Details

Time bar (total: 9.4s)

analyze7.0ms (0.1%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
33.3%25%50%0%0%25%0%3
60%37.5%25%0%0%37.5%0%4
77.8%43.7%12.5%0%0%43.7%0%5
88.2%46.9%6.2%0%0%46.9%0%6
93.9%48.4%3.1%0%0%48.4%0%7
96.9%49.2%1.6%0%0%49.2%0%8
98.4%49.6%0.8%0%0%49.6%0%9
99.2%49.8%0.4%0%0%49.8%0%10
99.6%49.9%0.2%0%0%49.9%0%11
99.8%49.9%0.1%0%0%49.9%0%12
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.0s (20.9%)

Results
797.0ms2104×body1024valid
725.0ms4930×body256valid
276.0ms1022×body512valid
105.0ms200×body2048valid
0.0ms3×body256invalid
Bogosity

preprocess21.0ms (0.2%)

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)

simplify12.0ms (0.1%)

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
27.9b
Counts
2 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶27.9b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 8 to 6 computations (25% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(sqrt.f64 (+.f64 x 1))
✓3.1b
(-.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))

rewrite70.0ms (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))))))

simplify90.0ms (1%)

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

Useful iterations: 4 (0.0ms)

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

eval18.0ms (0.2%)

Compiler

Compiled 829 to 549 computations (33.8% saved)

prune31.0ms (0.3%)

Pruning

19 alts after pruning (18 fresh and 1 done)

PrunedKeptTotal
New471865
Fresh000
Picked011
Done000
Total471966
Error
26.5b
Counts
66 → 19
Alt Table
Click to see full alt table
StatusErrorProgram
▶27.9b
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
▶27.5b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
27.8b
(-.f64 (pow.f64 (pow.f64 (+.f64 x 1) 1/4) 2) (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))))
28.0b
(-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 3) (sqrt.f64 x))
27.9b
(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3))
✓27.9b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
29.6b
1
28.0b
(-.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x))
27.8b
(/.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 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (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)))
27.9b
(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))
28.2b
(/.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))))
27.9b
(*.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)))
▶28.8b
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
▶27.9b
(-.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 x))
28.0b
(+.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)))
Compiler

Compiled 564 to 410 computations (27.3% saved)

localize34.0ms (0.4%)

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))
✓0.1b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
✓2.7b
(+.f64 x (-.f64 1 x))
Compiler

Compiled 40 to 25 computations (37.5% saved)

series9.0ms (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))

rewrite106.0ms (1.1%)

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
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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)))))))

simplify13.0ms (0.1%)

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

localize13.0ms (0.1%)

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))

rewrite61.0ms (0.7%)

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)

localize43.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (+.f64 x 1) x)
✓0.1b
(/.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))))
✓11.7b
(-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))
✓12.6b
(sqrt.f64 (*.f64 (+.f64 x 1) x))
Compiler

Compiled 74 to 52 computations (29.7% saved)

series17.0ms (0.2%)

Counts
4 → 41
Calls

12 calls:

TimeVariablePointExpression
5.0ms
x
@-inf
(/.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))))
3.0ms
x
@inf
(/.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))))
2.0ms
x
@-inf
(-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))
1.0ms
x
@0
(/.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))))
1.0ms
x
@inf
(-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))

rewrite172.0ms (1.8%)

Algorithm
1×batch-egg-rewrite
Rules
746×log-prod_binary64
498×fma-neg_binary64
264×log1p-udef_binary64
263×expm1-udef_binary64
222×log-pow_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01362
131562
2491356
Stop Event
1×node limit
Counts
4 → 182
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (+.f64 x 1) x))
(-.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))
(/.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 x 1) x)
Outputs
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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 x (+.f64 x 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (+.f64 x 1) 2) (+.f64 x (-.f64 1 x))) (/.f64 (*.f64 x x) (+.f64 x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (+.f64 x 1))) (cbrt.f64 (pow.f64 (+.f64 x (+.f64 x 1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x (+.f64 x 1)) 2)) (cbrt.f64 (+.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (+.f64 x 1))) (sqrt.f64 (+.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x 1) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 x 1) 2) (*.f64 x (-.f64 x (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (+.f64 x 1) 2) (*.f64 x x)) (/.f64 1 (+.f64 x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 x 1) 2) (*.f64 x (-.f64 x (+.f64 x 1)))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x 1) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 x (-.f64 1 x)) (-.f64 (pow.f64 (+.f64 x 1) 2) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x 1) 3)) (+.f64 (pow.f64 (+.f64 x 1) 2) (*.f64 x (-.f64 x (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x 1) 3)) (+.f64 (*.f64 x x) (-.f64 (pow.f64 (+.f64 x 1) 2) (+.f64 x (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x 1) 2) (*.f64 x x)) (+.f64 x (-.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 x 1) 3))) (neg.f64 (+.f64 (pow.f64 (+.f64 x 1) 2) (*.f64 x (-.f64 x (+.f64 x 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 x 1) 2) (*.f64 x x))) (neg.f64 (+.f64 x (-.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 x 1) 2)) (-.f64 x (+.f64 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (+.f64 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x (+.f64 x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x (+.f64 x 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x (+.f64 x 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x (+.f64 x 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 x (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 x)) (exp.f64 (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 x) (+.f64 1 (expm1.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 x)) (+.f64 1 (expm1.f64 (+.f64 x 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 x 1))) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (+.f64 x 1)) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (+.f64 x 1))) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x (+.f64 x 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x (+.f64 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (+.f64 x x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 x 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2) (cbrt.f64 (+.f64 x 1)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (+.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)) x)))))

