math.exp on complex, imaginary part

Details

Time bar (total: 4.3s)

analyze0.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
100%99.9%0%0.1%0%0%0%1
Compiler

Compiled 8 to 6 computations (25% saved)

sample4.0s (93.5%)

Results
2.2s2159×body8192exit
1.1s5957×body256valid
469.0ms1275×body1024valid
164.0ms636×body512valid
40.0ms243×body256infinite
37.0ms88×body1024infinite
16.0ms57×body512infinite
Bogosity

preprocess16.0ms (0.4%)

Algorithm
2×egg-herbie
Rules
4×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01130
11330
022
Stop Event
1×saturated
1×saturated
Calls
Call 1
Inputs
0
1
Outputs
0
1
Call 2
Inputs
(*.f64 (exp.f64 re) (sin.f64 im))
(*.f64 (exp.f64 im) (sin.f64 re))
Outputs
(*.f64 (exp.f64 re) (sin.f64 im))
(*.f64 (exp.f64 im) (sin.f64 re))
Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify13.0ms (0.3%)

Algorithm
1×egg-herbie
Rules
2×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0815
1915
Stop Event
1×saturated
Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 (exp.f64 re) (sin.f64 im))
Outputs
(*.f64 (exp.f64 re) (sin.f64 im))

eval0.0ms (0%)

Compiler

Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Accurracy
100.0%
Counts
2 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(*.f64 (exp.f64 re) (sin.f64 im))
▶100.0%
(*.f64 (exp.f64 re) (sin.f64 im))
Compiler

Compiled 14 to 10 computations (28.6% saved)

localize88.0ms (2%)

Local Accuracy

Found 1 expressions with local accuracy:

NewAccuracyProgram
✓100.0%
(*.f64 (exp.f64 re) (sin.f64 im))
Compiler

Compiled 14 to 6 computations (57.1% saved)

series3.0ms (0.1%)

Counts
1 → 24
Calls

6 calls:

TimeVariablePointExpression
1.0ms
re
@inf
(*.f64 (exp.f64 re) (sin.f64 im))
1.0ms
im
@0
(*.f64 (exp.f64 re) (sin.f64 im))
0.0ms
re
@0
(*.f64 (exp.f64 re) (sin.f64 im))
0.0ms
im
@inf
(*.f64 (exp.f64 re) (sin.f64 im))
0.0ms
re
@-inf
(*.f64 (exp.f64 re) (sin.f64 im))

rewrite53.0ms (1.2%)

Algorithm
1×batch-egg-rewrite
Rules
1408×pow1
1278×add-exp-log
1278×log1p-expm1-u
1278×expm1-log1p-u
1246×add-log-exp
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0815
115215
2176115
Stop Event
1×node limit
Counts
1 → 11
Calls
Call 1
Inputs
(*.f64 (exp.f64 re) (sin.f64 im))
Outputs
(-.f64 (+.f64 1 (*.f64 (exp.f64 re) (sin.f64 im))) 1)
(pow.f64 (*.f64 (exp.f64 re) (sin.f64 im)) 1)
(pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (sin.f64 im))) 3)
(pow.f64 (pow.f64 (*.f64 (exp.f64 re) (sin.f64 im)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im))) 2)
(sqrt.f64 (pow.f64 (*.f64 (exp.f64 re) (sin.f64 im)) 2))
(log.f64 (pow.f64 (exp.f64 (exp.f64 re)) (sin.f64 im)))
(cbrt.f64 (pow.f64 (*.f64 (exp.f64 re) (sin.f64 im)) 3))
(expm1.f64 (log1p.f64 (*.f64 (exp.f64 re) (sin.f64 im))))
(exp.f64 (+.f64 re (log.f64 (sin.f64 im))))
(log1p.f64 (expm1.f64 (*.f64 (exp.f64 re) (sin.f64 im))))

