Details

Time bar (total: 4.4s)

analyze6.0ms (0.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%50%50%2
0%50%50%3
12.5%25%62.5%4
18.7%12.5%68.8%5
21.9%6.2%71.9%6
23.4%3.1%73.5%7
24.2%1.6%74.2%8
24.6%0.8%74.6%9
24.8%0.4%74.8%10
24.9%0.2%74.9%11
24.9%0.1%75%12
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.1s (24.3%)

Results
1.1s8256×body256valid
1.0ms13×body256invalid

preprocess21.0ms (0.5%)

Algorithm
2×egg-herbie
Rules
1×+-commutative_binary64
1×*-commutative_binary64
1×sub-neg_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11311
21411
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))
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))
Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify6.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
1×+-commutative_binary64
1×*-commutative_binary64
1×sub-neg_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
11311
21411
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Outputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))

eval1.0ms (0%)

Compiler

Compiled 15 to 10 computations (33.3% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
0.4b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.4b
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 8 to 6 computations (25% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.4b
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 19 to 12 computations (36.8% saved)

series3.0ms (0.1%)

Counts
1 → 8
Calls

3 calls:

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

rewrite46.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
648×pow1_binary64
603×add-log-exp_binary64
602×log1p-expm1-u_binary64
602×expm1-log1p-u_binary64
587×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
11469
217599
Stop Event
1×node limit
Counts
1 → 14
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x -1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (+.f64 x -1) 3/2) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3/2) (pow.f64 (+.f64 x -1) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))))

simplify62.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
744×associate-/r/_binary64
666×div-sub_binary64
253×*-commutative_binary64
240×fma-def_binary64
234×distribute-rgt-neg-in_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
03268
18868
224468
367764
4312062
5718662
Stop Event
1×node limit
Counts
22 → 25
Calls
Call 1
Inputs
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))
(+.f64 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2)))
(+.f64 (*.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (+.f64 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2))))
(+.f64 (*.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 x 2))) (+.f64 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2)))))
Outputs
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 (+.f64 x -1/2) (*.f64 (/.f64 -1 x) (+.f64 (/.f64 1/16 x) 1/8)))
(+.f64 x (fma.f64 (/.f64 -1 x) (+.f64 1/8 (/.f64 1/16 x)) -1/2))
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
(*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x))
x
(+.f64 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2)))
(+.f64 x -1/2)
(-.f64 x 1/2)
(+.f64 (*.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (+.f64 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (*.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (+.f64 (*.f64 1/16 (/.f64 (pow.f64 (sqrt.f64 -1) 2) (pow.f64 x 2))) (+.f64 (*.f64 -1 (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)) (*.f64 1/2 (pow.f64 (sqrt.f64 -1) 2)))))
(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 (+.f64 x -1/2) (*.f64 (/.f64 -1 x) (+.f64 (/.f64 1/16 x) 1/8)))
(+.f64 x (fma.f64 (/.f64 -1 x) (+.f64 1/8 (/.f64 1/16 x)) -1/2))
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))

eval6.0ms (0.1%)

Compiler

Compiled 254 to 206 computations (18.9% saved)

prune7.0ms (0.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New19625
Fresh000
Picked011
Done000
Total19726
Error
0b
Counts
26 → 7
Alt Table
Click to see full alt table
StatusErrorProgram
▶30.5b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
▶0.9b
(-.f64 x 1/2)
▶30.7b
(pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 2)
1.4b
x
▶0.6b
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
▶0.7b
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
✓0.4b
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 92 to 69 computations (25% saved)

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))
✓0.0b
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
✓0.0b
(/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)
Compiler

Compiled 40 to 30 computations (25% saved)

series5.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
2.0ms
x
@0
(/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)
1.0ms
x
@-inf
(/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)
0.0ms
x
@inf
(/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)
0.0ms
x
@0
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
0.0ms
x
@inf
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))

rewrite84.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
824×prod-diff_binary64
521×log-prod_binary64
394×fma-def_binary64
217×expm1-udef_binary64
217×log1p-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01039
124239
2350339
Stop Event
1×node limit
Counts
3 → 154
Calls
Call 1
Inputs
(/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
(+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))) (cbrt.f64 (exp.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 2) (*.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 2) (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (*.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) (sqrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/8 (neg.f64 (/.f64 -1/16 x))) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (+.f64 -1/8 (/.f64 -1/16 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 2) 1) (/.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 1) (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (+.f64 -1/8 (/.f64 -1/16 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 1))))))
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(+.f64 -1/8 (/.f64 -1/16 x)) x) 3)) (fma.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) (-.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) -1/2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1/8 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 3)) (+.f64 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 2) (-.f64 1/4 (*.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 2)) (-.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 -1/8 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 3))) (neg.f64 (fma.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) (-.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) -1/2) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/4 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 2))) (neg.f64 (-.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 2) 1/4) (-.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) -1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) -1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) -1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (/.f64 1 x) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) 1 -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 2) (*.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (/.f64 1 x)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) (pow.f64 (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) 2) (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (*.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (/.f64 1 x)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) (sqrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1/8 (neg.f64 (/.f64 -1/16 x))) (/.f64 1 (neg.f64 x)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (+.f64 -1/8 (/.f64 -1/16 x)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 2) 1) (/.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) x) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 1) (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) x) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (cbrt.f64 x)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (cbrt.f64 x)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) (sqrt.f64 x)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (+.f64 -1/8 (/.f64 -1/16 x))) (sqrt.f64 x)) -1/2)))))

simplify70.0ms (1.6%)

Algorithm
1×egg-herbie
Rules
762×fma-neg_binary64
530×cancel-sign-sub-inv_binary64
478×associate-/l*_binary64
457×unswap-sqr_binary64
411×div-sub_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
029427
170387
2165387
3381387
4967387
52609387
66366387
Stop Event
1×node limit
Counts
190 → 172
Calls
Call 1
Inputs
(/.f64 -1/16 (pow.f64 x 2))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(/.f64 -1/8 x)
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(/.f64 -1/8 x)
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(/.f64 -1/16 (pow.f64 x 2))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(/.f64 -1/16 (pow.f64 x 2))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
-1/2
(neg.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))))
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))))
-1/2
(neg.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))))
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))))
Outputs
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x)))
(-.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 1/8 x))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x)))
(-.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 1/8 x))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x)))
(-.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 1/8 x))
(/.f64 -1/8 x)
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x)))
(-.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 1/8 x))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x)))
(-.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 1/8 x))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x)))
(-.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 1/8 x))
(/.f64 -1/8 x)
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x)))
(-.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 1/8 x))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x)))
(-.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 1/8 x))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x)))
(-.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 1/8 x))
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x)))
(-.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 1/8 x))
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(+.f64 -1/2 (neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x))))
(+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (-.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 1/8 x)) -1/2)
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 (+.f64 x -1/2) (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x))))
(+.f64 (+.f64 (+.f64 x -1/2) (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (-.f64 (+.f64 x -1/2) (/.f64 1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 (/.f64 1/8 x) 1/2))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
(+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 (+.f64 x -1/2) (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x))))
(+.f64 (+.f64 (+.f64 x -1/2) (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (-.f64 (+.f64 x -1/2) (/.f64 1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 (/.f64 1/8 x) 1/2))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
(+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 (+.f64 x -1/2) (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x))))
(+.f64 (+.f64 (+.f64 x -1/2) (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (-.f64 (+.f64 x -1/2) (/.f64 1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x)))
(-.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 1/8 x))
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(+.f64 -1/2 (neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x))))
(+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (-.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 1/8 x)) -1/2)
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(+.f64 -1/2 (neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x))))
(+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (-.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 1/8 x)) -1/2)
-1/2
(neg.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(+.f64 -1/2 (neg.f64 (/.f64 1/8 x)))
(+.f64 -1/2 (/.f64 -1/8 x))
(-.f64 -1/2 (/.f64 1/8 x))
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))))
(+.f64 -1/2 (neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x))))
(+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (-.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 1/8 x)) -1/2)
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))))
(+.f64 -1/2 (neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x))))
(+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (-.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 1/8 x)) -1/2)
-1/2
(neg.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(+.f64 -1/2 (neg.f64 (/.f64 1/8 x)))
(+.f64 -1/2 (/.f64 -1/8 x))
(-.f64 -1/2 (/.f64 1/8 x))
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))))
(+.f64 -1/2 (neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x))))
(+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (-.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 1/8 x)) -1/2)
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 2))))))
(+.f64 -1/2 (neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x))))
(+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (-.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 1/8 x)) -1/2)

localize3.0ms (0.1%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
Compiler

Compiled 19 to 14 computations (26.3% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
0.0ms
x
@-inf
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
0.0ms
x
@inf
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))

rewrite156.0ms (3.5%)

Algorithm
1×batch-egg-rewrite
Rules
975×pow1_binary64
921×add-log-exp_binary64
921×log1p-expm1-u_binary64
921×expm1-log1p-u_binary64
86×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
116710
2237710
Stop Event
1×node limit
Counts
1 → 36
Calls
Call 1
Inputs
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (-.f64 (-.f64 x -1/2) (/.f64 -1/8 x))) (/.f64 (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 2) (-.f64 (-.f64 x -1/2) (/.f64 -1/8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))) (pow.f64 (cbrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))) 2) (cbrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))) (sqrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 3)) (/.f64 1 (fma.f64 x x (*.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (-.f64 (+.f64 -1/2 (/.f64 -1/8 x)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 2)) (/.f64 1 (-.f64 (-.f64 x -1/2) (/.f64 -1/8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (*.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (-.f64 (+.f64 -1/2 (/.f64 -1/8 x)) x))) (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (-.f64 x -1/2) (/.f64 -1/8 x)) (-.f64 (*.f64 x x) (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 3)) (fma.f64 x x (*.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (-.f64 (+.f64 -1/2 (/.f64 -1/8 x)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 3)) (+.f64 (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 2) (-.f64 (*.f64 x x) (*.f64 x (+.f64 -1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 2)) (-.f64 (-.f64 x -1/2) (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 x 3) (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 3))) (neg.f64 (fma.f64 x x (*.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (-.f64 (+.f64 -1/2 (/.f64 -1/8 x)) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 2))) (neg.f64 (-.f64 (-.f64 x -1/2) (/.f64 -1/8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x -1/2) 3) (/.f64 -1/512 (pow.f64 x 3))) (+.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (-.f64 (/.f64 1/64 (*.f64 x x)) (*.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 2) (*.f64 x x)) (-.f64 (+.f64 -1/2 (/.f64 -1/8 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (/.f64 -1/8 x) (+.f64 x -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (+.f64 -1/2 (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 -1/2 (/.f64 -1/8 x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 -1/2 (/.f64 -1/8 x))) 2) (cbrt.f64 (+.f64 -1/2 (/.f64 -1/8 x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (+.f64 -1/2 (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 -1/2 (/.f64 -1/8 x))) (sqrt.f64 (+.f64 -1/2 (/.f64 -1/8 x))) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (+.f64 -1/2 (/.f64 -1/8 x)))))))

simplify35.0ms (0.8%)

