Metrics for bug366, discussion (missed optimization)

start0.0ms (0%)

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

analyze40.0ms (2.8%)

Memory

-10.1MiB live, 36.9MiB allocated; 28ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
30.8%	25%	56.2%	0.1%	0%	18.7%	0%	5
32%	25%	53.1%	0.1%	0%	21.9%	0%	6
55.8%	37.5%	29.7%	0.1%	0%	32.8%	0%	7
57.8%	37.5%	27.3%	0.1%	0%	35.1%	0%	8
74.2%	43.7%	15.2%	0.1%	0%	41%	0%	9
75.9%	43.7%	13.9%	0.1%	0%	42.3%	0%	10
85.9%	46.8%	7.7%	0.1%	0%	45.4%	0%	11
87%	46.8%	7%	0.1%	0%	46.1%	0%	12

Compiler

Compiled 10 to 8 computations (20% saved)

sample889.0ms (62.4%)

Memory

17.7MiB live, 577.1MiB allocated; 769ms collecting garbage

Samples

625.0ms	8 256×	0	valid
25.0ms	606×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 178.0ms

ival-mult!: 89.0ms (50% of total)

ival-sqrt: 68.0ms (38.2% of total)

ival-sub!: 19.0ms (10.7% of total)

adjust: 2.0ms (1.1% of total)

Bogosity

explain67.0ms (4.7%)

Memory

19.2MiB live, 66.6MiB allocated; 4ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
130	-	1	(6.242381616159041e-160 -6.015716055374162e-235)	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
20	-	0	-	`(-.f64 (.f64 a a) (.f64 b b))`
0	-	0	-	`(*.f64 a a)`
0	-	0	-	`a`
0	-	0	-	`b`
0	-	0	-	`(*.f64 b b)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`	oflow-rescue	115	0
↳	`(*.f64 b b)`	overflow	20
↳	`(-.f64 (.f64 a a) (.f64 b b))`	overflow	115
↳	`(*.f64 a a)`	overflow	115
`-.f64`	`(-.f64 (.f64 a a) (.f64 b b))`	nan-rescue	20	0
↳	`(*.f64 a a)`	overflow	115
↳	`(*.f64 b b)`	overflow	20
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`	uflow-rescue	14	0
↳	`(*.f64 b b)`	underflow	102
↳	`(-.f64 (.f64 a a) (.f64 b b))`	underflow	14
↳	`(*.f64 a a)`	underflow	14

Confusion

	Predicted +	Predicted -
+	129	1
-	0	126

Precision

1.0

Recall

0.9923076923076923

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	129	0	1
-	0	0	126

Precision?

1.0

Recall?

0.9923076923076923

Freqs

test

number	freq
0	127
1	109
2	20

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

23.0ms

512×

valid

Compiler

Compiled 58 to 22 computations (62.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult!: 5.0ms (48.1% of total)

ival-sqrt: 4.0ms (38.5% of total)

ival-sub!: 1.0ms (9.6% of total)

adjust: 0.0ms (0% of total)

preprocess48.0ms (3.4%)

Memory

-27.3MiB live, 19.1MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	50
1	55	50
2	214	50
3	344	50
4	875	50
5	1839	50
6	3017	50
7	3359	50
8	3437	50
9	3437	50
10	3633	50

Stop Event

1×

saturated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.3%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Symmetry

(abs a)

(abs b)

Compiler

Compiled 16 to 12 computations (25% saved)

series7.0ms (0.5%)

Memory

6.9MiB live, 6.9MiB allocated; 0ms collecting garbage

Counts

6 → 32

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
(-.f64 (.f64 a a) (.f64 b b))
(*.f64 a a)
a
(*.f64 b b)
b

Outputs
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (* -1 (pow b 2))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (- (pow a 2) (pow b 2))))
#s(approx (* a a) #s(hole binary64 (pow a 2)))
#s(approx a #s(hole binary64 a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (pow a 2)))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 a)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* -1/2 (/ (pow b 2) a)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (+ (* -1 (pow b 2)) (pow a 2))))
#s(approx (* b b) #s(hole binary64 (pow b 2)))
#s(approx b #s(hole binary64 b))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))))

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	a	@	0	((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) a (* b b) b)
1.0ms	b	@	inf	((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) a (* b b) b)
1.0ms	a	@	inf	((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) a (* b b) b)
1.0ms	a	@	-inf	((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) a (* b b) b)
1.0ms	b	@	0	((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) a (* b b) b)

rewrite59.0ms (4.2%)

Memory

-3.5MiB live, 42.3MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	159	856
0	164	821
0	818	795

Stop Event

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

Counts

38 → 57

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
(-.f64 (.f64 a a) (.f64 b b))
(*.f64 a a)
a
(*.f64 b b)
b
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (* -1 (pow b 2))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (- (pow a 2) (pow b 2))))
#s(approx (* a a) #s(hole binary64 (pow a 2)))
#s(approx a #s(hole binary64 a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (pow a 2)))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 a)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* -1/2 (/ (pow b 2) a)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (+ (* -1 (pow b 2)) (pow a 2))))
#s(approx (* b b) #s(hole binary64 (pow b 2)))
#s(approx b #s(hole binary64 b))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))))