simplify72.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
1898×fma-def
858×distribute-lft-out
788×*-commutative
622×associate-*r*
572×fma-neg
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
071733
1185729
2537689
32244641
45281639
57011639
Stop Event
1×node limit
Counts
35 → 45
Calls
Call 1
Inputs
(sin.f64 im)
(+.f64 (sin.f64 im) (*.f64 (sin.f64 im) re))
(+.f64 (sin.f64 im) (+.f64 (*.f64 (sin.f64 im) re) (*.f64 1/2 (*.f64 (sin.f64 im) (pow.f64 re 2)))))
(+.f64 (sin.f64 im) (+.f64 (*.f64 (sin.f64 im) re) (+.f64 (*.f64 1/6 (*.f64 (sin.f64 im) (pow.f64 re 3))) (*.f64 1/2 (*.f64 (sin.f64 im) (pow.f64 re 2))))))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (exp.f64 re) im)
(+.f64 (*.f64 -1/6 (*.f64 (exp.f64 re) (pow.f64 im 3))) (*.f64 (exp.f64 re) im))
(+.f64 (*.f64 -1/6 (*.f64 (exp.f64 re) (pow.f64 im 3))) (+.f64 (*.f64 1/120 (*.f64 (exp.f64 re) (pow.f64 im 5))) (*.f64 (exp.f64 re) im)))
(+.f64 (*.f64 -1/6 (*.f64 (exp.f64 re) (pow.f64 im 3))) (+.f64 (*.f64 1/120 (*.f64 (exp.f64 re) (pow.f64 im 5))) (+.f64 (*.f64 -1/5040 (*.f64 (exp.f64 re) (pow.f64 im 7))) (*.f64 (exp.f64 re) im))))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(-.f64 (+.f64 1 (*.f64 (exp.f64 re) (sin.f64 im))) 1)
(pow.f64 (*.f64 (exp.f64 re) (sin.f64 im)) 1)
(pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (sin.f64 im))) 3)
(pow.f64 (pow.f64 (*.f64 (exp.f64 re) (sin.f64 im)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im))) 2)
(sqrt.f64 (pow.f64 (*.f64 (exp.f64 re) (sin.f64 im)) 2))
(log.f64 (pow.f64 (exp.f64 (exp.f64 re)) (sin.f64 im)))
(cbrt.f64 (pow.f64 (*.f64 (exp.f64 re) (sin.f64 im)) 3))
(expm1.f64 (log1p.f64 (*.f64 (exp.f64 re) (sin.f64 im))))
(exp.f64 (+.f64 re (log.f64 (sin.f64 im))))
(log1p.f64 (expm1.f64 (*.f64 (exp.f64 re) (sin.f64 im))))
Outputs
(sin.f64 im)
(+.f64 (sin.f64 im) (*.f64 (sin.f64 im) re))
(*.f64 (+.f64 re 1) (sin.f64 im))
(*.f64 (sin.f64 im) (+.f64 re 1))
(fma.f64 (sin.f64 im) re (sin.f64 im))
(+.f64 (sin.f64 im) (+.f64 (*.f64 (sin.f64 im) re) (*.f64 1/2 (*.f64 (sin.f64 im) (pow.f64 re 2)))))
(+.f64 (sin.f64 im) (fma.f64 (sin.f64 im) re (*.f64 1/2 (*.f64 (sin.f64 im) (*.f64 re re)))))
(+.f64 (*.f64 (+.f64 re 1) (sin.f64 im)) (*.f64 (*.f64 re re) (*.f64 (sin.f64 im) 1/2)))
(*.f64 (sin.f64 im) (+.f64 (+.f64 re 1) (*.f64 re (*.f64 re 1/2))))
(*.f64 (sin.f64 im) (+.f64 re (fma.f64 re (*.f64 re 1/2) 1)))
(+.f64 (sin.f64 im) (+.f64 (*.f64 (sin.f64 im) re) (+.f64 (*.f64 1/6 (*.f64 (sin.f64 im) (pow.f64 re 3))) (*.f64 1/2 (*.f64 (sin.f64 im) (pow.f64 re 2))))))
(+.f64 (sin.f64 im) (fma.f64 (sin.f64 im) re (fma.f64 1/6 (*.f64 (sin.f64 im) (pow.f64 re 3)) (*.f64 1/2 (*.f64 (sin.f64 im) (*.f64 re re))))))
(+.f64 (*.f64 (+.f64 re 1) (sin.f64 im)) (fma.f64 1/2 (*.f64 (sin.f64 im) (*.f64 re re)) (*.f64 (pow.f64 re 3) (*.f64 (sin.f64 im) 1/6))))
(fma.f64 (+.f64 re 1) (sin.f64 im) (*.f64 (sin.f64 im) (+.f64 (*.f64 re (*.f64 re 1/2)) (*.f64 1/6 (pow.f64 re 3)))))
(*.f64 (sin.f64 im) (+.f64 (+.f64 re 1) (*.f64 (*.f64 re re) (+.f64 (*.f64 re 1/6) 1/2))))
