Metrics for sqrtexp (problem 3.4.4)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze2.0ms (0%)

Memory

4.5MiB live, 4.5MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (23.9%)

Memory

49.9MiB live, 913.6MiB allocated; 870ms collecting garbage

Samples

718.0ms	8 256×	0	valid
145.0ms	2 690×	0	exit

Precisions

Click to see histograms. Total time spent on operations: 656.0ms

ival-div: 351.0ms (53.5% of total)

ival-expm1: 127.0ms (19.4% of total)

ival-mult: 87.0ms (13.3% of total)

ival-sqrt: 70.0ms (10.7% of total)

ival-true: 8.0ms (1.2% of total)

exact: 6.0ms (0.9% of total)

ival-assert: 4.0ms (0.6% of total)

adjust: 3.0ms (0.5% of total)

Bogosity

explain128.0ms (2.5%)

Memory

-20.6MiB live, 125.7MiB allocated; 15ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
163	0	-	-	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`
162	1	(0.0023952394400004254)	-	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`
2	0	-	-	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
0	0	-	-	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(*.f64 #s(literal 2 binary64) x)`
0	0	-	-	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(exp.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	cancellation	163	0
`-.f64`	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	cancellation	163	0
`/.f64`	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`	o/o	2	0
↳	`(exp.f64 (*.f64 #s(literal 2 binary64) x))`	overflow	2
↳	`(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))`	overflow	2
↳	`(exp.f64 x)`	overflow	2
↳	`(-.f64 (exp.f64 x) #s(literal 1 binary64))`	overflow	2

Confusion

	Predicted +	Predicted -
+	164	0
-	1	91

Precision

0.9939393939393939

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	164	0	0
-	1	0	91

Precision?

0.9939393939393939

Recall?

1.0

Freqs

test

number	freq
0	91
1	2
2	163

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

40.0ms

512×

valid

Compiler

Compiled 106 to 34 computations (67.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-exp: 7.0ms (28.8% of total)

ival-expm1: 6.0ms (24.7% of total)

ival-mult: 4.0ms (16.5% of total)

ival-div: 3.0ms (12.3% of total)

ival-sqrt: 3.0ms (12.3% of total)

exact: 1.0ms (4.1% of total)

adjust: 0.0ms (0% of total)

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

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

preprocess192.0ms (3.7%)

Memory

-9.2MiB live, 128.3MiB allocated; 17ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	35	27
2	80	27
3	250	27
4	1179	13
0	10	12
0	17	12
1	33	12
2	59	12
3	146	12
4	695	7
5	6520	7
0	8067	7

Stop Event

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

Calls

Call 1

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

Outputs

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

(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))

Compiler

Compiled 12 to 10 computations (16.7% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	38.7%	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify138.0ms (2.6%)

Memory

17.3MiB live, 107.6MiB allocated; 6ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	45
0	17	45
1	33	45
2	59	45
3	146	45
4	695	35
5	6520	35
0	8067	31

Stop Event

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

Calls

Call 1

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

Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
(sqrt.f64 (*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
(expm1.f64 (*.f64 x #s(literal 2 binary64)))
(exp.f64 (*.f64 #s(literal 2 binary64) x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) x)
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
x
#s(literal 1 binary64)
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(expm1.f64 x)
(exp.f64 x)

localize26.0ms (0.5%)

Memory

25.7MiB live, 25.7MiB allocated; 0ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))
accuracy	0.41796875000000006	(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))
accuracy	36.71824067686659	(-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
accuracy	36.74336006214114	(-.f64 (exp.f64 x) #s(literal 1 binary64))

Samples

19.0ms

256×

valid

Compiler

Compiled 47 to 12 computations (74.5% saved)

Precisions

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

ival-exp: 3.0ms (25.1% of total)

ival-expm1: 3.0ms (25.1% of total)

ival-div: 2.0ms (16.7% of total)

ival-mult: 2.0ms (16.7% of total)

ival-sqrt: 2.0ms (16.7% of total)

adjust: 0.0ms (0% 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

-42.9MiB live, 3.1MiB allocated; 3ms collecting garbage

Counts

4 → 20

Calls

Call 1

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

Outputs
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(- (exp (* 2 x)) 1)
(- (exp x) 1)
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	((- (exp (* 2 x)) 1) (- (exp x) 1) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))
1.0ms	x	@	0	((- (exp (* 2 x)) 1) (- (exp x) 1) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))
1.0ms	x	@	-inf	((- (exp (* 2 x)) 1) (- (exp x) 1) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))

Time

Variable

Point

Expression

3.0ms

inf

((- (exp (* 2 x)) 1) (- (exp x) 1) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))

1.0ms

((- (exp (* 2 x)) 1) (- (exp x) 1) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))

1.0ms

-inf

((- (exp (* 2 x)) 1) (- (exp x) 1) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))

simplify172.0ms (3.3%)

Memory

36.2MiB live, 133.1MiB allocated; 34ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	213
1	302	173
2	1041	172
3	3429	170
0	8155	135

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 19

Calls

Call 1

Inputs
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(- (exp (* 2 x)) 1)
(- (exp x) 1)
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))

Outputs
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x #s(literal 2 binary64)) x #s(literal 2 binary64)) x)
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/3 binary64) x #s(literal 4/3 binary64)) x #s(literal 2 binary64)) x #s(literal 2 binary64)) x)
x
(* x (+ 1 (* 1/2 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* 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 2 binary64))
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(- (exp x) 1)
(expm1.f64 x)
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))

rewrite43.0ms (0.8%)

Memory

-8.2MiB live, 36.9MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	33
0	17	33
1	65	19
0	423	15