Outputs
(pow.f64 (*.f64 (+.f64 a b) (-.f64 a b)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (+.f64 a b) (-.f64 a b)))
(*.f64 (+.f64 a b) (-.f64 a b))
(/.f64 (-.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 (.f64 b b) (.f64 b b))) (fma.f64 a a (*.f64 b b)))
(/.f64 (-.f64 (pow.f64 (.f64 a a) #s(literal 3 binary64)) (pow.f64 (.f64 b b) #s(literal 3 binary64))) (fma.f64 (.f64 a a) (.f64 a a) (fma.f64 (.f64 b b) (.f64 b b) (.f64 (.f64 a a) (*.f64 b b)))))
(fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 a) (neg.f64 a) (*.f64 (neg.f64 b) b))
(fma.f64 (fabs.f64 a) (fabs.f64 a) (*.f64 (neg.f64 b) b))
(fma.f64 a a (*.f64 (neg.f64 b) b))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (.f64 a a) (.f64 (neg.f64 b) b))
(*.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)))
(*.f64 (neg.f64 a) (neg.f64 a))
(*.f64 (fabs.f64 a) (fabs.f64 a))
(*.f64 a a)
(pow.f64 a #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 a) #s(literal 2 binary64)))
a
(*.f64 (pow.f64 b #s(literal 1 binary64)) (pow.f64 b #s(literal 1 binary64)))
(*.f64 (neg.f64 b) (neg.f64 b))
(*.f64 (fabs.f64 b) (fabs.f64 b))
(*.f64 b b)
(pow.f64 b #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)))
b
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (.f64 a a) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (/.f64 (.f64 a a) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 b b) b))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) b))) (.f64 a a) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 a a)) (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) b) #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 b b) b)))) (.f64 a a) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) b))) (.f64 a a) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b)))
#s(approx (- (* a a) (* b b)) (*.f64 (+.f64 a b) (-.f64 a b)))
#s(approx (* a a) (*.f64 a a))
#s(approx a a)
#s(approx (sqrt (- (* a a) (* b b))) a)
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (fma.f64 (/.f64 (.f64 b b) (*.f64 a a)) #s(literal -1/2 binary64) #s(literal 1 binary64)) a))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 b b) (.f64 a a)) #s(literal -1/2 binary64) #s(literal 1 binary64)) (.f64 (/.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 a a) (.f64 a a))) #s(literal -1/8 binary64))) a))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 b b) (.f64 a a)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (.f64 (.f64 (.f64 b b) b) (.f64 (.f64 b b) b)) (.f64 (.f64 (.f64 a a) a) (.f64 (.f64 a a) a))) #s(literal -1/16 binary64) (.f64 (/.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 a a) (.f64 a a))) #s(literal -1/8 binary64)))) #s(literal 1 binary64)) a))
#s(approx (- (* a a) (* b b)) (*.f64 a a))
#s(approx (- (* a a) (* b b)) (.f64 (+.f64 (/.f64 (neg.f64 (.f64 b b)) (.f64 a a)) #s(literal 1 binary64)) (.f64 a a)))
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (neg.f64 a) (fma.f64 (/.f64 (.f64 b b) (*.f64 a a)) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (neg.f64 a) (+.f64 (fma.f64 (/.f64 (.f64 b b) (.f64 a a)) #s(literal -1/2 binary64) #s(literal 1 binary64)) (.f64 (/.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 a a) (.f64 a a))) #s(literal -1/8 binary64)))))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (neg.f64 a) (+.f64 (fma.f64 (/.f64 (.f64 b b) (.f64 a a)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (.f64 (.f64 (.f64 b b) b) (.f64 (.f64 b b) b)) (.f64 (.f64 (.f64 a a) a) (.f64 (.f64 a a) a))) #s(literal -1/16 binary64) (.f64 (/.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 a a) (.f64 a a))) #s(literal -1/8 binary64)))) #s(literal 1 binary64))))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (-.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 b b)) (.f64 (.f64 a a) a)) (/.f64 #s(literal 1/2 binary64) a)) (*.f64 b b) a))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (-.f64 (.f64 (-.f64 (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 b b)) (pow.f64 a #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 a a) a))) (.f64 b b)) (/.f64 #s(literal 1/2 binary64) a)) (*.f64 b b) a))
#s(approx (- (* a a) (* b b)) (fma.f64 a a (neg.f64 (*.f64 b b))))
#s(approx (* b b) (*.f64 b b))
#s(approx b b)
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (fma.f64 (/.f64 (.f64 a a) (.f64 (.f64 b b) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) b))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))) #s(literal -1/8 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 a a)) (.f64 (.f64 b b) (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64))) b))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 (.f64 (.f64 a a) a) (.f64 (.f64 a a) a)) (.f64 (.f64 (.f64 (.f64 b b) b) (.f64 (.f64 b b) b)) (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64)))) #s(literal 1/16 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 a a)) (.f64 (*.f64 b b) (sqrt.f64 #s(literal -1 binary64)))))) (sqrt.f64 #s(literal -1 binary64))) b))
#s(approx (- (* a a) (* b b)) (.f64 (-.f64 (/.f64 (.f64 a a) (.f64 b b)) #s(literal 1 binary64)) (.f64 b b)))
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 (.f64 (fma.f64 (/.f64 (.f64 a a) (.f64 (.f64 b b) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) b)))
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 (.f64 (+.f64 (fma.f64 (/.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))) #s(literal -1/8 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 a a)) (.f64 (.f64 b b) (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64))) b)))
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 (.f64 (+.f64 (fma.f64 (/.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 (.f64 (.f64 a a) a) (.f64 (.f64 a a) a)) (.f64 (.f64 (.f64 (.f64 b b) b) (.f64 (.f64 b b) b)) (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64)))) #s(literal 1/16 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 a a)) (.f64 (*.f64 b b) (sqrt.f64 #s(literal -1 binary64)))))) (sqrt.f64 #s(literal -1 binary64))) b)))

eval5.0ms (0.4%)

Memory: 6.3MiB live, 6.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 222 to 226 computations (81.5% saved)

prune2.0ms (0.1%)

Memory

2.6MiB live, 2.6MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	51	3	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	3	55

Accuracy

99.3%

Counts

55 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.0%	(sqrt.f64 (*.f64 (+.f64 a b) (-.f64 a b)))
▶	1.1%	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
▶	98.6%	#s(approx (sqrt (- (* a a) (* b b))) a)

Compiler

Compiled 29 to 21 computations (27.6% saved)

series9.0ms (0.7%)

Memory

8.6MiB live, 8.6MiB allocated; 0ms collecting garbage

Counts

9 → 75

Calls

Call 1

Inputs
#s(approx (sqrt (- (* a a) (* b b))) a)
a
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
(neg.f64 a)
(sqrt.f64 (*.f64 (+.f64 a b) (-.f64 a b)))
(*.f64 (+.f64 a b) (-.f64 a b))
(+.f64 a b)
b
(-.f64 a b)

Outputs
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx a #s(hole binary64 a))
#s(approx (neg a) #s(hole binary64 (* -1 a)))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (* -1 (pow b 2))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))))
#s(approx (+ a b) #s(hole binary64 b))
#s(approx (+ a b) #s(hole binary64 (+ a b)))
#s(approx (- a b) #s(hole binary64 (* -1 b)))
#s(approx (- a b) #s(hole binary64 (- a b)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 a))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (pow a 2)))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))))
#s(approx (+ a b) #s(hole binary64 a))
#s(approx (+ a b) #s(hole binary64 (* a (+ 1 (/ b a)))))
#s(approx (- a b) #s(hole binary64 a))
#s(approx (- a b) #s(hole binary64 (* a (+ 1 (* -1 (/ b a))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 a)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* -1 (* a (pow (sqrt -1) 2)))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))))
#s(approx (+ a b) #s(hole binary64 (* -1 (* a (- (* -1 (/ b a)) 1)))))
#s(approx (- a b) #s(hole binary64 (* -1 (* a (- (/ b a) 1)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* -1/2 (/ (pow b 2) a)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (+ (* b (+ a (* -1 a))) (pow a 2))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))))
#s(approx b #s(hole binary64 b))
#s(approx (- a b) #s(hole binary64 (+ a (* -1 b))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))))
#s(approx (+ a b) #s(hole binary64 (* b (+ 1 (/ a b)))))
#s(approx (- a b) #s(hole binary64 (* b (- (/ a b) 1))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))))
#s(approx (+ a b) #s(hole binary64 (* -1 (* b (- (* -1 (/ a b)) 1)))))
#s(approx (- a b) #s(hole binary64 (* -1 (* b (+ 1 (* -1 (/ a b)))))))

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	a	@	0	((sqrt (- (* a a) (* b b))) a (sqrt (- (* a a) (* b b))) (neg a) (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) b (- a b))
2.0ms	a	@	-inf	((sqrt (- (* a a) (* b b))) a (sqrt (- (* a a) (* b b))) (neg a) (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) b (- a b))
2.0ms	b	@	inf	((sqrt (- (* a a) (* b b))) a (sqrt (- (* a a) (* b b))) (neg a) (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) b (- a b))
1.0ms	a	@	inf	((sqrt (- (* a a) (* b b))) a (sqrt (- (* a a) (* b b))) (neg a) (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) b (- a b))
1.0ms	b	@	-inf	((sqrt (- (* a a) (* b b))) a (sqrt (- (* a a) (* b b))) (neg a) (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) b (- a b))

rewrite91.0ms (6.4%)

Memory

8.1MiB live, 57.4MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	424	2255
0	428	2003
0	2603	1929

