Metrics for exp neg sub

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample809.0ms (13.9%)

Memory

-22.5MiB live, 1 086.6MiB allocated

Samples

545.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 345.0ms

ival-mult: 107.0ms (31% of total)

ival-exp: 100.0ms (29% of total)

ival-neg: 79.0ms (22.9% of total)

ival-sub: 46.0ms (13.3% of total)

ival-true: 6.0ms (1.7% of total)

exact: 4.0ms (1.2% of total)

ival-assert: 3.0ms (0.9% of total)

Bogosity

explain76.0ms (1.3%)

Memory

14.3MiB live, 173.6MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`exp.f64`	`(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))`	sensitivity	1	0

Confusion

	Predicted +	Predicted -
+	1	0
-	0	255

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	255

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	255
1	1

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

27.0ms

512×

valid

Compiler

Compiled 57 to 22 computations (61.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-exp: 6.0ms (38% of total)

ival-mult: 4.0ms (25.3% of total)

ival-sub: 2.0ms (12.7% of total)

ival-neg: 2.0ms (12.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess377.0ms (6.5%)

Memory

-4.3MiB live, 215.6MiB allocated

Algorithm

1×	egg-herbie

Rules

7 302×	`lower-fma.f64`
7 302×	`lower-fma.f32`
2 712×	`lower-*.f32`
2 710×	`lower-*.f64`
2 292×	`exp-sum`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	30	13
2	74	13
3	156	13
4	282	13
5	410	13
6	635	13
7	968	13
8	1625	13
9	3013	13
10	6135	13
0	6	7
0	10	7
1	22	6
2	51	6
3	106	6
4	192	6
5	293	6
6	468	6
7	776	6
8	1277	6
9	2109	6
10	4291	6
11	7386	6
0	8073	5

Stop Event

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

Calls

Call 1

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

Outputs
(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))

Symmetry

(abs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify391.0ms (6.7%)

Memory

-0.5MiB live, 208.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(-.f64 #s(literal 1 binary64) (*.f64 x x))
cost-diff	0	(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
cost-diff	256	(neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

Rules

7 302×	`lower-fma.f64`
7 302×	`lower-fma.f32`
2 712×	`lower-*.f32`
2 710×	`lower-*.f64`
2 292×	`exp-sum`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	23
0	10	23
1	22	21
2	51	21
3	106	21
4	192	21
5	293	21
6	468	21
7	776	21
8	1277	21
9	2109	21
10	4291	21
11	7386	21
0	8073	19

Stop Event

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

Calls

Call 1

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

Outputs
(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(fma.f64 x x #s(literal -1 binary64))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
x

localize75.0ms (1.3%)

Memory

-5.8MiB live, 32.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 #s(literal 1 binary64) (*.f64 x x))
accuracy	0	(*.f64 x x)
accuracy	0	(neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
accuracy	0.03236485241743066	(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))

Samples

12.0ms

256×

valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-exp: 2.0ms (30.2% of total)

ival-mult: 2.0ms (30.2% of total)

ival-sub: 1.0ms (15.1% of total)

ival-neg: 1.0ms (15.1% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0%)

Memory

6.0MiB live, 6.0MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())
#s(alt (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (patch (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())

Outputs
#s(alt -1 (taylor 0 x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (exp -1) (taylor 0 x) (#s(alt (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (patch (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (exp -1))) (taylor 0 x) (#s(alt (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (patch (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1)))))) (taylor 0 x) (#s(alt (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (patch (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1))))))) (taylor 0 x) (#s(alt (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (patch (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow x 2))) (taylor 0 x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (patch (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (patch (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (patch (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (patch (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) (patch (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (patch (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (patch (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (patch (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) (patch (exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (/ 1 (pow x 2)) 1)) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) (.f64 x x)) (patch (-.f64 #s(literal 1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	((neg (- 1 (* x x))) (exp (neg (- 1 (* x x)))) (- 1 (* x x)) (* x x))
1.0ms	x	@	inf	((neg (- 1 (* x x))) (exp (neg (- 1 (* x x)))) (- 1 (* x x)) (* x x))
0.0ms	x	@	-inf	((neg (- 1 (* x x))) (exp (neg (- 1 (* x x)))) (- 1 (* x x)) (* x x))

Time

Variable

Point

Expression

1.0ms

((neg (- 1 (* x x))) (exp (neg (- 1 (* x x)))) (- 1 (* x x)) (* x x))

1.0ms

inf

((neg (- 1 (* x x))) (exp (neg (- 1 (* x x)))) (- 1 (* x x)) (* x x))

0.0ms

-inf

((neg (- 1 (* x x))) (exp (neg (- 1 (* x x)))) (- 1 (* x x)) (* x x))

simplify208.0ms (3.6%)

Memory

41.0MiB live, 184.8MiB allocated

Algorithm

1×	egg-herbie

Rules

9 734×	`lower-fma.f64`
9 734×	`lower-fma.f32`
3 654×	`lower-*.f64`
3 654×	`lower-*.f32`
1 572×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	254
1	81	241
2	247	237
3	605	234
4	1328	234
5	2025	234
6	3122	234
7	5538	234
0	8219	211

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
(exp -1)
(+ (exp -1) (* (pow x 2) (exp -1)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1))))))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1)))))))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
-1
#s(literal -1 binary64)
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(exp -1)
(exp.f64 #s(literal -1 binary64))
(+ (exp -1) (* (pow x 2) (exp -1)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1))))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64) (fma.f64 x x #s(literal 1 binary64))) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1)))))))
(.f64 (fma.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(+ 1 (* -1 (pow x 2)))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite175.0ms (3%)

Memory

4.1MiB live, 311.9MiB allocated

Rules

5 524×	`lower-fma.f64`
5 524×	`lower-fma.f32`
3 714×	`lower-/.f64`
3 714×	`lower-/.f32`
2 654×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	37	19
2	227	19
3	1923	19
0	9304	16

Stop Event

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

Counts

4 → 500

Calls

Call 1

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

Outputs
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eval114.0ms (2%)

Memory: -31.0MiB live, 269.5MiB allocated
Compiler: Compiled 10 865 to 1 802 computations (83.4% saved)

prune12.0ms (0.2%)

Memory

7.2MiB live, 46.8MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	542	6	548
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	543	6	549

Accuracy

100.0%

Counts

549 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(pow.f64 (*.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)))
	100.0%	(/.f64 (pow.f64 (exp.f64 x) x) (E.f64))
▶	99.9%	(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
▶	56.0%	(exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x)))
▶	53.2%	(exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))
▶	75.4%	#s(approx (exp (neg (- 1 (* x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))))

Compiler

Compiled 78 to 64 computations (17.9% saved)

simplify115.0ms (2%)

Memory

-15.7MiB live, 142.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score
cost-diff	0	(exp.f64 #s(literal -1 binary64))
cost-diff	0	(fma.f64 x x #s(literal 1 binary64))
cost-diff	0	#s(approx (exp (neg (- 1 (* x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))))
cost-diff	6016	(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
cost-diff	0	(fma.f64 x x #s(literal -1 binary64))
cost-diff	0	(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (neg (- 1 (* x x))) (*.f64 x x))
cost-diff	0	(exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x)))
cost-diff	0	#s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))
cost-diff	0	(exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))
cost-diff	0	(exp.f64 #s(literal -1 binary64))
cost-diff	0	(pow.f64 (*.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)))
cost-diff	384	(/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))
cost-diff	6720	(*.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64)))

Rules

4 848×	`lower-fma.f32`
4 844×	`lower-fma.f64`
2 928×	`lower-*.f32`
2 922×	`lower-*.f64`
1 772×	`lower-/.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	117
0	33	111
1	54	101
2	101	101
3	198	101
4	420	99
5	1042	99
6	2880	99
7	4348	99
8	6651	99
0	8212	99

Stop Event

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

Calls

Call 1

Inputs
(pow.f64 (*.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)))
(*.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64)))
(exp.f64 #s(literal -1 binary64))
#s(literal -1 binary64)
(/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -2 binary64)
(exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))
#s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))
#s(literal -1 binary64)
(exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x)))
#s(approx (neg (- 1 (* x x))) (*.f64 x x))
(*.f64 x x)
x
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
#s(approx (exp (neg (- 1 (* x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(fma.f64 x x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(exp.f64 #s(literal -1 binary64))
#s(literal -1 binary64)