Algorithm
1×egg-herbie
Rules
180×fma-neg_binary64
110×fma-def_binary64
47×cancel-sign-sub-inv_binary64
36×associate-/l*_binary64
33×sub-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01383
12981
26081
310481
419081
527881
646381
761581
869381
976581
1083781
1185781
1287581
Stop Event
1×saturated
Counts
48 → 44
Calls
Call 1
Inputs
(/.f64 -1/8 x)
(neg.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
Outputs
(/.f64 -1/8 x)
(neg.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(+.f64 -1/2 (neg.f64 (/.f64 1/8 x)))
(+.f64 -1/2 (/.f64 -1/8 x))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓28.4b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
Compiler

Compiled 17 to 11 computations (35.3% saved)

series1.0ms (0%)

Counts
1 → 8
Calls

3 calls:

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

rewrite100.0ms (2.2%)

Algorithm
1×batch-egg-rewrite
Rules
646×pow1_binary64
602×add-log-exp_binary64
602×log1p-expm1-u_binary64
602×expm1-log1p-u_binary64
590×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
11299
216459
Stop Event
1×node limit
Counts
1 → 22
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 x (+.f64 x -1)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) (cbrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) (pow.f64 (*.f64 x (+.f64 x -1)) 1/4))))) (#(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 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 x -1)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))))

simplify131.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
616×times-frac_binary64
536×fma-neg_binary64
520×div-sub_binary64
498×associate-/r*_binary64
479×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02574
16570
215070
336570
488370
5229270
6768870
Stop Event
1×node limit
Counts
30 → 37
Calls
Call 1
Inputs
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(*.f64 -1 x)
(+.f64 1/2 (*.f64 -1 x))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (*.f64 1/8 (/.f64 1 x))))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
Outputs
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 x (-.f64 -1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 (-.f64 x 1/2) (-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x))))
(+.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (+.f64 x -1/2) (+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x))))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 1/2 (*.f64 -1 x))
(+.f64 1/2 (neg.f64 x))
(-.f64 1/2 x)
(+.f64 1/2 (+.f64 (*.f64 -1 x) (*.f64 1/8 (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1 x (/.f64 1/8 x)))
(+.f64 1/2 (-.f64 (/.f64 1/8 x) x))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(+.f64 1/2 (fma.f64 -1 x (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 1/2 (+.f64 (/.f64 1/16 (*.f64 x x)) (-.f64 (/.f64 1/8 x) x)))
(+.f64 1/2 (+.f64 (/.f64 1/8 x) (-.f64 (/.f64 1/16 (*.f64 x x)) x)))
(-.f64 (-.f64 1/2 x) (+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x))))

localize15.0ms (0.3%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.4b
(pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 2)
28.4b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
Compiler

Compiled 34 to 24 computations (29.4% saved)

series3.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite66.0ms (1.5%)

Algorithm
1×batch-egg-rewrite
Rules
783×pow1_binary64
730×add-log-exp_binary64
729×log1p-expm1-u_binary64
729×expm1-log1p-u_binary64
714×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
099
11939
220539
Stop Event
1×node limit
Counts
1 → 22
Calls
Call 1
Inputs
(pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) (pow.f64 (*.f64 x (+.f64 x -1)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) (cbrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)) (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/4) (*.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/4) (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)))))) (#(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 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/4)) (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))))) (cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))))

simplify62.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
616×times-frac_binary64
500×fma-neg_binary64
384×distribute-rgt-out_binary64
350×+-commutative_binary64
350×*-commutative_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
054281
1148275
2385203
31574145
43890138
56376127
Stop Event
1×node limit
Counts
34 → 45
Calls
Call 1
Inputs
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)
(+.f64 (*.f64 -1/2 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2) x)) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2))
(+.f64 (*.f64 -1/2 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2) x)) (+.f64 (*.f64 (+.f64 (*.f64 -3/16 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)) (*.f64 1/16 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2))) (pow.f64 x 2)) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)))
(+.f64 (*.f64 -1/2 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2) x)) (+.f64 (*.f64 (+.f64 (*.f64 -3/16 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)) (*.f64 1/16 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2))) (pow.f64 x 2)) (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2) (*.f64 (+.f64 (*.f64 3/64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)) (*.f64 -7/64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2))) (pow.f64 x 3)))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(*.f64 -1 x)
(+.f64 1/2 (*.f64 -1 x))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (*.f64 1/8 (/.f64 1 x))))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
Outputs
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2)
(pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 x 1/4)) 2)
(sqrt.f64 (neg.f64 x))
(sqrt.f64 x)
(+.f64 (*.f64 -1/2 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2) x)) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2))
(fma.f64 -1/2 (*.f64 x (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2)) (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2))
(*.f64 (+.f64 (*.f64 x -1/2) 1) (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 x 1/4)) 2))
(*.f64 (sqrt.f64 (neg.f64 x)) (+.f64 1 (*.f64 x -1/2)))
(fma.f64 -1/2 (pow.f64 x 3/2) (sqrt.f64 x))
(+.f64 (*.f64 -1/2 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2) x)) (+.f64 (*.f64 (+.f64 (*.f64 -3/16 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)) (*.f64 1/16 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2))) (pow.f64 x 2)) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)))
(fma.f64 -1/2 (*.f64 x (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2)) (fma.f64 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2) -1/8) (*.f64 x x) (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2)))
(+.f64 (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 x 1/4)) 2) (*.f64 (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 x 1/4)) 2) (+.f64 (*.f64 x -1/2) (*.f64 (*.f64 x x) -1/8))))
(*.f64 (sqrt.f64 (neg.f64 x)) (+.f64 (+.f64 1 (*.f64 x -1/2)) (*.f64 (*.f64 x x) -1/8)))
(*.f64 (+.f64 (*.f64 x (+.f64 -1/2 (*.f64 x -1/8))) 1) (sqrt.f64 (neg.f64 x)))
(fma.f64 -1/2 (pow.f64 x 3/2) (fma.f64 (pow.f64 x 5/2) -1/8 (sqrt.f64 x)))
(+.f64 (*.f64 -1/2 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2) x)) (+.f64 (*.f64 (+.f64 (*.f64 -3/16 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)) (*.f64 1/16 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2))) (pow.f64 x 2)) (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2) (*.f64 (+.f64 (*.f64 3/64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)) (*.f64 -7/64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2))) (pow.f64 x 3)))))
(fma.f64 -1/2 (*.f64 x (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2)) (+.f64 (fma.f64 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2) -1/8) (*.f64 x x) (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2)) (*.f64 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2) -1/16) (pow.f64 x 3))))
(fma.f64 -1/2 (*.f64 x (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2)) (fma.f64 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2) -1/8) (*.f64 x x) (fma.f64 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2) -1/16) (pow.f64 x 3) (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2))))
(+.f64 (*.f64 (+.f64 (*.f64 x -1/2) 1) (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 x 1/4)) 2)) (*.f64 (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 x 1/4)) 2) (+.f64 (*.f64 (pow.f64 x 3) -1/16) (*.f64 (*.f64 x x) -1/8))))
(+.f64 (sqrt.f64 (neg.f64 x)) (*.f64 (sqrt.f64 (neg.f64 x)) (+.f64 (*.f64 x -1/2) (*.f64 (*.f64 x x) (+.f64 (*.f64 x -1/16) -1/8)))))
(*.f64 (sqrt.f64 (neg.f64 x)) (+.f64 (+.f64 1 (*.f64 x -1/2)) (*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x -1/16)))))
(*.f64 (sqrt.f64 x) (+.f64 (+.f64 1 (*.f64 x -1/2)) (*.f64 (*.f64 x x) (+.f64 -1/8 (*.f64 x -1/16)))))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 -1/2 (+.f64 x (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(-.f64 (+.f64 x -1/2) (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x))))
(+.f64 x (-.f64 -1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 x (-.f64 (/.f64 -1/8 x) (-.f64 1/2 (/.f64 -1/16 (*.f64 x x)))))
(+.f64 x (-.f64 -1/2 (-.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 -1/8 x))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 1/2 (*.f64 -1 x))
(+.f64 1/2 (neg.f64 x))
(-.f64 1/2 x)
(+.f64 1/2 (+.f64 (*.f64 -1 x) (*.f64 1/8 (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1 x (/.f64 1/8 x)))
(+.f64 (/.f64 1/8 x) (-.f64 1/2 x))
(-.f64 1/2 (+.f64 x (/.f64 -1/8 x)))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(+.f64 1/2 (fma.f64 -1 x (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 (+.f64 (/.f64 1/8 x) (-.f64 1/2 x)) (/.f64 1/16 (*.f64 x x)))
(+.f64 (/.f64 1/8 x) (+.f64 (/.f64 1/16 (*.f64 x x)) (-.f64 1/2 x)))
(+.f64 1/2 (-.f64 (/.f64 1/16 (*.f64 x x)) (+.f64 x (/.f64 -1/8 x))))

eval138.0ms (3.1%)

Compiler

Compiled 5220 to 3977 computations (23.8% saved)

prune76.0ms (1.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New3314335
Fresh011
Picked101
Done235
Total3348342
Error
0b
Counts
342 → 8
Alt Table
Click to see full alt table
StatusErrorProgram
✓30.5b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
✓0.9b
(-.f64 x 1/2)
▶30.7b
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 2)
▶31.3b
(/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
✓0.6b
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
1.4b
x
▶0.7b
(+.f64 -1/2 (+.f64 x (/.f64 -1/8 x)))
▶0.6b
(+.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))
Compiler

Compiled 79 to 58 computations (26.6% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 -1/2 (+.f64 x (/.f64 -1/8 x)))
Compiler

