Details

Time bar (total: 3.2s)

analyze2.0ms (0.1%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%74.6%25.4%0
0%74.6%25.4%1
37.3%37.3%25.4%2
37.3%18.7%44%3
46.7%9.3%44%4
46.7%4.7%48.7%5
49%2.3%48.7%6
49%1.2%49.8%7
49.6%0.6%49.8%8
49.9%0.3%49.8%9
49.9%0.1%50%10
49.9%0.1%50.1%11
49.9%0%50.1%12
Compiler

Compiled 8 to 6 computations (25% saved)

sample1.9s (60%)

Results
1.2s4115×body1024valid
366.0ms2084×body512valid
168.0ms1650×body256valid
124.0ms407×body2048valid
0.0ms2×body256invalid

preprocess16.0ms (0.5%)

Algorithm
2×egg-herbie
Rules
1×+-commutative_binary64
1×sub-neg_binary64
1×1-exp_binary64
1×expm1-def_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
053
1113
2123
011
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
Outputs
0
Call 2
Inputs
(-.f64 (exp.f64 x) 1)
Outputs
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify6.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
1×+-commutative_binary64
1×sub-neg_binary64
1×1-exp_binary64
1×expm1-def_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
053
1113
2123
Stop Event
1×saturated
Counts
1 → 2
Calls
Call 1
Inputs
(-.f64 (exp.f64 x) 1)
Outputs
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)

eval0.0ms (0%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.0b
Counts
3 → 2
Alt Table
Click to see full alt table
StatusErrorProgram
▶0.0b
(expm1.f64 x)
▶57.5b
(-.f64 (exp.f64 x) 1)
Compiler

Compiled 8 to 6 computations (25% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(expm1.f64 x)
Compiler

Compiled 4 to 2 computations (50% saved)

series2.0ms (0%)

Counts
1 → 12
Calls

3 calls:

TimeVariablePointExpression
1.0ms
x
@0
(expm1.f64 x)
0.0ms
x
@inf
(expm1.f64 x)
0.0ms
x
@-inf
(expm1.f64 x)

rewrite87.0ms (2.7%)

Algorithm
1×batch-egg-rewrite
Rules
382×expm1-udef_binary64
382×log1p-udef_binary64
255×associate-*r*_binary64
252×pow1_binary64
244×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
033
1573
26403
369853
Stop Event
1×node limit
Counts
1 → 63
Calls
Call 1
Inputs
(expm1.f64 x)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 x)))) (log.f64 (sqrt.f64 (exp.f64 (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (expm1.f64 x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (exp.f64 x) 3) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) 2) (*.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (expm1.f64 x) 1/6) (*.f64 (pow.f64 (expm1.f64 x) 1/6) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 4))) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) 2) (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (expm1.f64 x) 1/4) (sqrt.f64 (pow.f64 (expm1.f64 x) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (expm1.f64 x) 1/4) (*.f64 (pow.f64 (expm1.f64 x) 1/4) (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -1) (/.f64 1 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (exp.f64 x) (exp.f64 x) -1) (/.f64 1 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (expm1.f64 x)) (pow.f64 (expm1.f64 x) 1/4)) (pow.f64 (expm1.f64 x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 5/2)) (pow.f64 (expm1.f64 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 4)) 2)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (expm1.f64 x) 3/2)) (pow.f64 (expm1.f64 x) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 5)) (pow.f64 (expm1.f64 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 4)) 2) 1/3) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (expm1.f64 x) 5/2) 1/3) (pow.f64 (expm1.f64 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 (expm1.f64 x))) (pow.f64 (expm1.f64 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (exp.f64 x)) 1) (-.f64 (sqrt.f64 (exp.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (expm1.f64 x)) (cbrt.f64 (cbrt.f64 (pow.f64 (expm1.f64 x) 4)))) (pow.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (expm1.f64 x))) 2)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (pow.f64 (expm1.f64 x) 1/6)) (pow.f64 (expm1.f64 x) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (+.f64 (pow.f64 (exp.f64 x) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (exp.f64 x)) (fma.f64 (exp.f64 x) (exp.f64 x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -1) (+.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (*.f64 (exp.f64 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (exp.f64 x) (exp.f64 x) -1) (+.f64 1 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (exp.f64 x) (exp.f64 x) -1) (-.f64 (exp.f64 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -1)) (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) -1)) (neg.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -1) 1) (+.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) -1) 1) (+.f64 1 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (expm1.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (expm1.f64 x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (expm1.f64 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (expm1.f64 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (expm1.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (expm1.f64 x)) 2))) (cbrt.f64 (log.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (expm1.f64 x)))) (sqrt.f64 (log.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (expm1.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (expm1.f64 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (expm1.f64 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (expm1.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (exp.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) -1)))))