Outputs
(pow.f64 (*.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)))
(pow.f64 (exp.f64 #s(literal -2 binary64)) (*.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64)))
(exp.f64 #s(literal -2 binary64))
(exp.f64 #s(literal -1 binary64))
#s(literal -1 binary64)
(/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))
(*.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -2 binary64)
(exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))
#s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))
#s(literal -1 binary64)
(exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x)))
#s(approx (neg (- 1 (* x x))) (*.f64 x x))
(*.f64 x x)
x
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
#s(approx (exp (neg (- 1 (* x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))))
#s(approx (exp (neg (- 1 (* x x)))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (E.f64)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(/.f64 (fma.f64 x x #s(literal 1 binary64)) (E.f64))
(fma.f64 x x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(exp.f64 #s(literal -1 binary64))
#s(literal -1 binary64)

localize68.0ms (1.2%)

Memory

30.7MiB live, 152.4MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x x #s(literal 1 binary64))
accuracy	0	(exp.f64 #s(literal -1 binary64))
accuracy	0.08203125	(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
accuracy	15.749480307460875	#s(approx (exp (neg (- 1 (* x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))))
accuracy	0	(fma.f64 x x #s(literal -1 binary64))
accuracy	0.03236485241743066	(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
accuracy	0	(*.f64 x x)
accuracy	0.03236485241743066	(exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x)))
accuracy	33.503467368885254	#s(approx (neg (- 1 (* x x))) (*.f64 x x))
accuracy	0.03236485241743066	(exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))
accuracy	30.642800304566002	#s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))
accuracy	0	(/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))
accuracy	0	(*.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64)))
accuracy	0	(exp.f64 #s(literal -1 binary64))
accuracy	0.01171875	(pow.f64 (*.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)))

Samples

56.0ms

256×

valid

Compiler

Compiled 106 to 18 computations (83% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

exact: 14.0ms (34.2% of total)

ival-exp: 10.0ms (24.5% of total)

ival-pow: 5.0ms (12.2% of total)

ival-mult: 4.0ms (9.8% of total)

ival-div: 2.0ms (4.9% of total)

ival-add: 2.0ms (4.9% of total)

ival-sub: 1.0ms (2.4% of total)

ival-neg: 1.0ms (2.4% of total)

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

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

series9.0ms (0.2%)

Memory

-17.3MiB live, 21.2MiB allocated

Counts

14 → 144

Calls

Call 1

Inputs
#s(alt (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (patch (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) (patch (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) #<representation binary64>) () ())
#s(alt (exp.f64 #s(literal -1 binary64)) (patch (exp.f64 #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) (patch (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) (patch #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) (.f64 x x))) (patch (exp.f64 #s(approx (neg (- 1 ( x x))) (*.f64 x x))) #<representation binary64>) () ())
#s(alt #s(approx (neg (- 1 (* x x))) (.f64 x x)) (patch #s(approx (neg (- 1 ( x x))) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (exp.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (exp.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (exp (neg (- 1 (* x x)))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) (patch #s(approx (exp (neg (- 1 ( x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())

Outputs
#s(alt 1/2 (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp -1) (taylor 0 x) (#s(alt (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) (patch (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* -1/2 (* (pow x 2) (* (exp -1) (log (pow (exp -1) 2)))))) (taylor 0 x) (#s(alt (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) (patch (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (+ (* -1/2 (* (exp -1) (log (pow (exp -1) 2)))) (* 1/8 (* (pow x 2) (* (exp -1) (pow (log (pow (exp -1) 2)) 2))))))) (taylor 0 x) (#s(alt (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) (patch (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (+ (* -1/2 (* (exp -1) (log (pow (exp -1) 2)))) (* (pow x 2) (+ (* -1/48 (* (pow x 2) (* (exp -1) (pow (log (pow (exp -1) 2)) 3)))) (* 1/8 (* (exp -1) (pow (log (pow (exp -1) 2)) 2)))))))) (taylor 0 x) (#s(alt (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) (patch (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp -1) (taylor 0 x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) (patch (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (exp -1))) (taylor 0 x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) (patch (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1)))))) (taylor 0 x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) (patch (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1))))))) (taylor 0 x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) (patch (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) (patch #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) (patch #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) (patch #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) (patch #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp -1) (taylor 0 x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) (.f64 x x))) (patch (exp.f64 #s(approx (neg (- 1 ( x x))) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (exp -1))) (taylor 0 x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) (.f64 x x))) (patch (exp.f64 #s(approx (neg (- 1 ( x x))) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1)))))) (taylor 0 x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) (.f64 x x))) (patch (exp.f64 #s(approx (neg (- 1 ( x x))) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1))))))) (taylor 0 x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) (.f64 x x))) (patch (exp.f64 #s(approx (neg (- 1 ( x x))) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt #s(approx (neg (- 1 (* x x))) (.f64 x x)) (patch #s(approx (neg (- 1 ( x x))) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt #s(approx (neg (- 1 (* x x))) (.f64 x x)) (patch #s(approx (neg (- 1 ( x x))) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt #s(approx (neg (- 1 (* x x))) (.f64 x x)) (patch #s(approx (neg (- 1 ( x x))) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt #s(approx (neg (- 1 (* x x))) (.f64 x x)) (patch #s(approx (neg (- 1 ( x x))) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (exp -1) (taylor 0 x) (#s(alt (exp.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (exp.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (exp -1))) (taylor 0 x) (#s(alt (exp.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (exp.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1)))))) (taylor 0 x) (#s(alt (exp.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (exp.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1))))))) (taylor 0 x) (#s(alt (exp.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (exp.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp -1) (taylor 0 x) (#s(alt (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (exp -1))) (taylor 0 x) (#s(alt (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (exp -1))) (taylor 0 x) (#s(alt (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (exp -1))) (taylor 0 x) (#s(alt (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp -1) (taylor 0 x) (#s(alt #s(approx (exp (neg (- 1 (* x x)))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) (patch #s(approx (exp (neg (- 1 ( x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (exp -1))) (taylor 0 x) (#s(alt #s(approx (exp (neg (- 1 (* x x)))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) (patch #s(approx (exp (neg (- 1 ( x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1)))))) (taylor 0 x) (#s(alt #s(approx (exp (neg (- 1 (* x x)))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) (patch #s(approx (exp (neg (- 1 ( x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1))))))) (taylor 0 x) (#s(alt #s(approx (exp (neg (- 1 (* x x)))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) (patch #s(approx (exp (neg (- 1 ( x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow x 2)) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (pow x 2)) (taylor inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2)) (taylor inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2)) (taylor inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2)) (taylor inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1)))) (taylor inf x) (#s(alt (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) (patch (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1)))) (taylor inf x) (#s(alt (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) (patch (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1)))) (taylor inf x) (#s(alt (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) (patch (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1)))) (taylor inf x) (#s(alt (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) (patch (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) (patch (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) (patch (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) (patch (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) (patch (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) (patch #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) (patch #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) (patch #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) (patch #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) (.f64 x x))) (patch (exp.f64 #s(approx (neg (- 1 ( x x))) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) (.f64 x x))) (patch (exp.f64 #s(approx (neg (- 1 ( x x))) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) (.f64 x x))) (patch (exp.f64 #s(approx (neg (- 1 ( x x))) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) (.f64 x x))) (patch (exp.f64 #s(approx (neg (- 1 ( x x))) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt #s(approx (neg (- 1 (* x x))) (.f64 x x)) (patch #s(approx (neg (- 1 ( x x))) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (neg (- 1 (* x x))) (.f64 x x)) (patch #s(approx (neg (- 1 ( x x))) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (neg (- 1 (* x x))) (.f64 x x)) (patch #s(approx (neg (- 1 ( x x))) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt #s(approx (neg (- 1 (* x x))) (.f64 x x)) (patch #s(approx (neg (- 1 ( x x))) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (exp.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (exp.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (exp.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (exp.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (exp.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (exp.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (exp.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (exp.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (exp -1)) (taylor inf x) (#s(alt (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (exp -1) (/ (exp -1) (pow x 2)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (exp -1) (/ (exp -1) (pow x 2)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (exp -1) (/ (exp -1) (pow x 2)))) (taylor inf x) (#s(alt (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt #s(approx (exp (neg (- 1 (* x x)))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) (patch #s(approx (exp (neg (- 1 ( x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt #s(approx (exp (neg (- 1 (* x x)))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) (patch #s(approx (exp (neg (- 1 ( x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt #s(approx (exp (neg (- 1 (* x x)))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) (patch #s(approx (exp (neg (- 1 ( x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt #s(approx (exp (neg (- 1 (* x x)))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) (patch #s(approx (exp (neg (- 1 ( x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) (patch (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1)))) (taylor -inf x) (#s(alt (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) (patch (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1)))) (taylor -inf x) (#s(alt (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) (patch (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1)))) (taylor -inf x) (#s(alt (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) (patch (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1)))) (taylor -inf x) (#s(alt (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) (patch (pow.f64 (.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) (patch (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) (patch (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) (patch (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) (patch (exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) (patch #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) (patch #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) (patch #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) (patch #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) (.f64 x x))) (patch (exp.f64 #s(approx (neg (- 1 ( x x))) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) (.f64 x x))) (patch (exp.f64 #s(approx (neg (- 1 ( x x))) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) (.f64 x x))) (patch (exp.f64 #s(approx (neg (- 1 ( x x))) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (exp.f64 #s(approx (neg (- 1 (* x x))) (.f64 x x))) (patch (exp.f64 #s(approx (neg (- 1 ( x x))) (*.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (neg (- 1 (* x x))) (.f64 x x)) (patch #s(approx (neg (- 1 ( x x))) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (neg (- 1 (* x x))) (.f64 x x)) (patch #s(approx (neg (- 1 ( x x))) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (neg (- 1 (* x x))) (.f64 x x)) (patch #s(approx (neg (- 1 ( x x))) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt #s(approx (neg (- 1 (* x x))) (.f64 x x)) (patch #s(approx (neg (- 1 ( x x))) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (exp.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (exp.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (exp.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (exp.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (exp.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (exp.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (exp.f64 (fma.f64 x x #s(literal -1 binary64))) (patch (exp.f64 (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (exp -1)) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (exp -1) (/ (exp -1) (pow x 2)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (exp -1) (/ (exp -1) (pow x 2)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ (exp -1) (/ (exp -1) (pow x 2)))) (taylor -inf x) (#s(alt (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) (patch (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt #s(approx (exp (neg (- 1 (* x x)))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) (patch #s(approx (exp (neg (- 1 ( x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt #s(approx (exp (neg (- 1 (* x x)))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) (patch #s(approx (exp (neg (- 1 ( x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt #s(approx (exp (neg (- 1 (* x x)))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) (patch #s(approx (exp (neg (- 1 ( x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt #s(approx (exp (neg (- 1 (* x x)))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) (patch #s(approx (exp (neg (- 1 ( x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal 1 binary64)) (patch (fma.f64 x x #s(literal 1 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