Stop Event

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

Counts

84 → 102

Calls

Call 1

Inputs
#s(approx (sqrt (- (* a a) (* b b))) a)
a
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
(neg.f64 a)
(sqrt.f64 (*.f64 (+.f64 a b) (-.f64 a b)))
(*.f64 (+.f64 a b) (-.f64 a b))
(+.f64 a b)
b
(-.f64 a b)
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx a #s(hole binary64 a))
#s(approx (neg a) #s(hole binary64 (* -1 a)))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (* -1 (pow b 2))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))))
#s(approx (+ a b) #s(hole binary64 b))
#s(approx (+ a b) #s(hole binary64 (+ a b)))
#s(approx (- a b) #s(hole binary64 (* -1 b)))
#s(approx (- a b) #s(hole binary64 (- a b)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 a))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (pow a 2)))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))))
#s(approx (+ a b) #s(hole binary64 a))
#s(approx (+ a b) #s(hole binary64 (* a (+ 1 (/ b a)))))
#s(approx (- a b) #s(hole binary64 a))
#s(approx (- a b) #s(hole binary64 (* a (+ 1 (* -1 (/ b a))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 a)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* -1 (* a (pow (sqrt -1) 2)))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))))
#s(approx (+ a b) #s(hole binary64 (* -1 (* a (- (* -1 (/ b a)) 1)))))
#s(approx (- a b) #s(hole binary64 (* -1 (* a (- (/ b a) 1)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* -1/2 (/ (pow b 2) a)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (+ (* b (+ a (* -1 a))) (pow a 2))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))))
#s(approx b #s(hole binary64 b))
#s(approx (- a b) #s(hole binary64 (+ a (* -1 b))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))))
#s(approx (+ a b) #s(hole binary64 (* b (+ 1 (/ a b)))))
#s(approx (- a b) #s(hole binary64 (* b (- (/ a b) 1))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (sqrt (* (+ a b) (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))))
#s(approx (* (+ a b) (- a b)) #s(hole binary64 (* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))))
#s(approx (+ a b) #s(hole binary64 (* -1 (* b (- (* -1 (/ a b)) 1)))))
#s(approx (- a b) #s(hole binary64 (* -1 (* b (+ 1 (* -1 (/ a b)))))))

