Metrics for expfmod (used to be hard to sample)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze208.0ms (2.3%)

Memory

9.5MiB live, 295.3MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
50%	50%	50%	0%	0%	0%	0%	3
50%	50%	50%	0%	0%	0%	0%	4
50%	50%	50%	0%	0%	0%	0%	5
50%	50%	50%	0%	0%	0%	0%	6
50%	50%	50%	0%	0%	0%	0%	7
50%	50%	50%	0%	0%	0%	0%	8
50%	50%	50%	0%	0%	0%	0%	9
50%	50%	50%	0%	0%	0%	0%	10
50%	50%	50%	0%	0%	0%	0%	11
50%	50%	50%	0%	0%	0%	0%	12

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample4.6s (51%)

Memory

77.1MiB live, 4 684.3MiB allocated

Samples

1.4s	1 598×	5	exit
1.1s	2 572×	2	valid
758.0ms	3 575×	1	valid
396.0ms	3 327×	0	invalid
239.0ms	2 109×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 3.5s

ival-cos: 1.2s (35.3% of total)

ival-fmod: 799.0ms (23.1% of total)

ival-exp: 673.0ms (19.5% of total)

adjust: 268.0ms (7.8% of total)

ival-sqrt: 253.0ms (7.3% of total)

ival-mult: 166.0ms (4.8% of total)

ival-neg: 56.0ms (1.6% of total)

ival-true: 12.0ms (0.3% of total)

ival-assert: 6.0ms (0.2% of total)

Bogosity

explain240.0ms (2.7%)

Memory

16.0MiB live, 214.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
203	-	203	(7.676403953281974e-52)	`(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))`
0	-	0	-	`(sqrt.f64 (cos.f64 x))`
0	-	0	-	`(cos.f64 x)`
0	-	0	-	`(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))`
0	-	0	-	`(exp.f64 x)`
0	-	0	-	`(exp.f64 (neg.f64 x))`
0	-	0	-	`(neg.f64 x)`
0	-	0	-	`x`

Confusion

	Predicted +	Predicted -
+	0	252
-	0	4

Precision

0/0

Recall

0.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	252
-	0	1	3

Precision?

0.0

Recall?

0.0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

74.0ms	144×	2	valid
59.0ms	256×	1	valid
13.0ms	98×	1	exit
2.0ms	14×	0	valid

Compiler

Compiled 72 to 28 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 120.0ms

ival-exp: 41.0ms (34.2% of total)

ival-fmod: 29.0ms (24.2% of total)

ival-cos: 22.0ms (18.3% of total)

adjust: 10.0ms (8.3% of total)

ival-sqrt: 8.0ms (6.7% of total)

ival-mult: 6.0ms (5% of total)

ival-neg: 3.0ms (2.5% of total)

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

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

preprocess55.0ms (0.6%)

Memory

-69.8MiB live, 9.0MiB allocated

Algorithm

1×	egg-herbie

Rules

32×	`sub-neg`
28×	`div-sub`
24×	`lower-*.f32`
22×	`lower-*.f64`
22×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	29	21
2	68	21
3	122	21
4	168	21
5	188	21
6	205	21
7	224	21
8	231	21
0	8	10
0	15	10
1	22	10
2	32	9
3	38	9
4	43	9
5	49	9
6	56	9
7	62	9
8	63	9
0	63	9

Stop Event

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

Calls

Call 1

Inputs
(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))

Outputs
(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))

Compiler

Compiled 10 to 8 computations (20% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune1.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	5.7%	(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))

Compiler

Compiled 10 to 8 computations (20% saved)

simplify5.0ms (0.1%)

Memory

1.9MiB live, 1.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(cos.f64 x)
cost-diff	0	(sqrt.f64 (cos.f64 x))
cost-diff	0	(exp.f64 x)
cost-diff	0	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Rules

24×	`lower-*.f32`
22×	`lower-*.f64`
12×	`lower-/.f32`
12×	`lower-/.f64`
8×	`lower-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	29
0	15	29
1	22	29
2	32	28
3	38	28
4	43	28
5	49	28
6	56	28
7	62	28
8	63	28
0	63	28

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp.f64 x)
x
(sqrt.f64 (cos.f64 x))
(cos.f64 x)
(exp.f64 (neg.f64 x))
(neg.f64 x)

Outputs
(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp.f64 x)
x
(sqrt.f64 (cos.f64 x))
(cos.f64 x)
(exp.f64 (neg.f64 x))
(neg.f64 x)

localize93.0ms (1%)

Memory

15.6MiB live, 124.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(exp.f64 (neg.f64 x))
accuracy	0	(exp.f64 x)
accuracy	0	(cos.f64 x)
accuracy	48.09630519353874	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))

Samples

33.0ms	128×	1	valid
33.0ms	72×	2	valid
7.0ms	49×	1	exit
1.0ms	7×	0	valid

Compiler

Compiled 31 to 10 computations (67.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-exp: 21.0ms (33.8% of total)

ival-fmod: 17.0ms (27.3% of total)

ival-cos: 11.0ms (17.7% of total)

adjust: 5.0ms (8% of total)

ival-sqrt: 4.0ms (6.4% of total)

ival-mult: 3.0ms (4.8% of total)

ival-neg: 1.0ms (1.6% of total)

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

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

series2.0ms (0%)

Memory

3.7MiB live, 3.7MiB allocated

Counts

5 → 60

Calls

Call 1

Inputs
#s(alt (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())
#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())
#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())
#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())

Outputs
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/4 (pow x 2))) (taylor 0 x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* -1/96 (pow x 2)) 1/4))) (taylor 0 x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -19/5760 (pow x 2)) 1/96)) 1/4))) (taylor 0 x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 1/2 x) 1))) (taylor 0 x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1))) (taylor 0 x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor inf x) (#s(alt (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor inf x) (#s(alt (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor inf x) (#s(alt (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor inf x) (#s(alt (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt (cos x)) (taylor inf x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (cos x)) (taylor inf x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (cos x)) (taylor inf x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (cos x)) (taylor inf x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp (neg x)) (taylor inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp (neg x)) (taylor inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp (neg x)) (taylor inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp (neg x)) (taylor inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor -inf x) (#s(alt (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor -inf x) (#s(alt (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor -inf x) (#s(alt (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor -inf x) (#s(alt (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt (cos x)) (taylor -inf x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (cos x)) (taylor -inf x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (cos x)) (taylor -inf x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (cos x)) (taylor -inf x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	((fmod (exp x) (sqrt (cos x))) (exp x) (sqrt (cos x)) (cos x) (exp (neg x)))
0.0ms	x	@	-inf	((fmod (exp x) (sqrt (cos x))) (exp x) (sqrt (cos x)) (cos x) (exp (neg x)))
0.0ms	x	@	inf	((fmod (exp x) (sqrt (cos x))) (exp x) (sqrt (cos x)) (cos x) (exp (neg x)))

Time

Variable

Point

Expression

1.0ms

((fmod (exp x) (sqrt (cos x))) (exp x) (sqrt (cos x)) (cos x) (exp (neg x)))

0.0ms

-inf

((fmod (exp x) (sqrt (cos x))) (exp x) (sqrt (cos x)) (cos x) (exp (neg x)))

0.0ms

inf

((fmod (exp x) (sqrt (cos x))) (exp x) (sqrt (cos x)) (cos x) (exp (neg x)))

simplify261.0ms (2.9%)

Memory

-4.7MiB live, 153.9MiB allocated

Algorithm

1×	egg-herbie

Rules

14 924×	`lower-fma.f64`
14 924×	`lower-fma.f32`
3 728×	`lower-*.f64`
3 728×	`lower-*.f32`
3 006×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	285
1	151	284
2	311	284
3	810	284
4	1446	284
5	1991	284
6	2988	284
7	4040	284
8	5014	284
9	6166	284
10	6710	284
11	6836	284
12	6862	284
13	6878	284
14	7232	284
15	7924	284
0	8498	262

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

Inputs
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/96 (pow x 2)) 1/4)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -19/5760 (pow x 2)) 1/96)) 1/4)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(exp x)
(exp x)
(exp x)
(exp x)
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(exp (neg x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(exp x)
(exp x)
(exp x)
(exp x)
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))

Outputs
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
1
#s(literal 1 binary64)
(+ 1 x)
(-.f64 x #s(literal -1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/4 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/96 (pow x 2)) 1/4)))
(fma.f64 (fma.f64 #s(literal -1/96 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -19/5760 (pow x 2)) 1/96)) 1/4)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -19/5760 binary64) (.f64 x x) #s(literal -1/96 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(exp (neg x))
(exp.f64 (neg.f64 x))
(exp (neg x))
(exp.f64 (neg.f64 x))
(exp (neg x))
(exp.f64 (neg.f64 x))
(exp (neg x))
(exp.f64 (neg.f64 x))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(exp (* -1 x))
(exp.f64 (neg.f64 x))
(exp (* -1 x))
(exp.f64 (neg.f64 x))
(exp (* -1 x))
(exp.f64 (neg.f64 x))
(exp (* -1 x))
(exp.f64 (neg.f64 x))

rewrite75.0ms (0.8%)

