Details

Time bar (total: 2.5s)

analyze16.0ms (0.6%)

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)

sample1.8s (70.9%)

Results
1.8s8256×body128valid
Compiler

Compiled 58 to 38 computations (34.5% saved)

preprocess53.0ms (2.1%)

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)

simplify44.0ms (1.7%)

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))))

prune8.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
6.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
46.0b
(/.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))
▶6.0b
(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
Compiler

Compiled 107 to 74 computations (30.8% saved)

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.5b
(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
✓9.6b
(/.f64 i (pow.f64 i 3))

series8.0ms (0.3%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
2.0ms
i
@0
(/.f64 1/4 (-.f64 4 (/.f64 i (pow.f64 i 3))))
2.0ms
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
@-inf
(/.f64 i (pow.f64 i 3))

rewrite82.0ms (3.2%)

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
0920
121514
2267414
Stop Event
1×node limit
Counts
2 → 68
Calls
Call 1
Inputs
(/.f64 i (pow.f64 i 3))
(/.f64 1/4 (-.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 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 log1p.f64 (expm1.f64 (pow.f64 i -2)))))) (#(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 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 log1p.f64 (expm1.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))))

simplify56.0ms (2.2%)

Algorithm
1×egg-herbie
Rules
438×associate-*l*_binary64
438×fma-neg_binary64
413×unswap-sqr_binary64
320×cancel-sign-sub-inv_binary64
291×associate-*r*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
041273
1104271
2285267
31068267
44284267
Stop Event
1×node limit
Counts
92 → 85
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))))))
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 (*.f64 i -1/4)) (pow.f64 i 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 (*.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 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 1/16 (+.f64 (/.f64 (/.f64 1/64 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 1/16 (+.f64 (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/256 (pow.f64 i 4))) (/.f64 1/1024 (pow.f64 i 6))))
(+.f64 1/16 (+.f64 (/.f64 (/.f64 1/64 i) i) (+.f64 (/.f64 1/256 (pow.f64 i 4)) (/.f64 1/1024 (pow.f64 i 6)))))
(+.f64 (+.f64 1/16 (/.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 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 1/16 (+.f64 (/.f64 (/.f64 1/64 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 1/16 (+.f64 (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/256 (pow.f64 i 4))) (/.f64 1/1024 (pow.f64 i 6))))
(+.f64 1/16 (+.f64 (/.f64 (/.f64 1/64 i) i) (+.f64 (/.f64 1/256 (pow.f64 i 4)) (/.f64 1/1024 (pow.f64 i 6)))))
(+.f64 (+.f64 1/16 (/.f64 1/64 (*.f64 i i))) (+.f64 (/.f64 1/256 (pow.f64 i 4)) (/.f64 1/1024 (pow.f64 i 6))))

prune91.0ms (3.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New83285
Fresh101
Picked101
Done000
Total85287
Error
0b
Counts
87 → 2
Alt Table
StatusErrorProgram
28.5b
(*.f64 -1/4 (pow.f64 i 2))
▶0.4b
(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
Compiler

Compiled 1075 to 862 computations (19.8% saved)

localize13.0ms (0.5%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.1b
(/.f64 1 (pow.f64 i 2))
✓0.5b
(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))

series8.0ms (0.3%)

Counts
2 → 12
Calls

6 calls:

TimeVariablePointExpression
2.0ms
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
@-inf
(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
1.0ms
i
@-inf
(/.f64 1 (pow.f64 i 2))

rewrite62.0ms (2.4%)

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
01014
122514
2259514
Stop Event
1×node limit
Counts
2 → 61
Calls
Call 1
Inputs
(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
(/.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 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 log1p.f64 (expm1.f64 (/.f64 1/4 (-.f64 4 (pow.f64 i -2)))))))) (#(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 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 log1p.f64 (expm1.f64 (pow.f64 i -2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 i -2)))))))

simplify46.0ms (1.8%)

Algorithm
1×egg-herbie
Rules
448×associate-*l*_binary64
438×fma-neg_binary64
413×unswap-sqr_binary64
320×cancel-sign-sub-inv_binary64
291×associate-*r*_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
041189
1104187
2285183
31067183
44298183
Stop Event
1×node limit
Counts
73 → 76
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))))))
Outputs
(*.f64 -1/4 (pow.f64 i 2))
(*.f64 -1/4 (*.f64 i i))
(*.f64 i (*.f64 -1/4 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 (*.f64 i (*.f64 -1/4 i)) (pow.f64 i 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 (fma.f64 (*.f64 i i) 1/4 (*.f64 4 (pow.f64 i 6)))) (pow.f64 i 4))
(-.f64 (*.f64 i (*.f64 -1/4 i)) (fma.f64 4 (pow.f64 i 6) (pow.f64 i 4)))
(-.f64 (fma.f64 (pow.f64 i 6) -4 (*.f64 i (*.f64 -1/4 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 1/16 (+.f64 (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/256 (pow.f64 i 4))) (/.f64 1/1024 (pow.f64 i 6))))
(+.f64 (/.f64 1/256 (pow.f64 i 4)) (+.f64 1/16 (+.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 1/16 (+.f64 (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/256 (pow.f64 i 4))) (/.f64 1/1024 (pow.f64 i 6))))
(+.f64 (/.f64 1/256 (pow.f64 i 4)) (+.f64 1/16 (+.f64 (/.f64 1/64 (*.f64 i i)) (/.f64 1/1024 (pow.f64 i 6)))))

prune84.0ms (3.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New76076
Fresh011
Picked011
Done000
Total76278
Error
0b
Counts
78 → 2
Alt Table
StatusErrorProgram
▶28.5b
(*.f64 -1/4 (pow.f64 i 2))
✓0.4b
(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
Compiler

Compiled 900 to 767 computations (14.8% saved)

localize5.0ms (0.2%)

prune2.0ms (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
✓28.5b
(*.f64 -1/4 (pow.f64 i 2))
✓0.4b
(/.f64 1/4 (-.f64 4 (/.f64 1 (pow.f64 i 2))))
Compiler

Compiled 16 to 14 computations (12.5% saved)

regimes61.0ms (2.4%)

Accuracy

Total 0.3b remaining (97.4%)

Threshold costs 0.3b (97.4%)

Counts
10 → 1
Compiler

Compiled 328 to 241 computations (26.5% saved)

simplify5.0ms (0.2%)

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))))

end84.0ms (3.3%)

Stop Event
1×done
Compiler

Compiled 36 to 32 computations (11.1% saved)

Profiling

Loading profile data...