Details

Time bar (total: 3.1s)

analyze4.0ms (0.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
25%75%0%3
62.5%37.5%0%4
68.7%18.7%12.5%5
71.8%9.4%18.8%6
73.4%4.7%21.9%7
74.2%2.3%23.5%8
74.6%1.2%24.3%9
75%0.6%24.5%10
75.1%0.3%24.6%11
75.1%0.1%24.7%12
Compiler

Compiled 8 to 6 computations (25% saved)

sample1.9s (59.3%)

Results
1.0s2744×body1024valid
474.0ms3871×body256valid
273.0ms1373×body512valid
99.0ms268×body2048valid
1.0msbody256invalid

preprocess22.0ms (0.7%)

Algorithm
egg-herbie
Rules
95×fma-def_binary64
80×fma-neg_binary64
32×distribute-rgt-in_binary64
28×cancel-sign-sub-inv_binary64
26×distribute-lft-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
066
1156
2186
3226
4306
5406
6596
71006
81466
92226
103496
115076
125796
136156
011
Stop Event
saturated
saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(/.f64 (-.f64 (exp.f64 x) 1) x)
Outputs
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
Compiler

Compiled 8 to 6 computations (25% saved)

simplify13.0ms (0.4%)

Algorithm
egg-herbie
Rules
95×fma-def_binary64
80×fma-neg_binary64
32×distribute-rgt-in_binary64
28×cancel-sign-sub-inv_binary64
26×distribute-lft-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
066
1156
2186
3226
4306
5406
6596
71006
81466
92226
103496
115076
125796
136156
Stop Event
saturated
Counts
1 → 2
Calls
Call 1
Inputs
(/.f64 (-.f64 (exp.f64 x) 1) x)
Outputs
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)

eval1.0ms (0%)

Compiler

Compiled 11 to 7 computations (36.4% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.0b
Counts
3 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
0.0b
(/.f64 (expm1.f64 x) x)
Compiler

Compiled 5 to 3 computations (40% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (expm1.f64 x) x)
0.0b
(/.f64 (expm1.f64 x) x)

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@-inf
(/.f64 (expm1.f64 x) x)
1.0ms
x
@inf
(/.f64 (expm1.f64 x) x)
1.0ms
x
@0
(/.f64 (expm1.f64 x) x)

rewrite37.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
449×pow1_binary64
430×add-sqr-sqrt_binary64
424×*-un-lft-identity_binary64
417×add-log-exp_binary64
417×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
046
1836
211046
Stop Event
node limit
Counts
1 → 31
Calls
Call 1
Inputs
(/.f64 (expm1.f64 x) x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (expm1.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (expm1.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))))))

simplify37.0ms (1.2%)

Algorithm
egg-herbie
Rules
688×times-frac_binary64
634×associate-/l/_binary64
536×unswap-sqr_binary64
497×associate-*l*_binary64
474×associate-/r*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02287
16085
212085
332679
479276
5243076
6439876
Stop Event
node limit
Counts
43 → 40
Calls
Call 1
Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
Outputs
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) 1))
(fma.f64 x (fma.f64 x 1/6 1/2) 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (+.f64 (fma.f64 1/6 (*.f64 x x) 1) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) 1))
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)

eval7.0ms (0.2%)

Compiler

Compiled 345 to 161 computations (53.3% saved)

prune8.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New36440
Fresh000
Picked011
Done000
Total36541
Error
0b
Counts
41 → 5
Alt Table
Click to see full alt table
StatusErrorProgram
0.0b
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
19.6b
1
19.6b
(+.f64 (*.f64 1/2 x) 1)
18.1b
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
0.0b
(/.f64 (expm1.f64 x) x)
Compiler

Compiled 29 to 22 computations (24.1% saved)

localize5.0ms (0.1%)

Local error

Found 6 expressions with local error:

NewErrorProgram
1.3b
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
0.0b
(/.f64 (expm1.f64 x) x)
0.0b
(+.f64 1 (/.f64 (expm1.f64 x) x))
0.0b
(+.f64 1 (/.f64 (expm1.f64 x) x))
0.0b
(/.f64 (expm1.f64 x) x)
1.3b
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)

series2.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
0.0ms
x
@0
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
0.0ms
x
@inf
(+.f64 1 (/.f64 (expm1.f64 x) x))
0.0ms
x
@0
(+.f64 1 (/.f64 (expm1.f64 x) x))
0.0ms
x
@-inf
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
0.0ms
x
@inf
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)

rewrite60.0ms (1.9%)