Memory

11.6MiB live, 62.9MiB allocated

Rules

566×	`lower-/.f64`
566×	`lower-/.f32`
554×	`lower-*.f64`
554×	`lower-*.f32`
252×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
0	13	16
1	21	16
2	55	16
3	229	16
0	1910	16

Stop Event

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

Counts

5 → 61

Calls

Call 1

Inputs
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp.f64 x)
(sqrt.f64 (cos.f64 x))
(cos.f64 x)
(exp.f64 (neg.f64 x))

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval16.0ms (0.2%)

Memory: -11.8MiB live, 25.2MiB allocated
Compiler: Compiled 1 610 to 303 computations (81.2% saved)

prune4.0ms (0%)

Memory

9.8MiB live, 9.8MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	117	4	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	4	122

Accuracy

24.8%

Counts

122 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	5.7%	(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (/.f64 #s(literal 1 binary64) (exp.f64 x)))
▶	4.8%	(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
▶	5.7%	(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (exp.f64 (neg.f64 x)))
▶	22.6%	(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))

Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify11.0ms (0.1%)

Memory

-21.7MiB live, 15.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (cos.f64 x))
cost-diff	0	(exp.f64 x)
cost-diff	0	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
cost-diff	576	(/.f64 #s(literal 1 binary64) (exp.f64 x))
cost-diff	0	(sqrt.f64 (cos.f64 x))
cost-diff	0	(exp.f64 x)
cost-diff	0	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
cost-diff	0	(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
cost-diff	0	(exp.f64 (neg.f64 x))
cost-diff	0	#s(approx (sqrt (cos x)) #s(literal 1 binary64))
cost-diff	0	(exp.f64 x)
cost-diff	0	(fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
cost-diff	0	(cos.f64 x)
cost-diff	0	(sqrt.f64 (cos.f64 x))
cost-diff	0	#s(approx (exp x) #s(literal 1 binary64))
cost-diff	0	(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x)))

Rules

60×	`lower-*.f32`
52×	`lower-*.f64`
28×	`lower-/.f32`
26×	`lower-/.f64`
14×	`associate-*r/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	132
0	36	130
1	49	129
2	64	127
3	83	127
4	87	127
5	93	127
6	100	127
7	112	127
8	115	127
9	116	127
10	118	127
11	118	127
0	118	127

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))
(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x)))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 (cos.f64 x))
(cos.f64 x)
x
(exp.f64 (neg.f64 x))
(neg.f64 x)
(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (exp.f64 (neg.f64 x)))
(fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
(exp.f64 x)
x
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
(exp.f64 (neg.f64 x))
(neg.f64 x)
(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp.f64 x)
x
(sqrt.f64 (cos.f64 x))
(cos.f64 x)
#s(approx (exp (neg x)) #s(literal 1 binary64))
#s(literal 1 binary64)
(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (/.f64 #s(literal 1 binary64) (exp.f64 x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp.f64 x)
x
(sqrt.f64 (cos.f64 x))
(cos.f64 x)
(/.f64 #s(literal 1 binary64) (exp.f64 x))
#s(literal 1 binary64)

Outputs
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))
(/.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x)))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 (cos.f64 x))
(cos.f64 x)
x
(exp.f64 (neg.f64 x))
(neg.f64 x)
(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (exp.f64 (neg.f64 x)))
(/.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (exp.f64 x))
(fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
(exp.f64 x)
x
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
(exp.f64 (neg.f64 x))
(neg.f64 x)
(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(*.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp.f64 x)
x
(sqrt.f64 (cos.f64 x))
(cos.f64 x)
#s(approx (exp (neg x)) #s(literal 1 binary64))
#s(literal 1 binary64)
(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (/.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp.f64 x)
x
(sqrt.f64 (cos.f64 x))
(cos.f64 x)
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(exp.f64 (neg.f64 x))
#s(literal 1 binary64)

localize130.0ms (1.5%)

Memory

9.5MiB live, 133.1MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0	(exp.f64 x)
accuracy	0	(cos.f64 x)
accuracy	0.01171875	(/.f64 #s(literal 1 binary64) (exp.f64 x))
accuracy	48.09630519353874	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
accuracy	0	(exp.f64 x)
accuracy	0	(cos.f64 x)
accuracy	0.8254554116682715	#s(approx (exp (neg x)) #s(literal 1 binary64))
accuracy	48.09630519353874	(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
accuracy	0	(exp.f64 (neg.f64 x))
accuracy	0	(exp.f64 x)
accuracy	0.4431808105406079	#s(approx (sqrt (cos x)) #s(literal 1 binary64))
accuracy	48.09630519353874	(fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
accuracy	0	(exp.f64 (neg.f64 x))
accuracy	0	(cos.f64 x)
accuracy	0.8170215648909979	#s(approx (exp x) #s(literal 1 binary64))
accuracy	48.09630519353874	(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x)))

Samples

56.0ms	72×	2	valid
44.0ms	128×	1	valid
9.0ms	49×	1	exit
1.0ms	7×	0	valid

Compiler

Compiled 118 to 13 computations (89% saved)

Precisions

Click to see histograms. Total time spent on operations: 83.0ms

ival-sqrt: 18.0ms (21.6% of total)

ival-exp: 17.0ms (20.4% of total)

ival-fmod: 16.0ms (19.2% of total)

ival-cos: 14.0ms (16.8% of total)

adjust: 6.0ms (7.2% of total)

ival-mult: 6.0ms (7.2% of total)

ival-div: 4.0ms (4.8% of total)

ival-neg: 1.0ms (1.2% of total)

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

4.7MiB live, 4.7MiB allocated

Counts

12 → 144

Calls

Call 1

Inputs
#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())
#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())
#s(alt (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (cos x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())
#s(alt (.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (exp.f64 x)) (patch (/.f64 #s(literal 1 binary64) (exp.f64 x)) #<representation binary64>) () ())
#s(alt #s(approx (exp (neg x)) #s(literal 1 binary64)) (patch #s(approx (exp (neg x)) #s(literal 1 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/4 (pow x 2))) (taylor 0 x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* -1/96 (pow x 2)) 1/4))) (taylor 0 x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -19/5760 (pow x 2)) 1/96)) 1/4))) (taylor 0 x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (pow x 2))) (taylor 0 x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
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#s(alt (fmod (exp x) (sqrt (cos x))) (taylor -inf x) (#s(alt (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor -inf x) (#s(alt (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt (cos x)) (taylor -inf x) (#s(alt #s(approx (sqrt (cos x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (cos x)) (taylor -inf x) (#s(alt #s(approx (sqrt (cos x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (cos x)) (taylor -inf x) (#s(alt #s(approx (sqrt (cos x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (cos x)) (taylor -inf x) (#s(alt #s(approx (sqrt (cos x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x)))) (taylor -inf x) (#s(alt (.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x)))) (taylor -inf x) (#s(alt (.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x)))) (taylor -inf x) (#s(alt (.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x)))) (taylor -inf x) (#s(alt (.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor -inf x) (#s(alt (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor -inf x) (#s(alt (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor -inf x) (#s(alt (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor -inf x) (#s(alt (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (exp x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (exp.f64 x)) (patch (/.f64 #s(literal 1 binary64) (exp.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (exp x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (exp.f64 x)) (patch (/.f64 #s(literal 1 binary64) (exp.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (exp x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (exp.f64 x)) (patch (/.f64 #s(literal 1 binary64) (exp.f64 x)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (exp x)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (exp.f64 x)) (patch (/.f64 #s(literal 1 binary64) (exp.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) #s(literal 1 binary64)) (patch #s(approx (exp (neg x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) #s(literal 1 binary64)) (patch #s(approx (exp (neg x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) #s(literal 1 binary64)) (patch #s(approx (exp (neg x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) #s(literal 1 binary64)) (patch #s(approx (exp (neg x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

((fmod (exp x) (sqrt (cos x))) (exp x) (sqrt (cos x)) (cos x) (fmod (exp x) (sqrt (cos x))) (exp x) (sqrt (cos x)) (exp (neg x)) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (fmod (exp x) (sqrt (cos x))) (/ 1 (exp x)) (exp (neg x)))

