Details

Time bar (total: 1.5s)

analyze8.0ms (0.5%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%50%50%0
0%50%50%1
0%50%50%2
0%50%50%3
31.2%18.7%50%4
40.6%9.4%50%5
45.3%4.7%50%6
47.6%2.3%50%7
48.8%1.2%50%8
49.4%0.6%50%9
49.7%0.3%50%10
49.8%0.1%50%11
49.9%0.1%50%12
49.9%0%50%13
50%0%50%14
Compiler

Compiled 29 to 19 computations (34.5% saved)

sample1.0s (67.9%)

Results
1.0s8256×body128valid
Compiler

Compiled 58 to 38 computations (34.5% saved)

preprocess30.0ms (2%)

Algorithm
2×egg-herbie
Rules
554×associate-/r*_binary64
513×distribute-rgt-in_binary64
416×associate-/r/_binary64
349×fma-def_binary64
319×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01131
14026
220017
3131613
4358513
011
Stop Event
1×saturated
1×node limit
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))
Outputs
(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))
(/.f64 (/.f64 (*.f64 i (*.f64 i (*.f64 i i))) (*.f64 4 (*.f64 i i))) (+.f64 (*.f64 4 (*.f64 i i)) -1))
(*.f64 (/.f64 i (fma.f64 4 (*.f64 i i) -1)) (/.f64 (pow.f64 i 3) (*.f64 i (*.f64 i 4))))
(*.f64 (/.f64 i (fma.f64 (*.f64 i i) 4 -1)) (/.f64 i 4))
(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify21.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
554×associate-/r*_binary64
513×distribute-rgt-in_binary64
416×associate-/r/_binary64
349×fma-def_binary64
319×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01131
14026
220017
3131613
4358513
Stop Event
1×node limit
Counts
1 → 2
Calls
Call 1
Inputs
(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))
Outputs
(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))
(/.f64 (/.f64 (*.f64 i (*.f64 i (*.f64 i i))) (*.f64 4 (*.f64 i i))) (+.f64 (*.f64 4 (*.f64 i i)) -1))
(*.f64 (/.f64 i (fma.f64 4 (*.f64 i i) -1)) (/.f64 (pow.f64 i 3) (*.f64 i (*.f64 i 4))))
(*.f64 (/.f64 i (fma.f64 (*.f64 i i) 4 -1)) (/.f64 i 4))
(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))

prune4.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
6.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
47.6b
(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))
▶6.3b
(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
Compiler

Compiled 107 to 74 computations (30.8% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 4 (/.f64 i (pow.f64 i 3)))
✓0.3b
(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
✓9.0b
(/.f64 i (pow.f64 i 3))

series6.0ms (0.4%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
1.0ms
i
@0
(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
1.0ms
i
@0
(/.f64 i (pow.f64 i 3))
1.0ms
i
@inf
(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
1.0ms
i
@-inf
(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
1.0ms
i
@0
(-.f64 4 (/.f64 i (pow.f64 i 3)))

rewrite52.0ms (3.4%)