Outputs
#s(approx (sqrt (- (* a a) (* b b))) a)
a
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
(*.f64 #s(literal -1 binary64) a)
(*.f64 a #s(literal -1 binary64))
(neg.f64 a)
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
(pow.f64 (*.f64 (-.f64 a b) (+.f64 b a)) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 (+.f64 b a) (-.f64 a b))
(/.f64 (-.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 (.f64 b b) (.f64 b b))) (fma.f64 a a (*.f64 b b)))
(/.f64 (-.f64 (pow.f64 (.f64 a a) #s(literal 3 binary64)) (pow.f64 (.f64 b b) #s(literal 3 binary64))) (fma.f64 (.f64 a a) (.f64 a a) (fma.f64 (.f64 b b) (.f64 b b) (.f64 (.f64 a a) (*.f64 b b)))))
(fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 b) b))
(fma.f64 (fabs.f64 a) (fabs.f64 a) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 a) (neg.f64 a) (*.f64 (neg.f64 b) b))
(fma.f64 a a (*.f64 (neg.f64 b) b))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (.f64 a a) (.f64 (neg.f64 b) b))
(/.f64 (fma.f64 (.f64 a a) a (.f64 (.f64 b b) b)) (fma.f64 a a (-.f64 (.f64 b b) (*.f64 a b))))
(/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (-.f64 a b))
(+.f64 b a)
(+.f64 a b)
b
(/.f64 (-.f64 (.f64 (.f64 a a) a) (.f64 (.f64 b b) b)) (fma.f64 a a (fma.f64 b b (*.f64 a b))))
(/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (+.f64 b a))
(-.f64 a b)
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (.f64 a a) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)) #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (/.f64 (.f64 a a) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (.f64 b b) b))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) b))) (.f64 a a) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 a a)) (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) b) #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (.f64 b b) b)))) (.f64 a a) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) b))) (.f64 a a) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx a a)
#s(approx (neg a) (neg.f64 a))
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal 0 binary64) b) a) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)) #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 a (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 (.f64 #s(literal 0 binary64) b) (.f64 #s(literal 0 binary64) b)) (neg.f64 (.f64 b b))) #s(literal 1/4 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)) (/.f64 (.f64 #s(literal 0 binary64) b) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)))) a (.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 (.f64 (.f64 #s(literal 0 binary64) b) a) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 (.f64 #s(literal 0 binary64) b) (.f64 #s(literal 0 binary64) b)) (neg.f64 (.f64 b b))) #s(literal 1/4 binary64)))) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (.f64 b b) b))) #s(literal -1/4 binary64) (.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 (.f64 #s(literal 0 binary64) b) (.f64 #s(literal 0 binary64) b)) (neg.f64 (.f64 b b))) #s(literal 1/4 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)) #s(literal 1/2 binary64))) a (/.f64 (.f64 (.f64 #s(literal 0 binary64) b) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) b))) a (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (* (+ a b) (- a b)) (neg.f64 (*.f64 b b)))
#s(approx (* (+ a b) (- a b)) (fma.f64 (.f64 #s(literal 0 binary64) b) a (neg.f64 (.f64 b b))))
#s(approx (* (+ a b) (- a b)) (fma.f64 (fma.f64 #s(literal 0 binary64) b a) a (neg.f64 (*.f64 b b))))
#s(approx (+ a b) b)
#s(approx (+ a b) (+.f64 b a))
#s(approx (- a b) (neg.f64 b))
#s(approx (- a b) (-.f64 a b))
#s(approx (sqrt (- (* a a) (* b b))) a)
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (fma.f64 (/.f64 (.f64 b b) (*.f64 a a)) #s(literal -1/2 binary64) #s(literal 1 binary64)) a))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 b b) (.f64 a a)) #s(literal -1/2 binary64) #s(literal 1 binary64)) (.f64 (/.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 a a) (.f64 a a))) #s(literal -1/8 binary64))) a))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 b b) (.f64 a a)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (.f64 (.f64 (.f64 b b) b) (.f64 (.f64 b b) b)) (.f64 (.f64 (.f64 a a) a) (.f64 (.f64 a a) a))) #s(literal -1/16 binary64) (.f64 (/.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 a a) (.f64 a a))) #s(literal -1/8 binary64)))) #s(literal 1 binary64)) a))
#s(approx (sqrt (- (* a a) (* b b))) a)
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (fma.f64 (.f64 #s(literal 0 binary64) (/.f64 b a)) #s(literal 1/2 binary64) #s(literal 1 binary64)) a))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (fma.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 0 binary64) (/.f64 b a) (/.f64 (-.f64 (neg.f64 (.f64 b b)) (.f64 (.f64 (.f64 #s(literal 0 binary64) b) (.f64 #s(literal 0 binary64) b)) #s(literal 1/4 binary64))) (*.f64 a a))) #s(literal 1 binary64)) a))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 (-.f64 (neg.f64 (.f64 b b)) (.f64 (.f64 (.f64 #s(literal 0 binary64) b) (.f64 #s(literal 0 binary64) b)) #s(literal 1/4 binary64))) (.f64 #s(literal 0 binary64) b)) (.f64 (.f64 a a) a)) #s(literal -1/4 binary64) (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 0 binary64) (/.f64 b a) (/.f64 (-.f64 (neg.f64 (.f64 b b)) (.f64 (.f64 (.f64 #s(literal 0 binary64) b) (.f64 #s(literal 0 binary64) b)) #s(literal 1/4 binary64))) (*.f64 a a))))) #s(literal 1 binary64)) a))
#s(approx (* (+ a b) (- a b)) (*.f64 a a))
#s(approx (* (+ a b) (- a b)) (.f64 (fma.f64 #s(literal 0 binary64) (/.f64 b a) #s(literal 1 binary64)) (.f64 a a)))
#s(approx (* (+ a b) (- a b)) (.f64 (+.f64 (+.f64 (/.f64 (neg.f64 b) a) #s(literal 1 binary64)) (+.f64 (/.f64 (neg.f64 (.f64 b b)) (.f64 a a)) (/.f64 b a))) (.f64 a a)))
#s(approx (+ a b) a)
#s(approx (+ a b) (*.f64 (+.f64 (/.f64 b a) #s(literal 1 binary64)) a))
#s(approx (- a b) a)
#s(approx (- a b) (*.f64 (+.f64 (/.f64 (neg.f64 b) a) #s(literal 1 binary64)) a))
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (neg.f64 a) (fma.f64 (/.f64 (.f64 b b) (*.f64 a a)) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (neg.f64 a) (+.f64 (fma.f64 (/.f64 (.f64 b b) (.f64 a a)) #s(literal -1/2 binary64) #s(literal 1 binary64)) (.f64 (/.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 a a) (.f64 a a))) #s(literal -1/8 binary64)))))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (neg.f64 a) (+.f64 (fma.f64 (/.f64 (.f64 b b) (.f64 a a)) #s(literal -1/2 binary64) (fma.f64 (/.f64 (.f64 (.f64 (.f64 b b) b) (.f64 (.f64 b b) b)) (.f64 (.f64 (.f64 a a) a) (.f64 (.f64 a a) a))) #s(literal -1/16 binary64) (.f64 (/.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (.f64 a a) (.f64 a a))) #s(literal -1/8 binary64)))) #s(literal 1 binary64))))
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 (neg.f64 a)))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (neg.f64 a) (fma.f64 (.f64 #s(literal 0 binary64) (/.f64 b a)) #s(literal -1/2 binary64) #s(literal -1 binary64))))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (neg.f64 a) (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 b b (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 #s(literal 0 binary64) b) (.f64 #s(literal 0 binary64) b)) #s(literal -1 binary64)))) a) #s(literal -1/2 binary64) (.f64 (*.f64 #s(literal 0 binary64) b) #s(literal 1/2 binary64))) a)) #s(literal -1 binary64))))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (neg.f64 a) (+.f64 (neg.f64 (/.f64 (fma.f64 (.f64 #s(literal 0 binary64) b) #s(literal 1/2 binary64) (neg.f64 (/.f64 (fma.f64 (/.f64 (.f64 (fma.f64 b b (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 #s(literal 0 binary64) b) (.f64 #s(literal 0 binary64) b)) #s(literal -1 binary64)))) (.f64 #s(literal 0 binary64) b)) (neg.f64 a)) #s(literal 1/4 binary64) (.f64 (fma.f64 b b (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 #s(literal 0 binary64) b) (*.f64 #s(literal 0 binary64) b)) #s(literal -1 binary64)))) #s(literal 1/2 binary64))) a))) a)) #s(literal -1 binary64))))
#s(approx (* (+ a b) (- a b)) (.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 (.f64 b b) a) (neg.f64 (.f64 #s(literal 0 binary64) b))) a)) #s(literal 1 binary64)) (.f64 a a)))
#s(approx (+ a b) (*.f64 (neg.f64 a) (-.f64 (/.f64 (neg.f64 b) a) #s(literal 1 binary64))))
#s(approx (- a b) (*.f64 (neg.f64 a) (-.f64 (/.f64 b a) #s(literal 1 binary64))))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (-.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 b b)) (.f64 (.f64 a a) a)) (/.f64 #s(literal 1/2 binary64) a)) (*.f64 b b) a))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (-.f64 (.f64 (-.f64 (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 b b)) (pow.f64 a #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 a a) a))) (.f64 b b)) (/.f64 #s(literal 1/2 binary64) a)) (*.f64 b b) a))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) b) a) #s(literal 1/2 binary64) a))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (.f64 b (/.f64 (fma.f64 (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) (.f64 #s(literal 0 binary64) a)) (.f64 a a)) #s(literal 1/4 binary64) #s(literal 1 binary64)) a)) #s(literal -1/2 binary64) (.f64 (/.f64 (*.f64 #s(literal 0 binary64) a) a) #s(literal 1/2 binary64))) b a))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (fma.f64 (.f64 b (/.f64 (.f64 (fma.f64 (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) (.f64 #s(literal 0 binary64) a)) (.f64 a a)) #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 #s(literal 0 binary64) a)) (.f64 (.f64 a a) a))) #s(literal 1/4 binary64) (.f64 (/.f64 (fma.f64 (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) (.f64 #s(literal 0 binary64) a)) (.f64 a a)) #s(literal 1/4 binary64) #s(literal 1 binary64)) a) #s(literal -1/2 binary64))) b (.f64 (/.f64 (.f64 #s(literal 0 binary64) a) a) #s(literal 1/2 binary64))) b a))
#s(approx (* (+ a b) (- a b)) (fma.f64 (.f64 #s(literal 0 binary64) a) b (.f64 a a)))
#s(approx (* (+ a b) (- a b)) (fma.f64 (fma.f64 #s(literal 0 binary64) a (neg.f64 b)) b (*.f64 a a)))
#s(approx b b)
#s(approx (- a b) (+.f64 (neg.f64 b) a))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (fma.f64 (/.f64 (.f64 a a) (.f64 (.f64 b b) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) b))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) #s(literal -1/8 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 a a)) (.f64 (*.f64 b b) (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64))) b))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 (.f64 (.f64 a a) a) (.f64 (.f64 a a) a)) (.f64 (.f64 (.f64 (.f64 b b) b) (.f64 (.f64 b b) b)) (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64)))) #s(literal 1/16 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 a a)) (.f64 (.f64 b b) (sqrt.f64 #s(literal -1 binary64)))))) (sqrt.f64 #s(literal -1 binary64))) b))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (fma.f64 (/.f64 (.f64 #s(literal 0 binary64) a) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) b))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 #s(literal 0 binary64) a) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)) (/.f64 (fma.f64 a a (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) (.f64 #s(literal 0 binary64) a)) #s(literal -1 binary64)))) (.f64 (*.f64 b b) (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64))) b))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 (fma.f64 a a (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) (.f64 #s(literal 0 binary64) a)) #s(literal -1 binary64)))) (.f64 #s(literal 0 binary64) a)) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (.f64 b b) b))) #s(literal -1/4 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 #s(literal 0 binary64) a) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)) (/.f64 (fma.f64 a a (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) (.f64 #s(literal 0 binary64) a)) #s(literal -1 binary64)))) (.f64 (.f64 b b) (sqrt.f64 #s(literal -1 binary64))))))) (sqrt.f64 #s(literal -1 binary64))) b))
#s(approx (* (+ a b) (- a b)) (.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 a b)) #s(literal 1 binary64)) (*.f64 b b)))
#s(approx (* (+ a b) (- a b)) (.f64 (-.f64 (fma.f64 #s(literal 0 binary64) (/.f64 a b) (/.f64 (.f64 a a) (.f64 b b))) #s(literal 1 binary64)) (.f64 b b)))
#s(approx (+ a b) (*.f64 (+.f64 (/.f64 a b) #s(literal 1 binary64)) b))
#s(approx (- a b) (*.f64 (-.f64 (/.f64 a b) #s(literal 1 binary64)) b))
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (neg.f64 b) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (neg.f64 b) (fma.f64 (/.f64 (.f64 a a) (.f64 (.f64 b b) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (neg.f64 b) (+.f64 (fma.f64 (/.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) #s(literal -1/8 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 a a)) (.f64 (*.f64 b b) (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (neg.f64 b) (+.f64 (fma.f64 (/.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 (.f64 (.f64 a a) a) (.f64 (.f64 a a) a)) (.f64 (.f64 (.f64 (.f64 b b) b) (.f64 (.f64 b b) b)) (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64)))) #s(literal 1/16 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 a a)) (.f64 (.f64 b b) (sqrt.f64 #s(literal -1 binary64)))))) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (neg.f64 b) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (neg.f64 b) (fma.f64 (/.f64 (.f64 #s(literal 0 binary64) a) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)) #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (neg.f64 b) (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (.f64 #s(literal 0 binary64) a) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (.f64 (/.f64 (fma.f64 a a (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) (.f64 #s(literal 0 binary64) a)) #s(literal -1 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)) #s(literal -1/2 binary64))) b)) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (neg.f64 b) (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (.f64 #s(literal 0 binary64) a) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (neg.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 a a (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) (.f64 #s(literal 0 binary64) a)) #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (.f64 (/.f64 (.f64 (fma.f64 a a (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) (.f64 #s(literal 0 binary64) a)) #s(literal -1 binary64)))) (.f64 #s(literal 0 binary64) a)) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) b)) #s(literal 1/4 binary64))) b))) b)) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (* (+ a b) (- a b)) (.f64 (-.f64 (neg.f64 (.f64 #s(literal 0 binary64) (/.f64 a b))) #s(literal 1 binary64)) (*.f64 b b)))
#s(approx (* (+ a b) (- a b)) (.f64 (-.f64 (neg.f64 (/.f64 (fma.f64 #s(literal 0 binary64) a (neg.f64 (/.f64 (.f64 a a) b))) b)) #s(literal 1 binary64)) (*.f64 b b)))
#s(approx (+ a b) (*.f64 (neg.f64 b) (-.f64 (/.f64 (neg.f64 a) b) #s(literal 1 binary64))))
#s(approx (- a b) (*.f64 (neg.f64 b) (+.f64 (/.f64 (neg.f64 a) b) #s(literal 1 binary64))))