simplify91.0ms (2.9%)

Algorithm
1×egg-herbie
Rules
881×fma-def_binary64
803×unswap-sqr_binary64
610×associate-/l/_binary64
507×distribute-lft-out_binary64
349×*-commutative_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02270
15970
212670
337264
4116463
5303463
6509863
7541963
8617663
Stop Event
1×node limit
Counts
75 → 71
Calls
Call 1
Inputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x)))
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
(-.f64 (exp.f64 x) 1)
Outputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(fma.f64 1/2 (*.f64 x x) x)
(*.f64 x (fma.f64 x 1/2 1))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) x))
(fma.f64 x (*.f64 x 1/2) (fma.f64 1/6 (pow.f64 x 3) x))
(fma.f64 (*.f64 x x) (fma.f64 x 1/6 1/2) x)
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 4) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 x (*.f64 x 1/2) (fma.f64 1/24 (pow.f64 x 4) x)))
(fma.f64 (*.f64 x x) (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 4) x))
(fma.f64 x (*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/24 1/6)))) x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)
(-.f64 (exp.f64 x) 1)
(expm1.f64 x)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓7.6b
(-.f64 (exp.f64 x) 1)
Compiler

Compiled 9 to 5 computations (44.4% saved)

series1.0ms (0%)

Counts
1 → 4
Calls

3 calls:

TimeVariablePointExpression
0.0ms
x
@0
(-.f64 (exp.f64 x) 1)
0.0ms
x
@-inf
(-.f64 (exp.f64 x) 1)
0.0ms
x
@inf
(-.f64 (exp.f64 x) 1)

rewrite41.0ms (1.3%)

Algorithm
1×batch-egg-rewrite
Rules
459×pow1_binary64
448×add-sqr-sqrt_binary64
440×*-un-lft-identity_binary64
428×add-log-exp_binary64
427×log1p-expm1-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
053
11013
211963
Stop Event
1×node limit
Counts
1 → 31
Calls
Call 1
Inputs
(-.f64 (exp.f64 x) 1)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (exp.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (expm1.f64 x)) (pow.f64 (cbrt.f64 (expm1.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 x)) 2) (cbrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -1) (/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (/.f64 1 (+.f64 (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (exp.f64 x)) 1) (-.f64 (sqrt.f64 (exp.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) 1)) (+.f64 (pow.f64 (exp.f64 x) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (exp.f64 x) 1) (+.f64 (pow.f64 (exp.f64 x) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -1) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -1) (+.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (*.f64 (exp.f64 x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (-.f64 (exp.f64 x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 3) -1)) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1)) (neg.f64 (+.f64 (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (expm1.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (expm1.f64 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (expm1.f64 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (expm1.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (expm1.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (expm1.f64 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 x)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (exp.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) -1)))))

simplify127.0ms (4%)

