -5/72)) (fma.f64 (pow.f64 x 3) 55/1296 1))
(fma.f64 (pow.f64 x 3) 55/1296 (fma.f64 x 1/6 (fma.f64 (*.f64 x x) -5/72 1)))
(fma.f64 x (fma.f64 x -5/72 1/6) (fma.f64 (pow.f64 x 3) 55/1296 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))))
(+.f64 (pow.f64 x 1/6) (fma.f64 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (*.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) (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 1/6 (pow.f64 (/.f64 1 (pow.f64 x 5)) 1/6) (*.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)))
(fma.f64 55/1296 (pow.f64 (/.f64 1 (pow.f64 x 17)) 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))))
(fma.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) (fma.f64 -5/72 (pow.f64 (/.f64 1 (pow.f64 x 11)) 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 (*.f64 1/6 (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 (pow.f64 (/.f64 -1 x) -1/6) (/.f64 x (pow.f64 -1 1/6))) (*.f64 (pow.f64 (/.f64 -1 x) -1/6) (pow.f64 -1 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 (*.f64 1/6 (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 (pow.f64 (/.f64 -1 x) -1/6) (/.f64 x (pow.f64 -1 1/6))) (+.f64 (/.f64 -5/72 x) 1/6)))
(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 (*.f64 1/6 (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 (/.f64 -1 x) -1/6) (pow.f64 -1 1/6)) (pow.f64 x 3)) (fma.f64 (pow.f64 (/.f64 -1 x) -1/6) (pow.f64 -1 1/6) (*.f64 (/.f64 (pow.f64 (/.f64 -1 x) -1/6) (/.f64 x (pow.f64 -1 1/6))) (+.f64 (/.f64 -5/72 x) 1/6))))
(+.f64 (pow.f64 (exp.f64 1/6) (log.f64 x)) (*.f64 (/.f64 (pow.f64 (exp.f64 1/6) (log.f64 x)) x) (+.f64 (/.f64 55/1296 (*.f64 x x)) (+.f64 1/6 (/.f64 -5/72 x)))))
(+.f64 (pow.f64 x 1/6) (*.f64 (/.f64 (pow.f64 x 1/6) x) (+.f64 (/.f64 55/1296 (*.f64 x x)) (+.f64 1/6 (/.f64 -5/72 x)))))
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(fma.f64 x 1/2 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 x 1/2 1))
(fma.f64 x 1/2 (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 (pow.f64 x 3) 1/16)))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 x 1/2 (fma.f64 (pow.f64 x 3) 1/16 1)))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x -1/8) (fma.f64 (pow.f64 x 3) 1/16 1)))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)) 1))

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
0.3b
(cbrt.f64 (sqrt.f64 (+.f64 x 1)))
0.3b
(cbrt.f64 (+.f64 x 1))
✓27.7b
(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)

series3.0ms (0%)

Counts
1 → 1
Calls

3 calls:

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

rewrite53.0ms (0.7%)

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
01021
120011
2239711
Stop Event
1×node limit
Counts
1 → 22
Calls
Call 1
Inputs
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
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))))))))

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

eval455.0ms (6.3%)

Compiler

Compiled 13984 to 9301 computations (33.5% saved)

prune153.0ms (2.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New7616767
Fresh10212
Picked101
Done325
Total77510785
Error
0.1b
Counts
785 → 10
Alt Table
Click to see full alt table
StatusErrorProgram
✓27.7b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
▶28.8b
(+.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 1/2 x))
▶0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
▶27.7b
(-.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1)
▶28.7b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
✓28.7b
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
29.5b
1
27.2b
(*.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))))
▶27.7b
(-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x))
28.2b
(/.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))))
Compiler

Compiled 235 to 179 computations (23.8% saved)

localize155.0ms (2.1%)

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)))

rewrite65.0ms (0.9%)

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

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiled 21 to 13 computations (38.1% saved)

series1.0ms (0%)

Counts
1 → 3
Calls

3 calls:

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

rewrite96.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
941×pow1_binary64
880×add-log-exp_binary64
880×log1p-expm1-u_binary64
880×expm1-log1p-u_binary64
863×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0812
117510
2237710
Stop Event
1×node limit
Counts
1 → 39
Calls
Call 1
Inputs
(+.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 1/2 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 1 (+.f64 (sqrt.f64 x) (*.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (-.f64 1 (sqrt.f64 x)) 2) (+.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 -1/2 x))) (/.f64 (pow.f64 (*.f64 x 1/2) 2) (+.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 x 1/2) 1) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x)))) (pow.f64 (cbrt.f64 (fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x)))) 2) (cbrt.f64 (fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x)))) (sqrt.f64 (fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (-.f64 1 (sqrt.f64 x)) 3) (*.f64 1/8 (pow.f64 x 3))) (/.f64 1 (+.f64 (pow.f64 (-.f64 1 (sqrt.f64 x)) 2) (*.f64 (*.f64 x 1/2) (-.f64 (*.f64 x 1/2) (-.f64 1 (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (-.f64 1 (sqrt.f64 x)) 2) (pow.f64 (*.f64 x 1/2) 2)) (/.f64 1 (+.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (-.f64 1 (sqrt.f64 x)) 2) (*.f64 (*.f64 x 1/2) (-.f64 (*.f64 x 1/2) (-.f64 1 (sqrt.f64 x))))) (+.f64 (pow.f64 (-.f64 1 (sqrt.f64 x)) 3) (*.f64 1/8 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 -1/2 x)) (-.f64 (pow.f64 (-.f64 1 (sqrt.f64 x)) 2) (pow.f64 (*.f64 x 1/2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (-.f64 1 (sqrt.f64 x)) 3) (*.f64 1/8 (pow.f64 x 3))) (+.f64 (pow.f64 (-.f64 1 (sqrt.f64 x)) 2) (*.f64 (*.f64 x 1/2) (-.f64 (*.f64 x 1/2) (-.f64 1 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (-.f64 1 (sqrt.f64 x)) 3) (*.f64 1/8 (pow.f64 x 3))) (+.f64 (pow.f64 (*.f64 x 1/2) 2) (-.f64 (pow.f64 (-.f64 1 (sqrt.f64 x)) 2) (*.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (-.f64 1 (sqrt.f64 x)) 2) (pow.f64 (*.f64 x 1/2) 2)) (+.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (-.f64 1 (sqrt.f64 x)) 3) (*.f64 1/8 (pow.f64 x 3)))) (neg.f64 (+.f64 (pow.f64 (-.f64 1 (sqrt.f64 x)) 2) (*.f64 (*.f64 x 1/2) (-.f64 (*.f64 x 1/2) (-.f64 1 (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (-.f64 1 (sqrt.f64 x)) 2) (pow.f64 (*.f64 x 1/2) 2))) (neg.f64 (+.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 (sqrt.f64 x) (*.f64 -1/2 x)) 3)) (+.f64 1 (+.f64 (*.f64 (+.f64 (sqrt.f64 x) (*.f64 -1/2 x)) (+.f64 (sqrt.f64 x) (*.f64 -1/2 x))) (+.f64 (sqrt.f64 x) (*.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (+.f64 (sqrt.f64 x) (*.f64 -1/2 x)) (+.f64 (sqrt.f64 x) (*.f64 -1/2 x)))) (+.f64 1 (+.f64 (sqrt.f64 x) (*.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 x 1/2) 2) (pow.f64 (-.f64 1 (sqrt.f64 x)) 2)) (-.f64 (*.f64 x 1/2) (-.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x 1/2 (-.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 1 (sqrt.f64 x)) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 1/2) (-.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 1/2 x (-.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 1 (sqrt.f64 x))) 2) (cbrt.f64 (-.f64 1 (sqrt.f64 x))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 1/2)) 2) (cbrt.f64 (*.f64 x 1/2)) (-.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 1 (sqrt.f64 x))) (sqrt.f64 (-.f64 1 (sqrt.f64 x))) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/2)) (sqrt.f64 (*.f64 x 1/2)) (-.f64 1 (sqrt.f64 x)))))))

simplify7.0ms (0.1%)