Stop Event

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

Counts

4 → 50

Calls

Call 1

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

Outputs
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x))
(/.f64 (neg.f64 (expm1.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (expm1.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 2 binary64))))))
(/.f64 (expm1.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 2 binary64))) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)))
(/.f64 (expm1.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 3 binary64))) (+.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 2 binary64)))))
(expm1.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) x))
(expm1.f64 (*.f64 x #s(literal 2 binary64)))
(-.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 2 binary64))) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 x #s(literal 3 binary64))) (+.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 x #s(literal 2 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 x #s(literal 2 binary64))))))
(-.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) #s(literal 1 binary64))
(+.f64 (cosh.f64 (.f64 x #s(literal 2 binary64))) (-.f64 (sinh.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)))
(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (neg.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(expm1.f64 x)
(-.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (+.f64 (exp.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64)))))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 (cosh.f64 x) (-.f64 (sinh.f64 x) #s(literal 1 binary64)))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(.f64 (/.f64 (expm1.f64 (.f64 x #s(literal 2 binary64))) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 (exp.f64 x) #s(literal 1 binary64))))
(*.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (expm1.f64 x)) (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (expm1.f64 x))) (.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))) (+.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (expm1.f64 x)) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (expm1.f64 x)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (expm1.f64 x)) (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (expm1.f64 x)) (fma.f64 (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)) (*.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (expm1.f64 x)) (pow.f64 (expm1.f64 x) #s(literal -1 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 #s(literal 2 binary64)) x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (exp.f64 x))))
(/.f64 (neg.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (neg.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (-.f64 (.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (expm1.f64 x)) (.f64 (expm1.f64 x) #s(literal 1 binary64))) (*.f64 (expm1.f64 x) (expm1.f64 x)))
(/.f64 (expm1.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 2 binary64))) (*.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x)))
(/.f64 (expm1.f64 (.f64 (.f64 x #s(literal 2 binary64)) #s(literal 3 binary64))) (.f64 (+.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (pow.f64 (exp.f64 #s(literal 2 binary64)) (.f64 x #s(literal 2 binary64)))) (expm1.f64 x)))
(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (neg.f64 (expm1.f64 x)))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(neg.f64 (/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (expm1.f64 x)))
(neg.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (neg.f64 (expm1.f64 x))))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal 1 binary64))
(-.f64 (/.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) x) (expm1.f64 x)) (pow.f64 (expm1.f64 x) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (exp.f64 x)) #s(literal 1 binary64)))
(+.f64 (cosh.f64 x) (+.f64 (sinh.f64 x) #s(literal 1 binary64)))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(*.f64 (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64)))) (sqrt.f64 (expm1.f64 x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal 1/2 binary64)))

eval8.0ms (0.2%)

Memory: 11.6MiB live, 11.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 189 to 297 computations (75% saved)

prune6.0ms (0.1%)

Memory

9.4MiB live, 9.4MiB allocated; 0ms collecting garbage

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	61	8	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	8	70

Accuracy

100.0%

Counts

70 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
▶	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
	63.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp 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 2 binary64))))
▶	65.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
	63.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
▶	69.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	64.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
▶	65.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))

Compiler

Compiled 274 to 218 computations (20.4% saved)

simplify160.0ms (3.1%)

Memory

-45.8MiB live, 147.2MiB allocated; 25ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x #s(literal 2 binary64))
cost-diff	0	(expm1.f64 (*.f64 x #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
cost-diff	3	(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
cost-diff	0	(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
cost-diff	0	(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(fma.f64 #s(literal 1/2 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 2 binary64))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
cost-diff	0	(exp.f64 x)
cost-diff	0	(+.f64 (exp.f64 x) #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	163
0	52	147
1	90	147
2	175	147
3	485	142
4	1861	132
0	8399	132

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
x
#s(literal 1 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
#s(literal 3/16 binary64)
x
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(expm1.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(expm1.f64 x)

Outputs
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(exp.f64 x)
x
#s(literal 1 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(literal 1/2 binary64)
x
#s(literal 1 binary64)
#s(literal 2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
#s(literal 3/16 binary64)
x
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(expm1.f64 (*.f64 x #s(literal 2 binary64)))
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
x
#s(literal 2 binary64)
(expm1.f64 x)

localize66.0ms (1.3%)

Memory

40.5MiB live, 85.1MiB allocated; 3ms collecting garbage

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.0	(expm1.f64 x)
accuracy	0.00390625	(expm1.f64 (*.f64 x #s(literal 2 binary64)))
accuracy	0.0078125	(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
accuracy	0.41796875000000006	(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.05859375	(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.849941259768442	(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	22.38231687368238	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
accuracy	0.0	(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
accuracy	0.0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy	0.0078125	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
accuracy	22.432136485901097	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
accuracy	0.0078125	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
accuracy	20.111144462426083	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
accuracy	0.0	(exp.f64 x)
accuracy	0.00390625	(+.f64 (exp.f64 x) #s(literal 1 binary64))
accuracy	0.0078125	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))

Samples

46.0ms	243×	0	valid
3.0ms	9×	1	valid
2.0ms	4×	2	valid

Compiler

Compiled 162 to 29 computations (82.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-mult: 9.0ms (26.3% of total)

ival-add: 6.0ms (17.5% of total)

ival-sqrt: 6.0ms (17.5% of total)

ival-div: 5.0ms (14.6% of total)

ival-expm1: 4.0ms (11.7% of total)

ival-exp: 2.0ms (5.8% of total)

adjust: 1.0ms (2.9% of total)

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

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

exact: 0.0ms (0% of total)

series31.0ms (0.6%)

Memory

-28.8MiB live, 24.5MiB allocated; 18ms collecting garbage

Counts

19 → 46

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(expm1.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(expm1.f64 x)

Outputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (* 1/2 x))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
1/2
(+ 1/2 (* 3/16 x))
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* 3/16 x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(- (exp (* 2 x)) 1)
(- (exp x) 1)
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))

Calls

3 calls:

Time	Variable		Point	Expression
26.0ms	x	@	-inf	((sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (/ (+ (* 3/16 x) 1/2) (sqrt 2)) (+ (* 3/16 x) 1/2) (/ (- (exp (* x 2)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* x 2)) 1) (- (exp x) 1))) (- (exp (* x 2)) 1) (* x 2) (sqrt 2) (- (exp x) 1))
3.0ms	x	@	inf	((sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (/ (+ (* 3/16 x) 1/2) (sqrt 2)) (+ (* 3/16 x) 1/2) (/ (- (exp (* x 2)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* x 2)) 1) (- (exp x) 1))) (- (exp (* x 2)) 1) (* x 2) (sqrt 2) (- (exp x) 1))
2.0ms	x	@	0	((sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (/ (+ (* 3/16 x) 1/2) (sqrt 2)) (+ (* 3/16 x) 1/2) (/ (- (exp (* x 2)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* x 2)) 1) (- (exp x) 1))) (- (exp (* x 2)) 1) (* x 2) (sqrt 2) (- (exp x) 1))

