Metrics for bug366, discussion (missed optimization)

start0.0ms (0%)

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

analyze34.0ms (2.2%)

Memory

10.9MiB live, 53.2MiB allocated; 8ms 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)

sample1.1s (68.8%)

Memory

-60.3MiB live, 489.8MiB allocated; 950ms collecting garbage

Samples

802.0ms	8 256×	0	valid
25.0ms	635×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 310.0ms

ival-mult!: 204.0ms (65.8% of total)

ival-sqrt: 64.0ms (20.6% of total)

ival-sub!: 40.0ms (12.9% of total)

adjust: 2.0ms (0.6% of total)

Bogosity

preprocess67.0ms (4.3%)

Memory

-16.0MiB live, 33.5MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	50
1	75	50
2	293	50
3	546	50
4	1771	50
5	5877	50

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	0.5%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Symmetry

(abs a)

(abs b)

(sort a b)

Compiler

Compiled 12 to 12 computations (0% saved)

series6.0ms (0.4%)

Memory

6.2MiB live, 6.2MiB allocated; 0ms collecting garbage

Counts

6 → 30

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 (+ 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) (+ 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	@	-inf	((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) a (* b b) b)

rewrite57.0ms (3.6%)

Memory

-13.5MiB live, 32.9MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	157	835
0	160	799
0	941	774
1	2787	774

Stop Event

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

Counts

36 → 64

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 (+ 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) (+ 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)))
(fabs.f64 (sqrt.f64 (*.f64 (+.f64 a b) (-.f64 a b))))
(*.f64 (+.f64 a b) (-.f64 a b))
(neg.f64 (-.f64 (.f64 b b) (.f64 a a)))
(fma.f64 (fabs.f64 a) (fabs.f64 a) (*.f64 (neg.f64 b) b))
(fma.f64 (fabs.f64 a) (fabs.f64 a) (neg.f64 (*.f64 b b)))
(fma.f64 (neg.f64 a) (neg.f64 a) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 a) (neg.f64 a) (neg.f64 (*.f64 b b)))
(fma.f64 (.f64 b b) #s(literal -1 binary64) (.f64 a a))
(fma.f64 #s(literal -1 binary64) (.f64 b b) (.f64 a a))
(fma.f64 a a (*.f64 (neg.f64 b) b))
(fma.f64 a a (neg.f64 (*.f64 b b)))
(-.f64 (neg.f64 (.f64 b b)) (neg.f64 (.f64 a a)))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (neg.f64 (.f64 b b)) (.f64 a a))
(+.f64 (.f64 a a) (.f64 (neg.f64 b) b))
(+.f64 (.f64 a a) (neg.f64 (.f64 b b)))
(*.f64 (fabs.f64 a) (fabs.f64 a))
(*.f64 (neg.f64 a) (neg.f64 a))
(*.f64 a a)
(pow.f64 (fabs.f64 a) #s(literal 2 binary64))
(pow.f64 (neg.f64 a) #s(literal 2 binary64))
(pow.f64 a #s(literal 2 binary64))
(fabs.f64 (*.f64 a a))
a
(*.f64 (fabs.f64 b) (fabs.f64 b))
(*.f64 (neg.f64 b) (neg.f64 b))
(*.f64 b b)
(pow.f64 (fabs.f64 b) #s(literal 2 binary64))
(pow.f64 (neg.f64 b) #s(literal 2 binary64))
(pow.f64 b #s(literal 2 binary64))
(fabs.f64 (*.f64 b b))
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))) (.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 #s(literal -1/8 binary64) (pow.f64 b #s(literal 4 binary64))) (pow.f64 a #s(literal 4 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)) (fma.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))) #s(literal -1/16 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 b #s(literal 4 binary64))) (pow.f64 a #s(literal 4 binary64))))) 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 #s(literal -1/8 binary64) (pow.f64 b #s(literal 4 binary64))) (pow.f64 a #s(literal 4 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)) (fma.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))) #s(literal -1/16 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 b #s(literal 4 binary64))) (pow.f64 a #s(literal 4 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)) (*.f64 (+.f64 a b) (-.f64 a 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 a a) (.f64 (.f64 b b) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 a #s(literal 4 binary64))) (.f64 (pow.f64 b #s(literal 4 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (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 (pow.f64 a #s(literal 4 binary64)) (.f64 (pow.f64 b #s(literal 4 binary64)) (.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 (pow.f64 a #s(literal 6 binary64)) (.f64 (pow.f64 b #s(literal 6 binary64)) (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 a a) (.f64 (.f64 b b) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 a #s(literal 4 binary64))) (.f64 (pow.f64 b #s(literal 4 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (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 (pow.f64 a #s(literal 4 binary64)) (.f64 (pow.f64 b #s(literal 4 binary64)) (.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 (pow.f64 a #s(literal 6 binary64)) (.f64 (pow.f64 b #s(literal 6 binary64)) (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 (0.3%)

Memory: 6.8MiB live, 6.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 563 to 223 computations (60.4% saved)

prune3.0ms (0.2%)

Memory

4.0MiB live, 4.0MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	53	5	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	5	59

Accuracy

98.5%

Counts

59 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	0.5%	(sqrt.f64 (*.f64 (+.f64 a b) (-.f64 a b)))
▶	0.0%	(sqrt.f64 #s(approx (- (* a a) (* b b)) (.f64 (-.f64 (/.f64 (.f64 a a) (.f64 b b)) #s(literal 1 binary64)) (.f64 b b))))
▶	0.5%	(sqrt.f64 #s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b))))
▶	1.2%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a))
▶	1.9%	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))

Compiler

Compiled 96 to 94 computations (2.1% saved)

series22.0ms (1.4%)