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
42 → 41
Calls
Call 1
Inputs
1
(*.f64 1/2 x)
(*.f64 1/2 x)
Outputs
1
(*.f64 1/2 x)
(*.f64 1/2 x)

localize35.0ms (0.5%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
✓0.0b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
1.9b
(+.f64 x (-.f64 1 x))
Compiler

Compiled 44 to 29 computations (34.1% saved)

series5.0ms (0.1%)

Counts
2 → 6
Calls

6 calls:

TimeVariablePointExpression
2.0ms
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))

rewrite99.0ms (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
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))) (cbrt.f64 (exp.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (+.f64 x 1) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))) (/.f64 x (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (-.f64 1 x)) (/.f64 1 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))) (pow.f64 (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))) 2) (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))))) (#(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 1 (fma.f64 x 1/2 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))) (sqrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))))) (#(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 1 (fma.f64 x 1/2 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (+.f64 x (-.f64 1 x))) (/.f64 1 (neg.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))) (+.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 1 (fma.f64 x 1/2 (sqrt.f64 x)))))))) (#(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 1 (fma.f64 x 1/2 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))) 2)) (/.f64 (+.f64 x (-.f64 1 x)) (cbrt.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) 2) (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))) 2)) (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))) 2)) (/.f64 (sqrt.f64 (+.f64 x (-.f64 1 x))) (cbrt.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))) (/.f64 (+.f64 x (-.f64 1 x)) (sqrt.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) 2) (sqrt.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))) (/.f64 (cbrt.f64 (+.f64 x (-.f64 1 x))) (sqrt.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (fma.f64 x 1/2 1) 3) (pow.f64 x 3/2))) (-.f64 (+.f64 (pow.f64 (fma.f64 x 1/2 1) 2) x) (*.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 x (-.f64 1 x)) (-.f64 (pow.f64 (fma.f64 x 1/2 1) 2) x)) (-.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))) (+.f64 x (-.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))) (+.f64 x (-.f64 1 x))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 x (-.f64 1 x)) (neg.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))) 3))))) (#(struct:change 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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (fma.f64 x 1/2 1) 2) (-.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) (/.f64 x (-.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))) (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))) 2) (cbrt.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))) (sqrt.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 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(fma.f64 x 1/2 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (+.f64 1 (sqrt.f64 x))) (pow.f64 (exp.f64 x) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (+.f64 1 (sqrt.f64 x))) (+.f64 1 (expm1.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (fma.f64 x 1/2 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (fma.f64 x 1/2 (sqrt.f64 x))) 1))))) (#(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 x 1/2 (*.f64 (+.f64 1 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 1/2) (+.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 1/2) (*.f64 (+.f64 1 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x 1/2 1) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 x) (fma.f64 x 1/2 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (sqrt.f64 x)) (*.f64 x 1/2))))) (#(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 1/2 x (*.f64 (+.f64 1 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x 1/2) 1 (+.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x 1/2) 1 (*.f64 (+.f64 1 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 x 1/2 1) 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) 1 (fma.f64 x 1/2 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/2) (+.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) 1/2) (*.f64 (+.f64 1 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (fma.f64 x 1/2 1)) (pow.f64 (cbrt.f64 (fma.f64 x 1/2 1)) 2) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/2 1)) 2) (cbrt.f64 (fma.f64 x 1/2 1)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 x)) (fma.f64 x 1/2 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/2) (+.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) 1/2) (*.f64 (+.f64 1 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 x) (fma.f64 x 1/2 1))))) (#(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 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))))))

simplify9.0ms (0.1%)

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)

localize69.0ms (1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
0.0b
(sqrt.f64 (+.f64 x 1))
✓1.8b
(-.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1)
2.5b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 39 to 26 computations (33.3% saved)

series3.0ms (0%)

Counts
2 → 3
Calls

6 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)))
1.0ms
x
@inf
(-.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1)
0.0ms
x
@0
(-.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1)
0.0ms
x
@-inf
(-.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1)

rewrite128.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
716×fma-def_binary64
411×log-prod_binary64
390×fma-neg_binary64
306×pow-prod-down_binary64
248×pow2_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0931
121625
2329925
Stop Event
1×node limit
Counts
2 → 225
Calls
Call 1
Inputs
(-.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1)
(+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Outputs
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egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 1 x)) (fma.f64 -1 (sqrt.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 1 x)) (neg.f64 (-.f64 (sqrt.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 x)) 1 (fma.f64 -1 (sqrt.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 x)) 1 (neg.f64 (-.f64 (sqrt.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1 x) 1/6) (cbrt.f64 (+.f64 1 x)) (fma.f64 -1 (sqrt.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1 x) 1/6) (cbrt.f64 (+.f64 1 x)) (neg.f64 (-.f64 (sqrt.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1 x)) (pow.f64 (+.f64 1 x) 1/6) (fma.f64 -1 (sqrt.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x 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simplify10.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
023
153
Stop Event
1×saturated
Counts
228 → 227
Calls
Call 1
Inputs
1
2
1
Outputs
1
2
1

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiled 37 to 28 computations (24.3% saved)

series13.0ms (0.2%)

Counts
3 → 9
Calls

9 calls:

TimeVariablePointExpression
10.0ms
x
@inf
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)
1.0ms
x
@inf
(-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x))
0.0ms
x
@-inf
(-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x))
0.0ms
x
@-inf
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0ms
x
@0
(-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x))

rewrite102.0ms (1.4%)