Algorithm
1×batch-egg-rewrite
Rules
436×log-prod_binary64
172×expm1-udef_binary64
172×log1p-udef_binary64
168×pow1/3_binary64
150×pow3_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0930
121521
2267421
Stop Event
1×node limit
Counts
3 → 113
Calls
Call 1
Inputs
(/.f64 i (pow.f64 i 3))
(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
(-.f64 4 (/.f64 i (pow.f64 i 3)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 i -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 i -2))) (cbrt.f64 (exp.f64 (pow.f64 i -2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 i -2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 i -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 i (pow.f64 i -3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 i -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 i -2) (/.f64 i i))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 i -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 i) i) (pow.f64 (/.f64 (cbrt.f64 i) i) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (cbrt.f64 i) i) 2) (/.f64 (cbrt.f64 i) i))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 i) 2) (*.f64 (cbrt.f64 i) (pow.f64 i -3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 i) (/.f64 1 i))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 i) (/.f64 i (*.f64 i i)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 i) (*.f64 (sqrt.f64 i) (pow.f64 i -3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 i) (/.f64 1 (neg.f64 (pow.f64 i 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 i -3) i)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 i) 2) i) (/.f64 (cbrt.f64 i) (*.f64 i i)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 i) i) (/.f64 (sqrt.f64 i) (*.f64 i i)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 i) (*.f64 i i)) (/.f64 (sqrt.f64 i) i))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 i) 2) 1) (/.f64 (cbrt.f64 i) (pow.f64 i 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 i) 1) (/.f64 (sqrt.f64 i) (pow.f64 i 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 i) 2) (*.f64 i i)) (/.f64 (cbrt.f64 i) i))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 i 3/2)) (/.f64 i (pow.f64 i 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 i) 2) (pow.f64 i 3/2)) (/.f64 (cbrt.f64 i) (pow.f64 i 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 i -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 i -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 i i) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cbrt.f64 i) i) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 i) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (pow.f64 i 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 i i) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 i (neg.f64 (pow.f64 i 3))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (pow.f64 i -2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 1 (pow.f64 i 6)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -2 (log.f64 i)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -2 (log.f64 i)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 i -2)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))) (cbrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (/.f64 1 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) (pow.f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 2) (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (sqrt.f64 (-.f64 4 (pow.f64 i -2)))) (/.f64 1/2 (sqrt.f64 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/4 (/.f64 1 (neg.f64 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 4 (pow.f64 i -2))) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 (-.f64 64 (/.f64 1 (pow.f64 i 6)))) (fma.f64 (pow.f64 i -2) (+.f64 (pow.f64 i -2) 4) 16))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 (-.f64 16 (pow.f64 (pow.f64 i -2) 2))) (+.f64 (pow.f64 i -2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (sqrt.f64 (-.f64 4 (pow.f64 i -2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 16 (/.f64 (pow.f64 i -2) 1/4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 16 (/.f64 (pow.f64 i -2) 1/4)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/16 (pow.f64 (-.f64 4 (pow.f64 i -2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 4 (neg.