Memory

-26.8MiB live, 19.3MiB allocated; 3ms collecting garbage

Counts

23 → 82

Calls

Call 1

Inputs
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
(neg.f64 a)
a
(sqrt.f64 #s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b))))
#s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b)))
(neg.f64 (*.f64 b b))
(*.f64 b b)
b
(sqrt.f64 (*.f64 (+.f64 a b) (-.f64 a b)))
(*.f64 (+.f64 a b) (-.f64 a b))
(+.f64 a b)
(-.f64 a b)
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a))
(fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a)
(/.f64 (*.f64 b b) a)
#s(literal -1/2 binary64)
(sqrt.f64 #s(approx (- (* a a) (* b b)) (.f64 (-.f64 (/.f64 (.f64 a a) (.f64 b b)) #s(literal 1 binary64)) (.f64 b b))))
#s(approx (- (* a a) (* b b)) (.f64 (-.f64 (/.f64 (.f64 a a) (.f64 b b)) #s(literal 1 binary64)) (.f64 b b)))
(.f64 (-.f64 (/.f64 (.f64 a a) (.f64 b b)) #s(literal 1 binary64)) (.f64 b b))
(-.f64 (/.f64 (.f64 a a) (.f64 b b)) #s(literal 1 binary64))
(/.f64 (.f64 a a) (.f64 b b))
(*.f64 a a)
#s(literal 1 binary64)

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 (neg a) #s(hole binary64 (* -1 a)))
#s(approx a #s(hole binary64 a))
#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 (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)) (* 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 (+ (* (/ (* b b) a) -1/2) a) #s(hole binary64 (* -1/2 (/ (pow b 2) a))))
#s(approx (+ (* (/ (* b b) a) -1/2) a) #s(hole binary64 (/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)))
#s(approx (/ (* b b) a) #s(hole binary64 (/ (pow b 2) a)))
#s(approx (* (- (/ (* a a) (* b b)) 1) (* b b)) #s(hole binary64 (+ (* -1 (pow b 2)) (pow a 2))))
#s(approx (- (/ (* a a) (* b b)) 1) #s(hole binary64 -1))
#s(approx (- (/ (* a a) (* b b)) 1) #s(hole binary64 (- (/ (pow a 2) (pow b 2)) 1)))
#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 (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) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))))
#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) (+ 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 (+ 1 (/ b a)))))
#s(approx (- a b) #s(hole binary64 (* a (+ 1 (* -1 (/ b a))))))
#s(approx (- (/ (* a a) (* b b)) 1) #s(hole binary64 (* (pow a 2) (- (/ 1 (pow b 2)) (/ 1 (pow a 2))))))
#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 (+ (* (/ (* b b) a) -1/2) a) #s(hole binary64 (* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 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 (* b b) #s(hole binary64 (pow b 2)))
#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 (- a b) #s(hole binary64 (+ a (* -1 b))))
#s(approx (- (/ (* a a) (* b b)) 1) #s(hole binary64 (/ (+ (* -1 (pow b 2)) (pow a 2)) (pow b 2))))
#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 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 (+ (* (/ (* b b) a) -1/2) a) #s(hole binary64 (* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))))
#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) (* -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
4.0ms	a	@	-inf	((sqrt (- (* a a) (* b b))) (neg a) a (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (neg (* b b)) (* b b) b (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) (- a b) (sqrt (- (* a a) (* b b))) (+ (* (/ (* b b) a) -1/2) a) (/ (* b b) a) -1/2 (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* (- (/ (* a a) (* b b)) 1) (* b b)) (- (/ (* a a) (* b b)) 1) (/ (* a a) (* b b)) (* a a) 1)
3.0ms	a	@	0	((sqrt (- (* a a) (* b b))) (neg a) a (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (neg (* b b)) (* b b) b (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) (- a b) (sqrt (- (* a a) (* b b))) (+ (* (/ (* b b) a) -1/2) a) (/ (* b b) a) -1/2 (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* (- (/ (* a a) (* b b)) 1) (* b b)) (- (/ (* a a) (* b b)) 1) (/ (* a a) (* b b)) (* a a) 1)
3.0ms	b	@	inf	((sqrt (- (* a a) (* b b))) (neg a) a (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (neg (* b b)) (* b b) b (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) (- a b) (sqrt (- (* a a) (* b b))) (+ (* (/ (* b b) a) -1/2) a) (/ (* b b) a) -1/2 (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* (- (/ (* a a) (* b b)) 1) (* b b)) (- (/ (* a a) (* b b)) 1) (/ (* a a) (* b b)) (* a a) 1)
3.0ms	a	@	inf	((sqrt (- (* a a) (* b b))) (neg a) a (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (neg (* b b)) (* b b) b (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) (- a b) (sqrt (- (* a a) (* b b))) (+ (* (/ (* b b) a) -1/2) a) (/ (* b b) a) -1/2 (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* (- (/ (* a a) (* b b)) 1) (* b b)) (- (/ (* a a) (* b b)) 1) (/ (* a a) (* b b)) (* a a) 1)
2.0ms	b	@	0	((sqrt (- (* a a) (* b b))) (neg a) a (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (neg (* b b)) (* b b) b (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) (- a b) (sqrt (- (* a a) (* b b))) (+ (* (/ (* b b) a) -1/2) a) (/ (* b b) a) -1/2 (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* (- (/ (* a a) (* b b)) 1) (* b b)) (- (/ (* a a) (* b b)) 1) (/ (* a a) (* b b)) (* a a) 1)

rewrite42.0ms (2.7%)

Memory

26.7MiB live, 26.7MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	471	2584
0	492	2528
1	1285	2528

Stop Event

1×	saturated
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

105 → 106

Calls

Call 1

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

eval9.0ms (0.6%)

Memory: 11.1MiB live, 11.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 322 to 533 computations (59.7% saved)

prune5.0ms (0.3%)

Memory

6.1MiB live, 6.1MiB allocated; 0ms collecting garbage

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	84	9	93

Accuracy

99.4%

Counts

93 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	0.5%	(sqrt.f64 (*.f64 (+.f64 a b) (-.f64 a b)))
▶	0.5%	(sqrt.f64 (.f64 (+.f64 a b) #s(approx (- a b) (.f64 b (-.f64 (/.f64 a b) #s(literal 1 binary64))))))
▶	0.5%	(sqrt.f64 (.f64 (+.f64 a b) #s(approx (- a b) (.f64 #s(literal -1 binary64) b))))
▶	0.5%	(sqrt.f64 (*.f64 #s(approx (+ a b) b) (-.f64 a b)))
✓	0.5%	(sqrt.f64 #s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b))))
✓	1.2%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a))
✓	1.9%	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
▶	0.3%	#s(approx (sqrt (* (+ a b) (- a b))) (+.f64 a (.f64 b (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))) a) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) a))))))
▶	5.0%	#s(approx (sqrt (* (+ a b) (- a b))) (+.f64 a (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b (+.f64 a (*.f64 #s(literal -1 binary64) a))) a))))