Time

Variable

Point

Expression

26.0ms

-inf

((sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (/ (+ (* 3/16 x) 1/2) (sqrt 2)) (+ (* 3/16 x) 1/2) (/ (- (exp (* x 2)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* x 2)) 1) (- (exp x) 1))) (- (exp (* x 2)) 1) (* x 2) (sqrt 2) (- (exp x) 1))

3.0ms

inf

((sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (/ (+ (* 3/16 x) 1/2) (sqrt 2)) (+ (* 3/16 x) 1/2) (/ (- (exp (* x 2)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* x 2)) 1) (- (exp x) 1))) (- (exp (* x 2)) 1) (* x 2) (sqrt 2) (- (exp x) 1))

2.0ms

((sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* 1/2 x) 1) x) 2) (+ (* 1/2 x) 1) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (/ (+ (* 3/16 x) 1/2) (sqrt 2)) (+ (* 3/16 x) 1/2) (/ (- (exp (* x 2)) 1) (- (exp x) 1)) (sqrt (/ (- (exp (* x 2)) 1) (- (exp x) 1))) (- (exp (* x 2)) 1) (* x 2) (sqrt 2) (- (exp x) 1))

simplify204.0ms (3.9%)

Memory

4.4MiB live, 136.9MiB allocated; 25ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	125	428
1	470	359
2	1558	346
3	6700	344
0	8024	291

Stop Event

1×	iter limit
1×	node limit

Counts

46 → 45

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (* 1/2 x))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
1/2
(+ 1/2 (* 3/16 x))
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(* 3/16 (/ x (sqrt 2)))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* 3/16 x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(- (exp (* 2 x)) 1)
(- (exp x) 1)
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* 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 2 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 (* 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 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(/ 1/2 (sqrt 2))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 3/16 x))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (* 2 x)))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x #s(literal 2 binary64)) x #s(literal 2 binary64)) x)
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/3 binary64) x #s(literal 4/3 binary64)) x #s(literal 2 binary64)) x #s(literal 2 binary64)) x)
x
(* x (+ 1 (* 1/2 x)))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) x #s(literal 1/6 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.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) (/ 2 (pow x 2)))))
(*.f64 (fma.f64 #s(literal 1/2 binary64) x (+.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64))) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(*.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x)
(* 3/16 (/ x (sqrt 2)))
(*.f64 #s(literal 3/16 binary64) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))
(* x (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 3/16 x)
(*.f64 #s(literal 3/16 binary64) x)
(* x (+ 3/16 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 #s(literal 2 binary64) x))
(- (exp x) 1)
(expm1.f64 x)
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(*.f64 (+.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x)

rewrite237.0ms (4.6%)

Memory

6.2MiB live, 151.1MiB allocated; 20ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	150
0	52	119
1	198	119
2	1173	119
0	8341	119

Stop Event

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

Counts

19 → 581

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp.f64 x)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64)))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(expm1.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(sqrt.f64 #s(literal 2 binary64))
(expm1.f64 x)

Outputs
(*.f64 (neg.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64))))
(.f64 (sqrt.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(.f64 (sqrt.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 #s(literal 2 binary64) x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(.f64 (pow.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(.f64 (pow.f64 (/.f64 (expm1.f64 (.f64 #s(literal 2 binary64) x)) (expm1.f64 (*.f64 #s(literal 2 binary64) x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log1p.f64 (exp.f64 x))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (neg.f64 (sinh.f64 (acosh.f64 (exp.f64 x))))) (neg.f64 (neg.f64 (sqrt.f64 (expm1.f64 x)))))
(/.f64 (neg.f64 (cosh.f64 (asinh.f64 (pow.f64 (exp.f64 x) #s(literal 3/2 binary64))))) (neg.f64 (sqrt.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))))) (neg.f64 (sqrt.f64 (neg.f64 (expm1.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (pow.f64 (expm1.f64 x) #s(literal -2 binary64)))) (sqrt.f64 (/.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (expm1.f64 x))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (exp.f64 x) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) (pow.f64 (expm1.f64 x) #s(literal 3 binary64))) (pow.f64 (expm1.f64 x) #s(literal -3 binary64)))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64))) (+.f64 (pow.f64 (expm1.f64 x) #s(literal -2 binary64)) (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (pow.f64 (expm1.f64 x) #s(literal 2 binary64)))))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (-.f64 #s(literal 1 binary64) (exp.f64 x))))))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))))) (sqrt.f64 (neg.f64 (neg.f64 (expm1.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (expm1.f64 x)) (.f64 (expm1.f64 x) #s(literal 1 binary64)))) (sqrt.f64 (pow.f64 (expm1.f64 x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (sinh.f64 (acosh.f64 (exp.f64 x)))) (neg.f64 (sqrt.f64 (expm1.f64 x))))
(/.f64 (cosh.f64 (asinh.f64 (pow.f64 (exp.f64 x) #s(literal 3/2 binary64)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (exp.f64 x)))))
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(/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x))) (neg.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(expm1.f64 (*.f64 x #s(literal 1 binary64)))
(expm1.f64 x)
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) (.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(-.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 6 binary64)) (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (pow.f64 (+.f64 (+.f64 (pow.f64 (exp.f64 x) #s(literal 4 binary64)) #s(literal 1 binary64)) (pow.f64 (exp.f64 x) #s(literal 2 binary64))) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 3 binary64)) (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (pow.f64 (fma.f64 (exp.f64 x) (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 (exp.f64 x) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (pow.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal -1 binary64)))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 (/.f64 (cosh.f64 (.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (-.f64 (sinh.f64 (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(+.f64 (cosh.f64 x) (-.f64 (sinh.f64 x) #s(literal 1 binary64)))

eval115.0ms (2.2%)

Memory: -12.1MiB live, 98.5MiB allocated; 20ms collecting garbage
Compiler: Compiled 16 930 to 2 382 computations (85.9% saved)

prune27.0ms (0.5%)

Memory

-9.4MiB live, 35.9MiB allocated; 3ms collecting garbage

Pruning

15 alts after pruning (11 fresh and 4 done)

	Pruned	Kept	Total
New	520	8	528
Fresh	0	3	3
Picked	1	4	5
Done	0	0	0
Total	521	15	536

Accuracy

100.0%

Counts

536 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	63.0%	(sqrt.f64 (/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
✓	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
▶	63.7%	(sqrt.f64 (+.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(literal 1 binary64)))
▶	65.3%	(sqrt.f64 (+.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(literal 1 binary64)))
	63.0%	(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
▶	63.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp 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 2 binary64))))
✓	65.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
▶	63.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
	3.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
▶	5.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
✓	69.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
	64.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
✓	65.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
	4.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
	4.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))