eval9.0ms (0.7%)

Memory: 11.7MiB live, 11.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 2 447 to 467 computations (80.9% saved)

prune3.0ms (0.2%)

Memory

4.4MiB live, 4.4MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	93	4	97

Accuracy

99.6%

Counts

97 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
✓	53.0%	(sqrt.f64 (*.f64 (+.f64 a b) (-.f64 a b)))
✓	1.1%	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
✓	98.6%	#s(approx (sqrt (- (* a a) (* b b))) a)

Compiler

Compiled 38 to 28 computations (26.3% saved)

series13.0ms (0.9%)

Memory

-36.5MiB live, 10.1MiB allocated; 2ms collecting garbage

Counts

7 → 83

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
(sqrt.f64 (+.f64 b a))
(+.f64 b a)
b
a
(sqrt.f64 (-.f64 a b))
(-.f64 a b)

Outputs
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (sqrt b)))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))))
#s(approx (+ b a) #s(hole binary64 b))
#s(approx (+ b a) #s(hole binary64 (+ a b)))
#s(approx a #s(hole binary64 a))
#s(approx (sqrt (- a b)) #s(hole binary64 (* (sqrt b) (sqrt -1))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))))
#s(approx (- a b) #s(hole binary64 (* -1 b)))
#s(approx (- a b) #s(hole binary64 (- a b)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (sqrt a)))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))))
#s(approx (+ b a) #s(hole binary64 a))
#s(approx (+ b a) #s(hole binary64 (* a (+ 1 (/ b a)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (sqrt a)))
#s(approx (sqrt (- a b)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))))
#s(approx (- a b) #s(hole binary64 a))
#s(approx (- a b) #s(hole binary64 (* a (+ 1 (* -1 (/ b a))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* (sqrt a) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))))
#s(approx (+ b a) #s(hole binary64 (* -1 (* a (- (* -1 (/ b a)) 1)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* (sqrt a) (pow (sqrt -1) 2)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (* (pow b 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))))
#s(approx (- a b) #s(hole binary64 (* -1 (* a (- (/ b a) 1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b)))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))))
#s(approx b #s(hole binary64 b))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))))
#s(approx (- a b) #s(hole binary64 (+ a (* -1 b))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* b (+ (sqrt (/ 1 b)) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (pow a 3) (sqrt (/ 1 (pow b 7))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))))
#s(approx (+ b a) #s(hole binary64 (* b (+ 1 (/ a b)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))))
#s(approx (- a b) #s(hole binary64 (* b (- (/ a b) 1))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* (sqrt b) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))))
#s(approx (+ b a) #s(hole binary64 (* -1 (* b (- (* -1 (/ a b)) 1)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* (sqrt b) (sqrt -1)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))))
#s(approx (- a b) #s(hole binary64 (* -1 (* b (+ 1 (* -1 (/ a b)))))))

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	a	@	-inf	((* (sqrt (+ b a)) (sqrt (- a b))) (sqrt (+ b a)) (+ b a) b a (sqrt (- a b)) (- a b))
2.0ms	b	@	-inf	((* (sqrt (+ b a)) (sqrt (- a b))) (sqrt (+ b a)) (+ b a) b a (sqrt (- a b)) (- a b))
2.0ms	a	@	0	((* (sqrt (+ b a)) (sqrt (- a b))) (sqrt (+ b a)) (+ b a) b a (sqrt (- a b)) (- a b))
2.0ms	b	@	inf	((* (sqrt (+ b a)) (sqrt (- a b))) (sqrt (+ b a)) (+ b a) b a (sqrt (- a b)) (- a b))
1.0ms	a	@	inf	((* (sqrt (+ b a)) (sqrt (- a b))) (sqrt (+ b a)) (+ b a) b a (sqrt (- a b)) (- a b))

rewrite116.0ms (8.2%)

Memory

28.7MiB live, 74.4MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	526	2709
0	532	2268
0	3177	2164

Stop Event

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

Counts

90 → 101

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
(sqrt.f64 (+.f64 b a))
(+.f64 b a)
b
a
(sqrt.f64 (-.f64 a b))
(-.f64 a b)
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (sqrt b)))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))))
#s(approx (+ b a) #s(hole binary64 b))
#s(approx (+ b a) #s(hole binary64 (+ a b)))
#s(approx a #s(hole binary64 a))
#s(approx (sqrt (- a b)) #s(hole binary64 (* (sqrt b) (sqrt -1))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))))
#s(approx (- a b) #s(hole binary64 (* -1 b)))
#s(approx (- a b) #s(hole binary64 (- a b)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (sqrt a)))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))))
#s(approx (+ b a) #s(hole binary64 a))
#s(approx (+ b a) #s(hole binary64 (* a (+ 1 (/ b a)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (sqrt a)))
#s(approx (sqrt (- a b)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))))
#s(approx (- a b) #s(hole binary64 a))
#s(approx (- a b) #s(hole binary64 (* a (+ 1 (* -1 (/ b a))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* (sqrt a) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))))
#s(approx (+ b a) #s(hole binary64 (* -1 (* a (- (* -1 (/ b a)) 1)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* (sqrt a) (pow (sqrt -1) 2)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (* (pow b 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))))
#s(approx (- a b) #s(hole binary64 (* -1 (* a (- (/ b a) 1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b)))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))))
#s(approx b #s(hole binary64 b))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))))
#s(approx (- a b) #s(hole binary64 (+ a (* -1 b))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* b (+ (sqrt (/ 1 b)) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (pow a 3) (sqrt (/ 1 (pow b 7))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))))
#s(approx (+ b a) #s(hole binary64 (* b (+ 1 (/ a b)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))))
#s(approx (- a b) #s(hole binary64 (* b (- (/ a b) 1))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* (sqrt b) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))))
#s(approx (+ b a) #s(hole binary64 (* -1 (* b (- (* -1 (/ a b)) 1)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* (sqrt b) (sqrt -1)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))))
#s(approx (- a b) #s(hole binary64 (* -1 (* b (+ 1 (* -1 (/ a b)))))))