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 4 (*.f64 (neg.f64 (pow.f64 i -2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (pow.f64 i -2)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 4 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (-.f64 4 (pow.f64 i -2)))) (cbrt.f64 (exp.f64 (-.f64 4 (pow.f64 i -2)))))) (log.f64 (cbrt.f64 (exp.f64 (-.f64 4 (pow.f64 i -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 4 (pow.f64 i -2))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 4 (pow.f64 i -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 4 (pow.f64 i -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 4 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 4 (pow.f64 i -2))) (pow.f64 (cbrt.f64 (-.f64 4 (pow.f64 i -2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 4 (pow.f64 i -2))) 2) (cbrt.f64 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 4 (pow.f64 i -2))) (sqrt.f64 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 64 (/.f64 1 (pow.f64 i 6))) (/.f64 1 (fma.f64 (pow.f64 i -2) (+.f64 (pow.f64 i -2) 4) 16)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 16 (pow.f64 (pow.f64 i -2) 2)) (/.f64 1 (+.f64 (pow.f64 i -2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (pow.f64 i -2) (+.f64 (pow.f64 i -2) 4) 16) (-.f64 64 (/.f64 1 (pow.f64 i 6)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 i -2) 4) (-.f64 16 (pow.f64 (pow.f64 i -2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 64 (/.f64 1 (pow.f64 i 6))) (fma.f64 (pow.f64 i -2) (+.f64 (pow.f64 i -2) 4) 16))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 16 (pow.f64 (pow.f64 i -2) 2)) (+.f64 (pow.f64 i -2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 64 (/.f64 1 (pow.f64 i 6)))) (neg.f64 (fma.f64 (pow.f64 i -2) (+.f64 (pow.f64 i -2) 4) 16)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 16 (pow.f64 (pow.f64 i -2) 2))) (neg.f64 (+.f64 (pow.f64 i -2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 64 (pow.f64 (neg.f64 (pow.f64 i -2)) 3)) (+.f64 16 (-.f64 (*.f64 (neg.f64 (pow.f64 i -2)) (neg.f64 (pow.f64 i -2))) (*.f64 4 (neg.f64 (pow.f64 i -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 16 (*.f64 (neg.f64 (pow.f64 i -2)) (neg.f64 (pow.f64 i -2)))) (-.f64 4 (neg.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 4 (pow.f64 i -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 4 (pow.f64 i -2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 4 (pow.f64 i -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 4 (pow.f64 i -2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (pow.f64 i -2) (+.f64 (pow.f64 i -2) 4) 16) (-.f64 64 (/.f64 1 (pow.f64 i 6)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (pow.f64 i -2) 4) (-.f64 16 (pow.f64 (pow.f64 i -2) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 4 (pow.f64 i -2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 4 (pow.f64 i -2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 i (neg.f64 (pow.f64 i -3)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (neg.f64 (pow.f64 i -2)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (/.f64 (cbrt.f64 i) i) 2) (neg.f64 (/.f64 (cbrt.f64 i) i)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 i) (neg.f64 (/.f64 1 i)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 i) (pow.f64 i -3) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (neg.f64 (pow.f64 i -2))) (cbrt.f64 (neg.f64 (pow.f64 i -2)))) (cbrt.f64 (neg.f64 (pow.f64 i -2))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (neg.f64 (pow.f64 i -2))) (sqrt.f64 (neg.f64 (pow.f64 i -2))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (pow.f64 i -2) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (/.f64 (cbrt.f64 i) i) 2)) (/.f64 (cbrt.f64 i) i) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (/.f64 1 i)) (/.f64 1 i) 4)))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 4 (pow.f64 i -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 4 (pow.f64 i -2))))))))

