Details

Time bar (total: 2.6s)

analyze4.0ms (0.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
25%50%25%3
37.5%25%37.5%4
43.7%12.5%43.8%5
46.9%6.2%46.9%6
48.4%3.1%48.5%7
49.2%1.6%49.2%8
49.6%0.8%49.6%9
49.8%0.4%49.8%10
49.9%0.2%49.9%11
49.9%0.1%50%12
50%0%50%13
50%0%50%14
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.4s (51.8%)

Results
549.0ms1996×body1024valid
399.0ms4443×body128valid
239.0ms1067×body512valid
88.0ms542×body256valid
68.0ms208×body2048valid
0.0ms2×body128invalid
Compiler

Compiled 18 to 14 computations (22.2% saved)

preprocess18.0ms (0.7%)

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
712311
816611
920211
1022811
1123011
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 8 to 6 computations (25% saved)

simplify10.0ms (0.4%)

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
712311
816611
920211
1022811
1123011
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))

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
28.8b
Counts
2 → 1
Alt Table
StatusErrorProgram
▶28.8b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 24 to 18 computations (25% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (+.f64 x 1))
✓2.6b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series6.0ms (0.2%)

Counts
2 → 5
Calls

6 calls:

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

rewrite45.0ms (1.7%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0717
115317
2208617
Stop Event
1×node limit
Counts
2 → 63
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 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 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 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 log1p.f64 (expm1.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))))) (#(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 -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 x 1)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (fma.f64 x x -1)) (sqrt.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 1 (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/2 (log1p.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/2 (log1p.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (+.f64 x 1))))))))

simplify30.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
664×fma-def_binary64
612×associate-*l*_binary64
536×unswap-sqr_binary64
370×associate-*r*_binary64
222×fma-neg_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01848
15144
212338
339434
4112629
5374429
Stop Event
1×node limit
Counts
68 → 70
Calls
Call 1
Inputs
1
1
(+.f64 1 (*.f64 1/2 x))
(-.f64 (+.f64 1 (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3)))) (*.f64 1/8 (pow.f64 x 2)))
Outputs
1
1
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(-.f64 (+.f64 1 (*.f64 1/2 x)) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 1 (-.f64 (*.f64 1/2 x) (*.f64 1/8 (*.f64 x x))))
(+.f64 1 (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8)))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/2 x 1))
(fma.f64 x (+.f64 1/2 (*.f64 x -1/8)) 1)
(fma.f64 x (fma.f64 x -1/8 1/2) 1)
(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) (*.f64 1/16 (pow.f64 x 3)))) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 1 (-.f64 (fma.f64 1/2 x (*.f64 1/16 (pow.f64 x 3))) (*.f64 1/8 (*.f64 x x))))
(+.f64 1 (+.f64 (*.f64 1/16 (pow.f64 x 3)) (fma.f64 1/2 x (*.f64 (*.f64 x x) -1/8))))
(fma.f64 (*.f64 x x) -1/8 (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 1)))
(fma.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)) (fma.f64 1/2 x 1))
(fma.f64 x (fma.f64 x (fma.f64 x 1/16 -1/8) 1/2) 1)

prune79.0ms (3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New62870
Fresh000
Picked101
Done000
Total63871
Error
27.1b
Counts
71 → 8
Alt Table
StatusErrorProgram
28.7b
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
29.1b
(+.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)))
28.8b
(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
▶27.9b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
28.9b
(+.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)))
29.9b
1
28.8b
(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
29.1b
(/.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))))))
Compiler

Compiled 1119 to 748 computations (33.2% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series5.0ms (0.2%)

Counts
3 → 14
Calls

9 calls:

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

rewrite84.0ms (3.2%)

