Metrics for bug333 (missed optimization)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50%	50%	0%	0%	0%	0
100%	50%	0%	50%	0%	0%	0%	1

Compiler

Compiled 17 to 12 computations (29.4% saved)

sample1.9s (70.9%)

Memory

28.6MiB live, 1 858.4MiB allocated; 253ms collecting garbage

Samples

761.0ms	3 377×	2	valid
673.0ms	4 733×	1	valid
7.0ms	146×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.1s

adjust: 473.0ms (41.3% of total)

ival-sqrt: 314.0ms (27.4% of total)

ival-sub: 215.0ms (18.8% of total)

ival-add: 134.0ms (11.7% of total)

exact: 8.0ms (0.7% of total)

ival-assert: 2.0ms (0.2% of total)

Bogosity

explain164.0ms (6.3%)

Memory

-5.6MiB live, 200.3MiB allocated; 44ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
255	-	-	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))`
0	-	-	`(sqrt.f64 (+.f64 #s(literal 1 binary64) x))`
0	-	-	`(+.f64 #s(literal 1 binary64) x)`
0	-	-	`(-.f64 #s(literal 1 binary64) x)`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(sqrt.f64 (-.f64 #s(literal 1 binary64) x))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))`	cancellation	255	0

Confusion

	Predicted +	Predicted -
+	255	0
-	0	1

Precision

1.0

Recall

1.0

Confusion?

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

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	1
1	255

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

58.0ms	302×	1	valid
48.0ms	208×	2	valid
0.0ms	2×	0	valid

Compiler

Compiled 63 to 25 computations (60.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 84.0ms

ival-sqrt: 36.0ms (42.8% of total)

adjust: 29.0ms (34.5% of total)

ival-sub: 11.0ms (13.1% of total)

ival-add: 7.0ms (8.3% of total)

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

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

exact: 0.0ms (0% of total)

preprocess249.0ms (9.5%)

Memory

18.3MiB live, 160.1MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	18	32
2	21	32
3	39	28
4	90	28
5	321	28
6	2660	28
7	6135	28
0	7	9
0	12	9
1	15	9
2	18	9
3	31	9
4	70	9
5	285	9
6	2420	9
7	5845	9
0	8084	9

Stop Event

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

Calls

Call 1

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

Outputs

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

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

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

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.5%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 9 to 7 computations (22.2% saved)

series7.0ms (0.3%)

Memory

7.8MiB live, 7.8MiB allocated; 0ms collecting garbage

Counts

7 → 46

Calls

Call 1

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

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* 1/8 (pow x 2))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 1))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (+ 1 x) #s(hole binary64 1))
#s(approx (+ 1 x) #s(hole binary64 (+ 1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- 1 x)) #s(hole binary64 1))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* -1/2 x))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* -1/8 x) 1/2)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))))
#s(approx (- 1 x) #s(hole binary64 1))
#s(approx (- 1 x) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))))
#s(approx (+ 1 x) #s(hole binary64 x))
#s(approx (+ 1 x) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* (sqrt x) (sqrt -1))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (- 1 x) #s(hole binary64 (* -1 x)))
#s(approx (- 1 x) #s(hole binary64 (* x (- (/ 1 x) 1))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* (sqrt x) (sqrt -1)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))))
#s(approx (- 1 x) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ 1 x) 1 x (sqrt (- 1 x)) (- 1 x))
2.0ms	x	@	inf	((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ 1 x) 1 x (sqrt (- 1 x)) (- 1 x))
1.0ms	x	@	0	((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ 1 x) 1 x (sqrt (- 1 x)) (- 1 x))

Time

Variable

Point

Expression

3.0ms

-inf

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ 1 x) 1 x (sqrt (- 1 x)) (- 1 x))

2.0ms

inf

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ 1 x) 1 x (sqrt (- 1 x)) (- 1 x))

1.0ms

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ 1 x) 1 x (sqrt (- 1 x)) (- 1 x))

rewrite61.0ms (2.3%)

Memory

9.7MiB live, 56.4MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	223	1305
0	229	1094
0	1250	1036

Stop Event

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

Counts

53 → 62

Calls

Call 1

Inputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* 1/8 (pow x 2))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 1))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (+ 1 x) #s(hole binary64 1))
#s(approx (+ 1 x) #s(hole binary64 (+ 1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- 1 x)) #s(hole binary64 1))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* -1/2 x))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* -1/8 x) 1/2)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))))
#s(approx (- 1 x) #s(hole binary64 1))
#s(approx (- 1 x) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))))
#s(approx (+ 1 x) #s(hole binary64 x))
#s(approx (+ 1 x) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* (sqrt x) (sqrt -1))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (- 1 x) #s(hole binary64 (* -1 x)))
#s(approx (- 1 x) #s(hole binary64 (* x (- (/ 1 x) 1))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* (sqrt x) (sqrt -1)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))))
#s(approx (- 1 x) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))

