Metrics for expm1 (example 3.7)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB 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)

sample348.0ms (47.4%)

Memory

4.2MiB live, 415.6MiB allocated; 111ms collecting garbage

Samples

215.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 75.0ms

ival-expm1: 74.0ms (98.7% of total)

adjust: 1.0ms (1.3% of total)

Bogosity

preprocess34.0ms (4.6%)

Memory

-12.9MiB live, 32.0MiB allocated; 6ms 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
▶	8.5%	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Compiler

Compiled 8 to 8 computations (0% saved)

series1.0ms (0.2%)

Memory

1.8MiB live, 1.8MiB 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)

rewrite155.0ms (21.2%)

Memory

34.5MiB live, 127.4MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	114
0	39	114
1	262	114
2	1808	114

Stop Event

1×	iter-limit
1×	unsound
1×	node-limit
1×	iter-limit

Counts

14 → 8

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

eval0.0ms (0.1%)

Memory: 0.7MiB live, 0.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 18 to 13 computations (27.8% saved)

prune1.0ms (0.1%)

Memory

1.1MiB live, 1.1MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	3	1	4
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	3	2	5

Accuracy

99.0%

Counts

5 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	8.5%	(-.f64 (exp.f64 x) #s(literal 1 binary64))
▶	98.0%	#s(approx (- (exp x) 1) x)

Compiler

Compiled 9 to 9 computations (0% saved)

series1.0ms (0.1%)

Memory

1.1MiB live, 1.1MiB allocated; 0ms collecting garbage

Counts

2 → 5

Calls

Call 1

Inputs
#s(approx (- (exp x) 1) x)
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)
0.0ms	x	@	inf	((- (exp x) 1) x)
0.0ms	x	@	0	((- (exp x) 1) x)

rewrite166.0ms (22.6%)

Memory

9.5MiB live, 147.1MiB allocated; 19ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	70
0	27	70
1	205	70
2	1391	70

Stop Event

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

Counts

7 → 3

Calls

Call 1

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

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0.1%)

Memory

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

Pruning

2 alts after pruning (0 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	1	1
Total	2	2

Accuracy

99.0%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	8.5%	(-.f64 (exp.f64 x) #s(literal 1 binary64))
✓	98.0%	#s(approx (- (exp x) 1) x)

Compiler

Compiled 17 to 17 computations (0% saved)

regimes5.0ms (0.6%)

Memory

-38.7MiB live, 7.1MiB allocated; 4ms collecting garbage

Accuracy

Total -57.9b remaining (-4468.2%)

Threshold costs -57.9b (-4468.2%)

Counts

2 → 1

Calls

Call 1

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

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
98.0%	1	`(exp.f64 x)`
98.0%	1	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
98.0%	1	`x`

Compiler

Compiled 7 to 7 computations (0% saved)

derivations12.0ms (1.6%)

Memory

12.3MiB live, 12.3MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 5 to 5 computations (0% saved)

preprocess10.0ms (1.4%)

Memory: 17.9MiB live, 17.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 11 to 11 computations (0% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample348.0ms (47.4%)

preprocess34.0ms (4.6%)

series1.0ms (0.2%)

rewrite155.0ms (21.2%)

eval0.0ms (0.1%)

prune1.0ms (0.1%)

series1.0ms (0.1%)

rewrite166.0ms (22.6%)

eval0.0ms (0%)

prune1.0ms (0.1%)

regimes5.0ms (0.6%)

derivations12.0ms (1.6%)

preprocess10.0ms (1.4%)

end0.0ms (0%)

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