Details

Time bar (total: 2.7s)

analyze0.0ms (0%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
99.9%0%0.1%1
Compiler

Compiled 13 to 12 computations (7.7% saved)

sample2.0s (71.8%)

Results
989.0ms2137×body1024valid
462.0ms4382×body128valid
289.0ms1032×body512valid
102.0ms210×body2048valid
95.0ms495×body256valid
Compiler

Compiled 26 to 24 computations (7.7% saved)

preprocess37.0ms (1.4%)

Algorithm
2×egg-herbie
Rules
868×unswap-sqr_binary64
380×associate-*l*_binary64
316×associate-/l/_binary64
260×associate-*r*_binary64
252×associate-/r/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01630
12930
24130
35830
410330
522630
660230
7187930
8493430
022
Stop Event
1×saturated
1×node limit
Calls
Call 1
Inputs
0
1
Outputs
0
1
Call 2
Inputs
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 y)))) 1)
Outputs
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 y)))) 1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) y))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 y) -2))) -1)
Compiler

Compiled 12 to 11 computations (8.3% saved)

simplify26.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
978×times-frac_binary64
434×unswap-sqr_binary64
374×associate-*l/_binary64
342×associate-/l*_binary64
228×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
11915
22515
33415
45915
512415
631115
797215
8254915
9418915
Stop Event
1×node limit
Counts
1 → 2
Calls
Call 1
Inputs
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
Outputs
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (/.f64 x -1/2)))) -1)

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
30.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶30.8b
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
Compiler

Compiled 46 to 42 computations (8.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1 (exp.f64 (*.f64 -2 x)))
✓0.0b
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
✓2.3b
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

series9.0ms (0.3%)

Counts
3 → 20
Calls

9 calls:

TimeVariablePointExpression
3.0ms
x
@0
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
1.0ms
x
@inf
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
1.0ms
x
@-inf
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
1.0ms
x
@inf
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
1.0ms
x
@-inf
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))

rewrite56.0ms (2%)

Algorithm
1×batch-egg-rewrite
Rules
426×log-prod_binary64
259×prod-diff_binary64
227×fma-def_binary64
175×expm1-udef_binary64
175×log1p-udef_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01036
121736
2271236
Stop Event
1×node limit
Counts
3 → 114
Calls
Call 1
Inputs
(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)
(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
(+.f64 1 (exp.f64 (*.f64 -2 x)))
Outputs
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(/.f64 2 (-.f64 1 (pow.f64 (pow.f64 (exp.f64 x) -2) 2))) (-.f64 1 (pow.f64 (exp.f64 x) -2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))))) (cbrt.f64 (exp.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 x) -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -2 (/.f64 1 (+.f64 -1 (neg.f64 (pow.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) (cbrt.f64 (/.f64 4 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 4 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2)) 2))) (cbrt.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 4 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2)) 2))) (*.f64 (cbrt.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) (sqrt.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) (*.f64 (sqrt.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (pow.f64 (exp.f64 x) -2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 x) -2) 3))) (fma.f64 (pow.f64 (exp.f64 x) -2) (expm1.f64 (*.f64 -2 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 2 (-.f64 1 (pow.f64 (pow.f64 (exp.f64 x) -2) 2))) (-.f64 1 (pow.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 8 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2)) 1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 4 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 8 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))))) (cbrt.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))))) (cbrt.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))))) (sqrt.f64 (+.f64 1 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (pow.f64 (exp.f64 x) -2))) (/.f64 (pow.f64 (pow.f64 (exp.f64 x) -2) 2) (-.f64 1 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (pow.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2))) (pow.f64 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2))) 2) (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2))) (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 x) -2) 3)) (/.f64 1 (fma.f64 (pow.f64 (exp.f64 x) -2) (expm1.f64 (*.f64 -2 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (pow.f64 (exp.f64 x) -2) 2)) (/.f64 1 (-.f64 1 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (pow.f64 (exp.f64 x) -2) (expm1.f64 (*.f64 -2 x)) 1) (+.f64 1 (pow.f64 (pow.f64 (exp.f64 x) -2) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (pow.f64 (exp.f64 x) -2)) (-.f64 1 (pow.f64 (pow.f64 (exp.f64 x) -2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 x) -2) 3)) (fma.f64 (pow.f64 (exp.f64 x) -2) (expm1.f64 (*.f64 -2 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 x) -2) 3)) (+.f64 (pow.f64 (pow.f64 (exp.f64 x) -2) 2) (-.f64 1 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (pow.f64 (exp.f64 x) -2) 2)) (-.f64 1 (pow.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (pow.f64 (exp.f64 x) -2) 3))) (neg.f64 (fma.f64 (pow.f64 (exp.f64 x) -2) (expm1.f64 (*.f64 -2 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (pow.f64 (exp.f64 x) -2) 2))) (neg.f64 (-.f64 1 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 (*.f64 2 (*.f64 -2 x))) (expm1.f64 (*.f64 -2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 (exp.f64 x) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (exp.f64 x) -2) 1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (exp.f64 x) -2)) (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) -2) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) -2) 2)) (cbrt.f64 (pow.f64 (exp.f64 x) -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 (exp.f64 x) -2)) (sqrt.f64 (pow.f64 (exp.f64 x) -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (pow.f64 (exp.f64 x) -2))))))))