Algorithm
batch-egg-rewrite
Rules
831×pow1_binary64
779×add-log-exp_binary64
779×log1p-expm1-u_binary64
779×expm1-log1p-u_binary64
765×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0721
115915
2224815
Stop Event
node limit
Counts
2 → 97
Calls
Call 1
Inputs
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(+.f64 1 (/.f64 (expm1.f64 x) x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (/.f64 (expm1.f64 x) x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (expm1.f64 x) x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 1 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (expm1.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (*.f64 (cbrt.f64 (expm1.f64 x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (expm1.f64 x)) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) -1) (/.f64 1 (+.f64 (/.f64 (expm1.f64 x) x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 1) (-.f64 (sqrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 x (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 x (expm1.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2)) (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (/.f64 (expm1.f64 x) x) 2) (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 x (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 x (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (expm1.f64 x)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 3) -1) (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 3) -1) (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (-.f64 1 (*.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) -1) (+.f64 (/.f64 (expm1.f64 x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) -1) (-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (neg.f64 (expm1.f64 x))) (neg.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) (+.f64 (/.f64 (expm1.f64 x) x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2) -1)) (neg.f64 (+.f64 (/.f64 (expm1.f64 x) x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1) (+.f64 (/.f64 (expm1.f64 x) x) -1)) (+.f64 (/.f64 (expm1.f64 x) x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (+.f64 (/.f64 (expm1.f64 x) x) -1) (+.f64 (/.f64 (expm1.f64 x) x) -1))) (-.f64 1 (+.f64 (/.f64 (expm1.f64 x) x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 x) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (expm1.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 1 (/.f64 (expm1.f64 x) x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 2) (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) (sqrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (/.f64 (expm1.f64 x) x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 1 (/.f64 (expm1.f64 x) x))) (/.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2) (-.f64 1 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 2) (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 2) (*.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) (sqrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) (*.f64 (sqrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 3)) (/.f64 1 (+.f64 1 (-.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2) (/.f64 (expm1.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 2)) (/.f64 1 (-.f64 1 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (-.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2) (/.f64 (expm1.f64 x) x))) (+.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (/.f64 (expm1.f64 x) x)) (-.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 3)) (+.f64 1 (-.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2) (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 3)) (+.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2) (-.f64 1 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 2)) (-.f64 1 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 3))) (neg.f64 (+.f64 1 (-.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2) (/.f64 (expm1.f64 x) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 2))) (neg.f64 (-.f64 1 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2) 1) (+.f64 (/.f64 (expm1.f64 x) x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 3)) 1) (+.f64 1 (-.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 2) (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (/.f64 (expm1.f64 x) x) 2)) 1) (-.f64 1 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (expm1.f64 x) (/.f64 1 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log.f64 (+.f64 (/.f64 (expm1.f64 x) x) 2)))))))

simplify44.0ms (1.4%)

Algorithm
egg-herbie
Rules
655×fma-def_binary64
565×associate-/r*_binary64
536×unswap-sqr_binary64
500×associate-/l*_binary64
488×associate-*l*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
032218
187178
2177178
3456166
41027160
52791160
64934160
Stop Event
node limit
Counts
121 → 114
Calls
Call 1
Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
2
(+.f64 (*.f64 1/2 x) 2)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 2))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 2 (*.f64 1/24 (pow.f64 x 3)))))
1
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) 1) (/.f64 1 x))
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) 1) (/.f64 1 x))
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) 1) (/.f64 1 x))
1
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) 1) (/.f64 1 x))
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) 1) (/.f64 1 x))
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) 1) (/.f64 1 x))
Outputs
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) 1))
(fma.f64 x (fma.f64 x 1/6 1/2) 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (+.f64 (fma.f64 1/6 (*.f64 x x) 1) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 x (*.f64 x 1/6) (fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 x (*.f64 x (fma.f64 x 1/24 1/6)) (fma.f64 1/2 x 1))
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
2
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 2)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 2))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 2))
(fma.f64 x (*.f64 x 1/6) (fma.f64 1/2 x 2))
(fma.f64 x (fma.f64 x 1/6 1/2) 2)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 2 (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (+.f64 2 (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 2)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 2)))
(fma.f64 x (*.f64 x (fma.f64 x 1/24 1/6)) (fma.f64 1/2 x 2))
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 2)
1
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) 1) (/.f64 1 x))
(+.f64 (/.f64 (exp.f64 x) x) (-.f64 1 (/.f64 1 x)))
(+.f64 1 (/.f64 (expm1.f64 x) x))
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) 1) (/.f64 1 x))
(+.f64 (/.f64 (exp.f64 x) x) (-.f64 1 (/.f64 1 x)))
(+.f64 1 (/.f64 (expm1.f64 x) x))
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) 1) (/.f64 1 x))
(+.f64 (/.f64 (exp.f64 x) x) (-.f64 1 (/.f64 1 x)))
(+.f64 1 (/.f64 (expm1.f64 x) x))
1
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) 1) (/.f64 1 x))
(+.f64 (/.f64 (exp.f64 x) x) (-.f64 1 (/.f64 1 x)))
(+.f64 1 (/.f64 (expm1.f64 x) x))
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) 1) (/.f64 1 x))
(+.f64 (/.f64 (exp.f64 x) x) (-.f64 1 (/.f64 1 x)))
(+.f64 1 (/.f64 (expm1.f64 x) x))
(-.f64 (+.f64 (/.f64 (exp.f64 x) x) 1) (/.f64 1 x))
(+.f64 (/.f64 (exp.f64 x) x) (-.f64 1 (/.f64 1 x)))
(+.f64 1 (/.f64 (expm1.f64 x) x))

