Metrics for exp neg sub

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.6MiB live, 0.6MiB 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)

sample1.2s (26.9%)

Memory

16.7MiB live, 1 236.4MiB allocated

Samples

990.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 782.0ms

ival-exp: 520.0ms (66.5% of total)

ival-mult: 148.0ms (18.9% of total)

ival-neg: 52.0ms (6.7% of total)

ival-sub: 47.0ms (6% of total)

ival-true: 6.0ms (0.8% of total)

exact: 5.0ms (0.6% of total)

ival-assert: 4.0ms (0.5% of total)

Bogosity

explain160.0ms (3.5%)

Memory

-18.4MiB live, 282.8MiB allocated

FPErrors

Click to see full error table

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

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

99.0ms

512×

valid

Compiler

Compiled 57 to 22 computations (61.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

ival-mult: 60.0ms (85.6% of total)

ival-exp: 4.0ms (5.7% of total)

ival-sub: 2.0ms (2.9% of total)

ival-neg: 2.0ms (2.9% of total)

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

exact: 0.0ms (0% of total)

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

preprocess232.0ms (5.1%)

Memory

14.8MiB live, 248.4MiB allocated

Algorithm

1×	egg-herbie

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: 0.6MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.9MiB live, 1.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify141.0ms (3.1%)

Memory

-1.3MiB live, 153.4MiB 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)))

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

localize19.0ms (0.4%)

Memory

9.2MiB live, 47.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0	(neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
accuracy	0.00390625	(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))
accuracy	0.009070031620653759	(-.f64 #s(literal 1 binary64) (*.f64 x x))

Samples

14.0ms

256×

valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-exp: 2.0ms (24.7% of total)

ival-mult: 2.0ms (24.7% of total)

ival-neg: 2.0ms (24.7% of total)

ival-sub: 1.0ms (12.3% of total)

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

exact: 0.0ms (0% of total)

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

series62.0ms (1.4%)

Memory

-30.5MiB live, 17.7MiB 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
42.0ms	x	@	0	((neg (- 1 (* x x))) (exp (neg (- 1 (* x x)))) (- 1 (* x x)) (* x x))
19.0ms	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

42.0ms

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

19.0ms

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))

simplify158.0ms (3.5%)

Memory

17.0MiB live, 181.4MiB allocated

Algorithm

1×	egg-herbie

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)

rewrite141.0ms (3.1%)

Memory

1.3MiB live, 224.8MiB allocated

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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eval137.0ms (3%)

Memory: -0.8MiB live, 186.3MiB allocated
Compiler: Compiled 10 865 to 1 802 computations (83.4% saved)

prune15.0ms (0.3%)

Memory

1.5MiB live, 49.7MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	544	4	548
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	545	4	549

Accuracy

100.0%

Counts

549 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) #s(literal 2 binary64))
▶	100.0%	(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
▶	60.8%	(exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x)))
▶	48.1%	(exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))

Compiler

Compiled 24 to 21 computations (12.5% saved)

simplify170.0ms (3.7%)

Memory

17.8MiB live, 130.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score
cost-diff	0	(exp.f64 #s(literal -1 binary64))
cost-diff	384	(/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))
cost-diff	6144	(pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)))
cost-diff	7104	(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) #s(literal 2 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)))

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	19	90
0	28	84
1	44	76
2	78	76
3	167	76
4	436	76
5	1193	76
6	4678	73
0	8131	73

Stop Event

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

Calls

Call 1

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

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

localize132.0ms (2.9%)

Memory

-74.7MiB live, 101.1MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)))
accuracy	0	(/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))
accuracy	0	(exp.f64 #s(literal -1 binary64))
accuracy	0.01171875	(pow.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64))) #s(literal 2 binary64))
accuracy	0	(fma.f64 x x #s(literal -1 binary64))
accuracy	0.00390625	(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x)))
accuracy	29.829746111496238	#s(approx (neg (- 1 (* x x))) (*.f64 x x))
accuracy	0.00390625	(exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))
accuracy	33.95231598558757	#s(approx (neg (- 1 (* x x))) #s(literal -1 binary64))

Samples

78.0ms

256×

valid

Compiler

Compiled 86 to 17 computations (80.2% saved)

Precisions

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

ival-exp: 23.0ms (56.3% of total)

ival-pow: 6.0ms (14.7% of total)

ival-pow2: 3.0ms (7.3% of total)

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

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

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

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

exact: 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)

series7.0ms (0.2%)