simplify31.0ms (1.1%)

Algorithm
1×egg-herbie
Rules
652×fma-def_binary64
431×distribute-rgt-neg-in_binary64
352×distribute-lft-neg-in_binary64
349×cancel-sign-sub-inv_binary64
277×fma-neg_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
042257
1126252
2325238
31082231
43632231
Stop Event
1×node limit
Counts
134 → 136
Calls
Call 1
Inputs
x
(-.f64 x (*.f64 1/3 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (+.f64 (*.f64 17/315 (pow.f64 x 7)) (*.f64 1/3 (pow.f64 x 3))))
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (*.f64 -2 x))))) 1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (*.f64 -2 x))))) 1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (*.f64 -2 x))))) 1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (*.f64 -2 x))))) 1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (*.f64 -2 x))))) 1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (*.f64 -2 x))))) 1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (*.f64 -2 x))))) 1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (*.f64 -2 x))))) 1)
1
(+.f64 1 x)
(-.f64 (+.f64 1 x) (*.f64 1/3 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) (+.f64 1 x)) (*.f64 1/3 (pow.f64 x 3)))
2
(-.f64 2 (*.f64 2 x))
(-.f64 (+.f64 2 (*.f64 2 (pow.f64 x 2))) (*.f64 2 x))
(-.f64 (+.f64 2 (*.f64 2 (pow.f64 x 2))) (+.f64 (*.f64 2 x) (*.f64 4/3 (pow.f64 x 3))))
Outputs
x
(-.f64 x (*.f64 1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 x)
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (+.f64 (*.f64 17/315 (pow.f64 x 7)) (*.f64 1/3 (pow.f64 x 3))))
(-.f64 (fma.f64 2/15 (pow.f64 x 5) x) (fma.f64 17/315 (pow.f64 x 7) (*.f64 1/3 (pow.f64 x 3))))
(-.f64 (fma.f64 2/15 (pow.f64 x 5) x) (fma.f64 1/3 (pow.f64 x 3) (*.f64 17/315 (pow.f64 x 7))))
(+.f64 (*.f64 (pow.f64 x 7) -17/315) (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x)))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 (pow.f64 x 7) -17/315 (fma.f64 2/15 (pow.f64 x 5) x)))
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (*.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (*.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (*.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (*.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (*.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (*.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (*.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
(-.f64 (*.f64 2 (/.f64 1 (+.f64 1 (exp.f64 (*.f64 -2 x))))) 1)
(+.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 x -2)))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 -2) x))) -1)
(+.f64 (/.f64 2 (+.f64 1 (pow.f64 (exp.f64 x) -2))) -1)
1
(+.f64 1 x)
(+.f64 x 1)
(-.f64 (+.f64 1 x) (*.f64 1/3 (pow.f64 x 3)))
(+.f64 1 (+.f64 x (*.f64 -1/3 (pow.f64 x 3))))
(+.f64 (+.f64 x 1) (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 (+.f64 x 1))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) (+.f64 1 x)) (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) (+.f64 x 1)) (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 (+.f64 (fma.f64 2/15 (pow.f64 x 5) x) 1) (*.f64 (pow.f64 x 3) -1/3))
(+.f64 1 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x)))
2
(-.f64 2 (*.f64 2 x))
(-.f64 2 (*.f64 x 2))
(+.f64 2 (*.f64 x -2))
(fma.f64 x -2 2)
(-.f64 (+.f64 2 (*.f64 2 (pow.f64 x 2))) (*.f64 2 x))
(+.f64 2 (-.f64 (*.f64 2 (*.f64 x x)) (*.f64 x 2)))
(+.f64 2 (*.f64 2 (-.f64 (*.f64 x x) x)))
(*.f64 2 (-.f64 (fma.f64 x x 1) x))
(fma.f64 x (fma.f64 x 2 -2) 2)
(-.f64 (+.f64 2 (*.f64 2 (pow.f64 x 2))) (+.f64 (*.f64 2 x) (*.f64 4/3 (pow.f64 x 3))))
(+.f64 2 (-.f64 (*.f64 2 (*.f64 x x)) (fma.f64 2 x (*.f64 (pow.f64 x 3) 4/3))))
(-.f64 (fma.f64 2 (*.f64 x x) 2) (fma.f64 x 2 (*.f64 (pow.f64 x 3) 4/3)))
(fma.f64 (fma.f64 x x 1) 2 (fma.f64 x -2 (*.f64 (pow.f64 x 3) -4/3)))
(fma.f64 (pow.f64 x 3) -4/3 (fma.f64 x (fma.f64 x 2 -2) 2))