Compiler

Compiled 176 to 172 computations (2.3% saved)

series88.0ms (5.6%)

Memory

0.6MiB live, 98.1MiB allocated; 10ms collecting garbage

Counts

43 → 80

Calls

Call 1

Inputs
#s(approx (sqrt (* (+ a b) (- a b))) (+.f64 a (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b (+.f64 a (*.f64 #s(literal -1 binary64) a))) a))))
(+.f64 a (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b (+.f64 a (*.f64 #s(literal -1 binary64) a))) a)))
a
(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b (+.f64 a (*.f64 #s(literal -1 binary64) a))) a))
#s(literal 1/2 binary64)
(/.f64 (.f64 b (+.f64 a (.f64 #s(literal -1 binary64) a))) a)
(.f64 b (+.f64 a (.f64 #s(literal -1 binary64) a)))
b
(+.f64 a (*.f64 #s(literal -1 binary64) a))
(*.f64 #s(literal -1 binary64) a)
#s(literal -1 binary64)
(sqrt.f64 (*.f64 #s(approx (+ a b) b) (-.f64 a b)))
(*.f64 #s(approx (+ a b) b) (-.f64 a b))
#s(approx (+ a b) b)
(-.f64 a b)
(sqrt.f64 (.f64 (+.f64 a b) #s(approx (- a b) (.f64 #s(literal -1 binary64) b))))
(.f64 (+.f64 a b) #s(approx (- a b) (.f64 #s(literal -1 binary64) b)))
(+.f64 a b)
#s(approx (- a b) (*.f64 #s(literal -1 binary64) b))
(*.f64 #s(literal -1 binary64) b)
(sqrt.f64 (.f64 (+.f64 a b) #s(approx (- a b) (.f64 b (-.f64 (/.f64 a b) #s(literal 1 binary64))))))
(.f64 (+.f64 a b) #s(approx (- a b) (.f64 b (-.f64 (/.f64 a b) #s(literal 1 binary64)))))
#s(approx (- a b) (*.f64 b (-.f64 (/.f64 a b) #s(literal 1 binary64))))
(*.f64 b (-.f64 (/.f64 a b) #s(literal 1 binary64)))
(-.f64 (/.f64 a b) #s(literal 1 binary64))
(/.f64 a b)
#s(literal 1 binary64)
#s(approx (sqrt (* (+ a b) (- a b))) (+.f64 a (.f64 b (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))) a) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) a))))))
(+.f64 a (.f64 b (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))) a) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) a)))))
(.f64 b (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))) a) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) a))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))) a) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (*.f64 #s(literal -1 binary64) a)) a)))
#s(literal -1/2 binary64)
(/.f64 (.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (*.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))) a)
(.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (*.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64))))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))
(.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64))))
#s(literal 1/4 binary64)
(/.f64 (pow.f64 (+.f64 a (*.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))
(pow.f64 (+.f64 a (*.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64))
#s(literal 2 binary64)
(pow.f64 a #s(literal 2 binary64))
(.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) a))
(/.f64 (+.f64 a (*.f64 #s(literal -1 binary64) a)) a)

Outputs
#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 (* 1/2 (/ (* b (+ a (* -1 a))) a))) #s(hole binary64 a))
#s(approx (* 1/2 (/ (* b (+ a (* -1 a))) a)) #s(hole binary64 0))
#s(approx (* -1 a) #s(hole binary64 (* -1 a)))
#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 (* b (- (/ a b) 1)) #s(hole binary64 (+ a (* -1 b))))
#s(approx (- (/ a b) 1) #s(hole binary64 -1))
#s(approx (- (/ a b) 1) #s(hole binary64 (- (/ a b) 1)))
#s(approx (/ a b) #s(hole binary64 (/ a b)))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* -1/2 (/ (pow b 2) a))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* -1/2 (/ b a))))
#s(approx (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a) #s(hole binary64 (/ b a)))
#s(approx (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) #s(hole binary64 1))
#s(approx (pow a 2) #s(hole binary64 (pow a 2)))
#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) (+ 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 (+ 1 (/ b a)))))
#s(approx (- a b) #s(hole binary64 (* a (+ 1 (* -1 (/ b a))))))
#s(approx (- (/ a b) 1) #s(hole binary64 (* a (- (/ 1 b) (/ 1 a)))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#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 (- (/ a b) 1) #s(hole binary64 (* -1 (* a (- (/ 1 a) (/ 1 b))))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))))
#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 (* 1/2 (/ (* b (+ a (* -1 a))) a)) #s(hole binary64 (* 1/2 (/ (* b (+ a (* -1 a))) a))))
#s(approx (/ (* b (+ a (* -1 a))) a) #s(hole binary64 (/ (* b (+ a (* -1 a))) a)))
#s(approx (* b (+ a (* -1 a))) #s(hole binary64 (* b (+ a (* -1 a)))))
#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 (- (/ a b) 1) #s(hole binary64 (/ (+ a (* -1 b)) b)))
#s(approx (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))) #s(hole binary64 (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* 1/2 (/ (+ a (* -1 a)) a))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
#s(approx (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a) #s(hole binary64 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)))
#s(approx (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) #s(hole binary64 (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))))))
#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 (* 1/2 (/ (* b (+ a (* -1 a))) a))) #s(hole binary64 (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (/ a b)))))
#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 (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* -1/2 (/ (* (pow b 2) (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* (pow b 2) (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/2 (/ (+ a (* -1 a)) (* a b)))))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* (pow b 2) (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (+ (* 1/2 (/ (+ a (* -1 a)) (* a b))) (/ a (pow b 2)))))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/2 (/ (+ a (* -1 a)) (* a b)))))))
#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 (* 1/2 (/ (* b (+ a (* -1 a))) a))) #s(hole binary64 (* -1 (* b (+ (* -1 (/ a b)) (* -1/2 (/ (+ a (* -1 a)) a)))))))
#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)))))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* (pow b 2) (+ (* -1 (/ (+ (* -1 (/ a b)) (* -1/2 (/ (+ a (* -1 a)) a))) b)) (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a))))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* -1 (* b (+ (* -1/2 (/ (+ a (* -1 a)) (* a b))) (* 1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)))))))

