Metrics for Kahan's exp quotient

start0.0ms (0%)

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

analyze1.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 8 to 5 computations (37.5% saved)

sample1.3s (41.2%)

Memory

47.8MiB live, 452.8MiB allocated; 95ms collecting garbage

Samples

854.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 285.0ms

ival-div: 176.0ms (61.7% of total)

ival-expm1: 99.0ms (34.7% of total)

ival-true: 5.0ms (1.8% of total)

ival-assert: 3.0ms (1.1% of total)

adjust: 2.0ms (0.7% of total)

Bogosity

explain115.0ms (3.6%)

Memory

-58.4MiB live, 115.4MiB allocated; 85ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
128	-	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
0	-	-	`(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(exp.f64 x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	128	0

Confusion

	Predicted +	Predicted -
+	128	0
-	0	128

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	128	0	0
-	0	0	128

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	128
1	128

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

26.0ms

512×

valid

Compiler

Compiled 38 to 19 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-div: 4.0ms (32.8% of total)

ival-exp: 4.0ms (32.8% of total)

ival-expm1: 3.0ms (24.6% of total)

ival-true: 0.0ms (0% of total)

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

preprocess113.0ms (3.5%)

Memory

38.6MiB live, 83.9MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	32	15
2	74	15
3	211	15
4	929	15
0	8	8
0	12	8
1	14	8
2	17	8
3	25	8
4	51	8
5	188	8
6	1429	8
7	4347	8
0	8019	8

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.0%	(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify537.0ms (16.5%)

Memory

-42.2MiB live, 102.7MiB allocated; 15ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(exp.f64 x)
cost-diff	0	(-.f64 (exp.f64 x) #s(literal 1 binary64))
cost-diff	0	(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
0	12	20
1	14	20
2	17	20
3	25	20
4	51	20
5	188	20
6	1429	20
7	4347	20
0	8019	20

Stop Event

1×	saturated
1×	node limit
1×	iter limit

Calls

Call 1

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

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

localize16.0ms (0.5%)

Memory

21.7MiB live, 21.7MiB allocated; 0ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)
accuracy	0.0	(exp.f64 x)
accuracy	30.096964980110112	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

11.0ms

256×

valid

Compiler

Compiled 16 to 7 computations (56.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-div: 2.0ms (33.2% of total)

ival-exp: 2.0ms (33.2% of total)

ival-expm1: 2.0ms (33.2% of total)

ival-true: 0.0ms (0% of total)

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series2.0ms (0.1%)

Memory

2.6MiB live, 2.6MiB allocated; 0ms collecting garbage

Counts

3 → 15

Calls

Call 1

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

Outputs
#s(approx (/ (- (exp x) 1) x) #s(hole binary64 1))
#s(approx (/ (- (exp x) 1) x) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (/ (- (exp x) 1) x) #s(hole binary64 (+ 1 (* x (+ 1/2 (* 1/6 x))))))
#s(approx (/ (- (exp x) 1) x) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 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) #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) x) #s(hole binary64 (/ (- (exp x) 1) 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
1.0ms	x	@	-inf	((/ (- (exp x) 1) x) (- (exp x) 1) (exp x))
1.0ms	x	@	inf	((/ (- (exp x) 1) x) (- (exp x) 1) (exp x))
0.0ms	x	@	0	((/ (- (exp x) 1) x) (- (exp x) 1) (exp x))

simplify259.0ms (8%)

Memory

4.9MiB live, 148.7MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	203
1	138	203
2	373	203
3	1180	203
4	4708	203
0	8266	190
1	10433	190
2	19614	190
3	21446	190
4	21672	190
5	21675	190

Stop Event

1×	saturated
1×	node limit

Counts

15 → 4

Calls

Call 1

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

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

rewrite51.0ms (1.6%)

Memory

-24.8MiB live, 67.9MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	12	16
2	14	16
3	16	16
4	18	16
0	18	16
1	43	16
0	243	8
1	309	8
2	444	8
3	537	8
4	558	8
5	561	8

Stop Event

1×	saturated
1×	iter limit
1×	iter limit
1×	unsound
1×	saturated

Counts

3 → 25

Calls

Call 1

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

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

eval3.0ms (0.1%)