Compiled 19 to 13 computations (31.6% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
(+.f64 -1/2 (+.f64 x (/.f64 -1/8 x)))
0.0ms
x
@inf
(+.f64 -1/2 (+.f64 x (/.f64 -1/8 x)))
0.0ms
x
@-inf
(+.f64 -1/2 (+.f64 x (/.f64 -1/8 x)))

rewrite55.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
979×pow1_binary64
924×add-log-exp_binary64
924×log1p-expm1-u_binary64
924×expm1-log1p-u_binary64
86×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0710
116710
2238510
Stop Event
1×node limit
Counts
1 → 33
Calls
Call 1
Inputs
(+.f64 -1/2 (+.f64 x (/.f64 -1/8 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/4 (-.f64 (-.f64 -1/2 x) (/.f64 -1/8 x))) (/.f64 (pow.f64 (+.f64 x (/.f64 -1/8 x)) 2) (-.f64 (-.f64 -1/2 x) (/.f64 -1/8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x))) (pow.f64 (cbrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x))) 2) (cbrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x))) (sqrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1/8 (pow.f64 (+.f64 x (/.f64 -1/8 x)) 3)) (/.f64 1 (+.f64 1/4 (*.f64 (+.f64 x (/.f64 -1/8 x)) (-.f64 (+.f64 x (/.f64 -1/8 x)) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/4 (pow.f64 (+.f64 x (/.f64 -1/8 x)) 2)) (/.f64 1 (-.f64 (-.f64 -1/2 x) (/.f64 -1/8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1/4 (*.f64 (+.f64 x (/.f64 -1/8 x)) (-.f64 (+.f64 x (/.f64 -1/8 x)) -1/2))) (+.f64 -1/8 (pow.f64 (+.f64 x (/.f64 -1/8 x)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (-.f64 -1/2 x) (/.f64 -1/8 x)) (-.f64 1/4 (pow.f64 (+.f64 x (/.f64 -1/8 x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1/8 (pow.f64 (+.f64 x (/.f64 -1/8 x)) 3)) (+.f64 1/4 (*.f64 (+.f64 x (/.f64 -1/8 x)) (-.f64 (+.f64 x (/.f64 -1/8 x)) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1/8 (pow.f64 (+.f64 x (/.f64 -1/8 x)) 3)) (+.f64 (pow.f64 (+.f64 x (/.f64 -1/8 x)) 2) (-.f64 1/4 (*.f64 -1/2 (+.f64 x (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/4 (pow.f64 (+.f64 x (/.f64 -1/8 x)) 2)) (-.f64 (-.f64 -1/2 x) (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 -1/8 (pow.f64 (+.f64 x (/.f64 -1/8 x)) 3))) (neg.f64 (+.f64 1/4 (*.f64 (+.f64 x (/.f64 -1/8 x)) (-.f64 (+.f64 x (/.f64 -1/8 x)) -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/4 (pow.f64 (+.f64 x (/.f64 -1/8 x)) 2))) (neg.f64 (-.f64 (-.f64 -1/2 x) (/.f64 -1/8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 -1/2 x) 3) (/.f64 -1/512 (pow.f64 x 3))) (+.f64 (*.f64 (+.f64 -1/2 x) (+.f64 -1/2 x)) (-.f64 (/.f64 1/64 (*.f64 x x)) (*.f64 (+.f64 -1/2 x) (/.f64 -1/8 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x (/.f64 -1/8 x)) 2) 1/4) (-.f64 (+.f64 x (/.f64 -1/8 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 -1/2 x) (+.f64 -1/2 x)) (/.f64 1/64 (*.f64 x x))) (-.f64 (+.f64 -1/2 x) (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (/.f64 -1/8 x) (+.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 x (/.f64 -1/8 x)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x (/.f64 -1/8 x))) 2) (cbrt.f64 (+.f64 x (/.f64 -1/8 x))) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x (/.f64 -1/8 x))) (sqrt.f64 (+.f64 x (/.f64 -1/8 x))) -1/2)))))

simplify32.0ms (0.7%)

Algorithm
1×egg-herbie
Rules
180×fma-neg_binary64
110×fma-def_binary64
47×cancel-sign-sub-inv_binary64
36×associate-/l*_binary64
33×sub-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01383
12981
26081
310481
419081
527881
646381
761581
869381
976581
1083781
1185781
1287581
Stop Event
1×saturated
Counts
45 → 41
Calls
Call 1
Inputs
(/.f64 -1/8 x)
(neg.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
Outputs
(/.f64 -1/8 x)
(neg.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(+.f64 -1/2 (neg.f64 (/.f64 1/8 x)))
(+.f64 -1/2 (/.f64 -1/8 x))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))

localize25.0ms (0.6%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))
✓0.0b
(+.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))
✓0.6b
(/.f64 -1/16 (*.f64 x x))
Compiler

Compiled 41 to 26 computations (36.6% saved)

series3.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@0
(/.f64 -1/16 (*.f64 x x))
0.0ms
x
@inf
(/.f64 -1/16 (*.f64 x x))
0.0ms
x
@0
(+.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))
0.0ms
x
@inf
(+.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))
0.0ms
x
@-inf
(+.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))

rewrite89.0ms (2%)

Algorithm
1×batch-egg-rewrite
Rules
653×fma-def_binary64
565×log-prod_binary64
334×fma-neg_binary64
271×log-div_binary64
239×expm1-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01136
127334
2416834
Stop Event
1×node limit
Counts
3 → 187
Calls
Call 1
Inputs
(/.f64 -1/16 (*.f64 x x))
(+.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))
(+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 -1/16 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/16) (pow.f64 x -2))) (cbrt.f64 (pow.f64 (exp.f64 -1/16) (pow.f64 x -2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/16) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/16) (pow.f64 x -2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/16) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 -1/16 (pow.f64 x -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/16 (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1/16 (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 -1/16 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 -1/16 (pow.f64 x -2))) (cbrt.f64 (/.f64 1/256 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/256 (pow.f64 x 4))) (cbrt.f64 (*.f64 -1/16 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 -1/16) x) (/.f64 (sqrt.f64 -1/16) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/16 (/.f64 1 (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) -1/16)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1/16 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/16 (pow.f64 x -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 -1/16 (pow.f64 x -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 -1/16) x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/4096 (pow.f64 (pow.f64 x -2) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) -16) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/256 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/16) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 -1/16 (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 -1/4096 (pow.f64 (pow.f64 x -2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/16 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/16 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 -1/16 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 -1/16 (pow.f64 x -2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 x -1/2) (-.f64 (/.f64 1/8 x) (*.f64 -1/16 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (fma.f64 -1/16 (pow.f64 x -2) x) (+.f64 -1/2 (/.f64 -1/8 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2) (+.f64 x (-.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (*.f64 -1/16 (pow.f64 x -2))))) (/.f64 (/.f64 1/256 (pow.f64 x 4)) (+.f64 x (-.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (*.f64 -1/16 (pow.f64 x -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (fma.f64 -1/16 (pow.f64 x -2) (+.f64 x -1/2)) (/.f64 1/8 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (fma.f64 -1/16 (pow.f64 x -2) x) (+.f64 -1/2 (/.f64 -1/8 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (fma.f64 -1/16 (pow.f64 x -2) x) (+.f64 -1/2 (/.f64 -1/8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (fma.f64 -1/16 (pow.f64 x -2) x) (+.f64 -1/2 (/.f64 -1/8 x)))) (pow.f64 (cbrt.f64 (+.f64 (fma.f64 -1/16 (pow.f64 x -2) x) (+.f64 -1/2 (/.f64 -1/8 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (fma.f64 -1/16 (pow.f64 x -2) x) (+.f64 -1/2 (/.f64 -1/8 x)))) 2) (cbrt.f64 (+.f64 (fma.f64 -1/16 (pow.f64 x -2) x) (+.f64 -1/2 (/.f64 -1/8 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (fma.f64 -1/16 (pow.f64 x -2) x) (+.f64 -1/2 (/.f64 -1/8 x)))) (sqrt.f64 (+.f64 (fma.f64 -1/16 (pow.f64 x -2) x) (+.f64 -1/2 (/.f64 -1/8 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -1/4096 (pow.f64 (pow.f64 x -2) 3) (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 3)) (/.f64 1 (fma.f64 (*.f64 -1/16 (pow.f64 x -2)) (-.f64 (*.f64 -1/16 (pow.f64 x -2)) (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))) (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2) (/.f64 1/256 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simplify66.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
775×fma-neg_binary64
526×cancel-sign-sub-inv_binary64
482×associate-/l*_binary64
457×unswap-sqr_binary64
411×div-sub_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
025294
162288
2155288
3361288
4898288
52604288
66346288
Stop Event
1×node limit
Counts
223 → 202
Calls
Call 1
Inputs
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (pow.f64 x 2))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(/.f64 -1/8 x)
(neg.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
Outputs
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(/.f64 (/.f64 -1/16 x) x)
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(/.f64 (/.f64 -1/16 x) x)
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(/.f64 (/.f64 -1/16 x) x)
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(/.f64 (/.f64 -1/16 x) x)
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(/.f64 (/.f64 -1/16 x) x)
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(/.f64 (/.f64 -1/16 x) x)
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(/.f64 (/.f64 -1/16 x) x)
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(/.f64 (/.f64 -1/16 x) x)
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(/.f64 (/.f64 -1/16 x) x)
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(/.f64 (/.f64 -1/16 x) x)
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(/.f64 (/.f64 -1/16 x) x)
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(/.f64 (/.f64 -1/16 x) x)
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(/.f64 (/.f64 -1/16 x) x)
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/16 (*.f64 x x)) (/.f64 1/8 x)))
(+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (/.f64 -1/8 x) (/.f64 (/.f64 -1/16 x) x))
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(neg.f64 (+.f64 (+.f64 1/2 (/.f64 1/16 (*.f64 x x))) (/.f64 1/8 x)))
(+.f64 (+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x))) -1/2)
(+.f64 (/.f64 -1/8 x) (+.f64 -1/2 (/.f64 -1/16 (*.f64 x x))))
(+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(-.f64 -1/2 (-.f64 (/.f64 1/8 x) (/.f64 (/.f64 -1/16 x) x)))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 (+.f64 1/2 (/.f64 1/16 (*.f64 x x))) (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x))))
(+.f64 x (+.f64 (+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x))) -1/2))
(+.f64 (-.f64 (+.f64 x -1/2) (/.f64 1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (/.f64 -1/16 (*.f64 x x)))
(+.f64 x (-.f64 -1/2 (-.f64 (/.f64 1/8 x) (/.f64 (/.f64 -1/16 x) x))))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 (/.f64 1/8 x) 1/2))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 (+.f64 1/2 (/.f64 1/16 (*.f64 x x))) (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x))))
(+.f64 x (+.f64 (+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x))) -1/2))
(+.f64 (-.f64 (+.f64 x -1/2) (/.f64 1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (/.f64 -1/16 (*.f64 x x)))
(+.f64 x (-.f64 -1/2 (-.f64 (/.f64 1/8 x) (/.f64 (/.f64 -1/16 x) x))))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 (/.f64 1/8 x) 1/2))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 (+.f64 1/2 (/.f64 1/16 (*.f64 x x))) (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x))))
(+.f64 x (+.f64 (+.f64 (/.f64 -1/8 x) (/.f64 -1/16 (*.f64 x x))) -1/2))
(+.f64 (-.f64 (+.f64 x -1/2) (/.f64 1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (/.f64 -1/16 (*.f64 x x)))
(+.f64 x (-.f64 -1/2 (-.f64 (/.f64 1/8 x) (/.f64 (/.f64 -1/16 x) x))))
(/.f64 -1/8 x)
(neg.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(+.f64 -1/2 (neg.f64 (/.f64 1/8 x)))
(+.f64 -1/2 (/.f64 -1/8 x))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 (/.f64 1/8 x) 1/2))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 (/.f64 1/8 x) 1/2))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 (/.f64 1/8 x) 1/2))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 (/.f64 1/8 x) 1/2))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 (/.f64 1/8 x) 1/2))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 (/.f64 1/8 x) 1/2))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(-.f64 (+.f64 x -1/2) (/.f64 1/8 x))

localize24.0ms (0.5%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x)))
✓0.5b
(/.f64 1/64 (*.f64 x x))
✓28.5b
(/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
Compiler