prune93.0ms (3.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1342136
Fresh000
Picked101
Done000
Total1352137
Error
0b
Counts
137 → 2
Alt Table
StatusErrorProgram
30.8b
(expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))))
▶30.0b
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))
Compiler

Compiled 2309 to 1906 computations (17.5% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
✓0.0b
(fma.f64 2/15 (pow.f64 x 5) x)
✓20.9b
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))

series7.0ms (0.3%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
3.0ms
x
@-inf
(fma.f64 2/15 (pow.f64 x 5) x)
1.0ms
x
@0
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))
1.0ms
x
@inf
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))
1.0ms
x
@-inf
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))
1.0ms
x
@inf
(fma.f64 2/15 (pow.f64 x 5) x)

rewrite43.0ms (1.6%)

Algorithm
1×batch-egg-rewrite
Rules
835×log1p-expm1-u_binary64
835×expm1-log1p-u_binary64
100×add-sqr-sqrt_binary64
97×add-log-exp_binary64
95×add-cube-cbrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01023
121823
2225923
Stop Event
1×node limit
Counts
2 → 47
Calls
Call 1
Inputs
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))
(fma.f64 2/15 (pow.f64 x 5) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 (pow.f64 x 3) -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 x 3) -1/3) (fma.f64 2/15 (pow.f64 x 5) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (pow.f64 x 3) -1/3) 1) (fma.f64 2/15 (pow.f64 x 5) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 (pow.f64 x 3) -1/3) (*.f64 2/15 (pow.f64 x 5))) x)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))) (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))) 2) (cbrt.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))) (sqrt.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 (pow.f64 x 3) -1/3) 3) (pow.f64 (fma.f64 2/15 (pow.f64 x 5) x) 3)) (+.f64 (*.f64 (*.f64 (pow.f64 x 3) -1/3) (*.f64 (pow.f64 x 3) -1/3)) (-.f64 (pow.f64 (fma.f64 2/15 (pow.f64 x 5) x) 2) (*.f64 (*.f64 (pow.f64 x 3) -1/3) (fma.f64 2/15 (pow.f64 x 5) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 (pow.f64 x 3) -1/3) (*.f64 (pow.f64 x 3) -1/3)) (pow.f64 (fma.f64 2/15 (pow.f64 x 5) x) 2)) (-.f64 (*.f64 (pow.f64 x 3) -1/3) (fma.f64 2/15 (pow.f64 x 5) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x (*.f64 2/15 (pow.f64 x 5)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 2/15 (pow.f64 x 5)) x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 2/15 (pow.f64 x 5)) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 2/15 (pow.f64 x 5) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 2/15 (pow.f64 x 5) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 2/15 (pow.f64 x 5) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 2/15 (pow.f64 x 5) x)) (pow.f64 (cbrt.f64 (fma.f64 2/15 (pow.f64 x 5) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 2/15 (pow.f64 x 5) x)) 2) (cbrt.f64 (fma.f64 2/15 (pow.f64 x 5) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 2/15 (pow.f64 x 5) x)) (sqrt.f64 (fma.f64 2/15 (pow.f64 x 5) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 2/15 (pow.f64 x 5)) 3) (pow.f64 x 3)) (+.f64 (*.f64 (*.f64 2/15 (pow.f64 x 5)) (*.f64 2/15 (pow.f64 x 5))) (-.f64 (*.f64 x x) (*.f64 (*.f64 2/15 (pow.f64 x 5)) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 2/15 (pow.f64 x 5)) (*.f64 2/15 (pow.f64 x 5))) (*.f64 x x)) (-.f64 (*.f64 2/15 (pow.f64 x 5)) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 2/15 (pow.f64 x 5) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 2/15 (pow.f64 x 5) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 2/15 (pow.f64 x 5) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 2/15 (pow.f64 x 5) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 2/15 (pow.f64 x 5) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 2/15 (pow.f64 x 5) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 2/15 (pow.f64 x 5) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 2/15 (pow.f64 x 5) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 2/15 (pow.f64 x 5) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 2/15 (pow.f64 x 5) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 2/15 (pow.f64 x 5) x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 2/15 (pow.f64 x 5) x)))))))

