Details

Time bar (total: 2.5s)

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 (78%)

Results
1.2s4106×body1024valid
367.0ms2100×body512valid
155.0ms1602×body256valid
153.0ms448×body2048valid
0.0ms2×body256invalid

preprocess16.0ms (0.7%)

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 (0.1%)

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)
▶58.1b
(-.f64 (exp.f64 x) 1)
Compiler

Compiled 8 to 6 computations (25% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
8.3b
(-.f64 (exp.f64 x) 1)
✓8.3b
(-.f64 (exp.f64 x) 1)
Compiler

Compiled 9 to 5 computations (44.4% saved)

series2.0ms (0.1%)

Counts
1 → 4
Calls

3 calls:

TimeVariablePointExpression
1.0ms
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)

rewrite39.0ms (1.6%)

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
211943
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 (+.f64 (pow.f64 (exp.f64 x) 2) (+.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 (+.f64 (pow.f64 (exp.f64 x) 2) (+.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) (+.f64 (pow.f64 (exp.f64 x) 2) (+.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 (+.f64 (pow.f64 (exp.f64 x) 2) (+.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 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)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 x)))))

simplify93.0ms (3.8%)

Algorithm
1×egg-herbie
Rules
881×fma-def_binary64
803×unswap-sqr_binary64
538×*-commutative_binary64
521×distribute-lft-out_binary64
505×sqr-pow_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01946
15146
211946
336840
4109539
5292839
6493639
7508539
8533939
9566539
10618139
11677339
12728839
13783939
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)
(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)
(+.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 x (*.f64 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)
(fma.f64 (*.f64 x x) (+.f64 1/2 (*.f64 x (fma.f64 x 1/24 1/6))) x)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiled 4 to 2 computations (50% saved)

series1.0ms (0%)

Counts
1 → 12
Calls

3 calls:

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

rewrite80.0ms (3.3%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
033
1573
26403
369343
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 (cbrt.f64 (pow.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) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 1 (exp.f64 x)))) (/.f64 1 (fma.f64 (exp.f64 x) (exp.f64 x) (+.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 (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 (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 (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 (fma.f64 (exp.f64 x) (exp.f64 x) (+.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 (cbrt.f64 (pow.f64 (expm1.f64 x) 4)) 2)) (cbrt.f64 (cbrt.f64 (expm1.f64 x))))))) (#(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 (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 (sqrt.f64 (pow.f64 (expm1.f64 x) 3/2)) (pow.f64 (expm1.f64 x) 1/4))))) (#(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 (fma.f64 (exp.f64 x) (exp.f64 x) (+.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) (fma.f64 (exp.f64 x) (exp.f64 x) (+.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 (fma.f64 (exp.f64 x) (exp.f64 x) (+.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) (fma.f64 (exp.f64 x) (exp.f64 x) (+.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)))))

simplify54.0ms (2.2%)

Algorithm
1×egg-herbie
Rules
881×fma-def_binary64
803×unswap-sqr_binary64
609×associate-/l/_binary64
499×distribute-lft-out_binary64
494×associate-/r/_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02270
15970
212670
337264
4109763
5294863
6501263
7533363
8608963
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)
(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 1/6 (pow.f64 x 3) (fma.f64 x (*.f64 x 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))
(fma.f64 x (*.f64 x (+.f64 1/2 (*.f64 x (fma.f64 x 1/24 1/6)))) x)
(fma.f64 (*.f64 x 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)

eval23.0ms (0.9%)

Compiler

Compiled 1057 to 567 computations (46.4% saved)

prune15.0ms (0.6%)

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
✓0.0b
(expm1.f64 x)
2.0b
x
▶35.9b
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 2))
✓58.1b
(-.f64 (exp.f64 x) 1)
Compiler

Compiled 18 to 14 computations (22.2% saved)

localize11.0ms (0.5%)

Local error

Found 6 expressions with local error:

NewErrorProgram
2.6b
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 2))
0.0b
(expm1.f64 x)
0.0b
(log.f64 (sqrt.f64 (expm1.f64 x)))
✓0.0b
(log.f64 (sqrt.f64 (expm1.f64 x)))
0.0b
(expm1.f64 x)
✓2.6b
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 2))
Compiler

Compiled 25 to 10 computations (60% saved)

series51.0ms (2.1%)

Counts
2 → 16
Calls

6 calls:

TimeVariablePointExpression
26.0ms
x
@inf
(log.f64 (sqrt.f64 (expm1.f64 x)))
20.0ms
x
@-inf
(log.f64 (sqrt.f64 (expm1.f64 x)))
1.0ms
x
@0
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 2))
1.0ms
x
@0
(log.f64 (sqrt.f64 (expm1.f64 x)))
1.0ms
x
@-inf
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 2))

rewrite52.0ms (2.1%)