1.0ms

inf

((fmod (exp x) (sqrt (cos x))) (exp x) (sqrt (cos x)) (cos x) (fmod (exp x) (sqrt (cos x))) (exp x) (sqrt (cos x)) (exp (neg x)) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (fmod (exp x) (sqrt (cos x))) (/ 1 (exp x)) (exp (neg x)))

0.0ms

((fmod (exp x) (sqrt (cos x))) (exp x) (sqrt (cos x)) (cos x) (fmod (exp x) (sqrt (cos x))) (exp x) (sqrt (cos x)) (exp (neg x)) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (fmod (exp x) (sqrt (cos x))) (/ 1 (exp x)) (exp (neg x)))

simplify175.0ms (2%)

Memory

-13.0MiB live, 139.7MiB allocated

Algorithm

1×	egg-herbie

Rules

15 400×	`lower-fma.f64`
15 400×	`lower-fma.f32`
4 340×	`lower-*.f64`
4 340×	`lower-*.f32`
2 290×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	87	804
1	206	778
2	454	765
3	1123	758
4	1992	758
5	3768	758
6	5106	758
7	6158	758
8	7423	758
0	8120	710

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

Inputs
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/96 (pow x 2)) 1/4)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -19/5760 (pow x 2)) 1/96)) 1/4)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/96 (pow x 2)) 1/4)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -19/5760 (pow x 2)) 1/96)) 1/4)))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(fmod (exp x) (sqrt (cos x)))
(+ (* -1 (* x (fmod (exp x) (sqrt (cos x))))) (fmod (exp x) (sqrt (cos x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* 1/2 (* x (fmod (exp x) (sqrt (cos x))))))) (fmod (exp x) (sqrt (cos x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* x (+ (* -1/6 (* x (fmod (exp x) (sqrt (cos x))))) (* 1/2 (fmod (exp x) (sqrt (cos x)))))))) (fmod (exp x) (sqrt (cos x))))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(exp x)
(exp x)
(exp x)
(exp x)
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(exp x)
(exp x)
(exp x)
(exp x)
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(/ 1 (exp x))
(/ 1 (exp x))
(/ 1 (exp x))
(/ 1 (exp x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(exp x)
(exp x)
(exp x)
(exp x)
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(cos x)
(cos x)
(cos x)
(cos x)
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(exp x)
(exp x)
(exp x)
(exp x)
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(/ 1 (exp x))
(/ 1 (exp x))
(/ 1 (exp x))
(/ 1 (exp x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))

Outputs
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
1
#s(literal 1 binary64)
(+ 1 x)
(-.f64 x #s(literal -1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/4 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/96 (pow x 2)) 1/4)))
(fma.f64 (fma.f64 #s(literal -1/96 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -19/5760 (pow x 2)) 1/96)) 1/4)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -19/5760 binary64) (.f64 x x) #s(literal -1/96 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
1
#s(literal 1 binary64)
(+ 1 x)
(-.f64 x #s(literal -1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/4 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/96 (pow x 2)) 1/4)))
(fma.f64 (fma.f64 #s(literal -1/96 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -19/5760 (pow x 2)) 1/96)) 1/4)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -19/5760 binary64) (.f64 x x) #s(literal -1/96 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(+ (* -1 (* x (fmod (exp x) (sqrt (cos x))))) (fmod (exp x) (sqrt (cos x))))
(*.f64 (-.f64 #s(literal 1 binary64) x) (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* 1/2 (* x (fmod (exp x) (sqrt (cos x))))))) (fmod (exp x) (sqrt (cos x))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* x (+ (* -1/6 (* x (fmod (exp x) (sqrt (cos x))))) (* 1/2 (fmod (exp x) (sqrt (cos x)))))))) (fmod (exp x) (sqrt (cos x))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(exp (neg x))
(exp.f64 (neg.f64 x))
(exp (neg x))
(exp.f64 (neg.f64 x))
(exp (neg x))
(exp.f64 (neg.f64 x))
(exp (neg x))
(exp.f64 (neg.f64 x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(/ 1 (exp x))
(exp.f64 (neg.f64 x))
(/ 1 (exp x))
(exp.f64 (neg.f64 x))
(/ 1 (exp x))
(exp.f64 (neg.f64 x))
(/ 1 (exp x))
(exp.f64 (neg.f64 x))
(exp (neg x))
(exp.f64 (neg.f64 x))
(exp (neg x))
(exp.f64 (neg.f64 x))
(exp (neg x))
(exp.f64 (neg.f64 x))
(exp (neg x))
(exp.f64 (neg.f64 x))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(exp (* -1 x))
(exp.f64 (neg.f64 x))
(exp (* -1 x))
(exp.f64 (neg.f64 x))
(exp (* -1 x))
(exp.f64 (neg.f64 x))
(exp (* -1 x))
(exp.f64 (neg.f64 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(/ 1 (exp x))
(exp.f64 (neg.f64 x))
(/ 1 (exp x))
(exp.f64 (neg.f64 x))
(/ 1 (exp x))
(exp.f64 (neg.f64 x))
(/ 1 (exp x))
(exp.f64 (neg.f64 x))
(exp (* -1 x))
(exp.f64 (neg.f64 x))
(exp (* -1 x))
(exp.f64 (neg.f64 x))
(exp (* -1 x))
(exp.f64 (neg.f64 x))
(exp (* -1 x))
(exp.f64 (neg.f64 x))

rewrite64.0ms (0.7%)

Memory

23.4MiB live, 60.1MiB allocated

Rules

768×	`lower-*.f32`
768×	`lower-/.f32`
766×	`lower-*.f64`
766×	`lower-/.f64`
430×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	62
0	29	61
1	44	61
2	98	61
3	336	61
0	2445	61

Stop Event

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

Counts

12 → 169

Calls

Call 1

Inputs
(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x)))
#s(approx (exp x) #s(literal 1 binary64))
(sqrt.f64 (cos.f64 x))
(cos.f64 x)
(fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
(exp.f64 x)
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
(exp.f64 (neg.f64 x))
(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
#s(approx (exp (neg x)) #s(literal 1 binary64))

Outputs
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eval110.0ms (1.2%)

Memory: 9.4MiB live, 89.4MiB allocated
Compiler: Compiled 9 789 to 1 032 computations (89.5% saved)

prune22.0ms (0.2%)

Memory

-25.9MiB live, 48.5MiB allocated

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	659	11	670
Fresh	0	0	0
Picked	3	1	4
Done	0	0	0
Total	662	12	674

Accuracy

24.8%

Counts

674 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	5.7%	(.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (exp.f64 (neg.f64 x)) #s(literal -1/2 binary64)) (pow.f64 (exp.f64 (neg.f64 x)) #s(literal -1/2 binary64)))))
	5.7%	(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (exp.f64 x)))
✓	5.7%	(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (exp.f64 (neg.f64 x)))
▶	5.1%	(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
	5.1%	(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
	5.0%	(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)))
▶	4.8%	(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
	5.1%	(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
	14.9%	(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (exp.f64 (neg.f64 x)))
▶	4.0%	(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)))
▶	4.1%	(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
▶	22.5%	(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (exp.f64 (neg.f64 x)))

Compiler

Compiled 285 to 220 computations (22.8% saved)

simplify70.0ms (0.8%)

Memory

21.7MiB live, 57.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#s(approx (sqrt (cos x)) #s(literal 1 binary64))
cost-diff	0	(exp.f64 x)
cost-diff	0	(fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
cost-diff	0	(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
cost-diff	0	(sqrt.f64 (cos.f64 x))
cost-diff	0	#s(approx (exp x) #s(literal 1 binary64))
cost-diff	0	(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x)))
cost-diff	0	(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)))
cost-diff	0	(sqrt.f64 (cos.f64 x))
cost-diff	0	#s(approx (exp x) #s(literal 1 binary64))
cost-diff	0	(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x)))
cost-diff	0	(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
cost-diff	0	#s(approx (sqrt (cos x)) #s(literal 1 binary64))
cost-diff	0	(exp.f64 x)
cost-diff	0	(fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
cost-diff	0	(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
cost-diff	0	(exp.f64 (neg.f64 x))
cost-diff	0	#s(approx (sqrt (cos x)) #s(literal 1 binary64))
cost-diff	0	#s(approx (exp x) #s(literal 1 binary64))
cost-diff	0	(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))

Rules

2 440×	`lower-fma.f32`
2 434×	`lower-fma.f64`
684×	`lower-*.f32`
674×	`lower-*.f64`
460×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	237
0	53	237
1	70	237
2	96	236
3	177	236
4	345	236
5	589	236
6	1049	236
7	1928	236
8	2407	236
9	2465	236
10	2466	236
11	2466	236
0	2466	236

