Details

Time bar (total: 2.3s)

analyze61.0ms (2.6%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
50%50%0.1%3
50%50%0.1%4
62.4%37.5%0.1%5
62.4%31.2%6.3%6
68.7%21.9%9.5%7
68.7%17.2%14.1%8
71.8%11.7%16.5%9
71.8%9%19.2%10
73.4%6%20.6%11
73.4%4.6%22%12
74.1%3.1%22.8%13
74.1%2.3%23.5%14
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.1s (89.3%)

Results
804.0ms1572×body2048valid
594.0ms1832×body1024valid
273.0ms3121×body128valid
261.0ms1149×body512valid
91.0ms582×body256valid
17.0ms161×body128invalid

preprocess34.0ms (1.5%)

Algorithm
2×egg-herbie
Rules
736×unswap-sqr_binary64
572×associate-*l*_binary64
458×associate-*r*_binary64
278×fma-def_binary64
262×distribute-rgt-in_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01012
12212
23012
34812
49812
525612
687512
7391312
022
122
Stop Event
1×unsound
1×node limit
Calls
Call 1
Inputs
0
1
Outputs
0
1
0
Call 2
Inputs
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 x a)) 1)
Outputs
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 x a)) 1)
(expm1.f64 (*.f64 a x))
Symmetry

(sort a x)

Compiler

Compiled 8 to 6 computations (25% saved)

simplify20.0ms (0.9%)

Algorithm
1×egg-herbie
Rules
440×unswap-sqr_binary64
329×associate-*l*_binary64
275×associate-+l+_binary64
252×associate-*r*_binary64
201×associate-/l/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
076
1166
2236
3356
4706
51756
65566
723316
Stop Event
1×node limit
Counts
1 → 2
Calls
Call 1
Inputs
(-.f64 (exp.f64 (*.f64 a x)) 1)
Outputs
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
▶0.0b
(expm1.f64 (*.f64 a x))
Compiler

Compiled 24 to 15 computations (37.5% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

NewErrorProgram
✓0.0b
(expm1.f64 (*.f64 a x))

series3.0ms (0.1%)

Counts
1 → 24
Calls

6 calls:

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

rewrite28.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
442×pow1_binary64
405×add-log-exp_binary64
405×log1p-expm1-u_binary64
405×expm1-log1p-u_binary64
395×add-exp-log_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
1966
211136
Stop Event
1×node limit
Counts
1 → 18
Calls
Call 1
Inputs
(expm1.f64 (*.f64 a x))
Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (exp.f64 x) a) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (exp.f64 x) a) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (expm1.f64 (*.f64 a x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (expm1.f64 (*.f64 a x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) 2) (cbrt.f64 (expm1.f64 (*.f64 a x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) (sqrt.f64 (expm1.f64 (*.f64 a x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (pow.f64 (exp.f64 x) a) 3) 1) (+.f64 (*.f64 (pow.f64 (exp.f64 x) a) (pow.f64 (exp.f64 x) a)) (+.f64 1 (*.f64 (pow.f64 (exp.f64 x) a) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 (exp.f64 x) a) (pow.f64 (exp.f64 x) a)) 1) (+.f64 (pow.f64 (exp.f64 x) a) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (expm1.f64 (*.f64 a x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (expm1.f64 (*.f64 a x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (expm1.f64 (*.f64 a x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (expm1.f64 (*.f64 a x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (expm1.f64 (*.f64 a x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (expm1.f64 (*.f64 a x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (expm1.f64 (*.f64 a x))))))))