simplify37.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
453×associate-*l*_binary64
438×fma-neg_binary64
320×cancel-sign-sub-inv_binary64
296×associate-*r*_binary64
251×times-frac_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
044372
1108370
2295366
31091366
44377366
Stop Event
1×node limit
Counts
149 → 135
Calls
Call 1
Inputs
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (pow.f64 i 2))
(*.f64 -1/4 (pow.f64 i 2))
(neg.f64 (+.f64 (pow.f64 i 4) (*.f64 1/4 (pow.f64 i 2))))
(neg.f64 (+.f64 (pow.f64 i 4) (+.f64 (*.f64 1/4 (pow.f64 i 2)) (*.f64 4 (pow.f64 i 6)))))
(neg.f64 (+.f64 (pow.f64 i 4) (+.f64 (*.f64 1/4 (pow.f64 i 2)) (+.f64 (*.f64 16 (pow.f64 i 8)) (*.f64 4 (pow.f64 i 6))))))
1/16
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 1/16 (+.f64 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))) (*.f64 1/256 (/.f64 1 (pow.f64 i 4)))))
(+.f64 (*.f64 1/1024 (/.f64 1 (pow.f64 i 6))) (+.f64 1/16 (+.f64 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))) (*.f64 1/256 (/.f64 1 (pow.f64 i 4))))))
1/16
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 1/16 (+.f64 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))) (*.f64 1/256 (/.f64 1 (pow.f64 i 4)))))
(+.f64 (*.f64 1/1024 (/.f64 1 (pow.f64 i 6))) (+.f64 1/16 (+.f64 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))) (*.f64 1/256 (/.f64 1 (pow.f64 i 4))))))
(/.f64 -1 (pow.f64 i 2))
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
4
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
4
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
Outputs
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(/.f64 1 (pow.f64 i 2))
(/.f64 1 (*.f64 i i))
(*.f64 -1/4 (pow.f64 i 2))
(*.f64 (*.f64 i i) -1/4)
(*.f64 i (*.f64 i -1/4))
(neg.f64 (+.f64 (pow.f64 i 4) (*.f64 1/4 (pow.f64 i 2))))
(neg.f64 (+.f64 (pow.f64 i 4) (*.f64 (*.f64 i i) 1/4)))
(-.f64 (*.f64 (*.f64 i i) -1/4) (pow.f64 i 4))
(*.f64 (*.f64 i i) (neg.f64 (fma.f64 i i 1/4)))
(*.f64 i (-.f64 (*.f64 i -1/4) (pow.f64 i 3)))
(neg.f64 (+.f64 (pow.f64 i 4) (+.f64 (*.f64 1/4 (pow.f64 i 2)) (*.f64 4 (pow.f64 i 6)))))
(neg.f64 (+.f64 (pow.f64 i 4) (fma.f64 1/4 (*.f64 i i) (*.f64 4 (pow.f64 i 6)))))
(-.f64 (neg.f64 (pow.f64 i 4)) (fma.f64 (*.f64 i i) 1/4 (*.f64 4 (pow.f64 i 6))))
(-.f64 (*.f64 i (*.f64 i -1/4)) (fma.f64 4 (pow.f64 i 6) (pow.f64 i 4)))
(neg.f64 (+.f64 (pow.f64 i 4) (+.f64 (*.f64 1/4 (pow.f64 i 2)) (+.f64 (*.f64 16 (pow.f64 i 8)) (*.f64 4 (pow.f64 i 6))))))
(neg.f64 (+.f64 (pow.f64 i 4) (fma.f64 1/4 (*.f64 i i) (fma.f64 16 (pow.f64 i 8) (*.f64 4 (pow.f64 i 6))))))
(-.f64 (neg.f64 (pow.f64 i 4)) (fma.f64 (*.f64 i i) 1/4 (fma.f64 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))))
(neg.f64 (fma.f64 (*.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))))
(-.f64 (*.f64 (pow.f64 i 6) -4) (fma.f64 (*.f64 i i) (fma.f64 i i 1/4) (*.f64 16 (pow.f64 i 8))))
1/16
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 1/16 (/.f64 1/64 (*.f64 i i)))