Algorithm
1×batch-egg-rewrite
Rules
689×fma-def_binary64
347×fma-neg_binary64
199×expm1-udef_binary64
199×log1p-udef_binary64
138×egg-rr
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01038
123629
2359729
Stop Event
1×node limit
Counts
3 → 275
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
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simplify13.0ms (0.5%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0114
1414
Stop Event
1×saturated
Counts
289 → 276
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

prune287.0ms (10.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New3053308
Fresh527
Picked101
Done000
Total3115316
Error
0.1b
Counts
316 → 5
Alt Table
StatusErrorProgram
28.8b
(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
27.9b
(/.f64 (+.f64 x (-.f64 1 x)) (fma.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 x) (sqrt.f64 (+.f64 x 1))))
28.5b
(*.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) (sqrt.f64 (fma.f64 x x x))))
28.8b
(expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
▶0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Compiler

Compiled 6691 to 4235 computations (36.7% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series1.0ms (0%)

Counts
1 → 1
Calls

3 calls:

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

rewrite44.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
845×log1p-expm1-u_binary64
845×expm1-log1p-u_binary64
90×add-sqr-sqrt_binary64
86×*-un-lft-identity_binary64
86×pow1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0814
117814
2244214
Stop Event
1×node limit
Counts
1 → 25
Calls
Call 1
Inputs
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)) (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4)) -1) (pow.f64 (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 1 x) x) (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 log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.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 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1))))) (#(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 expm1.f64 (log1p.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))))

simplify6.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
011
141
Stop Event
1×saturated
Counts
26 → 26
Calls
Call 1
Inputs
1
Outputs
1

prune127.0ms (4.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1007107
Fresh314
Picked101
Done000
Total1048112
Error
0.0b
Counts
112 → 8
Alt Table
StatusErrorProgram
0.2b
(/.f64 1 (fma.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x 1))))
9.2b
(/.f64 1 (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x)))
28.8b
(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
▶0.2b
(/.f64 1 (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))
8.6b
(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
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)
14.4b
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 (+.f64 1 x) x))))
Compiler

Compiled 1767 to 1283 computations (27.4% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(sqrt.f64 (+.f64 x 1))
✓0.1b
(fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1)))
✓0.1b
(/.f64 1 (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))

series14.0ms (0.5%)

Counts
2 → 8
Calls

6 calls:

TimeVariablePointExpression
6.0ms
x
@inf
(/.f64 1 (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))
5.0ms
x
@-inf
(/.f64 1 (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))
2.0ms
x
@0
(/.f64 1 (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))
1.0ms
x
@-inf
(fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1)))
1.0ms
x
@inf
(fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1)))

rewrite48.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
799×log1p-expm1-u_binary64
799×expm1-log1p-u_binary64
93×add-sqr-sqrt_binary64
89×add-log-exp_binary64
88×add-cbrt-cube_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0935
119625
2231425
Stop Event
1×node limit
Counts
2 → 51
Calls
Call 1
Inputs
(/.f64 1 (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))
(fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) -2)) (/.f64 1 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) -1/2) (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) -1) (pow.f64 (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 x) (hypot.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 x) 1) (hypot.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 2) (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 2) (/.f64 1 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (sqrt.f64 x) 3) (pow.f64 (+.f64 1 x) 3/2)) (+.f64 x (-.f64 (+.f64 1 x) (*.f64 (sqrt.f64 x) (hypot.f64 1 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 x (+.f64 1 x)) (-.f64 (sqrt.f64 x) (hypot.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))))

simplify26.0ms (1%)