simplify132.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
588×fma-def_binary64
475×times-frac_binary64
413×associate-/r*_binary64
343×associate-/l*_binary64
276×associate-+l+_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01801807
15411405
21993920
Stop Event
1×node limit
Counts
223 → 236
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 (pow.f64 x 3/2))
(-.f64 (+.f64 1 (*.f64 3/2 x)) (pow.f64 x 3/2))
(-.f64 (+.f64 1 (+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 3/2 x))) (pow.f64 x 3/2))
(-.f64 (+.f64 (*.f64 -1/16 (pow.f64 x 3)) (+.f64 1 (+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 3/2 x)))) (pow.f64 x 3/2))
(*.f64 3/2 (sqrt.f64 x))
(+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 x))) (*.f64 3/2 (sqrt.f64 x)))
(+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (*.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/2 (sqrt.f64 x))))
(+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (*.f64 3/128 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (*.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 3/2 (sqrt.f64 x)))))
(*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))
(+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (*.f64 -1/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(+.f64 (*.f64 3/128 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 4))) (+.f64 (*.f64 -1/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
(-.f64 1 (pow.f64 x 3/2))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/8 (sqrt.f64 (pow.f64 x 3))) (*.f64 1/4 (sqrt.f64 (pow.f64 x 3)))) (pow.f64 x 4))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x))))) (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (+.f64 (*.f64 1/128 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 1/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (+.f64 (*.f64 -1/2 (/.f64 (-.f64 (*.f64 1/8 (sqrt.f64 (pow.f64 x 3))) (*.f64 1/4 (sqrt.f64 (pow.f64 x 3)))) (pow.f64 x 4))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))))) (+.f64 (*.f64 -1/24 (/.f64 (-.f64 (*.f64 1/8 (sqrt.f64 (pow.f64 x 3))) (*.f64 1/4 (sqrt.f64 (pow.f64 x 3)))) (pow.f64 x 5))) (+.f64 (*.f64 1/96 (sqrt.f64 (/.f64 1 (pow.f64 x 7)))) (+.f64 (*.f64 -1/4 (/.f64 (-.f64 (*.f64 1/8 (sqrt.f64 (pow.f64 x 3))) (*.f64 1/4 (sqrt.f64 (pow.f64 x 3)))) (pow.f64 x 5))) (*.f64 1/4 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))))
(*.f64 -3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) (pow.f64 x 2))))
(+.f64 (*.f64 -3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) (pow.f64 x 2)))) (*.f64 -1 (/.f64 (-.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2))) (*.f64 -9/4 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) 2)))) (pow.f64 x 3))))
(-.f64 (+.f64 (*.f64 -3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) (pow.f64 x 2)))) (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2))) (*.f64 -9/4 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) 2)))) (pow.f64 x 3))) (*.f64 1/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) (pow.f64 x 4)))))) (+.f64 (*.f64 3/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 (pow.f64 (sqrt.f64 -1) 2) (*.f64 (pow.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) 2) (pow.f64 x 4))))) (*.f64 3/2 (/.f64 (-.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2))) (*.f64 -9/4 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) 2)))) (*.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) (pow.f64 x 4))))))
(-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 3/128 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2))) (+.f64 (*.f64 -1/8 (/.f64 (-.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2))) (*.f64 -9/4 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) 2)))) (*.f64 (pow.f64 (sqrt.f64 -1) 2) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2)))) (+.f64 (*.f64 -3/32 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) 2)))) (*.f64 3/2 (/.f64 (-.f64 (*.f64 1/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2))) (+.f64 (*.f64 3/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) 2)))) (*.f64 3/2 (/.f64 (-.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2))) (*.f64 -9/4 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) 2)))) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2))))) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2)))))) (pow.f64 x 5))) (+.f64 (*.f64 -3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) (pow.f64 x 2)))) (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2))) (*.f64 -9/4 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) 2)))) (pow.f64 x 3))) (*.f64 1/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) (pow.f64 x 4))))))) (+.f64 (*.f64 3/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 (pow.f64 (sqrt.f64 -1) 2) (*.f64 (pow.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) 2) (pow.f64 x 4))))) (*.f64 3/2 (/.f64 (-.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2))) (*.f64 -9/4 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) 2)))) (*.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) (pow.f64 x 4))))))
1
(+.f64 (*.f64 2 x) 1)
(+.f64 (*.f64 2 x) 1)
(+.f64 (*.f64 2 x) 1)
(*.f64 2 x)
(+.f64 1 (*.f64 2 x))
(+.f64 1 (*.f64 2 x))
(+.f64 1 (*.f64 2 x))
(*.f64 2 x)
(+.f64 1 (*.f64 2 x))
(+.f64 1 (*.f64 2 x))
(+.f64 1 (*.f64 2 x))
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))
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(-.f64 (fma.f64 -3/2 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 (*.f64 x x) (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2))) (fma.f64 -1 (/.f64 (+.f64 (*.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2))) (*.f64 9/4 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2) 2)))) (pow.f64 x 3)) (*.f64 1/16 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 (pow.f64 x 4) (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2)))))) (fma.f64 3/16 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2) 2)) (pow.f64 x 4))) (*.f64 3/2 (/.f64 (+.f64 (*.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2))) (*.f64 9/4 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2) 2)))) (*.f64 (pow.f64 x 4) (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2))))))
(+.f64 (-.f64 (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x))) (/.f64 (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) -3) (*.f64 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 9) 9/4)) (pow.f64 x 3))) (-.f64 (*.f64 -1/48 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 4))) (fma.f64 3/2 (/.f64 (-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) -3) -8) (/.f64 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 9) 4/3)) (pow.f64 x 4)) (*.f64 -1/48 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 4))))))
(fma.f64 1/2 (*.f64 (/.f64 (pow.f64 (/.f64 -1 x) -3/2) x) (/.f64 (pow.f64 -1 3/2) x)) (fma.f64 -1 (/.f64 (neg.f64 (*.f64 -1/8 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2)))) (pow.f64 x 3)) (*.f64 -3/2 (/.f64 (/.f64 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2)) -24) (pow.f64 x 4)))))
(-.f64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 3/128 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2))) (+.f64 (*.f64 -1/8 (/.f64 (-.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2))) (*.f64 -9/4 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) 2)))) (*.f64 (pow.f64 (sqrt.f64 -1) 2) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2)))) (+.f64 (*.f64 -3/32 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) 2)))) (*.f64 3/2 (/.f64 (-.f64 (*.f64 1/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2))) (+.f64 (*.f64 3/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) 2)))) (*.f64 3/2 (/.f64 (-.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2))) (*.f64 -9/4 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) 2)))) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2))))) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2)))))) (pow.f64 x 5))) (+.f64 (*.f64 -3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) (pow.f64 x 2)))) (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2))) (*.f64 -9/4 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) 2)))) (pow.f64 x 3))) (*.f64 1/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) (pow.f64 x 4))))))) (+.f64 (*.f64 3/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 (pow.f64 (sqrt.f64 -1) 2) (*.f64 (pow.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) 2) (pow.f64 x 4))))) (*.f64 3/2 (/.f64 (-.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2))) (*.f64 -9/4 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) 2)))) (*.f64 (-.f64 (pow.f64 (sqrt.f64 -1) 2) 2) (pow.f64 x 4))))))
(-.f64 (fma.f64 -1 (/.f64 (-.f64 (*.f64 3/128 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2))) (fma.f64 -1/8 (/.f64 (+.f64 (*.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2))) (*.f64 9/4 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2) 2)))) (*.f64 (pow.f64 (sqrt.f64 -1) 2) (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2))) (fma.f64 -3/32 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 (pow.f64 (sqrt.f64 -1) 4) (pow.f64 (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2) 2))) (*.f64 3/2 (/.f64 (-.f64 (*.f64 1/16 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2))) (fma.f64 3/16 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2) 2))) (*.f64 3/2 (/.f64 (+.f64 (*.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2))) (*.f64 9/4 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2) 2)))) (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2))))) (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2)))))) (pow.f64 x 5)) (fma.f64 -3/2 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 (*.f64 x x) (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2))) (fma.f64 -1 (/.f64 (+.f64 (*.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2))) (*.f64 9/4 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2) 2)))) (pow.f64 x 3)) (*.f64 1/16 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 (pow.f64 x 4) (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2))))))) (fma.f64 3/16 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 (*.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2) 2)) (pow.f64 x 4))) (*.f64 3/2 (/.f64 (+.f64 (*.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2))) (*.f64 9/4 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2) 2)))) (*.f64 (pow.f64 x 4) (+.f64 (pow.f64 (sqrt.f64 -1) 2) -2))))))
(-.f64 (-.f64 (+.f64 (-.f64 (*.f64 1/2 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x))) (/.f64 (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) -3) (*.f64 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 9) 9/4)) (pow.f64 x 3))) (*.f64 -1/48 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 4)))) (/.f64 (-.f64 (*.f64 3/128 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) -3)) (fma.f64 -1/8 (-.f64 (*.f64 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 9) -3/8) (*.f64 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) -9) 3/4)) (fma.f64 3/2 (-.f64 (/.f64 (*.f64 1/16 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) 9) (/.f64 (fma.f64 3/2 (-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) -3) -8) (/.f64 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 9) 4/3)) (*.f64 3/16 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) -9))) -3)) (*.f64 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 9) -3/32)))) (pow.f64 x 5))) (fma.f64 3/2 (/.f64 (-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) -3) -8) (/.f64 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) 9) 4/3)) (pow.f64 x 4)) (*.f64 -1/48 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 4)))))
(-.f64 (fma.f64 1/2 (*.f64 (/.f64 (pow.f64 (/.f64 -1 x) -3/2) x) (/.f64 (pow.f64 -1 3/2) x)) (fma.f64 -1 (/.f64 (neg.f64 (*.f64 -1/8 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2)))) (pow.f64 x 3)) (*.f64 -3/2 (/.f64 (/.f64 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2)) -24) (pow.f64 x 4))))) (/.f64 (-.f64 (*.f64 -1/128 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2))) (fma.f64 1/8 (/.f64 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2)) -24) (fma.f64 -1/96 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2)) (*.f64 -1/2 (-.f64 (*.f64 -1/48 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2))) (fma.f64 3/2 (/.f64 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2)) -24) (*.f64 -1/48 (*.f64 (pow.f64 -1 3/2) (pow.f64 (/.f64 -1 x) -3/2))))))))) (pow.f64 x 5)))
1
(+.f64 (*.f64 2 x) 1)
(fma.f64 2 x 1)
(fma.f64 x 2 1)
(+.f64 (*.f64 2 x) 1)
(fma.f64 2 x 1)
(fma.f64 x 2 1)
(+.f64 (*.f64 2 x) 1)
(fma.f64 2 x 1)
(fma.f64 x 2 1)
(*.f64 2 x)
(*.f64 x 2)
(+.f64 1 (*.f64 2 x))
(fma.f64 2 x 1)
(fma.f64 x 2 1)
(+.f64 1 (*.f64 2 x))
(fma.f64 2 x 1)
(fma.f64 x 2 1)
(+.f64 1 (*.f64 2 x))
(fma.f64 2 x 1)
(fma.f64 x 2 1)
(*.f64 2 x)
(*.f64 x 2)
(+.f64 1 (*.f64 2 x))
(fma.f64 2 x 1)
(fma.f64 x 2 1)
(+.f64 1 (*.f64 2 x))
(fma.f64 2 x 1)
(fma.f64 x 2 1)
(+.f64 1 (*.f64 2 x))
(fma.f64 2 x 1)
(fma.f64 x 2 1)