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (exp.f64 (neg.f64 x)))
(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
(exp.f64 (neg.f64 x))
(neg.f64 x)
x
(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
(exp.f64 x)
x
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (exp (neg x)) #s(literal 1 binary64))
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x)))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 (cos.f64 x))
(cos.f64 x)
x
#s(approx (exp (neg x)) #s(literal 1 binary64))
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)))
(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x)))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 (cos.f64 x))
(cos.f64 x)
x
#s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
(exp.f64 x)
x
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))
(fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64))
#s(literal -1/6 binary64)
#s(literal 1/2 binary64)
#s(literal -1 binary64)

Outputs
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (exp.f64 (neg.f64 x)))
(/.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (exp.f64 x))
(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
(exp.f64 (neg.f64 x))
(neg.f64 x)
x
(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(*.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))))
(fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
(exp.f64 x)
x
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (exp (neg x)) #s(literal 1 binary64))
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x)))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 (cos.f64 x))
(cos.f64 x)
x
#s(approx (exp (neg x)) #s(literal 1 binary64))
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)) (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))))
(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x)))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 (cos.f64 x))
(cos.f64 x)
x
#s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))))
(fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
(exp.f64 x)
x
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))
(fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64))
#s(literal -1/6 binary64)
#s(literal 1/2 binary64)
#s(literal -1 binary64)

localize143.0ms (1.6%)

Memory

0.3MiB live, 123.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
accuracy	0.362617004338903	#s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
accuracy	0.4431808105406079	#s(approx (sqrt (cos x)) #s(literal 1 binary64))
accuracy	48.09630519353874	(fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
accuracy	0	(cos.f64 x)
accuracy	0.4761742800494465	#s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x))
accuracy	0.8170215648909979	#s(approx (exp x) #s(literal 1 binary64))
accuracy	48.09630519353874	(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x)))
accuracy	0	(cos.f64 x)
accuracy	0.8170215648909979	#s(approx (exp x) #s(literal 1 binary64))
accuracy	0.8254554116682715	#s(approx (exp (neg x)) #s(literal 1 binary64))
accuracy	48.09630519353874	(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x)))
accuracy	0	(exp.f64 x)
accuracy	0.4431808105406079	#s(approx (sqrt (cos x)) #s(literal 1 binary64))
accuracy	0.8254554116682715	#s(approx (exp (neg x)) #s(literal 1 binary64))
accuracy	48.09630519353874	(fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
accuracy	0	(exp.f64 (neg.f64 x))
accuracy	0.4431808105406079	#s(approx (sqrt (cos x)) #s(literal 1 binary64))
accuracy	0.8170215648909979	#s(approx (exp x) #s(literal 1 binary64))
accuracy	48.09630519353874	(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))

Samples

50.0ms	128×	1	valid
46.0ms	72×	2	valid
21.0ms	49×	1	exit
2.0ms	7×	0	valid

Compiler

Compiled 171 to 21 computations (87.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 89.0ms

adjust: 18.0ms (20.1% of total)

ival-exp: 16.0ms (17.9% of total)

ival-cos: 15.0ms (16.8% of total)

ival-fmod: 14.0ms (15.7% of total)

ival-mult: 8.0ms (8.9% of total)

ival-add: 7.0ms (7.8% of total)

ival-sqrt: 4.0ms (4.5% of total)

const: 4.0ms (4.5% of total)

ival-sub: 1.0ms (1.1% of total)

ival-neg: 1.0ms (1.1% of total)

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

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

exact: 0.0ms (0% of total)

series8.0ms (0.1%)

Memory

9.7MiB live, 9.7MiB allocated

Counts

17 → 204

Calls

Call 1

Inputs
#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (cos x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())
#s(alt (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())
#s(alt (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())
#s(alt (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x))) (patch (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())
#s(alt (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (exp (neg x)) #s(literal 1 binary64)) (patch #s(approx (exp (neg x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())
#s(alt #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (cos x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/4 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (sqrt (cos x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* -1/96 (pow x 2)) 1/4))) (taylor 0 x) (#s(alt #s(approx (sqrt (cos x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -19/5760 (pow x 2)) 1/96)) 1/4))) (taylor 0 x) (#s(alt #s(approx (sqrt (cos x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 x)) (taylor 0 x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* 1/2 x) 1))) (taylor 0 x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1))) (taylor 0 x) (#s(alt (exp.f64 (neg.f64 x)) (patch (exp.f64 (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* x (fmod (exp x) (sqrt (cos x))))) (fmod (exp x) (sqrt (cos x)))) (taylor 0 x) (#s(alt (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* 1/2 (* x (fmod (exp x) (sqrt (cos x))))))) (fmod (exp x) (sqrt (cos x)))) (taylor 0 x) (#s(alt (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* x (+ (* -1/6 (* x (fmod (exp x) (sqrt (cos x))))) (* 1/2 (fmod (exp x) (sqrt (cos x)))))))) (fmod (exp x) (sqrt (cos x)))) (taylor 0 x) (#s(alt (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* x (fmod (exp x) (sqrt (cos x))))) (fmod (exp x) (sqrt (cos x)))) (taylor 0 x) (#s(alt (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* 1/2 (* x (fmod (exp x) (sqrt (cos x))))))) (fmod (exp x) (sqrt (cos x)))) (taylor 0 x) (#s(alt (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* x (+ (* -1/6 (* x (fmod (exp x) (sqrt (cos x))))) (* 1/2 (fmod (exp x) (sqrt (cos x)))))))) (fmod (exp x) (sqrt (cos x)))) (taylor 0 x) (#s(alt (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/4 (pow x 2))) (taylor 0 x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* -1/96 (pow x 2)) 1/4))) (taylor 0 x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -19/5760 (pow x 2)) 1/96)) 1/4))) (taylor 0 x) (#s(alt (sqrt.f64 (cos.f64 x)) (patch (sqrt.f64 (cos.f64 x)) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x))) (patch (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* x (fmod (exp x) (sqrt (cos x))))) (fmod (exp x) (sqrt (cos x)))) (taylor 0 x) (#s(alt (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x))) (patch (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
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#s(alt (* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x)))) (taylor -inf x) (#s(alt (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x))) (patch (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x))) #<representation binary64>) () ())) ())
#s(alt (* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x)))) (taylor -inf x) (#s(alt (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x)))) (taylor -inf x) (#s(alt (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x)))) (taylor -inf x) (#s(alt (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x)))) (taylor -inf x) (#s(alt (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) #s(literal 1 binary64)) (patch #s(approx (exp (neg x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) #s(literal 1 binary64)) (patch #s(approx (exp (neg x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) #s(literal 1 binary64)) (patch #s(approx (exp (neg x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) #s(literal 1 binary64)) (patch #s(approx (exp (neg x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (cos x) (taylor -inf x) (#s(alt (cos.f64 x) (patch (cos.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)) (patch #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/6 (pow x 3)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/6 (* 1/2 (/ 1 x))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (- 1/2 (/ 1 x)) x))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

((fmod (exp x) (sqrt (cos x))) (exp x) (sqrt (cos x)) (exp (neg x)) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (fmod (exp x) (sqrt (cos x))) (exp x) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (fmod (exp x) (sqrt (cos x))) (sqrt (cos x)) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (exp (neg x)) (cos x) (exp (neg x)) (exp (neg x)) (+ (* (+ (* (+ (* -1/6 x) 1/2) x) -1) x) 1))

1.0ms

inf

((fmod (exp x) (sqrt (cos x))) (exp x) (sqrt (cos x)) (exp (neg x)) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (fmod (exp x) (sqrt (cos x))) (exp x) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (fmod (exp x) (sqrt (cos x))) (sqrt (cos x)) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (exp (neg x)) (cos x) (exp (neg x)) (exp (neg x)) (+ (* (+ (* (+ (* -1/6 x) 1/2) x) -1) x) 1))

1.0ms

-inf

((fmod (exp x) (sqrt (cos x))) (exp x) (sqrt (cos x)) (exp (neg x)) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (fmod (exp x) (sqrt (cos x))) (exp x) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (fmod (exp x) (sqrt (cos x))) (sqrt (cos x)) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (exp (neg x)) (cos x) (exp (neg x)) (exp (neg x)) (+ (* (+ (* (+ (* -1/6 x) 1/2) x) -1) x) 1))

simplify133.0ms (1.5%)

Memory

6.0MiB live, 126.5MiB allocated

Algorithm

1×	egg-herbie

Rules

12 442×	`lower-fma.f64`
12 442×	`lower-fma.f32`
3 930×	`lower-*.f64`
3 930×	`lower-*.f32`
1 958×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	119	1467
1	309	1366
2	856	1314
3	2637	1286
4	6480	1282
0	8625	1197