Outputs
(/.f64 (-.f64 (.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) (.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))
(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) (.f64 #s(literal 1 binary64) x))))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) (+.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 #s(literal 1 binary64) x))))
(-.f64 #s(literal 1 binary64) x)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) x)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
#s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (+ 1 x) #s(literal 1 binary64))
#s(approx (+ 1 x) (+.f64 x #s(literal 1 binary64)))
#s(approx x x)
#s(approx (sqrt (- 1 x)) #s(literal 1 binary64))
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
#s(approx (sqrt (- 1 x)) (fma.f64 (-.f64 (*.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt (- 1 x)) (fma.f64 (-.f64 (.f64 (-.f64 (.f64 #s(literal -1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (- 1 x) #s(literal 1 binary64))
#s(approx (- 1 x) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (-.f64 (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (-.f64 (fma.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) (fma.f64 (.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (-.f64 (+.f64 (fma.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1/8 binary64) (.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1/8 binary64)) (pow.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)))))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (-.f64 (+.f64 (fma.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1/8 binary64) (fma.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/16 binary64) (.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1/8 binary64)) (pow.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/16 binary64)) (pow.f64 (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal 5 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))))))) x))
#s(approx (sqrt (+ 1 x)) (pow.f64 x #s(literal 1/2 binary64)))
#s(approx (sqrt (+ 1 x)) (.f64 (fma.f64 (pow.f64 (pow.f64 (.f64 (*.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))) x))
#s(approx (sqrt (+ 1 x)) (fma.f64 (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) x (.f64 (fma.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1/8 binary64) (.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))) x)))
#s(approx (sqrt (+ 1 x)) (fma.f64 (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) x (.f64 (fma.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1/8 binary64) (fma.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/16 binary64) (.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))) x)))
#s(approx (+ 1 x) x)
#s(approx (+ 1 x) (*.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) x))
#s(approx (sqrt (- 1 x)) (*.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))
#s(approx (sqrt (- 1 x)) (.f64 (fma.f64 (.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)))) x))
#s(approx (sqrt (- 1 x)) (.f64 (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1/8 binary64)) (pow.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))))) x))
#s(approx (sqrt (- 1 x)) (.f64 (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1/8 binary64)) (pow.f64 (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/16 binary64)) (pow.f64 (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal 5 binary64)) #s(literal -1 binary64)) (fma.f64 (.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)))))) x))
#s(approx (- 1 x) (*.f64 #s(literal -1 binary64) x))
#s(approx (- 1 x) (*.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (.f64 #s(literal -1 binary64) x) (*.f64 (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (.f64 #s(literal -1 binary64) x) (-.f64 (fma.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (.f64 (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (fma.f64 (.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (.f64 #s(literal -1 binary64) x) (-.f64 (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (.f64 (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)))) (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1/8 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (fma.f64 (.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (.f64 #s(literal -1 binary64) x) (-.f64 (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/16 binary64)) #s(literal 1 binary64) (fma.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (.f64 (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64))))) (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1/8 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/16 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (fma.f64 (.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)))))))))
#s(approx (sqrt (+ 1 x)) (.f64 (.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))
#s(approx (sqrt (+ 1 x)) (.f64 (.f64 (fma.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (*.f64 (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64))) x) #s(literal -1 binary64)))
#s(approx (sqrt (+ 1 x)) (.f64 (.f64 (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (.f64 (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)))) x) #s(literal -1 binary64)))
#s(approx (sqrt (+ 1 x)) (.f64 (.f64 (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/16 binary64)) #s(literal 1 binary64) (fma.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (*.f64 (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64))))) x) #s(literal -1 binary64)))
#s(approx (sqrt (- 1 x)) (.f64 (.f64 (pow.f64 x #s(literal 1/2 binary64)) #s(literal -1 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))
#s(approx (sqrt (- 1 x)) (.f64 (.f64 #s(literal -1 binary64) x) (fma.f64 (.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))))))
#s(approx (sqrt (- 1 x)) (.f64 (.f64 #s(literal -1 binary64) x) (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1/8 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (fma.f64 (.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)))))))
#s(approx (sqrt (- 1 x)) (.f64 (.f64 #s(literal -1 binary64) x) (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1/8 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/16 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (fma.f64 (.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))))))))
#s(approx (- 1 x) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64))) x) #s(literal -1 binary64)))

eval27.0ms (1%)

Memory: -28.1MiB live, 22.7MiB allocated; 6ms collecting garbage
Compiler: Compiled 1 795 to 274 computations (84.7% saved)

prune7.0ms (0.3%)