localize46.0ms (0.5%)

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))
✓10.7b
(-.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)

series16.0ms (0.2%)

Counts
4 → 21
Calls

12 calls:

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

rewrite108.0ms (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))))))

simplify98.0ms (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))

localize64.0ms (0.7%)

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))
✓27.9b
(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)

series6.0ms (0.1%)

Counts
1 → 1
Calls

3 calls:

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

rewrite69.0ms (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))))))))

simplify16.0ms (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
23 → 23
Calls
Call 1
Inputs
1
Outputs
1

eval950.0ms (10.1%)

Compiler

Compiled 20042 to 13829 computations (31% saved)

prune227.0ms (2.4%)

Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New8638871
Fresh12113
Picked101
Done235
Total87812890
Error
0.0b
Counts
890 → 12
Alt Table
Click to see full alt table
StatusErrorProgram
▶27.4b
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))))
▶0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
29.6b
1
▶27.5b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x)))
▶32.5b
(*.f64 1/2 (sqrt.f64 (/.f64 1 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))))
▶28.9b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
27.5b
(/.f64 (+.f64 x (-.f64 1 x)) (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))
✓27.9b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓28.8b
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
28.8b
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
45.5b
(/.f64 (*.f64 3/2 (sqrt.f64 x)) (+.f64 (+.f64 (+.f64 x 1) x) (sqrt.f64 (*.f64 (+.f64 x 1) x))))
Compiler

Compiled 286 to 214 computations (25.2% saved)

localize21.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiled 28 to 18 computations (35.7% saved)

series15.0ms (0.2%)

Counts
1 → 1
Calls

3 calls:

TimeVariablePointExpression
13.0ms
x
@inf
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
2.0ms
x
@-inf
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
1.0ms
x
@0
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite106.0ms (1.1%)

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

Useful iterations: 0 (0.0ms)

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

simplify15.0ms (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
23 → 23
Calls
Call 1
Inputs
1
Outputs
1

localize15.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiled 17 to 13 computations (23.5% saved)

series3.0ms (0%)

Counts
1 → 0
Calls

3 calls:

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

rewrite98.0ms (1%)

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

Useful iterations: 1 (0.0ms)

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

simplify15.0ms (0.2%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

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

localize39.0ms (0.4%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
✓0.1b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
2.7b
(+.f64 x (-.f64 1 x))
Compiler

Compiled 44 to 29 computations (34.1% saved)

series13.0ms (0.1%)

Counts
2 → 6
Calls

6 calls:

TimeVariablePointExpression
5.0ms
x
@-inf
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
4.0ms
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)))
1.0ms
x
@-inf
(+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
1.0ms
x
@inf
(+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))

rewrite130.0ms (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 #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 x (-.f64 1 x)) 3) (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 (+.f64 x (-.f64 1 x)) (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (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 exp.f64 (-.f64 (log1p.f64 (fma.f64 -1 x x)) (log1p.f64 (fma.f64 x 1/2 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log1p.f64 (fma.f64 -1 x x)) (log1p.f64 (fma.f64 x 1/2 (sqrt.f64 x)))) 1))))))
((#(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 (pow.f64 (fma.f64 x 1/2 1) 3) (pow.f64 x 3/2)) (/.f64 1 (-.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 (pow.f64 (fma.f64 x 1/2 1) 2) x) (/.f64 1 (-.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (+.f64 (pow.f64 (fma.f64 x 1/2 1) 2) x) (*.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) (+.f64 (pow.f64 (fma.f64 x 1/2 1) 3) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)) (-.f64 (pow.f64 (fma.f64 x 1/2 1) 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.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 (pow.f64 (fma.f64 x 1/2 1) 3) (pow.f64 x 3/2)) (+.f64 x (-.f64 (pow.f64 (fma.f64 x 1/2 1) 2) (*.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.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 (neg.f64 (+.f64 (pow.f64 (fma.f64 x 1/2 1) 3) (pow.f64 x 3/2))) (neg.f64 (-.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 (neg.f64 (-.f64 (pow.f64 (fma.f64 x 1/2 1) 2) x)) (neg.f64 (-.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/8 (pow.f64 x 3) (pow.f64 (+.f64 1 (sqrt.f64 x)) 3)) (fma.f64 (*.f64 x x) 1/4 (-.f64 (*.f64 (+.f64 1 (sqrt.f64 x)) (+.f64 1 (sqrt.f64 x))) (*.f64 (*.f64 x 1/2) (+.f64 1 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) 1/4) (*.f64 (+.f64 1 (sqrt.f64 x)) (+.f64 1 (sqrt.f64 x)))) (-.f64 (*.f64 x 1/2) (+.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 x (pow.f64 (fma.f64 x 1/2 1) 2)) (-.f64 (sqrt.f64 x) (fma.f64 x 1/2 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.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 1 (fma.f64 x 1/2 (sqrt.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (+.f64 (pow.f64 (fma.f64 x 1/2 1) 2) x) (*.f64 (fma.f64 x 1/2 1) (sqrt.f64 x))) (+.f64 (pow.f64 (fma.f64 x 1/2 1) 3) (pow.f64 x 3/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (fma.f64 x 1/2 1) (sqrt.f64 x)) (-.f64 (pow.f64 (fma.f64 x 1/2 1) 2) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (fma.f64 x 1/2 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 x 1/2))) (exp.f64 (+.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (fma.f64 x 1/2 1))) (exp.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (fma.f64 x 1/2 1)) (+.f64 1 (expm1.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (fma.f64 x 1/2 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 (fma.f64 x 1/2 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (sqrt.f64 x)) (+.f64 1 (expm1.f64 (fma.f64 x 1/2 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 x))) (+.f64 1 (expm1.f64 (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))))))