simplify36.0ms (1.3%)

Algorithm
1×egg-herbie
Rules
759×fma-neg_binary64
416×unswap-sqr_binary64
405×cancel-sign-sub-inv_binary64
315×associate-*l*_binary64
304×fma-def_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
014246
142242
296228
3285228
4693228
51942228
63515228
Stop Event
1×node limit
Counts
71 → 56
Calls
Call 1
Inputs
x
(-.f64 x (*.f64 1/3 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(*.f64 2/15 (pow.f64 x 5))
(-.f64 (*.f64 2/15 (pow.f64 x 5)) (*.f64 1/3 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(*.f64 2/15 (pow.f64 x 5))
(-.f64 (*.f64 2/15 (pow.f64 x 5)) (*.f64 1/3 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
x
(+.f64 (*.f64 2/15 (pow.f64 x 5)) x)
(+.f64 (*.f64 2/15 (pow.f64 x 5)) x)
(+.f64 (*.f64 2/15 (pow.f64 x 5)) x)
(*.f64 2/15 (pow.f64 x 5))
(+.f64 (*.f64 2/15 (pow.f64 x 5)) x)
(+.f64 (*.f64 2/15 (pow.f64 x 5)) x)
(+.f64 (*.f64 2/15 (pow.f64 x 5)) x)
(*.f64 2/15 (pow.f64 x 5))
(+.f64 (*.f64 2/15 (pow.f64 x 5)) x)
(+.f64 (*.f64 2/15 (pow.f64 x 5)) x)
(+.f64 (*.f64 2/15 (pow.f64 x 5)) x)
Outputs
x
(-.f64 x (*.f64 1/3 (pow.f64 x 3)))
(+.f64 x (*.f64 -1/3 (pow.f64 x 3)))
(fma.f64 (pow.f64 x 3) -1/3 x)
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))
(*.f64 2/15 (pow.f64 x 5))
(-.f64 (*.f64 2/15 (pow.f64 x 5)) (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (*.f64 2/15 (pow.f64 x 5)) (*.f64 -1/3 (pow.f64 x 3)))
(fma.f64 2/15 (pow.f64 x 5) (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 (*.f64 2/15 (pow.f64 x 5)))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))
(*.f64 2/15 (pow.f64 x 5))
(-.f64 (*.f64 2/15 (pow.f64 x 5)) (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (*.f64 2/15 (pow.f64 x 5)) (*.f64 -1/3 (pow.f64 x 3)))
(fma.f64 2/15 (pow.f64 x 5) (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 (*.f64 2/15 (pow.f64 x 5)))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))
(-.f64 (+.f64 (*.f64 2/15 (pow.f64 x 5)) x) (*.f64 1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 -1/3 (pow.f64 x 3)))
(+.f64 (fma.f64 2/15 (pow.f64 x 5) x) (*.f64 (pow.f64 x 3) -1/3))
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))
x
(+.f64 (*.f64 2/15 (pow.f64 x 5)) x)
(fma.f64 2/15 (pow.f64 x 5) x)
(+.f64 (*.f64 2/15 (pow.f64 x 5)) x)
(fma.f64 2/15 (pow.f64 x 5) x)
(+.f64 (*.f64 2/15 (pow.f64 x 5)) x)
(fma.f64 2/15 (pow.f64 x 5) x)
(*.f64 2/15 (pow.f64 x 5))
(+.f64 (*.f64 2/15 (pow.f64 x 5)) x)
(fma.f64 2/15 (pow.f64 x 5) x)
(+.f64 (*.f64 2/15 (pow.f64 x 5)) x)
(fma.f64 2/15 (pow.f64 x 5) x)
(+.f64 (*.f64 2/15 (pow.f64 x 5)) x)
(fma.f64 2/15 (pow.f64 x 5) x)
(*.f64 2/15 (pow.f64 x 5))
(+.f64 (*.f64 2/15 (pow.f64 x 5)) x)
(fma.f64 2/15 (pow.f64 x 5) x)
(+.f64 (*.f64 2/15 (pow.f64 x 5)) x)
(fma.f64 2/15 (pow.f64 x 5) x)
(+.f64 (*.f64 2/15 (pow.f64 x 5)) x)
(fma.f64 2/15 (pow.f64 x 5) x)