Memory

12.9MiB live, 12.9MiB allocated

Counts

11 → 120

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	((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) (pow (pow (exp -1) (/ (+ (* x x) -1) -2)) 2) (pow (exp -1) (/ (+ (* x x) -1) -2)) (/ (+ (* x x) -1) -2) (exp -1))
1.0ms	x	@	inf	((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) (pow (pow (exp -1) (/ (+ (* x x) -1) -2)) 2) (pow (exp -1) (/ (+ (* x x) -1) -2)) (/ (+ (* x x) -1) -2) (exp -1))
1.0ms	x	@	-inf	((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) (pow (pow (exp -1) (/ (+ (* x x) -1) -2)) 2) (pow (exp -1) (/ (+ (* x x) -1) -2)) (/ (+ (* x x) -1) -2) (exp -1))

Time

Variable

Point

Expression

2.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

simplify214.0ms (4.7%)

Memory

10.7MiB live, 196.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	71	804
1	208	781
2	723	755
3	1833	740
4	3403	740
5	5794	740
0	8564	634

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

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
(- (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)
(pow (exp -1/2) 2)
(+ (* (pow x 2) (pow (exp -1/2) 2)) (pow (exp -1/2) 2))
(+ (* (pow x 2) (+ (* 1/2 (* (pow x 2) (pow (exp -1/2) 2))) (pow (exp -1/2) 2))) (pow (exp -1/2) 2))
(+ (* (pow x 2) (+ (* (pow x 2) (+ (* 1/2 (pow (exp -1/2) 2)) (* (pow x 2) (+ (* 1/24 (pow (exp -1/2) 2)) (* 1/8 (pow (exp -1/2) 2)))))) (pow (exp -1/2) 2))) (pow (exp -1/2) 2))
(exp -1/2)
(+ (exp -1/2) (* 1/2 (* (pow x 2) (exp -1/2))))
(+ (exp -1/2) (* (pow x 2) (+ (* 1/8 (* (pow x 2) (exp -1/2))) (* 1/2 (exp -1/2)))))
(+ (exp -1/2) (* (pow x 2) (+ (* 1/2 (exp -1/2)) (* (pow x 2) (+ (* 1/48 (* (pow x 2) (exp -1/2))) (* 1/8 (exp -1/2)))))))
1/2
(+ 1/2 (* -1/2 (pow x 2)))
(+ 1/2 (* -1/2 (pow x 2)))
(+ 1/2 (* -1/2 (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))))
(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 (exp (* 1/2 (- (pow x 2) 1))) 2)
(pow (exp (* 1/2 (- (pow x 2) 1))) 2)
(pow (exp (* 1/2 (- (pow x 2) 1))) 2)
(pow (exp (* 1/2 (- (pow x 2) 1))) 2)
(exp (* 1/2 (- (pow x 2) 1)))
(exp (* 1/2 (- (pow x 2) 1)))
(exp (* 1/2 (- (pow x 2) 1)))
(exp (* 1/2 (- (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))
(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 (exp (* 1/2 (- (pow x 2) 1))) 2)
(pow (exp (* 1/2 (- (pow x 2) 1))) 2)
(pow (exp (* 1/2 (- (pow x 2) 1))) 2)
(pow (exp (* 1/2 (- (pow x 2) 1))) 2)
(exp (* 1/2 (- (pow x 2) 1)))
(exp (* 1/2 (- (pow x 2) 1)))
(exp (* 1/2 (- (pow x 2) 1)))
(exp (* 1/2 (- (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))

