Details

Time bar (total: 4.4s)

analyze6.0ms (0.1%)

Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
0%0%100%0%0%0%0%2
25%25%75%0%0%0%0%3
62.5%62.5%37.5%0%0%0%0%4
78.6%68.7%18.7%0%12.5%0%0%5
88.5%71.8%9.4%0%18.7%0%0%6
94%73.4%4.7%0%21.9%0%0%7
96.9%74.2%2.3%0%23.4%0%0%8
98.5%74.6%1.2%0%24.2%0%0%9
99.2%75%0.6%0%24.4%0%0%10
99.6%75.1%0.3%0%24.6%0%0%11
99.8%75.1%0.1%0%24.7%0%0%12
Compiler

Compiled 8 to 6 computations (25% saved)

sample2.5s (56.5%)

Results
1.4s2696×body1024valid
567.0ms3909×body256valid
364.0ms1367×body512valid
109.0ms284×body2048valid
1.0msbody256infinite
Bogosity

preprocess131.0ms (3%)

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
81456
92236
103526
115116
125836
136196
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)

simplify43.0ms (1%)

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
81456
92236
103526
115116
125836
136196
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)

prune2.0ms (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)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiled 8 to 3 computations (62.5% saved)

series4.0ms (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)

rewrite63.0ms (1.4%)

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) (pow.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 x) (pow.f64 x -1))))) (#(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)) (pow.f64 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 (expm1.f64 x)) (*.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 x -1)))))) (#(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 (pow.f64 x -1) (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 expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))))) (#(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)))))))

simplify57.0ms (1.3%)

Algorithm
egg-herbie
Rules
688×times-frac_binary64
636×associate-/l/_binary64
536×unswap-sqr_binary64
495×associate-*l*_binary64
448×fma-def_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02287
16085
212085
332579
481676
5252276
6451076
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 x (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 3) 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)

eval8.0ms (0.2%)

Compiler

Compiled 345 to 161 computations (53.3% saved)

prune12.0ms (0.3%)

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
17.6b
1
0.2b
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
17.6b
(+.f64 (*.f64 1/2 x) 1)
0.0b
(/.f64 (expm1.f64 x) x)
17.4b
(fma.f64 x (fma.f64 x 1/6 1/2) 1)
Compiler

Compiled 29 to 22 computations (24.1% saved)

localize6.0ms (0.1%)

Compiler

Compiled 12 to 9 computations (25% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (expm1.f64 x) x)
0.0b
(sqrt.f64 (/.f64 (expm1.f64 x) x))
0.1b
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
Compiler

Compiled 21 to 7 computations (66.7% saved)

series15.0ms (0.3%)

Counts
2 → 8
Calls

6 calls:

TimeVariablePointExpression
7.0ms
x
@0
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
3.0ms
x
@-inf
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
2.0ms
x
@inf
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
1.0ms
x
@-inf
(sqrt.f64 (/.f64 (expm1.f64 x) x))
1.0ms
x
@inf
(sqrt.f64 (/.f64 (expm1.f64 x) x))

rewrite105.0ms (2.4%)

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: 0 (0.0ms)

IterNodesCost
0714
114914
2156214
Stop Event
node limit
Counts
2 → 71
Calls
Call 1
Inputs
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
(sqrt.f64 (/.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 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(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 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (*.f64 (cbrt.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 (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 (pow.f64 (/.f64 (expm1.f64 x) x) 1/4) (*.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/4) (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 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (pow.f64 (/.f64 (expm1.f64 x) x) 1/4)) (pow.f64 (/.f64 (expm1.f64 x) x) 1/4))))) (#(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 (expm1.f64 x) x)) (cbrt.f64 (/.f64 (expm1.f64 x) x))) (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 x) 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 -1 (neg.f64 (/.f64 x (expm1.f64 x))))))) (#(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 (/.f64 (expm1.f64 x) (sqrt.f64 x)) (sqrt.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 (expm1.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (/.f64 (expm1.f64 x) x))) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) (sqrt.f64 (expm1.f64 x))) (sqrt.f64 x))))) (#(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 expm1.f64 (log1p.f64 (/.f64 (expm1.f64 x) x)))))) (#(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 -.f64 (+.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))) (cbrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (/.f64 1 x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 x)) (/.f64 1 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/4) (pow.f64 (/.f64 (expm1.f64 x) x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2)) (sqrt.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 2) 1/2) (pow.f64 (cbrt.f64 (/.f64 (expm1.f64 x) x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 x) (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (neg.f64 (expm1.f64 x))) (sqrt.f64 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sqrt.f64 (expm1.f64 x))) (neg.f64 (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (expm1.f64 x) x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (expm1.f64 x) x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x))))))))

simplify161.0ms (3.7%)