(+.f64 1/16 (+.f64 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))) (*.f64 1/256 (/.f64 1 (pow.f64 i 4)))))
(+.f64 1/16 (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/256 (pow.f64 i 4))))
(+.f64 (*.f64 1/1024 (/.f64 1 (pow.f64 i 6))) (+.f64 1/16 (+.f64 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))) (*.f64 1/256 (/.f64 1 (pow.f64 i 4))))))
(+.f64 (+.f64 1/16 (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/256 (pow.f64 i 4)))) (/.f64 1/1024 (pow.f64 i 6)))
(+.f64 (+.f64 (/.f64 1/1024 (pow.f64 i 6)) (+.f64 1/16 (/.f64 1/64 (*.f64 i i)))) (/.f64 1/256 (pow.f64 i 4)))
(+.f64 (/.f64 1/64 (*.f64 i i)) (+.f64 (/.f64 1/1024 (pow.f64 i 6)) (+.f64 1/16 (/.f64 1/256 (pow.f64 i 4)))))
(+.f64 1/16 (+.f64 (/.f64 1/256 (pow.f64 i 4)) (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/1024 (pow.f64 i 6)))))
1/16
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 1/16 (/.f64 1/64 (*.f64 i i)))
(+.f64 1/16 (+.f64 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))) (*.f64 1/256 (/.f64 1 (pow.f64 i 4)))))
(+.f64 1/16 (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/256 (pow.f64 i 4))))
(+.f64 (*.f64 1/1024 (/.f64 1 (pow.f64 i 6))) (+.f64 1/16 (+.f64 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))) (*.f64 1/256 (/.f64 1 (pow.f64 i 4))))))
(+.f64 (+.f64 1/16 (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/256 (pow.f64 i 4)))) (/.f64 1/1024 (pow.f64 i 6)))
(+.f64 (+.f64 (/.f64 1/1024 (pow.f64 i 6)) (+.f64 1/16 (/.f64 1/64 (*.f64 i i)))) (/.f64 1/256 (pow.f64 i 4)))
(+.f64 (/.f64 1/64 (*.f64 i i)) (+.f64 (/.f64 1/1024 (pow.f64 i 6)) (+.f64 1/16 (/.f64 1/256 (pow.f64 i 4)))))
(+.f64 1/16 (+.f64 (/.f64 1/256 (pow.f64 i 4)) (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/1024 (pow.f64 i 6)))))
(/.f64 -1 (pow.f64 i 2))
(/.f64 -1 (*.f64 i i))
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
(-.f64 4 (/.f64 1 (*.f64 i i)))
(+.f64 4 (/.f64 -1 (*.f64 i i)))
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
(-.f64 4 (/.f64 1 (*.f64 i i)))
(+.f64 4 (/.f64 -1 (*.f64 i i)))
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
(-.f64 4 (/.f64 1 (*.f64 i i)))
(+.f64 4 (/.f64 -1 (*.f64 i i)))
4
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
(-.f64 4 (/.f64 1 (*.f64 i i)))
(+.f64 4 (/.f64 -1 (*.f64 i i)))
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
(-.f64 4 (/.f64 1 (*.f64 i i)))
(+.f64 4 (/.f64 -1 (*.f64 i i)))
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
(-.f64 4 (/.f64 1 (*.f64 i i)))
(+.f64 4 (/.f64 -1 (*.f64 i i)))
4
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
(-.f64 4 (/.f64 1 (*.f64 i i)))
(+.f64 4 (/.f64 -1 (*.f64 i i)))
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
(-.f64 4 (/.f64 1 (*.f64 i i)))
(+.f64 4 (/.f64 -1 (*.f64 i i)))
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
(-.f64 4 (/.f64 1 (*.f64 i i)))
(+.f64 4 (/.f64 -1 (*.f64 i i)))