localize3.0ms (0.1%)

localize4.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 x (expm1.f64 x))
0.0b
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
0.0b
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
0.0b
(/.f64 x (expm1.f64 x))

series5.0ms (0.2%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@inf
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
1.0ms
x
@inf
(/.f64 x (expm1.f64 x))
1.0ms
x
@0
(/.f64 x (expm1.f64 x))
1.0ms
x
@-inf
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
1.0ms
x
@-inf
(/.f64 x (expm1.f64 x))

rewrite50.0ms (1.6%)

Algorithm
batch-egg-rewrite
Rules
605×pow1_binary64
565×add-log-exp_binary64
565×log1p-expm1-u_binary64
565×expm1-log1p-u_binary64
551×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0615
112512
2155812
Stop Event
node limit
Counts
2 → 70
Calls
Call 1
Inputs
(/.f64 x (expm1.f64 x))
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 x (expm1.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (expm1.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2) (cbrt.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (/.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) (sqrt.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 x) (/.f64 1 (neg.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (expm1.f64 x)) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 x (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (/.f64 (sqrt.f64 x) (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (expm1.f64 x))) (/.f64 x (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (sqrt.f64 (expm1.f64 x))) (/.f64 (cbrt.f64 x) (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (expm1.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (neg.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (expm1.f64 x))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (expm1.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2)) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1) (pow.f64 (/.f64 1 (expm1.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (neg.f64 x)) (neg.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1 (neg.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 x (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 x (expm1.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (/.f64 x (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 x (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (expm1.f64 x)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 x) (/.f64 1 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 x) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2)) (cbrt.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (expm1.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))))))

simplify41.0ms (1.3%)

Algorithm
egg-herbie
Rules
933×fma-def_binary64
803×unswap-sqr_binary64
583×associate-/l/_binary64
562×times-frac_binary64
380×associate-/r*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
035176
188170
2187170
3522158
41422155
52981155
64954155
Stop Event
node limit
Counts
94 → 86
Calls
Call 1
Inputs
1
(+.f64 (*.f64 -1/2 x) 1)
(+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2))))
(+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2)))))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
Outputs
1
(+.f64 (*.f64 -1/2 x) 1)
(fma.f64 -1/2 x 1)
(+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2))))
(+.f64 (fma.f64 -1/2 x 1) (*.f64 1/12 (*.f64 x x)))
(fma.f64 -1/2 x (fma.f64 1/12 (*.f64 x x) 1))
(fma.f64 -1/2 x (fma.f64 x (*.f64 x 1/12) 1))
(fma.f64 x (fma.f64 x 1/12 -1/2) 1)
(+.f64 (*.f64 -1/720 (pow.f64 x 4)) (+.f64 (*.f64 -1/2 x) (+.f64 1 (*.f64 1/12 (pow.f64 x 2)))))
(fma.f64 -1/720 (pow.f64 x 4) (+.f64 (fma.f64 -1/2 x 1) (*.f64 1/12 (*.f64 x x))))
(fma.f64 -1/720 (pow.f64 x 4) (fma.f64 -1/2 x (fma.f64 1/12 (*.f64 x x) 1)))
(fma.f64 -1/2 x (fma.f64 -1/720 (pow.f64 x 4) (fma.f64 x (*.f64 x 1/12) 1)))
(fma.f64 x (fma.f64 x 1/12 -1/2) (fma.f64 -1/720 (pow.f64 x 4) 1))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
(/.f64 x (-.f64 (exp.f64 x) 1))
(/.f64 x (expm1.f64 x))
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(fma.f64 x 1/2 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) 1/6 1))
(fma.f64 x (*.f64 x 1/6) (fma.f64 x 1/2 1))
(fma.f64 x (fma.f64 x 1/6 1/2) 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (+.f64 (fma.f64 1/6 (*.f64 x x) 1) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 x 1/2 (fma.f64 (*.f64 x x) 1/6 (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 x 1/2 (fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) (fma.f64 x 1/2 1))
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)

eval183.0ms (5.8%)