Compiler

Compiled 561 to 421 computations (25% saved)

simplify124.0ms (2.4%)

Memory

3.5MiB live, 151.0MiB allocated; 17ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	302
0	57	302
1	95	302
2	192	302
3	548	302
4	1707	272
0	8146	269

Stop Event

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

Calls

Call 1

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

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

localize99.0ms (1.9%)

Memory

1.0MiB live, 47.1MiB allocated; 3ms collecting garbage

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.02734375	(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	0.04296875	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.1171875	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	22.8683649181726	#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)))
accuracy	0.02734375	(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 2 binary64))
accuracy	0.04296875	(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.1171875	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	23.082699336158836	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp 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 2 binary64)))
accuracy	0.00390625	(.f64 (.f64 x x) #s(literal 1/2 binary64))
accuracy	0.0078125	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
accuracy	22.432136485901097	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
accuracy	39.95126512717369	#s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
accuracy	0.0	(+.f64 #s(literal 2 binary64) x)
accuracy	0.0078125	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
accuracy	23.43783507819147	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x))
accuracy	0.0	(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
accuracy	0.00390625	(+.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(literal 1 binary64))
accuracy	0.0078125	(sqrt.f64 (+.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(literal 1 binary64)))
accuracy	22.987844448348586	#s(approx (exp x) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 1 binary64)))

Samples

50.0ms

256×

valid

Compiler

Compiled 197 to 30 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-mult: 11.0ms (31.1% of total)

ival-add: 10.0ms (28.2% of total)

const: 4.0ms (11.3% of total)

ival-expm1: 3.0ms (8.5% of total)

ival-sqrt: 3.0ms (8.5% of total)

ival-div: 2.0ms (5.6% of total)

ival-exp: 2.0ms (5.6% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

7.0MiB live, 7.0MiB allocated; 0ms collecting garbage

Counts

21 → 42

Calls

Call 1

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

Outputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/2 (pow x 2))
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
1/2
(+ 1/2 (* 1/6 x))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (/ 1 (pow x 3))))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1/6)))

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

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

2.0ms

-inf

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

1.0ms

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

simplify176.0ms (3.4%)

Memory

7.8MiB live, 150.3MiB allocated; 22ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	114	377
1	404	331
2	1448	323
3	6805	320
0	8222	273

Stop Event

1×	iter limit
1×	node limit

Counts

42 → 41

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/2 (pow x 2))
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
1/2
(+ 1/2 (* 1/6 x))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)
(* (pow x 2) (+ 1/2 (/ 1 x)))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
x
(* x (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (/ 1 (pow x 3))))))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1/6)))

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
2
#s(literal 2 binary64)
(+ 2 x)
(-.f64 x #s(literal -2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* 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 2 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 (* 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))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(+ 1 (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* 1/6 x))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/6 x))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(exp x)
(exp.f64 x)
(* (pow x 2) (+ 1/2 (/ 1 x)))
(fma.f64 (*.f64 x x) #s(literal 1/2 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))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 #s(literal 2 binary64) x)) (expm1.f64 x))
x
(* x (+ 1 (* 2 (/ 1 x))))
(-.f64 x #s(literal -2 binary64))
(* (pow x 2) (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(* 1/6 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(* (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)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(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 2 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(* (pow x 2) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (/ 1 (pow x 3))))))
(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))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64))
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)) x) #s(literal 1/6 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 (/.f64 (neg.f64 (+.f64 (/.f64 (/.f64 (-.f64 x #s(literal -2 binary64)) x) x) #s(literal 1/2 binary64))) x) #s(literal 1/6 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1/6)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 (/.f64 (+.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)) x) #s(literal -1/2 binary64)) x) #s(literal 1/6 binary64)))

rewrite183.0ms (3.5%)

Memory

-1.9MiB live, 190.5MiB allocated; 23ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	272
0	57	272
1	230	230
2	1634	230
0	8754	227

Stop Event

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

Counts

21 → 325

Calls

Call 1

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

Outputs
(*.f64 (neg.f64 (pow.f64 (+.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(literal 1 binary64)) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (+.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(literal 1 binary64)) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (+.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(literal 1 binary64)) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (+.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(literal 1 binary64)) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 (+.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(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.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(literal 1 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log1p.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(literal 1/2 binary64))
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eval73.0ms (1.4%)

Memory: 5.0MiB live, 50.5MiB allocated; 4ms collecting garbage
Compiler: Compiled 16 356 to 1 908 computations (88.3% saved)

prune14.0ms (0.3%)

Memory

21.0MiB live, 21.0MiB allocated; 0ms collecting garbage

Pruning

17 alts after pruning (8 fresh and 9 done)

	Pruned	Kept	Total
New	421	2	423
Fresh	0	6	6
Picked	0	5	5
Done	0	4	4
Total	421	17	438

Accuracy

100.0%

Counts

438 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.0%	(sqrt.f64 (/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
✓	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
✓	63.7%	(sqrt.f64 (+.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(literal 1 binary64)))
✓	65.3%	(sqrt.f64 (+.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(literal 1 binary64)))
▶	63.0%	(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
✓	63.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp 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 2 binary64))))
✓	65.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	63.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
	2.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))))
▶	3.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
	3.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
✓	5.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
✓	69.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
▶	64.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
✓	65.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
	4.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
▶	4.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))

Compiler

Compiled 607 to 452 computations (25.5% saved)

simplify158.0ms (3%)

Memory

-27.2MiB live, 113.7MiB allocated; 29ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
cost-diff	0	#s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x))
cost-diff	0	(/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x))
cost-diff	0	(sqrt.f64 (/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
cost-diff	0	(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
cost-diff	0	(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
cost-diff	0	#s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
cost-diff	0	(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
cost-diff	0	#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))
cost-diff	0	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
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	(+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
cost-diff	0	(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	338
0	80	338
1	139	338
2	297	338
3	868	326
4	3516	318
0	8162	302

Stop Event

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

Calls

Call 1

Inputs
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
x
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) 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
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)))
#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
x
#s(literal 1/2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
#s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 3/16 binary64)
(sqrt.f64 (/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
(/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x))
#s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
(fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64))
#s(literal 2 binary64)
x
(expm1.f64 x)