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/96 (pow x 2)) 1/4)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -19/5760 (pow x 2)) 1/96)) 1/4)))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(fmod (exp x) (sqrt (cos x)))
(+ (* -1 (* x (fmod (exp x) (sqrt (cos x))))) (fmod (exp x) (sqrt (cos x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* 1/2 (* x (fmod (exp x) (sqrt (cos x))))))) (fmod (exp x) (sqrt (cos x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* x (+ (* -1/6 (* x (fmod (exp x) (sqrt (cos x))))) (* 1/2 (fmod (exp x) (sqrt (cos x)))))))) (fmod (exp x) (sqrt (cos x))))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fmod (exp x) (sqrt (cos x)))
(+ (* -1 (* x (fmod (exp x) (sqrt (cos x))))) (fmod (exp x) (sqrt (cos x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* 1/2 (* x (fmod (exp x) (sqrt (cos x))))))) (fmod (exp x) (sqrt (cos x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* x (+ (* -1/6 (* x (fmod (exp x) (sqrt (cos x))))) (* 1/2 (fmod (exp x) (sqrt (cos x)))))))) (fmod (exp x) (sqrt (cos x))))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/96 (pow x 2)) 1/4)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -19/5760 (pow x 2)) 1/96)) 1/4)))
(fmod (exp x) (sqrt (cos x)))
(+ (* -1 (* x (fmod (exp x) (sqrt (cos x))))) (fmod (exp x) (sqrt (cos x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* 1/2 (* x (fmod (exp x) (sqrt (cos x))))))) (fmod (exp x) (sqrt (cos x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* x (+ (* -1/6 (* x (fmod (exp x) (sqrt (cos x))))) (* 1/2 (fmod (exp x) (sqrt (cos x)))))))) (fmod (exp x) (sqrt (cos x))))
(fmod (exp x) (sqrt (cos x)))
(+ (* -1 (* x (fmod (exp x) (sqrt (cos x))))) (fmod (exp x) (sqrt (cos x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* 1/2 (* x (fmod (exp x) (sqrt (cos x))))))) (fmod (exp x) (sqrt (cos x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* x (+ (* -1/6 (* x (fmod (exp x) (sqrt (cos x))))) (* 1/2 (fmod (exp x) (sqrt (cos x)))))))) (fmod (exp x) (sqrt (cos x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(exp x)
(exp x)
(exp x)
(exp x)
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(exp x)
(exp x)
(exp x)
(exp x)
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(cos x)
(cos x)
(cos x)
(cos x)
(exp (neg x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(* -1/6 (pow x 3))
(* (pow x 3) (- (* 1/2 (/ 1 x)) 1/6))
(* (pow x 3) (- (* 1/2 (/ 1 x)) (+ 1/6 (/ 1 (pow x 2)))))
(* (pow x 3) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/6 (/ 1 (pow x 2)))))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(exp x)
(exp x)
(exp x)
(exp x)
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(exp x)
(exp x)
(exp x)
(exp x)
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(cos x)
(cos x)
(cos x)
(cos x)
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(* -1/6 (pow x 3))
(* -1 (* (pow x 3) (- 1/6 (* 1/2 (/ 1 x)))))
(* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (- 1/2 (/ 1 x)) x)))))
(* -1 (* (pow x 3) (+ 1/6 (* -1 (/ (+ 1/2 (* -1 (/ (- 1 (/ 1 x)) x))) x)))))

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

rewrite261.0ms (2.9%)

Memory

-7.5MiB live, 273.9MiB allocated

Rules

6 548×	`lower-fma.f32`
6 542×	`lower-fma.f64`
3 964×	`lower-*.f32`
3 956×	`lower-*.f64`
2 770×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	148
0	49	148
1	115	148
2	609	148
3	6726	148
0	8134	148

Stop Event

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

Counts

17 → 160

Calls

Call 1

Inputs
(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
#s(approx (exp x) #s(literal 1 binary64))
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
(exp.f64 (neg.f64 x))
(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
(exp.f64 x)
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x)))
(sqrt.f64 (cos.f64 x))
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
#s(approx (exp (neg x)) #s(literal 1 binary64))
(cos.f64 x)
#s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x))
#s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))

Outputs
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eval60.0ms (0.7%)

Memory: -22.5MiB live, 134.2MiB allocated
Compiler: Compiled 9 298 to 819 computations (91.2% saved)

prune16.0ms (0.2%)

Memory

-2.6MiB live, 36.6MiB allocated

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	502	7	509
Fresh	4	2	6
Picked	4	1	5
Done	0	1	1
Total	510	11	521

Accuracy

24.8%

Counts

521 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	5.7%	(.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (exp.f64 (neg.f64 x)) #s(literal -1/2 binary64)) (pow.f64 (exp.f64 (neg.f64 x)) #s(literal -1/2 binary64)))))
▶	5.7%	(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (exp.f64 x)))
✓	5.7%	(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (exp.f64 (neg.f64 x)))
✓	5.1%	(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
	11.0%	(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
▶	11.0%	(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
▶	14.6%	(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
	10.4%	(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
▶	23.5%	(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
	4.5%	(.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
▶	22.5%	(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))

Compiler

Compiled 312 to 223 computations (28.5% saved)

simplify84.0ms (0.9%)

Memory

33.1MiB live, 72.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (sqrt (cos x)) #s(literal 1 binary64))
cost-diff	0	(exp.f64 x)
cost-diff	0	(fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
cost-diff	576	(/.f64 #s(literal 1 binary64) (exp.f64 x))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
cost-diff	0	#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
cost-diff	0	(fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
cost-diff	0	(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
cost-diff	0	#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
cost-diff	0	(fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
cost-diff	0	(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
cost-diff	0	#s(approx (sqrt (cos x)) #s(literal 1 binary64))
cost-diff	0	#s(approx (exp x) #s(literal 1 binary64))
cost-diff	0	(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
cost-diff	0	(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
cost-diff	0	(fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
cost-diff	0	(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))

Rules

2 760×	`lower-fma.f32`
2 750×	`lower-fma.f64`
764×	`lower-*.f32`
754×	`lower-*.f64`
528×	`lower--.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	311
0	57	309
1	81	308
2	110	308
3	197	308
4	404	308
5	744	308
6	1296	308
7	2042	308
8	2367	308
9	2511	308
10	2545	308
11	2550	308
12	2550	308
0	2550	308

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
#s(approx (exp (neg x)) #s(literal 1 binary64))
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
#s(approx (exp (neg x)) #s(literal 1 binary64))
(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
#s(approx (exp (neg x)) #s(literal 1 binary64))
(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
#s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))
(fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64))
#s(literal -1/6 binary64)
#s(literal -1 binary64)
(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (exp.f64 x)))
(fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
(exp.f64 x)
x
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (exp.f64 x))

Outputs
(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(*.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) (fmod.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))))
(fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
(fmod.f64 #s(approx (exp x) (-.f64 x #s(literal -1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
#s(approx (exp x) (-.f64 x #s(literal -1 binary64)))
(+.f64 #s(literal 1 binary64) x)
(-.f64 x #s(literal -1 binary64))
#s(literal 1 binary64)
x
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
#s(approx (exp (neg x)) #s(literal 1 binary64))
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
#s(approx (exp x) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
#s(approx (exp (neg x)) #s(literal 1 binary64))
(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
#s(approx (exp (neg x)) #s(literal 1 binary64))
(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(*.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))))
(fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
#s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64))
(fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64))
#s(literal -1/6 binary64)
#s(literal -1 binary64)
(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (exp.f64 x))
(fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
(exp.f64 x)
x
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(exp.f64 (neg.f64 x))

localize197.0ms (2.2%)

Memory

-11.2MiB live, 108.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(exp.f64 x)
accuracy	0.01171875	(/.f64 #s(literal 1 binary64) (exp.f64 x))
accuracy	0.4431808105406079	#s(approx (sqrt (cos x)) #s(literal 1 binary64))
accuracy	48.09630519353874	(fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
accuracy	0.362617004338903	#s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
accuracy	0.39839604011668867	#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
accuracy	0.4431808105406079	#s(approx (sqrt (cos x)) #s(literal 1 binary64))
accuracy	48.09630519353874	(fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
accuracy	0.39839604011668867	#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
accuracy	0.4431808105406079	#s(approx (sqrt (cos x)) #s(literal 1 binary64))
accuracy	0.8254554116682715	#s(approx (exp (neg x)) #s(literal 1 binary64))
accuracy	48.09630519353874	(fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
accuracy	0.4431808105406079	#s(approx (sqrt (cos x)) #s(literal 1 binary64))
accuracy	0.8170215648909979	#s(approx (exp x) #s(literal 1 binary64))
accuracy	0.8254554116682715	#s(approx (exp (neg x)) #s(literal 1 binary64))
accuracy	48.09630519353874	(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
accuracy	0.4431808105406079	#s(approx (sqrt (cos x)) #s(literal 1 binary64))
accuracy	0.5013653551823473	#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
accuracy	0.8254554116682715	#s(approx (exp (neg x)) #s(literal 1 binary64))
accuracy	48.09630519353874	(fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))