prune81.0ms (5.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1332135
Fresh101
Picked101
Done000
Total1352137
Error
0b
Counts
137 → 2
Alt Table
StatusErrorProgram
27.6b
(*.f64 -1/4 (pow.f64 i 2))
▶0.3b
(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
Compiler

Compiled 1737 to 1421 computations (18.2% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
✓0.2b
(/.f64 1 (pow.f64 i 2))
✓0.3b
(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))

series10.0ms (0.7%)

Counts
3 → 15
Calls

9 calls:

TimeVariablePointExpression
5.0ms
i
@-inf
(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
1.0ms
i
@0
(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
1.0ms
i
@inf
(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
1.0ms
i
@0
(/.f64 1 (pow.f64 i 2))
1.0ms
i
@0
(-.f64 4 (/.f64 1 (pow.f64 i 2)))

rewrite45.0ms (2.9%)

Algorithm
1×batch-egg-rewrite
Rules
386×log-prod_binary64
246×pow2_binary64
171×expm1-udef_binary64
171×log1p-udef_binary64
168×pow1/3_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01021
122521
2259521
Stop Event
1×node limit
Counts
3 → 105
Calls
Call 1
Inputs
(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
(/.f64 1 (pow.f64 i 2))
(-.f64 4 (/.f64 1 (pow.f64 i 2)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (/.f64 1 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) (pow.f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 2) (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/2 (sqrt.f64 (-.f64 4 (pow.f64 i -2)))) (/.f64 1/2 (sqrt.f64 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/4 (/.f64 1 (neg.f64 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 4 (pow.f64 i -2))) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 (-.f64 64 (pow.f64 i -6))) (fma.f64 (pow.f64 i -2) (+.f64 4 (pow.f64 i -2)) 16))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/4 (-.f64 16 (pow.f64 i -4))) (+.f64 4 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/2 (sqrt.f64 (-.f64 4 (pow.f64 i -2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 16 (/.f64 (pow.f64 i -2) 1/4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 16 (/.f64 (pow.f64 i -2) 1/4)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 i -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 i -2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 i -2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 i -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 i -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 i -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 i -2)) (cbrt.f64 (pow.f64 i -4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 i -4)) (cbrt.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 i -1) (pow.f64 i -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (neg.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 i) 2) -2) (pow.f64 (cbrt.f64 i) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 i) -2) (pow.f64 (sqrt.f64 i) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 i 4))) (cbrt.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 i -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 i i) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 i -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 i -4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 i -2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 i -1) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 i -6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 i) -2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (*.f64 i (neg.f64 i))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 i -4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 i -6))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 -2 (log.f64 i)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 i) -2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 i i)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 -2 (log.f64 i)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 i -2)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 4 (neg.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 4 (*.f64 (neg.f64 (pow.f64 i -2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 4 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (pow.f64 i -2)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (-.f64 4 (pow.f64 i -2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (-.f64 4 (pow.f64 i -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 4 (pow.f64 i -2))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 4 (pow.f64 i -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 4 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 4 (pow.f64 i -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 4 (pow.f64 i -2))) (pow.f64 (cbrt.f64 (-.f64 4 (pow.f64 i -2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 4 (pow.f64 i -2))) 2) (cbrt.f64 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 4 (pow.f64 i -2))) (sqrt.f64 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 64 (pow.f64 i -6)) (/.f64 1 (fma.f64 (pow.f64 i -2) (+.f64 4 (pow.f64 i -2)) 16)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 16 (pow.f64 i -4)) (/.f64 1 (+.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (pow.f64 i -2) (+.f64 4 (pow.f64 i -2)) 16) (-.f64 64 (pow.f64 i -6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 4 (pow.f64 i -2)) (-.f64 16 (pow.f64 i -4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 64 (pow.f64 i -6)) (fma.f64 (pow.f64 i -2) (+.f64 4 (pow.f64 i -2)) 16))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 16 (pow.f64 i -4)) (+.f64 4 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 64 (pow.f64 i -6))) (neg.f64 (fma.f64 (pow.f64 i -2) (+.f64 4 (pow.f64 i -2)) 16)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 16 (pow.f64 i -4))) (neg.f64 (+.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 64 (pow.f64 (neg.f64 (pow.f64 i -2)) 3)) (+.f64 16 (-.f64 (pow.f64 (neg.f64 (pow.f64 i -2)) 2) (*.f64 4 (neg.f64 (pow.f64 i -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 16 (pow.f64 (neg.f64 (pow.f64 i -2)) 2)) (-.f64 4 (neg.f64 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 4 (pow.f64 i -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 4 (pow.f64 i -2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 4 (pow.f64 i -2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 4 (pow.f64 i -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 4 (pow.f64 i -2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (pow.f64 i -2) (+.f64 4 (pow.f64 i -2)) 16) (-.f64 64 (pow.f64 i -6))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 4 (pow.f64 i -2)) (-.f64 16 (pow.f64 i -4))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 4 (pow.f64 i -2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 4 (pow.f64 i -2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (neg.f64 (pow.f64 i -2)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 i -4)) (neg.f64 (cbrt.f64 (pow.f64 i -2))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 i -1) (neg.f64 (pow.f64 i -1)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (pow.f64 i -2) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (neg.f64 (pow.f64 i -2))) 2) (cbrt.f64 (neg.f64 (pow.f64 i -2))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (neg.f64 (pow.f64 i -2))) (sqrt.f64 (neg.f64 (pow.f64 i -2))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (pow.f64 i -4))) (cbrt.f64 (pow.f64 i -2)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 i -1)) (pow.f64 i -1) 4)))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 4 (pow.f64 i -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 4 (pow.f64 i -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 4 (pow.f64 i -2))))))))

simplify36.0ms (2.4%)