(*.f64 (sin.f64 im) (+.f64 (fma.f64 1/6 (pow.f64 re 3) re) (fma.f64 re (*.f64 re 1/2) 1)))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (exp.f64 re) im)
(*.f64 im (exp.f64 re))
(+.f64 (*.f64 -1/6 (*.f64 (exp.f64 re) (pow.f64 im 3))) (*.f64 (exp.f64 re) im))
(fma.f64 -1/6 (*.f64 (exp.f64 re) (pow.f64 im 3)) (*.f64 im (exp.f64 re)))
(fma.f64 im (exp.f64 re) (*.f64 (exp.f64 re) (*.f64 (pow.f64 im 3) -1/6)))
(*.f64 (exp.f64 re) (+.f64 im (*.f64 -1/6 (pow.f64 im 3))))
(*.f64 (exp.f64 re) (fma.f64 -1/6 (pow.f64 im 3) im))
(+.f64 (*.f64 -1/6 (*.f64 (exp.f64 re) (pow.f64 im 3))) (+.f64 (*.f64 1/120 (*.f64 (exp.f64 re) (pow.f64 im 5))) (*.f64 (exp.f64 re) im)))
(fma.f64 -1/6 (*.f64 (exp.f64 re) (pow.f64 im 3)) (fma.f64 1/120 (*.f64 (exp.f64 re) (pow.f64 im 5)) (*.f64 im (exp.f64 re))))
(fma.f64 im (exp.f64 re) (*.f64 (exp.f64 re) (+.f64 (*.f64 -1/6 (pow.f64 im 3)) (*.f64 1/120 (pow.f64 im 5)))))
(*.f64 (exp.f64 re) (+.f64 (*.f64 -1/6 (pow.f64 im 3)) (fma.f64 1/120 (pow.f64 im 5) im)))
(+.f64 (*.f64 -1/6 (*.f64 (exp.f64 re) (pow.f64 im 3))) (+.f64 (*.f64 1/120 (*.f64 (exp.f64 re) (pow.f64 im 5))) (+.f64 (*.f64 -1/5040 (*.f64 (exp.f64 re) (pow.f64 im 7))) (*.f64 (exp.f64 re) im))))
(fma.f64 -1/6 (*.f64 (exp.f64 re) (pow.f64 im 3)) (fma.f64 1/120 (*.f64 (exp.f64 re) (pow.f64 im 5)) (fma.f64 -1/5040 (*.f64 (exp.f64 re) (pow.f64 im 7)) (*.f64 im (exp.f64 re)))))
(fma.f64 -1/6 (*.f64 (exp.f64 re) (pow.f64 im 3)) (fma.f64 1/120 (*.f64 (exp.f64 re) (pow.f64 im 5)) (fma.f64 im (exp.f64 re) (*.f64 (*.f64 -1/5040 (pow.f64 im 7)) (exp.f64 re)))))
(+.f64 (*.f64 (exp.f64 re) (+.f64 im (*.f64 -1/6 (pow.f64 im 3)))) (*.f64 (exp.f64 re) (+.f64 (*.f64 1/120 (pow.f64 im 5)) (*.f64 -1/5040 (pow.f64 im 7)))))
(*.f64 (exp.f64 re) (+.f64 (fma.f64 -1/6 (pow.f64 im 3) im) (fma.f64 1/120 (pow.f64 im 5) (*.f64 -1/5040 (pow.f64 im 7)))))
(*.f64 (exp.f64 re) (+.f64 (fma.f64 -1/6 (pow.f64 im 3) (*.f64 1/120 (pow.f64 im 5))) (fma.f64 -1/5040 (pow.f64 im 7) im)))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (sin.f64 im) (exp.f64 re))
(-.f64 (+.f64 1 (*.f64 (exp.f64 re) (sin.f64 im))) 1)
(*.f64 (sin.f64 im) (exp.f64 re))
(pow.f64 (*.f64 (exp.f64 re) (sin.f64 im)) 1)
(*.f64 (sin.f64 im) (exp.f64 re))
(pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (sin.f64 im))) 3)
(*.f64 (sin.f64 im) (exp.f64 re))
(pow.f64 (pow.f64 (*.f64 (exp.f64 re) (sin.f64 im)) 3) 1/3)
(*.f64 (sin.f64 im) (exp.f64 re))
(pow.f64 (sqrt.f64 (*.f64 (exp.f64 re) (sin.f64 im))) 2)
(*.f64 (sin.f64 im) (exp.f64 re))
(sqrt.f64 (pow.f64 (*.f64 (exp.f64 re) (sin.f64 im)) 2))
(*.f64 (sin.f64 im) (exp.f64 re))
(log.f64 (pow.f64 (exp.f64 (exp.f64 re)) (sin.f64 im)))
(*.f64 (sin.f64 im) (exp.f64 re))
(cbrt.f64 (pow.f64 (*.f64 (exp.f64 re) (sin.f64 im)) 3))
(*.f64 (sin.f64 im) (exp.f64 re))
(expm1.f64 (log1p.f64 (*.f64 (exp.f64 re) (sin.f64 im))))
(*.f64 (sin.f64 im) (exp.f64 re))
(exp.f64 (+.f64 re (log.f64 (sin.f64 im))))
(*.f64 (sin.f64 im) (exp.f64 re))
(log1p.f64 (expm1.f64 (*.f64 (exp.f64 re) (sin.f64 im))))
(*.f64 (sin.f64 im) (exp.f64 re))