Samples

85.0ms	72×	2	valid
72.0ms	128×	1	valid
15.0ms	49×	1	exit
2.0ms	7×	0	valid

Compiler

Compiled 195 to 27 computations (86.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 112.0ms

adjust: 33.0ms (29.5% of total)

ival-exp: 17.0ms (15.2% of total)

ival-fmod: 14.0ms (12.5% of total)

ival-mult: 13.0ms (11.6% of total)

ival-cos: 11.0ms (9.8% of total)

ival-sqrt: 7.0ms (6.3% of total)

ival-add: 7.0ms (6.3% of total)

ival-div: 4.0ms (3.6% of total)

const: 4.0ms (3.6% of total)

ival-neg: 1.0ms (0.9% of total)

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

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

exact: 0.0ms (0% of total)

series9.0ms (0.1%)

Memory

8.8MiB live, 8.8MiB allocated

Counts

18 → 216

Calls

Call 1

Inputs
#s(alt (.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) (patch #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal 1 binary64) x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())
#s(alt (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (cos x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)) (patch (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (patch (.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (exp.f64 x)) (patch (/.f64 #s(literal 1 binary64) (exp.f64 x)) #<representation binary64>) () ())
#s(alt (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())
#s(alt #s(approx (exp (neg x)) #s(literal 1 binary64)) (patch #s(approx (exp (neg x)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())

Outputs
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* x (fmod (exp x) (sqrt (cos x))))) (fmod (exp x) (sqrt (cos x)))) (taylor 0 x) (#s(alt (.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* 1/2 (* x (fmod (exp x) (sqrt (cos x))))))) (fmod (exp x) (sqrt (cos x)))) (taylor 0 x) (#s(alt (.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* x (+ (* -1/6 (* x (fmod (exp x) (sqrt (cos x))))) (* 1/2 (fmod (exp x) (sqrt (cos x)))))))) (fmod (exp x) (sqrt (cos x)))) (taylor 0 x) (#s(alt (.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) (patch #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) (patch #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) (patch #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) (patch #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #<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 (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* x (fmod (exp x) (sqrt (cos x))))) (fmod (exp x) (sqrt (cos x)))) (taylor 0 x) (#s(alt (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* 1/2 (* x (fmod (exp x) (sqrt (cos x))))))) (fmod (exp x) (sqrt (cos x)))) (taylor 0 x) (#s(alt (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* x (+ (* -1/6 (* x (fmod (exp x) (sqrt (cos x))))) (* 1/2 (fmod (exp x) (sqrt (cos x)))))))) (fmod (exp x) (sqrt (cos x)))) (taylor 0 x) (#s(alt (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (patch (.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor 0 x) (#s(alt (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt #s(approx (exp x) #s(literal 1 binary64)) (patch #s(approx (exp x) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt #s(approx (sqrt (cos x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/4 (pow x 2))) (taylor 0 x) (#s(alt #s(approx (sqrt (cos x)) #s(literal 1 binary64)) (patch #s(approx (sqrt (cos x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
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#s(alt (fmod (exp x) (sqrt (cos x))) (taylor -inf x) (#s(alt (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (fmod (exp x) (sqrt (cos x))) (taylor -inf x) (#s(alt (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (patch (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) #s(literal 1 binary64)) (patch #s(approx (exp (neg x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) #s(literal 1 binary64)) (patch #s(approx (exp (neg x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) #s(literal 1 binary64)) (patch #s(approx (exp (neg x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) #s(literal 1 binary64)) (patch #s(approx (exp (neg x)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* -1 x)) (taylor -inf x) (#s(alt #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (patch #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

((* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (fmod (exp x) (sqrt (cos x))) (exp x) (+ 1 x) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (fmod (exp x) (sqrt (cos x))) (exp x) (sqrt (cos x)) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (fmod (exp x) (sqrt (cos x))) (exp x) (+ (* (+ (* 1/2 x) 1) x) 1) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (/ 1 (exp x)) (fmod (exp x) (sqrt (cos x))) (exp x) (exp (neg x)) (exp (neg x)))

1.0ms

inf

((* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (fmod (exp x) (sqrt (cos x))) (exp x) (+ 1 x) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (fmod (exp x) (sqrt (cos x))) (exp x) (sqrt (cos x)) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (fmod (exp x) (sqrt (cos x))) (exp x) (+ (* (+ (* 1/2 x) 1) x) 1) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (/ 1 (exp x)) (fmod (exp x) (sqrt (cos x))) (exp x) (exp (neg x)) (exp (neg x)))

0.0ms

((* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (fmod (exp x) (sqrt (cos x))) (exp x) (+ 1 x) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (fmod (exp x) (sqrt (cos x))) (exp x) (sqrt (cos x)) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (fmod (exp x) (sqrt (cos x))) (exp x) (+ (* (+ (* 1/2 x) 1) x) 1) (* (fmod (exp x) (sqrt (cos x))) (exp (neg x))) (/ 1 (exp x)) (fmod (exp x) (sqrt (cos x))) (exp x) (exp (neg x)) (exp (neg x)))

simplify269.0ms (3%)

Memory

-8.7MiB live, 116.6MiB allocated

Algorithm

1×	egg-herbie

Rules

18 026×	`lower-fma.f64`
18 026×	`lower-fma.f32`
4 500×	`lower-*.f64`
4 500×	`lower-*.f32`
2 668×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	1457
1	206	1358
2	446	1306
3	1619	1278
4	4648	1278
5	7971	1278
0	8106	1203

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 214

Calls

Call 1

Inputs
(fmod (exp x) (sqrt (cos x)))
(+ (* -1 (* x (fmod (exp x) (sqrt (cos x))))) (fmod (exp x) (sqrt (cos x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* 1/2 (* x (fmod (exp x) (sqrt (cos x))))))) (fmod (exp x) (sqrt (cos x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* x (+ (* -1/6 (* x (fmod (exp x) (sqrt (cos x))))) (* 1/2 (fmod (exp x) (sqrt (cos x)))))))) (fmod (exp x) (sqrt (cos x))))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
(fmod (exp x) (sqrt (cos x)))
(+ (* -1 (* x (fmod (exp x) (sqrt (cos x))))) (fmod (exp x) (sqrt (cos x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* 1/2 (* x (fmod (exp x) (sqrt (cos x))))))) (fmod (exp x) (sqrt (cos x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* x (+ (* -1/6 (* x (fmod (exp x) (sqrt (cos x))))) (* 1/2 (fmod (exp x) (sqrt (cos x)))))))) (fmod (exp x) (sqrt (cos x))))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 (* -1/4 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/96 (pow x 2)) 1/4)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -19/5760 (pow x 2)) 1/96)) 1/4)))
(fmod (exp x) (sqrt (cos x)))
(+ (* -1 (* x (fmod (exp x) (sqrt (cos x))))) (fmod (exp x) (sqrt (cos x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* 1/2 (* x (fmod (exp x) (sqrt (cos x))))))) (fmod (exp x) (sqrt (cos x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* x (+ (* -1/6 (* x (fmod (exp x) (sqrt (cos x))))) (* 1/2 (fmod (exp x) (sqrt (cos x)))))))) (fmod (exp x) (sqrt (cos x))))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fmod (exp x) (sqrt (cos x)))
(+ (* -1 (* x (fmod (exp x) (sqrt (cos x))))) (fmod (exp x) (sqrt (cos x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* 1/2 (* x (fmod (exp x) (sqrt (cos x))))))) (fmod (exp x) (sqrt (cos x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* x (+ (* -1/6 (* x (fmod (exp x) (sqrt (cos x))))) (* 1/2 (fmod (exp x) (sqrt (cos x)))))))) (fmod (exp x) (sqrt (cos x))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
1
(+ 1 (* -1 x))
(+ 1 (* x (- (* 1/2 x) 1)))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(exp x)
(exp x)
(exp x)
(exp x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(exp x)
(exp x)
(exp x)
(exp x)
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(exp x)
(exp x)
(exp x)
(exp x)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/ 1 (exp x))
(/ 1 (exp x))
(/ 1 (exp x))
(/ 1 (exp x))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(exp x)
(exp x)
(exp x)
(exp x)
(exp (neg x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(exp (neg x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(exp x)
(exp x)
(exp x)
(exp x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(exp x)
(exp x)
(exp x)
(exp x)
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(sqrt (cos x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(exp x)
(exp x)
(exp x)
(exp x)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/ 1 (exp x))
(/ 1 (exp x))
(/ 1 (exp x))
(/ 1 (exp x))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(fmod (exp x) (sqrt (cos x)))
(exp x)
(exp x)
(exp x)
(exp x)
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))
(exp (* -1 x))