Algorithm
egg-herbie
Rules
1218×fma-def_binary64
750×sqr-pow_binary64
605×cube-prod_binary64
423×fabs-mul_binary64
370×pow-sqr_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
03182
17878
218575
353362
4139956
5242156
6294356
7307656
8322956
9341656
10367156
11431956
12472856
13525756
14591756
15674556
16714456
17751256
18785256
Stop Event
node limit
Counts
79 → 84
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)))))
1
(+.f64 1 (*.f64 1/4 x))
(+.f64 1 (+.f64 (*.f64 1/4 x) (*.f64 5/96 (pow.f64 x 2))))
(+.f64 1 (+.f64 (*.f64 1/4 x) (+.f64 (*.f64 1/128 (pow.f64 x 3)) (*.f64 5/96 (pow.f64 x 2)))))
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 1/24 (pow.f64 x 3) (fma.f64 x (fma.f64 x 1/6 1/2) 1))
(fma.f64 x (fma.f64 x (fma.f64 x 1/24 1/6) 1/2) 1)
1
(+.f64 1 (*.f64 1/4 x))
(+.f64 1 (*.f64 x 1/4))
(fma.f64 x 1/4 1)
(+.f64 1 (+.f64 (*.f64 1/4 x) (*.f64 5/96 (pow.f64 x 2))))
(+.f64 1 (fma.f64 1/4 x (*.f64 (*.f64 x x) 5/96)))
(+.f64 1 (fma.f64 x 1/4 (*.f64 x (*.f64 x 5/96))))
(fma.f64 x 1/4 (fma.f64 (*.f64 x x) 5/96 1))
(fma.f64 x (fma.f64 x 5/96 1/4) 1)
(+.f64 1 (+.f64 (*.f64 1/4 x) (+.f64 (*.f64 1/128 (pow.f64 x 3)) (*.f64 5/96 (pow.f64 x 2)))))
(+.f64 1 (fma.f64 1/4 x (fma.f64 1/128 (pow.f64 x 3) (*.f64 (*.f64 x x) 5/96))))
(+.f64 1 (fma.f64 x 1/4 (fma.f64 (*.f64 x x) 5/96 (*.f64 (pow.f64 x 3) 1/128))))
(+.f64 (fma.f64 x 1/4 1) (*.f64 (*.f64 x x) (+.f64 5/96 (*.f64 x 1/128))))
(fma.f64 (*.f64 x x) (fma.f64 x 1/128 5/96) (fma.f64 x 1/4 1))
(fma.f64 x (fma.f64 x (fma.f64 x 1/128 5/96) 1/4) 1)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 x (fma.f64 x 1/6 1/2) 1)
0.1b
(fma.f64 x 1/6 1/2)
Compiler

Compiled 16 to 12 computations (25% saved)

series3.0ms (0.1%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
0.0ms
x
@0
(fma.f64 x 1/6 1/2)
0.0ms
x
@-inf
(fma.f64 x 1/6 1/2)
0.0ms
x
@-inf
(fma.f64 x (fma.f64 x 1/6 1/2) 1)
0.0ms
x
@inf
(fma.f64 x 1/6 1/2)
0.0ms
x
@inf
(fma.f64 x (fma.f64 x 1/6 1/2) 1)