Outputs
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
#s(literal 7/192 binary64)
x
#s(literal 3/16 binary64)
#s(literal 1/2 binary64)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) 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
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)))
#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
x
#s(literal 1/2 binary64)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x)))
#s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))
#s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x)
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
x
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
#s(literal 3/16 binary64)
(sqrt.f64 (/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 x #s(literal 2 binary64) #s(literal 2 binary64)) x)) (expm1.f64 x)))
(/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x))
(/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 x #s(literal 2 binary64) #s(literal 2 binary64)) x)) (expm1.f64 x))
#s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x))
#s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 x #s(literal 2 binary64) #s(literal 2 binary64)) x))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
(*.f64 (fma.f64 x #s(literal 2 binary64) #s(literal 2 binary64)) x)
(fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64))
(fma.f64 x #s(literal 2 binary64) #s(literal 2 binary64))
#s(literal 2 binary64)
x
(expm1.f64 x)

localize128.0ms (2.5%)

Memory

29.0MiB live, 118.9MiB allocated; 8ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
accuracy	0.0078125	(sqrt.f64 (/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
accuracy	0.41796875000000006	(/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x))
accuracy	23.52087194813354	#s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x))
accuracy	0.16796875	(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
accuracy	0.46484375	(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
accuracy	22.38231687368238	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
accuracy	39.966397252695046	#s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))
accuracy	0.05078125	(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
accuracy	0.1171875	(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
accuracy	23.082699336158836	#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)))
accuracy	39.47966225320426	#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))
accuracy	0.0	(+.f64 #s(literal 1 binary64) x)
accuracy	0.00390625	(+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
accuracy	0.0078125	(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
accuracy	23.199189854241567	#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
accuracy	0.0703125	(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
accuracy	0.15234375	(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
accuracy	0.7109375	(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
accuracy	23.04027471516013	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))

Samples

91.0ms	242×	0	valid
6.0ms	9×	1	valid
4.0ms	5×	2	valid

Compiler

Compiled 235 to 47 computations (80% saved)

Precisions

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

ival-mult: 39.0ms (46.7% of total)

ival-add: 12.0ms (14.4% of total)

ival-div: 8.0ms (9.6% of total)

const: 7.0ms (8.4% of total)

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

ival-expm1: 5.0ms (6% of total)

adjust: 3.0ms (3.6% of total)

ival-exp: 2.0ms (2.4% of total)

exact: 1.0ms (1.2% of total)

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

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

series15.0ms (0.3%)

Memory

-26.1MiB live, 16.8MiB allocated; 7ms collecting garbage

Counts

24 → 71

Calls

Call 1

Inputs
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)))
#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
#s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(sqrt.f64 (/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
(/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x))
#s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))

Outputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
1/2
(+ 1/2 (* 3/16 x))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/ (pow x 2) (sqrt 2))
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
3/16
(+ 3/16 (* 7/192 x))
(+ 1/2 (* 1/6 x))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(/ x (sqrt 2))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* 7/192 (pow x 2))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)
x
(* x (+ 1 (/ 1 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(- (exp (* 2 x)) 1)
(* 2 (pow x 2))
(* (pow x 2) (+ 2 (* 2 (/ 1 x))))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))

Calls

3 calls:

Time

Variable

Point

Expression

8.0ms

inf

((sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (+ 1 x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (* (* (+ (* 1/6 x) 1/2) x) x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (* (* (/ x (sqrt 2)) x) 3/16) (* (/ x (sqrt 2)) x) (sqrt (/ (- (exp (* x 2)) 1) (- (exp x) 1))) (/ (- (exp (* x 2)) 1) (- (exp x) 1)) (- (exp (* x 2)) 1) (* (+ (* 2 x) 2) x) (+ (* 7/192 x) 3/16) (+ (* 1/6 x) 1/2) (* (+ (* 1/6 x) 1/2) x) (/ x (sqrt 2)))

4.0ms

-inf

((sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (+ 1 x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (* (* (+ (* 1/6 x) 1/2) x) x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (* (* (/ x (sqrt 2)) x) 3/16) (* (/ x (sqrt 2)) x) (sqrt (/ (- (exp (* x 2)) 1) (- (exp x) 1))) (/ (- (exp (* x 2)) 1) (- (exp x) 1)) (- (exp (* x 2)) 1) (* (+ (* 2 x) 2) x) (+ (* 7/192 x) 3/16) (+ (* 1/6 x) 1/2) (* (+ (* 1/6 x) 1/2) x) (/ x (sqrt 2)))

3.0ms

((sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt (+ (exp x) 1)) (+ (exp x) 1) (exp x) (+ 1 x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (* (* (+ (* 1/6 x) 1/2) x) x) (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (* (* (/ x (sqrt 2)) x) 3/16) (* (/ x (sqrt 2)) x) (sqrt (/ (- (exp (* x 2)) 1) (- (exp x) 1))) (/ (- (exp (* x 2)) 1) (- (exp x) 1)) (- (exp (* x 2)) 1) (* (+ (* 2 x) 2) x) (+ (* 7/192 x) 3/16) (+ (* 1/6 x) 1/2) (* (+ (* 1/6 x) 1/2) x) (/ x (sqrt 2)))

simplify166.0ms (3.2%)

Memory

33.6MiB live, 182.4MiB allocated; 18ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	198	772
1	738	645
2	2592	615
3	7350	615
0	8106	547

Stop Event

1×	iter limit
1×	node limit

Counts

71 → 70

Calls

Call 1

Inputs
(sqrt 2)
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(/ 1/2 (sqrt 2))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
1/2
(+ 1/2 (* 3/16 x))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(* 3/16 (/ (pow x 2) (sqrt 2)))
(/ (pow x 2) (sqrt 2))
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
3/16
(+ 3/16 (* 7/192 x))
(+ 1/2 (* 1/6 x))
(* 1/2 x)
(* x (+ 1/2 (* 1/6 x)))
(/ x (sqrt 2))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(* 7/192 (pow x 2))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(sqrt (+ 1 (exp x)))
(+ 1 (exp x))
(exp x)
x
(* x (+ 1 (/ 1 x)))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/2 (/ 1 x))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(- (exp (* 2 x)) 1)
(* 2 (pow x 2))
(* (pow x 2) (+ 2 (* 2 (/ 1 x))))
(* 7/192 x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(* 1/6 x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))