Algorithm
1×egg-herbie
Rules
881×fma-def_binary64
803×unswap-sqr_binary64
525×distribute-lft-out_binary64
507×*-commutative_binary64
486×sqr-pow_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01946
15146
211946
336940
4115539
5299439
6500239
7515139
8540539
9573339
10624739
11683939
12735539
13790939
Stop Event
1×node limit
Counts
35 → 38
Calls
Call 1
Inputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x)))
Outputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(fma.f64 1/2 (*.f64 x x) x)
(*.f64 x (fma.f64 x 1/2 1))
(fma.f64 x (*.f64 x 1/2) x)
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) x))
(fma.f64 x (*.f64 x 1/2) (fma.f64 1/6 (pow.f64 x 3) x))
(fma.f64 (*.f64 x x) (fma.f64 x 1/6 1/2) x)
(fma.f64 x (*.f64 x (fma.f64 x 1/6 1/2)) x)
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 4) x)))
(fma.f64 x (*.f64 x 1/2) (fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/24 (pow.f64 x 4) x)))
(fma.f64 1/24 (pow.f64 x 4) (fma.f64 (*.f64 x x) (fma.f64 x 1/6 1/2) x))
(fma.f64 x (*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/24 1/6)))) x)

eval23.0ms (0.7%)

Compiler

Compiled 1057 to 573 computations (45.8% saved)

prune15.0ms (0.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1072109
Fresh000
Picked011
Done011
Total1074111
Error
0b
Counts
111 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
2.2b
x
▶57.5b
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
✓0.0b
(expm1.f64 x)
✓57.5b
(-.f64 (exp.f64 x) 1)
Compiler

Compiled 27 to 19 computations (29.6% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))
✓0.0b
(/.f64 1 (+.f64 1 (exp.f64 x)))
✓0.0b
(pow.f64 (exp.f64 x) 2)
✓7.5b
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
Compiler

Compiled 45 to 27 computations (40% saved)

series6.0ms (0.2%)

Counts
4 → 16
Calls

12 calls:

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

rewrite99.0ms (3.1%)

Algorithm
1×batch-egg-rewrite
Rules
508×log-prod_binary64
481×fma-def_binary64
352×pow-prod-down_binary64
278×pow2_binary64
255×fma-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01046
122942
2333942
Stop Event
1×node limit
Counts
4 → 257
Calls
Call 1
Inputs
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(pow.f64 (exp.f64 x) 2)
(/.f64 1 (+.f64 1 (exp.f64 x)))
(/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x)))) (/.f64 -1 (+.f64 (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x)))) (*.f64 (/.f64 -1 (+.f64 (exp.f64 x) 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1)) (fma.f64 (/.f64 -1 (+.f64 (exp.f64 x) 1)) 1 (/.f64 1 (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1)) (fma.f64 (neg.f64 (/.f64 1 (cbrt.f64 (+.f64 (exp.f64 x) 1)))) (cbrt.f64 (pow.f64 (+.f64 (exp.f64 x) 1) -2)) (/.f64 1 (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1)) (+.f64 (/.f64 -1 (+.f64 (exp.f64 x) 1)) (/.f64 1 (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 -1 (+.f64 (exp.f64 x) 1)) (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (exp.f64 x) 1)) (expm1.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 (exp.f64 x) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x)))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x))))))) (log.f64 (sqrt.f64 (exp.f64 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 x) (*.f64 (exp.f64 x) (/.f64 1 (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (exp.f64 x) 2) (/.f64 1 (+.f64 (exp.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 (exp.f64 x) 1)) (pow.f64 (exp.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x))))) (cbrt.f64 (exp.f64 (-.f64 (*.f64 4 x) (*.f64 2 (log1p.f64 (exp.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (exp.f64 (-.f64 (*.f64 4 x) (*.f64 2 (log1p.f64 (exp.f64 x)))))) (cbrt.f64 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 4)) (*.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 2)) (/.f64 1 (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (exp.f64 (-.f64 x (*.f64 1/2 (log1p.f64 (exp.f64 x))))) (exp.f64 (-.f64 x (*.f64 1/2 (log1p.f64 (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 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(exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 4)) (sqrt.f64 (+.f64 (exp.f64 x) 1))) (/.f64 (cbrt.f64 (pow.f64 (exp.f64 x) 2)) (sqrt.f64 (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 (*.f64 3 x)))) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (pow.f64 (exp.f64 x) 2))) (-.f64 1 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (exp.f64 x) 2) (cbrt.f64 (pow.f64 (+.f64 (exp.f64 x) 1) -2))) (/.f64 1 (cbrt.f64 (+.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (+.f64 (exp.f64 x) 1) -1/2)) (pow.f64 (+.f64 (exp.f64 x) 1) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (-.f64 (*.f64 4 x) (*.f64 2 (log1p.f64 (exp.f64 x))))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (-.f64 x (*.f64 1/2 (log1p.f64 (exp.f64 x))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (-.f64 (log1p.f64 (exp.f64 x)) (+.f64 x x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (exp.f64 (-.f64 (log1p.f64 (exp.f64 x)) (+.f64 x x))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (+.f64 (exp.f64 x) 1) -1/2) (exp.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (+.f64 (exp.f64 x) 1) -3) (pow.f64 (exp.f64 x) 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 (cbrt.f64 (+.f64 (exp.f64 x) 1))) (cbrt.f64 (pow.f64 (exp.f64 x) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 -1 (neg.f64 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (exp.f64 (-.f64 (*.f64 4 x) (*.f64 2 (log1p.f64 (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (-.f64 (+.f64 x x) (log1p.f64 (exp.f64 x))) 1))))))