Outputs
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(+ (* -1 (* x (fmod (exp x) (sqrt (cos x))))) (fmod (exp x) (sqrt (cos x))))
(*.f64 (-.f64 #s(literal 1 binary64) x) (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* 1/2 (* x (fmod (exp x) (sqrt (cos x))))))) (fmod (exp x) (sqrt (cos x))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* x (+ (* -1/6 (* x (fmod (exp x) (sqrt (cos x))))) (* 1/2 (fmod (exp x) (sqrt (cos x)))))))) (fmod (exp x) (sqrt (cos x))))
(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(+ (* -1 (* x (fmod (exp x) (sqrt (cos x))))) (fmod (exp x) (sqrt (cos x))))
(*.f64 (-.f64 #s(literal 1 binary64) x) (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* 1/2 (* x (fmod (exp x) (sqrt (cos x))))))) (fmod (exp x) (sqrt (cos x))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* x (+ (* -1/6 (* x (fmod (exp x) (sqrt (cos x))))) (* 1/2 (fmod (exp x) (sqrt (cos x)))))))) (fmod (exp x) (sqrt (cos x))))
(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1/4 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/96 (pow x 2)) 1/4)))
(fma.f64 (fma.f64 #s(literal -1/96 binary64) (.f64 x x) #s(literal -1/4 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -19/5760 (pow x 2)) 1/96)) 1/4)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -19/5760 binary64) (.f64 x x) #s(literal -1/96 binary64)) (.f64 x x) #s(literal -1/4 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(+ (* -1 (* x (fmod (exp x) (sqrt (cos x))))) (fmod (exp x) (sqrt (cos x))))
(*.f64 (-.f64 #s(literal 1 binary64) x) (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* 1/2 (* x (fmod (exp x) (sqrt (cos x))))))) (fmod (exp x) (sqrt (cos x))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* x (+ (* -1/6 (* x (fmod (exp x) (sqrt (cos x))))) (* 1/2 (fmod (exp x) (sqrt (cos x)))))))) (fmod (exp x) (sqrt (cos x))))
(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(+ (* -1 (* x (fmod (exp x) (sqrt (cos x))))) (fmod (exp x) (sqrt (cos x))))
(*.f64 (-.f64 #s(literal 1 binary64) x) (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* 1/2 (* x (fmod (exp x) (sqrt (cos x))))))) (fmod (exp x) (sqrt (cos x))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64)) (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))))
(+ (* x (+ (* -1 (fmod (exp x) (sqrt (cos x)))) (* x (+ (* -1/6 (* x (fmod (exp x) (sqrt (cos x))))) (* 1/2 (fmod (exp x) (sqrt (cos x)))))))) (fmod (exp x) (sqrt (cos x))))
(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* x (- (* 1/2 x) 1)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(+ 1 (* x (- (* x (+ 1/2 (* -1/6 x))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (neg x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(/ 1 (exp x))
(exp.f64 (neg.f64 x))
(/ 1 (exp x))
(exp.f64 (neg.f64 x))
(/ 1 (exp x))
(exp.f64 (neg.f64 x))
(/ 1 (exp x))
(exp.f64 (neg.f64 x))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp (neg x))
(exp.f64 (neg.f64 x))
(exp (neg x))
(exp.f64 (neg.f64 x))
(exp (neg x))
(exp.f64 (neg.f64 x))
(exp (neg x))
(exp.f64 (neg.f64 x))
(exp (neg x))
(exp.f64 (neg.f64 x))
(exp (neg x))
(exp.f64 (neg.f64 x))
(exp (neg x))
(exp.f64 (neg.f64 x))
(exp (neg x))
(exp.f64 (neg.f64 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(sqrt (cos x))
(sqrt.f64 (cos.f64 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(* (exp (* -1 x)) (fmod (exp x) (sqrt (cos x))))
(/.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 x))
(/ 1 (exp x))
(exp.f64 (neg.f64 x))
(/ 1 (exp x))
(exp.f64 (neg.f64 x))
(/ 1 (exp x))
(exp.f64 (neg.f64 x))
(/ 1 (exp x))
(exp.f64 (neg.f64 x))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(fmod (exp x) (sqrt (cos x)))
(fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp (* -1 x))
(exp.f64 (neg.f64 x))
(exp (* -1 x))
(exp.f64 (neg.f64 x))
(exp (* -1 x))
(exp.f64 (neg.f64 x))
(exp (* -1 x))
(exp.f64 (neg.f64 x))
(exp (* -1 x))
(exp.f64 (neg.f64 x))
(exp (* -1 x))
(exp.f64 (neg.f64 x))
(exp (* -1 x))
(exp.f64 (neg.f64 x))
(exp (* -1 x))
(exp.f64 (neg.f64 x))

rewrite229.0ms (2.6%)

Memory

10.7MiB live, 167.9MiB allocated

Rules

9 268×	`lower-fma.f32`
9 258×	`lower-fma.f64`
5 388×	`lower-*.f32`
5 380×	`lower-*.f64`
3 868×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	193
0	55	192
1	151	192
2	887	192
0	8402	192

Stop Event

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

Counts

18 → 175

Calls

Call 1

Inputs
(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
#s(approx (exp x) #s(literal 1 binary64))
#s(approx (sqrt (cos x)) #s(literal 1 binary64))
(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))
(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (exp.f64 x))
(fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))
(exp.f64 x)
#s(approx (exp (neg x)) #s(literal 1 binary64))
#s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))

Outputs
#<batchref>
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#<batchref>
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval96.0ms (1.1%)

Memory: 12.0MiB live, 122.0MiB allocated
Compiler: Compiled 11 343 to 1 037 computations (90.9% saved)

prune29.0ms (0.3%)

Memory

-13.2MiB live, 66.3MiB allocated

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	601	7	608
Fresh	2	2	4
Picked	3	2	5
Done	0	2	2
Total	606	13	619

Accuracy

62.9%

Counts

619 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	5.1%	(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
✓	5.7%	(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (exp.f64 (neg.f64 x)))
✓	5.1%	(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
	11.0%	(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
	14.9%	(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
	14.7%	(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)))
	23.7%	(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)))
✓	23.5%	(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
	47.5%	(.f64 (fmod.f64 #s(approx (exp x) #s(approx (+ ( (+ (* 1/2 x) 1) x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
	51.4%	(.f64 (fmod.f64 #s(approx (exp x) #s(approx (+ ( (+ (* 1/2 x) 1) x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
	14.2%	(.f64 (fmod.f64 #s(approx (exp x) #s(approx (+ ( (+ (* 1/2 x) 1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
	4.5%	(.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
✓	22.5%	(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))

Compiler

Compiled 617 to 236 computations (61.8% saved)

regimes21.0ms (0.2%)

Memory

11.2MiB live, 47.7MiB allocated

Counts

30 → 2

Calls

Call 1

Inputs
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)))
(.f64 (fmod.f64 #s(approx (exp x) #s(approx (+ ( (+ (* 1/2 x) 1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(.f64 (fmod.f64 #s(approx (exp x) #s(approx (+ ( (+ (* 1/2 x) 1) x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(.f64 (fmod.f64 #s(approx (exp x) #s(approx (+ ( (+ (* 1/2 x) 1) x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (exp.f64 (neg.f64 x)))
(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (exp.f64 (neg.f64 x)))
(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) #s(approx (exp x) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (exp.f64 (neg.f64 x)))
(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(*.f64 (fmod.f64 (exp.f64 x) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (exp.f64 x)))
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))
(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))
(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (/.f64 #s(literal 1 binary64) (exp.f64 x)))
(.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 (exp.f64 (neg.f64 x)) #s(literal -1/2 binary64)) (pow.f64 (exp.f64 (neg.f64 x)) #s(literal -1/2 binary64)))))

Outputs

(*.f64 (fmod.f64 #s(approx (exp x) #s(approx (+ (* (+ (* 1/2 x) 1) x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))

(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)))

Calls

2 calls:

10.0ms	(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))
9.0ms	x

Results

Accuracy	Segments	Branch
62.6%	3	`x`
61.1%	2	`(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 11 to 9 computations (18.2% saved)

regimes5.0ms (0.1%)

Memory

-27.8MiB live, 11.0MiB allocated

Counts

10 → 2

Calls

Call 1

Inputs
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)))
(.f64 (fmod.f64 #s(approx (exp x) #s(approx (+ ( (+ (* 1/2 x) 1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(.f64 (fmod.f64 #s(approx (exp x) #s(approx (+ ( (+ (* 1/2 x) 1) x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))))
(*.f64 (fmod.f64 #s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal -1 binary64)) x #s(literal 1 binary64))))

