Metrics for expm1 (example 3.7)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50%	50%	0%	0%	0%	0
100%	50%	0%	50%	0%	0%	0%	1

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample349.0ms (54.9%)

Memory

17.5MiB live, 341.0MiB allocated; 101ms collecting garbage

Samples

210.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-expm1: 62.0ms (98.4% of total)

adjust: 1.0ms (1.6% of total)

Bogosity

preprocess30.0ms (4.7%)

Memory

31.3MiB live, 31.3MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	29	14
2	94	14
3	554	14

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.4%	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Compiler

Compiled 8 to 8 computations (0% saved)

series1.0ms (0.2%)

Memory

1.7MiB live, 1.7MiB allocated; 0ms collecting garbage

Counts

4 → 10

Calls

Call 1

Inputs
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
x
#s(literal 1 binary64)

Outputs
#s(approx (- (exp x) 1) #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))
#s(approx (exp x) #s(hole binary64 (exp x)))

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	((- (exp x) 1) (exp x) x 1)
0.0ms	x	@	inf	((- (exp x) 1) (exp x) x 1)
0.0ms	x	@	0	((- (exp x) 1) (exp x) x 1)

rewrite99.0ms (15.6%)

Memory

-2.1MiB live, 96.0MiB allocated; 32ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	114
0	39	114
1	248	114
0	2212	89
1	6518	89

Stop Event

1×	saturated
1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

14 → 32

Calls

Call 1

Inputs
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
x
#s(literal 1 binary64)
#s(approx (- (exp x) 1) #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (exp x) #s(hole binary64 1))
#s(approx (exp x) #s(hole binary64 (+ 1 x)))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* 1/2 x))))))
#s(approx (exp x) #s(hole binary64 (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))
#s(approx (exp x) #s(hole binary64 (exp x)))

Outputs
(neg.f64 (neg.f64 (expm1.f64 x)))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal -1 binary64))
(expm1.f64 (+.f64 x #s(literal 0 binary64)))
(expm1.f64 x)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal -1 binary64) (exp.f64 x))
(+.f64 (cosh.f64 x) (+.f64 (sinh.f64 x) #s(literal -1 binary64)))
(+.f64 (cosh.f64 x) (-.f64 (sinh.f64 x) #s(literal 1 binary64)))
(+.f64 (exp.f64 x) #s(literal -1 binary64))
(*.f64 (exp.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (exp.f64 x))
(sqrt.f64 (exp.f64 (+.f64 x x)))
(-.f64 (cosh.f64 x) (neg.f64 (sinh.f64 x)))
(fabs.f64 (neg.f64 (exp.f64 x)))
(fabs.f64 (exp.f64 x))
(exp.f64 (+.f64 x #s(literal 0 binary64)))
(exp.f64 x)
(+.f64 (sinh.f64 x) (cosh.f64 x))
(+.f64 (cosh.f64 x) (sinh.f64 x))
x
#s(literal 1 binary64)
#s(approx (- (exp x) 1) x)
#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
#s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))
#s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))
#s(approx (exp x) #s(literal 1 binary64))
#s(approx (exp x) (-.f64 x #s(literal -1 binary64)))
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
#s(approx (- (exp x) 1) (expm1.f64 x))
#s(approx (exp x) (exp.f64 x))

eval18.0ms (2.8%)

Memory: -39.0MiB live, 5.2MiB allocated; 28ms collecting garbage
Compiler: Compiled 110 to 75 computations (31.8% saved)

prune1.0ms (0.2%)

Memory

2.2MiB live, 2.2MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	2	29

Accuracy

100.0%

Counts

29 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(expm1.f64 x)
▶	98.5%	#s(approx (- (exp x) 1) x)

Compiler

Compiled 7 to 7 computations (0% saved)

series1.0ms (0.1%)

Memory

1.4MiB live, 1.4MiB allocated; 0ms collecting garbage

Counts

3 → 5

Calls

Call 1

Inputs
#s(approx (- (exp x) 1) x)
x
(expm1.f64 x)