prune32.0ms (1.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New56056
Fresh011
Picked011
Done000
Total56258
Error
0b
Counts
58 → 2
Alt Table
StatusErrorProgram
▶30.8b
(expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))))
✓30.0b
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))
Compiler

Compiled 909 to 707 computations (22.2% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
✓0.0b
(pow.f64 (exp.f64 x) -2)
✓0.2b
(log1p.f64 (pow.f64 (exp.f64 x) -2))
✓2.6b
(-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))

series70.0ms (2.6%)

Counts
3 → 36
Calls

9 calls:

TimeVariablePointExpression
44.0ms
x
@inf
(-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))
20.0ms
x
@-inf
(-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))
4.0ms
x
@0
(-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))
0.0ms
x
@0
(log1p.f64 (pow.f64 (exp.f64 x) -2))
0.0ms
x
@inf
(pow.f64 (exp.f64 x) -2)

rewrite52.0ms (1.9%)

Algorithm
1×batch-egg-rewrite
Rules
808×expm1-log1p-u_binary64
807×log1p-expm1-u_binary64
94×add-sqr-sqrt_binary64
91×add-log-exp_binary64
90×pow1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0927
118827
2225227
Stop Event
1×node limit
Counts
3 → 69
Calls
Call 1
Inputs
(-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))
(log1p.f64 (pow.f64 (exp.f64 x) -2))
(pow.f64 (exp.f64 x) -2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 2) (neg.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 2) (*.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))) (fma.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))) 1 (log1p.f64 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))) (fma.f64 (neg.f64 (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)))) (pow.f64 (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))) 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))) (fma.f64 (neg.f64 (sqrt.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)))) (sqrt.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))) (log1p.f64 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))) (log.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))) (pow.f64 (cbrt.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))) 2) (cbrt.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))) (sqrt.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)) 3)) (/.f64 1 (+.f64 (pow.f64 (log.f64 2) 2) (*.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)) (+.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (log.f64 2) 2) (pow.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)) 2)) (/.f64 1 (+.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (log.f64 2)) (sqrt.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)))) (-.f64 (sqrt.f64 (log.f64 2)) (sqrt.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (log.f64 2) 2) (*.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)) (+.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))))) (-.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))) (-.f64 (pow.f64 (log.f64 2) 2) (pow.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)) 3)) (+.f64 (pow.f64 (log.f64 2) 2) (*.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)) (+.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (log.f64 2) 2) (pow.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)) 2)) (+.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)) 3))) (neg.f64 (+.f64 (pow.f64 (log.f64 2) 2) (*.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)) (+.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (log.f64 2) 2) (pow.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)) 2))) (neg.f64 (+.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (log.f64 2) 3) (pow.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))) 3)) (+.f64 (pow.f64 (log.f64 2) 2) (-.f64 (*.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))) (neg.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)))) (*.f64 (log.f64 2) (neg.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (log.f64 2) 2) (*.f64 (neg.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))) (neg.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))))) (-.f64 (log.f64 2) (neg.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 2 (+.f64 (pow.f64 (exp.f64 x) -2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (-.f64 (/.f64 2 (+.f64 (pow.f64 (exp.f64 x) -2) 1)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (log.f64 2) (neg.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (log.f64 2)) 2) (cbrt.f64 (log.f64 2)) (neg.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (log.f64 2)) (sqrt.f64 (log.f64 2)) (neg.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (-.f64 (/.f64 2 (+.f64 (pow.f64 (exp.f64 x) -2) 1)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log1p.f64 (pow.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))) (pow.f64 (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))) 2) (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))) (sqrt.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 (pow.f64 (exp.f64 x) -2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (pow.f64 (exp.f64 x) -2) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 x) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (exp.f64 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (exp.f64 x) -2)) (cbrt.f64 (pow.f64 (exp.f64 x) -4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (exp.f64 x) -4)) (cbrt.f64 (pow.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (exp.f64 x)) (/.f64 1 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) -2) (pow.f64 (cbrt.f64 (exp.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (exp.f64 x)) -2) (pow.f64 (sqrt.f64 (exp.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (exp.f64 x) -4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (exp.f64 x) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (exp.f64 x) -2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 x -2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (exp.f64 x) -2)))))))