rewrite54.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
581×pow1_binary64
540×add-log-exp_binary64
540×log1p-expm1-u_binary64
540×expm1-log1p-u_binary64
531×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0714
113614
2141114
Stop Event
node limit
Counts
2 → 42
Calls
Call 1
Inputs
(fma.f64 x 1/6 1/2)
(fma.f64 x (fma.f64 x 1/6 1/2) 1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (*.f64 x 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x 1/6) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x 1/6) 1) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x 1/6 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x 1/6 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x 1/6 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x 1/6 1/2)) (pow.f64 (cbrt.f64 (fma.f64 x 1/6 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x 1/6 1/2)) 2) (cbrt.f64 (fma.f64 x 1/6 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x 1/6 1/2)) (sqrt.f64 (fma.f64 x 1/6 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x 1/6) 3) 1/8) (+.f64 (*.f64 (*.f64 x 1/6) (*.f64 x 1/6)) (-.f64 1/4 (*.f64 (*.f64 x 1/6) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x 1/6) (*.f64 x 1/6)) 1/4) (-.f64 (*.f64 x 1/6) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x 1/6 1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 1/6 1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x 1/6 1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x 1/6 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x 1/6 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x 1/6 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x 1/6 1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x 1/6 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x 1/6 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x 1/6 1/2)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 x (fma.f64 x 1/6 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x (fma.f64 x 1/6 1/2) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x (fma.f64 x 1/6 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)) (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)) 2) (cbrt.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)) (sqrt.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 3) 1) (+.f64 (*.f64 (*.f64 x (fma.f64 x 1/6 1/2)) (*.f64 x (fma.f64 x 1/6 1/2))) (-.f64 1 (*.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x (fma.f64 x 1/6 1/2)) (*.f64 x (fma.f64 x 1/6 1/2))) 1) (-.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)))))))

simplify152.0ms (3.5%)

Algorithm
egg-herbie
Rules
778×sqr-pow_binary64
543×associate-*l*_binary64
540×cube-prod_binary64
535×fabs-mul_binary64
513×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
017186
138168
254156
386144
4193144
5529144
61811144
73151144
83357144
93570144
103790144
114105144
124509144
135018144
145585144
156277144
167114144
177506144
187794144
Stop Event
node limit
Counts
66 → 56
Calls
Call 1
Inputs
1/2
(+.f64 1/2 (*.f64 1/6 x))
(+.f64 1/2 (*.f64 1/6 x))
(+.f64 1/2 (*.f64 1/6 x))
(*.f64 1/6 x)
(+.f64 1/2 (*.f64 1/6 x))
(+.f64 1/2 (*.f64 1/6 x))
(+.f64 1/2 (*.f64 1/6 x))
(*.f64 1/6 x)
(+.f64 1/2 (*.f64 1/6 x))
(+.f64 1/2 (*.f64 1/6 x))
(+.f64 1/2 (*.f64 1/6 x))
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)) 1))
(*.f64 1/6 (pow.f64 x 2))
(+.f64 (*.f64 1/2 x) (*.f64 1/6 (pow.f64 x 2)))
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/6 (pow.f64 x 2))))
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/6 (pow.f64 x 2))))
(*.f64 1/6 (pow.f64 x 2))
(+.f64 (*.f64 1/2 x) (*.f64 1/6 (pow.f64 x 2)))
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/6 (pow.f64 x 2))))
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/6 (pow.f64 x 2))))
Outputs
1/2
(+.f64 1/2 (*.f64 1/6 x))
(fma.f64 1/6 x 1/2)
(+.f64 1/2 (*.f64 1/6 x))
(fma.f64 1/6 x 1/2)
(+.f64 1/2 (*.f64 1/6 x))
(fma.f64 1/6 x 1/2)
(*.f64 1/6 x)
(+.f64 1/2 (*.f64 1/6 x))
(fma.f64 1/6 x 1/2)
(+.f64 1/2 (*.f64 1/6 x))
(fma.f64 1/6 x 1/2)
(+.f64 1/2 (*.f64 1/6 x))
(fma.f64 1/6 x 1/2)
(*.f64 1/6 x)
(+.f64 1/2 (*.f64 1/6 x))
(fma.f64 1/6 x 1/2)
(+.f64 1/2 (*.f64 1/6 x))
(fma.f64 1/6 x 1/2)
(+.f64 1/2 (*.f64 1/6 x))
(fma.f64 1/6 x 1/2)
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))
(+.f64 1 (*.f64 x (fma.f64 1/6 x 1/2)))
(fma.f64 x (fma.f64 1/6 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))
(+.f64 1 (*.f64 x (fma.f64 1/6 x 1/2)))
(fma.f64 x (fma.f64 1/6 x 1/2) 1)
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(+.f64 (*.f64 1/2 x) (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 1/2 x (*.f64 1/6 (*.f64 x x)))
(fma.f64 1/6 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (fma.f64 1/6 x 1/2))
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/6 (pow.f64 x 2))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(+.f64 1 (*.f64 x (fma.f64 1/6 x 1/2)))
(fma.f64 x (fma.f64 1/6 x 1/2) 1)
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/6 (pow.f64 x 2))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(+.f64 1 (*.f64 x (fma.f64 1/6 x 1/2)))
(fma.f64 x (fma.f64 1/6 x 1/2) 1)
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(+.f64 (*.f64 1/2 x) (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 1/2 x (*.f64 1/6 (*.f64 x x)))
(fma.f64 1/6 (*.f64 x x) (*.f64 1/2 x))
(*.f64 x (fma.f64 1/6 x 1/2))
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/6 (pow.f64 x 2))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(+.f64 1 (*.f64 x (fma.f64 1/6 x 1/2)))
(fma.f64 x (fma.f64 1/6 x 1/2) 1)
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/6 (pow.f64 x 2))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(+.f64 1 (*.f64 x (fma.f64 1/6 x 1/2)))
(fma.f64 x (fma.f64 1/6 x 1/2) 1)