Outputs
(sqrt 2)
(sqrt.f64 #s(literal 2 binary64))
(+ (sqrt 2) (* 1/2 (/ x (sqrt 2))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 1/2 (/ (* x (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 1/2 (/ (* x (- 1/6 (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (pow (sqrt 2) 2))))) (sqrt 2))) (* 1/2 (/ (- 1/2 (* 1/4 (/ 1 (pow (sqrt 2) 2)))) (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(+ (sqrt 2) (* x (+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(/ 1/2 (sqrt 2))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 3/16 (/ x (sqrt 2))) (* 1/2 (/ 1 (sqrt 2))))
(/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* x (+ (* 7/192 (/ x (sqrt 2))) (* 3/16 (/ 1 (sqrt 2))))) (* 1/2 (/ 1 (sqrt 2))))
(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 3/16 x))
(fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* x (+ 3/16 (* 7/192 x))))
(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 x #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))
(+ 2 (* 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 2 binary64))
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))
(* 1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/2 (* 1/6 x)))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
(* 3/16 (/ (pow x 2) (sqrt 2)))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
(/ (pow x 2) (sqrt 2))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* 2 x)))
(*.f64 (fma.f64 x #s(literal 2 binary64) #s(literal 2 binary64)) x)
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(*.f64 (fma.f64 (fma.f64 #s(literal 4/3 binary64) x #s(literal 2 binary64)) x #s(literal 2 binary64)) x)
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 2/3 binary64) x #s(literal 4/3 binary64)) x #s(literal 2 binary64)) x #s(literal 2 binary64)) x)
3/16
#s(literal 3/16 binary64)
(+ 3/16 (* 7/192 x))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(+ 1/2 (* 1/6 x))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/6 x)))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(/ x (sqrt 2))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(* 7/192 (/ (pow x 3) (sqrt 2)))
(*.f64 (/.f64 #s(literal 7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(.f64 (.f64 x x) (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)
(* (pow x 3) (+ (/ 3/16 (* x (sqrt 2))) (+ (* 7/192 (/ 1 (sqrt 2))) (+ (* 1/2 (/ 1 (* (pow x 2) (sqrt 2)))) (/ (sqrt 2) (pow x 3))))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (*.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 x #s(literal 3 binary64))))
(* 7/192 (/ (pow x 2) (sqrt 2)))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 7/192 binary64))
(* (pow x 2) (+ (* 7/192 (/ 1 (sqrt 2))) (* 3/16 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)
(* (pow x 2) (+ (/ 3/16 (* x (sqrt 2))) (+ (/ 1/2 (* (pow x 2) (sqrt 2))) (* 7/192 (/ 1 (sqrt 2))))))
(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 7/192 (pow x 2))
(.f64 (.f64 x x) #s(literal 7/192 binary64))
(* (pow x 2) (+ 7/192 (* 3/16 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x)
(* (pow x 2) (+ 7/192 (+ (/ 1/2 (pow x 2)) (* 3/16 (/ 1 x)))))
(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
(sqrt (+ 1 (exp x)))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(+ 1 (exp x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
x
(* x (+ 1 (/ 1 x)))
(-.f64 x #s(literal -1 binary64))
(/ (- (exp (* 2 x)) 1) (- (exp x) 1))
(/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x))
(* 1/6 (pow x 3))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/6 binary64))
(* (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)
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))))
(*.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) x) #s(literal 1/6 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (+ 1/6 (+ (* 1/2 (/ 1 x)) (+ (/ 1 (pow x 2)) (* 2 (/ 1 (pow x 3)))))))
(*.f64 (+.f64 (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)) x) #s(literal 1/2 binary64)) x) #s(literal 1/6 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 2) (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))))
(*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)
(* (pow x 2) (+ (/ 1/2 (* x (sqrt 2))) (+ (* 3/16 (/ 1 (sqrt 2))) (/ (sqrt 2) (pow x 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x)
(- (exp (* 2 x)) 1)
(expm1.f64 (*.f64 x #s(literal 2 binary64)))
(* 2 (pow x 2))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* (pow x 2) (+ 2 (* 2 (/ 1 x))))
(*.f64 (fma.f64 x #s(literal 2 binary64) #s(literal 2 binary64)) x)
(* 7/192 x)
(*.f64 #s(literal 7/192 binary64) x)
(* x (+ 7/192 (* 3/16 (/ 1 x))))
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* x (+ 1/6 (* 1/2 (/ 1 x))))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (+ 1/6 (* 1/2 (/ 1 x))))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* 3/16 (/ 1 (sqrt 2))) (* 1/2 (/ 1 (* x (sqrt 2))))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(fma.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64))) (*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))) x)) (* 7/192 (/ 1 (sqrt 2))))))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (fma.f64 (+.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -7/192 binary64) (sqrt.f64 #s(literal 2 binary64)))))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (/ 1 x)) x)) 1/6)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/2 binary64)) x) #s(literal 1/6 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ 1/2 (+ (/ 1 x) (/ 2 (pow x 2)))) x)) 1/6)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 (/.f64 (neg.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)) x) #s(literal 1/2 binary64))) x) #s(literal 1/6 binary64)))
(* (pow x 2) (+ (* -1 (/ (- (* -1 (/ (sqrt 2) x)) (* 1/2 (/ 1 (sqrt 2)))) x)) (* 3/16 (/ 1 (sqrt 2)))))
(*.f64 (fma.f64 (/.f64 (/.f64 (sqrt.f64 #s(literal 2 binary64)) x) x) x (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x)

rewrite253.0ms (4.9%)

Memory

-27.2MiB live, 266.1MiB allocated; 40ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	313
0	80	313
1	321	293
2	2123	293
0	9113	277

Stop Event

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

Counts

24 → 354

Calls

Call 1

Inputs
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
(fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))
(/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
#s(approx (exp x) (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
#s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)))
#s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))
(.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x)
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
#s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64)))
(.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))
(*.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x)
(sqrt.f64 (/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
(/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x))
#s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x))
(*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)
(fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64))
(fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64))
(*.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x)
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))