Algorithm
1×batch-egg-rewrite
Rules
767×fma-def_binary64
415×fma-neg_binary64
408×log-prod_binary64
309×pow-prod-down_binary64
247×pow2_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0938
121626
2338526
Stop Event
1×node limit
Counts
3 → 275
Calls
Call 1
Inputs
(-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (-.f64 (expm1.f64 (*.f64 1/2 (log1p.f64 x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 1 x)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 1 x)) (*.f64 (neg.f64 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (+.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (neg.f64 (+.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (-.f64 -1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) (+.f64 -1 (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (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 1 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 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1 x)))) (/.f64 (+.f64 1 x) (-.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 2) (*.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) (*.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (+.f64 1 x) 3/2)) (/.f64 1 (-.f64 (+.f64 1 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 0 x) (/.f64 1 (-.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (+.f64 1 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (+.f64 1 (pow.f64 (+.f64 1 x) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x))) (-.f64 0 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 x (expm1.f64 (*.f64 1/2 (log1p.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 1 x) 3/2)) (-.f64 (+.f64 1 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 1 x) 3/2)) (+.f64 (+.f64 1 x) (-.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 0 x) (-.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 1 x) 3/2))) (neg.f64 (-.f64 (+.f64 1 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 0 x)) (neg.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (pow.f64 (+.f64 1 x) 3/2)) 1) (-.f64 (+.f64 1 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 0 x) 1) (-.f64 1 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (+.f64 1 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (+.f64 1 (pow.f64 (+.f64 1 x) 3/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (sqrt.f64 (+.f64 1 x))) (-.f64 0 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 x)) 1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1 x) 1/6) (cbrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1 x)) (pow.f64 (+.f64 1 x) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (expm1.f64 (*.f64 3 (log1p.f64 (sqrt.f64 (+.f64 1 x))))) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (sqrt.f64 (+.f64 1 x))) 2) (+.f64 (sqrt.f64 (+.f64 1 x)) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (expm1.f64 (*.f64 2 (log1p.f64 (sqrt.f64 (+.f64 1 x))))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) 2) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) 2)) 2) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) 2)) (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) 1) (-.f64 (hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) 1) 1)))))

simplify97.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
660×distribute-rgt-in_binary64
641×fma-def_binary64
606×distribute-lft-in_binary64
536×unswap-sqr_binary64
495×associate-*l*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02379
16475
214775
341163
493261
5264961
6427861
7450661
8480561
9536261
10650961
Stop Event
1×node limit
Counts
284 → 289
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)))))
2
(+.f64 (*.f64 1/2 x) 2)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 2))
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 2 (*.f64 1/16 (pow.f64 x 3)))))
Outputs
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 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 -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 (*.f64 x (fma.f64 x 1/16 -1/8)) (fma.f64 1/2 x 1))
(fma.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))) 1)
2
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 2)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) 2))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x 2))
(fma.f64 1/2 x (fma.f64 -1/8 (*.f64 x x) 2))
(fma.f64 x (fma.f64 x -1/8 1/2) 2)
(+.f64 (*.f64 -1/8 (pow.f64 x 2)) (+.f64 (*.f64 1/2 x) (+.f64 2 (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 -1/8 (*.f64 x x) (+.f64 (fma.f64 1/2 x 2) (*.f64 1/16 (pow.f64 x 3))))
(fma.f64 -1/8 (*.f64 x x) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 2)))
(fma.f64 1/2 x (fma.f64 -1/8 (*.f64 x x) (fma.f64 1/16 (pow.f64 x 3) 2)))
(fma.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)) (fma.f64 1/2 x 2))
(fma.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))) 2)

eval644.0ms (8.9%)

Compiler

Compiled 18027 to 12584 computations (30.2% saved)

prune197.0ms (2.7%)

Pruning

23 alts after pruning (18 fresh and 5 done)

PrunedKeptTotal
New97618994
Fresh303
Picked011
Done246
Total981231004
Error
0.0b
Counts
1004 → 23
Alt Table
Click to see full alt table
StatusErrorProgram
29.5b
1
▶0.2b
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
0.3b
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)
12.6b
(/.f64 1 (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x)))
0.7b
(pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3)
✓28.7b
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
0.6b
(/.f64 1 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3))
▶0.4b
(/.f64 1 (pow.f64 (hypot.f64 (pow.f64 x 1/4) (pow.f64 (+.f64 x 1) 1/4)) 2))
0.3b
(/.f64 1 (+.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 x)))
28.0b
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
1.9b
(/.f64 1 (+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x)))
✓28.8b
(+.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 1/2 x))
▶27.7b
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (+.f64 1 (sqrt.f64 x))))
✓27.7b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
▶16.6b
(*.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))))))
✓27.7b
(-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x))
0.7b
(*.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))
0.2b
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 x)))
0.5b
(*.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)))
✓0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
28.8b
(-.f64 (-.f64 (+.f64 (*.f64 1/2 x) 2) 1) (sqrt.f64 x))
▶60.1b
(/.f64 2 x)
30.2b
(-.f64 (-.f64 2 1) (sqrt.f64 x))
Compiler

Compiled 512 to 416 computations (18.8% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (+.f64 1 x))
✓0.0b
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓0.1b
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
✓0.3b
(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)
Compiler

Compiled 39 to 26 computations (33.3% saved)

series11.0ms (0.2%)

Counts
4 → 7
Calls

12 calls:

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

rewrite115.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
439×fma-def_binary64
435×prod-exp_binary64
414×log-prod_binary64
298×exp-prod_binary64
297×pow-prod-down_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01045
121645
2274545
Stop Event
1×node limit
Counts
4 → 190
Calls
Call 1
Inputs
(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
(sqrt.f64 (+.f64 1 x))
Outputs
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x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (neg.f64 (-.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 x (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 x (-.f64 1 x))) (neg.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 x (+.f64 1 x)) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 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 (E.f64) (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 x (+.f64 1 x)))) (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (+.f64 x (-.f64 1 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 2)) (cbrt.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(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 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 x)))) (exp.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (sqrt.f64 (+.f64 1 x))) (+.f64 1 (expm1.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 x)))) (+.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 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (sqrt.f64 x)) (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 x))) (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 x)) 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) 1 (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1 x) 1/6) (cbrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/6) (cbrt.f64 x) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (pow.f64 x 1/6) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1 x)) (pow.f64 (+.f64 1 x) 1/6) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4) (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 1 x)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 x))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (+.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) 1/6) (cbrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 x)) (pow.f64 (+.f64 1 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 (+.f64 1 x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (hypot.f64 1 (pow.f64 x 3/2)) (sqrt.f64 (fma.f64 x (-.f64 x 1) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (*.f64 1/2 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 x)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 x) 1/4) 2)))) (#(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 (exp.f64 1/2) (log1p.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 (log1p.f64 x))) 2)) (cbrt.f64 (*.f64 1/2 (log1p.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (*.f64 1/2 (log1p.f64 x)))) (sqrt.f64 (*.f64 1/2 (log1p.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/2 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 1))))) (#(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 1/4 (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 (*.f64 (log1p.f64 x) 1) 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))))))

simplify97.0ms (1.3%)

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
01842
14740
210540
330034
474433
5241433
6405933
7428733
8458633
9512533
10612233
Stop Event
1×node limit
Counts
197 → 197
Calls
Call 1
Inputs
1
1
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
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)

localize3.0ms (0%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 1 x))
✓0.0b
(+.f64 1 (sqrt.f64 x))
✓2.5b
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (+.f64 1 (sqrt.f64 x))))
✓6.4b
(-.f64 1 (+.f64 1 (sqrt.f64 x)))
Compiler

Compiled 33 to 22 computations (33.3% saved)

series5.0ms (0.1%)

Counts
3 → 2
Calls

9 calls:

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

rewrite94.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
655×fma-def_binary64
443×log-prod_binary64
330×pow-prod-down_binary64
311×fma-neg_binary64
268×pow2_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0926
121122
2313922
Stop Event
1×node limit
Counts
3 → 170
Calls
Call 1
Inputs
(-.f64 1 (+.f64 1 (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (+.f64 1 (sqrt.f64 x))))
(+.f64 1 (sqrt.f64 x))
Outputs
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(hypot.f64 1 (pow.f64 (+.f64 1 x) 1/4)) (+.f64 (neg.f64 (sqrt.f64 x)) -1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 2 (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (sqrt.f64 x))) (/.f64 x (-.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 x))) 2) (cbrt.f64 (+.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (pow.f64 x 1/4)) (hypot.f64 1 (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 x 3/2)) (/.f64 1 (+.f64 1 (-.f64 x (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 x) (/.f64 1 (-.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (-.f64 x (sqrt.f64 x))) (+.f64 1 (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (sqrt.f64 x)) (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 x 3/2)) (+.f64 1 (-.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 x 3/2)) (+.f64 x (-.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 x) (-.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 x 3/2))) (neg.f64 (+.f64 1 (-.f64 x (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 x)) (neg.f64 (-.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 x 1) (-.f64 (sqrt.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (pow.f64 x 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1 (-.f64 x (sqrt.f64 x))) (+.f64 1 (pow.f64 x 3/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (sqrt.f64 x)) (-.f64 1 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log.f64 (+.f64 2 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/3 (log1p.f64 (sqrt.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log1p.f64 (sqrt.f64 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 2 (sqrt.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) 1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (pow.f64 x 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/6) (cbrt.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 2 (sqrt.f64 x))) 2) (cbrt.f64 (+.f64 2 (sqrt.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 2 (sqrt.f64 x))) (sqrt.f64 (+.f64 2 (sqrt.f64 x))) -1)))))

simplify13.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
012
142
Stop Event
1×saturated
Counts
172 → 171
Calls
Call 1
Inputs
1
1
Outputs
1
1

localize86.0ms (1.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.4b
(/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))
✓2.3b
(-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))
✓12.1b
(*.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))))))
✓15.3b
(sqrt.f64 (*.f64 (+.f64 1 x) x))
Compiler

Compiled 100 to 71 computations (29% saved)

series34.0ms (0.5%)

Counts
4 → 37
Calls

12 calls:

TimeVariablePointExpression
8.0ms
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))))))
6.0ms
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))))))
4.0ms
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))))))
3.0ms
x
@inf
(sqrt.f64 (*.f64 (+.f64 1 x) x))
2.0ms
x
@inf
(-.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x)))

rewrite152.0ms (2.1%)

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
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (hypot.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 x))) (cbrt.f64 (+.f64 x (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (*.f64 x x))) (cbrt.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (hypot.f64 x (sqrt.f64 x))) (sqrt.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 x (*.f64 x x)) 2))) (sqrt.f64 (cbrt.f64 (+.f64 x (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (hypot.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 x (*.f64 x x)) 2)) 1/2) (pow.f64 (cbrt.f64 (+.f64 x (*.f64 x x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (*.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 x (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 x (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 x (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (hypot.f64 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (hypot.f64 x (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 x (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 x (cbrt.f64 (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 x (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (cbrt.f64 (pow.f64 x 3/2)) x)))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (+.f64 (log.f64 x) (log1p.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (hypot.f64 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 (-.f64 x (-.f64 (hypot.f64 x (sqrt.f64 x)) x)) (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))))))) (#(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 x (-.f64 (hypot.f64 x (sqrt.f64 x)) x)) (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (-.f64 x (-.f64 (hypot.f64 x (sqrt.f64 x)) x)) (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 1 x) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))) (*.f64 (-.f64 x (hypot.f64 x (sqrt.f64 x))) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 1 x)) (*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (-.f64 x (hypot.f64 x (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 1 (-.f64 x (-.f64 (hypot.f64 x (sqrt.f64 x)) x))) (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (+.f64 1 (-.f64 x (-.f64 (hypot.f64 x (sqrt.f64 x)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (-.f64 x (-.f64 (hypot.f64 x (sqrt.f64 x)) x))) (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (+.f64 1 (-.f64 x (-.f64 (hypot.f64 x (sqrt.f64 x)) x))) 2)) (/.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (cbrt.f64 (+.f64 1 (-.f64 x (-.f64 (hypot.f64 x (sqrt.f64 x)) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1 (-.f64 x (-.f64 (hypot.f64 x (sqrt.f64 x)) x)))) (/.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (sqrt.f64 (+.f64 1 (-.f64 x (-.f64 (hypot.f64 x (sqrt.f64 x)) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (-.f64 x (-.f64 (hypot.f64 x (sqrt.f64 x)) x)) 3)) (*.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (-.f64 (+.f64 1 (pow.f64 (-.f64 x (-.f64 (hypot.f64 x (sqrt.f64 x)) x)) 2)) (-.f64 x (-.f64 (hypot.f64 x (sqrt.f64 x)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (-.f64 x (-.f64 (hypot.f64 x (sqrt.f64 x)) x)) 2)) (*.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (+.f64 (-.f64 1 (+.f64 x x)) (hypot.f64 x (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (-.f64 x (-.f64 (hypot.f64 x (sqrt.f64 x)) x)))) (neg.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (+.f64 1 (pow.f64 (-.f64 x (-.f64 (hypot.f64 x (sqrt.f64 x)) x)) 3))) (*.f64 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(-.f64 x (hypot.f64 x (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 x (hypot.f64 x (sqrt.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (neg.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1 (neg.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 3/2)) (cbrt.f64 (pow.f64 x 3/2)) (neg.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (cbrt.f64 (*.f64 x x)) (neg.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 x x)) (cbrt.f64 x) (neg.f64 (hypot.f64 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (neg.f64 (hypot.f64 x (sqrt.f64 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))) (cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) -2)) (/.f64 1 (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) -2)) (*.f64 (/.f64 1 (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 (pow.f64 x 3/4) (pow.f64 (+.f64 1 x) 3/4))) (/.f64 1 (hypot.f64 (pow.f64 x 3/4) (pow.f64 (+.f64 1 x) 3/4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 (pow.f64 x 3/4) (pow.f64 (+.f64 1 x) 3/4))) (*.f64 (/.f64 1 (hypot.f64 (pow.f64 x 3/4) (pow.f64 (+.f64 1 x) 3/4))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) 2) -1) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 (pow.f64 x 3/4) (pow.f64 (+.f64 1 x) 3/4)) -1) (pow.f64 (hypot.f64 (pow.f64 x 3/4) (pow.f64 (+.f64 1 x) 3/4)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 9/2) (pow.f64 x 9/2))) (+.f64 (pow.f64 (+.f64 1 x) 3) (-.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 x (sqrt.f64 x)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 (pow.f64 (+.f64 1 x) 3) (pow.f64 x 3))) (-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (hypot.f64 (pow.f64 x 3/4) (pow.f64 (+.f64 1 x) 3/4))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)))) 1))))))

simplify86.0ms (1.2%)