eval113.0ms (2.6%)

Compiler

Compiled 1904 to 1100 computations (42.2% saved)

prune63.0ms (1.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1782180
Fresh011
Picked101
Done033
Total1796185
Error
0b
Counts
185 → 6
Alt Table
Click to see full alt table
StatusErrorProgram
17.6b
1
61.7b
(*.f64 1/6 (*.f64 x x))
0.2b
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
17.6b
(+.f64 (*.f64 1/2 x) 1)
0.0b
(/.f64 (expm1.f64 x) x)
17.4b
(fma.f64 x (+.f64 (*.f64 x 1/6) 1/2) 1)
Compiler

Compiled 36 to 27 computations (25% saved)

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.2b
(*.f64 1/6 (*.f64 x x))
Compiler

Compiled 11 to 5 computations (54.5% saved)

series3.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
(*.f64 1/6 (*.f64 x x))
1.0ms
x
@inf
(*.f64 1/6 (*.f64 x x))
1.0ms
x
@-inf
(*.f64 1/6 (*.f64 x x))

rewrite83.0ms (1.9%)

Algorithm
batch-egg-rewrite
Rules
432×pow1_binary64
421×add-sqr-sqrt_binary64
411×*-un-lft-identity_binary64
402×add-log-exp_binary64
402×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
11027
211487
Stop Event
node limit
Counts
1 → 14
Calls
Call 1
Inputs
(*.f64 1/6 (*.f64 x x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 1/6 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 1/6) (*.f64 x x))) (cbrt.f64 (pow.f64 (exp.f64 1/6) (*.f64 x x))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/6) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/6) (*.f64 x x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 1/6) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 1/6 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/6 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 1/6 (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 1/6 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 1/6)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/36 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/6) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 1/6 (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 1/6 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 1/6 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 1/6 (*.f64 x x))))))))

simplify206.0ms (4.7%)

Algorithm
egg-herbie
Rules
1082×sqr-pow_binary64
617×cube-prod_binary64
554×fabs-mul_binary64
523×pow-sqr_binary64
441×associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0684
11284
22384
34484
410584
533184
6125084
7212384
8228784
9247184
10267984
11297684
12337184
13385284
14441884
15510284
16593584
17632784
18661984
19689584
20696984
21700384
22794484
Stop Event
node limit
Counts
26 → 16
Calls
Call 1
Inputs
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
Outputs
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 x (*.f64 1/6 x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 x (*.f64 1/6 x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 x (*.f64 1/6 x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 x (*.f64 1/6 x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 x (*.f64 1/6 x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 x (*.f64 1/6 x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 x (*.f64 1/6 x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 x (*.f64 1/6 x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 x (*.f64 1/6 x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 x (*.f64 1/6 x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 x (*.f64 1/6 x))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(*.f64 x (*.f64 1/6 x))

localize18.0ms (0.4%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 x (+.f64 (*.f64 x 1/6) 1/2) 1)
0.3b
(*.f64 x 1/6)
Compiler