Compiled 67 to 43 computations (35.8% saved)

series5.0ms (0.1%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
1.0ms
x
@inf
(/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
1.0ms
x
@0
(/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
0.0ms
x
@-inf
(/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
0.0ms
x
@0
(/.f64 1/64 (*.f64 x x))
0.0ms
x
@inf
(/.f64 1/64 (*.f64 x x))

rewrite132.0ms (3%)

Algorithm
1×batch-egg-rewrite
Rules
702×fma-def_binary64
323×fma-neg_binary64
313×log-div_binary64
237×expm1-udef_binary64
237×log1p-udef_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01351
132330
2536130
Stop Event
1×node limit
Counts
3 → 398
Calls
Call 1
Inputs
(/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
(/.f64 1/64 (*.f64 x x))
(-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 (+.f64 -1/2 (/.f64 -1/8 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1/2 (+.f64 x (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x -1/2) (/.f64 -1/8 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (fma.f64 (neg.f64 (/.f64 1 x)) -1/8 (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (fma.f64 (neg.f64 (/.f64 -1/2 (cbrt.f64 x))) (*.f64 1/4 (cbrt.f64 (pow.f64 x -2))) (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (+.f64 (/.f64 -1/8 x) (/.f64 -1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 -1/8 x) (+.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (pow.f64 (+.f64 x -1/2) 2) (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))) (neg.f64 (*.f64 1/64 (/.f64 (pow.f64 x -2) (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 -1/2 (/.f64 -1/8 x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 x -1/2) (/.f64 -1/8 x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (+.f64 x -1/2) 2) (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))) (*.f64 1/64 (/.f64 (pow.f64 x -2) (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (+.f64 x -1/2) 3) (fma.f64 (/.f64 -1/8 x) (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (pow.f64 (+.f64 x -1/2) 2))) (/.f64 (/.f64 -1/512 (pow.f64 x 3)) (fma.f64 (/.f64 -1/8 x) (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (pow.f64 (+.f64 x -1/2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2) (/.f64 1 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (*.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (/.f64 1 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))) (cbrt.f64 (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2)) (cbrt.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2)) 2) (*.f64 (cbrt.f64 (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2)) (/.f64 1 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))) (sqrt.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2)) (/.f64 1 (+.f64 (neg.f64 (+.f64 x -1/2)) (/.f64 -1/8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (+.f64 x -1/2) 3) (/.f64 -1/512 (pow.f64 x 3))) (/.f64 1 (fma.f64 (/.f64 -1/8 x) (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (pow.f64 (+.f64 x -1/2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))) (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2)) 2)) (sqrt.f64 (cbrt.f64 (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2))) (/.f64 (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2) (cbrt.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))))) (/.f64 (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2) (sqrt.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (cbrt.f64 (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2))) (/.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (cbrt.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2)) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2)) (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2)) 2) (sqrt.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))))) (/.f64 (cbrt.f64 (pow.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) 2)) (sqrt.f64 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(+.f64 -1/2 (/.f64 -1/8 x)))) (+.f64 (*.f64 1/64 (pow.f64 x -2)) (*.f64 1/64 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 x -1/2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (+.f64 (fma.f64 x -1/2 1/4) (*.f64 1/64 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 x -1/2) (sqrt.f64 x)) (sqrt.f64 x) (+.f64 (fma.f64 x -1/2 1/4) (*.f64 1/64 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (+.f64 x -1/2)) 2)) (cbrt.f64 (+.f64 x -1/2)) (+.f64 (fma.f64 x -1/2 1/4) (*.f64 1/64 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 (+.f64 x -1/2))) (sqrt.f64 (+.f64 x -1/2)) (+.f64 (fma.f64 x -1/2 1/4) (*.f64 1/64 (pow.f64 x -2))))))))

simplify75.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
653×div-sub_binary64
603×associate-/l/_binary64
428×associate-/l*_binary64
356×distribute-rgt-in_binary64
339×fma-def_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
030305
171294
2161284
3397284
41158284
53382284
67489284
Stop Event
1×node limit
Counts
434 → 421
Calls
Call 1
Inputs
(/.f64 -1/8 x)
(neg.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 -1/64 (pow.f64 x 2))
(-.f64 1/4 (*.f64 1/64 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 1/4 (*.f64 -1 x)) (*.f64 1/64 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 1/4 (+.f64 (*.f64 -1 x) (pow.f64 x 2))) (*.f64 1/64 (/.f64 1 (pow.f64 x 2))))
(pow.f64 x 2)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 1/4 (+.f64 (*.f64 -1 x) (pow.f64 x 2)))
(-.f64 (+.f64 1/4 (+.f64 (*.f64 -1 x) (pow.f64 x 2))) (*.f64 1/64 (/.f64 1 (pow.f64 x 2))))
(pow.f64 x 2)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(+.f64 1/4 (+.f64 (*.f64 -1 x) (pow.f64 x 2)))
(-.f64 (+.f64 1/4 (+.f64 (*.f64 -1 x) (pow.f64 x 2))) (*.f64 1/64 (/.f64 1 (pow.f64 x 2))))
Outputs
(/.f64 -1/8 x)
(neg.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 -1/2 (/.f64 -1/8 x))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 (/.f64 1/64 x) x)
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 (/.f64 1/64 x) x)
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 (/.f64 1/64 x) x)
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 (/.f64 1/64 x) x)
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 (/.f64 1/64 x) x)
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 (/.f64 1/64 x) x)
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 (/.f64 1/64 x) x)
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 (/.f64 1/64 x) x)
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 (/.f64 1/64 x) x)
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 (/.f64 1/64 x) x)
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 (/.f64 1/64 x) x)
(/.f64 1/64 (pow.f64 x 2))
(/.f64 1/64 (*.f64 x x))
(/.f64 (/.f64 1/64 x) x)
(/.f64 -1/64 (pow.f64 x 2))
(/.f64 -1/64 (*.f64 x x))
(-.f64 1/4 (*.f64 1/64 (/.f64 1 (pow.f64 x 2))))
(-.f64 1/4 (/.f64 1/64 (*.f64 x x)))
(-.f64 1/4 (/.f64 (/.f64 1/64 x) x))
(+.f64 1/4 (/.f64 -1/64 (*.f64 x x)))
(-.f64 (+.f64 1/4 (*.f64 -1 x)) (*.f64 1/64 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/4 (-.f64 (neg.f64 x) (/.f64 1/64 (*.f64 x x))))
(-.f64 (-.f64 1/4 x) (/.f64 (/.f64 1/64 x) x))
(+.f64 (-.f64 1/4 x) (/.f64 -1/64 (*.f64 x x)))
(+.f64 1/4 (-.f64 (/.f64 -1/64 (*.f64 x x)) x))
(-.f64 (+.f64 1/4 (+.f64 (*.f64 -1 x) (pow.f64 x 2))) (*.f64 1/64 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/4 (-.f64 (fma.f64 -1 x (*.f64 x x)) (/.f64 1/64 (*.f64 x x))))
(+.f64 1/4 (-.f64 (*.f64 x (+.f64 x -1)) (/.f64 (/.f64 1/64 x) x)))
(+.f64 1/4 (fma.f64 x (+.f64 x -1) (/.f64 -1/64 (*.f64 x x))))
(-.f64 (/.f64 -1/64 (*.f64 x x)) (-.f64 x (fma.f64 x x 1/4)))
(+.f64 (-.f64 1/4 x) (fma.f64 x x (/.f64 -1/64 (*.f64 x x))))
(+.f64 1/4 (-.f64 (fma.f64 x x (/.f64 -1/64 (*.f64 x x))) x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(*.f64 x (+.f64 x -1))
(-.f64 (*.f64 x x) x)
(+.f64 1/4 (+.f64 (*.f64 -1 x) (pow.f64 x 2)))
(+.f64 1/4 (fma.f64 -1 x (*.f64 x x)))
(+.f64 1/4 (*.f64 x (+.f64 x -1)))
(-.f64 (fma.f64 x x 1/4) x)
(-.f64 (+.f64 1/4 (+.f64 (*.f64 -1 x) (pow.f64 x 2))) (*.f64 1/64 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/4 (-.f64 (fma.f64 -1 x (*.f64 x x)) (/.f64 1/64 (*.f64 x x))))
(+.f64 1/4 (-.f64 (*.f64 x (+.f64 x -1)) (/.f64 (/.f64 1/64 x) x)))
(+.f64 1/4 (fma.f64 x (+.f64 x -1) (/.f64 -1/64 (*.f64 x x))))
(-.f64 (/.f64 -1/64 (*.f64 x x)) (-.f64 x (fma.f64 x x 1/4)))
(+.f64 (-.f64 1/4 x) (fma.f64 x x (/.f64 -1/64 (*.f64 x x))))
(+.f64 1/4 (-.f64 (fma.f64 x x (/.f64 -1/64 (*.f64 x x))) x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1 x) (pow.f64 x 2))
(fma.f64 -1 x (*.f64 x x))
(*.f64 x (+.f64 x -1))
(-.f64 (*.f64 x x) x)
(+.f64 1/4 (+.f64 (*.f64 -1 x) (pow.f64 x 2)))
(+.f64 1/4 (fma.f64 -1 x (*.f64 x x)))
(+.f64 1/4 (*.f64 x (+.f64 x -1)))
(-.f64 (fma.f64 x x 1/4) x)
(-.f64 (+.f64 1/4 (+.f64 (*.f64 -1 x) (pow.f64 x 2))) (*.f64 1/64 (/.f64 1 (pow.f64 x 2))))
(+.f64 1/4 (-.f64 (fma.f64 -1 x (*.f64 x x)) (/.f64 1/64 (*.f64 x x))))
(+.f64 1/4 (-.f64 (*.f64 x (+.f64 x -1)) (/.f64 (/.f64 1/64 x) x)))
(+.f64 1/4 (fma.f64 x (+.f64 x -1) (/.f64 -1/64 (*.f64 x x))))
(-.f64 (/.f64 -1/64 (*.f64 x x)) (-.f64 x (fma.f64 x x 1/4)))
(+.f64 (-.f64 1/4 x) (fma.f64 x x (/.f64 -1/64 (*.f64 x x))))
(+.f64 1/4 (-.f64 (fma.f64 x x (/.f64 -1/64 (*.f64 x x))) x))

localize17.0ms (0.4%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.4b
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 2)
✓29.3b
(pow.f64 (*.f64 x (+.f64 x -1)) 1/4)
Compiler