Compiler

Compiled 2818 to 1454 computations (48.4% saved)

prune69.0ms (2.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New2373240
Fresh101
Picked101
Done033
Total2396245
Error
0b
Counts
245 → 6
Alt Table
Click to see full alt table
StatusErrorProgram
19.6b
(+.f64 (*.f64 1/2 x) 1)
0.0b
(/.f64 1 (/.f64 x (expm1.f64 x)))
19.6b
1
18.1b
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
19.6b
(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) 1)) 1)
0.0b
(/.f64 (expm1.f64 x) x)
Compiler

Compiled 39 to 31 computations (20.5% saved)

localize5.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series3.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

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

rewrite62.0ms (2%)

Algorithm
batch-egg-rewrite
Rules
895×pow1_binary64
838×add-log-exp_binary64
838×log1p-expm1-u_binary64
838×expm1-log1p-u_binary64
825×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0819
118712
2249612
Stop Event
node limit
Counts
2 → 83
Calls
Call 1
Inputs
(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) 1)) 1)
(+.f64 1 (+.f64 (*.f64 1/2 x) 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 1/2 x 1) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 1/2 x) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 (*.f64 1/2 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 1/2 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 1/2 x 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 1/2 x 1)) (pow.f64 (cbrt.f64 (fma.f64 1/2 x 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x 1)) 2) (cbrt.f64 (fma.f64 1/2 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 1/2 x 1)) (sqrt.f64 (fma.f64 1/2 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 2) (+.f64 (fma.f64 1/2 x 1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (*.f64 1/8 (pow.f64 x 3))) (/.f64 1 (+.f64 (*.f64 1/4 (*.f64 x x)) (-.f64 1 (*.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 2) -1) (/.f64 1 (+.f64 (fma.f64 1/2 x 1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 1/4 (*.f64 x x)) -1) (/.f64 1 (fma.f64 1/2 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (+.f64 (*.f64 1/2 x) 2)) 1) (-.f64 (sqrt.f64 (+.f64 (*.f64 1/2 x) 2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 1/4 (*.f64 x x)) (-.f64 1 (*.f64 1/2 x))) (+.f64 1 (*.f64 1/8 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 1/2 x -1) (+.f64 (*.f64 1/4 (*.f64 x x)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 2) (+.f64 (fma.f64 1/2 x 1) 2)) (+.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (fma.f64 1/2 x 1) 2) (+.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 3) -1) (+.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 2) (+.f64 (fma.f64 1/2 x 1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 3) -1) (+.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 2) (-.f64 1 (*.f64 (+.f64 (*.f64 1/2 x) 2) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (*.f64 1/8 (pow.f64 x 3))) (+.f64 (*.f64 1/4 (*.f64 x x)) (-.f64 1 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (*.f64 1/8 (pow.f64 x 3))) (+.f64 1 (-.f64 (*.f64 1/4 (*.f64 x x)) (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 2) -1) (+.f64 (fma.f64 1/2 x 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 2) -1) (-.f64 (+.f64 (*.f64 1/2 x) 2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 1/4 (*.f64 x x)) -1) (fma.f64 1/2 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (*.f64 1/8 (pow.f64 x 3)))) (neg.f64 (+.f64 (*.f64 1/4 (*.f64 x x)) (-.f64 1 (*.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (*.f64 1/4 (*.f64 x x)) -1)) (neg.f64 (fma.f64 1/2 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 2) (+.f64 (fma.f64 1/2 x 1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 2) -1)) (neg.f64 (+.f64 (fma.f64 1/2 x 1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 1/4 (*.f64 x x))) (-.f64 1 (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 1/2 x 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 1/2 x 1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 1/2 x 1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 1/2 x 1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 1/2 x 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 1/2 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 1/2 x 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 1/2 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 1/2 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (*.f64 1/2 x) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 x 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/2 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 1/2 x)) 2) (cbrt.f64 (*.f64 1/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2) (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 1/2 x)) (sqrt.f64 (*.f64 1/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (*.f64 1/2 x) 2)) (sqrt.f64 (+.f64 (*.f64 1/2 x) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 1/2 x 1)))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (fma.f64 1/2 x 1) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (-.f64 0 (*.f64 1/2 x))) (/.f64 (pow.f64 (fma.f64 1/2 x 1) 2) (-.f64 0 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (*.f64 1/2 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 1/2 x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2) (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2) (*.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (*.f64 1/2 x) 2)) (sqrt.f64 (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (*.f64 1/2 x) 2)) (*.f64 (sqrt.f64 (+.f64 (*.f64 1/2 x) 2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3)) (/.f64 1 (+.f64 1 (*.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2)) (/.f64 1 (-.f64 0 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (*.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x))) (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 0 (*.f64 1/2 x)) (-.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3)) (+.f64 1 (*.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3)) (+.f64 (pow.f64 (fma.f64 1/2 x 1) 2) (-.f64 0 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2)) (-.f64 0 (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3))) (neg.f64 (+.f64 1 (*.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2))) (neg.f64 (-.f64 0 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 1/2 x 1) 2) 1) (*.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (pow.f64 (fma.f64 1/2 x 1) 3)) 1) (+.f64 1 (*.f64 (fma.f64 1/2 x 1) (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (pow.f64 (fma.f64 1/2 x 1) 2)) 1) (-.f64 0 (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (*.f64 1/2 x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (*.f64 1/2 x) 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (*.f64 1/2 x) 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (*.f64 1/2 x) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (*.f64 1/2 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (fma.f64 1/2 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 1/2 x 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 1/2 x 1)) 2) (cbrt.f64 (fma.f64 1/2 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 1/2 x 1)) (sqrt.f64 (fma.f64 1/2 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (*.f64 1/2 x) 2)))))))