simplify146.0ms (4.6%)

Algorithm
1×egg-herbie
Rules
809×fma-def_binary64
668×distribute-lft-out_binary64
663×*-commutative_binary64
410×sqr-pow_binary64
394×distribute-rgt-out_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
047169
1121165
2323151
31019139
42905139
54405139
65136139
75567139
86425139
96649139
106931139
117344139
127743139
Stop Event
1×node limit
Counts
273 → 284
Calls
Call 1
Inputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x)))
1
(+.f64 (*.f64 2 x) 1)
(+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 (*.f64 2 x) 1))
(+.f64 (*.f64 4/3 (pow.f64 x 3)) (+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 (*.f64 2 x) 1)))
1/2
(+.f64 1/2 (*.f64 -1/4 x))
(+.f64 1/2 (+.f64 (*.f64 -1/4 x) (*.f64 1/48 (pow.f64 x 3))))
(+.f64 (*.f64 -1/480 (pow.f64 x 5)) (+.f64 1/2 (+.f64 (*.f64 -1/4 x) (*.f64 1/48 (pow.f64 x 3)))))
1/2
(+.f64 1/2 (*.f64 3/4 x))
(+.f64 1/2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 3/4 x)))
(+.f64 (*.f64 3/16 (pow.f64 x 3)) (+.f64 1/2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 3/4 x))))
Outputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(fma.f64 1/2 (*.f64 x x) x)
(fma.f64 x (*.f64 x 1/2) x)
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) x))
(fma.f64 x (*.f64 x 1/2) (fma.f64 1/6 (pow.f64 x 3) x))
(fma.f64 (*.f64 x x) (fma.f64 x 1/6 1/2) x)
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 4) x)))
(fma.f64 x (*.f64 x 1/2) (fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/24 (pow.f64 x 4) x)))
(fma.f64 (*.f64 x x) (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 4) x))
1
(+.f64 (*.f64 2 x) 1)
(fma.f64 2 x 1)
(fma.f64 x 2 1)
(+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 (*.f64 2 x) 1))
(fma.f64 2 (*.f64 x x) (fma.f64 2 x 1))
(fma.f64 2 (*.f64 x x) (fma.f64 x 2 1))
(fma.f64 2 (fma.f64 x x x) 1)
(fma.f64 x (fma.f64 x 2 2) 1)
(+.f64 (*.f64 4/3 (pow.f64 x 3)) (+.f64 (*.f64 2 (pow.f64 x 2)) (+.f64 (*.f64 2 x) 1)))
(fma.f64 4/3 (pow.f64 x 3) (fma.f64 2 (*.f64 x x) (fma.f64 2 x 1)))
(fma.f64 (pow.f64 x 3) 4/3 (fma.f64 2 (*.f64 x x) (fma.f64 x 2 1)))
(fma.f64 (pow.f64 x 3) 4/3 (fma.f64 2 (fma.f64 x x x) 1))
(fma.f64 x (fma.f64 x 2 2) (fma.f64 (pow.f64 x 3) 4/3 1))
(fma.f64 x 2 (fma.f64 (*.f64 x x) (fma.f64 x 4/3 2) 1))
1/2
(+.f64 1/2 (*.f64 -1/4 x))
(+.f64 1/2 (*.f64 x -1/4))
(fma.f64 x -1/4 1/2)
(+.f64 1/2 (+.f64 (*.f64 -1/4 x) (*.f64 1/48 (pow.f64 x 3))))
(+.f64 1/2 (fma.f64 -1/4 x (*.f64 (pow.f64 x 3) 1/48)))
(+.f64 1/2 (fma.f64 (pow.f64 x 3) 1/48 (*.f64 x -1/4)))
(fma.f64 x -1/4 (fma.f64 (pow.f64 x 3) 1/48 1/2))
(+.f64 (*.f64 -1/480 (pow.f64 x 5)) (+.f64 1/2 (+.f64 (*.f64 -1/4 x) (*.f64 1/48 (pow.f64 x 3)))))
(fma.f64 -1/480 (pow.f64 x 5) (+.f64 1/2 (fma.f64 -1/4 x (*.f64 (pow.f64 x 3) 1/48))))
(+.f64 (fma.f64 (pow.f64 x 3) 1/48 (*.f64 x -1/4)) (fma.f64 -1/480 (pow.f64 x 5) 1/2))
(fma.f64 -1/480 (pow.f64 x 5) (fma.f64 x -1/4 (fma.f64 (pow.f64 x 3) 1/48 1/2)))
(fma.f64 (pow.f64 x 3) 1/48 (fma.f64 -1/480 (pow.f64 x 5) (fma.f64 x -1/4 1/2)))
(fma.f64 x -1/4 (fma.f64 -1/480 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) 1/48 1/2)))
1/2
(+.f64 1/2 (*.f64 3/4 x))
(+.f64 1/2 (*.f64 x 3/4))
(fma.f64 x 3/4 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 3/4 x)))
(+.f64 1/2 (fma.f64 1/2 (*.f64 x x) (*.f64 x 3/4)))
(+.f64 (*.f64 (*.f64 1/2 x) x) (fma.f64 x 3/4 1/2))
(fma.f64 x 3/4 (*.f64 1/2 (fma.f64 x x 1)))
(fma.f64 x (fma.f64 x 1/2 3/4) 1/2)
(+.f64 (*.f64 3/16 (pow.f64 x 3)) (+.f64 1/2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 3/4 x))))
(fma.f64 3/16 (pow.f64 x 3) (+.f64 1/2 (fma.f64 1/2 (*.f64 x x) (*.f64 x 3/4))))
(fma.f64 (pow.f64 x 3) 3/16 (+.f64 (*.f64 (*.f64 1/2 x) x) (fma.f64 x 3/4 1/2)))
(fma.f64 (pow.f64 x 3) 3/16 (fma.f64 x 3/4 (*.f64 1/2 (fma.f64 x x 1))))
(fma.f64 x (fma.f64 x 1/2 3/4) (fma.f64 (pow.f64 x 3) 3/16 1/2))

eval115.0ms (3.6%)

Compiler

Compiled 6579 to 3916 computations (40.5% saved)

prune34.0ms (1.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New2831284
Fresh011
Picked101
Done022
Total2844288
Error
0b
Counts
288 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
2.2b
x
▶57.4b
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
✓0.0b
(expm1.f64 x)
✓57.5b
(-.f64 (exp.f64 x) 1)
Compiler

Compiled 27 to 19 computations (29.6% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.0b
(+.f64 1 (exp.f64 x))
✓0.0b
(/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x)))
0.0b
(/.f64 1 (+.f64 1 (exp.f64 x)))
✓7.7b
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
Compiler

Compiled 47 to 22 computations (53.2% saved)

series4.0ms (0.1%)

Counts
3 → 28
Calls

9 calls:

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

rewrite94.0ms (2.9%)