Calls

6 calls:

Time	Variable		Point	Expression
65.0ms	a	@	0	((sqrt (* (+ a b) (- a b))) (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a (* 1/2 (/ (* b (+ a (* -1 a))) a)) 1/2 (/ (* b (+ a (* -1 a))) a) (* b (+ a (* -1 a))) b (+ a (* -1 a)) (* -1 a) -1 (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) (- a b) (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) (- a b) (* -1 b) (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (- a b) (* b (- (/ a b) 1)) (- (/ a b) 1) (/ a b) 1 (sqrt (* (+ a b) (- a b))) (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))) (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a) (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))) 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)) (pow (+ a (* -1 a)) 2) 2 (pow a 2) (* 1/2 (/ (+ a (* -1 a)) a)) (/ (+ a (* -1 a)) a))
5.0ms	b	@	-inf	((sqrt (* (+ a b) (- a b))) (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a (* 1/2 (/ (* b (+ a (* -1 a))) a)) 1/2 (/ (* b (+ a (* -1 a))) a) (* b (+ a (* -1 a))) b (+ a (* -1 a)) (* -1 a) -1 (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) (- a b) (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) (- a b) (* -1 b) (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (- a b) (* b (- (/ a b) 1)) (- (/ a b) 1) (/ a b) 1 (sqrt (* (+ a b) (- a b))) (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))) (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a) (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))) 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)) (pow (+ a (* -1 a)) 2) 2 (pow a 2) (* 1/2 (/ (+ a (* -1 a)) a)) (/ (+ a (* -1 a)) a))
5.0ms	b	@	0	((sqrt (* (+ a b) (- a b))) (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a (* 1/2 (/ (* b (+ a (* -1 a))) a)) 1/2 (/ (* b (+ a (* -1 a))) a) (* b (+ a (* -1 a))) b (+ a (* -1 a)) (* -1 a) -1 (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) (- a b) (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) (- a b) (* -1 b) (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (- a b) (* b (- (/ a b) 1)) (- (/ a b) 1) (/ a b) 1 (sqrt (* (+ a b) (- a b))) (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))) (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a) (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))) 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)) (pow (+ a (* -1 a)) 2) 2 (pow a 2) (* 1/2 (/ (+ a (* -1 a)) a)) (/ (+ a (* -1 a)) a))
4.0ms	b	@	inf	((sqrt (* (+ a b) (- a b))) (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a (* 1/2 (/ (* b (+ a (* -1 a))) a)) 1/2 (/ (* b (+ a (* -1 a))) a) (* b (+ a (* -1 a))) b (+ a (* -1 a)) (* -1 a) -1 (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) (- a b) (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) (- a b) (* -1 b) (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (- a b) (* b (- (/ a b) 1)) (- (/ a b) 1) (/ a b) 1 (sqrt (* (+ a b) (- a b))) (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))) (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a) (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))) 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)) (pow (+ a (* -1 a)) 2) 2 (pow a 2) (* 1/2 (/ (+ a (* -1 a)) a)) (/ (+ a (* -1 a)) a))
3.0ms	a	@	-inf	((sqrt (* (+ a b) (- a b))) (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a (* 1/2 (/ (* b (+ a (* -1 a))) a)) 1/2 (/ (* b (+ a (* -1 a))) a) (* b (+ a (* -1 a))) b (+ a (* -1 a)) (* -1 a) -1 (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) (- a b) (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (+ a b) (- a b) (* -1 b) (sqrt (* (+ a b) (- a b))) (* (+ a b) (- a b)) (- a b) (* b (- (/ a b) 1)) (- (/ a b) 1) (/ a b) 1 (sqrt (* (+ a b) (- a b))) (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))) (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a) (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))) 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)) (pow (+ a (* -1 a)) 2) 2 (pow a 2) (* 1/2 (/ (+ a (* -1 a)) a)) (/ (+ a (* -1 a)) a))

rewrite42.0ms (2.6%)

Memory

-20.4MiB live, 25.7MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	412	3091
0	462	3046
1	1102	3046

