Details

Time bar (total: 10.6s)

analyze7.0ms (0.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
50%25%25%4
50%12.5%37.5%5
50%6.2%43.8%6
50%3.1%46.9%7
50%1.6%48.5%8
50%0.8%49.2%9
50.4%0.4%49.2%10
50.4%0.2%49.4%11
50.4%0.1%49.5%12
50.4%0%49.6%13
50.4%0%49.6%14
Compiler

Compiled 10 to 8 computations (20% saved)

sample9.7s (91.6%)

Results
7.1s4347×body2048valid
1.7s2004×body1024valid
579.0ms1060×body512valid
181.0ms481×body256valid
70.0ms364×body128valid
0.0ms1×body128invalid
Compiler

Compiled 20 to 16 computations (20% saved)

preprocess56.0ms (0.5%)

Algorithm
2×egg-herbie
Rules
624×fma-def_binary64
581×fma-neg_binary64
548×unswap-sqr_binary64
284×cancel-sign-sub-inv_binary64
199×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
12013
23613
36013
412213
527213
669713
7169913
8311013
011
Stop Event
1×saturated
1×node limit
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
Outputs
(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
(+.f64 (+.f64 (exp.f64 x) -2) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 x) (+.f64 -2 (exp.f64 (neg.f64 x))))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify54.0ms (0.5%)

Algorithm
1×egg-herbie
Rules
624×fma-def_binary64
581×fma-neg_binary64
548×unswap-sqr_binary64
284×cancel-sign-sub-inv_binary64
199×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
12013
23613
36013
412213
527213
669713
7169913
8311013
Stop Event
1×node limit
Counts
1 → 2
Calls
Call 1
Inputs
(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
Outputs
(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
(+.f64 (+.f64 (exp.f64 x) -2) (exp.f64 (neg.f64 x)))
(+.f64 (exp.f64 x) (+.f64 -2 (exp.f64 (neg.f64 x))))
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))

prune6.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
28.5b
Counts
3 → 2
Alt Table
StatusErrorProgram
▶28.5b
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
28.5b
(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
Compiler

Compiled 53 to 38 computations (28.3% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 (exp.f64 (neg.f64 x)) -2)
✓3.8b
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))

series7.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@0
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
1.0ms
x
@inf
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
1.0ms
x
@0
(+.f64 (exp.f64 (neg.f64 x)) -2)
1.0ms
x
@-inf
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
1.0ms
x
@inf
(+.f64 (exp.f64 (neg.f64 x)) -2)

rewrite95.0ms (0.9%)