((* (exp -1) (exp -1)) (/ (+ (* x x) -1) -2) (pow (* (exp -1) (exp -1)) (/ (+ (* x x) -1) -2)) (exp -1) (exp (neg (- 1 (* x x)))) (neg (- 1 (* x x))) (exp (neg (- 1 (* x x)))) (neg (- 1 (* x x))) (* x x) (exp (+ (* x x) -1)) (+ (* x x) -1) (* (+ (* x x) 1) (exp -1)) (exp (neg (- 1 (* x x)))) (+ (* x x) 1))

1.0ms

inf

((* (exp -1) (exp -1)) (/ (+ (* x x) -1) -2) (pow (* (exp -1) (exp -1)) (/ (+ (* x x) -1) -2)) (exp -1) (exp (neg (- 1 (* x x)))) (neg (- 1 (* x x))) (exp (neg (- 1 (* x x)))) (neg (- 1 (* x x))) (* x x) (exp (+ (* x x) -1)) (+ (* x x) -1) (* (+ (* x x) 1) (exp -1)) (exp (neg (- 1 (* x x)))) (+ (* x x) 1))

1.0ms

-inf

((* (exp -1) (exp -1)) (/ (+ (* x x) -1) -2) (pow (* (exp -1) (exp -1)) (/ (+ (* x x) -1) -2)) (exp -1) (exp (neg (- 1 (* x x)))) (neg (- 1 (* x x))) (exp (neg (- 1 (* x x)))) (neg (- 1 (* x x))) (* x x) (exp (+ (* x x) -1)) (+ (* x x) -1) (* (+ (* x x) 1) (exp -1)) (exp (neg (- 1 (* x x)))) (+ (* x x) 1))

simplify279.0ms (4.8%)

Memory

-30.1MiB live, 273.4MiB allocated

Algorithm

1×	egg-herbie

Rules

34 434×	`lower-fma.f64`
34 434×	`lower-fma.f32`
5 796×	`lower-*.f64`
5 796×	`lower-*.f32`
2 798×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	1565
1	195	1407
2	618	879
3	2144	864
4	4032	864
5	6084	864
0	8064	740

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/2 (pow x 2)))
(+ 1/2 (* -1/2 (pow x 2)))
(+ 1/2 (* -1/2 (pow x 2)))
(exp -1)
(+ (exp -1) (* -1/2 (* (pow x 2) (* (exp -1) (log (pow (exp -1) 2))))))
(+ (exp -1) (* (pow x 2) (+ (* -1/2 (* (exp -1) (log (pow (exp -1) 2)))) (* 1/8 (* (pow x 2) (* (exp -1) (pow (log (pow (exp -1) 2)) 2)))))))
(+ (exp -1) (* (pow x 2) (+ (* -1/2 (* (exp -1) (log (pow (exp -1) 2)))) (* (pow x 2) (+ (* -1/48 (* (pow x 2) (* (exp -1) (pow (log (pow (exp -1) 2)) 3)))) (* 1/8 (* (exp -1) (pow (log (pow (exp -1) 2)) 2))))))))
(exp -1)
(+ (exp -1) (* (pow x 2) (exp -1)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1))))))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1)))))))
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
(exp -1)
(+ (exp -1) (* (pow x 2) (exp -1)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1))))))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1)))))))
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(exp -1)
(+ (exp -1) (* (pow x 2) (exp -1)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1))))))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1)))))))
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
(exp -1)
(+ (exp -1) (* (pow x 2) (exp -1)))
(+ (exp -1) (* (pow x 2) (exp -1)))
(+ (exp -1) (* (pow x 2) (exp -1)))
(exp -1)
(+ (exp -1) (* (pow x 2) (exp -1)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1))))))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1)))))))
1
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(+ 1 (pow x 2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1))))
(exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1))))
(exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1))))
(exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1))))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (exp -1))
(* (pow x 2) (+ (exp -1) (/ (exp -1) (pow x 2))))
(* (pow x 2) (+ (exp -1) (/ (exp -1) (pow x 2))))
(* (pow x 2) (+ (exp -1) (/ (exp -1) (pow x 2))))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1))))
(exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1))))
(exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1))))
(exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1))))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (exp -1))
(* (pow x 2) (+ (exp -1) (/ (exp -1) (pow x 2))))
(* (pow x 2) (+ (exp -1) (/ (exp -1) (pow x 2))))
(* (pow x 2) (+ (exp -1) (/ (exp -1) (pow x 2))))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/2 (pow x 2)))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1/2 binary64))
(+ 1/2 (* -1/2 (pow x 2)))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1/2 binary64))
(+ 1/2 (* -1/2 (pow x 2)))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1/2 binary64))
(exp -1)
(exp.f64 #s(literal -1 binary64))
(+ (exp -1) (* -1/2 (* (pow x 2) (* (exp -1) (log (pow (exp -1) 2))))))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* (pow x 2) (+ (* -1/2 (* (exp -1) (log (pow (exp -1) 2)))) (* 1/8 (* (pow x 2) (* (exp -1) (pow (log (pow (exp -1) 2)) 2)))))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64) (fma.f64 x x #s(literal 1 binary64))) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* (pow x 2) (+ (* -1/2 (* (exp -1) (log (pow (exp -1) 2)))) (* (pow x 2) (+ (* -1/48 (* (pow x 2) (* (exp -1) (pow (log (pow (exp -1) 2)) 3)))) (* 1/8 (* (exp -1) (pow (log (pow (exp -1) 2)) 2))))))))
(.f64 (exp.f64 #s(literal -1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal 1/2 binary64)) (fma.f64 x x #s(literal 1 binary64))))
(exp -1)
(exp.f64 #s(literal -1 binary64))
(+ (exp -1) (* (pow x 2) (exp -1)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1))))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64) (fma.f64 x x #s(literal 1 binary64))) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1)))))))
(.f64 (exp.f64 #s(literal -1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal 1/2 binary64)) (fma.f64 x x #s(literal 1 binary64))))
-1
#s(literal -1 binary64)
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(exp -1)
(exp.f64 #s(literal -1 binary64))
(+ (exp -1) (* (pow x 2) (exp -1)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1))))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64) (fma.f64 x x #s(literal 1 binary64))) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1)))))))
(.f64 (exp.f64 #s(literal -1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal 1/2 binary64)) (fma.f64 x x #s(literal 1 binary64))))
-1
#s(literal -1 binary64)
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(exp -1)
(exp.f64 #s(literal -1 binary64))
(+ (exp -1) (* (pow x 2) (exp -1)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1))))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64) (fma.f64 x x #s(literal 1 binary64))) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1)))))))
(.f64 (exp.f64 #s(literal -1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal 1/2 binary64)) (fma.f64 x x #s(literal 1 binary64))))
-1
#s(literal -1 binary64)
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(exp -1)
(exp.f64 #s(literal -1 binary64))
(+ (exp -1) (* (pow x 2) (exp -1)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* (pow x 2) (exp -1)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* (pow x 2) (exp -1)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(exp -1)
(exp.f64 #s(literal -1 binary64))
(+ (exp -1) (* (pow x 2) (exp -1)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1))))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64) (fma.f64 x x #s(literal 1 binary64))) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1)))))))
(.f64 (exp.f64 #s(literal -1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal 1/2 binary64)) (fma.f64 x x #s(literal 1 binary64))))
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(* -1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1/2 binary64))
(exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (exp -1))
(.f64 (.f64 (exp.f64 #s(literal -1 binary64)) x) x)
(* (pow x 2) (+ (exp -1) (/ (exp -1) (pow x 2))))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(* (pow x 2) (+ (exp -1) (/ (exp -1) (pow x 2))))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(* (pow x 2) (+ (exp -1) (/ (exp -1) (pow x 2))))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* -1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1/2 binary64))
(exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* -1/2 (* (log (pow (exp -1) 2)) (- (pow x 2) 1))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (exp -1))
(.f64 (.f64 (exp.f64 #s(literal -1 binary64)) x) x)
(* (pow x 2) (+ (exp -1) (/ (exp -1) (pow x 2))))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(* (pow x 2) (+ (exp -1) (/ (exp -1) (pow x 2))))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(* (pow x 2) (+ (exp -1) (/ (exp -1) (pow x 2))))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))