Outputs
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)))) (-.f64 (.f64 (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64))))) (.f64 (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64))))))))
(/.f64 (neg.f64 (-.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))) (neg.f64 (neg.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64) (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64))))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) #s(literal 2 binary64))) (.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64))) (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (fma.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64))) (.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)))) (.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64))) (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))) (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 2 binary64) (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64))) (neg.f64 (-.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 2 binary64) (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 2 binary64) (-.f64 (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (/.f64 x (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))))))
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(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) x)) (neg.f64 (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))))
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(/.f64 (neg.f64 (.f64 x (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (neg.f64 (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (.f64 x (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64))))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) #s(literal 1/4 binary64)) x) (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) x) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64)))))
(/.f64 (.f64 x (-.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) x) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 (*.f64 #s(literal 1/6 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (.f64 x (fma.f64 #s(literal 1/216 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 #s(literal 1/36 binary64) (.f64 x x) (-.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/12 binary64)))))
(fma.f64 (.f64 #s(literal 1/6 binary64) x) x (.f64 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) x (.f64 (.f64 #s(literal 1/6 binary64) x) x))
(fma.f64 x (.f64 #s(literal 1/6 binary64) x) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 #s(literal 1/6 binary64) x)))
(+.f64 (.f64 (.f64 #s(literal 1/6 binary64) x) x) (*.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 (*.f64 #s(literal 1/6 binary64) x) x))
(+.f64 (.f64 x (.f64 #s(literal 1/6 binary64) x)) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (*.f64 #s(literal 1/6 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(*.f64 (/.f64 x (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))))))
(/.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(/.f64 (neg.f64 x) (neg.f64 (sqrt.f64 #s(literal 2 binary64))))
(/.f64 x (sqrt.f64 #s(literal 2 binary64)))
(neg.f64 (/.f64 (neg.f64 x) (sqrt.f64 #s(literal 2 binary64))))
(neg.f64 (/.f64 x (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))

eval52.0ms (1%)

Memory: 0.1MiB live, 88.9MiB allocated; 8ms collecting garbage
Compiler: Compiled 16 359 to 2 016 computations (87.7% saved)

prune21.0ms (0.4%)

Memory

4.7MiB live, 50.1MiB allocated; 3ms collecting garbage

Pruning

21 alts after pruning (9 fresh and 12 done)

	Pruned	Kept	Total
New	409	6	415
Fresh	0	3	3
Picked	1	4	5
Done	1	8	9
Total	411	21	432

Accuracy

100.0%

Counts

432 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	63.0%	(sqrt.f64 (/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
✓	100.0%	(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
✓	63.7%	(sqrt.f64 (+.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(literal 1 binary64)))
✓	65.3%	(sqrt.f64 (+.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(literal 1 binary64)))
✓	63.0%	(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
✓	63.7%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp 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 2 binary64))))
✓	65.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
✓	63.0%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
	2.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))))
✓	3.4%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
	2.1%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 #s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x) x))))
	3.9%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
✓	5.2%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
✓	69.3%	(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
✓	64.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
	64.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64))))
	64.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x)))
	2.7%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
	3.1%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 x x) (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
	4.0%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
	4.3%	#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x)))

Compiler

Compiled 1 169 to 556 computations (52.4% saved)

regimes41.0ms (0.8%)

Memory

-45.4MiB live, 38.4MiB allocated; 26ms collecting garbage

Counts

25 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 #s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x) x))))
(sqrt.f64 (+.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(literal 1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp 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 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
(sqrt.f64 (+.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(literal 1 binary64)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 x x) (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64))))
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(sqrt.f64 (/.f64 #s(approx (- (exp (* x 2)) 1) (*.f64 (fma.f64 #s(literal 2 binary64) x #s(literal 2 binary64)) x)) (expm1.f64 x)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x #s(literal 2 binary64))) (expm1.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))

Outputs
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))

Calls

3 calls:

28.0ms

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

7.0ms

5.0ms

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

Results

Accuracy	Segments	Branch
100.0%	1	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
100.0%	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
100.0%	1	`x`

Compiler

Compiled 24 to 20 computations (16.7% saved)

regimes15.0ms (0.3%)

Memory

15.3MiB live, 15.3MiB allocated; 0ms collecting garbage

Counts

21 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 #s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x) x))))
(sqrt.f64 (+.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(literal 1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp 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 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
(sqrt.f64 (+.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(literal 1 binary64)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 x x) (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))) #s(literal 2 binary64)) x (sqrt.f64 #s(literal 2 binary64))))

Outputs

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

#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x)))

Calls

3 calls:

5.0ms

4.0ms

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

4.0ms

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

Results

Accuracy	Segments	Branch
71.0%	2	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
71.0%	2	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
71.0%	2	`x`

Compiler

Compiled 24 to 20 computations (16.7% saved)

regimes14.0ms (0.3%)

Memory

21.2MiB live, 21.2MiB allocated; 0ms collecting garbage

Counts

19 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 #s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x) x))))
(sqrt.f64 (+.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(literal 1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp 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 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
(sqrt.f64 (+.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(literal 1 binary64)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 x x) (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))

Outputs

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

#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))

Calls

3 calls:

5.0ms

4.0ms

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

4.0ms

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

Results

Accuracy	Segments	Branch
71.0%	2	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
71.0%	2	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
71.0%	2	`x`

Compiler

Compiled 24 to 20 computations (16.7% saved)

regimes99.0ms (1.9%)

Memory

-30.2MiB live, 16.2MiB allocated; 4ms collecting garbage

Counts

18 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 #s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x) x))))
(sqrt.f64 (+.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(literal 1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp 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 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))
(sqrt.f64 (+.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(literal 1 binary64)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 x x) (/.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* (+ (* 7/192 x) 3/16) x) 1/2) (sqrt 2)) x) (sqrt 2)) (*.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 #s(literal 3/16 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64))))

Outputs

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

(sqrt.f64 (+.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(literal 1 binary64)))

Calls

3 calls:

90.0ms

4.0ms

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

4.0ms

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

Results

Accuracy	Segments	Branch
71.0%	2	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
71.0%	2	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
71.0%	2	`x`

Compiler

Compiled 24 to 20 computations (16.7% saved)

regimes11.0ms (0.2%)

Memory

19.5MiB live, 19.5MiB allocated; 0ms collecting garbage

Counts

13 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (+.f64 #s(literal 2 binary64) x)))
(sqrt.f64 (+.f64 #s(approx (exp x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (.f64 (.f64 x x) #s(literal 1/2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* 1/2 x) 1) x) 2) (*.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) x #s(literal 2 binary64))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 #s(approx (+ (* 1/6 x) 1/2) (*.f64 #s(literal 1/6 binary64) x)) x) x))))
(sqrt.f64 (+.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(literal 1 binary64)))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(approx (+ (* (+ (* (+ (* 1/6 x) 1/2) x) 1) x) 2) (*.f64 (fma.f64 (fma.f64 #s(literal 1/6 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)) x))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp 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 2 binary64))))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) #s(literal 3/16 binary64)) x)))
#s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) #s(approx (+ (* (/ (+ (* 3/16 x) 1/2) (sqrt 2)) x) (sqrt 2)) (.f64 (.f64 (/.f64 x (sqrt.f64 #s(literal 2 binary64))) x) #s(literal 3/16 binary64))))