simplify25.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
541×fma-def_binary64
527×associate-*l*_binary64
498×cancel-sign-sub-inv_binary64
477×associate-*r*_binary64
307×fma-neg_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
042433
1121424
2332343
31176331
Stop Event
1×node limit
Counts
105 → 95
Calls
Call 1
Inputs
x
(-.f64 x (*.f64 1/2 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/12 (pow.f64 x 4)) x) (*.f64 1/2 (pow.f64 x 2)))
(-.f64 (+.f64 (*.f64 1/12 (pow.f64 x 4)) x) (+.f64 (*.f64 1/45 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))
(-.f64 (log.f64 2) (log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))))
(-.f64 (log.f64 2) (log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))))
(-.f64 (log.f64 2) (log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))))
(-.f64 (log.f64 2) (log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))))
(-.f64 (log.f64 2) (log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))))
(-.f64 (log.f64 2) (log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))))
(-.f64 (log.f64 2) (log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))))
(-.f64 (log.f64 2) (log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))))
(log.f64 2)
(-.f64 (log.f64 2) x)
(-.f64 (+.f64 (log.f64 2) (*.f64 1/2 (pow.f64 x 2))) x)
(-.f64 (+.f64 (log.f64 2) (*.f64 1/2 (pow.f64 x 2))) (+.f64 (*.f64 1/12 (pow.f64 x 4)) x))
(log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
1
(-.f64 1 (*.f64 2 x))
(-.f64 (+.f64 1 (*.f64 2 (pow.f64 x 2))) (*.f64 2 x))
(-.f64 (+.f64 1 (*.f64 2 (pow.f64 x 2))) (+.f64 (*.f64 2 x) (*.f64 4/3 (pow.f64 x 3))))
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(/.f64 1 (pow.f64 (exp.f64 x) 2))
Outputs
x
(-.f64 x (*.f64 1/2 (pow.f64 x 2)))
(+.f64 x (*.f64 -1/2 (*.f64 x x)))
(+.f64 x (*.f64 (*.f64 x x) -1/2))
(fma.f64 (*.f64 x x) -1/2 x)
(*.f64 x (fma.f64 x -1/2 1))
(-.f64 (+.f64 (*.f64 1/12 (pow.f64 x 4)) x) (*.f64 1/2 (pow.f64 x 2)))
(-.f64 (fma.f64 1/12 (pow.f64 x 4) x) (*.f64 1/2 (*.f64 x x)))
(+.f64 (fma.f64 1/12 (pow.f64 x 4) x) (*.f64 (*.f64 x x) -1/2))
(fma.f64 (*.f64 x x) -1/2 (fma.f64 1/12 (pow.f64 x 4) x))
(fma.f64 x (*.f64 x -1/2) (fma.f64 1/12 (pow.f64 x 4) x))
(-.f64 (+.f64 (*.f64 1/12 (pow.f64 x 4)) x) (+.f64 (*.f64 1/45 (pow.f64 x 6)) (*.f64 1/2 (pow.f64 x 2))))
(-.f64 (fma.f64 1/12 (pow.f64 x 4) x) (fma.f64 1/45 (pow.f64 x 6) (*.f64 1/2 (*.f64 x x))))
(-.f64 (fma.f64 1/12 (pow.f64 x 4) x) (fma.f64 1/2 (*.f64 x x) (*.f64 1/45 (pow.f64 x 6))))
(+.f64 (fma.f64 1/12 (pow.f64 x 4) x) (fma.f64 (*.f64 x x) -1/2 (*.f64 (pow.f64 x 6) -1/45)))
(fma.f64 (fma.f64 x -1/2 1) x (fma.f64 1/12 (pow.f64 x 4) (*.f64 (pow.f64 x 6) -1/45)))
(-.f64 (log.f64 2) (log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))))
(-.f64 (log.f64 2) (log1p.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))
(-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))
(-.f64 (log.f64 2) (log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))))
(-.f64 (log.f64 2) (log1p.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))
(-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))
(-.f64 (log.f64 2) (log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))))
(-.f64 (log.f64 2) (log1p.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))
(-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))
(-.f64 (log.f64 2) (log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))))
(-.f64 (log.f64 2) (log1p.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))
(-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))
(-.f64 (log.f64 2) (log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))))
(-.f64 (log.f64 2) (log1p.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))
(-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))
(-.f64 (log.f64 2) (log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))))
(-.f64 (log.f64 2) (log1p.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))
(-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))
(-.f64 (log.f64 2) (log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))))