Compiled 21 to 16 computations (23.8% saved)

series38.0ms (0.9%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
33.0ms
x
@inf
(*.f64 x 1/6)
1.0ms
x
@-inf
(*.f64 x 1/6)
1.0ms
x
@0
(*.f64 x 1/6)
1.0ms
x
@inf
(fma.f64 x (+.f64 (*.f64 x 1/6) 1/2) 1)
1.0ms
x
@0
(fma.f64 x (+.f64 (*.f64 x 1/6) 1/2) 1)

rewrite96.0ms (2.2%)

Algorithm
batch-egg-rewrite
Rules
788×pow1_binary64
737×add-log-exp_binary64
737×log1p-expm1-u_binary64
737×expm1-log1p-u_binary64
725×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
116713
2192813
Stop Event
node limit
Counts
2 → 32
Calls
Call 1
Inputs
(*.f64 x 1/6)
(fma.f64 x (+.f64 (*.f64 x 1/6) 1/2) 1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x 1/6)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x 1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x 1/6)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 3) 1/216) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 x x) 1/36))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) 1/216))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x 1/6)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 x (fma.f64 x 1/6 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x (fma.f64 x 1/6 1/2) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x (fma.f64 x 1/6 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)) (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)) 2) (cbrt.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)) (sqrt.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 3) 1) (+.f64 (*.f64 (*.f64 x (fma.f64 x 1/6 1/2)) (*.f64 x (fma.f64 x 1/6 1/2))) (-.f64 1 (*.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x (fma.f64 x 1/6 1/2)) (*.f64 x (fma.f64 x 1/6 1/2))) 1) (-.f64 (*.f64 x (fma.f64 x 1/6 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (fma.f64 x 1/6 1/2) 1)))))))

simplify188.0ms (4.3%)

Algorithm
egg-herbie
Rules
778×sqr-pow_binary64
540×cube-prod_binary64
534×associate-*l*_binary64
529×fabs-mul_binary64
514×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
016162
136162
250160
385138
4197138
5534138
61811138
73139138
83345138
93558138
103778138
114091138
124491138
135004138
145571138
156255138
167092138
177488138
187774138
Stop Event
node limit
Counts
56 → 43
Calls
Call 1
Inputs
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
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)) 1))
(*.f64 1/6 (pow.f64 x 2))
(+.f64 (*.f64 1/2 x) (*.f64 1/6 (pow.f64 x 2)))
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/6 (pow.f64 x 2))))
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/6 (pow.f64 x 2))))
(*.f64 1/6 (pow.f64 x 2))
(+.f64 (*.f64 1/2 x) (*.f64 1/6 (pow.f64 x 2)))
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/6 (pow.f64 x 2))))
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/6 (pow.f64 x 2))))
Outputs
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 x)
(*.f64 1/6 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 1/6 (*.f64 x x) 1))
(fma.f64 1/6 (*.f64 x x) (fma.f64 x 1/2 1))
(fma.f64 x (fma.f64 1/6 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 1/6 (*.f64 x x) 1))
(fma.f64 1/6 (*.f64 x x) (fma.f64 x 1/2 1))
(fma.f64 x (fma.f64 1/6 x 1/2) 1)
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(+.f64 (*.f64 1/2 x) (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 1/2 x (*.f64 1/6 (*.f64 x x)))
(fma.f64 1/6 (*.f64 x x) (*.f64 x 1/2))
(*.f64 x (+.f64 1/2 (*.f64 1/6 x)))
(*.f64 x (fma.f64 1/6 x 1/2))
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/6 (pow.f64 x 2))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(fma.f64 x 1/2 (fma.f64 1/6 (*.f64 x x) 1))
(fma.f64 1/6 (*.f64 x x) (fma.f64 x 1/2 1))
(fma.f64 x (fma.f64 1/6 x 1/2) 1)
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/6 (pow.f64 x 2))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(fma.f64 x 1/2 (fma.f64 1/6 (*.f64 x x) 1))
(fma.f64 1/6 (*.f64 x x) (fma.f64 x 1/2 1))
(fma.f64 x (fma.f64 1/6 x 1/2) 1)
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (*.f64 x x))
(+.f64 (*.f64 1/2 x) (*.f64 1/6 (pow.f64 x 2)))
(fma.f64 1/2 x (*.f64 1/6 (*.f64 x x)))
(fma.f64 1/6 (*.f64 x x) (*.f64 x 1/2))
(*.f64 x (+.f64 1/2 (*.f64 1/6 x)))
(*.f64 x (fma.f64 1/6 x 1/2))
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/6 (pow.f64 x 2))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(fma.f64 x 1/2 (fma.f64 1/6 (*.f64 x x) 1))
(fma.f64 1/6 (*.f64 x x) (fma.f64 x 1/2 1))
(fma.f64 x (fma.f64 1/6 x 1/2) 1)
(+.f64 (*.f64 1/2 x) (+.f64 1 (*.f64 1/6 (pow.f64 x 2))))
(fma.f64 1/2 x (fma.f64 1/6 (*.f64 x x) 1))
(fma.f64 x 1/2 (fma.f64 1/6 (*.f64 x x) 1))
(fma.f64 1/6 (*.f64 x x) (fma.f64 x 1/2 1))
(fma.f64 x (fma.f64 1/6 x 1/2) 1)

