math.exp on complex, imaginary part

Time bar (total: 1.4s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated; 0ms collecting garbage
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 7 to 7 computations (0% saved)

sample921.0ms (63.9%)

Memory
6.1MiB live, 1 058.0MiB allocated; 198ms collecting garbage
Samples
678.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 412.0ms
ival-sin: 212.0ms (51.5% of total)
ival-exp: 115.0ms (27.9% of total)
ival-mult: 80.0ms (19.4% of total)
ival-assert: 3.0ms (0.7% of total)
adjust: 2.0ms (0.5% of total)
Bogosity

explain87.0ms (6.1%)

Memory
-15.1MiB live, 137.1MiB allocated; 38ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(*.f64 (exp.f64 re) (sin.f64 im))
00-0-(sin.f64 im)
00-0-re
00-0-(exp.f64 re)
00-0-im
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
56.0ms512×0valid
Compiler

Compiled 31 to 19 computations (38.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 43.0ms
ival-mult: 23.0ms (53.7% of total)
ival-sin: 15.0ms (35% of total)
ival-exp: 4.0ms (9.3% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess181.0ms (12.6%)

Memory
20.9MiB live, 246.8MiB allocated; 26ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01634
14034
212032
341632
4169632
055
085
1125
2265
3675
42795
522965
081255
Stop Event
1×iter limit
1×node limit
1×iter limit
1×node limit
Calls
Call 1
Inputs
(*.f64 (exp.f64 re) (sin.f64 im))
Outputs
(*.f64 (exp.f64 re) (sin.f64 im))
(*.f64 (/.f64 (sin.f64 im) #s(literal 1 binary64)) (exp.f64 re))
Symmetry

(negabs im)

Compiler

Compiled 5 to 5 computations (0% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.8MiB live, 0.8MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(*.f64 (exp.f64 re) (sin.f64 im))
Compiler

Compiled 5 to 5 computations (0% saved)

series5.0ms (0.3%)

Memory
8.4MiB live, 8.4MiB allocated; 0ms collecting garbage
Counts
5 → 21
Calls
Call 1
Inputs
(*.f64 (exp.f64 re) (sin.f64 im))
(exp.f64 re)
re
(sin.f64 im)
im
Outputs
#s(approx (* (exp re) (sin im)) #s(hole binary64 (sin im)))
#s(approx (* (exp re) (sin im)) #s(hole binary64 (+ (sin im) (* re (sin im)))))
#s(approx (* (exp re) (sin im)) #s(hole binary64 (+ (sin im) (* re (+ (sin im) (* 1/2 (* re (sin im))))))))
#s(approx (* (exp re) (sin im)) #s(hole binary64 (+ (sin im) (* re (+ (sin im) (* re (+ (* 1/6 (* re (sin im))) (* 1/2 (sin im)))))))))
#s(approx (exp re) #s(hole binary64 1))
#s(approx (exp re) #s(hole binary64 (+ 1 re)))
#s(approx (exp re) #s(hole binary64 (+ 1 (* re (+ 1 (* 1/2 re))))))
#s(approx (exp re) #s(hole binary64 (+ 1 (* re (+ 1 (* re (+ 1/2 (* 1/6 re))))))))
#s(approx re #s(hole binary64 re))
#s(approx (* (exp re) (sin im)) #s(hole binary64 (* (exp re) (sin im))))
#s(approx (exp re) #s(hole binary64 (exp re)))
#s(approx (* (exp re) (sin im)) #s(hole binary64 (* im (exp re))))
#s(approx (* (exp re) (sin im)) #s(hole binary64 (* im (+ (exp re) (* -1/6 (* (pow im 2) (exp re)))))))
#s(approx (* (exp re) (sin im)) #s(hole binary64 (* im (+ (exp re) (* (pow im 2) (+ (* -1/6 (exp re)) (* 1/120 (* (pow im 2) (exp re)))))))))
#s(approx (* (exp re) (sin im)) #s(hole binary64 (* im (+ (exp re) (* (pow im 2) (+ (* -1/6 (exp re)) (* (pow im 2) (+ (* -1/5040 (* (pow im 2) (exp re))) (* 1/120 (exp re))))))))))
#s(approx (sin im) #s(hole binary64 im))
#s(approx (sin im) #s(hole binary64 (* im (+ 1 (* -1/6 (pow im 2))))))
#s(approx (sin im) #s(hole binary64 (* im (+ 1 (* (pow im 2) (- (* 1/120 (pow im 2)) 1/6))))))
#s(approx (sin im) #s(hole binary64 (* im (+ 1 (* (pow im 2) (- (* (pow im 2) (+ 1/120 (* -1/5040 (pow im 2)))) 1/6))))))
#s(approx im #s(hole binary64 im))
#s(approx (sin im) #s(hole binary64 (sin im)))
Calls