Compiled 29 to 21 computations (27.6% saved)

series3.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@0
(pow.f64 (*.f64 x (+.f64 x -1)) 1/4)
1.0ms
x
@inf
(pow.f64 (*.f64 x (+.f64 x -1)) 1/4)
1.0ms
x
@-inf
(pow.f64 (*.f64 x (+.f64 x -1)) 1/4)
0.0ms
x
@0
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 2)
0.0ms
x
@-inf
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 2)

rewrite136.0ms (3.1%)

Algorithm
1×batch-egg-rewrite
Rules
887×pow1_binary64
831×add-log-exp_binary64
830×log1p-expm1-u_binary64
830×expm1-log1p-u_binary64
813×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0920
120419
2239219
Stop Event
1×node limit
Counts
2 → 45
Calls
Call 1
Inputs
(pow.f64 (*.f64 x (+.f64 x -1)) 1/4)
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)) (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) (cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 1/4) (pow.f64 (+.f64 x -1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x -1) 1/4) (pow.f64 x 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/8) (pow.f64 (*.f64 x (+.f64 x -1)) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (*.f64 x (+.f64 x -1)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/4) (pow.f64 (*.f64 x (+.f64 x -1)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 2) 1/4) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/4) (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 1/4 (log.f64 (*.f64 x (+.f64 x -1)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) (pow.f64 (*.f64 x (+.f64 x -1)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) (cbrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)) (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)))))) (#(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 (pow.f64 x 1/4) (*.f64 (pow.f64 (+.f64 x -1) 1/4) (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/8) (*.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/8) (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 x 1/4) (pow.f64 x 1/4)) (*.f64 (pow.f64 (+.f64 x -1) 1/4) (pow.f64 (+.f64 x -1) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) (pow.f64 (*.f64 x (+.f64 x -1)) 1/8)) (pow.f64 (*.f64 x (+.f64 x -1)) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x -1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 x 1/4) 2) (pow.f64 (pow.f64 (+.f64 x -1) 1/4) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))))) (cbrt.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) (pow.f64 x 1/4)) (pow.f64 (+.f64 x -1) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (+.f64 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (*.f64 x (+.f64 x -1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))))))))