simplify9.0ms (0.3%)

Algorithm
egg-herbie
Rules
fma-def_binary64
+-commutative_binary64
*-commutative_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
010108
115108
217108
Stop Event
saturated
Counts
107 → 89
Calls
Call 1
Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 1/2 x) 1)
(*.f64 1/2 x)
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 1/2 x))
(*.f64 1/2 x)
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 1/2 x))
(+.f64 1 (*.f64 1/2 x))
2
(+.f64 (*.f64 1/2 x) 2)
(+.f64 (*.f64 1/2 x) 2)
(+.f64 (*.f64 1/2 x) 2)
(*.f64 1/2 x)
(+.f64 2 (*.f64 1/2 x))
(+.f64 2 (*.f64 1/2 x))
(+.f64 2 (*.f64 1/2 x))
(*.f64 1/2 x)
(+.f64 2 (*.f64 1/2 x))
(+.f64 2 (*.f64 1/2 x))
(+.f64 2 (*.f64 1/2 x))
Outputs
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(*.f64 1/2 x)
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(*.f64 1/2 x)
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
(+.f64 1 (*.f64 1/2 x))
(fma.f64 1/2 x 1)
2
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 2)
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 2)
(+.f64 (*.f64 1/2 x) 2)
(fma.f64 1/2 x 2)
(*.f64 1/2 x)
(+.f64 2 (*.f64 1/2 x))
(fma.f64 1/2 x 2)
(+.f64 2 (*.f64 1/2 x))
(fma.f64 1/2 x 2)
(+.f64 2 (*.f64 1/2 x))
(fma.f64 1/2 x 2)
(*.f64 1/2 x)
(+.f64 2 (*.f64 1/2 x))
(fma.f64 1/2 x 2)
(+.f64 2 (*.f64 1/2 x))
(fma.f64 1/2 x 2)
(+.f64 2 (*.f64 1/2 x))
(fma.f64 1/2 x 2)

localize4.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 x (expm1.f64 x))
0.0b
(/.f64 1 (/.f64 x (expm1.f64 x)))
0.0b
(/.f64 1 (/.f64 x (expm1.f64 x)))
0.0b
(/.f64 x (expm1.f64 x))

series33.0ms (1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
32.0ms
x
@inf
(/.f64 1 (/.f64 x (expm1.f64 x)))
0.0ms
x
@0
(/.f64 1 (/.f64 x (expm1.f64 x)))
0.0ms
x
@-inf
(/.f64 1 (/.f64 x (expm1.f64 x)))

rewrite40.0ms (1.3%)

Algorithm
batch-egg-rewrite
Rules
606×pow1_binary64
562×add-log-exp_binary64
562×log1p-expm1-u_binary64
562×expm1-log1p-u_binary64
548×add-exp-log_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
069
11246
215846
Stop Event
node limit
Counts
1 → 36
Calls
Call 1
Inputs
(/.f64 1 (/.f64 x (expm1.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (expm1.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (/.f64 (neg.f64 x) (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (pow.f64 (/.f64 1 (expm1.f64 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (/.f64 x (expm1.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1) (pow.f64 (sqrt.f64 (/.f64 x (expm1.f64 x))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) 1) (/.f64 (cbrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) 1) (/.f64 (sqrt.f64 (expm1.f64 x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (expm1.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (expm1.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (sqrt.f64 x)) (/.f64 (cbrt.f64 (expm1.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)) (/.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (neg.f64 x)) (neg.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 x) 1) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 x) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)) (cbrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 x) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (expm1.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 x (expm1.f64 x)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))))))

simplify36.0ms (1.2%)