eval34.0ms (0.8%)

Compiler

Compiled 596 to 447 computations (25% saved)

prune42.0ms (1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New59059
Fresh011
Picked011
Done044
Total59665
Error
0b
Counts
65 → 6
Alt Table
Click to see full alt table
StatusErrorProgram
17.6b
1
61.7b
(*.f64 1/6 (*.f64 x x))
0.2b
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
17.6b
(+.f64 (*.f64 1/2 x) 1)
0.0b
(/.f64 (expm1.f64 x) x)
17.4b
(fma.f64 x (+.f64 (*.f64 x 1/6) 1/2) 1)
Compiler

Compiled 36 to 27 computations (25% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune5.0ms (0.1%)

Pruning

6 alts after pruning (1 fresh and 5 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done055
Total066
Error
0b
Counts
6 → 6
Alt Table
Click to see full alt table
StatusErrorProgram
17.6b
1
61.7b
(*.f64 1/6 (*.f64 x x))
0.2b
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
17.6b
(+.f64 (*.f64 1/2 x) 1)
0.0b
(/.f64 (expm1.f64 x) x)
17.4b
(fma.f64 x (+.f64 (*.f64 x 1/6) 1/2) 1)
Compiler

Compiled 36 to 27 computations (25% saved)

regimes66.0ms (1.5%)

Counts
8 → 1
Calls
Call 1
Inputs
1
(*.f64 1/6 (*.f64 x x))
(+.f64 (*.f64 1/2 x) 1)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(fma.f64 x (+.f64 (*.f64 x 1/6) 1/2) 1)
(fma.f64 x (fma.f64 x 1/6 1/2) 1)
(pow.f64 (sqrt.f64 (/.f64 (expm1.f64 x) x)) 2)
Outputs
(/.f64 (expm1.f64 x) x)
Calls

3 calls:

46.0ms
(/.f64 (-.f64 (exp.f64 x) 1) x)
11.0ms
x
5.0ms
(/.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 60 to 40 computations (33.3% saved)

regimes12.0ms (0.3%)

Accuracy

Total -44.4b remaining (-252.6%)

Threshold costs -44.4b (-252.6%)

Counts
3 → 1
Calls
Call 1
Inputs
1
(*.f64 1/6 (*.f64 x x))
(+.f64 (*.f64 1/2 x) 1)
Outputs
1
Calls

1 calls:

10.0ms
x
Results
ErrorSegmentsBranch
17.6b1x
Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify6.0ms (0.1%)

Algorithm
egg-herbie
Rules
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
177
Stop Event
fuel
saturated
Calls
Call 1
Inputs
(/.f64 (expm1.f64 x) x)
1
Outputs
(/.f64 (expm1.f64 x) x)
1
Compiler

Compiled 7 to 5 computations (28.6% saved)

soundness42.0ms (1%)

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
81456
92236
103526
115116
125836
136196
Stop Event
saturated
Compiler

Compiled 12 to 8 computations (33.3% saved)

end31.0ms (0.7%)

Compiler

Compiled 6 to 4 computations (33.3% saved)

Profiling

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