rewrite137.0ms (2.4%)

Memory

32.1MiB live, 187.0MiB allocated

Rules

4 434×	`lower-fma.f32`
4 430×	`lower-fma.f64`
3 164×	`lower-*.f32`
3 158×	`lower-*.f64`
2 930×	`lower-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	101
0	33	99
1	103	89
2	598	81
3	7165	81
0	8073	81

Stop Event

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

Counts

14 → 771

Calls

Call 1

Inputs
(*.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64)))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))
(pow.f64 (*.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)))
(exp.f64 #s(literal -1 binary64))
(exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))
#s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))
(exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x)))
#s(approx (neg (- 1 (* x x))) (*.f64 x x))
(*.f64 x x)
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 x x #s(literal -1 binary64))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
#s(approx (exp (neg (- 1 (* x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))))
(fma.f64 x x #s(literal 1 binary64))

Outputs
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eval261.0ms (4.5%)

Memory: -23.8MiB live, 327.4MiB allocated
Compiler: Compiled 20 710 to 2 707 computations (86.9% saved)

prune48.0ms (0.8%)

Memory

7.6MiB live, 92.9MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	1 177	2	1 179
Fresh	1	0	1
Picked	1	4	5
Done	0	0	0
Total	1 179	6	1 185

Accuracy

100.0%

Counts

1 185 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x))
▶	100.0%	(pow.f64 (exp.f64 #s(literal -2 binary64)) (*.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
✓	99.9%	(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
✓	56.0%	(exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x)))
✓	53.2%	(exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))
✓	75.4%	#s(approx (exp (neg (- 1 (* x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))))

Compiler

Compiled 38 to 33 computations (13.2% saved)

simplify151.0ms (2.6%)

Memory

34.6MiB live, 182.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	-512	(exp.f64 (-.f64 x #s(literal 1 binary64)))
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	(-.f64 x #s(literal 1 binary64))
cost-diff	0	(pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x))
cost-diff	0	(fma.f64 x x #s(literal -1 binary64))
cost-diff	0	(*.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))
cost-diff	0	(exp.f64 #s(literal -2 binary64))
cost-diff	0	(pow.f64 (exp.f64 #s(literal -2 binary64)) (*.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))

Rules

13 686×	`lower-fma.f32`
13 684×	`lower-fma.f64`
3 072×	`lower-*.f32`
3 070×	`lower-*.f64`
2 120×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	45
0	22	45
1	41	45
2	62	45
3	124	45
4	225	45
5	441	45
6	856	45
7	2892	45
8	4206	45
9	5894	45
0	8148	45

Stop Event

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

Calls

Call 1

Inputs
(pow.f64 (exp.f64 #s(literal -2 binary64)) (*.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
(exp.f64 #s(literal -2 binary64))
#s(literal -2 binary64)
(*.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))
#s(literal -1/2 binary64)
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x))
(exp.f64 (-.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(+.f64 #s(literal 1 binary64) x)

Outputs
(pow.f64 (exp.f64 #s(literal -2 binary64)) (*.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
(pow.f64 (exp.f64 #s(literal -2 binary64)) (*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(exp.f64 #s(literal -2 binary64))
#s(literal -2 binary64)
(*.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x))
(pow.f64 (/.f64 (exp.f64 x) (E.f64)) (-.f64 x #s(literal -1 binary64)))
(exp.f64 (-.f64 x #s(literal 1 binary64)))
(/.f64 (exp.f64 x) (E.f64))
(-.f64 x #s(literal 1 binary64))
x
#s(literal 1 binary64)
(+.f64 #s(literal 1 binary64) x)
(-.f64 x #s(literal -1 binary64))

localize51.0ms (0.9%)

Memory

-36.8MiB live, 82.0MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x #s(literal 1 binary64))
accuracy	0	(+.f64 #s(literal 1 binary64) x)
accuracy	0.01171875	(exp.f64 (-.f64 x #s(literal 1 binary64)))
accuracy	0.028601281620653757	(pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x))
accuracy	0	(fma.f64 x x #s(literal -1 binary64))
accuracy	0	(*.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))
accuracy	0	(exp.f64 #s(literal -2 binary64))
accuracy	0.01171875	(pow.f64 (exp.f64 #s(literal -2 binary64)) (*.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))

Samples

35.0ms

256×

valid

Compiler

Compiled 50 to 16 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-pow: 10.0ms (37.5% of total)

ival-exp: 7.0ms (26.2% of total)

ival-sub: 3.0ms (11.2% of total)

ival-mult: 3.0ms (11.2% of total)

ival-add: 2.0ms (7.5% of total)

exact: 1.0ms (3.7% of total)

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

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

series5.0ms (0.1%)

Memory

9.9MiB live, 9.9MiB allocated

Counts

8 → 84

Calls

Call 1

Inputs
#s(alt (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt (exp.f64 #s(literal -2 binary64)) (patch (exp.f64 #s(literal -2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (exp.f64 (-.f64 x #s(literal 1 binary64))) (patch (exp.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())