simplify65.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
528×distribute-rgt-out_binary64
523×*-commutative_binary64
435×fma-def_binary64
381×associate-+l+_binary64
306×distribute-lft-out_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
098656
1264646
2674493
32438398
45480377
Stop Event
1×node limit
Counts
69 → 90
Calls
Call 1
Inputs
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x))))
(+.f64 (*.f64 -1/4 (*.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) x)) (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))))
(+.f64 (*.f64 -1/4 (*.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) x)) (+.f64 (*.f64 -3/32 (*.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) (pow.f64 x 2))) (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x))))))
(+.f64 (*.f64 -1/4 (*.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) x)) (+.f64 (*.f64 -3/32 (*.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) (pow.f64 x 2))) (+.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) (*.f64 -7/128 (*.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) (pow.f64 x 3))))))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) (*.f64 -1/4 (sqrt.f64 (/.f64 1 x))))
(+.f64 (sqrt.f64 x) (+.f64 (*.f64 -1/4 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (*.f64 -7/128 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (sqrt.f64 x) (+.f64 (*.f64 -1/4 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(*.f64 (sqrt.f64 -1) (sqrt.f64 x))
(+.f64 (*.f64 -1/4 (*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 x)))) (*.f64 (sqrt.f64 -1) (sqrt.f64 x)))
(+.f64 (*.f64 -1/4 (*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 x)))) (+.f64 (*.f64 -3/32 (*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (*.f64 (sqrt.f64 -1) (sqrt.f64 x))))
(+.f64 (*.f64 -1/4 (*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 x)))) (+.f64 (*.f64 -3/32 (*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (*.f64 (sqrt.f64 -1) (sqrt.f64 x)) (*.f64 -7/128 (*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)
(+.f64 (*.f64 -1/2 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2) x)) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2))
(+.f64 (*.f64 -1/2 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2) x)) (+.f64 (*.f64 (+.f64 (*.f64 -3/16 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)) (*.f64 1/16 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2))) (pow.f64 x 2)) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)))
(+.f64 (*.f64 -1/2 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2) x)) (+.f64 (*.f64 (+.f64 (*.f64 -3/16 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)) (*.f64 1/16 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2))) (pow.f64 x 2)) (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2) (*.f64 (+.f64 (*.f64 3/64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)) (*.f64 -7/64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2))) (pow.f64 x 3)))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(*.f64 -1 x)
(+.f64 1/2 (*.f64 -1 x))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (*.f64 1/8 (/.f64 1 x))))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
Outputs
(exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x)))
(*.f64 (pow.f64 -1 1/4) (pow.f64 x 1/4))
(pow.f64 (neg.f64 x) 1/4)
(+.f64 (*.f64 -1/4 (*.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) x)) (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))))
(fma.f64 -1/4 (*.f64 x (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x)))) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))))
(*.f64 (+.f64 (*.f64 x -1/4) 1) (*.f64 (pow.f64 -1 1/4) (pow.f64 x 1/4)))
(*.f64 (pow.f64 (neg.f64 x) 1/4) (+.f64 1 (*.f64 x -1/4)))
(+.f64 (*.f64 -1/4 (*.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) x)) (+.f64 (*.f64 -3/32 (*.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) (pow.f64 x 2))) (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x))))))
(fma.f64 -1/4 (*.f64 x (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x)))) (fma.f64 -3/32 (*.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) (*.f64 x x)) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x)))))
(fma.f64 (pow.f64 -1 1/4) (pow.f64 x 1/4) (*.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 x 1/4)) (+.f64 (*.f64 x -1/4) (*.f64 -3/32 (*.f64 x x)))))
(*.f64 (pow.f64 (neg.f64 x) 1/4) (+.f64 (*.f64 x -1/4) (+.f64 1 (*.f64 -3/32 (*.f64 x x)))))
(*.f64 (+.f64 (*.f64 x (+.f64 -1/4 (*.f64 x -3/32))) 1) (pow.f64 (neg.f64 x) 1/4))
(+.f64 (*.f64 -1/4 (*.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) x)) (+.f64 (*.f64 -3/32 (*.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) (pow.f64 x 2))) (+.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) (*.f64 -7/128 (*.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) (pow.f64 x 3))))))
(fma.f64 -1/4 (*.f64 x (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x)))) (+.f64 (fma.f64 -3/32 (*.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) (*.f64 x x)) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x)))) (*.f64 -7/128 (*.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) (pow.f64 x 3)))))
(fma.f64 -1/4 (*.f64 x (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x)))) (fma.f64 -3/32 (*.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) (*.f64 x x)) (fma.f64 -7/128 (*.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) (pow.f64 x 3)) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))))))
(+.f64 (*.f64 (+.f64 (*.f64 x -1/4) 1) (*.f64 (pow.f64 -1 1/4) (pow.f64 x 1/4))) (*.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 x 1/4)) (+.f64 (*.f64 -7/128 (pow.f64 x 3)) (*.f64 -3/32 (*.f64 x x)))))
(+.f64 (pow.f64 (neg.f64 x) 1/4) (*.f64 (pow.f64 (neg.f64 x) 1/4) (+.f64 (*.f64 x -1/4) (*.f64 (*.f64 x x) (+.f64 (*.f64 x -7/128) -3/32)))))
(*.f64 (pow.f64 (neg.f64 x) 1/4) (+.f64 (+.f64 1 (*.f64 x -1/4)) (*.f64 (*.f64 x x) (+.f64 -3/32 (*.f64 x -7/128)))))
(sqrt.f64 x)
(+.f64 (sqrt.f64 x) (*.f64 -1/4 (sqrt.f64 (/.f64 1 x))))
(fma.f64 -1/4 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x))
(+.f64 (sqrt.f64 x) (+.f64 (*.f64 -1/4 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(+.f64 (sqrt.f64 x) (fma.f64 -1/4 (sqrt.f64 (/.f64 1 x)) (*.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))))
(fma.f64 -1/4 (sqrt.f64 (/.f64 1 x)) (fma.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 x)))
(+.f64 (*.f64 -7/128 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))) (+.f64 (sqrt.f64 x) (+.f64 (*.f64 -1/4 (sqrt.f64 (/.f64 1 x))) (*.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(fma.f64 -7/128 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (+.f64 (sqrt.f64 x) (fma.f64 -1/4 (sqrt.f64 (/.f64 1 x)) (*.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3)))))))
(+.f64 (fma.f64 -1/4 (sqrt.f64 (/.f64 1 x)) (*.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (fma.f64 -7/128 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (sqrt.f64 x)))
(fma.f64 -7/128 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/4 (sqrt.f64 (/.f64 1 x)) (fma.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 x))))
(*.f64 (sqrt.f64 -1) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 -1))
(sqrt.f64 (neg.f64 x))
(+.f64 (*.f64 -1/4 (*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 x)))) (*.f64 (sqrt.f64 -1) (sqrt.f64 x)))
(fma.f64 -1/4 (*.f64 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 -1)) (*.f64 (sqrt.f64 x) (sqrt.f64 -1)))
(*.f64 (sqrt.f64 -1) (fma.f64 -1/4 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)))
(*.f64 (fma.f64 -1/4 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x)) (sqrt.f64 -1))
(+.f64 (*.f64 -1/4 (*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 x)))) (+.f64 (*.f64 -3/32 (*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (*.f64 (sqrt.f64 -1) (sqrt.f64 x))))
(fma.f64 -1/4 (*.f64 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 -1)) (fma.f64 -3/32 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 -1)) (*.f64 (sqrt.f64 x) (sqrt.f64 -1))))
(fma.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 -3/32 (sqrt.f64 -1)) (*.f64 (sqrt.f64 -1) (fma.f64 -1/4 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x))))
(*.f64 (sqrt.f64 -1) (fma.f64 -1/4 (sqrt.f64 (/.f64 1 x)) (fma.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 x))))
(+.f64 (*.f64 -1/4 (*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 x)))) (+.f64 (*.f64 -3/32 (*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 (pow.f64 x 3))))) (+.f64 (*.f64 (sqrt.f64 -1) (sqrt.f64 x)) (*.f64 -7/128 (*.f64 (sqrt.f64 -1) (sqrt.f64 (/.f64 1 (pow.f64 x 5))))))))
(fma.f64 -1/4 (*.f64 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 -1)) (fma.f64 -3/32 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 -1)) (fma.f64 (sqrt.f64 -1) (sqrt.f64 x) (*.f64 (*.f64 -7/128 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))))
(fma.f64 -1/4 (*.f64 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 -1)) (fma.f64 -3/32 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 -1)) (fma.f64 -7/128 (*.f64 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (sqrt.f64 -1)) (*.f64 (sqrt.f64 x) (sqrt.f64 -1)))))
(+.f64 (*.f64 (sqrt.f64 -1) (fma.f64 -1/4 (sqrt.f64 (/.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 -1) (fma.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (*.f64 -7/128 (sqrt.f64 (/.f64 1 (pow.f64 x 5)))))))
(*.f64 (sqrt.f64 -1) (fma.f64 -7/128 (sqrt.f64 (/.f64 1 (pow.f64 x 5))) (fma.f64 -1/4 (sqrt.f64 (/.f64 1 x)) (fma.f64 -3/32 (sqrt.f64 (/.f64 1 (pow.f64 x 3))) (sqrt.f64 x)))))
(pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)
(*.f64 (sqrt.f64 x) (sqrt.f64 -1))
(sqrt.f64 (neg.f64 x))
(+.f64 (*.f64 -1/2 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2) x)) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2))
(fma.f64 -1/2 (*.f64 x (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2)) (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2))
(fma.f64 -1/2 (*.f64 x (pow.f64 (exp.f64 1/4) (*.f64 2 (+.f64 (log.f64 -1) (log.f64 x))))) (pow.f64 (exp.f64 1/4) (*.f64 2 (+.f64 (log.f64 -1) (log.f64 x)))))
(*.f64 (+.f64 (*.f64 x -1/2) 1) (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 x 1/4)) 2))
(*.f64 (sqrt.f64 (neg.f64 x)) (+.f64 1 (*.f64 x -1/2)))
(+.f64 (*.f64 -1/2 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2) x)) (+.f64 (*.f64 (+.f64 (*.f64 -3/16 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)) (*.f64 1/16 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2))) (pow.f64 x 2)) (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)))
(fma.f64 -1/2 (*.f64 x (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2)) (fma.f64 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2) -1/8) (*.f64 x x) (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2)))
(fma.f64 -1/2 (*.f64 x (pow.f64 (exp.f64 1/4) (*.f64 2 (+.f64 (log.f64 -1) (log.f64 x))))) (fma.f64 (*.f64 x x) (*.f64 (pow.f64 (exp.f64 1/4) (*.f64 2 (+.f64 (log.f64 -1) (log.f64 x)))) -1/8) (pow.f64 (exp.f64 1/4) (*.f64 2 (+.f64 (log.f64 -1) (log.f64 x))))))
(+.f64 (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 x 1/4)) 2) (*.f64 (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 x 1/4)) 2) (+.f64 (*.f64 x -1/2) (*.f64 (*.f64 x x) -1/8))))
(*.f64 (sqrt.f64 (neg.f64 x)) (+.f64 (+.f64 1 (*.f64 x -1/2)) (*.f64 x (*.f64 x -1/8))))
(*.f64 (+.f64 (*.f64 x (+.f64 (*.f64 x -1/8) -1/2)) 1) (sqrt.f64 (neg.f64 x)))
(+.f64 (*.f64 -1/2 (*.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2) x)) (+.f64 (*.f64 (+.f64 (*.f64 -3/16 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)) (*.f64 1/16 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2))) (pow.f64 x 2)) (+.f64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2) (*.f64 (+.f64 (*.f64 3/64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2)) (*.f64 -7/64 (pow.f64 (exp.f64 (*.f64 1/4 (+.f64 (log.f64 -1) (log.f64 x)))) 2))) (pow.f64 x 3)))))
(fma.f64 -1/2 (*.f64 x (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2)) (+.f64 (fma.f64 (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2) -1/8) (*.f64 x x) (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2)) (*.f64 (pow.f64 x 3) (*.f64 (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 -1) (log.f64 x))) 2) -1/16))))
(fma.f64 -1/2 (*.f64 x (pow.f64 (exp.f64 1/4) (*.f64 2 (+.f64 (log.f64 -1) (log.f64 x))))) (fma.f64 (*.f64 x x) (*.f64 (pow.f64 (exp.f64 1/4) (*.f64 2 (+.f64 (log.f64 -1) (log.f64 x)))) -1/8) (fma.f64 (pow.f64 x 3) (*.f64 (pow.f64 (exp.f64 1/4) (*.f64 2 (+.f64 (log.f64 -1) (log.f64 x)))) -1/16) (pow.f64 (exp.f64 1/4) (*.f64 2 (+.f64 (log.f64 -1) (log.f64 x)))))))
(+.f64 (*.f64 (+.f64 (*.f64 x -1/2) 1) (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 x 1/4)) 2)) (*.f64 (pow.f64 (*.f64 (pow.f64 -1 1/4) (pow.f64 x 1/4)) 2) (+.f64 (*.f64 (*.f64 x x) -1/8) (*.f64 (pow.f64 x 3) -1/16))))
(+.f64 (sqrt.f64 (neg.f64 x)) (*.f64 (sqrt.f64 (neg.f64 x)) (+.f64 (*.f64 x -1/2) (*.f64 (*.f64 x x) (+.f64 (*.f64 x -1/16) -1/8)))))
(*.f64 (sqrt.f64 (neg.f64 x)) (+.f64 (+.f64 1 (*.f64 x -1/2)) (*.f64 (*.f64 x x) (+.f64 (*.f64 x -1/16) -1/8))))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 (-.f64 x 1/2) (/.f64 1/8 x))
(+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))
(+.f64 -1/2 (+.f64 x (/.f64 -1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 (-.f64 x 1/2) (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x))))
(+.f64 x (-.f64 -1/2 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 -1/2 (-.f64 (+.f64 x (/.f64 -1/8 x)) (/.f64 1/16 (*.f64 x x))))
(+.f64 -1/2 (+.f64 (/.f64 -1/8 x) (+.f64 (/.f64 -1/16 (*.f64 x x)) x)))
(+.f64 x (-.f64 (/.f64 -1/16 (*.f64 x x)) (-.f64 1/2 (/.f64 -1/8 x))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 1/2 (*.f64 -1 x))
(+.f64 1/2 (neg.f64 x))
(-.f64 1/2 x)
(+.f64 1/2 (+.f64 (*.f64 -1 x) (*.f64 1/8 (/.f64 1 x))))
(+.f64 1/2 (fma.f64 -1 x (/.f64 1/8 x)))
(+.f64 1/2 (-.f64 (/.f64 1/8 x) x))
(+.f64 (/.f64 1/8 x) (-.f64 1/2 x))
(-.f64 1/2 (+.f64 x (/.f64 -1/8 x)))
(+.f64 1/2 (+.f64 (*.f64 -1 x) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(+.f64 1/2 (fma.f64 -1 x (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x)))))
(+.f64 1/2 (-.f64 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x))) x))
(+.f64 (/.f64 1/16 (*.f64 x x)) (+.f64 (/.f64 1/8 x) (-.f64 1/2 x)))
(-.f64 1/2 (+.f64 (/.f64 -1/8 x) (+.f64 (/.f64 -1/16 (*.f64 x x)) x)))
(+.f64 1/2 (-.f64 (/.f64 1/16 (*.f64 x x)) (+.f64 x (/.f64 -1/8 x))))

eval376.0ms (8.5%)

Compiler

Compiled 17503 to 13429 computations (23.3% saved)

prune107.0ms (2.4%)

Pruning

9 alts after pruning (3 fresh and 6 done)

PrunedKeptTotal
New7522754
Fresh011
Picked011
Done156
Total7539762
Error
0b
Counts
762 → 9
Alt Table
Click to see full alt table
StatusErrorProgram
✓30.5b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
✓0.9b
(-.f64 x 1/2)
✓0.6b
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
▶31.1b
(+.f64 (/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (+.f64 (+.f64 x -1/2) (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))
1.4b
x
▶31.9b
(/.f64 (*.f64 x x) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
✓0.7b
(+.f64 -1/2 (+.f64 x (/.f64 -1/8 x)))
✓0.6b
(+.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))
✓30.7b
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 2)
Compiler

Compiled 97 to 69 computations (28.9% saved)

localize101.0ms (2.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (+.f64 (+.f64 x -1/2) (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))
0.5b
(/.f64 1/64 (*.f64 x x))
0.6b
(/.f64 -1/16 (*.f64 x x))
✓28.5b
(/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (+.f64 (+.f64 x -1/2) (/.f64 1/8 x)))
Compiler

Compiled 100 to 63 computations (37% saved)

series4.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (+.f64 (+.f64 x -1/2) (/.f64 1/8 x)))
1.0ms
x
@0
(+.f64 (/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (+.f64 (+.f64 x -1/2) (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))
1.0ms
x
@inf
(/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (+.f64 (+.f64 x -1/2) (/.f64 1/8 x)))
1.0ms
x
@0
(/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (+.f64 (+.f64 x -1/2) (/.f64 1/8 x)))
1.0ms
x
@-inf
(+.f64 (/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (+.f64 (+.f64 x -1/2) (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))

rewrite288.0ms (6.5%)