Memory

10.5MiB live, 10.5MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	2	66

Accuracy

100.0%

Counts

66 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	7.5%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
▶	99.9%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x))

Status

Accuracy

Program

✓

7.5%

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

▶

99.9%

#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))

Compiler

Compiled 37 to 24 computations (35.1% saved)

series5.0ms (0.2%)

Memory

7.3MiB live, 7.3MiB allocated; 0ms collecting garbage

Counts

11 → 42

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64))
(fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64))
#s(literal 33/1024 binary64)
(*.f64 x x)
x
#s(literal 7/128 binary64)
#s(literal 1/8 binary64)
#s(literal 1 binary64)

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* 1/8 (pow x 2))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 x))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* 1/8 (pow x 2))))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))))
#s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (+ 1 (* 1/8 (pow x 2)))))
#s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))))
#s(approx (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) #s(hole binary64 1/8))
#s(approx (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) #s(hole binary64 (+ 1/8 (* 7/128 (pow x 2)))))
#s(approx (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) #s(hole binary64 (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))
#s(approx (+ (* 33/1024 (* x x)) 7/128) #s(hole binary64 7/128))
#s(approx (+ (* 33/1024 (* x x)) 7/128) #s(hole binary64 (+ 7/128 (* 33/1024 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* 33/1024 (pow x 7))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))))
#s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (* 33/1024 (pow x 6))))
#s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))))
#s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))))
#s(approx (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) #s(hole binary64 (* 33/1024 (pow x 4))))
#s(approx (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) #s(hole binary64 (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) #s(hole binary64 (* (pow x 4) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))))
#s(approx (+ (* 33/1024 (* x x)) 7/128) #s(hole binary64 (* 33/1024 (pow x 2))))
#s(approx (+ (* 33/1024 (* x x)) 7/128) #s(hole binary64 (* (pow x 2) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 4))) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (+ (* 33/1024 (* x x)) 7/128) 33/1024 (* x x) x 7/128 1/8 1)
2.0ms	x	@	-inf	((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (+ (* 33/1024 (* x x)) 7/128) 33/1024 (* x x) x 7/128 1/8 1)
1.0ms	x	@	0	((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (+ (* 33/1024 (* x x)) 7/128) 33/1024 (* x x) x 7/128 1/8 1)

Time

Variable

Point

Expression

2.0ms

inf

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (+ (* 33/1024 (* x x)) 7/128) 33/1024 (* x x) x 7/128 1/8 1)

2.0ms

-inf

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (+ (* 33/1024 (* x x)) 7/128) 33/1024 (* x x) x 7/128 1/8 1)

1.0ms

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (+ (* 33/1024 (* x x)) 7/128) 33/1024 (* x x) x 7/128 1/8 1)

rewrite56.0ms (2.1%)

Memory

-9.8MiB live, 37.6MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	209	1466
0	221	1319
0	1249	1276

Stop Event

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

Counts

53 → 90

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64))
(fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64))
(fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64))
#s(literal 33/1024 binary64)
(*.f64 x x)
x
#s(literal 7/128 binary64)
#s(literal 1/8 binary64)
#s(literal 1 binary64)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* 1/8 (pow x 2))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 x))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* 1/8 (pow x 2))))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))))
#s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (+ 1 (* 1/8 (pow x 2)))))
#s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))))
#s(approx (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) #s(hole binary64 1/8))
#s(approx (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) #s(hole binary64 (+ 1/8 (* 7/128 (pow x 2)))))
#s(approx (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) #s(hole binary64 (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2)))))))
#s(approx (+ (* 33/1024 (* x x)) 7/128) #s(hole binary64 7/128))
#s(approx (+ (* 33/1024 (* x x)) 7/128) #s(hole binary64 (+ 7/128 (* 33/1024 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (sqrt -1))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* 33/1024 (pow x 7))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* (pow x 7) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))))
#s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (* 33/1024 (pow x 6))))
#s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (* (pow x 6) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))))
#s(approx (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (* (pow x 6) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (+ (* 7/128 (/ 1 (pow x 2))) (/ 1 (pow x 6))))))))
#s(approx (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) #s(hole binary64 (* 33/1024 (pow x 4))))
#s(approx (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) #s(hole binary64 (* (pow x 4) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) #s(hole binary64 (* (pow x 4) (+ 33/1024 (+ (/ 1/8 (pow x 4)) (* 7/128 (/ 1 (pow x 2))))))))
#s(approx (+ (* 33/1024 (* x x)) 7/128) #s(hole binary64 (* 33/1024 (pow x 2))))
#s(approx (+ (* 33/1024 (* x x)) 7/128) #s(hole binary64 (* (pow x 2) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 x)) (sqrt -1)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1)))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (sqrt -1))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (sqrt -1))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (sqrt -1))) (* (sqrt (/ 1 x)) (sqrt -1))))))))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- (* -1 (/ (+ 7/128 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))) 33/1024)))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 7) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 4))) (+ 33/1024 (* 7/128 (/ 1 (pow x 2)))))))))