Algorithm
1×egg-herbie
Rules
456×fma-neg_binary64
357×associate-/l/_binary64
218×sub-neg_binary64
209×distribute-rgt-out_binary64
187×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
048274
1145274
2501249
32447245
Stop Event
1×node limit
Counts
59 → 65
Calls
Call 1
Inputs
(/.f64 1 (+.f64 1 (sqrt.f64 x)))
(-.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))) (*.f64 1/2 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 2))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (pow.f64 (+.f64 1 (sqrt.f64 x)) 3))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (+.f64 1 (sqrt.f64 x)) 2))) (/.f64 1 (+.f64 1 (sqrt.f64 x))))) (*.f64 1/2 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 2))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (pow.f64 (+.f64 1 (sqrt.f64 x)) 3))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (+.f64 1 (sqrt.f64 x)) 2))) (/.f64 1 (+.f64 1 (sqrt.f64 x))))) (+.f64 (*.f64 1/2 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 2))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 x)) 4))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 x)) 3))) (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)))))))
(+.f64 1 (sqrt.f64 x))
(+.f64 1 (+.f64 (*.f64 1/2 x) (sqrt.f64 x)))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) (sqrt.f64 x))) (*.f64 1/8 (pow.f64 x 2)))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/16 (pow.f64 x 3)) (sqrt.f64 x)))) (*.f64 1/8 (pow.f64 x 2)))
Outputs
(/.f64 1 (+.f64 1 (sqrt.f64 x)))
(-.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))) (*.f64 1/2 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 2))))
(+.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))) (*.f64 -1/2 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 2))))
(+.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))) (*.f64 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) -1/2))
(fma.f64 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) -1/2 (/.f64 1 (+.f64 1 (sqrt.f64 x))))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (pow.f64 (+.f64 1 (sqrt.f64 x)) 3))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (+.f64 1 (sqrt.f64 x)) 2))) (/.f64 1 (+.f64 1 (sqrt.f64 x))))) (*.f64 1/2 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 2))))
(+.f64 (fma.f64 1/4 (/.f64 (*.f64 x x) (pow.f64 (+.f64 1 (sqrt.f64 x)) 3)) (fma.f64 1/8 (/.f64 (*.f64 x x) (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (/.f64 1 (+.f64 1 (sqrt.f64 x))))) (*.f64 -1/2 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 2))))
(+.f64 (fma.f64 1/4 (/.f64 (*.f64 x x) (pow.f64 (+.f64 1 (sqrt.f64 x)) 3)) (fma.f64 1/8 (/.f64 x (/.f64 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2) x)) (/.f64 1 (+.f64 1 (sqrt.f64 x))))) (*.f64 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) -1/2))
(+.f64 (*.f64 (/.f64 x (/.f64 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2) x)) (+.f64 (/.f64 1/4 (+.f64 1 (sqrt.f64 x))) 1/8)) (fma.f64 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) -1/2 (/.f64 1 (+.f64 1 (sqrt.f64 x)))))
(+.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))) (fma.f64 (*.f64 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) x) (+.f64 (/.f64 1/4 (+.f64 1 (sqrt.f64 x))) 1/8) (*.f64 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) -1/2)))
(-.f64 (+.f64 (*.f64 1/4 (/.f64 (pow.f64 x 2) (pow.f64 (+.f64 1 (sqrt.f64 x)) 3))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 x 2) (pow.f64 (+.f64 1 (sqrt.f64 x)) 2))) (/.f64 1 (+.f64 1 (sqrt.f64 x))))) (+.f64 (*.f64 1/2 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 2))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 x)) 4))) (+.f64 (*.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 x)) 3))) (*.f64 1/16 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)))))))
(-.f64 (fma.f64 1/4 (/.f64 (*.f64 x x) (pow.f64 (+.f64 1 (sqrt.f64 x)) 3)) (fma.f64 1/8 (/.f64 (*.f64 x x) (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (/.f64 1 (+.f64 1 (sqrt.f64 x))))) (fma.f64 1/2 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (fma.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 x)) 4)) (fma.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 x)) 3)) (/.f64 (*.f64 (pow.f64 x 3) 1/16) (pow.f64 (+.f64 1 (sqrt.f64 x)) 2))))))