Algorithm
egg-herbie
Rules
688×times-frac_binary64
634×associate-/l/_binary64
536×unswap-sqr_binary64
497×associate-*l*_binary64
474×associate-/r*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02287
16085
212085
332679
479276
5243076
6439876
Stop Event
node limit
Counts
48 → 45
Calls
Call 1
Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
Outputs
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) 1))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) 1))
(fma.f64 x (fma.f64 x 1/6 1/2) 1)
(+.f64 (*.f64 1/2 x) (+.f64 (*.f64 1/6 (pow.f64 x 2)) (+.f64 1 (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (+.f64 (fma.f64 1/6 (*.f64 x x) 1) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/6) (fma.f64 1/24 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) 1))
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(/.f64 (expm1.f64 x) x)

eval51.0ms (1.6%)

Compiler

Compiled 1979 to 1399 computations (29.3% saved)

prune51.0ms (1.6%)

Pruning

6 alts after pruning (2 fresh and 4 done)

PrunedKeptTotal
New1721173
Fresh011
Picked011
Done134
Total1736179
Error
0b
Counts
179 → 6
Alt Table
Click to see full alt table
StatusErrorProgram
19.6b
(+.f64 (*.f64 1/2 x) 1)
0.0b
(/.f64 1 (/.f64 x (expm1.f64 x)))
16.2b
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
0.0b
(/.f64 (expm1.f64 x) x)
19.6b
1
18.1b
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
Compiler

Compiled 37 to 29 computations (21.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite76.0ms (2.4%)

Algorithm
batch-egg-rewrite
Rules
688×pow1_binary64
641×log1p-expm1-u_binary64
641×expm1-log1p-u_binary64
640×add-log-exp_binary64
628×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
11518
218208
Stop Event
node limit
Counts
1 → 22
Calls
Call 1
Inputs
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1 (fma.f64 -1/2 x 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (fma.f64 -1/2 x 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (fma.f64 -1/2 x 1))) (cbrt.f64 (pow.f64 (fma.f64 -1/2 x 1) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 -1/2 x 1) -2)) (/.f64 1 (cbrt.f64 (fma.f64 -1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (fma.f64 -1/2 x 1) -1/2) (pow.f64 (fma.f64 -1/2 x 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (fma.f64 -1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 -1/2 x 1)) 2) -1) (pow.f64 (cbrt.f64 (fma.f64 -1/2 x 1)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (fma.f64 -1/2 x 1)) -1) (pow.f64 (sqrt.f64 (fma.f64 -1/2 x 1)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 1 (*.f64 -1/8 (pow.f64 x 3)))) (+.f64 (*.f64 1/4 (*.f64 x x)) (-.f64 1 (*.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (*.f64 1/4 (*.f64 x x)) -1)) (fma.f64 -1/2 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 -1/2 x 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (fma.f64 -1/2 x 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 -1/2 x 1) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 -1/2 x 1) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (fma.f64 -1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (fma.f64 -1/2 x 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (fma.f64 -1/2 x 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log1p.f64 (*.f64 -1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (fma.f64 -1/2 x 1))))))))

simplify40.0ms (1.3%)