Algorithm
1×batch-egg-rewrite
Rules
562×fma-def_binary64
519×log-prod_binary64
300×fma-neg_binary64
276×pow2_binary64
222×log-div_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01037
123033
2365633
Stop Event
1×node limit
Counts
3 → 252
Calls
Call 1
Inputs
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x)))
(+.f64 1 (exp.f64 x))
Outputs
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(exp.f64 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (exp.f64 (/.f64 0 0))) (/.f64 1 (-.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1) (+.f64 1 (pow.f64 (exp.f64 x) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (exp.f64 (/.f64 0 0)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (expm1.f64 (/.f64 0 0)) (expm1.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (+.f64 1 (exp.f64 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (neg.f64 (exp.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (+.f64 (exp.f64 (/.f64 0 0)) (-.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (exp.f64 (/.f64 0 0))) (-.f64 1 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (neg.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (exp.f64 (/.f64 0 0)))) (neg.f64 (-.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) 1) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (exp.f64 (/.f64 0 0))) 1) (-.f64 1 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1 (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (+.f64 1 (exp.f64 x)))) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -1/2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) -3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1) (+.f64 1 (pow.f64 (exp.f64 x) 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (exp.f64 (/.f64 0 0)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1 (exp.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1 (exp.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (exp.f64 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (exp.f64 x) 1 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (exp.f64 x)) (cbrt.f64 (exp.f64 (/.f64 0 0))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (exp.f64 (/.f64 0 0))) (cbrt.f64 (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 4)) (sqrt.f64 (cbrt.f64 (exp.f64 (/.f64 0 0)))) 1)))))

simplify75.0ms (2.3%)