(-.f64 (fma.f64 1/4 (/.f64 (*.f64 x x) (pow.f64 (+.f64 1 (sqrt.f64 x)) 3)) (fma.f64 1/8 (/.f64 x (/.f64 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2) x)) (/.f64 1 (+.f64 1 (sqrt.f64 x))))) (fma.f64 1/2 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (fma.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 x)) 4)) (fma.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 x)) 3)) (/.f64 (pow.f64 x 3) (/.f64 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2) 1/16))))))
(+.f64 (*.f64 (/.f64 x (/.f64 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2) x)) (+.f64 (/.f64 1/4 (+.f64 1 (sqrt.f64 x))) 1/8)) (-.f64 (fma.f64 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) -1/2 (/.f64 1 (+.f64 1 (sqrt.f64 x)))) (fma.f64 1/8 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 x)) 4)) (*.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (+.f64 (/.f64 1/8 (+.f64 1 (sqrt.f64 x))) 1/16)))))
(+.f64 (/.f64 1 (+.f64 1 (sqrt.f64 x))) (-.f64 (*.f64 (*.f64 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) x) (+.f64 (/.f64 1/4 (+.f64 1 (sqrt.f64 x))) 1/8)) (fma.f64 1/2 (/.f64 x (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (*.f64 (/.f64 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (+.f64 (/.f64 1/8 (pow.f64 (+.f64 1 (sqrt.f64 x)) 2)) (+.f64 (/.f64 1/8 (+.f64 1 (sqrt.f64 x))) 1/16))))))
(+.f64 1 (sqrt.f64 x))
(+.f64 1 (+.f64 (*.f64 1/2 x) (sqrt.f64 x)))
(+.f64 1 (fma.f64 1/2 x (sqrt.f64 x)))
(+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) (sqrt.f64 x))) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 1 (-.f64 (fma.f64 1/2 x (sqrt.f64 x)) (*.f64 (*.f64 x x) 1/8)))
(+.f64 1 (+.f64 (fma.f64 x 1/2 (sqrt.f64 x)) (*.f64 (*.f64 x x) -1/8)))
(fma.f64 (*.f64 x x) -1/8 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))
(-.f64 (fma.f64 x 1/2 (sqrt.f64 x)) (fma.f64 (*.f64 x x) 1/8 -1))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/16 (pow.f64 x 3)) (sqrt.f64 x)))) (*.f64 1/8 (pow.f64 x 2)))
(+.f64 1 (-.f64 (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) (sqrt.f64 x))) (*.f64 (*.f64 x x) 1/8)))
(+.f64 (fma.f64 x 1/2 (fma.f64 (pow.f64 x 3) 1/16 (sqrt.f64 x))) (-.f64 1 (*.f64 (*.f64 x x) 1/8)))
(fma.f64 (*.f64 x x) -1/8 (+.f64 (fma.f64 (pow.f64 x 3) 1/16 (sqrt.f64 x)) (fma.f64 x 1/2 1)))
(-.f64 (fma.f64 x 1/2 (fma.f64 (pow.f64 x 3) 1/16 (sqrt.f64 x))) (fma.f64 (*.f64 x x) 1/8 -1))

prune116.0ms (4.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New97097
Fresh077
Picked011
Done000
Total978105
Error
0.0b
Counts
105 → 8
Alt Table
StatusErrorProgram
0.2b
(/.f64 1 (fma.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 x)) (sqrt.f64 (+.f64 x 1))))
9.2b
(/.f64 1 (+.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x)))
28.8b
(log.f64 (exp.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))
✓0.2b
(/.f64 1 (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))
8.6b
(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
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)
14.4b
(*.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (*.f64 (+.f64 1 x) x))))
Compiler

Compiled 1711 to 1223 computations (28.5% saved)

regimes155.0ms (5.9%)

Accuracy

Total 0.1b remaining (78.2%)

Threshold costs 0.1b (78.2%)

Counts
158 → 1
Compiler

Compiled 2149 to 1430 computations (33.5% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
2×+-commutative_binary64
1×*-commutative_binary64
1×*-lft-identity_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
11514
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 1 (+.f64 (*.f64 1 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x)))
Outputs
(/.f64 1 (+.f64 (*.f64 1 (sqrt.f64 (+.f64 x 1))) (sqrt.f64 x)))
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

end115.0ms (4.4%)

Stop Event
1×fuel
Compiler

Compiled 130 to 104 computations (20% saved)

Profiling

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