simplify18.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

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

localize87.0ms (0.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x))
✓0.0b
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)
✓0.1b
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x)))
2.7b
(+.f64 x (-.f64 1 x))
Compiler

Compiled 62 to 45 computations (27.4% saved)

series10.0ms (0.1%)

Counts
3 → 6
Calls

9 calls:

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

rewrite146.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
634×log-prod_binary64
552×fma-neg_binary64
270×log-div_binary64
236×log1p-udef_binary64
235×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01255
129928
2498028
Stop Event
1×node limit
Counts
3 → 188
Calls
Call 1
Inputs
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x)))
(-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1)
(+.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x))
Outputs
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(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 log.f64 (/.f64 (+.f64 1 (expm1.f64 (+.f64 1 (hypot.f64 1 (sqrt.f64 x))))) (exp.f64 (-.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (hypot.f64 1 (sqrt.f64 x)))) (exp.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (hypot.f64 1 (sqrt.f64 x))) (+.f64 1 (expm1.f64 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (hypot.f64 1 (sqrt.f64 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 (hypot.f64 1 (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (sqrt.f64 x)) (+.f64 1 (expm1.f64 (hypot.f64 1 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (sqrt.f64 x))) (+.f64 1 (expm1.f64 (hypot.f64 1 (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 expm1.f64 (log1p.f64 (+.f64 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))))) (#(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 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 fma.f64 1 (hypot.f64 1 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (hypot.f64 1 (sqrt.f64 x))) (neg.f64 (-.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 x) (hypot.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (hypot.f64 1 (sqrt.f64 x))) 1 (neg.f64 (-.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1 (hypot.f64 1 (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (sqrt.f64 x))) 2)) (neg.f64 (-.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (sqrt.f64 x))) 2)) (cbrt.f64 (+.f64 1 (hypot.f64 1 (sqrt.f64 x)))) (neg.f64 (-.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (+.f64 1 (hypot.f64 1 (sqrt.f64 x))) 2)) (*.f64 (cbrt.f64 (+.f64 1 (hypot.f64 1 (sqrt.f64 x)))) 1) (neg.f64 (-.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 x)) (hypot.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (hypot.f64 1 (sqrt.f64 x))) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) (neg.f64 (-.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) (*.f64 (hypot.f64 1 (pow.f64 (+.f64 x 1) 1/4)) 1) (neg.f64 (-.f64 1 (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) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (hypot.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (pow.f64 (+.f64 x 1) 3/2)) (/.f64 1 (+.f64 1 (+.f64 x (-.f64 1 (hypot.f64 1 (sqrt.f64 x)))))) (neg.f64 (-.f64 1 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 x) (/.f64 1 (-.f64 1 (hypot.f64 1 (sqrt.f64 x)))) (neg.f64 (-.f64 1 (sqrt.f64 x))))))))

simplify107.0ms (1.1%)

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

Useful iterations: 4 (0.0ms)

IterNodesCost
01841
14739
210539
330033
474432
5241432
6405932
7428732
8458632
9512532
10612232
Stop Event
1×node limit
Counts
194 → 195
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)))))
1
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)
1

localize117.0ms (1.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(pow.f64 (+.f64 x 1) 3/2)
✓0.0b
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))))
0.0b
(+.f64 (+.f64 x 1) x)
2.7b
(+.f64 x (-.f64 1 x))
Compiler

Compiled 94 to 59 computations (37.2% saved)

series14.0ms (0.2%)

Counts
2 → 17
Calls

6 calls:

TimeVariablePointExpression
5.0ms
x
@0
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))))
4.0ms
x
@-inf
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))))
3.0ms
x
@inf
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))))
1.0ms
x
@-inf
(pow.f64 (+.f64 x 1) 3/2)
1.0ms
x
@inf
(pow.f64 (+.f64 x 1) 3/2)

rewrite128.0ms (1.4%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01646
139246
2613146
Stop Event
1×node limit
Counts
2 → 62
Calls
Call 1
Inputs
(*.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))))
(pow.f64 (+.f64 x 1) 3/2)
Outputs
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simplify90.0ms (1%)