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))))))
(fma.f64 1/4 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) (fma.f64 1/2 (*.f64 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) x) (/.f64 -3/8 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))
(fma.f64 1/2 (/.f64 x (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))) (*.f64 (/.f64 1 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))) -1/8))
(-.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 1/4 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))) (-.f64 (fma.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)))) (neg.f64 (/.f64 (-.f64 (/.f64 1/16 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (fma.f64 -3/4 (-.f64 (/.f64 1/4 (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))))) (/.f64 (*.f64 -3/32 (+.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)))))) x))) (/.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))))))
(+.f64 (-.f64 (/.f64 (*.f64 1/2 x) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (/.f64 (-.f64 (/.f64 -1/16 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (fma.f64 -3/4 (fma.f64 1/4 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) (/.f64 -3/8 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))) (/.f64 -3/32 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))) x)) (fma.f64 1/4 (exp.f64 (*.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))) -3/2)) (/.f64 -3/8 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))))
(-.f64 (fma.f64 1/2 (/.f64 x (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))) (*.f64 (/.f64 1 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))) -1/8)) (/.f64 (-.f64 (/.f64 -1/16 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))) (fma.f64 -3/4 (*.f64 (/.f64 1 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))) -1/8) (/.f64 -3/32 (*.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 (*.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)))))))
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(/.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))))))

localize41.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

Compiled 49 to 39 computations (20.4% saved)

series21.0ms (0.3%)

Counts
4 → 48
Calls

12 calls:

TimeVariablePointExpression
5.0ms
x
@inf
(pow.f64 (hypot.f64 (pow.f64 x 1/4) (pow.f64 (+.f64 x 1) 1/4)) 2)
4.0ms
x
@-inf
(/.f64 1 (pow.f64 (hypot.f64 (pow.f64 x 1/4) (pow.f64 (+.f64 x 1) 1/4)) 2))
3.0ms
x
@-inf
(pow.f64 (hypot.f64 (pow.f64 x 1/4) (pow.f64 (+.f64 x 1) 1/4)) 2)
2.0ms
x
@inf
(/.f64 1 (pow.f64 (hypot.f64 (pow.f64 x 1/4) (pow.f64 (+.f64 x 1) 1/4)) 2))
1.0ms
x
@0
(pow.f64 (hypot.f64 (pow.f64 x 1/4) (pow.f64 (+.f64 x 1) 1/4)) 2)