Stop Event

1×	saturated
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

123 → 124

Calls

Call 1

Inputs
#s(approx (sqrt (* (+ a b) (- a b))) (+.f64 a (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b (+.f64 a (*.f64 #s(literal -1 binary64) a))) a))))
(+.f64 a (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b (+.f64 a (*.f64 #s(literal -1 binary64) a))) a)))
a
(.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b (+.f64 a (*.f64 #s(literal -1 binary64) a))) a))
#s(literal 1/2 binary64)
(/.f64 (.f64 b (+.f64 a (.f64 #s(literal -1 binary64) a))) a)
(.f64 b (+.f64 a (.f64 #s(literal -1 binary64) a)))
b
(+.f64 a (*.f64 #s(literal -1 binary64) a))
(*.f64 #s(literal -1 binary64) a)
#s(literal -1 binary64)
(sqrt.f64 (*.f64 #s(approx (+ a b) b) (-.f64 a b)))
(*.f64 #s(approx (+ a b) b) (-.f64 a b))
#s(approx (+ a b) b)
(-.f64 a b)
(sqrt.f64 (.f64 (+.f64 a b) #s(approx (- a b) (.f64 #s(literal -1 binary64) b))))
(.f64 (+.f64 a b) #s(approx (- a b) (.f64 #s(literal -1 binary64) b)))
(+.f64 a b)
#s(approx (- a b) (*.f64 #s(literal -1 binary64) b))
(*.f64 #s(literal -1 binary64) b)
(sqrt.f64 (.f64 (+.f64 a b) #s(approx (- a b) (.f64 b (-.f64 (/.f64 a b) #s(literal 1 binary64))))))
(.f64 (+.f64 a b) #s(approx (- a b) (.f64 b (-.f64 (/.f64 a b) #s(literal 1 binary64)))))
#s(approx (- a b) (*.f64 b (-.f64 (/.f64 a b) #s(literal 1 binary64))))
(*.f64 b (-.f64 (/.f64 a b) #s(literal 1 binary64)))
(-.f64 (/.f64 a b) #s(literal 1 binary64))
(/.f64 a b)
#s(literal 1 binary64)
#s(approx (sqrt (* (+ a b) (- a b))) (+.f64 a (.f64 b (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))) a) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) a))))))
(+.f64 a (.f64 b (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))) a) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) a)))))
(.f64 b (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))) a) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) a))))
(fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))) a) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (*.f64 #s(literal -1 binary64) a)) a)))
#s(literal -1/2 binary64)
(/.f64 (.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (*.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))) a)
(.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (*.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64))))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))
(.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64))))
#s(literal 1/4 binary64)
(/.f64 (pow.f64 (+.f64 a (*.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))
(pow.f64 (+.f64 a (*.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64))
#s(literal 2 binary64)
(pow.f64 a #s(literal 2 binary64))
(.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) a))
(/.f64 (+.f64 a (*.f64 #s(literal -1 binary64) a)) 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 (* 1/2 (/ (* b (+ a (* -1 a))) a))) #s(hole binary64 a))
#s(approx (* 1/2 (/ (* b (+ a (* -1 a))) a)) #s(hole binary64 0))
#s(approx (* -1 a) #s(hole binary64 (* -1 a)))
#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 (* b (- (/ a b) 1)) #s(hole binary64 (+ a (* -1 b))))
#s(approx (- (/ a b) 1) #s(hole binary64 -1))
#s(approx (- (/ a b) 1) #s(hole binary64 (- (/ a b) 1)))
#s(approx (/ a b) #s(hole binary64 (/ a b)))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* -1/2 (/ (pow b 2) a))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* -1/2 (/ b a))))
#s(approx (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a) #s(hole binary64 (/ b a)))
#s(approx (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) #s(hole binary64 1))
#s(approx (pow a 2) #s(hole binary64 (pow a 2)))
#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) (+ 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 (+ 1 (/ b a)))))
#s(approx (- a b) #s(hole binary64 (* a (+ 1 (* -1 (/ b a))))))
#s(approx (- (/ a b) 1) #s(hole binary64 (* a (- (/ 1 b) (/ 1 a)))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#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 (- (/ a b) 1) #s(hole binary64 (* -1 (* a (- (/ 1 a) (/ 1 b))))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))))
#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 (* 1/2 (/ (* b (+ a (* -1 a))) a)) #s(hole binary64 (* 1/2 (/ (* b (+ a (* -1 a))) a))))
#s(approx (/ (* b (+ a (* -1 a))) a) #s(hole binary64 (/ (* b (+ a (* -1 a))) a)))
#s(approx (* b (+ a (* -1 a))) #s(hole binary64 (* b (+ a (* -1 a)))))
#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 (- (/ a b) 1) #s(hole binary64 (/ (+ a (* -1 b)) b)))
#s(approx (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))) #s(hole binary64 (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* 1/2 (/ (+ a (* -1 a)) a))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
#s(approx (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a) #s(hole binary64 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)))
#s(approx (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) #s(hole binary64 (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))))))
#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 (* 1/2 (/ (* b (+ a (* -1 a))) a))) #s(hole binary64 (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (/ a b)))))
#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 (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* -1/2 (/ (* (pow b 2) (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* (pow b 2) (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/2 (/ (+ a (* -1 a)) (* a b)))))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* (pow b 2) (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (+ (* 1/2 (/ (+ a (* -1 a)) (* a b))) (/ a (pow b 2)))))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/2 (/ (+ a (* -1 a)) (* a b)))))))
#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 (* 1/2 (/ (* b (+ a (* -1 a))) a))) #s(hole binary64 (* -1 (* b (+ (* -1 (/ a b)) (* -1/2 (/ (+ a (* -1 a)) a)))))))
#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)))))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* (pow b 2) (+ (* -1 (/ (+ (* -1 (/ a b)) (* -1/2 (/ (+ a (* -1 a)) a))) b)) (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a))))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* -1 (* b (+ (* -1/2 (/ (+ a (* -1 a)) (* a b))) (* 1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)))))))

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

eval8.0ms (0.5%)

Memory: 10.4MiB live, 10.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 449 to 529 computations (63.5% saved)

prune3.0ms (0.2%)

Memory

3.5MiB live, 3.5MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	0	0
Picked	4	1	5
Done	2	2	4
Total	81	5	86

Accuracy

99.5%

Counts

86 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	0.5%	(sqrt.f64 (*.f64 (+.f64 a b) (-.f64 a b)))
✓	0.5%	(sqrt.f64 (.f64 (+.f64 a b) #s(approx (- a b) (.f64 b (-.f64 (/.f64 a b) #s(literal 1 binary64))))))
✓	1.9%	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
▶	0.9%	#s(approx (sqrt (* (+ a b) (- a b))) (+.f64 a (.f64 b #s(approx (+ ( -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (*.f64 #s(literal -1/2 binary64) (/.f64 b a))))))
▶	5.0%	#s(approx (sqrt (* (+ a b) (- a b))) #s(approx (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a))

Compiler

Compiled 75 to 73 computations (2.7% saved)

series18.0ms (1.1%)

Memory

-29.8MiB live, 16.5MiB allocated; 3ms collecting garbage

Counts

11 → 42

Calls

Call 1

Inputs
#s(approx (sqrt (* (+ a b) (- a b))) #s(approx (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a))
#s(approx (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a)
a
#s(approx (sqrt (* (+ a b) (- a b))) (+.f64 a (.f64 b #s(approx (+ ( -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (*.f64 #s(literal -1/2 binary64) (/.f64 b a))))))
(+.f64 a (.f64 b #s(approx (+ ( -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (*.f64 #s(literal -1/2 binary64) (/.f64 b a)))))
(.f64 b #s(approx (+ ( -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (*.f64 #s(literal -1/2 binary64) (/.f64 b a))))
b
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (*.f64 #s(literal -1/2 binary64) (/.f64 b a)))
(*.f64 #s(literal -1/2 binary64) (/.f64 b a))
#s(literal -1/2 binary64)
(/.f64 b a)