(-.f64 (log.f64 2) (log1p.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))
(-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))
(-.f64 (log.f64 2) (log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2)))))
(-.f64 (log.f64 2) (log1p.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(-.f64 (log.f64 2) (log1p.f64 (exp.f64 (*.f64 x -2))))
(-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))
(log.f64 2)
(-.f64 (log.f64 2) x)
(-.f64 (+.f64 (log.f64 2) (*.f64 1/2 (pow.f64 x 2))) x)
(+.f64 (log.f64 2) (-.f64 (*.f64 1/2 (*.f64 x x)) x))
(-.f64 (fma.f64 1/2 (*.f64 x x) (log.f64 2)) x)
(-.f64 (fma.f64 x (*.f64 x 1/2) (log.f64 2)) x)
(fma.f64 x (fma.f64 x 1/2 -1) (log.f64 2))
(-.f64 (+.f64 (log.f64 2) (*.f64 1/2 (pow.f64 x 2))) (+.f64 (*.f64 1/12 (pow.f64 x 4)) x))
(+.f64 (log.f64 2) (-.f64 (*.f64 1/2 (*.f64 x x)) (fma.f64 1/12 (pow.f64 x 4) x)))
(-.f64 (fma.f64 1/2 (*.f64 x x) (log.f64 2)) (fma.f64 1/12 (pow.f64 x 4) x))
(fma.f64 x (*.f64 x 1/2) (-.f64 (log.f64 2) (fma.f64 1/12 (pow.f64 x 4) x)))
(fma.f64 (pow.f64 x 4) -1/12 (fma.f64 x (fma.f64 x 1/2 -1) (log.f64 2)))
(log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(log1p.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)))
(log1p.f64 (exp.f64 (*.f64 x -2)))
(log1p.f64 (pow.f64 (exp.f64 x) -2))
(log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(log1p.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)))
(log1p.f64 (exp.f64 (*.f64 x -2)))
(log1p.f64 (pow.f64 (exp.f64 x) -2))
(log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(log1p.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)))
(log1p.f64 (exp.f64 (*.f64 x -2)))
(log1p.f64 (pow.f64 (exp.f64 x) -2))
(log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(log1p.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)))
(log1p.f64 (exp.f64 (*.f64 x -2)))
(log1p.f64 (pow.f64 (exp.f64 x) -2))
(log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(log1p.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)))
(log1p.f64 (exp.f64 (*.f64 x -2)))
(log1p.f64 (pow.f64 (exp.f64 x) -2))
(log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(log1p.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)))
(log1p.f64 (exp.f64 (*.f64 x -2)))
(log1p.f64 (pow.f64 (exp.f64 x) -2))
(log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(log1p.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)))
(log1p.f64 (exp.f64 (*.f64 x -2)))
(log1p.f64 (pow.f64 (exp.f64 x) -2))
(log.f64 (+.f64 1 (/.f64 1 (pow.f64 (exp.f64 x) 2))))
(log1p.f64 (/.f64 1 (pow.f64 (exp.f64 x) 2)))
(log1p.f64 (exp.f64 (*.f64 x -2)))
(log1p.f64 (pow.f64 (exp.f64 x) -2))
1
(-.f64 1 (*.f64 2 x))
(+.f64 1 (*.f64 -2 x))
(+.f64 1 (*.f64 x -2))
(fma.f64 x -2 1)
(-.f64 (+.f64 1 (*.f64 2 (pow.f64 x 2))) (*.f64 2 x))
(+.f64 1 (-.f64 (*.f64 2 (*.f64 x x)) (*.f64 x 2)))
(+.f64 1 (*.f64 2 (-.f64 (*.f64 x x) x)))
(fma.f64 2 (-.f64 (*.f64 x x) x) 1)
(fma.f64 x (fma.f64 x 2 -2) 1)
(-.f64 (+.f64 1 (*.f64 2 (pow.f64 x 2))) (+.f64 (*.f64 2 x) (*.f64 4/3 (pow.f64 x 3))))
(+.f64 1 (-.f64 (*.f64 2 (*.f64 x x)) (fma.f64 2 x (*.f64 4/3 (pow.f64 x 3)))))
(-.f64 (fma.f64 2 (*.f64 x x) 1) (fma.f64 4/3 (pow.f64 x 3) (*.f64 x 2)))
(+.f64 1 (fma.f64 2 (-.f64 (*.f64 x x) x) (*.f64 (pow.f64 x 3) -4/3)))
(fma.f64 (pow.f64 x 3) -4/3 (fma.f64 x (fma.f64 x 2 -2) 1))
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(exp.f64 (*.f64 x -2))
(pow.f64 (exp.f64 x) -2)
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(exp.f64 (*.f64 x -2))
(pow.f64 (exp.f64 x) -2)
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(exp.f64 (*.f64 x -2))
(pow.f64 (exp.f64 x) -2)
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(exp.f64 (*.f64 x -2))
(pow.f64 (exp.f64 x) -2)
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(exp.f64 (*.f64 x -2))
(pow.f64 (exp.f64 x) -2)
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(exp.f64 (*.f64 x -2))
(pow.f64 (exp.f64 x) -2)
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(exp.f64 (*.f64 x -2))
(pow.f64 (exp.f64 x) -2)
(/.f64 1 (pow.f64 (exp.f64 x) 2))
(exp.f64 (*.f64 x -2))
(pow.f64 (exp.f64 x) -2)