Outputs
#s(approx (- (exp x) 1) #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	((- (exp x) 1) x (- (exp x) 1))
0.0ms	x	@	-inf	((- (exp x) 1) x (- (exp x) 1))
0.0ms	x	@	0	((- (exp x) 1) x (- (exp x) 1))

rewrite76.0ms (12%)

Memory

26.3MiB live, 70.1MiB allocated; 31ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	58
0	28	58
1	196	58
0	1657	52
1	4888	52

Stop Event

1×	saturated
1×	iter-limit
1×	node-limit
1×	iter-limit

Counts

8 → 17

Calls

Call 1

Inputs
#s(approx (- (exp x) 1) x)
x
(expm1.f64 x)
#s(approx (- (exp x) 1) #s(hole binary64 x))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* 1/2 x)))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))))
#s(approx (- (exp x) 1) #s(hole binary64 (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))))
#s(approx (- (exp x) 1) #s(hole binary64 (- (exp x) 1)))

Outputs
#s(approx (- (exp x) 1) x)
x
(neg.f64 (neg.f64 (expm1.f64 x)))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal -1 binary64))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal -1 binary64))
(expm1.f64 (+.f64 x #s(literal 0 binary64)))
(expm1.f64 x)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal -1 binary64) (exp.f64 x))
(+.f64 (cosh.f64 x) (+.f64 (sinh.f64 x) #s(literal -1 binary64)))
(+.f64 (cosh.f64 x) (-.f64 (sinh.f64 x) #s(literal 1 binary64)))
(+.f64 (exp.f64 x) #s(literal -1 binary64))
#s(approx (- (exp x) 1) x)
#s(approx (- (exp x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))
#s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))
#s(approx (- (exp x) 1) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))
#s(approx (- (exp x) 1) (expm1.f64 x))

eval1.0ms (0.2%)

Memory: 1.8MiB live, 1.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 53 to 40 computations (24.5% saved)

prune1.0ms (0.2%)

Memory

1.5MiB live, 1.5MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	13	2	15

Accuracy

100.0%

Counts

15 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(expm1.f64 x)
✓	98.5%	#s(approx (- (exp x) 1) x)

Compiler

Compiled 16 to 16 computations (0% saved)

regimes4.0ms (0.6%)

Memory

6.2MiB live, 6.2MiB allocated; 0ms collecting garbage

Counts

3 → 1

Calls

Call 1

Inputs
#s(approx (- (exp x) 1) x)
(expm1.f64 x)
(-.f64 (exp.f64 x) #s(literal 1 binary64))

Outputs
(expm1.f64 x)

Calls

3 calls:

1.0ms	x
1.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))
1.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
100.0%	1	`(exp.f64 x)`
100.0%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
100.0%	1	`x`

Compiler

Compiled 7 to 7 computations (0% saved)

regimes2.0ms (0.4%)

Memory

4.6MiB live, 4.6MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (exp x) 1) x)

Outputs
#s(approx (- (exp x) 1) x)

Calls

3 calls:

1.0ms	x
1.0ms	(-.f64 (exp.f64 x) #s(literal 1 binary64))
1.0ms	(exp.f64 x)

Results

Accuracy	Segments	Branch
98.5%	1	`(exp.f64 x)`
98.5%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
98.5%	1	`x`

Compiler

Compiled 7 to 7 computations (0% saved)

derivations34.0ms (5.4%)

Memory

-54.3MiB live, 6.0MiB allocated; 14ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 6 to 6 computations (0% saved)

preprocess17.0ms (2.7%)

Memory: 28.6MiB live, 28.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 12 to 12 computations (0% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample349.0ms (54.9%)

preprocess30.0ms (4.7%)

series1.0ms (0.2%)

rewrite99.0ms (15.6%)

eval18.0ms (2.8%)

prune1.0ms (0.2%)

series1.0ms (0.1%)

rewrite76.0ms (12%)

eval1.0ms (0.2%)

prune1.0ms (0.2%)

regimes4.0ms (0.6%)

regimes2.0ms (0.4%)

derivations34.0ms (5.4%)

preprocess17.0ms (2.7%)

end0.0ms (0%)

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