Algorithm
1×batch-egg-rewrite
Rules
543×pow1_binary64
525×add-sqr-sqrt_binary64
502×add-log-exp_binary64
502×log1p-expm1-u_binary64
502×expm1-log1p-u_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0810
115410
2145010
Stop Event
1×node limit
Counts
2 → 48
Calls
Call 1
Inputs
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 2))
(log.f64 (sqrt.f64 (expm1.f64 x)))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (-.f64 (expm1.f64 x) 1))))) (#(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 (sqrt.f64 (expm1.f64 x)) (sqrt.f64 (expm1.f64 x)))))) (#(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 (cbrt.f64 (expm1.f64 x)) (*.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 x))) (sqrt.f64 (expm1.f64 x))))))) (#(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 (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 (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 (*.f64 (sqrt.f64 (expm1.f64 x)) (cbrt.f64 (expm1.f64 x))) (cbrt.f64 (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 (sqrt.f64 (expm1.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 2) (log.f64 (sqrt.f64 (expm1.f64 x))))))) (#(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 (exp.f64 1) (log.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.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 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 expm1.f64 x)))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (log.f64 (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (expm1.f64 x) 1/4)) (log.f64 (pow.f64 (expm1.f64 x) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (cbrt.f64 (expm1.f64 x))) (log.f64 (cbrt.f64 (sqrt.f64 (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (log.f64 (sqrt.f64 (expm1.f64 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log.f64 (expm1.f64 x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log.f64 (sqrt.f64 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log.f64 (sqrt.f64 (expm1.f64 x)))) (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (expm1.f64 x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (expm1.f64 x)))) 2) (cbrt.f64 (log.f64 (sqrt.f64 (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log.f64 (sqrt.f64 (expm1.f64 x)))) (sqrt.f64 (log.f64 (sqrt.f64 (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (log.f64 (expm1.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (expm1.f64 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log.f64 (sqrt.f64 (expm1.f64 x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (-.f64 (sqrt.f64 (expm1.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log.f64 (sqrt.f64 (expm1.f64 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log.f64 (sqrt.f64 (expm1.f64 x)))))))))

simplify8.0ms (0.3%)

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
0780
11380
21480
Stop Event
1×saturated
Counts
64 → 50
Calls
Call 1
Inputs
(-.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)
(log.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)))
(log.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)))
(log.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)))
(log.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)))
(log.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)))
(log.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)))
(log.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)))
(log.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)))
Outputs
(-.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)
(log.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)))
(log.f64 (sqrt.f64 (expm1.f64 x)))
(log.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)))
(log.f64 (sqrt.f64 (expm1.f64 x)))
(log.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)))
(log.f64 (sqrt.f64 (expm1.f64 x)))
(log.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)))
(log.f64 (sqrt.f64 (expm1.f64 x)))
(log.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)))
(log.f64 (sqrt.f64 (expm1.f64 x)))
(log.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)))
(log.f64 (sqrt.f64 (expm1.f64 x)))
(log.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)))
(log.f64 (sqrt.f64 (expm1.f64 x)))
(log.f64 (sqrt.f64 (-.f64 (exp.f64 x) 1)))
(log.f64 (sqrt.f64 (expm1.f64 x)))

eval32.0ms (1.3%)

Compiler

Compiled 1515 to 936 computations (38.2% saved)

prune16.0ms (0.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1210121
Fresh011
Picked011
Done022
Total1214125
Error
0b
Counts
125 → 4
Alt Table
Click to see full alt table
StatusErrorProgram
✓0.0b
(expm1.f64 x)
2.0b
x
✓35.9b
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 2))
✓58.1b
(-.f64 (exp.f64 x) 1)
Compiler

Compiled 18 to 14 computations (22.2% 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
✓0.0b
(expm1.f64 x)
2.0b
x
✓35.9b
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 2))
✓58.1b
(-.f64 (exp.f64 x) 1)
Compiler

Compiled 18 to 14 computations (22.2% 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
✓0.0b
(expm1.f64 x)
2.0b
x
✓35.9b
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (expm1.f64 x))) 2))
✓58.1b
(-.f64 (exp.f64 x) 1)
Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes9.0ms (0.4%)

Accuracy

Total -61.7b remaining (-790001.8%)

Threshold costs -61.7b (-790001.8%)

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

3 calls:

4.0ms
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)
Compiler

Compiled 25 to 17 computations (32% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

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

end16.0ms (0.6%)

Stop Event
1×fuel
Compiler

Compiled 9 to 5 computations (44.4% saved)

Profiling

Loading profile data...