Algorithm
1×egg-herbie
Rules
560×distribute-lft-out_binary64
544×fma-def_binary64
410×fma-neg_binary64
361×associate-/l*_binary64
317×distribute-rgt-out_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
044435
1113433
2265429
3774412
42185412
53952364
67622364
Stop Event
1×node limit
Counts
280 → 279
Calls
Call 1
Inputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x)))
(-.f64 (/.f64 (exp.f64 (*.f64 2 x)) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (exp.f64 (*.f64 2 x)) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (exp.f64 (*.f64 2 x)) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (exp.f64 (*.f64 2 x)) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
1/2
(+.f64 1/2 (*.f64 3/4 x))
(+.f64 1/2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 3/4 x)))
(+.f64 (*.f64 3/16 (pow.f64 x 3)) (+.f64 1/2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 3/4 x))))
(/.f64 (exp.f64 (*.f64 2 x)) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 (*.f64 2 x)) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 (*.f64 2 x)) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 (*.f64 2 x)) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) (+.f64 1 (exp.f64 x)))
2
(+.f64 2 x)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
Outputs
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(fma.f64 1/2 (*.f64 x x) x)
(fma.f64 x (*.f64 x 1/2) x)
(*.f64 x (fma.f64 x 1/2 1))
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) x))
(fma.f64 x (*.f64 x 1/2) (fma.f64 1/6 (pow.f64 x 3) x))
(fma.f64 x (*.f64 x (fma.f64 x 1/6 1/2)) x)
(fma.f64 (*.f64 x x) (fma.f64 x 1/6 1/2) x)
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 (*.f64 1/2 (pow.f64 x 2)) (+.f64 (*.f64 1/24 (pow.f64 x 4)) x)))
(fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/2 (*.f64 x x) (fma.f64 1/24 (pow.f64 x 4) x)))
(fma.f64 x (*.f64 x 1/2) (fma.f64 1/6 (pow.f64 x 3) (fma.f64 1/24 (pow.f64 x 4) x)))
(fma.f64 (*.f64 x x) (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 4) x))
(fma.f64 x (*.f64 x (fma.f64 x 1/6 1/2)) (fma.f64 1/24 (pow.f64 x 4) x))
(-.f64 (/.f64 (exp.f64 (*.f64 2 x)) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 -1 (+.f64 1 (exp.f64 x))))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x))) (/.f64 -1 (+.f64 1 (exp.f64 x))))
(*.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) (+.f64 (pow.f64 (exp.f64 x) 2) -1))
(-.f64 (/.f64 (exp.f64 (*.f64 2 x)) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 -1 (+.f64 1 (exp.f64 x))))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x))) (/.f64 -1 (+.f64 1 (exp.f64 x))))
(*.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) (+.f64 (pow.f64 (exp.f64 x) 2) -1))
(-.f64 (/.f64 (exp.f64 (*.f64 2 x)) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 -1 (+.f64 1 (exp.f64 x))))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x))) (/.f64 -1 (+.f64 1 (exp.f64 x))))
(*.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) (+.f64 (pow.f64 (exp.f64 x) 2) -1))
(-.f64 (/.f64 (exp.f64 (*.f64 2 x)) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 -1 (+.f64 1 (exp.f64 x))))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x))) (/.f64 -1 (+.f64 1 (exp.f64 x))))
(*.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) (+.f64 (pow.f64 (exp.f64 x) 2) -1))
(-.f64 (/.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 -1 (+.f64 1 (exp.f64 x))))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x))) (/.f64 -1 (+.f64 1 (exp.f64 x))))
(*.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) (+.f64 (pow.f64 (exp.f64 x) 2) -1))
(-.f64 (/.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 -1 (+.f64 1 (exp.f64 x))))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x))) (/.f64 -1 (+.f64 1 (exp.f64 x))))