Memory: 5.8MiB live, 5.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 342 to 97 computations (71.6% saved)

prune1.0ms (0%)

Memory

2.3MiB live, 2.3MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	27	2	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	2	30

Accuracy

100.0%

Counts

30 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 (expm1.f64 x) x)
▶	51.7%	(/.f64 #s(approx (- (exp x) 1) x) x)

Compiler

Compiled 12 to 9 computations (25% saved)

simplify306.0ms (9.4%)

Memory

24.3MiB live, 78.0MiB allocated; 3ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(expm1.f64 x)
cost-diff	0	(/.f64 (expm1.f64 x) x)
cost-diff	0	#s(approx (- (exp x) 1) x)
cost-diff	0	(/.f64 #s(approx (- (exp x) 1) x) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
0	13	22
1	18	22
2	31	22
3	65	22
4	246	22
5	2495	22
0	8702	22

Stop Event

1×	saturated
1×	node limit
1×	iter limit

Calls

Call 1

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

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

localize18.0ms (0.5%)

Memory

-14.2MiB live, 31.1MiB allocated; 4ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 (expm1.f64 x) x)
accuracy	0.0	(expm1.f64 x)
accuracy	0.0	(/.f64 #s(approx (- (exp x) 1) x) x)
accuracy	30.51930319589977	#s(approx (- (exp x) 1) x)

Samples

13.0ms

256×

valid

Compiler

Compiled 24 to 5 computations (79.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-expm1: 3.0ms (54% of total)

ival-div: 2.0ms (36% of total)

ival-true: 0.0ms (0% of total)

adjust: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series1.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated; 0ms collecting garbage

Counts

4 → 10

Calls

Call 1

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

Outputs
#s(approx (/ (- (exp x) 1) x) #s(hole binary64 1))
#s(approx (/ (- (exp x) 1) x) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (/ (- (exp x) 1) x) #s(hole binary64 (+ 1 (* x (+ 1/2 (* 1/6 x))))))
#s(approx (/ (- (exp x) 1) x) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 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) x) #s(hole binary64 (/ (- (exp x) 1) 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) (/ (- (exp x) 1) x) (- (exp x) 1))
0.0ms	x	@	inf	((/ (- (exp x) 1) x) (- (exp x) 1) (/ (- (exp x) 1) x) (- (exp x) 1))
0.0ms	x	@	0	((/ (- (exp x) 1) x) (- (exp x) 1) (/ (- (exp x) 1) x) (- (exp x) 1))

Time

Variable

Point

Expression

0.0ms

-inf

((/ (- (exp x) 1) x) (- (exp x) 1) (/ (- (exp x) 1) x) (- (exp x) 1))

0.0ms

inf

((/ (- (exp x) 1) x) (- (exp x) 1) (/ (- (exp x) 1) x) (- (exp x) 1))

0.0ms

((/ (- (exp x) 1) x) (- (exp x) 1) (/ (- (exp x) 1) x) (- (exp x) 1))

simplify333.0ms (10.3%)

Memory

-21.5MiB live, 125.9MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	150
1	119	150
2	303	150
3	945	150
4	3751	150
0	8130	139
1	10031	139
2	18865	139
3	20782	139
4	21067	139
5	21095	139
6	21097	139

Stop Event

1×	saturated
1×	node limit

Counts

10 → 3

Calls

Call 1

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

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

rewrite40.0ms (1.2%)

Memory

21.1MiB live, 67.8MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	13	20
2	14	20
3	16	20
0	16	20
1	41	20
0	241	20
1	297	20
2	432	20
3	531	20
4	558	20
5	562	20

Stop Event

1×	saturated
1×	iter limit
1×	iter limit
1×	unsound
1×	saturated

Counts

4 → 14

Calls

Call 1

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

Outputs
(/.f64 #s(approx (- (exp x) 1) x) x)
#s(approx (- (exp x) 1) x)
(/.f64 (neg.f64 (neg.f64 (expm1.f64 x))) (neg.f64 (neg.f64 x)))
(/.f64 (neg.f64 (expm1.f64 x)) (neg.f64 x))
(/.f64 (expm1.f64 (+.f64 x x)) (*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)) x))
(/.f64 (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (expm1.f64 x)) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) x))
(/.f64 (expm1.f64 x) x)
(neg.f64 (/.f64 (neg.f64 (expm1.f64 x)) x))
(neg.f64 (/.f64 (expm1.f64 x) (neg.f64 x)))
(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (expm1.f64 x))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))))
(/.f64 (expm1.f64 (+.f64 x x)) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(/.f64 (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (expm1.f64 x)) (fma.f64 (exp.f64 x) (exp.f64 x) (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(expm1.f64 x)

eval1.0ms (0%)