simplify33.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
846×distribute-lft-out_binary64
822×fma-def_binary64
303×*-commutative_binary64
300×unswap-sqr_binary64
174×associate-*l*_binary64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
031284
189284
2244280
31019262
43124248
54830248
Stop Event
1×node limit
Counts
42 → 27
Calls
Call 1
Inputs
(*.f64 a x)
(+.f64 (*.f64 1/2 (*.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(+.f64 (*.f64 1/2 (*.f64 (pow.f64 a 2) (pow.f64 x 2))) (+.f64 (*.f64 a x) (*.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(+.f64 (*.f64 1/2 (*.f64 (pow.f64 a 2) (pow.f64 x 2))) (+.f64 (*.f64 a x) (+.f64 (*.f64 1/24 (*.f64 (pow.f64 a 4) (pow.f64 x 4))) (*.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3))))))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(*.f64 a x)
(+.f64 (*.f64 1/2 (*.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(+.f64 (*.f64 1/2 (*.f64 (pow.f64 a 2) (pow.f64 x 2))) (+.f64 (*.f64 a x) (*.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(+.f64 (*.f64 1/2 (*.f64 (pow.f64 a 2) (pow.f64 x 2))) (+.f64 (*.f64 a x) (+.f64 (*.f64 1/24 (*.f64 (pow.f64 a 4) (pow.f64 x 4))) (*.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3))))))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
(-.f64 (exp.f64 (*.f64 a x)) 1)
Outputs
(*.f64 a x)
(+.f64 (*.f64 1/2 (*.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (*.f64 (*.f64 a a) (*.f64 x x)) (*.f64 a x))
(fma.f64 a x (*.f64 1/2 (*.f64 a (*.f64 a (*.f64 x x)))))
(*.f64 x (+.f64 (*.f64 x (*.f64 1/2 (*.f64 a a))) a))
(*.f64 x (fma.f64 1/2 (*.f64 a (*.f64 a x)) a))
(*.f64 x (fma.f64 x (*.f64 a (*.f64 a 1/2)) a))
(+.f64 (*.f64 1/2 (*.f64 (pow.f64 a 2) (pow.f64 x 2))) (+.f64 (*.f64 a x) (*.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(fma.f64 1/2 (*.f64 (*.f64 a a) (*.f64 x x)) (fma.f64 a x (*.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(fma.f64 1/2 (*.f64 a (*.f64 a (*.f64 x x))) (fma.f64 a x (*.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(fma.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)) (*.f64 x (+.f64 (*.f64 x (*.f64 1/2 (*.f64 a a))) a)))
(*.f64 x (+.f64 a (*.f64 x (fma.f64 a (*.f64 a 1/2) (*.f64 1/6 (*.f64 x (pow.f64 a 3)))))))
(fma.f64 x (fma.f64 x (*.f64 a (*.f64 a 1/2)) a) (*.f64 1/6 (pow.f64 (*.f64 a x) 3)))
(+.f64 (*.f64 1/2 (*.f64 (pow.f64 a 2) (pow.f64 x 2))) (+.f64 (*.f64 a x) (+.f64 (*.f64 1/24 (*.f64 (pow.f64 a 4) (pow.f64 x 4))) (*.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3))))))
(fma.f64 1/2 (*.f64 (*.f64 a a) (*.f64 x x)) (fma.f64 a x (fma.f64 1/24 (*.f64 (pow.f64 a 4) (pow.f64 x 4)) (*.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3))))))
(fma.f64 1/2 (*.f64 a (*.f64 a (*.f64 x x))) (fma.f64 a x (fma.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)) (*.f64 1/24 (*.f64 (pow.f64 a 4) (pow.f64 x 4))))))
(fma.f64 a x (fma.f64 1/2 (*.f64 a (*.f64 a (*.f64 x x))) (fma.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)) (*.f64 1/24 (*.f64 (pow.f64 a 4) (pow.f64 x 4))))))