Outputs
(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 a b)))
(*.f64 (sqrt.f64 (+.f64 a b)) (sqrt.f64 (-.f64 a b)))
(sqrt.f64 (*.f64 (+.f64 a b) (-.f64 a b)))
(pow.f64 (+.f64 a b) #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 a b))
(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (-.f64 a b))
(/.f64 (-.f64 (.f64 b b) (.f64 a a)) (-.f64 b a))
(/.f64 (fma.f64 (.f64 a a) a (.f64 (.f64 b b) b)) (fma.f64 a a (-.f64 (.f64 b b) (*.f64 a b))))
(/.f64 (fma.f64 (.f64 b b) b (.f64 (.f64 a a) a)) (fma.f64 b b (-.f64 (.f64 a a) (*.f64 b a))))
(+.f64 a b)
(+.f64 b a)
b
a
(pow.f64 (-.f64 a b) #s(literal 1/2 binary64))
(sqrt.f64 (-.f64 a b))
(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (+.f64 a b))
(/.f64 (-.f64 (.f64 (.f64 a a) a) (.f64 (.f64 b b) b)) (fma.f64 a a (fma.f64 b b (*.f64 a b))))
(-.f64 a b)
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal 0 binary64) b) a) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)) #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 a (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 (.f64 #s(literal 0 binary64) b) (.f64 #s(literal 0 binary64) b)) (neg.f64 (.f64 b b))) #s(literal 1/4 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)) (/.f64 (.f64 #s(literal 0 binary64) b) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)))) a (.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 (.f64 (.f64 #s(literal 0 binary64) b) a) (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 (.f64 #s(literal 0 binary64) b) (.f64 #s(literal 0 binary64) b)) (neg.f64 (.f64 b b))) #s(literal 1/4 binary64)))) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (.f64 b b) b))) #s(literal -1/4 binary64) (.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 (.f64 #s(literal 0 binary64) b) (.f64 #s(literal 0 binary64) b)) (neg.f64 (.f64 b b))) #s(literal 1/4 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)) #s(literal 1/2 binary64))) a (/.f64 (.f64 (.f64 #s(literal 0 binary64) b) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) b))) a (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (sqrt (+ b a)) (sqrt.f64 b))
#s(approx (sqrt (+ b a)) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 b)) a) #s(literal 1/2 binary64) (sqrt.f64 b)))
#s(approx (sqrt (+ b a)) (fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 b b) b))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 b)) #s(literal 1/2 binary64))) a (sqrt.f64 b)))
#s(approx (sqrt (+ b a)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) a) (sqrt.f64 (pow.f64 b #s(literal -5 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 b b) b))) #s(literal -1/8 binary64))) a (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 b)) #s(literal 1/2 binary64))) a (sqrt.f64 b)))
#s(approx (+ b a) b)
#s(approx (+ b a) (+.f64 a b))
#s(approx a a)
#s(approx (sqrt (- a b)) (sqrt.f64 (neg.f64 b)))
#s(approx (sqrt (- a b)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 a (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 b)) (sqrt.f64 (neg.f64 b))))
#s(approx (sqrt (- a b)) (fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 a (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 b b) b))) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 b)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))) a (sqrt.f64 (neg.f64 b))))
#s(approx (sqrt (- a b)) (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (/.f64 a (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64)))) (sqrt.f64 (pow.f64 b #s(literal -5 binary64))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 b b) b))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))))) a (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 b)) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))))) a (sqrt.f64 (neg.f64 b))))
#s(approx (- a b) (neg.f64 b))
#s(approx (- a b) (-.f64 a b))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) a)
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (.f64 (fma.f64 (/.f64 (.f64 #s(literal 0 binary64) b) a) #s(literal 1/2 binary64) #s(literal 1 binary64)) a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 #s(literal 0 binary64) b) a) (/.f64 (-.f64 (neg.f64 (.f64 b b)) (.f64 (.f64 (.f64 #s(literal 0 binary64) b) (.f64 #s(literal 0 binary64) b)) #s(literal 1/4 binary64))) (.f64 a a))) #s(literal 1 binary64)) a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 (-.f64 (neg.f64 (.f64 b b)) (.f64 (.f64 (.f64 #s(literal 0 binary64) b) (.f64 #s(literal 0 binary64) b)) #s(literal 1/4 binary64))) (.f64 #s(literal 0 binary64) b)) (.f64 (.f64 a a) a)) #s(literal -1/4 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 #s(literal 0 binary64) b) a) (/.f64 (-.f64 (neg.f64 (.f64 b b)) (.f64 (.f64 (.f64 #s(literal 0 binary64) b) (.f64 #s(literal 0 binary64) b)) #s(literal 1/4 binary64))) (.f64 a a))))) #s(literal 1 binary64)) a))
#s(approx (sqrt (+ b a)) (sqrt.f64 a))
#s(approx (sqrt (+ b a)) (.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 a a) a))) b) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 a))) a))
#s(approx (sqrt (+ b a)) (.f64 (+.f64 (fma.f64 (.f64 (sqrt.f64 (pow.f64 a #s(literal -5 binary64))) (.f64 b b)) #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 a a) a))) b) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 a))) a))
#s(approx (sqrt (+ b a)) (.f64 (+.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 a #s(literal -5 binary64)))) (.f64 b b) (fma.f64 (.f64 (sqrt.f64 (pow.f64 a #s(literal -7 binary64))) (.f64 (.f64 b b) b)) #s(literal 1/16 binary64) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 a a) a))) b) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 a))) a))
#s(approx (+ b a) a)
#s(approx (+ b a) (*.f64 (+.f64 (/.f64 b a) #s(literal 1 binary64)) a))
#s(approx (sqrt (- a b)) (sqrt.f64 a))
#s(approx (sqrt (- a b)) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 a a) a))) b) (/.f64 #s(literal 1 binary64) (sqrt.f64 a))) a))
#s(approx (sqrt (- a b)) (.f64 (+.f64 (fma.f64 (.f64 (sqrt.f64 (pow.f64 a #s(literal -5 binary64))) (.f64 b b)) #s(literal -1/8 binary64) (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (*.f64 a a) a))) b))) (/.f64 #s(literal 1 binary64) (sqrt.f64 a))) a))
#s(approx (sqrt (- a b)) (.f64 (+.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 a a) a)))) b (fma.f64 (.f64 #s(literal -1/16 binary64) (sqrt.f64 (pow.f64 a #s(literal -7 binary64)))) (.f64 (.f64 b b) b) (.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 a #s(literal -5 binary64)))) (.f64 b b)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 a))) a))
#s(approx (- a b) a)
#s(approx (- a b) (*.f64 (+.f64 (/.f64 (neg.f64 b) a) #s(literal 1 binary64)) a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (neg.f64 (neg.f64 a)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (.f64 (neg.f64 a) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 #s(literal 0 binary64) b) a) #s(literal -1 binary64))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (.f64 (neg.f64 a) (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 b b (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 #s(literal 0 binary64) b) (.f64 #s(literal 0 binary64) b)) #s(literal -1 binary64)))) a) #s(literal -1/2 binary64) (.f64 (*.f64 #s(literal 0 binary64) b) #s(literal 1/2 binary64))) a)) #s(literal -1 binary64))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (.f64 (neg.f64 a) (+.f64 (neg.f64 (/.f64 (fma.f64 (.f64 #s(literal 0 binary64) b) #s(literal 1/2 binary64) (neg.f64 (/.f64 (fma.f64 (/.f64 (.f64 (fma.f64 b b (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 #s(literal 0 binary64) b) (.f64 #s(literal 0 binary64) b)) #s(literal -1 binary64)))) (.f64 #s(literal 0 binary64) b)) (neg.f64 a)) #s(literal 1/4 binary64) (.f64 (fma.f64 b b (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 #s(literal 0 binary64) b) (*.f64 #s(literal 0 binary64) b)) #s(literal -1 binary64)))) #s(literal 1/2 binary64))) a))) a)) #s(literal -1 binary64))))
#s(approx (sqrt (+ b a)) (neg.f64 (*.f64 (sqrt.f64 a) #s(literal -1 binary64))))
#s(approx (sqrt (+ b a)) (.f64 (neg.f64 a) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 a a) a))) b) #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 a)) #s(literal -1 binary64)))))
#s(approx (sqrt (+ b a)) (.f64 (neg.f64 a) (fma.f64 (.f64 (/.f64 (.f64 b b) #s(literal -1 binary64)) (sqrt.f64 (pow.f64 a #s(literal -5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 a a) a))) b) #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 a)) #s(literal -1 binary64))))))
#s(approx (sqrt (+ b a)) (.f64 (neg.f64 a) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 a #s(literal -5 binary64)))) (/.f64 (.f64 b b) #s(literal -1 binary64)) (fma.f64 (.f64 (/.f64 (.f64 (.f64 b b) b) #s(literal 1 binary64)) (sqrt.f64 (pow.f64 a #s(literal -7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 a a) a))) b) #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 a)) #s(literal -1 binary64)))))))
#s(approx (+ b a) (*.f64 (neg.f64 a) (-.f64 (/.f64 (neg.f64 b) a) #s(literal 1 binary64))))
#s(approx (sqrt (- a b)) (neg.f64 (*.f64 (sqrt.f64 a) #s(literal -1 binary64))))
#s(approx (sqrt (- a b)) (.f64 (neg.f64 a) (fma.f64 (.f64 (neg.f64 b) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 a a) a)))) #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 a)) #s(literal -1 binary64)))))
#s(approx (sqrt (- a b)) (.f64 (neg.f64 a) (fma.f64 (.f64 (sqrt.f64 (pow.f64 a #s(literal -5 binary64))) (neg.f64 (.f64 b b))) #s(literal -1/8 binary64) (fma.f64 (.f64 (neg.f64 b) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 a a) a)))) #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 a)) #s(literal -1 binary64))))))