Outputs
#s(alt (exp -1) (taylor 0 x) (#s(alt (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (exp -1))) (taylor 0 x) (#s(alt (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1)))))) (taylor 0 x) (#s(alt (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1))))))) (taylor 0 x) (#s(alt (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 x) (#s(alt (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp -1) (taylor 0 x) (#s(alt (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (exp -1))) (taylor 0 x) (#s(alt (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1)))))) (taylor 0 x) (#s(alt (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1))))))) (taylor 0 x) (#s(alt (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- x 1) (taylor 0 x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (exp -1) (taylor 0 x) (#s(alt (exp.f64 (-.f64 x #s(literal 1 binary64))) (patch (exp.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* x (exp -1))) (taylor 0 x) (#s(alt (exp.f64 (-.f64 x #s(literal 1 binary64))) (patch (exp.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* x (+ (exp -1) (* 1/2 (* x (exp -1)))))) (taylor 0 x) (#s(alt (exp.f64 (-.f64 x #s(literal 1 binary64))) (patch (exp.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (exp -1) (* x (+ (exp -1) (* x (+ (* 1/6 (* x (exp -1))) (* 1/2 (exp -1))))))) (taylor 0 x) (#s(alt (exp.f64 (-.f64 x #s(literal 1 binary64))) (patch (exp.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor inf x) (#s(alt (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2)) (taylor inf x) (#s(alt (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2)) (taylor inf x) (#s(alt (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2)) (taylor inf x) (#s(alt (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ 1 x) (- x 1))) (taylor inf x) (#s(alt (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ 1 x) (- x 1))) (taylor inf x) (#s(alt (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ 1 x) (- x 1))) (taylor inf x) (#s(alt (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (exp (* (+ 1 x) (- x 1))) (taylor inf x) (#s(alt (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (- 1 (/ 1 x))) (taylor inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (exp (- x 1)) (taylor inf x) (#s(alt (exp.f64 (-.f64 x #s(literal 1 binary64))) (patch (exp.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- x 1)) (taylor inf x) (#s(alt (exp.f64 (-.f64 x #s(literal 1 binary64))) (patch (exp.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- x 1)) (taylor inf x) (#s(alt (exp.f64 (-.f64 x #s(literal 1 binary64))) (patch (exp.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- x 1)) (taylor inf x) (#s(alt (exp.f64 (-.f64 x #s(literal 1 binary64))) (patch (exp.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (- (pow x 2) 1)) (taylor -inf x) (#s(alt (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (exp.f64 #s(literal -2 binary64)) (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1/2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2)) (taylor -inf x) (#s(alt (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2)) (taylor -inf x) (#s(alt (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2)) (taylor -inf x) (#s(alt (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 (* (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 (* (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 (* (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 (* (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (/ 1 x) 1))) (taylor -inf x) (#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (exp (neg (+ 1 (* -1 x)))) (taylor -inf x) (#s(alt (exp.f64 (-.f64 x #s(literal 1 binary64))) (patch (exp.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (neg (+ 1 (* -1 x)))) (taylor -inf x) (#s(alt (exp.f64 (-.f64 x #s(literal 1 binary64))) (patch (exp.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (neg (+ 1 (* -1 x)))) (taylor -inf x) (#s(alt (exp.f64 (-.f64 x #s(literal 1 binary64))) (patch (exp.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (neg (+ 1 (* -1 x)))) (taylor -inf x) (#s(alt (exp.f64 (-.f64 x #s(literal 1 binary64))) (patch (exp.f64 (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

((pow (exp -2) (* -1/2 (+ (* x x) -1))) (exp -2) (* -1/2 (+ (* x x) -1)) (+ (* x x) -1) (pow (exp (- x 1)) (+ 1 x)) (- x 1) (+ 1 x) (exp (- x 1)))

1.0ms

inf

((pow (exp -2) (* -1/2 (+ (* x x) -1))) (exp -2) (* -1/2 (+ (* x x) -1)) (+ (* x x) -1) (pow (exp (- x 1)) (+ 1 x)) (- x 1) (+ 1 x) (exp (- x 1)))

1.0ms

-inf

((pow (exp -2) (* -1/2 (+ (* x x) -1))) (exp -2) (* -1/2 (+ (* x x) -1)) (+ (* x x) -1) (pow (exp (- x 1)) (+ 1 x)) (- x 1) (+ 1 x) (exp (- x 1)))

simplify156.0ms (2.7%)

Memory

20.4MiB live, 225.7MiB allocated

Algorithm

1×	egg-herbie

Rules

10 342×	`lower-fma.f64`
10 342×	`lower-fma.f32`
3 850×	`lower-*.f64`
3 850×	`lower-*.f32`
2 024×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	467
1	193	455
2	537	446
3	1837	438
4	5582	438
0	8384	388

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 80

Calls

Call 1

Inputs
(exp -1)
(+ (exp -1) (* (pow x 2) (exp -1)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1))))))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1)))))))
1/2
(+ 1/2 (* -1/2 (pow x 2)))
(+ 1/2 (* -1/2 (pow x 2)))
(+ 1/2 (* -1/2 (pow x 2)))
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
(exp -1)
(+ (exp -1) (* (pow x 2) (exp -1)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1))))))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1)))))))
-1
(- x 1)
(- x 1)
(- x 1)
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
(exp -1)
(+ (exp -1) (* x (exp -1)))
(+ (exp -1) (* x (+ (exp -1) (* 1/2 (* x (exp -1))))))
(+ (exp -1) (* x (+ (exp -1) (* x (+ (* 1/6 (* x (exp -1))) (* 1/2 (exp -1)))))))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(exp (* (+ 1 x) (- x 1)))
(exp (* (+ 1 x) (- x 1)))
(exp (* (+ 1 x) (- x 1)))
(exp (* (+ 1 x) (- x 1)))
x
(* x (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
(* x (- 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(exp (- x 1))
(exp (- x 1))
(exp (- x 1))
(exp (- x 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(exp (- (pow x 2) 1))
(* -1/2 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(exp (* -1 (* (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(exp (* -1 (* (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(exp (* -1 (* (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(exp (* -1 (* (+ 1 (* -1 x)) (- 1 (* -1 x)))))
x
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* x (- (/ 1 x) 1)))
(* -1 (* x (- (/ 1 x) 1)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(exp (neg (+ 1 (* -1 x))))
(exp (neg (+ 1 (* -1 x))))
(exp (neg (+ 1 (* -1 x))))
(exp (neg (+ 1 (* -1 x))))

Outputs
(exp -1)
(exp.f64 #s(literal -1 binary64))
(+ (exp -1) (* (pow x 2) (exp -1)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1))))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64) (fma.f64 x x #s(literal 1 binary64))) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1)))))))
(.f64 (exp.f64 #s(literal -1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal 1/2 binary64)) (fma.f64 x x #s(literal 1 binary64))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(+ 1/2 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1/2 binary64))
-1
#s(literal -1 binary64)
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(exp -1)
(exp.f64 #s(literal -1 binary64))
(+ (exp -1) (* (pow x 2) (exp -1)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* 1/2 (* (pow x 2) (exp -1))))))
(*.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64) (fma.f64 x x #s(literal 1 binary64))) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* (pow x 2) (+ (exp -1) (* (pow x 2) (+ (* 1/6 (* (pow x 2) (exp -1))) (* 1/2 (exp -1)))))))
(.f64 (exp.f64 #s(literal -1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 1/6 binary64) x) x #s(literal 1/2 binary64)) (fma.f64 x x #s(literal 1 binary64))))
-1
#s(literal -1 binary64)
(- x 1)
(-.f64 x #s(literal 1 binary64))
(- x 1)
(-.f64 x #s(literal 1 binary64))
(- x 1)
(-.f64 x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 x)
(-.f64 x #s(literal -1 binary64))
(+ 1 x)
(-.f64 x #s(literal -1 binary64))
(+ 1 x)
(-.f64 x #s(literal -1 binary64))
(exp -1)
(exp.f64 #s(literal -1 binary64))
(+ (exp -1) (* x (exp -1)))
(fma.f64 x (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* x (+ (exp -1) (* 1/2 (* x (exp -1))))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(+ (exp -1) (* x (+ (exp -1) (* x (+ (* 1/6 (* x (exp -1))) (* 1/2 (exp -1)))))))
(fma.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))) x (exp.f64 #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(exp (* (+ 1 x) (- x 1)))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* (+ 1 x) (- x 1)))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* (+ 1 x) (- x 1)))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* (+ 1 x) (- x 1)))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
x
(* x (- 1 (/ 1 x)))
(-.f64 x #s(literal 1 binary64))
(* x (- 1 (/ 1 x)))
(-.f64 x #s(literal 1 binary64))
(* x (- 1 (/ 1 x)))
(-.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(-.f64 x #s(literal -1 binary64))
(* x (+ 1 (/ 1 x)))
(-.f64 x #s(literal -1 binary64))
(* x (+ 1 (/ 1 x)))
(-.f64 x #s(literal -1 binary64))
(exp (- x 1))
(/.f64 (exp.f64 x) (E.f64))
(exp (- x 1))
(/.f64 (exp.f64 x) (E.f64))
(exp (- x 1))
(/.f64 (exp.f64 x) (E.f64))
(exp (- x 1))
(/.f64 (exp.f64 x) (E.f64))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (- (pow x 2) 1))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(* -1/2 (pow x 2))
(.f64 #s(literal -1/2 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/2))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(exp (* -1 (* (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* -1 (* (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* -1 (* (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* -1 (* (+ 1 (* -1 x)) (- 1 (* -1 x)))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
x
(* -1 (* x (- (/ 1 x) 1)))
(-.f64 x #s(literal 1 binary64))
(* -1 (* x (- (/ 1 x) 1)))
(-.f64 x #s(literal 1 binary64))
(* -1 (* x (- (/ 1 x) 1)))
(-.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(-.f64 x #s(literal -1 binary64))
(* x (+ 1 (/ 1 x)))
(-.f64 x #s(literal -1 binary64))
(* x (+ 1 (/ 1 x)))
(-.f64 x #s(literal -1 binary64))
(exp (neg (+ 1 (* -1 x))))
(/.f64 (exp.f64 x) (E.f64))
(exp (neg (+ 1 (* -1 x))))
(/.f64 (exp.f64 x) (E.f64))
(exp (neg (+ 1 (* -1 x))))
(/.f64 (exp.f64 x) (E.f64))
(exp (neg (+ 1 (* -1 x))))
(/.f64 (exp.f64 x) (E.f64))