Algorithm
1×egg-herbie
Rules
591×fma-def_binary64
482×times-frac_binary64
313×associate-/l*_binary64
312×associate-/r*_binary64
295×distribute-rgt-out_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
065452
1175428
2432329
31290262
45168227
Stop Event
1×node limit
Counts
79 → 92
Calls
Call 1
Inputs
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(*.f64 3/2 (/.f64 x (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
(-.f64 (*.f64 3/2 (/.f64 x (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 5/8 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))
1
(+.f64 1 (*.f64 3/2 x))
(+.f64 1 (+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 3/2 x)))
(+.f64 (*.f64 -1/16 (pow.f64 x 3)) (+.f64 1 (+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 3/2 x))))
(sqrt.f64 (pow.f64 x 3))
(+.f64 (sqrt.f64 (pow.f64 x 3)) (*.f64 3/2 (sqrt.f64 x)))
(+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (sqrt.f64 (pow.f64 x 3)) (*.f64 3/2 (sqrt.f64 x))))
(+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (sqrt.f64 (pow.f64 x 3)) (+.f64 (*.f64 3/2 (sqrt.f64 x)) (*.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(+.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(+.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 -1/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
Outputs
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(-.f64 (+.f64 (*.f64 1/2 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 1/2 (sqrt.f64 (/.f64 1 x)))) (*.f64 3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(+.f64 (*.f64 1/2 (+.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 (/.f64 1 x)))) (*.f64 -3/8 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))
(fma.f64 1/2 (+.f64 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 (/.f64 1 (pow.f64 x 3)))) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -3/8))
(fma.f64 1/2 (sqrt.f64 (/.f64 1 x)) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) 1/8))
(*.f64 3/2 (/.f64 x (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))
(*.f64 3/2 (/.f64 x (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))
(/.f64 (*.f64 x 3/2) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(*.f64 3/2 (/.f64 x (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))))
(*.f64 3/2 (/.f64 x (pow.f64 (exp.f64 3/2) (log.f64 x))))
(/.f64 x (/.f64 (pow.f64 x 3/2) 3/2))
(-.f64 (*.f64 3/2 (/.f64 x (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))) (*.f64 5/8 (/.f64 1 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))))
(-.f64 (*.f64 3/2 (/.f64 x (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))))) (/.f64 5/8 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1)))))
(fma.f64 3/2 (/.f64 x (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) (/.f64 -5/8 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))))
(fma.f64 3/2 (/.f64 x (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))) (/.f64 -5/8 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))))
(fma.f64 3/2 (/.f64 x (pow.f64 (exp.f64 3/2) (log.f64 x))) (*.f64 (pow.f64 (exp.f64 -3/2) (log.f64 x)) -5/8))
(fma.f64 x (/.f64 3/2 (pow.f64 x 3/2)) (*.f64 (pow.f64 x -3/2) -5/8))
1
(+.f64 1 (*.f64 3/2 x))
(+.f64 1 (*.f64 x 3/2))
(fma.f64 x 3/2 1)
(+.f64 1 (+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 3/2 x)))
(+.f64 1 (fma.f64 3/8 (*.f64 x x) (*.f64 x 3/2)))
(+.f64 1 (fma.f64 x 3/2 (*.f64 3/8 (*.f64 x x))))
(fma.f64 x 3/2 (fma.f64 3/8 (*.f64 x x) 1))
(fma.f64 x (fma.f64 x 3/8 3/2) 1)
(+.f64 (*.f64 -1/16 (pow.f64 x 3)) (+.f64 1 (+.f64 (*.f64 3/8 (pow.f64 x 2)) (*.f64 3/2 x))))
(fma.f64 -1/16 (pow.f64 x 3) (+.f64 1 (fma.f64 3/8 (*.f64 x x) (*.f64 x 3/2))))
(+.f64 (fma.f64 x 3/2 (*.f64 3/8 (*.f64 x x))) (fma.f64 (pow.f64 x 3) -1/16 1))
(fma.f64 (pow.f64 x 3) -1/16 (fma.f64 x 3/2 (fma.f64 3/8 (*.f64 x x) 1)))
(fma.f64 x (fma.f64 x 3/8 3/2) (fma.f64 (pow.f64 x 3) -1/16 1))
(sqrt.f64 (pow.f64 x 3))
(pow.f64 x 3/2)
(+.f64 (sqrt.f64 (pow.f64 x 3)) (*.f64 3/2 (sqrt.f64 x)))
(fma.f64 3/2 (sqrt.f64 x) (sqrt.f64 (pow.f64 x 3)))
(fma.f64 3/2 (sqrt.f64 x) (pow.f64 x 3/2))
(*.f64 (sqrt.f64 x) (+.f64 x 3/2))
(+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (sqrt.f64 (pow.f64 x 3)) (*.f64 3/2 (sqrt.f64 x))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 x)) (+.f64 (sqrt.f64 (pow.f64 x 3)) (*.f64 3/2 (sqrt.f64 x))))
(fma.f64 (sqrt.f64 (/.f64 1 x)) 3/8 (fma.f64 3/2 (sqrt.f64 x) (sqrt.f64 (pow.f64 x 3))))
(fma.f64 3/2 (sqrt.f64 x) (fma.f64 (sqrt.f64 (/.f64 1 x)) 3/8 (pow.f64 x 3/2)))
(fma.f64 (sqrt.f64 (/.f64 1 x)) 3/8 (*.f64 (sqrt.f64 x) (+.f64 x 3/2)))
(+.f64 (*.f64 3/8 (sqrt.f64 (/.f64 1 x))) (+.f64 (sqrt.f64 (pow.f64 x 3)) (+.f64 (*.f64 3/2 (sqrt.f64 x)) (*.f64 -1/16 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 3/8 (sqrt.f64 (/.f64 1 x)) (+.f64 (sqrt.f64 (pow.f64 x 3)) (fma.f64 3/2 (sqrt.f64 x) (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/16))))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/16 (*.f64 3/2 (sqrt.f64 x))) (fma.f64 (sqrt.f64 (/.f64 1 x)) 3/8 (sqrt.f64 (pow.f64 x 3))))
(fma.f64 (sqrt.f64 (/.f64 1 x)) 3/8 (fma.f64 3/2 (sqrt.f64 x) (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/16 (pow.f64 x 3/2))))
(fma.f64 3/2 (sqrt.f64 x) (fma.f64 (sqrt.f64 (/.f64 1 x)) 3/8 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/16 (pow.f64 x 3/2))))
(fma.f64 (sqrt.f64 (/.f64 1 x)) 3/8 (fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) -1/16 (*.f64 (sqrt.f64 x) (+.f64 x 3/2))))
(exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))
(sqrt.f64 (pow.f64 x 3))
(pow.f64 x 3/2)
(+.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))
(+.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))
(fma.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) x) (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))))
(fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) (*.f64 (/.f64 3/2 x) (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2))))
(*.f64 (+.f64 (/.f64 3/2 x) 1) (pow.f64 (exp.f64 3/2) (log.f64 x)))
(*.f64 (+.f64 1 (/.f64 3/2 x)) (pow.f64 x 3/2))
(+.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x))))
(+.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (*.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x))))
(+.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (/.f64 (*.f64 3/2 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x)))
(fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) (*.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) x) (+.f64 3/2 (/.f64 3/8 x))))
(fma.f64 (/.f64 (pow.f64 (exp.f64 3/2) (log.f64 x)) x) (+.f64 3/2 (/.f64 3/8 x)) (pow.f64 (exp.f64 3/2) (log.f64 x)))
(fma.f64 (/.f64 (pow.f64 x 3/2) x) (+.f64 3/2 (/.f64 3/8 x)) (pow.f64 x 3/2))
(+.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (+.f64 (*.f64 -1/16 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 3))) (+.f64 (*.f64 3/8 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (pow.f64 x 2))) (*.f64 3/2 (/.f64 (exp.f64 (*.f64 3/2 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) x)))))
(+.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (fma.f64 -1/16 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (pow.f64 x 3)) (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) (*.f64 x x)) (*.f64 3/2 (/.f64 (pow.f64 (exp.f64 3/2) (fma.f64 -1 (log.f64 (/.f64 -1 x)) (log.f64 -1))) x)))))
(+.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (fma.f64 -1/16 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (pow.f64 x 3)) (fma.f64 3/8 (/.f64 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x)))) (*.f64 x x)) (/.f64 (*.f64 3/2 (pow.f64 (exp.f64 3/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 x))))) x))))
(fma.f64 -1/16 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) (pow.f64 x 3)) (fma.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2) (*.f64 (/.f64 (*.f64 (pow.f64 (/.f64 -1 x) -3/2) (pow.f64 -1 3/2)) x) (+.f64 3/2 (/.f64 3/8 x)))))
(+.f64 (pow.f64 (exp.f64 3/2) (log.f64 x)) (*.f64 (/.f64 (pow.f64 (exp.f64 3/2) (log.f64 x)) x) (+.f64 3/2 (+.f64 (/.f64 3/8 x) (/.f64 -1/16 (*.f64 x x))))))
(+.f64 (pow.f64 x 3/2) (*.f64 (/.f64 (pow.f64 x 3/2) x) (+.f64 3/2 (+.f64 (/.f64 3/8 x) (/.f64 -1/16 (*.f64 x x))))))

eval1.8s (18.8%)