Algorithm
1×batch-egg-rewrite
Rules
799×log1p-expm1-u_binary64
799×expm1-log1p-u_binary64
94×add-sqr-sqrt_binary64
90×add-log-exp_binary64
89×*-un-lft-identity_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0821
117915
2261315
Stop Event
1×node limit
Counts
2 → 69
Calls
Call 1
Inputs
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(+.f64 (exp.f64 (neg.f64 x)) -2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (-.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))) (/.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (-.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 -2 (*.f64 2 (cosh.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))) (pow.f64 (cbrt.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))) 2) (cbrt.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))) (sqrt.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (+.f64 (exp.f64 x) -2) 3)) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (*.f64 (+.f64 (exp.f64 x) -2) (-.f64 (+.f64 (exp.f64 x) -2) (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (+.f64 (exp.f64 x) -2) 2)) (/.f64 1 (-.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (*.f64 (+.f64 (exp.f64 x) -2) (-.f64 (+.f64 (exp.f64 x) -2) (exp.f64 x)))) (+.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (+.f64 (exp.f64 x) -2) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)) (-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (+.f64 (exp.f64 x) -2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (+.f64 (exp.f64 x) -2) 3)) (+.f64 (pow.f64 (exp.f64 x) 2) (*.f64 (+.f64 (exp.f64 x) -2) (-.f64 (+.f64 (exp.f64 x) -2) (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (+.f64 (exp.f64 x) -2) 3)) (+.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (-.f64 (pow.f64 (exp.f64 x) 2) (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (+.f64 (exp.f64 x) -2) 2)) (-.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 (+.f64 (exp.f64 x) -2) 3))) (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (*.f64 (+.f64 (exp.f64 x) -2) (-.f64 (+.f64 (exp.f64 x) -2) (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (+.f64 (exp.f64 x) -2) 2))) (neg.f64 (-.f64 (exp.f64 x) (+.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 2 (cosh.f64 x)) 3) -8) (+.f64 (*.f64 (*.f64 2 (cosh.f64 x)) (*.f64 2 (cosh.f64 x))) (-.f64 4 (*.f64 (*.f64 2 (cosh.f64 x)) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2) (pow.f64 (exp.f64 x) 2)) (-.f64 (+.f64 (exp.f64 x) -2) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 2 (cosh.f64 x)) (*.f64 2 (cosh.f64 x))) 4) (-.f64 (*.f64 2 (cosh.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (exp.f64 x) (+.f64 (exp.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (exp.f64 x) -2) (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) (+.f64 (exp.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) -2)) 2) (cbrt.f64 (+.f64 (exp.f64 x) -2)) (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (+.f64 (exp.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (exp.f64 x) -2)) (sqrt.f64 (+.f64 (exp.f64 x) -2)) (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 -2 (*.f64 2 (cosh.f64 x)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (exp.f64 x) -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 (exp.f64 x) 2)) (/.f64 4 (+.f64 (exp.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (exp.f64 x) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (exp.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (exp.f64 x) -2)) (pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) -2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) -2)) 2) (cbrt.f64 (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (exp.f64 x) -2)) (sqrt.f64 (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -8 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (-.f64 (+.f64 (pow.f64 (exp.f64 x) 2) 4) (*.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (exp.f64 x) (exp.f64 x) -4) (/.f64 1 (+.f64 (exp.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (+.f64 (pow.f64 (exp.f64 x) 2) 4) (*.f64 (exp.f64 x) -2)) (+.f64 -8 (pow.f64 (exp.f64 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (exp.f64 x) 2) (fma.f64 (exp.f64 x) (exp.f64 x) -4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -8 (pow.f64 (exp.f64 x) 3)) (-.f64 (+.f64 (pow.f64 (exp.f64 x) 2) 4) (*.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -8 (pow.f64 (exp.f64 x) 3)) (+.f64 4 (-.f64 (pow.f64 (exp.f64 x) 2) (*.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (exp.f64 x) (exp.f64 x) -4) (+.f64 (exp.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 -8 (pow.f64 (exp.f64 x) 3))) (neg.f64 (-.f64 (+.f64 (pow.f64 (exp.f64 x) 2) 4) (*.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) -4)) (neg.f64 (+.f64 (exp.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 4 (pow.f64 (exp.f64 x) 2)) (-.f64 -2 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (exp.f64 x) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (exp.f64 x) -2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (exp.f64 x) -2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (exp.f64 x) -2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (exp.f64 x) -2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 (exp.f64 x) -2)) 1))))))

simplify59.0ms (0.6%)