#s(approx (sqrt (- a b)) (.f64 (neg.f64 a) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (pow.f64 a #s(literal -5 binary64)))) (neg.f64 (.f64 b b)) (fma.f64 (.f64 (.f64 (.f64 (.f64 b b) b) #s(literal -1 binary64)) (sqrt.f64 (pow.f64 a #s(literal -7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (.f64 (neg.f64 b) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 a a) a)))) #s(literal 1/2 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 a)) #s(literal -1 binary64)))))))
#s(approx (- a b) (*.f64 (neg.f64 a) (-.f64 (/.f64 b a) #s(literal 1 binary64))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) b) a) #s(literal 1/2 binary64) a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (fma.f64 (.f64 b (/.f64 (fma.f64 (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) (.f64 #s(literal 0 binary64) a)) (.f64 a a)) #s(literal 1/4 binary64) #s(literal 1 binary64)) a)) #s(literal -1/2 binary64) (.f64 (/.f64 (*.f64 #s(literal 0 binary64) a) a) #s(literal 1/2 binary64))) b a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (fma.f64 (fma.f64 (.f64 b (/.f64 (.f64 (fma.f64 (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) (.f64 #s(literal 0 binary64) a)) (.f64 a a)) #s(literal 1/4 binary64) #s(literal 1 binary64)) (.f64 #s(literal 0 binary64) a)) (.f64 (.f64 a a) a))) #s(literal 1/4 binary64) (.f64 (/.f64 (fma.f64 (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) (.f64 #s(literal 0 binary64) a)) (.f64 a a)) #s(literal 1/4 binary64) #s(literal 1 binary64)) a) #s(literal -1/2 binary64))) b (.f64 (/.f64 (.f64 #s(literal 0 binary64) a) a) #s(literal 1/2 binary64))) b a))
#s(approx (sqrt (+ b a)) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 a)) b) #s(literal 1/2 binary64) (sqrt.f64 a)))
#s(approx (sqrt (+ b a)) (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 a a) a))) b) #s(literal -1/8 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 a)) #s(literal 1/2 binary64))) b (sqrt.f64 a)))
#s(approx (sqrt (+ b a)) (fma.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (pow.f64 a #s(literal -5 binary64))) b) #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 a a) a))) #s(literal -1/8 binary64))) b (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 a)) #s(literal 1/2 binary64))) b (sqrt.f64 a)))
#s(approx b b)
#s(approx (sqrt (- a b)) (fma.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 a)) b) #s(literal -1/2 binary64) (sqrt.f64 a)))
#s(approx (sqrt (- a b)) (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 a a) a))) #s(literal -1/8 binary64)) b (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 a)))) b (sqrt.f64 a)))
#s(approx (sqrt (- a b)) (fma.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (pow.f64 a #s(literal -5 binary64))) b) #s(literal -1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 a a) a))) #s(literal -1/8 binary64))) b (*.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 a)))) b (sqrt.f64 a)))
#s(approx (- a b) (+.f64 (neg.f64 b) a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (.f64 (fma.f64 (/.f64 (.f64 #s(literal 0 binary64) a) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) b))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (.f64 (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 #s(literal 0 binary64) a) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)) (/.f64 (fma.f64 a a (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) (.f64 #s(literal 0 binary64) a)) #s(literal -1 binary64)))) (.f64 (*.f64 b b) (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64))) b))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 (fma.f64 a a (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) (.f64 #s(literal 0 binary64) a)) #s(literal -1 binary64)))) (.f64 #s(literal 0 binary64) a)) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (.f64 b b) b))) #s(literal -1/4 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 #s(literal 0 binary64) a) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)) (/.f64 (fma.f64 a a (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) (.f64 #s(literal 0 binary64) a)) #s(literal -1 binary64)))) (.f64 (.f64 b b) (sqrt.f64 #s(literal -1 binary64))))))) (sqrt.f64 #s(literal -1 binary64))) b))
#s(approx (sqrt (+ b a)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 b b) b))) (/.f64 #s(literal 1 binary64) (sqrt.f64 b))) b))
#s(approx (sqrt (+ b a)) (.f64 (+.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 b b) b))) (.f64 (.f64 #s(literal -1/8 binary64) (*.f64 a a)) (sqrt.f64 (pow.f64 b #s(literal -5 binary64))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 b))) b))
#s(approx (sqrt (+ b a)) (.f64 (+.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 a a)) (sqrt.f64 (pow.f64 b #s(literal -5 binary64))) (fma.f64 (.f64 #s(literal 1/16 binary64) (.f64 (.f64 a a) a)) (sqrt.f64 (pow.f64 b #s(literal -7 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 b b) b)))))) (/.f64 #s(literal 1 binary64) (sqrt.f64 b))) b))
#s(approx (+ b a) (*.f64 (+.f64 (/.f64 a b) #s(literal 1 binary64)) b))
#s(approx (sqrt (- a b)) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 a (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 b b) b))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) b) #s(literal -1 binary64)))) b))
#s(approx (sqrt (- a b)) (.f64 (fma.f64 (.f64 (/.f64 (.f64 a a) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (sqrt.f64 (pow.f64 b #s(literal -5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 a (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 b b) b))) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) b) #s(literal -1 binary64))))) b))
#s(approx (sqrt (- a b)) (.f64 (fma.f64 (.f64 (/.f64 (.f64 a a) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (sqrt.f64 (pow.f64 b #s(literal -5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (.f64 (/.f64 (.f64 (.f64 a a) a) (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64))) (sqrt.f64 (pow.f64 b #s(literal -7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 a (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 b b) b))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) b) #s(literal -1 binary64)))))) b))
#s(approx (- a b) (*.f64 (-.f64 (/.f64 a b) #s(literal 1 binary64)) b))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (*.f64 (neg.f64 b) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (.f64 (neg.f64 b) (fma.f64 (/.f64 (.f64 #s(literal 0 binary64) a) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)) #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (.f64 (neg.f64 b) (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (.f64 #s(literal 0 binary64) a) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (.f64 (/.f64 (fma.f64 a a (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) (.f64 #s(literal 0 binary64) a)) #s(literal -1 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)) #s(literal -1/2 binary64))) b)) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (.f64 (neg.f64 b) (+.f64 (neg.f64 (/.f64 (fma.f64 (/.f64 (.f64 #s(literal 0 binary64) a) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (neg.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 a a (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) (.f64 #s(literal 0 binary64) a)) #s(literal -1 binary64)))) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (.f64 (/.f64 (.f64 (fma.f64 a a (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 #s(literal 0 binary64) a) (.f64 #s(literal 0 binary64) a)) #s(literal -1 binary64)))) (.f64 #s(literal 0 binary64) a)) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) b)) #s(literal 1/4 binary64))) b))) b)) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (sqrt (+ b a)) (neg.f64 (*.f64 (sqrt.f64 b) #s(literal -1 binary64))))
#s(approx (sqrt (+ b a)) (.f64 (neg.f64 b) (fma.f64 (.f64 #s(literal 1/2 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 b b) b))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 b)) #s(literal -1 binary64)))))
#s(approx (sqrt (+ b a)) (.f64 (neg.f64 b) (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 a a) #s(literal -1 binary64))) (sqrt.f64 (pow.f64 b #s(literal -5 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 b b) b))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 b)) #s(literal -1 binary64))))))
#s(approx (sqrt (+ b a)) (.f64 (neg.f64 b) (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 a a) #s(literal -1 binary64))) (sqrt.f64 (pow.f64 b #s(literal -5 binary64))) (fma.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (.f64 a a) a) #s(literal 1 binary64))) (sqrt.f64 (pow.f64 b #s(literal -7 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 b b) b))) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 b)) #s(literal -1 binary64)))))))
#s(approx (+ b a) (*.f64 (neg.f64 b) (-.f64 (/.f64 (neg.f64 a) b) #s(literal 1 binary64))))
#s(approx (sqrt (- a b)) (neg.f64 (sqrt.f64 (neg.f64 b))))
#s(approx (sqrt (- a b)) (.f64 (neg.f64 b) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) a)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 b b) b))) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) b) #s(literal -1 binary64))))))
#s(approx (sqrt (- a b)) (.f64 (neg.f64 b) (fma.f64 (.f64 (.f64 (.f64 a a) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 b #s(literal -5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) a)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 b b) b))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) b) #s(literal -1 binary64)))))))
#s(approx (sqrt (- a b)) (.f64 (neg.f64 b) (fma.f64 (.f64 (.f64 (.f64 a a) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 b #s(literal -5 binary64)))) #s(literal -1/8 binary64) (fma.f64 (.f64 (.f64 (.f64 (.f64 a a) a) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 b #s(literal -7 binary64)))) #s(literal 1/16 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) a)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 b b) b))) (sqrt.f64 (*.f64 (/.f64 #s(literal 1 binary64) b) #s(literal -1 binary64))))))))
#s(approx (- a b) (*.f64 (neg.f64 b) (+.f64 (/.f64 (neg.f64 a) b) #s(literal 1 binary64))))