prune52.0ms (1.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New95095
Fresh000
Picked011
Done011
Total95297
Error
0b
Counts
97 → 2
Alt Table
StatusErrorProgram
✓30.8b
(expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2))))
✓30.0b
(fma.f64 (pow.f64 x 3) -1/3 (fma.f64 2/15 (pow.f64 x 5) x))
Compiler

Compiled 1461 to 1191 computations (18.5% saved)

regimes103.0ms (3.8%)

Accuracy

Total 0.2b remaining (94.3%)

Threshold costs 0.2b (94.3%)

Counts
21 → 2
Compiler

Compiled 306 to 252 computations (17.6% saved)

bsearch0.0ms (0%)

Algorithm
1×left-value
Calls

1 calls:

0.0ms
(*.f64 -2 x)
Steps
ItersPointRange
-2.0
∈ [
-3.1735963032855055
, 
-5.77616739417271e-5
]
Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01936
12936
24236
34836
45236
55336
Stop Event
1×saturated
Calls
Call 1
Inputs
(if (<=.f64 (*.f64 -2 x) -2) (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))) (expm1.f64 (-.f64 x (*.f64 1/2 (pow.f64 x 2)))))
Outputs
(if (<=.f64 (*.f64 -2 x) -2) (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))) (expm1.f64 (-.f64 x (*.f64 1/2 (pow.f64 x 2)))))
(if (<=.f64 (*.f64 -2 x) -2) (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))) (expm1.f64 (+.f64 x (*.f64 -1/2 (pow.f64 x 2)))))
(if (<=.f64 (*.f64 -2 x) -2) (expm1.f64 (-.f64 (log.f64 2) (log1p.f64 (pow.f64 (exp.f64 x) -2)))) (expm1.f64 (+.f64 x (*.f64 (pow.f64 x 2) -1/2))))

end72.0ms (2.6%)

Stop Event
1×done
Compiler

Compiled 74 to 62 computations (16.2% saved)

Profiling

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