Algorithm
1×egg-herbie
Rules
457×associate-*l*_binary64
438×fma-neg_binary64
320×cancel-sign-sub-inv_binary64
298×associate-*r*_binary64
238×times-frac_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
043198
1105196
2288192
31074192
44370192
Stop Event
1×node limit
Counts
120 → 123
Calls
Call 1
Inputs
(*.f64 -1/4 (pow.f64 i 2))
(neg.f64 (+.f64 (pow.f64 i 4) (*.f64 1/4 (pow.f64 i 2))))
(neg.f64 (+.f64 (pow.f64 i 4) (+.f64 (*.f64 1/4 (pow.f64 i 2)) (*.f64 4 (pow.f64 i 6)))))
(neg.f64 (+.f64 (pow.f64 i 4) (+.f64 (*.f64 1/4 (pow.f64 i 2)) (+.f64 (*.f64 16 (pow.f64 i 8)) (*.f64 4 (pow.f64 i 6))))))
1/16
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 1/16 (+.f64 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))) (*.f64 1/256 (/.f64 1 (pow.f64 i 4)))))
(+.f64 (*.f64 1/1024 (/.f64 1 (pow.f64 i 6))) (+.f64 1/16 (+.f64 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))) (*.f64 1/256 (/.f64 1 (pow.f64 i 4))))))
1/16
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 1/16 (+.f64 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))) (*.f64 1/256 (/.f64 1 (pow.f64 i 4)))))
(+.f64 (*.f64 1/1024 (/.f64 1 (pow.f64 i 6))) (+.f64 1/16 (+.f64 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))) (*.f64 1/256 (/.f64 1 (pow.f64 i 4))))))
(/.f64 -1 (pow.f64 i 2))
4
4
Outputs
(*.f64 -1/4 (pow.f64 i 2))
(*.f64 -1/4 (*.f64 i i))
(neg.f64 (+.f64 (pow.f64 i 4) (*.f64 1/4 (pow.f64 i 2))))
(neg.f64 (+.f64 (pow.f64 i 4) (*.f64 (*.f64 i i) 1/4)))
(-.f64 (*.f64 -1/4 (*.f64 i i)) (pow.f64 i 4))
(*.f64 i (*.f64 (neg.f64 i) (fma.f64 i i 1/4)))
(neg.f64 (+.f64 (pow.f64 i 4) (+.f64 (*.f64 1/4 (pow.f64 i 2)) (*.f64 4 (pow.f64 i 6)))))
(neg.f64 (+.f64 (pow.f64 i 4) (fma.f64 1/4 (*.f64 i i) (*.f64 4 (pow.f64 i 6)))))
(-.f64 (neg.f64 (pow.f64 i 4)) (fma.f64 (*.f64 i i) 1/4 (*.f64 4 (pow.f64 i 6))))
(-.f64 (fma.f64 -1/4 (*.f64 i i) (*.f64 (pow.f64 i 6) -4)) (pow.f64 i 4))
(-.f64 (fma.f64 (pow.f64 i 6) -4 (*.f64 -1/4 (*.f64 i i))) (pow.f64 i 4))
(neg.f64 (+.f64 (pow.f64 i 4) (+.f64 (*.f64 1/4 (pow.f64 i 2)) (+.f64 (*.f64 16 (pow.f64 i 8)) (*.f64 4 (pow.f64 i 6))))))
(neg.f64 (+.f64 (pow.f64 i 4) (fma.f64 1/4 (*.f64 i i) (fma.f64 16 (pow.f64 i 8) (*.f64 4 (pow.f64 i 6))))))
(-.f64 (neg.f64 (pow.f64 i 4)) (fma.f64 (*.f64 i i) 1/4 (fma.f64 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))))
(neg.f64 (fma.f64 (*.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))))
(-.f64 (*.f64 (pow.f64 i 6) -4) (fma.f64 (*.f64 i i) (fma.f64 i i 1/4) (*.f64 16 (pow.f64 i 8))))
1/16
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 1/16 (/.f64 1/64 (*.f64 i i)))
(+.f64 1/16 (+.f64 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))) (*.f64 1/256 (/.f64 1 (pow.f64 i 4)))))
(+.f64 1/16 (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/256 (pow.f64 i 4))))