(*.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) (+.f64 (pow.f64 (exp.f64 x) 2) -1))
(-.f64 (/.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 -1 (+.f64 1 (exp.f64 x))))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x))) (/.f64 -1 (+.f64 1 (exp.f64 x))))
(*.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) (+.f64 (pow.f64 (exp.f64 x) 2) -1))
(-.f64 (/.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
(+.f64 (/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x))) (/.f64 -1 (+.f64 1 (exp.f64 x))))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x))) (/.f64 -1 (+.f64 1 (exp.f64 x))))
(*.f64 (/.f64 1 (+.f64 1 (exp.f64 x))) (+.f64 (pow.f64 (exp.f64 x) 2) -1))
1/2
(+.f64 1/2 (*.f64 3/4 x))
(+.f64 1/2 (*.f64 x 3/4))
(fma.f64 x 3/4 1/2)
(+.f64 1/2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 3/4 x)))
(+.f64 1/2 (fma.f64 1/2 (*.f64 x x) (*.f64 x 3/4)))
(+.f64 1/2 (fma.f64 x 3/4 (*.f64 1/2 (*.f64 x x))))
(fma.f64 x 3/4 (fma.f64 x (*.f64 x 1/2) 1/2))
(fma.f64 x (fma.f64 x 1/2 3/4) 1/2)
(+.f64 (*.f64 3/16 (pow.f64 x 3)) (+.f64 1/2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) (*.f64 3/4 x))))
(fma.f64 3/16 (pow.f64 x 3) (+.f64 1/2 (fma.f64 1/2 (*.f64 x x) (*.f64 x 3/4))))
(+.f64 (fma.f64 x 3/4 (*.f64 1/2 (*.f64 x x))) (fma.f64 (pow.f64 x 3) 3/16 1/2))
(fma.f64 (pow.f64 x 3) 3/16 (fma.f64 x 3/4 (fma.f64 x (*.f64 x 1/2) 1/2)))
(fma.f64 x (fma.f64 x 1/2 3/4) (fma.f64 (pow.f64 x 3) 3/16 1/2))
(/.f64 (exp.f64 (*.f64 2 x)) (+.f64 1 (exp.f64 x)))
(/.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (exp.f64 x)))
(/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 x) (+.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 (exp.f64 (*.f64 2 x)) (+.f64 1 (exp.f64 x)))
(/.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (exp.f64 x)))
(/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 x) (+.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 (exp.f64 (*.f64 2 x)) (+.f64 1 (exp.f64 x)))
(/.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (exp.f64 x)))
(/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 x) (+.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 (exp.f64 (*.f64 2 x)) (+.f64 1 (exp.f64 x)))
(/.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (exp.f64 x)))
(/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 x) (+.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) (+.f64 1 (exp.f64 x)))
(/.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (exp.f64 x)))
(/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 x) (+.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) (+.f64 1 (exp.f64 x)))
(/.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (exp.f64 x)))
(/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 x) (+.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) (+.f64 1 (exp.f64 x)))
(/.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (exp.f64 x)))
(/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 x) (+.f64 1 (exp.f64 (neg.f64 x))))
(/.f64 (exp.f64 (neg.f64 (*.f64 -2 x))) (+.f64 1 (exp.f64 x)))
(/.f64 (pow.f64 (exp.f64 2) x) (+.f64 1 (exp.f64 x)))
(/.f64 (pow.f64 (exp.f64 x) 2) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x)))
(/.f64 (exp.f64 x) (+.f64 1 (exp.f64 (neg.f64 x))))
2
(+.f64 2 x)
(+.f64 x 2)
(+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x))
(+.f64 2 (fma.f64 1/2 (*.f64 x x) x))
(+.f64 x (fma.f64 x (*.f64 x 1/2) 2))
(fma.f64 (fma.f64 x 1/2 1) x 2)
(+.f64 (*.f64 1/6 (pow.f64 x 3)) (+.f64 2 (+.f64 (*.f64 1/2 (pow.f64 x 2)) x)))
(fma.f64 1/6 (pow.f64 x 3) (+.f64 2 (fma.f64 1/2 (*.f64 x x) x)))
(+.f64 (fma.f64 1/2 (*.f64 x x) x) (fma.f64 1/6 (pow.f64 x 3) 2))
(+.f64 (fma.f64 x (*.f64 x 1/2) x) (fma.f64 1/6 (pow.f64 x 3) 2))
(fma.f64 x (*.f64 x (fma.f64 x 1/6 1/2)) (+.f64 x 2))
(+.f64 x (fma.f64 (*.f64 x x) (fma.f64 x 1/6 1/2) 2))