6 calls:

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

rewrite186.0ms (12.9%)

Memory
2.3MiB live, 151.6MiB allocated; 11ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
095296
097295
1572284
05413264
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
26 → 35
Calls
Call 1
Inputs
(*.f64 (exp.f64 re) (sin.f64 im))
(exp.f64 re)
re
(sin.f64 im)
im
#s(approx (* (exp re) (sin im)) #s(hole binary64 (sin im)))
#s(approx (* (exp re) (sin im)) #s(hole binary64 (+ (sin im) (* re (sin im)))))
#s(approx (* (exp re) (sin im)) #s(hole binary64 (+ (sin im) (* re (+ (sin im) (* 1/2 (* re (sin im))))))))
#s(approx (* (exp re) (sin im)) #s(hole binary64 (+ (sin im) (* re (+ (sin im) (* re (+ (* 1/6 (* re (sin im))) (* 1/2 (sin im)))))))))
#s(approx (exp re) #s(hole binary64 1))
#s(approx (exp re) #s(hole binary64 (+ 1 re)))
#s(approx (exp re) #s(hole binary64 (+ 1 (* re (+ 1 (* 1/2 re))))))
#s(approx (exp re) #s(hole binary64 (+ 1 (* re (+ 1 (* re (+ 1/2 (* 1/6 re))))))))
#s(approx re #s(hole binary64 re))
#s(approx (* (exp re) (sin im)) #s(hole binary64 (* (exp re) (sin im))))
#s(approx (exp re) #s(hole binary64 (exp re)))
#s(approx (* (exp re) (sin im)) #s(hole binary64 (* im (exp re))))
#s(approx (* (exp re) (sin im)) #s(hole binary64 (* im (+ (exp re) (* -1/6 (* (pow im 2) (exp re)))))))
#s(approx (* (exp re) (sin im)) #s(hole binary64 (* im (+ (exp re) (* (pow im 2) (+ (* -1/6 (exp re)) (* 1/120 (* (pow im 2) (exp re)))))))))
#s(approx (* (exp re) (sin im)) #s(hole binary64 (* im (+ (exp re) (* (pow im 2) (+ (* -1/6 (exp re)) (* (pow im 2) (+ (* -1/5040 (* (pow im 2) (exp re))) (* 1/120 (exp re))))))))))
#s(approx (sin im) #s(hole binary64 im))
#s(approx (sin im) #s(hole binary64 (* im (+ 1 (* -1/6 (pow im 2))))))
#s(approx (sin im) #s(hole binary64 (* im (+ 1 (* (pow im 2) (- (* 1/120 (pow im 2)) 1/6))))))
#s(approx (sin im) #s(hole binary64 (* im (+ 1 (* (pow im 2) (- (* (pow im 2) (+ 1/120 (* -1/5040 (pow im 2)))) 1/6))))))
#s(approx im #s(hole binary64 im))
#s(approx (sin im) #s(hole binary64 (sin im)))
Outputs
(*.f64 (sin.f64 im) (exp.f64 re))
(*.f64 (exp.f64 re) (sin.f64 im))
(fma.f64 (cosh.f64 re) (sin.f64 im) (*.f64 (sinh.f64 re) (sin.f64 im)))
(fma.f64 (sin.f64 im) (cosh.f64 re) (*.f64 (sin.f64 im) (sinh.f64 re)))
(+.f64 (*.f64 (cosh.f64 re) (sin.f64 im)) (*.f64 (sinh.f64 re) (sin.f64 im)))
(+.f64 (*.f64 (sin.f64 im) (cosh.f64 re)) (*.f64 (sin.f64 im) (sinh.f64 re)))
(/.f64 (-.f64 (*.f64 (cosh.f64 re) (cosh.f64 re)) (*.f64 (sinh.f64 re) (sinh.f64 re))) (-.f64 (cosh.f64 re) (sinh.f64 re)))
(/.f64 (+.f64 (pow.f64 (cosh.f64 re) #s(literal 3 binary64)) (pow.f64 (sinh.f64 re) #s(literal 3 binary64))) (+.f64 (*.f64 (cosh.f64 re) (cosh.f64 re)) (-.f64 (*.f64 (sinh.f64 re) (sinh.f64 re)) (*.f64 (cosh.f64 re) (sinh.f64 re)))))
(exp.f64 re)
(+.f64 (sinh.f64 re) (cosh.f64 re))
(+.f64 (cosh.f64 re) (sinh.f64 re))
re
(sin.f64 im)
im
#s(approx (* (exp re) (sin im)) (sin.f64 im))
#s(approx (* (exp re) (sin im)) (fma.f64 (sin.f64 im) re (sin.f64 im)))
#s(approx (* (exp re) (sin im)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 im) re) (sin.f64 im)) re (sin.f64 im)))