rewrite81.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
432×log-prod_binary64
336×exp-prod_binary64
278×prod-exp_binary64
266×pow2_binary64
249×pow-prod-down_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01152
124745
2280745
Stop Event
1×node limit
Counts
4 → 169
Calls
Call 1
Inputs
(pow.f64 (hypot.f64 (pow.f64 x 1/4) (pow.f64 (+.f64 x 1) 1/4)) 2)
(hypot.f64 (pow.f64 x 1/4) (pow.f64 (+.f64 x 1) 1/4))
(/.f64 1 (pow.f64 (hypot.f64 (pow.f64 x 1/4) (pow.f64 (+.f64 x 1) 1/4)) 2))
(pow.f64 (+.f64 x 1) 1/4)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))))) (#(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 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))) (log.f64 (sqrt.f64 (exp.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.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 (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 (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 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1/4) (sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3/2)) (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 5/6) (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1/6))))) (#(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 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) -1/2))))) (#(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 (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 /.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3/2) (pow.f64 (+.f64 x 1) 3/2)) (+.f64 x (-.f64 (+.f64 x 1) (pow.f64 (*.f64 x (+.f64 x 1)) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 x (+.f64 x 1)) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.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 (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 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 exp.f64 (*.f64 (*.f64 3 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.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 (log.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 1) 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 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 1) (*.f64 -1/2 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.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 (*.f64 (log.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 1) (log.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (log.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) (*.f64 (log.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 1) (*.f64 (log.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))) 1)))))) (#(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 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 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (sqrt.f64 x))))) (#(struct:change 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simplify93.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
755×associate-/l*_binary64
343×distribute-rgt-in_binary64
332×distribute-lft-in_binary64
314×fma-def_binary64
233×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03173288
19992795
237842293
Stop Event
1×node limit
Counts
217 → 260
Calls
Call 1
Inputs
(+.f64 1 (sqrt.f64 x))
(+.f64 (*.f64 1/2 x) (+.f64 1 (sqrt.f64 x)))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 (+.f64 (*.f64 1/16 (/.f64 1 (+.f64 1 (sqrt.f64 x)))) (*.f64 -1 (+.f64 1/8 (pow.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) 2)))) (pow.f64 x 2)) (+.f64 1 (sqrt.f64 x))))
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1
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(+.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
(+.f64 1 (sqrt.f64 x))
(+.f64 (*.f64 1/2 x) (+.f64 1 (sqrt.f64 x)))
(fma.f64 1/2 x (+.f64 1 (sqrt.f64 x)))
(+.f64 (sqrt.f64 x) (fma.f64 x 1/2 1))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 (+.f64 (*.f64 1/16 (/.f64 1 (+.f64 1 (sqrt.f64 x)))) (*.f64 -1 (+.f64 1/8 (pow.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) 2)))) (pow.f64 x 2)) (+.f64 1 (sqrt.f64 x))))
(fma.f64 1/2 x (fma.f64 (+.f64 (/.f64 1/16 (+.f64 1 (sqrt.f64 x))) (neg.f64 (+.f64 1/8 (pow.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) 2)))) (*.f64 x x) (+.f64 1 (sqrt.f64 x))))
(fma.f64 x 1/2 (fma.f64 (-.f64 (/.f64 1/16 (+.f64 1 (sqrt.f64 x))) (+.f64 1/8 (pow.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) 2))) (*.f64 x x) (+.f64 1 (sqrt.f64 x))))
(fma.f64 x 1/2 (fma.f64 (+.f64 (/.f64 1/16 (+.f64 1 (sqrt.f64 x))) (-.f64 -1/8 (/.f64 1/16 (+.f64 1 (sqrt.f64 x))))) (*.f64 x x) (+.f64 1 (sqrt.f64 x))))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 (+.f64 (*.f64 1/16 (/.f64 1 (+.f64 1 (sqrt.f64 x)))) (*.f64 -1 (+.f64 1/8 (pow.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) 2)))) (pow.f64 x 2)) (+.f64 1 (+.f64 (sqrt.f64 x) (*.f64 1/16 (pow.f64 x 3))))))
(fma.f64 1/2 x (fma.f64 (+.f64 (/.f64 1/16 (+.f64 1 (sqrt.f64 x))) (neg.f64 (+.f64 1/8 (pow.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) 2)))) (*.f64 x x) (+.f64 (+.f64 1 (sqrt.f64 x)) (*.f64 1/16 (pow.f64 x 3)))))
(fma.f64 x 1/2 (fma.f64 (-.f64 (/.f64 1/16 (+.f64 1 (sqrt.f64 x))) (+.f64 1/8 (pow.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) 2))) (*.f64 x x) (+.f64 1 (fma.f64 1/16 (pow.f64 x 3) (sqrt.f64 x)))))
(fma.f64 x 1/2 (fma.f64 (+.f64 (/.f64 1/16 (+.f64 1 (sqrt.f64 x))) (-.f64 -1/8 (/.f64 1/16 (+.f64 1 (sqrt.f64 x))))) (*.f64 x x) (+.f64 1 (fma.f64 1/16 (pow.f64 x 3) (sqrt.f64 x)))))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (pow.f64 (sqrt.f64 2) 2))
(*.f64 (sqrt.f64 x) 2)
(+.f64 (*.f64 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 x)) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(fma.f64 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 x) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(fma.f64 (sqrt.f64 x) 2 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 x) 2))
(+.f64 (*.f64 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 x)) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 x) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16))))
(fma.f64 (sqrt.f64 x) 2 (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16))))
(fma.f64 (sqrt.f64 x) 2 (fma.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))
(+.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 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 x)) (+.f64 (*.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.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 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 x) (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (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 x) 2 (fma.f64 1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/16)))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 1/16))
(+.f64 (fma.f64 (sqrt.f64 x) 2 (fma.f64 -1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) 1/16))
(*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 (sqrt.f64 2) 2))
(*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))
(*.f64 2 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))
(*.f64 2 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 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) (pow.f64 (sqrt.f64 2) 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) (*.f64 (pow.f64 (sqrt.f64 2) 2) (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) (*.f64 2 (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) (*.f64 2 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 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 (*.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 (*.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 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 (sqrt.f64 2) 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) (fma.f64 -3/16 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (*.f64 x x)) (fma.f64 1/16 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (*.f64 x x)) (*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)))))
(+.f64 (*.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) (fma.f64 1/2 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) x) (*.f64 2 (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) (+.f64 (*.f64 2 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) (*.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (*.f64 x x)) -1/8)))
(+.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 (*.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 (*.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 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) (pow.f64 (sqrt.f64 2) 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) (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)) (fma.f64 -3/16 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (*.f64 x x)) (fma.f64 1/16 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (*.f64 x x)) (*.f64 (pow.f64 (sqrt.f64 2) 2) (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) (-.f64 (+.f64 (*.f64 2 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (*.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)) (/.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 (+.f64 (*.f64 2 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) (*.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) (*.f64 x x)) -1/8)) (*.f64 (/.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) x) (-.f64 1/2 (/.f64 -1/16 (*.f64 x x)))))
(sqrt.f64 (+.f64 1 (sqrt.f64 x)))
(+.f64 (*.f64 1/4 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x)))) x)) (sqrt.f64 (+.f64 1 (sqrt.f64 x))))
(fma.f64 1/4 (*.f64 x (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) (sqrt.f64 (+.f64 1 (sqrt.f64 x))))
(fma.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) x (sqrt.f64 (+.f64 1 (sqrt.f64 x))))
(+.f64 (*.f64 1/4 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x)))) x)) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (+.f64 1/8 (pow.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) 2)) (pow.f64 x 2)) (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x)))))) (sqrt.f64 (+.f64 1 (sqrt.f64 x)))))
(fma.f64 1/4 (*.f64 x (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) (fma.f64 -1/2 (*.f64 (+.f64 1/8 (pow.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) 2)) (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x)))))) (sqrt.f64 (+.f64 1 (sqrt.f64 x)))))
(fma.f64 1/4 (*.f64 x (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) (fma.f64 -1/2 (*.f64 (+.f64 1/8 (pow.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) 2)) (*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x)))) (*.f64 x x))) (sqrt.f64 (+.f64 1 (sqrt.f64 x)))))
(+.f64 (sqrt.f64 (+.f64 1 (sqrt.f64 x))) (*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x)))) (+.f64 (*.f64 x 1/4) (*.f64 (+.f64 -1/16 (*.f64 -1/2 (/.f64 1/16 (+.f64 1 (sqrt.f64 x))))) (*.f64 x x)))))
(+.f64 (*.f64 1/4 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x)))) x)) (+.f64 (*.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x)))) (*.f64 (-.f64 1/16 (*.f64 -1/4 (/.f64 (+.f64 1/8 (pow.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) 2)) (+.f64 1 (sqrt.f64 x))))) (pow.f64 x 3)))) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (+.f64 1/8 (pow.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) 2)) (pow.f64 x 2)) (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x)))))) (sqrt.f64 (+.f64 1 (sqrt.f64 x))))))
(fma.f64 1/4 (*.f64 x (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x)))) (*.f64 (pow.f64 x 3) (+.f64 1/16 (*.f64 1/4 (/.f64 (+.f64 1/8 (pow.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) 2)) (+.f64 1 (sqrt.f64 x))))))) (fma.f64 -1/2 (*.f64 (+.f64 1/8 (pow.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) 2)) (*.f64 (*.f64 x x) (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x)))))) (sqrt.f64 (+.f64 1 (sqrt.f64 x))))))
(fma.f64 1/4 (*.f64 x (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) (fma.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x)))) (*.f64 (pow.f64 x 3) (-.f64 1/16 (*.f64 -1/4 (/.f64 (+.f64 1/8 (pow.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) 2)) (+.f64 1 (sqrt.f64 x))))))) (fma.f64 -1/2 (*.f64 (+.f64 1/8 (pow.f64 (*.f64 1/4 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))))) 2)) (*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x)))) (*.f64 x x))) (sqrt.f64 (+.f64 1 (sqrt.f64 x))))))
(+.f64 (fma.f64 -1/2 (*.f64 (+.f64 1/8 (/.f64 1/16 (+.f64 1 (sqrt.f64 x)))) (*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x)))) (*.f64 x x))) (sqrt.f64 (+.f64 1 (sqrt.f64 x)))) (*.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x)))) (+.f64 (*.f64 x 1/4) (*.f64 1/2 (*.f64 (pow.f64 x 3) (+.f64 1/16 (/.f64 (+.f64 1/32 (*.f64 1/4 (/.f64 1/16 (+.f64 1 (sqrt.f64 x))))) (+.f64 1 (sqrt.f64 x)))))))))
(*.f64 (sqrt.f64 2) (pow.f64 (*.f64 1 x) 1/4))
(*.f64 (sqrt.f64 2) (pow.f64 x 1/4))
(+.f64 (*.f64 (sqrt.f64 2) (pow.f64 (*.f64 1 x) 1/4)) (*.f64 1/4 (*.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4))))
(fma.f64 (sqrt.f64 2) (pow.f64 x 1/4) (*.f64 (*.f64 1/4 (/.f64 1 (sqrt.f64 2))) (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4)))
(fma.f64 1/4 (/.f64 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (pow.f64 x 1/4)))
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(fma.f64 (sqrt.f64 2) (pow.f64 x 1/4) (fma.f64 1/2 (*.f64 (/.f64 (-.f64 (*.f64 (sqrt.f64 x) -1/8) (pow.f64 (*.f64 1/4 (*.f64 (pow.f64 x 1/4) (/.f64 1 (sqrt.f64 2)))) 2)) (sqrt.f64 2)) (pow.f64 (/.f64 1 (pow.f64 x 9)) 1/4)) (*.f64 (*.f64 1/4 (/.f64 1 (sqrt.f64 2))) (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4))))
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(+.f64 (/.f64 1/4 (*.f64 (pow.f64 (sqrt.f64 2) 6) (*.f64 (*.f64 x x) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)))) (-.f64 (+.f64 (+.f64 (/.f64 1/8 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 4)))) (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 2) 2) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2)))) (neg.f64 (/.f64 (-.f64 (/.f64 1/16 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (pow.f64 (sqrt.f64 2) 4))) (fma.f64 1/2 (/.f64 (-.f64 (fma.f64 1/16 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (pow.f64 (sqrt.f64 2) 2)) (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) -1/8)) (pow.f64 (*.f64 -1/4 (/.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (sqrt.f64 2))) 2)) (*.f64 (pow.f64 (sqrt.f64 2) 6) (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 4))) (*.f64 -1/2 (/.f64 (+.f64 (/.f64 1/4 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (pow.f64 (sqrt.f64 2) 6))) (/.f64 1/8 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2) (pow.f64 (sqrt.f64 2) 4)))) (pow.f64 (sqrt.f64 2) 2))))) (pow.f64 x 3)))) (/.f64 1/2 (*.f64 (pow.f64 (sqrt.f64 2) 4) (*.f64 x (pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) 2))))))
(+.f64 (/.f64 1/4 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) (*.f64 (*.f64 x x) (pow.f64 (sqrt.f64 2) 6)))) (+.f64 (/.f64 (/.f64 1/32 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (*.f64 x x)) (-.f64 (-.f64 (/.f64 1/2 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (/.f64 (-.f64 (/.f64 1/64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (fma.f64 -1/2 (/.f64 (+.f64 (/.f64 (/.f64 1/4 (pow.f64 (sqrt.f64 2) 6)) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2)) (/.f64 1/32 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))) 2) (*.f64 (/.f64 1/2 (pow.f64 (sqrt.f64 2) 6)) (/.f64 (-.f64 (fma.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) -1/8 (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) 32)) (/.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2) 32)) (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 4))))) (pow.f64 x 3))) (/.f64 1/8 (*.f64 x (pow.f64 (pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 2))))))
(+.f64 (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2))) (+.f64 (-.f64 (/.f64 1/2 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) (/.f64 (-.f64 (+.f64 (/.f64 1/64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) (*.f64 -1/16 (/.f64 (+.f64 (*.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2) -1/8) 0) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 4)))) (*.f64 -1/4 (+.f64 (/.f64 1/32 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2)) (/.f64 1/32 (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2))))) (pow.f64 x 3))) (+.f64 (/.f64 1/32 (*.f64 (*.f64 x x) (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2))) (/.f64 -1/8 (*.f64 x (pow.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) 2))))))
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 x 1/4 (*.f64 x (*.f64 x -3/32))))
(+.f64 1 (*.f64 x (+.f64 1/4 (*.f64 -3/32 x))))
(+.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 x 1/4 (*.f64 x (*.f64 x -3/32)))))
(+.f64 (*.f64 (*.f64 x x) (+.f64 -3/32 (*.f64 x 7/128))) (fma.f64 x 1/4 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))))
(+.f64 (fma.f64 1/4 (pow.f64 (/.f64 1 (pow.f64 x 3)) 1/4) (pow.f64 x 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)))))
(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)))
(exp.f64 (*.f64 1/4 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(pow.f64 (exp.f64 1/4) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))
(pow.f64 (exp.f64 1/4) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))
(*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 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 1/4 (/.f64 (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 (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)))))
(+.f64 (*.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 (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))))))
(+.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) (fma.f64 7/128 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) (pow.f64 x 3)) (*.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -1/4) (pow.f64 -1 1/4)) x) (+.f64 1/4 (/.f64 -3/32 x)))))