Compiler

Compiled 21823 to 14281 computations (34.6% saved)

prune226.0ms (2.4%)

Pruning

15 alts after pruning (12 fresh and 3 done)

PrunedKeptTotal
New92211933
Fresh314
Picked101
Done437
Total93015945
Error
0b
Counts
945 → 15
Alt Table
Click to see full alt table
StatusErrorProgram
30.0b
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
▶28.0b
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
▶0.2b
(/.f64 1 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x)))
34.5b
(*.f64 1/2 (exp.f64 (*.f64 -1/2 (log.f64 x))))
27.0b
(-.f64 (+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1)
59.2b
(*.f64 1/2 (-.f64 (+.f64 1 (pow.f64 x -1/2)) 1))
✓0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
▶60.0b
(/.f64 2 x)
32.4b
(*.f64 1/2 (pow.f64 x -1/2))
29.6b
1
13.6b
(*.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))))))
✓27.9b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓28.8b
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
▶32.5b
(*.f64 1/2 (/.f64 1 (sqrt.f64 x)))
▶28.8b
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
Compiler

Compiled 261 to 215 computations (17.6% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiled 50 to 38 computations (24% saved)

series4.0ms (0%)

Counts
2 → 5
Calls

6 calls:

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

rewrite119.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
771×fma-def_binary64
458×log-prod_binary64
420×fma-neg_binary64
273×pow2_binary64
185×pow1/3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01029
123923
2373423
Stop Event
1×node limit
Counts
2 → 79
Calls
Call 1
Inputs
(/.f64 1 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x)))
(+.f64 1 (sqrt.f64 (+.f64 x 1)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))))) (#(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 (/.f64 1 (+.f64 (pow.f64 x 3/2) (pow.f64 (+.f64 1 x) 3/2))) (-.f64 (+.f64 (+.f64 1 x) x) (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 (+.f64 1 x) x)) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.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 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 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2) 1/2)))) (#(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 pow.f64 (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))))) (#(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 -.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 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (+.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (sqrt.f64 (+.f64 1 x))) 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 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) 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)))))

simplify91.0ms (1%)

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

Useful iterations: 4 (0.0ms)

IterNodesCost
01840
14738
210538
329632
474331
5234931
6398731
7421531
8451531
9505431
10605131
Stop Event
1×node limit
Counts
84 → 87
Calls
Call 1
Inputs
1
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
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 x (*.f64 x -1/8) (fma.f64 1/2 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 x (*.f64 x -1/8) (fma.f64 1/2 x (fma.f64 1/16 (pow.f64 x 3) 2)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x (fma.f64 x 1/16 -1/8)) 2))
(fma.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/16 -1/8))) 2)

localize3.0ms (0%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.3b
(/.f64 1 (sqrt.f64 x))
Compiler

Compiled 16 to 10 computations (37.5% saved)

series2.0ms (0%)

Counts
1 → 0
Calls

3 calls:

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

rewrite46.0ms (0.5%)

Algorithm
1×batch-egg-rewrite
Rules
397×pow1_binary64
384×add-sqr-sqrt_binary64
374×*-un-lft-identity_binary64
369×add-log-exp_binary64
369×log1p-expm1-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
056
1984
210894
Stop Event
1×node limit
Counts
1 → 39
Calls
Call 1
Inputs
(/.f64 1 (sqrt.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x -1/2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 x -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (pow.f64 1 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x -1/2)) (cbrt.f64 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 x) -1/2) (pow.f64 (sqrt.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 -1/2) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) -1/2) (pow.f64 (cbrt.f64 (*.f64 x x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) -1/2) (pow.f64 (*.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 x 1/4) -1/2) (pow.f64 (*.f64 (pow.f64 x 1/4) (sqrt.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x x)) -1/2) (pow.f64 (cbrt.f64 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (pow.f64 x 1/4) 3) -1/2) (pow.f64 (pow.f64 x 1/4) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (sqrt.f64 x) (cbrt.f64 x)) -1/2) (pow.f64 (sqrt.f64 (cbrt.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 1 1/2) -1) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (pow.f64 x -1/2) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (pow.f64 x -1/2) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 1 x) (cbrt.f64 (/.f64 1 x))) 1/3) (cbrt.f64 (cbrt.f64 (pow.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (/.f64 1 x) (pow.f64 (sqrt.f64 x) -1/2)) 1/3) (cbrt.f64 (pow.f64 (sqrt.f64 x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (pow.f64 x -1/2))) 2) 3) (cbrt.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (pow.f64 x -1/2))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (pow.f64 x -1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 x -1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 x -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 x) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (sqrt.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 x -1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -1/2 (log.f64 x)))))))

simplify7.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
39 → 39
Calls
Call 1
Inputs
Outputs

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiled 23 to 14 computations (39.1% saved)

series2.0ms (0%)

Counts
2 → 5
Calls

6 calls:

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

rewrite88.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
926×pow1_binary64
865×add-log-exp_binary64
864×log1p-expm1-u_binary64
864×expm1-log1p-u_binary64
848×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0821
117621
2235821
Stop Event
1×node limit
Counts
2 → 71
Calls
Call 1
Inputs
(-.f64 (*.f64 1/2 x) (sqrt.f64 x))
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 x) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 x) (*.f64 (neg.f64 (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (sqrt.f64 x)) (*.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) (pow.f64 (cbrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) 2) (cbrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) (sqrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 1/8 (pow.f64 x 3)) (pow.f64 x 3/2)) (/.f64 1 (+.f64 (*.f64 1/4 (*.f64 x x)) (+.f64 x (*.f64 1/2 (pow.f64 x 3/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 1/4 (*.f64 x x)) x) (/.f64 1 (fma.f64 1/2 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (*.f64 1/2 x)) (pow.f64 x 1/4)) (-.f64 (sqrt.f64 (*.f64 1/2 x)) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 1/4 (*.f64 x x)) (+.f64 x (*.f64 1/2 (pow.f64 x 3/2)))) (-.f64 (*.f64 1/8 (pow.f64 x 3)) (pow.f64 x 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 1/2 x (sqrt.f64 x)) (-.f64 (*.f64 1/4 (*.f64 x x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 1/8 (pow.f64 x 3)) (pow.f64 x 3/2)) (+.f64 (*.f64 1/4 (*.f64 x x)) (+.f64 x (*.f64 1/2 (pow.f64 x 3/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 1/4 (*.f64 x x)) x) (fma.f64 1/2 x (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 1/8 (pow.f64 x 3)) (pow.f64 x 3/2))) (neg.f64 (+.f64 (*.f64 1/4 (*.f64 x x)) (+.f64 x (*.f64 1/2 (pow.f64 x 3/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 1/4 (*.f64 x x)) x)) (neg.f64 (fma.f64 1/2 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 1/8 (pow.f64 x 3)) (pow.f64 (neg.f64 (sqrt.f64 x)) 3)) (+.f64 (*.f64 1/4 (*.f64 x x)) (-.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (*.f64 (*.f64 1/2 x) (neg.f64 (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 1/4 (*.f64 x x)) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) (-.f64 (*.f64 1/2 x) (neg.f64 (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 x (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/2 (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/2 x) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 x)) 2) (cbrt.f64 (*.f64 1/2 x)) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/2 x)) (sqrt.f64 (*.f64 1/2 x)) (neg.f64 (sqrt.f64 x)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 1/2 x) (-.f64 (sqrt.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (+.f64 (-.f64 1 (*.f64 1/2 x)) (sqrt.f64 x))) (/.f64 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 2) (+.f64 (-.f64 1 (*.f64 1/2 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1)) (pow.f64 (cbrt.f64 (+.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1)) 2) (cbrt.f64 (+.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (sqrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))) (hypot.f64 1 (sqrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 3)) (/.f64 1 (+.f64 1 (-.f64 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 2) (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 2)) (/.f64 1 (+.f64 (-.f64 1 (*.f64 1/2 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (-.f64 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 2) (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))) (+.f64 1 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (-.f64 1 (*.f64 1/2 x)) (sqrt.f64 x)) (-.f64 1 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 3)) (+.f64 1 (-.f64 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 2) (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 3)) (+.f64 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 2) (+.f64 (-.f64 1 (*.f64 1/2 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 2)) (+.f64 (-.f64 1 (*.f64 1/2 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 3))) (neg.f64 (+.f64 1 (-.f64 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 2) (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 2))) (neg.f64 (+.f64 (-.f64 1 (*.f64 1/2 x)) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 1) 3) (pow.f64 x 3/2)) (+.f64 (*.f64 (+.f64 (*.f64 1/2 x) 1) (+.f64 (*.f64 1/2 x) 1)) (+.f64 x (*.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 (*.f64 1/2 x) 1) (+.f64 (*.f64 1/2 x) 1)) x) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 2) 1) (-.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (sqrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) 2) (cbrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) (sqrt.f64 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) 1)))))

simplify8.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0517
1817
Stop Event
1×saturated
Counts
76 → 73
Calls
Call 1
Inputs
(*.f64 1/2 x)
(*.f64 1/2 x)
1
(*.f64 1/2 x)
(*.f64 1/2 x)
Outputs
(*.f64 1/2 x)
(*.f64 1/2 x)
1
(*.f64 1/2 x)
(*.f64 1/2 x)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiled 32 to 22 computations (31.3% saved)

series1.0ms (0%)

Counts
1 → 3
Calls

3 calls:

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

rewrite158.0ms (1.7%)

Algorithm
1×batch-egg-rewrite
Rules
444×fma-def_binary64
419×log-prod_binary64
379×prod-exp_binary64
318×exp-prod_binary64
290×pow-prod-down_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0913
120213
2273313
Stop Event
1×node limit
Counts
1 → 44
Calls
Call 1
Inputs
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))))) (cbrt.f64 (pow.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))) -2)) (/.f64 1 (cbrt.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))) -1/2) (pow.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (pow.f64 (fma.f64 1/2 x 1) 3) (pow.f64 x 3/2))) (-.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 (/.f64 1 (-.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 (pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x)))) -2) (/.f64 1 (cbrt.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (neg.f64 (log1p.f64 (fma.f64 1/2 x (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))) 2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))) 3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x)))) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x)))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 -1) (log1p.f64 (fma.f64 1/2 x (sqrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (neg.f64 (log1p.f64 (fma.f64 1/2 x (sqrt.f64 x))))) 2)) (cbrt.f64 (neg.f64 (log1p.f64 (fma.f64 1/2 x (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (neg.f64 (log1p.f64 (fma.f64 1/2 x (sqrt.f64 x)))))) (sqrt.f64 (neg.f64 (log1p.f64 (fma.f64 1/2 x (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))) -3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 1 (fma.f64 1/2 x (sqrt.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log1p.f64 (fma.f64 1/2 x (sqrt.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (fma.f64 1/2 x (sqrt.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log1p.f64 (fma.f64 1/2 x (sqrt.f64 x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (neg.f64 (log1p.f64 (fma.f64 1/2 x (sqrt.f64 x))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (*.f64 1/3 (log1p.f64 (fma.f64 1/2 x (sqrt.f64 x))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -1/2 (log1p.f64 (fma.f64 1/2 x (sqrt.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 (fma.f64 1/2 x (sqrt.f64 x))) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log1p.f64 (fma.f64 1/2 x (sqrt.f64 x))) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (neg.f64 (log1p.f64 (fma.f64 1/2 x (sqrt.f64 x)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (*.f64 (log1p.f64 (fma.f64 1/2 x (sqrt.f64 x))) 1)))))))

simplify8.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
059
179
Stop Event
1×saturated
Counts
47 → 46
Calls
Call 1
Inputs
1
(/.f64 2 x)
(/.f64 2 x)
Outputs
1
(/.f64 2 x)
(/.f64 2 x)

eval649.0ms (6.9%)

Compiler

Compiled 7127 to 5173 computations (27.4% saved)

prune165.0ms (1.8%)

Pruning

16 alts after pruning (8 fresh and 8 done)

PrunedKeptTotal
New4493452
Fresh257
Picked011
Done077
Total45116467
Error
0b
Counts
467 → 16
Alt Table
Click to see full alt table
StatusErrorProgram
30.0b
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
✓28.0b
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
✓0.2b
(/.f64 1 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x)))
59.2b
(*.f64 1/2 (-.f64 (+.f64 1 (pow.f64 x -1/2)) 1))
34.5b
(*.f64 1/2 (exp.f64 (*.f64 -1/2 (log.f64 x))))
27.0b
(-.f64 (+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1)
31.8b
(/.f64 1 (+.f64 (-.f64 (/.f64 (-.f64 0 x) (-.f64 1 (sqrt.f64 (+.f64 1 x)))) 1) (sqrt.f64 x)))
✓0.2b
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
29.6b
1
13.6b
(*.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))))))
✓27.9b
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓28.8b
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
✓32.5b
(*.f64 1/2 (/.f64 1 (sqrt.f64 x)))
✓60.0b
(/.f64 2 x)
✓28.8b
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
32.4b
(*.f64 1/2 (pow.f64 x -1/2))
Compiler

Compiled 163 to 134 computations (17.8% saved)

regimes90.0ms (1%)