Outputs

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

(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp 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 2 binary64))))

Calls

3 calls:

4.0ms

3.0ms

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

3.0ms

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

Results

Accuracy	Segments	Branch
71.0%	2	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
71.0%	2	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
71.0%	2	`x`

Compiler

Compiled 24 to 20 computations (16.7% saved)

regimes13.0ms (0.2%)

Memory

-26.5MiB live, 17.0MiB allocated; 6ms collecting garbage

Accuracy

Total -43.5b remaining (-221.8%)

Threshold costs -43.5b (-221.8%)

Counts

10 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms

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

3.0ms

2.0ms

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

Results

Accuracy	Segments	Branch
69.3%	1	`(/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64)))`
69.3%	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (-.f64 (exp.f64 x) #s(literal 1 binary64))))`
69.3%	1	`x`

Compiler

Compiled 24 to 20 computations (16.7% saved)

bsearch15.0ms (0.3%)

Memory

21.4MiB live, 21.4MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	-2514.757887628712	-0.588237760103532

Samples

8.0ms

128×

valid

Compiler

Compiled 359 to 299 computations (16.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-expm1: 2.0ms (40.2% of total)

ival-div: 1.0ms (20.1% of total)

ival-mult: 1.0ms (20.1% of total)

ival-sqrt: 1.0ms (20.1% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

bsearch2.0ms (0%)

Memory

2.9MiB live, 2.9MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-2514.757887628712	-0.588237760103532

Compiler

Compiled 343 to 283 computations (17.5% saved)

bsearch8.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
7.0ms	-2514.757887628712	-0.588237760103532

Samples

4.0ms

64×

valid

Compiler

Compiled 255 to 211 computations (17.3% saved)

Precisions

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

ival-expm1: 1.0ms (39.8% of total)

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

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

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-2514.757887628712	-0.588237760103532

Compiler

Compiled 311 to 267 computations (14.1% saved)

simplify76.0ms (1.5%)

Memory

9.1MiB live, 52.5MiB allocated; 7ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	46	185
1	78	185
2	130	185
3	255	185
4	832	145
5	6500	145

Stop Event

1×	node limit

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(if (<=.f64 x #s(literal -6980579422424269/2251799813685248 binary64)) (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x))))
(if (<=.f64 x #s(literal -6980579422424269/2251799813685248 binary64)) (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -4278419646001971/2251799813685248 binary64)) (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) (sqrt.f64 (+.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(literal 1 binary64))))
(if (<=.f64 x #s(literal -4278419646001971/2251799813685248 binary64)) (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp 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 2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))

Outputs
(sqrt.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64)))
(if (<=.f64 x #s(literal -6980579422424269/2251799813685248 binary64)) (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (-.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (neg.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) x))))
(if (<=.f64 x #s(literal -6980579422424269/2251799813685248 binary64)) (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (+.f64 (sqrt.f64 #s(literal 2 binary64)) (*.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x))))
(if (<=.f64 x #s(literal -6980579422424269/2251799813685248 binary64)) (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) #s(approx (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (fma.f64 (/.f64 (fma.f64 (fma.f64 #s(literal 7/192 binary64) x #s(literal 3/16 binary64)) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) x (sqrt.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -4278419646001971/2251799813685248 binary64)) (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) (sqrt.f64 (+.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(literal 1 binary64))))
(if (<=.f64 x #s(literal -4278419646001971/2251799813685248 binary64)) (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64))) (sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp 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 2 binary64)))))
(sqrt.f64 #s(approx (/ (- (exp (* 2 x)) 1) (- (exp x) 1)) #s(literal 2 binary64)))

derivations543.0ms (10.4%)

Memory

-25.1MiB live, 312.5MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	33
0	17	33
1	65	19
0	423	15
0	125	428
1	470	359
2	1558	346
3	6700	344
0	8024	291
0	77	213
1	302	173
2	1041	172
3	3429	170
0	8155	135
0	56	313
0	80	313
1	321	293
2	2123	293
0	9113	277

Stop Event

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

Compiler

Compiled 185 to 47 computations (74.6% saved)

preprocess94.0ms (1.8%)

Memory: -0.4MiB live, 45.1MiB allocated; 3ms collecting garbage
Compiler: Compiled 394 to 114 computations (71.1% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze2.0ms (0%)

sample1.2s (23.9%)

explain128.0ms (2.5%)

preprocess192.0ms (3.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify138.0ms (2.6%)

localize26.0ms (0.5%)

series5.0ms (0.1%)

simplify172.0ms (3.3%)

rewrite43.0ms (0.8%)

eval8.0ms (0.2%)

prune6.0ms (0.1%)

simplify160.0ms (3.1%)

localize66.0ms (1.3%)

series31.0ms (0.6%)

simplify204.0ms (3.9%)

rewrite237.0ms (4.6%)

eval115.0ms (2.2%)

prune27.0ms (0.5%)

simplify124.0ms (2.4%)

localize99.0ms (1.9%)

series6.0ms (0.1%)

simplify176.0ms (3.4%)

rewrite183.0ms (3.5%)

eval73.0ms (1.4%)

prune14.0ms (0.3%)

simplify158.0ms (3%)

localize128.0ms (2.5%)

series15.0ms (0.3%)

simplify166.0ms (3.2%)

rewrite253.0ms (4.9%)

eval52.0ms (1%)

prune21.0ms (0.4%)

regimes41.0ms (0.8%)

regimes15.0ms (0.3%)

regimes14.0ms (0.3%)

regimes99.0ms (1.9%)

regimes11.0ms (0.2%)

regimes13.0ms (0.2%)

bsearch15.0ms (0.3%)

bsearch2.0ms (0%)

bsearch8.0ms (0.1%)

bsearch1.0ms (0%)

simplify76.0ms (1.5%)

derivations543.0ms (10.4%)

preprocess94.0ms (1.8%)

end0.0ms (0%)

Profiling