Algorithm
egg-herbie
Rules
724×fma-neg_binary64
686×times-frac_binary64
450×fma-def_binary64
405×associate-*l/_binary64
402×cancel-sign-sub-inv_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
041193
1112179
2306177
3982171
42948171
Stop Event
node limit
Counts
34 → 36
Calls
Call 1
Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/4 (pow.f64 x 2))))
(+.f64 (*.f64 1/2 x) (+.f64 1 (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 1/8 (pow.f64 x 3)))))
(/.f64 -2 x)
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x)))))
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 16 (/.f64 1 (pow.f64 x 4)))))))
(/.f64 -2 x)
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x))))
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x)))))
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 16 (/.f64 1 (pow.f64 x 4)))))))
Outputs
1
(+.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x 1)
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/4 (pow.f64 x 2))))
(+.f64 (fma.f64 1/2 x 1) (*.f64 1/4 (*.f64 x x)))
(fma.f64 1/2 x (fma.f64 1/4 (*.f64 x x) 1))
(fma.f64 1/4 (*.f64 x x) (fma.f64 1/2 x 1))
(fma.f64 x (fma.f64 x 1/4 1/2) 1)
(+.f64 (*.f64 1/2 x) (+.f64 1 (+.f64 (*.f64 1/4 (pow.f64 x 2)) (*.f64 1/8 (pow.f64 x 3)))))
(+.f64 (fma.f64 1/2 x 1) (fma.f64 1/4 (*.f64 x x) (*.f64 1/8 (pow.f64 x 3))))
(+.f64 (fma.f64 1/4 (*.f64 x x) (*.f64 1/8 (pow.f64 x 3))) (fma.f64 1/2 x 1))
(fma.f64 1/2 x (fma.f64 x (*.f64 x 1/4) (fma.f64 1/8 (pow.f64 x 3) 1)))
(fma.f64 1/2 x (fma.f64 x (*.f64 x (fma.f64 x 1/8 1/4)) 1))
(fma.f64 x (*.f64 x (fma.f64 x 1/8 1/4)) (fma.f64 1/2 x 1))
(/.f64 -2 x)
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 2 x)))
(-.f64 (/.f64 -2 x) (/.f64 (/.f64 4 x) x))
(-.f64 (/.f64 -2 x) (/.f64 4 (*.f64 x x)))
(+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x))
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x)))))
(neg.f64 (+.f64 (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 2 x)) (/.f64 8 (pow.f64 x 3))))
(+.f64 (-.f64 (/.f64 -2 x) (/.f64 (/.f64 4 x) x)) (/.f64 -8 (pow.f64 x 3)))
(+.f64 (-.f64 (/.f64 -2 x) (/.f64 4 (*.f64 x x))) (/.f64 -8 (pow.f64 x 3)))
(+.f64 (/.f64 -4 (*.f64 x x)) (+.f64 (/.f64 -8 (pow.f64 x 3)) (/.f64 -2 x)))
(+.f64 (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x)) (/.f64 -8 (pow.f64 x 3)))
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 16 (/.f64 1 (pow.f64 x 4)))))))
(neg.f64 (+.f64 (/.f64 8 (pow.f64 x 3)) (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 16 (pow.f64 x 4))))))
(-.f64 (/.f64 -8 (pow.f64 x 3)) (+.f64 (/.f64 2 x) (+.f64 (/.f64 16 (pow.f64 x 4)) (/.f64 (/.f64 4 x) x))))
(+.f64 (/.f64 -8 (pow.f64 x 3)) (+.f64 (-.f64 (/.f64 -2 x) (/.f64 4 (*.f64 x x))) (/.f64 -16 (pow.f64 x 4))))
(+.f64 (/.f64 -8 (pow.f64 x 3)) (+.f64 (/.f64 -2 x) (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -16 (pow.f64 x 4)))))
(+.f64 (/.f64 -8 (pow.f64 x 3)) (+.f64 (/.f64 -4 (*.f64 x x)) (+.f64 (/.f64 -2 x) (/.f64 -16 (pow.f64 x 4)))))
(/.f64 -2 x)
(neg.f64 (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 2 x)))
(-.f64 (/.f64 -2 x) (/.f64 (/.f64 4 x) x))
(-.f64 (/.f64 -2 x) (/.f64 4 (*.f64 x x)))
(+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x))
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (*.f64 2 (/.f64 1 x)))))
(neg.f64 (+.f64 (+.f64 (/.f64 4 (*.f64 x x)) (/.f64 2 x)) (/.f64 8 (pow.f64 x 3))))
(+.f64 (-.f64 (/.f64 -2 x) (/.f64 (/.f64 4 x) x)) (/.f64 -8 (pow.f64 x 3)))
(+.f64 (-.f64 (/.f64 -2 x) (/.f64 4 (*.f64 x x))) (/.f64 -8 (pow.f64 x 3)))
(+.f64 (/.f64 -4 (*.f64 x x)) (+.f64 (/.f64 -8 (pow.f64 x 3)) (/.f64 -2 x)))
(+.f64 (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x)) (/.f64 -8 (pow.f64 x 3)))
(neg.f64 (+.f64 (*.f64 8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 4 (/.f64 1 (pow.f64 x 2))) (+.f64 (*.f64 2 (/.f64 1 x)) (*.f64 16 (/.f64 1 (pow.f64 x 4)))))))
(neg.f64 (+.f64 (/.f64 8 (pow.f64 x 3)) (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 2 x) (/.f64 16 (pow.f64 x 4))))))
(-.f64 (/.f64 -8 (pow.f64 x 3)) (+.f64 (/.f64 2 x) (+.f64 (/.f64 16 (pow.f64 x 4)) (/.f64 (/.f64 4 x) x))))
(+.f64 (/.f64 -8 (pow.f64 x 3)) (+.f64 (-.f64 (/.f64 -2 x) (/.f64 4 (*.f64 x x))) (/.f64 -16 (pow.f64 x 4))))
(+.f64 (/.f64 -8 (pow.f64 x 3)) (+.f64 (/.f64 -2 x) (+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -16 (pow.f64 x 4)))))
(+.f64 (/.f64 -8 (pow.f64 x 3)) (+.f64 (/.f64 -4 (*.f64 x x)) (+.f64 (/.f64 -2 x) (/.f64 -16 (pow.f64 x 4)))))

eval11.0ms (0.4%)