eval534.0ms (7.4%)

Compiler

Compiled 21188 to 15931 computations (24.8% saved)

prune179.0ms (2.5%)

Pruning

19 alts after pruning (12 fresh and 7 done)

PrunedKeptTotal
New8868894
Fresh9413
Picked101
Done279
Total89819917
Error
0b
Counts
917 → 19
Alt Table
Click to see full alt table
StatusErrorProgram
28.8b
(-.f64 (-.f64 (+.f64 (*.f64 1/2 x) 2) 1) (sqrt.f64 x))
29.5b
1
32.6b
(/.f64 1 (*.f64 (sqrt.f64 x) 2))
0.3b
(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) -2)
✓28.7b
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
33.0b
(/.f64 1 (*.f64 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 x)))
✓28.8b
(+.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 1/2 x))
✓27.7b
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (+.f64 1 (sqrt.f64 x))))
✓27.7b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓60.1b
(/.f64 2 x)
25.1b
(/.f64 1 (+.f64 1 (sqrt.f64 x)))
32.5b
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
40.6b
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (+.f64 1 (+.f64 x -1/2)))
30.2b
(-.f64 (-.f64 2 1) (sqrt.f64 x))
12.6b
(/.f64 1 (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x)))
0.2b
(/.f64 1 (fma.f64 (pow.f64 x 3/8) (pow.f64 x 1/8) (sqrt.f64 (+.f64 x 1))))
28.0b
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
✓27.7b
(-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x))
✓0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Compiler

Compiled 181 to 149 computations (17.7% saved)

regimes91.0ms (1.2%)

Counts
50 → 1
Calls
Call 1
Inputs
1
1
1
1
(/.f64 2 x)
(/.f64 1 (*.f64 (sqrt.f64 x) 2))
(/.f64 1 (+.f64 1 (sqrt.f64 x)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(-.f64 (-.f64 2 1) (sqrt.f64 x))
(+.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 1/2 x))
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(-.f64 (-.f64 (+.f64 (*.f64 1/2 x) 2) 1) (sqrt.f64 x))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (+.f64 1 (sqrt.f64 x))))
(-.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1)
(-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 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 1 (*.f64 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 x)))
(/.f64 1 (+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x)))
(/.f64 1 (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x)))
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 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))))
(*.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))
(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) -2)
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
(pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2)
(-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 3) (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 1 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3))
(/.f64 1 (fma.f64 (pow.f64 x 3/8) (pow.f64 x 1/8) (sqrt.f64 (+.f64 x 1))))
(/.f64 1 (pow.f64 (hypot.f64 (pow.f64 x 1/4) (pow.f64 (+.f64 x 1) 1/4)) 2))
(-.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 x))
(-.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 1 (+.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (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 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)))
(/.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))))))
(*.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))
Outputs
(/.f64 1 (fma.f64 (pow.f64 x 3/8) (pow.f64 x 1/8) (sqrt.f64 (+.f64 x 1))))
Calls

3 calls:

35.0ms
x
6.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
6.0ms
(-.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 602 to 414 computations (31.2% saved)

regimes38.0ms (0.5%)

Counts
37 → 1
Calls
Call 1
Inputs
1
1
1
1
(/.f64 2 x)
(/.f64 1 (*.f64 (sqrt.f64 x) 2))
(/.f64 1 (+.f64 1 (sqrt.f64 x)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(-.f64 (-.f64 2 1) (sqrt.f64 x))
(+.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 1/2 x))
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(-.f64 (-.f64 (+.f64 (*.f64 1/2 x) 2) 1) (sqrt.f64 x))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(+.f64 (sqrt.f64 (+.f64 1 x)) (-.f64 1 (+.f64 1 (sqrt.f64 x))))
(-.f64 (+.f64 1 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 1)
(-.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 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 1 (*.f64 (pow.f64 (sqrt.f64 2) 2) (sqrt.f64 x)))
(/.f64 1 (+.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x)))
(/.f64 1 (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x)))
(/.f64 1 (+.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (sqrt.f64 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))))
(*.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))
(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
(pow.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) -2)
(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
(pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 2)
(-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 3) (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 1 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) 3))
Outputs
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Calls

3 calls:

16.0ms
x
5.0ms
(-.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 368 to 262 computations (28.8% saved)

regimes44.0ms (0.6%)

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

3 calls:

30.0ms
x
5.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
5.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Results
ErrorSegmentsBranch
0.5b2x
0.5b2(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.5b2(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 107 to 75 computations (29.9% saved)

bsearch55.0ms (0.8%)

Algorithm
1×binary-search
Steps
TimeLeftRight
54.0ms
25771631.476970162
126529898.0862913
Compiler

Compiled 12 to 9 computations (25% saved)

regimes17.0ms (0.2%)

Counts
14 → 2
Calls
Call 1
Inputs
1
1
1
1
(/.f64 2 x)
(/.f64 1 (*.f64 (sqrt.f64 x) 2))
(/.f64 1 (+.f64 1 (sqrt.f64 x)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(-.f64 (-.f64 2 1) (sqrt.f64 x))
(+.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 1/2 x))
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(-.f64 (-.f64 (+.f64 (*.f64 1/2 x) 2) 1) (sqrt.f64 x))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
Outputs
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
Calls

1 calls:

13.0ms
x
Results
ErrorSegmentsBranch
1.0b2x
Compiler

Compiled 84 to 59 computations (29.8% saved)

bsearch18.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
18.0ms
0.011197212236638863
144031.40892645018
Compiler

Compiled 12 to 9 computations (25% saved)

regimes13.0ms (0.2%)

Counts
10 → 2
Calls
Call 1
Inputs
1
1
1
1
(/.f64 2 x)
(/.f64 1 (*.f64 (sqrt.f64 x) 2))
(/.f64 1 (+.f64 1 (sqrt.f64 x)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(-.f64 (-.f64 2 1) (sqrt.f64 x))
(+.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 1/2 x))
Outputs
(+.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 1/2 x))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
Calls

1 calls:

11.0ms
x
Results
ErrorSegmentsBranch
1.0b2x
Compiler

Compiled 42 to 31 computations (26.2% saved)

bsearch18.0ms (0.3%)

Algorithm
1×binary-search
Steps
TimeLeftRight
18.0ms
0.011197212236638863
144031.40892645018
Compiler

Compiled 12 to 9 computations (25% saved)

regimes12.0ms (0.2%)

Counts
9 → 2
Calls
Call 1
Inputs
1
1
1
1
(/.f64 2 x)
(/.f64 1 (*.f64 (sqrt.f64 x) 2))
(/.f64 1 (+.f64 1 (sqrt.f64 x)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(-.f64 (-.f64 2 1) (sqrt.f64 x))
Outputs
(-.f64 (-.f64 2 1) (sqrt.f64 x))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
Calls

1 calls:

10.0ms
x
Results
ErrorSegmentsBranch
1.7b2x
Compiler

Compiled 34 to 26 computations (23.5% saved)

bsearch82.0ms (1.1%)

Algorithm
1×binary-search
Steps
TimeLeftRight
82.0ms
0.011197212236638863
144031.40892645018
Compiler

Compiled 12 to 9 computations (25% saved)

regimes11.0ms (0.2%)

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

1 calls:

10.0ms
x
Results
ErrorSegmentsBranch
1.7b2x
Compiler

Compiled 28 to 22 computations (21.4% saved)

bsearch18.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
18.0ms
0.011197212236638863
144031.40892645018
Compiler

Compiled 12 to 9 computations (25% saved)

regimes11.0ms (0.1%)

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

1 calls:

9.0ms
x
Results
ErrorSegmentsBranch
1.7b2x
Compiler

Compiled 22 to 17 computations (22.7% saved)

bsearch19.0ms (0.3%)

Algorithm
1×binary-search
Steps
TimeLeftRight
19.0ms
0.011197212236638863
144031.40892645018
Compiler

Compiled 12 to 9 computations (25% saved)

regimes10.0ms (0.1%)

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

1 calls:

8.0ms
x
Results
ErrorSegmentsBranch
2.5b2x
Compiler

Compiled 16 to 13 computations (18.8% saved)

bsearch45.0ms (0.6%)

Algorithm
1×binary-search
Steps
TimeLeftRight
44.0ms
0.011197212236638863
144031.40892645018
Compiler

Compiled 12 to 9 computations (25% saved)

regimes6.0ms (0.1%)

Accuracy

Total -30.7b remaining (-104.1%)

Threshold costs -30.7b (-104.1%)

Counts
5 → 1
Calls
Call 1
Inputs
1
1
1
1
(/.f64 2 x)
Outputs
1
Calls

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
29.5b1x
Compiler

Compiled 10 to 8 computations (20% saved)

simplify53.0ms (0.7%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
042199
156199
262199
364199
465199
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(/.f64 1 (fma.f64 (pow.f64 x 3/8) (pow.f64 x 1/8) (sqrt.f64 (+.f64 x 1))))
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(if (<=.f64 x 6918019647384439/268435456) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 3227376694816969/288230376151711744) (-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 3227376694816969/288230376151711744) (+.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 1/2 x)) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 3227376694816969/288230376151711744) (-.f64 (-.f64 2 1) (sqrt.f64 x)) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 3227376694816969/288230376151711744) (/.f64 1 (+.f64 1 (sqrt.f64 x))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 3227376694816969/288230376151711744) (/.f64 1 (+.f64 1 (sqrt.f64 x))) (/.f64 1 (*.f64 (sqrt.f64 x) 2)))
(if (<=.f64 x 3227376694816969/288230376151711744) 1 (/.f64 1 (*.f64 (sqrt.f64 x) 2)))
1
Outputs
(/.f64 1 (fma.f64 (pow.f64 x 3/8) (pow.f64 x 1/8) (sqrt.f64 (+.f64 x 1))))
(/.f64 1 (fma.f64 (pow.f64 x 3/8) (pow.f64 x 1/8) (sqrt.f64 (+.f64 1 x))))
(/.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 6918019647384439/268435456) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 6918019647384439/268435456) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 3227376694816969/288230376151711744) (-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 3227376694816969/288230376151711744) (-.f64 (+.f64 1 (*.f64 x 1/2)) (sqrt.f64 x)) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 3227376694816969/288230376151711744) (+.f64 (-.f64 1 (sqrt.f64 x)) (*.f64 1/2 x)) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 3227376694816969/288230376151711744) (+.f64 (*.f64 x 1/2) (-.f64 1 (sqrt.f64 x))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 3227376694816969/288230376151711744) (-.f64 (-.f64 2 1) (sqrt.f64 x)) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 3227376694816969/288230376151711744) (-.f64 1 (sqrt.f64 x)) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 3227376694816969/288230376151711744) (/.f64 1 (+.f64 1 (sqrt.f64 x))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))
(if (<=.f64 x 3227376694816969/288230376151711744) (/.f64 1 (+.f64 1 (sqrt.f64 x))) (/.f64 1 (*.f64 (sqrt.f64 x) 2)))
(if (<=.f64 x 3227376694816969/288230376151711744) 1 (/.f64 1 (*.f64 (sqrt.f64 x) 2)))
1
Compiler

Compiled 143 to 114 computations (20.3% saved)

soundness0.0ms (0%)

end148.0ms (2%)

Compiler

Compiled 134 to 98 computations (26.9% saved)

Profiling

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