Counts
41 → 1
Calls
Call 1
Inputs
1
1
(/.f64 2 x)
(*.f64 1/2 (pow.f64 x -1/2))
(*.f64 1/2 (pow.f64 x -1/2))
(*.f64 1/2 (/.f64 1 (sqrt.f64 x)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
(*.f64 1/2 (-.f64 (+.f64 1 (pow.f64 x -1/2)) 1))
(*.f64 1/2 (-.f64 (+.f64 1 (pow.f64 x -1/2)) 1))
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(*.f64 1/2 (exp.f64 (*.f64 -1/2 (log.f64 x))))
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 1 (+.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x)))
(-.f64 (+.f64 1 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) 1)
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 1 (+.f64 (-.f64 (/.f64 (-.f64 0 x) (-.f64 1 (sqrt.f64 (+.f64 1 x)))) 1) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (-.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) 1) (sqrt.f64 x)))
(/.f64 (*.f64 3/2 (sqrt.f64 x)) (+.f64 (+.f64 (+.f64 x 1) x) (sqrt.f64 (*.f64 (+.f64 x 1) x))))
(-.f64 (exp.f64 (*.f64 (log1p.f64 x) 1/2)) (sqrt.f64 x))
(-.f64 (cbrt.f64 (pow.f64 (+.f64 x 1) 3/2)) (sqrt.f64 x))
(-.f64 (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 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))))
(-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) 3) (sqrt.f64 x))
(cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3))
(-.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1)))) (sqrt.f64 x))
(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 1 x)) (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))
(*.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)))
(/.f64 (-.f64 (+.f64 x 1) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))
(*.f64 (/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 x 1) x) (hypot.f64 x (sqrt.f64 x))))
(fma.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x)))
(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))
(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))
(/.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 (neg.f64 (sqrt.f64 x)) 3)) (+.f64 (+.f64 x 1) (-.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (*.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))))
Outputs
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
Calls

3 calls:

34.0ms
x
17.0ms
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
10.0ms
(-.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 530 to 364 computations (31.3% saved)

regimes35.0ms (0.4%)

Counts
16 → 2
Calls
Call 1
Inputs
1
1
(/.f64 2 x)
(*.f64 1/2 (pow.f64 x -1/2))
(*.f64 1/2 (pow.f64 x -1/2))
(*.f64 1/2 (/.f64 1 (sqrt.f64 x)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
(*.f64 1/2 (-.f64 (+.f64 1 (pow.f64 x -1/2)) 1))
(*.f64 1/2 (-.f64 (+.f64 1 (pow.f64 x -1/2)) 1))
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(*.f64 1/2 (exp.f64 (*.f64 -1/2 (log.f64 x))))
(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Outputs
(*.f64 1/2 (pow.f64 x -1/2))
(-.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
0.3b2x
0.3b2(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
0.3b2(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 125 to 94 computations (24.8% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
2.9414066375466064e-5
0.00023167177778304904
Compiler

Compiled 12 to 9 computations (25% saved)

regimes22.0ms (0.2%)

Counts
15 → 2
Calls
Call 1
Inputs
1
1
(/.f64 2 x)
(*.f64 1/2 (pow.f64 x -1/2))
(*.f64 1/2 (pow.f64 x -1/2))
(*.f64 1/2 (/.f64 1 (sqrt.f64 x)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
(-.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x))
(*.f64 1/2 (-.f64 (+.f64 1 (pow.f64 x -1/2)) 1))
(*.f64 1/2 (-.f64 (+.f64 1 (pow.f64 x -1/2)) 1))
(/.f64 1 (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (+.f64 (*.f64 1/2 x) 1) (sqrt.f64 x)))
(*.f64 1/2 (exp.f64 (*.f64 -1/2 (log.f64 x))))
Outputs
(+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x)))
(*.f64 1/2 (pow.f64 x -1/2))
Calls

1 calls:

18.0ms
x
Results
ErrorSegmentsBranch
0.9b2x
Compiler

Compiled 102 to 78 computations (23.5% saved)

bsearch19.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
19.0ms
0.13137983386600421
4.597083892091637
Compiler

Compiled 12 to 9 computations (25% saved)

regimes13.0ms (0.1%)

Counts
8 → 2
Calls
Call 1
Inputs
1
1
(/.f64 2 x)
(*.f64 1/2 (pow.f64 x -1/2))
(*.f64 1/2 (pow.f64 x -1/2))
(*.f64 1/2 (/.f64 1 (sqrt.f64 x)))
(*.f64 1/2 (sqrt.f64 (/.f64 1 x)))
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
Outputs
(/.f64 1 (+.f64 1 (pow.f64 x 3/2)))
(*.f64 1/2 (pow.f64 x -1/2))
Calls

1 calls:

11.0ms
x
Results
ErrorSegmentsBranch
2.5b2x
Compiler

Compiled 37 to 30 computations (18.9% saved)

bsearch54.0ms (0.6%)

Algorithm
1×binary-search
Steps
TimeLeftRight
54.0ms
0.13137983386600421
4.597083892091637
Compiler

Compiled 12 to 9 computations (25% saved)

regimes26.0ms (0.3%)

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

1 calls:

24.0ms
x
Results
ErrorSegmentsBranch
2.5b2x
Compiler

Compiled 30 to 24 computations (20% saved)

bsearch18.0ms (0.2%)

Algorithm
1×binary-search
Steps
TimeLeftRight
18.0ms
0.13137983386600421
4.597083892091637
Compiler

Compiled 12 to 9 computations (25% saved)

regimes6.0ms (0.1%)

Accuracy

Total -30.5b remaining (-103.1%)

Threshold costs -30.5b (-103.1%)

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

1 calls:

5.0ms
x
Results
ErrorSegmentsBranch
29.6b1x
Compiler

Compiled 8 to 6 computations (25% saved)

simplify8.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
029111
140111
245111
347111
448111
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 7378697629483821/147573952589676412928) (*.f64 1/2 (pow.f64 x -1/2)) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(if (<=.f64 x 2366728683371737/18014398509481984) (+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) (*.f64 1/2 (pow.f64 x -1/2)))
(if (<=.f64 x 2366728683371737/18014398509481984) (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (*.f64 1/2 (pow.f64 x -1/2)))
(if (<=.f64 x 2366728683371737/18014398509481984) 1 (*.f64 1/2 (pow.f64 x -1/2)))
1
Outputs
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 7378697629483821/147573952589676412928) (*.f64 1/2 (pow.f64 x -1/2)) (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 7378697629483821/147573952589676412928) (*.f64 1/2 (pow.f64 x -1/2)) (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
(if (<=.f64 x 2366728683371737/18014398509481984) (+.f64 1 (-.f64 (*.f64 1/2 x) (sqrt.f64 x))) (*.f64 1/2 (pow.f64 x -1/2)))
(if (<=.f64 x 2366728683371737/18014398509481984) (+.f64 1 (-.f64 (*.f64 x 1/2) (sqrt.f64 x))) (*.f64 1/2 (pow.f64 x -1/2)))
(if (<=.f64 x 2366728683371737/18014398509481984) (/.f64 1 (+.f64 1 (pow.f64 x 3/2))) (*.f64 1/2 (pow.f64 x -1/2)))
(if (<=.f64 x 2366728683371737/18014398509481984) 1 (*.f64 1/2 (pow.f64 x -1/2)))
1
Compiler

Compiled 81 to 64 computations (21% saved)

soundness0.0ms (0%)

end58.0ms (0.6%)

Compiler

Compiled 76 to 57 computations (25% saved)

Profiling

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