(+.f64 (*.f64 1/1024 (/.f64 1 (pow.f64 i 6))) (+.f64 1/16 (+.f64 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))) (*.f64 1/256 (/.f64 1 (pow.f64 i 4))))))
(+.f64 (+.f64 1/16 (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/256 (pow.f64 i 4)))) (/.f64 1/1024 (pow.f64 i 6)))
(+.f64 (+.f64 (/.f64 1/1024 (pow.f64 i 6)) (+.f64 1/16 (/.f64 1/64 (*.f64 i i)))) (/.f64 1/256 (pow.f64 i 4)))
(+.f64 1/16 (+.f64 (+.f64 (/.f64 1/1024 (pow.f64 i 6)) (/.f64 1/64 (*.f64 i i))) (/.f64 1/256 (pow.f64 i 4))))
(+.f64 1/16 (+.f64 (/.f64 1/64 (*.f64 i i)) (+.f64 (/.f64 1/256 (pow.f64 i 4)) (/.f64 1/1024 (pow.f64 i 6)))))
1/16
(+.f64 1/16 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))))
(+.f64 1/16 (/.f64 1/64 (*.f64 i i)))
(+.f64 1/16 (+.f64 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))) (*.f64 1/256 (/.f64 1 (pow.f64 i 4)))))
(+.f64 1/16 (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/256 (pow.f64 i 4))))
(+.f64 (*.f64 1/1024 (/.f64 1 (pow.f64 i 6))) (+.f64 1/16 (+.f64 (*.f64 1/64 (/.f64 1 (pow.f64 i 2))) (*.f64 1/256 (/.f64 1 (pow.f64 i 4))))))
(+.f64 (+.f64 1/16 (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/256 (pow.f64 i 4)))) (/.f64 1/1024 (pow.f64 i 6)))
(+.f64 (+.f64 (/.f64 1/1024 (pow.f64 i 6)) (+.f64 1/16 (/.f64 1/64 (*.f64 i i)))) (/.f64 1/256 (pow.f64 i 4)))
(+.f64 1/16 (+.f64 (+.f64 (/.f64 1/1024 (pow.f64 i 6)) (/.f64 1/64 (*.f64 i i))) (/.f64 1/256 (pow.f64 i 4))))
(+.f64 1/16 (+.f64 (/.f64 1/64 (*.f64 i i)) (+.f64 (/.f64 1/256 (pow.f64 i 4)) (/.f64 1/1024 (pow.f64 i 6)))))
(/.f64 -1 (pow.f64 i 2))
(/.f64 -1 (*.f64 i i))
(/.f64 (/.f64 -1 i) i)
4
4

prune65.0ms (4.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1230123
Fresh011
Picked011
Done000
Total1232125
Error
0b
Counts
125 → 2
Alt Table
StatusErrorProgram
▶27.6b
(*.f64 -1/4 (pow.f64 i 2))
✓0.3b
(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
Compiler

Compiled 1497 to 1284 computations (14.2% saved)

localize3.0ms (0.2%)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New000
Fresh000
Picked011
Done011
Total022
Error
0b
Counts
2 → 2
Alt Table
StatusErrorProgram
✓27.6b
(*.f64 -1/4 (pow.f64 i 2))
✓0.3b
(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
Compiler

Compiled 16 to 14 computations (12.5% saved)

regimes35.0ms (2.3%)

Accuracy

Total 0.3b remaining (96.4%)

Threshold costs 0.3b (96.4%)

Counts
13 → 1
Compiler

Compiled 378 to 289 computations (23.5% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
2×+-commutative_binary64
2×sub-neg_binary64
1×*-commutative_binary64
1×distribute-neg-frac_binary64
1×neg-sub0_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
11413
22013
32213
42313
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
Outputs
(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))

end43.0ms (2.8%)

Stop Event
1×done
Compiler

Compiled 36 to 32 computations (11.1% saved)

Profiling

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