eval12.0ms (0.3%)

Compiler

Compiled 601 to 311 computations (48.3% saved)

prune23.0ms (0.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New38745
Fresh000
Picked011
Done000
Total38846
Accurracy
100.0%
Counts
46 → 8
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶98.7%
(pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (sin.f64 im))) 3)
64.5%
(+.f64 (sin.f64 im) (*.f64 (sin.f64 im) re))
▶64.5%
(*.f64 (+.f64 re 1) (sin.f64 im))
65.0%
(*.f64 (sin.f64 im) (+.f64 (+.f64 re 1) (*.f64 (*.f64 re re) (+.f64 (*.f64 re 1/6) 1/2))))
▶64.7%
(*.f64 (sin.f64 im) (+.f64 (+.f64 re 1) (*.f64 re (*.f64 re 1/2))))
✓100.0%
(*.f64 (exp.f64 re) (sin.f64 im))
▶66.7%
(*.f64 (exp.f64 re) im)
▶64.2%
(sin.f64 im)
▶98.7%
(pow.f64 (cbrt.f64 (*.f64 (exp.f64 re) (sin.f64 im))) 3)
64.5%
(+.f64 (sin.f64 im) (*.f64 (sin.f64 im) re))
▶64.5%
(*.f64 (+.f64 re 1) (sin.f64 im))
65.0%
(*.f64 (sin.f64 im) (+.f64 (+.f64 re 1) (*.f64 (*.f64 re re) (+.f64 (*.f64 re 1/6) 1/2))))
▶64.7%
(*.f64 (sin.f64 im) (+.f64 (+.f64 re 1) (*.f64 re (*.f64 re 1/2))))
✓100.0%
(*.f64 (exp.f64 re) (sin.f64 im))
▶66.7%
(*.f64 (exp.f64 re) im)
▶64.2%
(sin.f64 im)
Compiler

Compiled 290 to 206 computations (29% saved)

localize0.0ms (0%)

Compiler

Compiled 92 to 39 computations (57.6% saved)

end0.0ms (0%)

Profiling

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