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x)
(.f64 x (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)))
(fma.f64 x #s(literal 1 binary64) (.f64 x (.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x)))
(fma.f64 #s(literal 1 binary64) x (.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) x) x) x))
(+.f64 (.f64 x #s(literal 1 binary64)) (.f64 x (.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x)))
(+.f64 (.f64 #s(literal 1 binary64) x) (.f64 (.f64 (.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 33/1024 binary64) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x) x))
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#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (.f64 #s(literal -1 binary64) x) (*.f64 (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)) (-.f64 #s(literal -1 binary64) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (.f64 #s(literal -1 binary64) x) (-.f64 (fma.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (.f64 #s(literal -1 binary64) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)))) (fma.f64 (.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (.f64 #s(literal -1 binary64) x) (-.f64 (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (.f64 #s(literal -1 binary64) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))))) (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1/8 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (fma.f64 (.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (.f64 #s(literal -1 binary64) x) (-.f64 (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) #s(literal -1/8 binary64) (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/16 binary64)) #s(literal 1 binary64) (fma.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64) (.f64 #s(literal -1 binary64) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)))))) (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal -1/8 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (fma.f64 (.f64 (pow.f64 (pow.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/16 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (fma.f64 (.f64 (pow.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)))))))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) (.f64 (.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 7 binary64))) (-.f64 (/.f64 (.f64 #s(literal -1 binary64) (fma.f64 (pow.f64 (.f64 x x) #s(literal -1 binary64)) #s(literal 1/8 binary64) #s(literal 7/128 binary64))) (*.f64 x x)) #s(literal 33/1024 binary64))))
#s(approx (* (+ (* (+ (* (+ (* 33/1024 (* x x)) 7/128) (* x x)) 1/8) (* x x)) 1) x) (.f64 (.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 7 binary64))) (-.f64 (/.f64 (.f64 #s(literal -1 binary64) (+.f64 (pow.f64 (.f64 x x) #s(literal -1 binary64)) #s(literal 1/8 binary64))) (pow.f64 x #s(literal 4 binary64))) (fma.f64 (pow.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal 7/128 binary64) #s(literal 33/1024 binary64)))))

eval17.0ms (0.6%)

Memory: -25.5MiB live, 21.3MiB allocated; 4ms collecting garbage
Compiler: Compiled 4 388 to 526 computations (88% saved)

prune88.0ms (3.4%)

Memory

51.2MiB live, 141.1MiB allocated; 16ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	115	2	117

Accuracy

100.0%

Counts

117 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	7.5%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
✓	99.9%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x))

Status

Accuracy

Program

✓

7.5%

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

✓

99.9%

#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))

Compiler

Compiled 74 to 46 computations (37.8% saved)

regimes17.0ms (0.6%)

Memory

-36.9MiB live, 6.4MiB allocated; 16ms collecting garbage

Accuracy

Total -59.2b remaining (-72500.1%)

Threshold costs -59.2b (-72500.1%)

Counts

2 → 1

Calls

Call 1

Inputs

#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))

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

Outputs

#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))

Calls

2 calls:

15.0ms	x
1.0ms	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Results

Accuracy	Segments	Branch
99.9%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))`
99.9%	1	`x`

Compiler

Compiled 10 to 8 computations (20% saved)

simplify49.0ms (1.9%)

Memory

26.5MiB live, 26.5MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	28
1	19	28
2	22	28
3	36	28
4	68	28
5	278	28
6	2781	28
7	6878	28

Stop Event

1×	node limit

Calls

Call 1

Inputs

#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))

Outputs

#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (*.f64 x x) #s(literal 7/128 binary64)) (*.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))

derivations4.0ms (0.1%)

Memory

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

Stop Event

1×

done

Compiler

Compiled 28 to 17 computations (39.3% saved)

preprocess12.0ms (0.5%)

Memory: 10.2MiB live, 10.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 74 to 48 computations (35.1% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample1.9s (70.9%)

explain164.0ms (6.3%)

preprocess249.0ms (9.5%)

eval0.0ms (0%)

prune0.0ms (0%)

series7.0ms (0.3%)

rewrite61.0ms (2.3%)

eval27.0ms (1%)

prune7.0ms (0.3%)

series5.0ms (0.2%)

rewrite56.0ms (2.1%)

eval17.0ms (0.6%)

prune88.0ms (3.4%)

regimes17.0ms (0.6%)

simplify49.0ms (1.9%)

derivations4.0ms (0.1%)

preprocess12.0ms (0.5%)

end0.0ms (0%)

Profiling