Outputs
#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 (* 1/2 (/ (* b (+ a (* -1 a))) a))) #s(hole binary64 a))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* -1/2 (/ (pow b 2) a))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* -1/2 (/ b a))))
#s(approx (/ b a) #s(hole binary64 (/ b 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 (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#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 (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))))
#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 (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))) #s(hole binary64 (* 1/2 (/ (* b (+ a (* -1 a))) a))))
#s(approx (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))) #s(hole binary64 (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))))
#s(approx b #s(hole binary64 b))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* 1/2 (/ (+ a (* -1 a)) a))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (+ (* -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 (* 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 (* 1/2 (/ (* b (+ a (* -1 a))) a))) #s(hole binary64 (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (/ a b)))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* -1/2 (/ (* (pow b 2) (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* (pow b 2) (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/2 (/ (+ a (* -1 a)) (* a b)))))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* (pow b 2) (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (+ (* 1/2 (/ (+ a (* -1 a)) (* a b))) (/ a (pow b 2)))))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/2 (/ (+ a (* -1 a)) (* a b)))))))
#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 (* 1/2 (/ (* b (+ a (* -1 a))) a))) #s(hole binary64 (* -1 (* b (+ (* -1 (/ a b)) (* -1/2 (/ (+ a (* -1 a)) a)))))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* (pow b 2) (+ (* -1 (/ (+ (* -1 (/ a b)) (* -1/2 (/ (+ a (* -1 a)) a))) b)) (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a))))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* -1 (* b (+ (* -1/2 (/ (+ a (* -1 a)) (* a b))) (* 1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)))))))

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	b	@	inf	((sqrt (* (+ a b) (- a b))) (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a (sqrt (* (+ a b) (- a b))) (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))) b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (* -1/2 (/ b a)) -1/2 (/ b a))
3.0ms	a	@	0	((sqrt (* (+ a b) (- a b))) (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a (sqrt (* (+ a b) (- a b))) (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))) b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (* -1/2 (/ b a)) -1/2 (/ b a))
2.0ms	b	@	-inf	((sqrt (* (+ a b) (- a b))) (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a (sqrt (* (+ a b) (- a b))) (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))) b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (* -1/2 (/ b a)) -1/2 (/ b a))
2.0ms	b	@	0	((sqrt (* (+ a b) (- a b))) (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a (sqrt (* (+ a b) (- a b))) (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))) b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (* -1/2 (/ b a)) -1/2 (/ b a))
1.0ms	a	@	-inf	((sqrt (* (+ a b) (- a b))) (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a (sqrt (* (+ a b) (- a b))) (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))) b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (* -1/2 (/ b a)) -1/2 (/ b a))

rewrite30.0ms (1.9%)

Memory

19.4MiB live, 19.4MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	273	2238
0	277	2182
1	765	2182

Stop Event

1×	saturated
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

53 → 53

Calls

Call 1

Inputs
#s(approx (sqrt (* (+ a b) (- a b))) #s(approx (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a))
#s(approx (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a)
a
#s(approx (sqrt (* (+ a b) (- a b))) (+.f64 a (.f64 b #s(approx (+ ( -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (*.f64 #s(literal -1/2 binary64) (/.f64 b a))))))
(+.f64 a (.f64 b #s(approx (+ ( -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (*.f64 #s(literal -1/2 binary64) (/.f64 b a)))))
(.f64 b #s(approx (+ ( -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (*.f64 #s(literal -1/2 binary64) (/.f64 b a))))
b
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (*.f64 #s(literal -1/2 binary64) (/.f64 b a)))
(*.f64 #s(literal -1/2 binary64) (/.f64 b a))
#s(literal -1/2 binary64)
(/.f64 b 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 (* 1/2 (/ (* b (+ a (* -1 a))) a))) #s(hole binary64 a))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* -1/2 (/ (pow b 2) a))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* -1/2 (/ b a))))
#s(approx (/ b a) #s(hole binary64 (/ b 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 (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#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 (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))))
#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 (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))) #s(hole binary64 (* 1/2 (/ (* b (+ a (* -1 a))) a))))
#s(approx (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))) #s(hole binary64 (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))))
#s(approx b #s(hole binary64 b))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* 1/2 (/ (+ a (* -1 a)) a))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (+ (* -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 (* 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 (* 1/2 (/ (* b (+ a (* -1 a))) a))) #s(hole binary64 (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (/ a b)))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* -1/2 (/ (* (pow b 2) (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* (pow b 2) (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/2 (/ (+ a (* -1 a)) (* a b)))))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* (pow b 2) (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (+ (* 1/2 (/ (+ a (* -1 a)) (* a b))) (/ a (pow b 2)))))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/2 (/ (+ a (* -1 a)) (* a b)))))))
#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 (* 1/2 (/ (* b (+ a (* -1 a))) a))) #s(hole binary64 (* -1 (* b (+ (* -1 (/ a b)) (* -1/2 (/ (+ a (* -1 a)) a)))))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) #s(hole binary64 (* (pow b 2) (+ (* -1 (/ (+ (* -1 (/ a b)) (* -1/2 (/ (+ a (* -1 a)) a))) b)) (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a))))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) #s(hole binary64 (* -1 (* b (+ (* -1/2 (/ (+ a (* -1 a)) (* a b))) (* 1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)))))))

