Details

Time bar (total: 2.3s)

analyze4.0ms (0.2%)

Algorithm
1×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 (82.7%)

Results
975.0ms2795×body1024valid
456.0ms3825×body256valid
220.0ms1339×body512valid
208.0ms297×body2048valid
0.0ms6×body256invalid

preprocess24.0ms (1.1%)

Algorithm
2×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
1×saturated
1×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)

simplify24.0ms (1.1%)

Algorithm
1×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
1×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)

localize3.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series4.0ms (0.2%)

Counts
2 → 24
Calls

6 calls:

TimeVariablePointExpression
2.0ms
x
@0
(/.f64 (expm1.f64 x) x)
1.0ms
x
@-inf
(/.f64 (expm1.f64 x) x)
1.0ms
x
@inf
(/.f64 (expm1.f64 x) x)
0.0ms
x
@0
(expm1.f64 x)
0.0ms
x
@inf
(expm1.f64 x)

rewrite40.0ms (1.7%)

Algorithm
1×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
049
1839
211049
Stop Event
1×node limit
Counts
2 → 49
Calls
Call 1
Inputs
(/.f64 (expm1.f64 x) 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 (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 expm1.f64 (log1p.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 (exp.f64 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 x) 1)))) (#(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 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 (*.f64 (exp.f64 x) (exp.f64 x)) (+.f64 1 (*.f64 (exp.f64 x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (exp.f64 x) (exp.f64 x)) 1) (+.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 log1p.f64 (expm1.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (expm1.f64 x)))))))

simplify44.0ms (2%)

Algorithm
1×egg-herbie
Rules
803×unswap-sqr_binary64
583×associate-/l/_binary64
534×times-frac_binary64
493×distribute-lft-out_binary64
406×fma-def_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
032157
190155
2198155
3573143
41480143
52562143
65082143
Stop Event
1×node limit
Counts
73 → 66
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)
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
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 1/2 x (fma.f64 x (*.f64 x (fma.f64 x 1/24 1/6)) 1))
(fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) (fma.f64 1/2 x 1))
(fma.f64 x (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 3) 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)
x
(+.f64 (*.f64 1/2 (pow.f64 x 2)) x)
(fma.f64 1/2 (*.f64 x x) x)
(fma.f64 x (*.f64 1/2 x) x)
(*.f64 x (fma.f64 1/2 x 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 1/2 (*.f64 x x) (fma.f64 1/6 (pow.f64 x 3) x))
(*.f64 x (fma.f64 x (fma.f64 x 1/6 1/2) 1))
(+.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 1/2 (*.f64 x x) (fma.f64 1/6 (pow.f64 x 3) (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))
(fma.f64 (*.f64 x x) (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 4) x))
(*.f64 x (fma.f64 (*.f64 x x) (fma.f64 x 1/24 1/6) (fma.f64 1/2 x 1)))
(*.f64 x (fma.f64 x (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 3) 1)))
(-.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)

eval12.0ms (0.5%)

Compiler

Compiled 584 to 291 computations (50.2% saved)

prune35.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New63366
Fresh000
Picked011
Done000
Total63467
Error
0b
Counts
67 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
▶21.4b
(+.f64 (*.f64 1/2 x) 1)
21.1b
1
✓0.0b
(/.f64 (expm1.f64 x) x)
▶0b
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
Compiler

Compiled 20 to 15 computations (25% saved)

localize4.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series2.0ms (0.1%)

Counts
1 → 12
Calls

3 calls:

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

rewrite40.0ms (1.8%)

Algorithm
1×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
1×node limit
Counts
1 → 30
Calls
Call 1
Inputs
(/.f64 x (expm1.f64 x))
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 (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 pow.f64 (/.f64 (expm1.f64 x) x) -1)))) (#(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 expm1.f64 (log1p.f64 (/.f64 x (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (expm1.f64 x))))))))

simplify45.0ms (2%)

Algorithm
1×egg-herbie
Rules
734×associate-*l/_binary64
692×associate-*r/_binary64
439×associate-*l*_binary64
417×fma-def_binary64
342×unswap-sqr_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02089
14585
29285
323879
468079
5214179
6374279
7564879
Stop Event
1×node limit
Counts
42 → 39
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))
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 -1/720 (pow.f64 x 4) (fma.f64 -1/2 x (fma.f64 x (*.f64 x 1/12) 1)))
(fma.f64 -1/720 (pow.f64 x 4) (fma.f64 x (fma.f64 x 1/12 -1/2) 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))

localize3.0ms (0.1%)

eval16.0ms (0.7%)

Compiler

Compiled 704 to 417 computations (40.8% saved)

prune12.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New65065
Fresh011
Picked011
Done022
Total65469
Error
0b
Counts
69 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
✓21.4b
(+.f64 (*.f64 1/2 x) 1)
21.1b
1
✓0.0b
(/.f64 (expm1.f64 x) x)
✓0b
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
Compiler

Compiled 20 to 15 computations (25% 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
✓21.4b
(+.f64 (*.f64 1/2 x) 1)
21.1b
1
✓0.0b
(/.f64 (expm1.f64 x) x)
✓0b
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
Compiler

Compiled 20 to 15 computations (25% 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
✓21.4b
(+.f64 (*.f64 1/2 x) 1)
21.1b
1
✓0.0b
(/.f64 (expm1.f64 x) x)
✓0b
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
Compiler

Compiled 20 to 15 computations (25% saved)

regimes10.0ms (0.5%)

Counts
5 → 1
Calls
Call 1
Inputs
1
(+.f64 (*.f64 1/2 x) 1)
(/.f64 (expm1.f64 x) x)
(/.f64 (-.f64 (exp.f64 x) 1) x)
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
Outputs
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
Calls

3 calls:

4.0ms
x
2.0ms
(/.f64 (-.f64 (exp.f64 x) 1) x)
2.0ms
(/.f64 (-.f64 (exp.f64 x) 1) x)
Results
ErrorSegmentsBranch
0b1x
0b1(/.f64 (-.f64 (exp.f64 x) 1) x)
0b1(/.f64 (-.f64 (exp.f64 x) 1) x)
Compiler

Compiled 39 to 26 computations (33.3% saved)

regimes11.0ms (0.5%)

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

3 calls:

4.0ms
x
2.0ms
(/.f64 (-.f64 (exp.f64 x) 1) x)
2.0ms
(/.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 33 to 23 computations (30.3% saved)

regimes4.0ms (0.2%)

Accuracy

Total -0.8b remaining (-4%)

Threshold costs -0.8b (-4%)

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

1 calls:

3.0ms
x
Results
ErrorSegmentsBranch
21.1b1x
Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify27.0ms (1.2%)

Algorithm
1×egg-herbie
Rules
1×1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0816
11016
Stop Event
1×saturated
Calls
Call 1
Inputs
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
(/.f64 (expm1.f64 x) x)
1
Outputs
(pow.f64 (/.f64 x (expm1.f64 x)) -1)
(/.f64 (expm1.f64 x) x)
1

end21.0ms (0.9%)

Stop Event
1×fuel
Compiler

Compiled 26 to 17 computations (34.6% saved)

Profiling

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