(fma.f64 x (fma.f64 1/2 (*.f64 a (*.f64 a x)) a) (*.f64 (pow.f64 a 3) (+.f64 (*.f64 1/6 (pow.f64 x 3)) (*.f64 a (*.f64 1/24 (pow.f64 x 4))))))
(fma.f64 x (fma.f64 x (*.f64 a (*.f64 a 1/2)) a) (fma.f64 1/6 (pow.f64 (*.f64 a x) 3) (*.f64 1/24 (pow.f64 (*.f64 a x) 4))))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(*.f64 a x)
(+.f64 (*.f64 1/2 (*.f64 (pow.f64 a 2) (pow.f64 x 2))) (*.f64 a x))
(fma.f64 1/2 (*.f64 (*.f64 a a) (*.f64 x x)) (*.f64 a x))
(fma.f64 a x (*.f64 1/2 (*.f64 a (*.f64 a (*.f64 x x)))))
(*.f64 x (+.f64 (*.f64 x (*.f64 1/2 (*.f64 a a))) a))
(*.f64 x (fma.f64 1/2 (*.f64 a (*.f64 a x)) a))
(*.f64 x (fma.f64 x (*.f64 a (*.f64 a 1/2)) a))
(+.f64 (*.f64 1/2 (*.f64 (pow.f64 a 2) (pow.f64 x 2))) (+.f64 (*.f64 a x) (*.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(fma.f64 1/2 (*.f64 (*.f64 a a) (*.f64 x x)) (fma.f64 a x (*.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(fma.f64 1/2 (*.f64 a (*.f64 a (*.f64 x x))) (fma.f64 a x (*.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)))))
(fma.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)) (*.f64 x (+.f64 (*.f64 x (*.f64 1/2 (*.f64 a a))) a)))
(*.f64 x (+.f64 a (*.f64 x (fma.f64 a (*.f64 a 1/2) (*.f64 1/6 (*.f64 x (pow.f64 a 3)))))))
(fma.f64 x (fma.f64 x (*.f64 a (*.f64 a 1/2)) a) (*.f64 1/6 (pow.f64 (*.f64 a x) 3)))
(+.f64 (*.f64 1/2 (*.f64 (pow.f64 a 2) (pow.f64 x 2))) (+.f64 (*.f64 a x) (+.f64 (*.f64 1/24 (*.f64 (pow.f64 a 4) (pow.f64 x 4))) (*.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3))))))
(fma.f64 1/2 (*.f64 (*.f64 a a) (*.f64 x x)) (fma.f64 a x (fma.f64 1/24 (*.f64 (pow.f64 a 4) (pow.f64 x 4)) (*.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3))))))
(fma.f64 1/2 (*.f64 a (*.f64 a (*.f64 x x))) (fma.f64 a x (fma.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)) (*.f64 1/24 (*.f64 (pow.f64 a 4) (pow.f64 x 4))))))
(fma.f64 a x (fma.f64 1/2 (*.f64 a (*.f64 a (*.f64 x x))) (fma.f64 1/6 (*.f64 (pow.f64 a 3) (pow.f64 x 3)) (*.f64 1/24 (*.f64 (pow.f64 a 4) (pow.f64 x 4))))))
(fma.f64 x (fma.f64 1/2 (*.f64 a (*.f64 a x)) a) (*.f64 (pow.f64 a 3) (+.f64 (*.f64 1/6 (pow.f64 x 3)) (*.f64 a (*.f64 1/24 (pow.f64 x 4))))))
(fma.f64 x (fma.f64 x (*.f64 a (*.f64 a 1/2)) a) (fma.f64 1/6 (pow.f64 (*.f64 a x) 3) (*.f64 1/24 (pow.f64 (*.f64 a x) 4))))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))
(-.f64 (exp.f64 (*.f64 a x)) 1)
(expm1.f64 (*.f64 a x))

prune10.0ms (0.4%)

Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New27027
Fresh000
Picked011
Done000
Total27128
Error
0.0b
Counts
28 → 1
Alt Table
StatusErrorProgram
✓0.0b
(expm1.f64 (*.f64 a x))
Compiler

Compiled 307 to 143 computations (53.4% saved)

regimes18.0ms (0.8%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts
3 → 1
Compiler

Compiled 40 to 24 computations (40% saved)

simplify2.0ms (0.1%)

Algorithm
1×egg-herbie
Rules
1×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
166
Stop Event
1×saturated
Calls
Call 1
Inputs
(expm1.f64 (*.f64 a x))
Outputs
(expm1.f64 (*.f64 a x))

end29.0ms (1.3%)

Stop Event
1×done
Remove

(sort a x)

Compiler

Compiled 30 to 20 computations (33.3% saved)

Profiling

Loading profile data...