Algorithm
1×batch-egg-rewrite
Rules
617×fma-neg_binary64
344×expm1-udef_binary64
344×log1p-udef_binary64
209×add-sqr-sqrt_binary64
201×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01665
140727
2668227
Stop Event
1×node limit
Counts
2 → 152
Calls
Call 1
Inputs
(/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (+.f64 (+.f64 x -1/2) (/.f64 1/8 x)))
(+.f64 (/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (+.f64 (+.f64 x -1/2) (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (-.f64 -1/2 (/.f64 1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1/2 (-.f64 x (/.f64 1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x -1/2) (neg.f64 (/.f64 1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x -1/2) (*.f64 -1/8 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x -1/2) (*.f64 -1 (/.f64 1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x -1/2) (*.f64 (neg.f64 (/.f64 1/4 (pow.f64 (cbrt.f64 x) 2))) (cbrt.f64 (/.f64 1/8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x -1/2) (*.f64 (neg.f64 (sqrt.f64 (/.f64 1/8 x))) (sqrt.f64 (/.f64 1/8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))) (fma.f64 (neg.f64 (/.f64 1 x)) 1/8 (/.f64 1/8 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))) (fma.f64 (neg.f64 (/.f64 1/8 x)) 1 (/.f64 1/8 x)))))) (#(struct:change 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(*.f64 -1/64 (pow.f64 x -2))) (/.f64 1 (+.f64 x (+.f64 -1/2 (/.f64 1/8 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 (pow.f64 (+.f64 x -1/2) 2) (*.f64 -1/64 (pow.f64 x -2))) 2)) (*.f64 (cbrt.f64 (+.f64 (pow.f64 (+.f64 x -1/2) 2) (*.f64 -1/64 (pow.f64 x -2)))) (/.f64 1 (+.f64 x (+.f64 -1/2 (/.f64 1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))) (pow.f64 (cbrt.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))) 2) (cbrt.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (pow.f64 (+.f64 x -1/2) 2) (*.f64 -1/64 (pow.f64 x -2)))) (*.f64 (sqrt.f64 (+.f64 (pow.f64 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(neg.f64 (-.f64 (/.f64 (/.f64 1/64 (*.f64 x x)) (+.f64 x (+.f64 -1/2 (/.f64 1/8 x)))) (/.f64 -1/16 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (sqrt.f64 (+.f64 x (+.f64 -1/2 (/.f64 1/8 x))))) (/.f64 (pow.f64 (+.f64 x -1/2) 2) (sqrt.f64 (+.f64 x (+.f64 -1/2 (/.f64 1/8 x))))) (neg.f64 (-.f64 (/.f64 (/.f64 1/64 (*.f64 x x)) (+.f64 x (+.f64 -1/2 (/.f64 1/8 x)))) (/.f64 -1/16 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 x -1/2) 4)) (sqrt.f64 (+.f64 x (+.f64 -1/2 (/.f64 1/8 x))))) (/.f64 (pow.f64 (cbrt.f64 (+.f64 x -1/2)) 2) (sqrt.f64 (+.f64 x (+.f64 -1/2 (/.f64 1/8 x))))) (neg.f64 (-.f64 (/.f64 (/.f64 1/64 (*.f64 x x)) (+.f64 x (+.f64 -1/2 (/.f64 1/8 x)))) (/.f64 -1/16 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (+.f64 x -1/2) 2) (+.f64 (pow.f64 (+.f64 x -1/2) 3) (/.f64 1/512 (pow.f64 x 3)))) (+.f64 (pow.f64 (+.f64 x -1/2) 2) (*.f64 (/.f64 1/8 x) (-.f64 (/.f64 1/8 x) (+.f64 x -1/2)))) (neg.f64 (-.f64 (/.f64 (/.f64 1/64 (*.f64 x x)) (+.f64 x (+.f64 -1/2 (/.f64 1/8 x)))) (/.f64 -1/16 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (pow.f64 (+.f64 x -1/2) 2) (+.f64 (pow.f64 (+.f64 x -1/2) 2) (*.f64 -1/64 (pow.f64 x -2)))) (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))) (neg.f64 (-.f64 (/.f64 (/.f64 1/64 (*.f64 x x)) (+.f64 x (+.f64 -1/2 (/.f64 1/8 x)))) (/.f64 -1/16 (*.f64 x x)))))))))

simplify96.0ms (2.2%)

Algorithm
1×egg-herbie
Rules
775×fma-neg_binary64
525×cancel-sign-sub-inv_binary64
489×associate-/l*_binary64
457×unswap-sqr_binary64
411×div-sub_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
025210
162204
2155204
3361204
4903204
52604204
66333204
Stop Event
1×node limit
Counts
176 → 168
Calls
Call 1
Inputs
(/.f64 -1/8 x)
(neg.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(/.f64 -1/16 (pow.f64 x 2))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
x
(-.f64 x 1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
Outputs
(/.f64 -1/8 x)
(neg.f64 (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(+.f64 -1/2 (neg.f64 (/.f64 1/8 x)))
(+.f64 -1/2 (/.f64 -1/8 x))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 (-.f64 x 1/2) (/.f64 -1/8 x))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 (-.f64 x 1/2) (/.f64 -1/8 x))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 (-.f64 x 1/2) (/.f64 -1/8 x))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 (-.f64 x 1/2) (/.f64 -1/8 x))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 (-.f64 x 1/2) (/.f64 -1/8 x))
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 (-.f64 x 1/2) (/.f64 -1/8 x))
(/.f64 -1/16 (pow.f64 x 2))
(/.f64 -1/16 (*.f64 x x))
(neg.f64 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/8 x) (/.f64 1/16 (*.f64 x x))))
(+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x))
(-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x)))
(neg.f64 (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(neg.f64 (+.f64 (+.f64 1/2 (/.f64 1/16 (*.f64 x x))) (/.f64 1/8 x)))
(+.f64 (+.f64 (/.f64 -1/16 (*.f64 x x)) (/.f64 -1/8 x)) -1/2)
(+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
(+.f64 (-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x))) -1/2)
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 (+.f64 1/2 (/.f64 1/16 (*.f64 x x))) (/.f64 1/8 x)))
(-.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (/.f64 1/16 (*.f64 x x)))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x))))
(+.f64 x (+.f64 (-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x))) -1/2))
(+.f64 (+.f64 (-.f64 x 1/2) (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 (-.f64 x 1/2) (/.f64 -1/8 x))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 (+.f64 1/2 (/.f64 1/16 (*.f64 x x))) (/.f64 1/8 x)))
(-.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (/.f64 1/16 (*.f64 x x)))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x))))
(+.f64 x (+.f64 (-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x))) -1/2))
(+.f64 (+.f64 (-.f64 x 1/2) (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))
x
(-.f64 x 1/2)
(+.f64 x -1/2)
(-.f64 x (+.f64 1/2 (*.f64 1/8 (/.f64 1 x))))
(-.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(+.f64 (+.f64 x -1/2) (/.f64 -1/8 x))
(+.f64 (-.f64 x 1/2) (/.f64 -1/8 x))
(-.f64 x (+.f64 1/2 (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 2))) (*.f64 1/8 (/.f64 1 x)))))
(-.f64 x (+.f64 (+.f64 1/2 (/.f64 1/16 (*.f64 x x))) (/.f64 1/8 x)))
(-.f64 (+.f64 x (+.f64 -1/2 (/.f64 -1/8 x))) (/.f64 1/16 (*.f64 x x)))
(+.f64 x (+.f64 (+.f64 -1/2 (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x))))
(+.f64 x (+.f64 (-.f64 (/.f64 -1/8 x) (/.f64 1/16 (*.f64 x x))) -1/2))
(+.f64 (+.f64 (-.f64 x 1/2) (/.f64 -1/8 x)) (/.f64 -1/16 (*.f64 x x)))

localize13.0ms (0.3%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓28.5b
(/.f64 (*.f64 x x) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
Compiler

Compiled 31 to 19 computations (38.7% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
(/.f64 (*.f64 x x) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
0.0ms
x
@inf
(/.f64 (*.f64 x x) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
0.0ms
x
@-inf
(/.f64 (*.f64 x x) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))

rewrite60.0ms (1.4%)

Algorithm
1×batch-egg-rewrite
Rules
727×prod-diff_binary64
499×log-prod_binary64
361×fma-def_binary64
284×pow2_binary64
217×log-div_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0916
121616
2324716
Stop Event
1×node limit
Counts
1 → 42
Calls
Call 1
Inputs
(/.f64 (*.f64 x x) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 x (/.f64 1 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) (/.f64 1 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x))) (pow.f64 (cbrt.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x))) 2) (cbrt.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x 4)) (*.f64 (pow.f64 (cbrt.f64 x) 2) (/.f64 1 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (sqrt.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))))) (/.f64 x (sqrt.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (neg.f64 x)) (/.f64 1 (neg.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x)))) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x 1) (/.f64 x (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x)))) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 x 4)) 1) (/.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (pow.f64 (cbrt.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x)))) 2)) (/.f64 x (cbrt.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x)))) 2)) (/.f64 (*.f64 x x) (cbrt.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x)))) 2)) (cbrt.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))))) (/.f64 (*.f64 x x) (sqrt.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 x 4)) (sqrt.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))))) (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x x) (-.f64 (pow.f64 (+.f64 x -1/2) 3) (/.f64 -1/512 (pow.f64 x 3)))) (fma.f64 (/.f64 -1/8 x) (+.f64 -1/2 (+.f64 x (/.f64 -1/8 x))) (pow.f64 (+.f64 x -1/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 x x) (-.f64 (pow.f64 (+.f64 x -1/2) 2) (/.f64 1/64 (*.f64 x x)))) (+.f64 -1/2 (+.f64 x (/.f64 -1/8 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (sqrt.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) (*.f64 x x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 x x) 3) (pow.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) (*.f64 x x)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 x x) (neg.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 x 4) (pow.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 x x) 3) (pow.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 x (/.f64 (+.f64 x (-.f64 -1/2 (/.f64 -1/8 x))) x))) 1))))))