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 x x (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal 1/2 binary64)) #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 x x (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal 1/2 binary64)) #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 x x (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal 1/2 binary64)) #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 (exp -1/2) 2)
(exp.f64 #s(literal -1 binary64))
(+ (* (pow x 2) (pow (exp -1/2) 2)) (pow (exp -1/2) 2))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (exp.f64 #s(literal -1 binary64)))
(+ (* (pow x 2) (+ (* 1/2 (* (pow x 2) (pow (exp -1/2) 2))) (pow (exp -1/2) 2))) (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)))
(+ (* (pow x 2) (+ (* (pow x 2) (+ (* 1/2 (pow (exp -1/2) 2)) (* (pow x 2) (+ (* 1/24 (pow (exp -1/2) 2)) (* 1/8 (pow (exp -1/2) 2)))))) (pow (exp -1/2) 2))) (pow (exp -1/2) 2))
(.f64 (exp.f64 #s(literal -1 binary64)) (fma.f64 x x (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal 1/2 binary64)) #s(literal 1 binary64))))
(exp -1/2)
(exp.f64 #s(literal -1/2 binary64))
(+ (exp -1/2) (* 1/2 (* (pow x 2) (exp -1/2))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (exp.f64 #s(literal -1/2 binary64)))
(+ (exp -1/2) (* (pow x 2) (+ (* 1/8 (* (pow x 2) (exp -1/2))) (* 1/2 (exp -1/2)))))
(.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/8 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) (exp.f64 #s(literal -1/2 binary64)))
(+ (exp -1/2) (* (pow x 2) (+ (* 1/2 (exp -1/2)) (* (pow x 2) (+ (* 1/48 (* (pow x 2) (exp -1/2))) (* 1/8 (exp -1/2)))))))
(.f64 (exp.f64 #s(literal -1/2 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) x) x (fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(literal 1/48 binary64) (*.f64 x x) #s(literal 1/8 binary64)) #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))
(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 (exp (* 1/2 (- (pow x 2) 1))) 2)
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow (exp (* 1/2 (- (pow x 2) 1))) 2)
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow (exp (* 1/2 (- (pow x 2) 1))) 2)
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow (exp (* 1/2 (- (pow x 2) 1))) 2)
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* 1/2 (- (pow x 2) 1)))
(sqrt.f64 (exp.f64 (fma.f64 x x #s(literal -1 binary64))))
(exp (* 1/2 (- (pow x 2) 1)))
(sqrt.f64 (exp.f64 (fma.f64 x x #s(literal -1 binary64))))
(exp (* 1/2 (- (pow x 2) 1)))
(sqrt.f64 (exp.f64 (fma.f64 x x #s(literal -1 binary64))))
(exp (* 1/2 (- (pow x 2) 1)))
(sqrt.f64 (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))
(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 (exp (* 1/2 (- (pow x 2) 1))) 2)
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow (exp (* 1/2 (- (pow x 2) 1))) 2)
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow (exp (* 1/2 (- (pow x 2) 1))) 2)
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(pow (exp (* 1/2 (- (pow x 2) 1))) 2)
(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
(exp (* 1/2 (- (pow x 2) 1)))
(sqrt.f64 (exp.f64 (fma.f64 x x #s(literal -1 binary64))))
(exp (* 1/2 (- (pow x 2) 1)))
(sqrt.f64 (exp.f64 (fma.f64 x x #s(literal -1 binary64))))
(exp (* 1/2 (- (pow x 2) 1)))
(sqrt.f64 (exp.f64 (fma.f64 x x #s(literal -1 binary64))))
(exp (* 1/2 (- (pow x 2) 1)))
(sqrt.f64 (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))

rewrite201.0ms (4.4%)

Memory

-5.2MiB live, 272.5MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	78
0	28	72
1	92	62
2	529	61
3	5602	61
0	8954	61

Stop Event

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

Counts

11 → 1 141

Calls

Call 1

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

Outputs
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eval260.0ms (5.7%)

Memory: 55.3MiB live, 611.1MiB allocated
Compiler: Compiled 26 120 to 3 374 computations (87.1% saved)

prune128.0ms (2.8%)

Memory

-22.1MiB live, 127.3MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	1 556	1	1 557
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	1 557	4	1 561

Accuracy

100.0%

Counts

1 561 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64)))
✓	100.0%	(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
✓	60.8%	(exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x)))
✓	48.1%	(exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))

Compiler

Compiled 21 to 18 computations (14.3% saved)

simplify3.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	20
0	10	20
1	19	20
2	23	20
3	24	20
0	24	20

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize32.0ms (0.7%)

Memory

-7.7MiB live, 104.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x #s(literal 1 binary64))
accuracy	0	(+.f64 x #s(literal 1 binary64))
accuracy	0.01171875	(exp.f64 (-.f64 x #s(literal 1 binary64)))
accuracy	0.015625	(pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64)))

Samples

27.0ms

256×

valid

Compiler

Compiled 22 to 8 computations (63.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-sub: 10.0ms (52.5% of total)

ival-pow: 5.0ms (26.3% of total)

ival-exp: 3.0ms (15.8% of total)

ival-add: 1.0ms (5.3% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

9.9MiB live, 9.9MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#s(alt (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 x #s(literal 1 binary64)) (patch (-.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<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 (-.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 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 (-.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 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 (-.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 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 (-.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))) #<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 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+.f64 x #s(literal 1 binary64)) (patch (+.f64 x #s(literal 1 binary64)) #<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 (* (+ 1 x) (- x 1))) (taylor inf x) (#s(alt (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 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 x #s(literal 1 binary64))) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 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 x #s(literal 1 binary64))) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 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 x #s(literal 1 binary64))) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))) #<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 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 (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 (* -1 (* (+ 1 (* -1 x)) (- 1 (* -1 x))))) (taylor -inf x) (#s(alt (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 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 x #s(literal 1 binary64))) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 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 x #s(literal 1 binary64))) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 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 x #s(literal 1 binary64))) (patch (pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))) #<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 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 (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	x	@	0	((pow (exp (- x 1)) (+ x 1)) (- x 1) (+ x 1) (exp (- x 1)))
0.0ms	x	@	inf	((pow (exp (- x 1)) (+ x 1)) (- x 1) (+ x 1) (exp (- x 1)))
0.0ms	x	@	-inf	((pow (exp (- x 1)) (+ x 1)) (- x 1) (+ x 1) (exp (- x 1)))

simplify191.0ms (4.2%)