Algorithm
1×egg-herbie
Rules
749×unswap-sqr_binary64
623×fma-neg_binary64
554×associate-*l*_binary64
507×fma-def_binary64
411×associate-*r*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
047268
1120260
2265260
3832260
43789259
Stop Event
1×node limit
Counts
93 → 90
Calls
Call 1
Inputs
(pow.f64 x 2)
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (+.f64 (*.f64 1/360 (pow.f64 x 6)) (pow.f64 x 2)))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (+.f64 (*.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(-.f64 (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)) 2)
(-.f64 (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)) 2)
(-.f64 (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)) 2)
(-.f64 (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)) 2)
-1
(neg.f64 (+.f64 1 x))
(-.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 1 x))
(-.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 1 (+.f64 x (*.f64 1/6 (pow.f64 x 3)))))
(-.f64 (exp.f64 (neg.f64 x)) 2)
(-.f64 (exp.f64 (neg.f64 x)) 2)
(-.f64 (exp.f64 (neg.f64 x)) 2)
(-.f64 (exp.f64 (neg.f64 x)) 2)
(-.f64 (exp.f64 (*.f64 -1 x)) 2)
(-.f64 (exp.f64 (*.f64 -1 x)) 2)
(-.f64 (exp.f64 (*.f64 -1 x)) 2)
(-.f64 (exp.f64 (*.f64 -1 x)) 2)
Outputs
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (+.f64 (*.f64 1/360 (pow.f64 x 6)) (pow.f64 x 2)))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (*.f64 x x)))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 x x (*.f64 1/360 (pow.f64 x 6))))
(fma.f64 x x (fma.f64 1/12 (pow.f64 x 4) (*.f64 1/360 (pow.f64 x 6))))
(fma.f64 x x (fma.f64 1/360 (pow.f64 x 6) (*.f64 1/12 (pow.f64 x 4))))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (+.f64 (*.f64 1/360 (pow.f64 x 6)) (+.f64 (*.f64 1/20160 (pow.f64 x 8)) (pow.f64 x 2))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 1/20160 (pow.f64 x 8) (*.f64 x x))))
(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
(-.f64 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))) 2)
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
(-.f64 (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
(-.f64 (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
(-.f64 (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
(-.f64 (+.f64 (exp.f64 (*.f64 -1 x)) (exp.f64 x)) 2)
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
(+.f64 (exp.f64 (neg.f64 x)) (+.f64 (exp.f64 x) -2))
-1
(neg.f64 (+.f64 1 x))
(neg.f64 (+.f64 x 1))
(-.f64 -1 x)
(-.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 1 x))
(-.f64 (*.f64 (*.f64 x x) 1/2) (+.f64 x 1))
(fma.f64 (*.f64 x x) 1/2 (-.f64 -1 x))
(-.f64 (fma.f64 x (*.f64 x 1/2) -1) x)
(-.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 1 (+.f64 x (*.f64 1/6 (pow.f64 x 3)))))
(-.f64 (*.f64 (*.f64 x x) 1/2) (+.f64 1 (+.f64 x (*.f64 1/6 (pow.f64 x 3)))))
(-.f64 (fma.f64 (*.f64 x x) 1/2 -1) (fma.f64 1/6 (pow.f64 x 3) x))
(-.f64 (fma.f64 x (*.f64 x 1/2) -1) (fma.f64 1/6 (pow.f64 x 3) x))
(fma.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x -1/6)) (-.f64 -1 x))
(-.f64 (exp.f64 (neg.f64 x)) 2)
(+.f64 (exp.f64 (neg.f64 x)) -2)
(-.f64 (exp.f64 (neg.f64 x)) 2)
(+.f64 (exp.f64 (neg.f64 x)) -2)
(-.f64 (exp.f64 (neg.f64 x)) 2)
(+.f64 (exp.f64 (neg.f64 x)) -2)
(-.f64 (exp.f64 (neg.f64 x)) 2)
(+.f64 (exp.f64 (neg.f64 x)) -2)
(-.f64 (exp.f64 (*.f64 -1 x)) 2)
(+.f64 (exp.f64 (neg.f64 x)) -2)
(-.f64 (exp.f64 (*.f64 -1 x)) 2)
(+.f64 (exp.f64 (neg.f64 x)) -2)
(-.f64 (exp.f64 (*.f64 -1 x)) 2)
(+.f64 (exp.f64 (neg.f64 x)) -2)
(-.f64 (exp.f64 (*.f64 -1 x)) 2)
(+.f64 (exp.f64 (neg.f64 x)) -2)

prune108.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New89190
Fresh101
Picked011
Done000
Total90292
Error
0b
Counts
92 → 2
Alt Table
StatusErrorProgram
✓28.5b
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
▶0.8b
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
Compiler

Compiled 1247 to 778 computations (37.6% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
✓0.1b
(*.f64 1/12 (pow.f64 x 4))

series9.0ms (0.1%)