simplify50.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
697×associate-/l*_binary64
570×unswap-sqr_binary64
536×fma-def_binary64
500×associate-*l*_binary64
347×associate-*r*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
035138
196138
2229138
3587138
41384129
54107129
Stop Event
1×node limit
Counts
54 → 56
Calls
Call 1
Inputs
(*.f64 8 (pow.f64 x 3))
(+.f64 (*.f64 32 (pow.f64 x 4)) (*.f64 8 (pow.f64 x 3)))
(+.f64 (*.f64 32 (pow.f64 x 4)) (+.f64 (*.f64 64 (pow.f64 x 5)) (*.f64 8 (pow.f64 x 3))))
(+.f64 (*.f64 32 (pow.f64 x 4)) (+.f64 (*.f64 -512 (pow.f64 x 7)) (+.f64 (*.f64 64 (pow.f64 x 5)) (*.f64 8 (pow.f64 x 3)))))
x
(+.f64 1/2 x)
(+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) x))
(-.f64 (+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) x)) (*.f64 1/64 (/.f64 1 (pow.f64 x 3))))
x
(+.f64 1/2 x)
(+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) x))
(-.f64 (+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) x)) (*.f64 1/64 (/.f64 1 (pow.f64 x 3))))
Outputs
(*.f64 8 (pow.f64 x 3))
(+.f64 (*.f64 32 (pow.f64 x 4)) (*.f64 8 (pow.f64 x 3)))
(fma.f64 32 (pow.f64 x 4) (*.f64 8 (pow.f64 x 3)))
(fma.f64 8 (pow.f64 x 3) (*.f64 32 (pow.f64 x 4)))
(*.f64 (pow.f64 x 3) (fma.f64 x 32 8))
(+.f64 (*.f64 32 (pow.f64 x 4)) (+.f64 (*.f64 64 (pow.f64 x 5)) (*.f64 8 (pow.f64 x 3))))
(fma.f64 32 (pow.f64 x 4) (fma.f64 64 (pow.f64 x 5) (*.f64 8 (pow.f64 x 3))))
(fma.f64 32 (pow.f64 x 4) (fma.f64 8 (pow.f64 x 3) (*.f64 64 (pow.f64 x 5))))
(fma.f64 8 (pow.f64 x 3) (fma.f64 64 (pow.f64 x 5) (*.f64 32 (pow.f64 x 4))))
(fma.f64 8 (pow.f64 x 3) (fma.f64 32 (pow.f64 x 4) (*.f64 64 (pow.f64 x 5))))
(fma.f64 64 (pow.f64 x 5) (*.f64 (pow.f64 x 3) (fma.f64 x 32 8)))
(+.f64 (*.f64 32 (pow.f64 x 4)) (+.f64 (*.f64 -512 (pow.f64 x 7)) (+.f64 (*.f64 64 (pow.f64 x 5)) (*.f64 8 (pow.f64 x 3)))))
(fma.f64 32 (pow.f64 x 4) (fma.f64 -512 (pow.f64 x 7) (fma.f64 64 (pow.f64 x 5) (*.f64 8 (pow.f64 x 3)))))
(fma.f64 32 (pow.f64 x 4) (fma.f64 -512 (pow.f64 x 7) (fma.f64 8 (pow.f64 x 3) (*.f64 64 (pow.f64 x 5)))))
(fma.f64 -512 (pow.f64 x 7) (fma.f64 8 (pow.f64 x 3) (fma.f64 64 (pow.f64 x 5) (*.f64 32 (pow.f64 x 4)))))
(fma.f64 8 (pow.f64 x 3) (fma.f64 32 (pow.f64 x 4) (fma.f64 -512 (pow.f64 x 7) (*.f64 64 (pow.f64 x 5)))))
(fma.f64 64 (pow.f64 x 5) (fma.f64 -512 (pow.f64 x 7) (*.f64 (pow.f64 x 3) (fma.f64 x 32 8))))
x
(+.f64 1/2 x)
(+.f64 x 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) x))
(+.f64 1/2 (+.f64 x (/.f64 1/8 x)))
(+.f64 (+.f64 x 1/2) (/.f64 1/8 x))
(+.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(-.f64 (+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) x)) (*.f64 1/64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 1/2 (+.f64 x (/.f64 1/8 x))) (/.f64 1/64 (pow.f64 x 3)))
(+.f64 (+.f64 1/2 (+.f64 x (/.f64 1/8 x))) (/.f64 -1/64 (pow.f64 x 3)))
(+.f64 (+.f64 x 1/2) (+.f64 (/.f64 1/8 x) (/.f64 -1/64 (pow.f64 x 3))))
(+.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 -1/64 (pow.f64 x 3)))))
(-.f64 (+.f64 x (+.f64 1/2 (/.f64 1/8 x))) (/.f64 1/64 (pow.f64 x 3)))
(+.f64 x (+.f64 (/.f64 1/8 x) (-.f64 1/2 (/.f64 1/64 (pow.f64 x 3)))))
x
(+.f64 1/2 x)
(+.f64 x 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) x))
(+.f64 1/2 (+.f64 x (/.f64 1/8 x)))
(+.f64 (+.f64 x 1/2) (/.f64 1/8 x))
(+.f64 x (+.f64 1/2 (/.f64 1/8 x)))
(-.f64 (+.f64 1/2 (+.f64 (*.f64 1/8 (/.f64 1 x)) x)) (*.f64 1/64 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 1/2 (+.f64 x (/.f64 1/8 x))) (/.f64 1/64 (pow.f64 x 3)))
(+.f64 (+.f64 1/2 (+.f64 x (/.f64 1/8 x))) (/.f64 -1/64 (pow.f64 x 3)))
(+.f64 (+.f64 x 1/2) (+.f64 (/.f64 1/8 x) (/.f64 -1/64 (pow.f64 x 3))))
(+.f64 x (+.f64 1/2 (+.f64 (/.f64 1/8 x) (/.f64 -1/64 (pow.f64 x 3)))))
(-.f64 (+.f64 x (+.f64 1/2 (/.f64 1/8 x))) (/.f64 1/64 (pow.f64 x 3)))
(+.f64 x (+.f64 (/.f64 1/8 x) (-.f64 1/2 (/.f64 1/64 (pow.f64 x 3)))))

eval233.0ms (5.3%)

Compiler

Compiled 7844 to 5640 computations (28.1% saved)

prune67.0ms (1.5%)

Pruning

10 alts after pruning (2 fresh and 8 done)

PrunedKeptTotal
New2931294
Fresh011
Picked011
Done077
Total29310303
Error
0b
Counts
303 → 10
Alt Table
Click to see full alt table
StatusErrorProgram
✓30.5b
(sqrt.f64 (*.f64 x (+.f64 x -1)))
✓0.9b
(-.f64 x 1/2)
✓0.6b
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
✓31.1b
(+.f64 (/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (+.f64 (+.f64 x -1/2) (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))
1.4b
x
✓31.9b
(/.f64 (*.f64 x x) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
0.7b
(/.f64 (+.f64 (*.f64 (/.f64 -1/16 x) (/.f64 1 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))))) x) (*.f64 x (/.f64 1 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))))))
✓0.7b
(+.f64 -1/2 (+.f64 x (/.f64 -1/8 x)))
✓0.6b
(+.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))
✓30.7b
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 2)
Compiler

Compiled 125 to 90 computations (28% saved)

regimes23.0ms (0.5%)

Counts
14 → 1
Calls
Call 1
Inputs
x
(-.f64 x 1/2)
(+.f64 -1/2 (+.f64 x (/.f64 -1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(/.f64 (*.f64 x x) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
(+.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))
(/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
(/.f64 (+.f64 (*.f64 (/.f64 -1/16 x) (/.f64 1 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))))) x) (*.f64 x (/.f64 1 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))))))
(+.f64 (/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (+.f64 (+.f64 x -1/2) (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
(pow.f64 (pow.f64 (*.f64 x (+.f64 x -1)) 1/4) 2)
(pow.f64 (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x -1)))) 2)
Outputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Calls

2 calls:

10.0ms
x
8.0ms
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Results
ErrorSegmentsBranch
0.4b1x
0.4b1(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
Compiler

Compiled 170 to 117 computations (31.2% saved)

regimes13.0ms (0.3%)

Counts
11 → 1
Calls
Call 1
Inputs
x
(-.f64 x 1/2)
(+.f64 -1/2 (+.f64 x (/.f64 -1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(/.f64 (*.f64 x x) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
(+.f64 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))
(/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
(/.f64 (+.f64 (*.f64 (/.f64 -1/16 x) (/.f64 1 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))))) x) (*.f64 x (/.f64 1 (+.f64 x (-.f64 -1/2 (/.f64 1/8 x))))))
(+.f64 (/.f64 (-.f64 (*.f64 (+.f64 x -1/2) (+.f64 x -1/2)) (/.f64 1/64 (*.f64 x x))) (+.f64 (+.f64 x -1/2) (/.f64 1/8 x))) (/.f64 -1/16 (*.f64 x x)))
(sqrt.f64 (*.f64 x (+.f64 x -1)))
Outputs
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
Calls

1 calls:

9.0ms
x
Results
ErrorSegmentsBranch
0.6b1x
Compiler

Compiled 137 to 92 computations (32.8% saved)

regimes6.0ms (0.1%)

Counts
5 → 1
Calls
Call 1
Inputs
x
(-.f64 x 1/2)
(+.f64 -1/2 (+.f64 x (/.f64 -1/8 x)))
(+.f64 x (+.f64 -1/2 (/.f64 -1/8 x)))
(/.f64 (*.f64 x x) (-.f64 (+.f64 x -1/2) (/.f64 -1/8 x)))
Outputs
(+.f64 -1/2 (+.f64 x (/.f64 -1/8 x)))
Calls

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
0.7b1x
Compiler

Compiled 32 to 21 computations (34.4% saved)

regimes4.0ms (0.1%)

Accuracy

Total -0.4b remaining (-48.4%)

Threshold costs -0.4b (-48.4%)

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

1 calls:

3.0ms
x
Results
ErrorSegmentsBranch
0.9b1x
Compiler

Compiled 7 to 4 computations (42.9% saved)

simplify4.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
7×+-commutative_binary64
2×sub-neg_binary64
1×*-commutative_binary64
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02042
13342
23542
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
(+.f64 -1/2 (+.f64 x (/.f64 -1/8 x)))
(-.f64 x 1/2)
x
Outputs
(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (+.f64 x -1)) (sqrt.f64 x))
(+.f64 x (+.f64 -1/2 (/.f64 (+.f64 -1/8 (/.f64 -1/16 x)) x)))
(+.f64 -1/2 (+.f64 x (/.f64 -1/8 x)))
(-.f64 x 1/2)
(+.f64 x -1/2)
x
Compiler

Compiled 34 to 25 computations (26.5% saved)

soundness0.0ms (0%)

end38.0ms (0.9%)

Compiler

Compiled 30 to 21 computations (30% saved)

Profiling

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