Outputs
#s(approx (sqrt (* (+ a b) (- a b))) #s(approx (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a))
#s(approx (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a)
a
#s(approx (sqrt (* (+ a b) (- a b))) (+.f64 a (.f64 b #s(approx (+ ( -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (*.f64 #s(literal -1/2 binary64) (/.f64 b a))))))
(+.f64 a (.f64 b #s(approx (+ ( -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (*.f64 #s(literal -1/2 binary64) (/.f64 b a)))))
(.f64 b #s(approx (+ ( -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (*.f64 #s(literal -1/2 binary64) (/.f64 b a))))
b
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (*.f64 #s(literal -1/2 binary64) (/.f64 b a)))
(*.f64 #s(literal -1/2 binary64) (/.f64 b a))
#s(literal -1/2 binary64)
(/.f64 b a)
#s(approx (sqrt (* (+ a b) (- a b))) (*.f64 b (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (* (+ a b) (- a b))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 a (+.f64 b (.f64 #s(literal -1 binary64) b))) (.f64 b (sqrt.f64 #s(literal -1 binary64)))) (.f64 b (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (sqrt (* (+ a b) (- a b))) (fma.f64 a (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 a (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 b (.f64 #s(literal -1 binary64) b)) #s(literal 2 binary64)) (.f64 (pow.f64 b #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))))) (.f64 b (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 b (.f64 #s(literal -1 binary64) b)) (.f64 b (sqrt.f64 #s(literal -1 binary64)))))) (*.f64 b (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (sqrt (* (+ a b) (- a b))) (fma.f64 a (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 b (.f64 #s(literal -1 binary64) b)) (.f64 b (sqrt.f64 #s(literal -1 binary64)))) (.f64 a (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 a (.f64 (+.f64 b (.f64 #s(literal -1 binary64) b)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 b (.f64 #s(literal -1 binary64) b)) #s(literal 2 binary64)) (.f64 (pow.f64 b #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))))) (.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 b (.f64 #s(literal -1 binary64) b)) #s(literal 2 binary64)) (.f64 (pow.f64 b #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))) (.f64 b (sqrt.f64 #s(literal -1 binary64)))))))) (.f64 b (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a)
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (*.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 b #s(literal 2 binary64)) a)))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (/.f64 (fma.f64 #s(literal -1/2 binary64) (pow.f64 b #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64))) a))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (*.f64 #s(literal -1/2 binary64) (/.f64 b a)))
#s(approx (/ b a) (/.f64 b a))
#s(approx (sqrt (* (+ a b) (- a b))) (.f64 a (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 b (*.f64 #s(literal -1 binary64) b)) a)))))
#s(approx (sqrt (* (+ a b) (- a b))) (.f64 a (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 b (.f64 #s(literal -1 binary64) b)) a) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal -1 binary64) (pow.f64 b #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 b (.f64 #s(literal -1 binary64) b)) #s(literal 2 binary64)))) (pow.f64 a #s(literal 2 binary64))))))))
#s(approx (sqrt (* (+ a b) (- a b))) (.f64 a (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 b (.f64 #s(literal -1 binary64) b)) (-.f64 (.f64 #s(literal -1 binary64) (pow.f64 b #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 b (.f64 #s(literal -1 binary64) b)) #s(literal 2 binary64))))) (pow.f64 a #s(literal 3 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 b (.f64 #s(literal -1 binary64) b)) a) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (.f64 #s(literal -1 binary64) (pow.f64 b #s(literal 2 binary64))) (.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 b (*.f64 #s(literal -1 binary64) b)) #s(literal 2 binary64)))) (pow.f64 a #s(literal 2 binary64)))))))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (.f64 a (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 b #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))))
#s(approx (sqrt (* (+ a b) (- a b))) (.f64 #s(literal -1 binary64) (.f64 a (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))
#s(approx (sqrt (* (+ a b) (- a b))) (.f64 #s(literal -1 binary64) (.f64 a (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 b (*.f64 #s(literal -1 binary64) b)) a) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))))
#s(approx (sqrt (* (+ a b) (- a b))) (.f64 #s(literal -1 binary64) (.f64 a (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (pow.f64 b #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 b (.f64 #s(literal -1 binary64) b)) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))) a) (.f64 #s(literal 1/2 binary64) (+.f64 b (.f64 #s(literal -1 binary64) b)))) a) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))))
#s(approx (sqrt (* (+ a b) (- a b))) (.f64 #s(literal -1 binary64) (.f64 a (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (+.f64 b (.f64 #s(literal -1 binary64) b)) (-.f64 (pow.f64 b #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 b (.f64 #s(literal -1 binary64) b)) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))) (.f64 a (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))) (.f64 #s(literal 1/2 binary64) (-.f64 (pow.f64 b #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 b (.f64 #s(literal -1 binary64) b)) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))))) a) (.f64 #s(literal 1/2 binary64) (+.f64 b (.f64 #s(literal -1 binary64) b)))) a) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (.f64 #s(literal -1 binary64) (.f64 a (-.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 b #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))) #s(literal 1 binary64)))))
#s(approx (sqrt (* (+ a b) (- a b))) (+.f64 a (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b (+.f64 a (*.f64 #s(literal -1 binary64) a))) a))))
#s(approx (sqrt (* (+ a b) (- a b))) (+.f64 a (.f64 b (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))) a) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) a))))))
#s(approx (sqrt (* (+ a b) (- a b))) (+.f64 a (.f64 b (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) a) (.f64 b (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64))))) a) (.f64 #s(literal 1/4 binary64) (/.f64 (.f64 b (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64))))) (+.f64 a (*.f64 #s(literal -1 binary64) a)))) (pow.f64 a #s(literal 3 binary64))))))))))
#s(approx (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b (+.f64 a (*.f64 #s(literal -1 binary64) a))) a)))
#s(approx (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))) (.f64 b (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))) a) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) a)))))
#s(approx b b)
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) a)))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))) a) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (*.f64 #s(literal -1 binary64) a)) a))))
#s(approx (sqrt (* (+ a b) (- a b))) (.f64 b (+.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) (.f64 b (sqrt.f64 #s(literal -1 binary64))))))))
#s(approx (sqrt (* (+ a b) (- a b))) (.f64 b (+.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) (.f64 b (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (pow.f64 a #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))) (*.f64 (pow.f64 b #s(literal 2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))))))
#s(approx (sqrt (* (+ a b) (- a b))) (.f64 b (+.f64 (sqrt.f64 #s(literal -1 binary64)) (fma.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) (-.f64 (pow.f64 a #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))) (.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) (.f64 b (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (pow.f64 a #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))) (.f64 (pow.f64 b #s(literal 2 binary64)) (sqrt.f64 #s(literal -1 binary64))))))))))
#s(approx (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) (.f64 b (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) a) (/.f64 a b))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (pow.f64 b #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))) a)))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (.f64 (pow.f64 b #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64))))) a) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) (.f64 a b))))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (.f64 (pow.f64 b #s(literal 2 binary64)) (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64))))) a) (fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) (*.f64 a b)) (/.f64 a (pow.f64 b #s(literal 2 binary64)))))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (.f64 #s(literal -1/2 binary64) (/.f64 (.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))) a)))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (.f64 b (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64))))) a) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) (.f64 a b))))))
#s(approx (sqrt (* (+ a b) (- a b))) (.f64 #s(literal -1 binary64) (.f64 b (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (sqrt (* (+ a b) (- a b))) (.f64 #s(literal -1 binary64) (.f64 b (+.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) (*.f64 b (sqrt.f64 #s(literal -1 binary64)))))))))
#s(approx (sqrt (* (+ a b) (- a b))) (.f64 #s(literal -1 binary64) (.f64 b (+.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (pow.f64 a #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))) (.f64 b (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) (sqrt.f64 #s(literal -1 binary64))))) b))))))
#s(approx (sqrt (* (+ a b) (- a b))) (.f64 #s(literal -1 binary64) (.f64 b (+.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal 1/4 binary64) (/.f64 (.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) (-.f64 (pow.f64 a #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64)))))) (.f64 b (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)))) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (pow.f64 a #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 2 binary64))))) (sqrt.f64 #s(literal -1 binary64))))) b) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (*.f64 #s(literal -1 binary64) a)) (sqrt.f64 #s(literal -1 binary64))))) b))))))
#s(approx (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) (.f64 #s(literal -1 binary64) (.f64 b (fma.f64 #s(literal -1 binary64) (/.f64 a b) (.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) a))))))
#s(approx (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))))) (.f64 (pow.f64 b #s(literal 2 binary64)) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 a b) (.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) a))) b) (.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64))))) a)))))
#s(approx (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (.f64 #s(literal -1 binary64) (.f64 b (fma.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) (.f64 a b)) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (*.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64))))) a))))))