Compiler

Compiled 404 to 333 computations (17.6% saved)

prune38.0ms (1.2%)

Pruning

8 alts after pruning (3 fresh and 5 done)

PrunedKeptTotal
New33336
Fresh101
Picked011
Done044
Total34842
Error
0b
Counts
42 → 8
Alt Table
Click to see full alt table
StatusErrorProgram
19.6b
(+.f64 (*.f64 1/2 x) 1)
0.0b
(/.f64 1 (/.f64 x (expm1.f64 x)))
60.1b
(+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x))
18.1b
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
16.2b
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
0.0b
(/.f64 (expm1.f64 x) x)
19.6b
1
59.0b
(/.f64 -2 x)
Compiler

Compiled 51 to 39 computations (23.5% saved)

regimes21.0ms (0.7%)

Counts
13 → 1
Calls
Call 1
Inputs
1
1
1
(/.f64 -2 x)
(+.f64 (*.f64 1/2 x) 1)
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
(+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) 1)) 1)
(/.f64 (expm1.f64 x) x)
(/.f64 1 (/.f64 x (expm1.f64 x)))
(/.f64 (-.f64 (exp.f64 x) 1) x)
(-.f64 (+.f64 1 (/.f64 (expm1.f64 x) x)) 1)
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
Outputs
(/.f64 (expm1.f64 x) x)
Calls

3 calls:

8.0ms
x
7.0ms
(/.f64 (-.f64 (exp.f64 x) 1) x)
3.0ms
(/.f64 (-.f64 (exp.f64 x) 1) x)
Results
ErrorSegmentsBranch
0.0b1x
0.0b1(/.f64 (-.f64 (exp.f64 x) 1) x)
0.0b1(/.f64 (-.f64 (exp.f64 x) 1) x)
Compiler

Compiled 83 to 56 computations (32.5% saved)

regimes41.0ms (1.3%)

Counts
8 → 1
Calls
Call 1
Inputs
1
1
1
(/.f64 -2 x)
(+.f64 (*.f64 1/2 x) 1)
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
(+.f64 (/.f64 -4 (*.f64 x x)) (/.f64 -2 x))
(-.f64 (+.f64 1 (+.f64 (*.f64 1/2 x) 1)) 1)
Outputs
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
Calls

1 calls:

39.0ms
x
Results
ErrorSegmentsBranch
16.2b1x
Compiler

Compiled 39 to 31 computations (20.5% saved)

regimes30.0ms (1%)

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

1 calls:

9.0ms
x
Results
ErrorSegmentsBranch
16.3b2x
Compiler

Compiled 14 to 11 computations (21.4% saved)

bsearch18.0ms (0.6%)

Algorithm
binary-search
Steps
TimeLeftRight
18.0ms
-80162780.40680923
-5.185064830304864e-6
Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes10.0ms (0.3%)

Counts
4 → 2
Calls
Call 1
Inputs
1
1
1
(/.f64 -2 x)
Outputs
(/.f64 -2 x)
1
Calls

1 calls:

9.0ms
x
Results
ErrorSegmentsBranch
16.9b2x
Compiler

Compiled 9 to 7 computations (22.2% saved)

bsearch20.0ms (0.6%)

Algorithm
binary-search
Steps
TimeLeftRight
20.0ms
-80162780.40680923
-5.185064830304864e-6
Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes4.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0.0b (-0%)

Counts
3 → 1
Calls
Call 1
Inputs
1
1
1
Outputs
1
Calls

1 calls:

4.0ms
x
Results
ErrorSegmentsBranch
19.6b1x
Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01945
12545
Stop Event
saturated
Calls
Call 1
Inputs
(/.f64 (expm1.f64 x) x)
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
(if (<=.f64 x -344296520203675200/4294967296) (/.f64 -2 x) (+.f64 (*.f64 1/2 x) 1))
(if (<=.f64 x -344296520203675200/4294967296) (/.f64 -2 x) 1)
1
Outputs
(/.f64 (expm1.f64 x) x)
(/.f64 1 (+.f64 (*.f64 -1/2 x) 1))
(/.f64 1 (+.f64 1 (*.f64 x -1/2)))
(if (<=.f64 x -344296520203675200/4294967296) (/.f64 -2 x) (+.f64 (*.f64 1/2 x) 1))
(if (<=.f64 x -5379633128182425/67108864) (/.f64 -2 x) (+.f64 1 (*.f64 x 1/2)))
(if (<=.f64 x -344296520203675200/4294967296) (/.f64 -2 x) 1)
(if (<=.f64 x -5379633128182425/67108864) (/.f64 -2 x) 1)
1

end68.0ms (2.2%)

Stop Event
fuel
Compiler

Compiled 70 to 54 computations (22.9% saved)

Profiling

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