Memory

15.2MiB live, 247.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	254
1	168	246
2	477	241
3	1607	236
4	4854	236
0	8084	225

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 44

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

rewrite255.0ms (5.6%)

Memory

-23.5MiB live, 167.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	48	16
2	285	16
3	4995	16
0	8793	15

Stop Event

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

Counts

4 → 756

Calls

Call 1

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

Outputs
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eval158.0ms (3.5%)

Memory: -6.9MiB live, 199.6MiB allocated
Compiler: Compiled 18 098 to 2 484 computations (86.3% saved)

prune16.0ms (0.4%)

Memory

-2.2MiB live, 47.7MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	800	0	800
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	800	4	804

Accuracy

100.0%

Counts

804 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 (exp.f64 (-.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64)))
✓	100.0%	(exp.f64 (fma.f64 x x #s(literal -1 binary64)))
✓	60.8%	(exp.f64 #s(approx (neg (- 1 (* x x))) (*.f64 x x)))
✓	48.1%	(exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))

Compiler

Compiled 60 to 41 computations (31.7% saved)

regimes13.0ms (0.3%)

Memory

-9.6MiB live, 29.1MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

5 calls:

2.0ms	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
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)

regimes7.0ms (0.2%)

Memory

21.3MiB live, 21.3MiB allocated

Counts

2 → 2

Calls

Call 1

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

Outputs
(exp.f64 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))
(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
98.9%	2	`x`
98.9%	2	`(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))`
98.9%	2	`(neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
98.9%	2	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
98.9%	2	`(*.f64 x x)`

Compiler

Compiled 22 to 18 computations (18.2% saved)

regimes6.0ms (0.1%)

Memory

16.2MiB live, 16.2MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

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
48.1%	1	`x`
48.1%	1	`(exp.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))`
48.1%	1	`(neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
48.1%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
48.1%	1	`(*.f64 x x)`

Compiler

Compiled 22 to 18 computations (18.2% saved)

bsearch14.0ms (0.3%)

Memory

-14.7MiB live, 23.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	0.8818876715182359	576320411.2646981

Samples

6.0ms

144×

valid

Compiler

Compiled 64 to 91 computations (-42.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-sub: 1.0ms (32.7% of total)

ival-exp: 1.0ms (32.7% of total)

ival-neg: 1.0ms (32.7% of total)

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

exact: 0.0ms (0% of total)

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

simplify22.0ms (0.5%)

Memory

11.0MiB live, 49.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40
1	19	40

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 (*.f64 x x) #s(literal 8286623314361713/9007199254740992 binary64)) (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 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))

Outputs

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

(if (<=.f64 (*.f64 x x) #s(literal 8286623314361713/9007199254740992 binary64)) (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 #s(approx (neg (- 1 (* x x))) #s(literal -1 binary64)))

soundness386.0ms (8.4%)

Memory

5.8MiB live, 275.6MiB allocated

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

Stop Event

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

Compiler

Compiled 42 to 30 computations (28.6% saved)

preprocess54.0ms (1.2%)

Memory: -34.8MiB live, 83.9MiB allocated
Remove: (abs x)
Compiler: Compiled 68 to 44 computations (35.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample1.2s (26.9%)

explain160.0ms (3.5%)

preprocess232.0ms (5.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify141.0ms (3.1%)

localize19.0ms (0.4%)

series62.0ms (1.4%)

simplify158.0ms (3.5%)

rewrite141.0ms (3.1%)

eval137.0ms (3%)

prune15.0ms (0.3%)

simplify170.0ms (3.7%)

localize132.0ms (2.9%)

series7.0ms (0.2%)

simplify214.0ms (4.7%)

rewrite201.0ms (4.4%)

eval260.0ms (5.7%)

prune128.0ms (2.8%)

simplify3.0ms (0.1%)

localize32.0ms (0.7%)

series3.0ms (0.1%)

simplify191.0ms (4.2%)

rewrite255.0ms (5.6%)

eval158.0ms (3.5%)

prune16.0ms (0.4%)

regimes13.0ms (0.3%)

regimes7.0ms (0.2%)

regimes6.0ms (0.1%)

bsearch14.0ms (0.3%)

simplify22.0ms (0.5%)

soundness386.0ms (8.4%)

preprocess54.0ms (1.2%)

end0.0ms (0%)

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