Counts
2 → 12
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(*.f64 1/12 (pow.f64 x 4))
2.0ms
x
@-inf
(*.f64 1/12 (pow.f64 x 4))
2.0ms
x
@0
(*.f64 1/12 (pow.f64 x 4))
2.0ms
x
@0
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
1.0ms
x
@inf
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

rewrite87.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
600×pow1_binary64
558×add-log-exp_binary64
558×log1p-expm1-u_binary64
558×expm1-log1p-u_binary64
67×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0718
114618
2155818
Stop Event
1×node limit
Counts
2 → 34
Calls
Call 1
Inputs
(*.f64 1/12 (pow.f64 x 4))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 1/12 (pow.f64 x 4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/12 (pow.f64 x 4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/12 (pow.f64 x 4)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/12 (pow.f64 x 4))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) (sqrt.f64 1/12)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 8) 1/144))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/12) (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 1/12 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 1/12 (pow.f64 x 4)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/12 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/12 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/12 (pow.f64 x 4))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/12 (pow.f64 x 4)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 1/12 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) 1) (*.f64 1/12 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x x (*.f64 1/12 (pow.f64 x 4))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x x (*.f64 1/12 (pow.f64 x 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x x (*.f64 1/12 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))) (pow.f64 (cbrt.f64 (fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))) 2) (cbrt.f64 (fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x (*.f64 (*.f64 x x) (sqrt.f64 1/12))) (hypot.f64 x (*.f64 (*.f64 x x) (sqrt.f64 1/12))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x x) 3) (pow.f64 (*.f64 1/12 (pow.f64 x 4)) 3)) (+.f64 (pow.f64 x 4) (-.f64 (*.f64 (pow.f64 x 8) 1/144) (*.f64 (*.f64 x x) (*.f64 1/12 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) (*.f64 (pow.f64 x 8) 1/144)) (-.f64 (*.f64 x x) (*.f64 1/12 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x (*.f64 1/12 (pow.f64 x 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x (*.f64 1/12 (pow.f64 x 4))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (*.f64 (*.f64 x x) (sqrt.f64 1/12))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x (*.f64 1/12 (pow.f64 x 4))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x x (*.f64 1/12 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x (*.f64 1/12 (pow.f64 x 4))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))))))))

simplify119.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
963×fma-def_binary64
350×sqr-pow_binary64
342×unswap-sqr_binary64
331×associate-*l*_binary64
321×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09117
119117
238117
384117
4272117
51198117
62532117
73207117
83418117
93659117
103956117
114340117
124800117
Stop Event
1×node limit
Counts
46 → 39
Calls
Call 1
Inputs
(pow.f64 x 2)
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(*.f64 1/12 (pow.f64 x 4))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(*.f64 1/12 (pow.f64 x 4))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
Outputs
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(*.f64 1/12 (pow.f64 x 4))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(*.f64 1/12 (pow.f64 x 4))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))
(+.f64 (*.f64 1/12 (pow.f64 x 4)) (pow.f64 x 2))
(fma.f64 1/12 (pow.f64 x 4) (*.f64 x x))
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
(*.f64 x (fma.f64 1/12 (pow.f64 x 3) x))

prune87.0ms (0.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New39039
Fresh000
Picked011
Done011
Total39241
Error
0b
Counts
41 → 2
Alt Table
StatusErrorProgram
✓28.5b
(+.f64 (exp.f64 x) (+.f64 (exp.f64 (neg.f64 x)) -2))
✓0.8b
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
Compiler

Compiled 464 to 321 computations (30.8% saved)

regimes62.0ms (0.6%)

Accuracy

Total 0.6b remaining (91%)

Threshold costs 0.6b (91%)

Counts
10 → 1
Compiler

Compiled 164 to 122 computations (25.6% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0711
1811
Stop Event
1×saturated
Calls
Call 1
Inputs
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
Outputs
(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

end105.0ms (1%)

Stop Event
1×done
Compiler

Compiled 36 to 25 computations (30.6% saved)

Profiling

Loading profile data...