rewrite156.0ms (2.7%)

Memory

-2.3MiB live, 219.9MiB allocated

Rules

6 824×	`lower-fma.f32`
6 822×	`lower-fma.f64`
3 838×	`lower-*.f32`
3 836×	`lower-*.f64`
3 276×	`lower-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	39
0	22	40
1	96	34
2	590	32
3	6703	32
0	8521	32

Stop Event

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

Counts

8 → 1 079

Calls

Call 1

Inputs
(pow.f64 (exp.f64 #s(literal -2 binary64)) (*.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
(exp.f64 #s(literal -2 binary64))
(*.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))
(fma.f64 x x #s(literal -1 binary64))
(pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x))
(-.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
(exp.f64 (-.f64 x #s(literal 1 binary64)))

Outputs
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eval208.0ms (3.6%)

Memory: -23.0MiB live, 387.1MiB allocated
Compiler: Compiled 22 750 to 3 341 computations (85.3% saved)

prune21.0ms (0.4%)

Memory

9.9MiB live, 88.4MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	1 157	2	1 159
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	1 157	8	1 165

Accuracy

100.0%

Counts

1 165 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
✓	99.9%	(pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x))
✓	100.0%	(pow.f64 (exp.f64 #s(literal -2 binary64)) (*.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
▶	99.9%	(pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64)))
✓	99.9%	(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
✓	56.0%	(exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x)))
✓	53.2%	(exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))
✓	75.4%	#s(approx (exp (neg (- 1 (* x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))))

Compiler

Compiled 54 to 46 computations (14.8% saved)

simplify170.0ms (2.9%)

Memory

10.4MiB live, 132.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 x x #s(literal -1 binary64))
cost-diff	0	(*.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))
cost-diff	0	(E.f64)
cost-diff	0	(pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
cost-diff	0	(fma.f64 x x #s(literal -1 binary64))
cost-diff	0	(E.f64)
cost-diff	0	(pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64)))

Rules

17 640×	`lower-fma.f32`
17 638×	`lower-fma.f64`
2 642×	`lower-+.f64`
2 642×	`lower-+.f32`
2 444×	`lower--.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	40
0	16	40
1	30	38
2	49	38
3	83	38
4	175	38
5	361	38
6	736	38
7	1358	38
8	4039	38
9	6021	38
10	7897	38
0	8095	38

Stop Event

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

Calls

Call 1

Inputs
(pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64)))
(E.f64)
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (E.f64) (E.f64))
(E.f64)
(*.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))
#s(literal 1/2 binary64)
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)

Outputs
(pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64)))
(E.f64)
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)
(pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (E.f64) (E.f64))
(exp.f64 #s(literal 2 binary64))
(E.f64)
(*.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))
#s(literal 1/2 binary64)
(fma.f64 x x #s(literal -1 binary64))
x
#s(literal -1 binary64)

localize54.0ms (0.9%)

Memory

-7.6MiB live, 31.7MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))
accuracy	0	(E.f64)
accuracy	0.02999796913869315	(pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
accuracy	1.0	(*.f64 (E.f64) (E.f64))
accuracy	0	(fma.f64 x x #s(literal -1 binary64))
accuracy	0	(E.f64)
accuracy	0.0386040744115697	(pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64)))

Samples

47.0ms

256×

valid

Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 39.0ms

ival-mult: 26.0ms (66.4% of total)

ival-pow: 9.0ms (23% of total)

ival-e: 2.0ms (5.1% of total)

ival-add: 1.0ms (2.6% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

4.9MiB live, 4.9MiB allocated

Counts

6 → 48

Calls

Call 1

Inputs
#s(alt (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) (patch (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (E.f64) (patch (E.f64) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (E.f64) (E.f64)) (patch (.f64 (E.f64) (E.f64)) #<representation binary64>) () ())

Outputs
#s(alt (/ 1 (E)) (taylor 0 x) (#s(alt (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) (patch (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (/ 1 (E)) (/ (* (pow x 2) (log (E))) (E))) (taylor 0 x) (#s(alt (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) (patch (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow x 2) (+ (* 1/2 (/ (* (pow x 2) (pow (log (E)) 2)) (E))) (/ (log (E)) (E)))) (/ 1 (E))) (taylor 0 x) (#s(alt (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) (patch (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow x 2) (+ (* (pow x 2) (+ (* 1/6 (/ (* (pow x 2) (pow (log (E)) 3)) (E))) (* 1/2 (/ (pow (log (E)) 2) (E))))) (/ (log (E)) (E)))) (/ 1 (E))) (taylor 0 x) (#s(alt (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) (patch (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (E)) (taylor 0 x) (#s(alt (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ (* (pow x 2) (log (pow (E) 2))) (E))) (/ 1 (E))) (taylor 0 x) (#s(alt (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow x 2) (+ (* 1/8 (/ (* (pow x 2) (pow (log (pow (E) 2)) 2)) (E))) (* 1/2 (/ (log (pow (E) 2)) (E))))) (/ 1 (E))) (taylor 0 x) (#s(alt (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow x 2) (+ (* 1/2 (/ (log (pow (E) 2)) (E))) (* (pow x 2) (+ (* 1/48 (/ (* (pow x 2) (pow (log (pow (E) 2)) 3)) (E))) (* 1/8 (/ (pow (log (pow (E) 2)) 2) (E))))))) (/ 1 (E))) (taylor 0 x) (#s(alt (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt -1/2 (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/2 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (E)) (- (pow x 2) 1))) (taylor inf x) (#s(alt (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) (patch (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (E)) (- (pow x 2) 1))) (taylor inf x) (#s(alt (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) (patch (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (E)) (- (pow x 2) 1))) (taylor inf x) (#s(alt (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) (patch (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (E)) (- (pow x 2) 1))) (taylor inf x) (#s(alt (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) (patch (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1)))) (taylor inf x) (#s(alt (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1)))) (taylor inf x) (#s(alt (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1)))) (taylor inf x) (#s(alt (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1)))) (taylor inf x) (#s(alt (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/2 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/2 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/2 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (E)) (- (pow x 2) 1))) (taylor -inf x) (#s(alt (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) (patch (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (E)) (- (pow x 2) 1))) (taylor -inf x) (#s(alt (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) (patch (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (E)) (- (pow x 2) 1))) (taylor -inf x) (#s(alt (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) (patch (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* (log (E)) (- (pow x 2) 1))) (taylor -inf x) (#s(alt (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) (patch (pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -1 binary64)) (patch (fma.f64 x x #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1)))) (taylor -inf x) (#s(alt (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1)))) (taylor -inf x) (#s(alt (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1)))) (taylor -inf x) (#s(alt (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1)))) (taylor -inf x) (#s(alt (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) (patch (pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/2 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/2 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/2 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) (patch (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