#s(approx (* (exp re) (sin im)) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 (sin.f64 im) re) (*.f64 #s(literal 1/2 binary64) (sin.f64 im))) re (sin.f64 im)) re (sin.f64 im)))
#s(approx (exp re) #s(literal 1 binary64))
#s(approx (exp re) (-.f64 re #s(literal -1 binary64)))
#s(approx (exp re) (fma.f64 (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) re) #s(literal 1 binary64) #s(literal 1 binary64)) re) #s(literal 1 binary64) #s(literal 1 binary64)))
#s(approx (exp re) (fma.f64 (*.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) re #s(literal 1/2 binary64)) re) #s(literal 1 binary64) #s(literal 1 binary64)) re) #s(literal 1 binary64) #s(literal 1 binary64)))
#s(approx re re)
#s(approx (* (exp re) (sin im)) (*.f64 (sin.f64 im) (exp.f64 re)))
#s(approx (exp re) (exp.f64 re))
#s(approx (* (exp re) (sin im)) (*.f64 (exp.f64 re) im))
#s(approx (* (exp re) (sin im)) (*.f64 (fma.f64 (*.f64 (*.f64 (exp.f64 re) im) im) #s(literal -1/6 binary64) (exp.f64 re)) im))
#s(approx (* (exp re) (sin im)) (fma.f64 (*.f64 im (fma.f64 #s(literal 1/120 binary64) (*.f64 (*.f64 (exp.f64 re) im) im) (*.f64 #s(literal -1/6 binary64) (exp.f64 re)))) (*.f64 im im) (*.f64 (exp.f64 re) im)))
#s(approx (* (exp re) (sin im)) (fma.f64 (*.f64 im (*.f64 im im)) (fma.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 (*.f64 (exp.f64 re) im) im) (*.f64 #s(literal 1/120 binary64) (exp.f64 re))) im) im (*.f64 #s(literal -1/6 binary64) (exp.f64 re))) (*.f64 (exp.f64 re) im)))
#s(approx (sin im) im)
#s(approx (sin im) (*.f64 (fma.f64 (*.f64 (*.f64 im im) #s(literal -1/6 binary64)) #s(literal 1 binary64) #s(literal 1 binary64)) im))
#s(approx (sin im) (*.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/120 binary64) (*.f64 im im)) #s(literal 1/6 binary64)) (*.f64 im im) #s(literal 1 binary64)) im))
#s(approx (sin im) (fma.f64 (*.f64 im (*.f64 im im)) (-.f64 (*.f64 (*.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 im im) #s(literal 1/120 binary64)) im) im) #s(literal 1/6 binary64)) im))
#s(approx im im)
#s(approx (sin im) (sin.f64 im))

eval4.0ms (0.3%)

Memory
6.5MiB live, 6.5MiB allocated; 0ms collecting garbage
Compiler

Compiled 454 to 125 computations (72.5% saved)

prune7.0ms (0.5%)

Memory
11.8MiB live, 11.8MiB allocated; 0ms collecting garbage
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New35035
Fresh000
Picked011
Done000
Total35136
Accuracy
100.0%
Counts
36 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(*.f64 (exp.f64 re) (sin.f64 im))
Compiler

Compiled 10 to 10 computations (0% saved)

simplify34.0ms (2.3%)

Memory
-31.0MiB live, 16.3MiB allocated; 2ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
055
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 (exp.f64 re) (sin.f64 im))
Outputs
(*.f64 (exp.f64 re) (sin.f64 im))

derivations0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Stop Event
1×done
Compiler

Compiled 5 to 5 computations (0% saved)

preprocess15.0ms (1%)

Memory
30.4MiB live, 30.4MiB allocated; 0ms collecting garbage
Remove

(negabs im)

Compiler

Compiled 40 to 40 computations (0% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

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