Memory: 4.1MiB live, 4.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 206 to 44 computations (78.6% saved)

prune2.0ms (0%)

Memory

4.8MiB live, 4.8MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	16	2	18

Accuracy

100.0%

Counts

18 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (expm1.f64 x) x)
✓	51.7%	(/.f64 #s(approx (- (exp x) 1) x) x)

Compiler

Compiled 30 to 21 computations (30% saved)

regimes6.0ms (0.2%)

Memory

-37.0MiB live, 9.3MiB allocated; 3ms collecting garbage

Counts

3 → 1

Calls

Call 1

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

Outputs
(/.f64 (expm1.f64 x) x)

Calls

2 calls:

4.0ms	(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)
1.0ms	x

Results

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

regimes3.0ms (0.1%)

Memory

14.8MiB live, 14.8MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

Outputs
(/.f64 #s(approx (- (exp x) 1) x) x)

Calls

2 calls:

2.0ms	x
1.0ms	(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)

Results

Accuracy	Segments	Branch
51.7%	1	`(/.f64 (-.f64 (exp.f64 x) #s(literal 1 binary64)) x)`
51.7%	1	`x`

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify38.0ms (1.2%)

Memory

1.1MiB live, 47.9MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	31	12
3	68	12
4	255	12
5	2349	12

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations45.0ms (1.4%)

Memory

-15.3MiB live, 36.2MiB allocated; 4ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 12 to 8 computations (33.3% saved)

preprocess17.0ms (0.5%)

Memory: 33.8MiB live, 33.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 80 to 50 computations (37.5% saved)

end0.0ms (0%)

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

Iter	Nodes	Cost
0	8	16
1	12	16
2	14	16
3	16	16
4	18	16
0	18	16
1	43	16
0	243	8
1	309	8
2	444	8
3	537	8
4	558	8
5	561	8

Iter	Nodes	Cost
0	10	20
1	13	20
2	14	20
3	16	20
0	16	20
1	41	20
0	241	20
1	297	20
2	432	20
3	531	20
4	558	20
5	562	20

Iter	Nodes	Cost
0	8	16
1	12	16
2	14	16
3	16	16
4	18	16
0	18	16
1	43	16
0	243	8
1	309	8
2	444	8
3	537	8
4	558	8
5	561	8

Iter	Nodes	Cost
0	10	20
1	13	20
2	14	20
3	16	20
0	16	20
1	41	20
0	241	20
1	297	20
2	432	20
3	531	20
4	558	20
5	562	20

start0.0ms (0%)

analyze1.0ms (0%)

sample1.3s (41.2%)

explain115.0ms (3.6%)

preprocess113.0ms (3.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify537.0ms (16.5%)

localize16.0ms (0.5%)

series2.0ms (0.1%)

simplify259.0ms (8%)

rewrite51.0ms (1.6%)

eval3.0ms (0.1%)

prune1.0ms (0%)

simplify306.0ms (9.4%)

localize18.0ms (0.5%)

series1.0ms (0%)

simplify333.0ms (10.3%)

rewrite40.0ms (1.2%)

eval1.0ms (0%)

prune2.0ms (0%)

regimes6.0ms (0.2%)

regimes3.0ms (0.1%)

simplify38.0ms (1.2%)

derivations45.0ms (1.4%)

preprocess17.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	16
1	12	16
2	14	16
3	16	16
4	18	16
0	18	16
1	43	16
0	243	8
1	309	8
2	444	8
3	537	8
4	558	8
5	561	8

Iter	Nodes	Cost
0	10	20
1	13	20
2	14	20
3	16	20
0	16	20
1	41	20
0	241	20
1	297	20
2	432	20
3	531	20
4	558	20
5	562	20