eval9.0ms (0.6%)

Memory: 10.7MiB live, 10.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 2 896 to 554 computations (80.9% saved)

prune4.0ms (0.3%)

Memory

-41.9MiB live, 4.8MiB allocated; 2ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	97	4	101

Accuracy

99.6%

Counts

101 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
✓	53.0%	(sqrt.f64 (*.f64 (+.f64 a b) (-.f64 a b)))
✓	1.1%	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
✓	98.6%	#s(approx (sqrt (- (* a a) (* b b))) a)

Compiler

Compiled 84 to 49 computations (41.7% saved)

regimes11.0ms (0.7%)

Memory

14.6MiB live, 14.6MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (- (* a a) (* b b))) a)
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
(sqrt.f64 (*.f64 (+.f64 a b) (-.f64 a b)))
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))

Outputs
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))

Calls

6 calls:

2.0ms	a
2.0ms	b
2.0ms	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
2.0ms	(*.f64 a a)
2.0ms	(-.f64 (.f64 a a) (.f64 b b))

Results

Accuracy	Segments	Branch
99.3%	1	`(*.f64 b b)`
99.3%	1	`(*.f64 a a)`
99.3%	1	`(-.f64 (.f64 a a) (.f64 b b))`
99.3%	1	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
99.3%	1	`a`
99.3%	1	`b`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes9.0ms (0.7%)

Memory

14.4MiB live, 14.4MiB allocated; 0ms collecting garbage

Accuracy

Total -62.4b remaining (-7048.8%)

Threshold costs -62.4b (-7048.8%)

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (- (* a a) (* b b))) a)
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
(sqrt.f64 (*.f64 (+.f64 a b) (-.f64 a b)))
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Outputs
#s(approx (sqrt (- (* a a) (* b b))) a)

Calls

6 calls:

2.0ms	a
2.0ms	b
1.0ms	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
1.0ms	(-.f64 (.f64 a a) (.f64 b b))
1.0ms	(*.f64 a a)

Results

Accuracy	Segments	Branch
98.6%	1	`(*.f64 b b)`
98.6%	1	`(*.f64 a a)`
98.6%	1	`(-.f64 (.f64 a a) (.f64 b b))`
98.6%	1	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
98.6%	1	`a`
98.6%	1	`b`

Compiler

Compiled 23 to 21 computations (8.7% saved)

derivations10.0ms (0.7%)

Memory

5.5MiB live, 5.5MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 19 to 12 computations (36.8% saved)

preprocess23.0ms (1.6%)

Memory: -21.1MiB live, 26.2MiB allocated; 7ms collecting garbage
Remove: (abs b)
Compiler: Compiled 168 to 120 computations (28.6% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze40.0ms (2.8%)

sample889.0ms (62.4%)

explain67.0ms (4.7%)

preprocess48.0ms (3.4%)

series7.0ms (0.5%)

rewrite59.0ms (4.2%)

eval5.0ms (0.4%)

prune2.0ms (0.1%)

series9.0ms (0.7%)

rewrite91.0ms (6.4%)

eval9.0ms (0.7%)

prune3.0ms (0.2%)

series13.0ms (0.9%)

rewrite116.0ms (8.2%)

eval9.0ms (0.6%)

prune4.0ms (0.3%)

regimes11.0ms (0.7%)

regimes9.0ms (0.7%)

derivations10.0ms (0.7%)

preprocess23.0ms (1.6%)

end0.0ms (0%)

Profiling