eval161.0ms (5.1%)

Compiler

Compiled 8585 to 5766 computations (32.8% saved)

prune47.0ms (1.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New3761377
Fresh101
Picked011
Done022
Total3774381
Error
0b
Counts
381 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
✓57.4b
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
2.2b
x
✓0.0b
(expm1.f64 x)
✓57.5b
(-.f64 (exp.f64 x) 1)
Compiler

Compiled 27 to 19 computations (29.6% saved)

eval0.0ms (0%)

Compiler

Compiled 1 to 1 computations (0% saved)

prune2.0ms (0.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New000
Fresh011
Picked000
Done033
Total044
Error
0b
Counts
4 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
✓57.4b
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 1 (exp.f64 x))) (/.f64 1 (+.f64 1 (exp.f64 x))))
2.2b
x
✓0.0b
(expm1.f64 x)
✓57.5b
(-.f64 (exp.f64 x) 1)
Compiler

Compiled 27 to 19 computations (29.6% saved)

regimes13.0ms (0.4%)

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

4 calls:

5.0ms
x
3.0ms
(exp.f64 x)
2.0ms
(-.f64 (exp.f64 x) 1)
2.0ms
(exp.f64 x)
Results
ErrorSegmentsBranch
0.0b1x
0.0b1(-.f64 (exp.f64 x) 1)
0.0b1(exp.f64 x)
0.0b1(exp.f64 x)
Compiler

Compiled 54 to 34 computations (37% saved)

regimes4.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts
2 → 1
Calls
Call 1
Inputs
x
x
Outputs
x
Calls

1 calls:

3.0ms
x
Results
ErrorSegmentsBranch
2.2b1x
Compiler

Compiled 5 to 2 computations (60% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
034
Stop Event
1×fuel
1×saturated
Calls
Call 1
Inputs
(expm1.f64 x)
x
Outputs
(expm1.f64 x)
x
Compiler

Compiled 5 to 3 computations (40% saved)

soundness7.0ms (0.2%)

Algorithm
1×egg-herbie
Rules
1×+-commutative_binary64
1×sub-neg_binary64
1×1-exp_binary64
1×expm1-def_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
053
1113
2123
Stop Event
1×saturated
Compiler

Compiled 8 to 6 computations (25% saved)

end14.0ms (0.5%)

Compiler

Compiled 4 to 2 computations (50% saved)

Profiling

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