Outputs

(*.f64 (fmod.f64 #s(approx (exp x) #s(approx (+ (* (+ (* 1/2 x) 1) x) 1) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))

(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)))

Calls

1 calls:

4.0ms

(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))

Results

Accuracy	Segments	Branch
61.1%	2	`(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 10 to 8 computations (20% saved)

regimes5.0ms (0.1%)

Memory

15.4MiB live, 15.4MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)))
(.f64 (fmod.f64 #s(approx (exp x) #s(approx (+ ( (+ (* 1/2 x) 1) x) 1) (.f64 (.f64 x x) #s(literal 1/2 binary64)))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) (fma.f64 (.f64 x x) #s(literal -1/4 binary64) #s(literal 1 binary64)))) #s(approx (exp (neg x)) #s(literal 1 binary64)))

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

Calls

2 calls:

2.0ms	x
2.0ms	(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))

Results

Accuracy	Segments	Branch
23.7%	1	`x`
23.7%	1	`(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 11 to 9 computations (18.2% saved)

regimes3.0ms (0%)

Memory

10.1MiB live, 10.1MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs

(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))

(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))

Outputs
(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))

Calls

2 calls:

2.0ms	x
1.0ms	(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))

Results

Accuracy	Segments	Branch
23.5%	1	`x`
23.5%	1	`(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 11 to 9 computations (18.2% saved)

regimes3.0ms (0%)

Memory

7.3MiB live, 7.3MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))

Outputs
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))

Calls

2 calls:

1.0ms	x
1.0ms	(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))

Results

Accuracy	Segments	Branch
22.5%	1	`x`
22.5%	1	`(*.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x)))`

Compiler

Compiled 11 to 9 computations (18.2% saved)

bsearch0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.966049710711151e-11	1.0

Compiler

Compiled 13 to 12 computations (7.7% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.966049710711151e-11	1.0

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify26.0ms (0.3%)

Memory

-26.7MiB live, 59.9MiB allocated

Algorithm

1×	egg-herbie

Rules

16×	`-commutative-binary64-.f64`
6×	`+-commutative-binary64-+.f64`
4×	`sub-neg-binary64-neg.f64-+.f64--.f64`
2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	191
1	62	191
2	65	191
3	66	191

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x))) #s(literal 7737125245533627/154742504910672534362390528 binary64)) (.f64 (fmod.f64 #s(approx (exp x) #s(approx (+ (* (+ (* 1/2 x) 1) x) 1) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x))))
(if (<=.f64 (.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x))) #s(literal 7737125245533627/154742504910672534362390528 binary64)) (.f64 (fmod.f64 #s(approx (exp x) #s(approx (+ (* (+ (* 1/2 x) 1) x) 1) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x))))
(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))

Outputs
(if (<=.f64 (.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x))) #s(literal 7737125245533627/154742504910672534362390528 binary64)) (.f64 (fmod.f64 #s(approx (exp x) #s(approx (+ (* (+ (* 1/2 x) 1) x) 1) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64)))) (.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x))))
(if (<=.f64 (.f64 (exp.f64 (neg.f64 x)) (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) #s(literal 7737125245533627/154742504910672534362390528 binary64)) (.f64 #s(approx (exp (neg x)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal -1 binary64)) x #s(literal 1 binary64))) (fmod.f64 #s(approx (exp x) #s(approx (+ (* (+ (* 1/2 x) 1) x) 1) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))) (.f64 #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)) (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))))
(if (<=.f64 (.f64 (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x))) (exp.f64 (neg.f64 x))) #s(literal 7737125245533627/154742504910672534362390528 binary64)) (.f64 (fmod.f64 #s(approx (exp x) #s(approx (+ (* (+ (* 1/2 x) 1) x) 1) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64))) (.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x))))
(if (<=.f64 (.f64 (exp.f64 (neg.f64 x)) (fmod.f64 (exp.f64 x) (sqrt.f64 (cos.f64 x)))) #s(literal 7737125245533627/154742504910672534362390528 binary64)) (.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) (fmod.f64 #s(approx (exp x) #s(approx (+ (* (+ (* 1/2 x) 1) x) 1) (.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))) (.f64 #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)) (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64)))))
(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(approx (exp (neg x)) (-.f64 #s(literal 1 binary64) x)) (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))))
(*.f64 (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))
(*.f64 #s(approx (exp (neg x)) #s(literal 1 binary64)) (fmod.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))))
(*.f64 (fmod.f64 #s(approx (exp x) #s(literal 1 binary64)) #s(approx (sqrt (cos x)) #s(literal 1 binary64))) #s(approx (exp (neg x)) #s(literal 1 binary64)))

soundness1.2s (13.4%)

Memory

-0.9MiB live, 678.4MiB allocated

Rules

18 026×	`lower-fma.f64`
18 026×	`lower-fma.f32`
15 400×	`lower-fma.f64`
15 400×	`lower-fma.f32`
14 924×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	87	804
1	206	778
2	454	765
3	1123	758
4	1992	758
5	3768	758
6	5106	758
7	6158	758
8	7423	758
0	8120	710
0	119	1467
1	309	1366
2	856	1314
3	2637	1286
4	6480	1282
0	8625	1197
0	82	1457
1	206	1358
2	446	1306
3	1619	1278
4	4648	1278
5	7971	1278
0	8106	1203
0	69	285
1	151	284
2	311	284
3	810	284
4	1446	284
5	1991	284
6	2988	284
7	4040	284
8	5014	284
9	6166	284
10	6710	284
11	6836	284
12	6862	284
13	6878	284
14	7232	284
15	7924	284
0	8498	262

Stop Event

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

Compiler

Compiled 344 to 221 computations (35.8% saved)

preprocess38.0ms (0.4%)

Memory: 22.6MiB live, 61.1MiB allocated
Compiler: Compiled 254 to 94 computations (63% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	10	21
1	29	21
2	68	21
3	122	21
4	168	21
5	188	21
6	205	21
7	224	21
8	231	21
0	8	10
0	15	10
1	22	10
2	32	9
3	38	9
4	43	9
5	49	9
6	56	9
7	62	9
8	63	9
0	63	9

Iter	Nodes	Cost
0	23	132
0	36	130
1	49	129
2	64	127
3	83	127
4	87	127
5	93	127
6	100	127
7	112	127
8	115	127
9	116	127
10	118	127
11	118	127
0	118	127

Iter	Nodes	Cost
0	10	21
1	29	21
2	68	21
3	122	21
4	168	21
5	188	21
6	205	21
7	224	21
8	231	21
0	8	10
0	15	10
1	22	10
2	32	9
3	38	9
4	43	9
5	49	9
6	56	9
7	62	9
8	63	9
0	63	9

Iter	Nodes	Cost
0	23	132
0	36	130
1	49	129
2	64	127
3	83	127
4	87	127
5	93	127
6	100	127
7	112	127
8	115	127
9	116	127
10	118	127
11	118	127
0	118	127

start0.0ms (0%)

analyze208.0ms (2.3%)

sample4.6s (51%)

explain240.0ms (2.7%)

preprocess55.0ms (0.6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize93.0ms (1%)

series2.0ms (0%)

simplify261.0ms (2.9%)

rewrite75.0ms (0.8%)

eval16.0ms (0.2%)

prune4.0ms (0%)

simplify11.0ms (0.1%)

localize130.0ms (1.5%)

series5.0ms (0.1%)

simplify175.0ms (2%)

rewrite64.0ms (0.7%)

eval110.0ms (1.2%)

prune22.0ms (0.2%)

simplify70.0ms (0.8%)

localize143.0ms (1.6%)

series8.0ms (0.1%)

simplify133.0ms (1.5%)

rewrite261.0ms (2.9%)

eval60.0ms (0.7%)

prune16.0ms (0.2%)

simplify84.0ms (0.9%)

localize197.0ms (2.2%)

series9.0ms (0.1%)

simplify269.0ms (3%)

rewrite229.0ms (2.6%)

eval96.0ms (1.1%)

prune29.0ms (0.3%)

regimes21.0ms (0.2%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes3.0ms (0%)

regimes3.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify26.0ms (0.3%)

soundness1.2s (13.4%)

preprocess38.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	10	21
1	29	21
2	68	21
3	122	21
4	168	21
5	188	21
6	205	21
7	224	21
8	231	21
0	8	10
0	15	10
1	22	10
2	32	9
3	38	9
4	43	9
5	49	9
6	56	9
7	62	9
8	63	9
0	63	9

Iter	Nodes	Cost
0	23	132
0	36	130
1	49	129
2	64	127
3	83	127
4	87	127
5	93	127
6	100	127
7	112	127
8	115	127
9	116	127
10	118	127
11	118	127
0	118	127