((pow (E) (+ (* x x) -1)) (E) (+ (* x x) -1) (pow (* (E) (E)) (* 1/2 (+ (* x x) -1))) (* 1/2 (+ (* x x) -1)) (* (E) (E)))

0.0ms

inf

((pow (E) (+ (* x x) -1)) (E) (+ (* x x) -1) (pow (* (E) (E)) (* 1/2 (+ (* x x) -1))) (* 1/2 (+ (* x x) -1)) (* (E) (E)))

0.0ms

-inf

((pow (E) (+ (* x x) -1)) (E) (+ (* x x) -1) (pow (* (E) (E)) (* 1/2 (+ (* x x) -1))) (* 1/2 (+ (* x x) -1)) (* (E) (E)))

simplify184.0ms (3.2%)

Memory

-8.0MiB live, 109.7MiB allocated

Algorithm

1×	egg-herbie

Rules

10 766×	`lower-fma.f64`
10 766×	`lower-fma.f32`
5 100×	`lower-*.f64`
5 100×	`lower-*.f32`
1 964×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	366
1	210	326
2	604	314
3	1840	310
4	3622	308
5	5790	308
0	8188	262

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
(/ 1 (E))
(+ (/ 1 (E)) (/ (* (pow x 2) (log (E))) (E)))
(+ (* (pow x 2) (+ (* 1/2 (/ (* (pow x 2) (pow (log (E)) 2)) (E))) (/ (log (E)) (E)))) (/ 1 (E)))
(+ (* (pow x 2) (+ (* (pow x 2) (+ (* 1/6 (/ (* (pow x 2) (pow (log (E)) 3)) (E))) (* 1/2 (/ (pow (log (E)) 2) (E))))) (/ (log (E)) (E)))) (/ 1 (E)))
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
(/ 1 (E))
(+ (* 1/2 (/ (* (pow x 2) (log (pow (E) 2))) (E))) (/ 1 (E)))
(+ (* (pow x 2) (+ (* 1/8 (/ (* (pow x 2) (pow (log (pow (E) 2)) 2)) (E))) (* 1/2 (/ (log (pow (E) 2)) (E))))) (/ 1 (E)))
(+ (* (pow x 2) (+ (* 1/2 (/ (log (pow (E) 2)) (E))) (* (pow x 2) (+ (* 1/48 (/ (* (pow x 2) (pow (log (pow (E) 2)) 3)) (E))) (* 1/8 (/ (pow (log (pow (E) 2)) 2) (E))))))) (/ 1 (E)))
-1/2
(- (* 1/2 (pow x 2)) 1/2)
(- (* 1/2 (pow x 2)) 1/2)
(- (* 1/2 (pow x 2)) 1/2)
(exp (* (log (E)) (- (pow x 2) 1)))
(exp (* (log (E)) (- (pow x 2) 1)))
(exp (* (log (E)) (- (pow x 2) 1)))
(exp (* (log (E)) (- (pow x 2) 1)))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1))))
(exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1))))
(exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1))))
(exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1))))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/2 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/2 (* 1/2 (/ 1 (pow x 2)))))
(exp (* (log (E)) (- (pow x 2) 1)))
(exp (* (log (E)) (- (pow x 2) 1)))
(exp (* (log (E)) (- (pow x 2) 1)))
(exp (* (log (E)) (- (pow x 2) 1)))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1))))
(exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1))))
(exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1))))
(exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1))))
(* 1/2 (pow x 2))
(* (pow x 2) (- 1/2 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/2 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/2 (* 1/2 (/ 1 (pow x 2)))))

Outputs
(/ 1 (E))
(exp.f64 #s(literal -1 binary64))
(+ (/ 1 (E)) (/ (* (pow x 2) (log (E))) (E)))
(/.f64 (fma.f64 x x #s(literal 1 binary64)) (E.f64))
(+ (* (pow x 2) (+ (* 1/2 (/ (* (pow x 2) (pow (log (E)) 2)) (E))) (/ (log (E)) (E)))) (/ 1 (E)))
(/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64) (fma.f64 x x #s(literal 1 binary64))) (E.f64))
(+ (* (pow x 2) (+ (* (pow x 2) (+ (* 1/6 (/ (* (pow x 2) (pow (log (E)) 3)) (E))) (* 1/2 (/ (pow (log (E)) 2) (E))))) (/ (log (E)) (E)))) (/ 1 (E)))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (E.f64)) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 1/2 binary64)) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (E.f64)))
-1
#s(literal -1 binary64)
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(/ 1 (E))
(exp.f64 #s(literal -1 binary64))
(+ (* 1/2 (/ (* (pow x 2) (log (pow (E) 2))) (E))) (/ 1 (E)))
(/.f64 (fma.f64 x x #s(literal 1 binary64)) (E.f64))
(+ (* (pow x 2) (+ (* 1/8 (/ (* (pow x 2) (pow (log (pow (E) 2)) 2)) (E))) (* 1/2 (/ (log (pow (E) 2)) (E))))) (/ 1 (E)))
(/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64) (fma.f64 x x #s(literal 1 binary64))) (E.f64))
(+ (* (pow x 2) (+ (* 1/2 (/ (log (pow (E) 2)) (E))) (* (pow x 2) (+ (* 1/48 (/ (* (pow x 2) (pow (log (pow (E) 2)) 3)) (E))) (* 1/8 (/ (pow (log (pow (E) 2)) 2) (E))))))) (/ 1 (E)))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (E.f64)) (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 1/2 binary64)) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (E.f64)))
-1/2
#s(literal -1/2 binary64)
(- (* 1/2 (pow x 2)) 1/2)
(*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(- (* 1/2 (pow x 2)) 1/2)
(*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(- (* 1/2 (pow x 2)) 1/2)
(*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(exp (* (log (E)) (- (pow x 2) 1)))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* (log (E)) (- (pow x 2) 1)))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* (log (E)) (- (pow x 2) 1)))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* (log (E)) (- (pow x 2) 1)))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (- 1/2 (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- 1/2 (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- 1/2 (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(exp (* (log (E)) (- (pow x 2) 1)))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* (log (E)) (- (pow x 2) 1)))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* (log (E)) (- (pow x 2) 1)))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* (log (E)) (- (pow x 2) 1)))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal -1 binary64))
(exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* 1/2 (* (log (pow (E) 2)) (- (pow x 2) 1))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (- 1/2 (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- 1/2 (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (- 1/2 (* 1/2 (/ 1 (pow x 2)))))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1/2 binary64))

rewrite207.0ms (3.6%)

Memory

13.0MiB live, 95.7MiB allocated

Rules

4 142×	`lower-*.f32`
4 138×	`lower-*.f64`
3 980×	`lower-fma.f32`
3 978×	`lower-fma.f64`
3 502×	`lower-pow.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	30
0	16	26
1	77	25
2	506	23
3	4618	23
0	8501	23

Stop Event

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

Counts

6 → 931

Calls

Call 1

Inputs
(pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64)))
(E.f64)
(fma.f64 x x #s(literal -1 binary64))
(pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (E.f64) (E.f64))

Outputs
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eval262.0ms (4.5%)

Memory: -34.8MiB live, 141.6MiB allocated
Compiler: Compiled 28 637 to 3 342 computations (88.3% saved)

prune56.0ms (1%)

Memory

16.9MiB live, 56.7MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	1 489	1	1 490
Fresh	0	0	0
Picked	0	2	2
Done	2	4	6
Total	1 491	7	1 498

Accuracy

100.0%

Counts

1 498 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
✓	99.9%	(pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x))
✓	100.0%	(pow.f64 (exp.f64 #s(literal -2 binary64)) (*.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
✓	99.9%	(pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64)))
✓	99.9%	(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
✓	56.0%	(exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x)))
	75.4%	#s(approx (pow (* (E) (E)) (* 1/2 (+ (* x x) -1))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (E.f64)))

Compiler

Compiled 136 to 81 computations (40.4% saved)

regimes18.0ms (0.3%)

Memory

10.4MiB live, 10.4MiB allocated

Counts

12 → 1

Calls

Call 1

Inputs
#s(approx (pow (* (E) (E)) (* 1/2 (+ (* x x) -1))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (E.f64)))
(exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))
(exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x)))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64)))
(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
#s(approx (exp (neg (- 1 (* x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))))
(pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
(pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x))
(/.f64 (pow.f64 (exp.f64 x) x) (E.f64))
(pow.f64 (exp.f64 #s(literal -2 binary64)) (*.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
(pow.f64 (*.f64 (exp.f64 #s(literal -1 binary64)) (exp.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)))

Outputs
(pow.f64 (exp.f64 #s(literal -2 binary64)) (*.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))

Calls

5 calls:

4.0ms	x
4.0ms	(*.f64 x x)
3.0ms	(-.f64 #s(literal 1 binary64) (*.f64 x x))
3.0ms	(neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
3.0ms	(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))

Results

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

Compiler

Compiled 22 to 18 computations (18.2% saved)

regimes54.0ms (0.9%)

Memory

-29.4MiB live, 10.1MiB allocated

Counts

10 → 1

Calls

Call 1

Inputs
#s(approx (pow (* (E) (E)) (* 1/2 (+ (* x x) -1))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (E.f64)))
(exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))
(exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x)))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64)))
(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
#s(approx (exp (neg (- 1 (* x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))))
(pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
(pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x))
(/.f64 (pow.f64 (exp.f64 x) x) (E.f64))

Outputs
(/.f64 (pow.f64 (exp.f64 x) x) (E.f64))

Calls

5 calls:

41.0ms	(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
3.0ms	x
3.0ms	(*.f64 x x)
3.0ms	(-.f64 #s(literal 1 binary64) (*.f64 x x))
3.0ms	(neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

Results

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

Compiler

Compiled 22 to 18 computations (18.2% saved)

regimes14.0ms (0.2%)

Memory

9.1MiB live, 9.1MiB allocated

Counts

9 → 1

Calls

Call 1

Inputs
#s(approx (pow (* (E) (E)) (* 1/2 (+ (* x x) -1))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (E.f64)))
(exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))
(exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x)))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64)))
(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
#s(approx (exp (neg (- 1 (* x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))))
(pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
(pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x))

Outputs
(pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))

Calls

5 calls:

3.0ms	x
3.0ms	(*.f64 x x)
3.0ms	(-.f64 #s(literal 1 binary64) (*.f64 x x))
2.0ms	(neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
2.0ms	(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))`
99.9%	1	`(neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
99.9%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
99.9%	1	`(*.f64 x x)`

Compiler

Compiled 22 to 18 computations (18.2% saved)

regimes12.0ms (0.2%)

Memory

8.5MiB live, 8.5MiB allocated

Counts

7 → 1

Calls

Call 1

Inputs
#s(approx (pow (* (E) (E)) (* 1/2 (+ (* x x) -1))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (E.f64)))
(exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))
(exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x)))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow.f64 (E.f64) (fma.f64 x x #s(literal -1 binary64)))
(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
#s(approx (exp (neg (- 1 (* x x)))) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64))))

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

Calls

5 calls:

3.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(-.f64 #s(literal 1 binary64) (*.f64 x x))
2.0ms	(neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
2.0ms	(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))`
99.9%	1	`(neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
99.9%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
99.9%	1	`(*.f64 x x)`

Compiler

Compiled 22 to 18 computations (18.2% saved)

regimes8.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

#s(approx (pow (* (E) (E)) (* 1/2 (+ (* x x) -1))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (E.f64)))

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

(exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x)))

Outputs
#s(approx (pow (* (E) (E)) (* 1/2 (+ (* x x) -1))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (E.f64)))
(exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x)))

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
99.1%	2	`x`
99.1%	2	`(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))`
99.1%	2	`(neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
99.1%	2	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
99.1%	2	`(*.f64 x x)`

Compiler

Compiled 22 to 18 computations (18.2% saved)

regimes7.0ms (0.1%)

Memory

6.3MiB live, 6.3MiB allocated

Accuracy

Total -14.2b remaining (-90.2%)

Threshold costs -14.2b (-90.2%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (pow (* (E) (E)) (* 1/2 (+ (* x x) -1))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (E.f64)))
(exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))

Outputs
#s(approx (pow (* (E) (E)) (* 1/2 (+ (* x x) -1))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (E.f64)))

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
75.4%	1	`x`
75.4%	1	`(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))`
75.4%	1	`(neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
75.4%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
75.4%	1	`(*.f64 x x)`

Compiler

Compiled 22 to 18 computations (18.2% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0035891072538425427	690.9357297908474

Compiler

Compiled 10 to 10 computations (0% saved)

simplify39.0ms (0.7%)

Memory

-20.9MiB live, 19.0MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`-commutative-binary64-.f64`
2×	`1-exp-binary32-exp.f32`
2×	`e-exp-1-binary64-exp.f64-E.f64`
2×	`1-exp-binary64-exp.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	83
1	41	83

Stop Event

1×

saturated

Calls

Call 1

Inputs
(pow.f64 (exp.f64 #s(literal -2 binary64)) (*.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (pow.f64 (exp.f64 x) x) (E.f64))
(pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(if (<=.f64 (.f64 x x) #s(literal 5764607523034235/1152921504606846976 binary64)) #s(approx (pow ( (E) (E)) (* 1/2 (+ (* x x) -1))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (E.f64))) (exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x))))
#s(approx (pow (* (E) (E)) (* 1/2 (+ (* x x) -1))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (E.f64)))

Outputs
(pow.f64 (exp.f64 #s(literal -2 binary64)) (*.f64 #s(literal -1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
(pow.f64 (exp.f64 #s(literal -2 binary64)) (*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (exp.f64 x) x) (E.f64))
(pow.f64 (.f64 (E.f64) (E.f64)) (.f64 #s(literal 1/2 binary64) (fma.f64 x x #s(literal -1 binary64))))
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(if (<=.f64 (.f64 x x) #s(literal 5764607523034235/1152921504606846976 binary64)) #s(approx (pow ( (E) (E)) (* 1/2 (+ (* x x) -1))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (E.f64))) (exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x))))
#s(approx (pow (* (E) (E)) (* 1/2 (+ (* x x) -1))) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (E.f64)))

soundness781.0ms (13.4%)

Memory

2.4MiB live, 365.8MiB allocated

Rules

10 766×	`lower-fma.f64`
10 766×	`lower-fma.f32`
9 734×	`lower-fma.f64`
9 734×	`lower-fma.f32`
6 824×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	254
1	81	241
2	247	237
3	605	234
4	1328	234
5	2025	234
6	3122	234
7	5538	234
0	8219	211
0	76	366
1	210	326
2	604	314
3	1840	310
4	3622	308
5	5790	308
0	8188	262
0	6	21
0	10	21
1	37	19
2	227	19
3	1923	19
0	9304	16
0	22	101
0	33	99
1	103	89
2	598	81
3	7165	81
0	8073	81
0	13	39
0	22	40
1	96	34
2	590	32
3	6703	32
0	8521	32

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 231 to 127 computations (45% saved)

preprocess39.0ms (0.7%)

Memory: 6.1MiB live, 83.7MiB allocated
Remove: (abs x)
Compiler: Compiled 160 to 98 computations (38.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample809.0ms (13.9%)

explain76.0ms (1.3%)

preprocess377.0ms (6.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify391.0ms (6.7%)

localize75.0ms (1.3%)

series3.0ms (0%)

simplify208.0ms (3.6%)

rewrite175.0ms (3%)

eval114.0ms (2%)

prune12.0ms (0.2%)

simplify115.0ms (2%)

localize68.0ms (1.2%)

series9.0ms (0.2%)

simplify279.0ms (4.8%)

rewrite137.0ms (2.4%)

eval261.0ms (4.5%)

prune48.0ms (0.8%)

simplify151.0ms (2.6%)

localize51.0ms (0.9%)

series5.0ms (0.1%)

simplify156.0ms (2.7%)

rewrite156.0ms (2.7%)

eval208.0ms (3.6%)

prune21.0ms (0.4%)

simplify170.0ms (2.9%)

localize54.0ms (0.9%)

series5.0ms (0.1%)

simplify184.0ms (3.2%)

rewrite207.0ms (3.6%)

eval262.0ms (4.5%)

prune56.0ms (1%)

regimes18.0ms (0.3%)

regimes54.0ms (0.9%)

regimes14.0ms (0.2%)

regimes12.0ms (0.2%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

bsearch0.0ms (0%)

simplify39.0ms (0.7%)

soundness781.0ms (13.4%)

preprocess39.0ms (0.7%)

end0.0ms (0%)

Profiling