eval4.0ms (0.3%)

Memory: 5.3MiB live, 5.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 042 to 309 computations (70.3% saved)

prune4.0ms (0.2%)

Memory

4.6MiB live, 4.6MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	40	5	45

Accuracy

99.5%

Counts

45 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	0.5%	(sqrt.f64 (*.f64 (+.f64 a b) (-.f64 a b)))
✓	0.5%	(sqrt.f64 (.f64 (+.f64 a b) #s(approx (- a b) (.f64 b (-.f64 (/.f64 a b) #s(literal 1 binary64))))))
✓	1.9%	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
✓	0.9%	#s(approx (sqrt (* (+ a b) (- a b))) (+.f64 a (.f64 b #s(approx (+ ( -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (*.f64 #s(literal -1/2 binary64) (/.f64 b a))))))
✓	5.0%	#s(approx (sqrt (* (+ a b) (- a b))) #s(approx (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a))

Compiler

Compiled 206 to 174 computations (15.5% saved)

regimes27.0ms (1.7%)

Memory

-22.6MiB live, 24.8MiB allocated; 7ms collecting garbage

Accuracy

Total -3.2b remaining (-5.2%)

Threshold costs -3.2b (-5.2%)

Counts

13 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (* (+ a b) (- a b))) #s(approx (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a))
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
(sqrt.f64 #s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b))))
(sqrt.f64 (*.f64 #s(approx (+ a b) b) (-.f64 a b)))
(sqrt.f64 (*.f64 (+.f64 a b) (-.f64 a b)))
(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
(sqrt.f64 (.f64 (+.f64 a b) #s(approx (- a b) (.f64 #s(literal -1 binary64) b))))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a))
#s(approx (sqrt (* (+ a b) (- a b))) (+.f64 a (.f64 b #s(approx (+ ( -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a))) (*.f64 #s(literal -1/2 binary64) (/.f64 b a))))))
(sqrt.f64 (.f64 (+.f64 a b) #s(approx (- a b) (.f64 b (-.f64 (/.f64 a b) #s(literal 1 binary64))))))
#s(approx (sqrt (* (+ a b) (- a b))) (+.f64 a (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 b (+.f64 a (*.f64 #s(literal -1 binary64) a))) a))))
(sqrt.f64 #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 b) (- a b))) (+.f64 a (.f64 b (fma.f64 #s(literal -1/2 binary64) (/.f64 (.f64 b (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (/.f64 (pow.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 2 binary64)))))) a) (.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 a (.f64 #s(literal -1 binary64) a)) a))))))

Outputs
#s(approx (sqrt (* (+ a b) (- a b))) #s(approx (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a))) a))

Calls

6 calls:

6.0ms	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
5.0ms	(-.f64 (.f64 a a) (.f64 b b))
4.0ms	b
4.0ms	a
3.0ms	(*.f64 b b)

Results

Accuracy	Segments	Branch
5.0%	1	`(*.f64 b b)`
5.0%	1	`(*.f64 a a)`
5.0%	1	`(-.f64 (.f64 a a) (.f64 b b))`
5.0%	1	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
5.0%	1	`a`
5.0%	1	`b`

Compiler

Compiled 17 to 21 computations (-23.5% saved)

derivations4.0ms (0.3%)

Memory

2.3MiB live, 2.3MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 16 to 16 computations (0% saved)

preprocess12.0ms (0.8%)

Memory

14.7MiB live, 14.7MiB allocated; 0ms collecting garbage

Remove

(abs b)

(sort a b)

Compiler

Compiled 214 to 214 computations (0% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze34.0ms (2.2%)

sample1.1s (68.8%)

preprocess67.0ms (4.3%)

series6.0ms (0.4%)

rewrite57.0ms (3.6%)

eval5.0ms (0.3%)

prune3.0ms (0.2%)

series22.0ms (1.4%)

rewrite42.0ms (2.7%)

eval9.0ms (0.6%)

prune5.0ms (0.3%)

series88.0ms (5.6%)

rewrite42.0ms (2.6%)

eval8.0ms (0.5%)

prune3.0ms (0.2%)

series18.0ms (1.1%)

rewrite30.0ms (1.9%)

eval4.0ms (0.3%)

prune4.0ms (0.2%)

regimes27.0ms (1.7%)

derivations4.0ms (0.3%)

preprocess12.0ms (0.8%)

end0.0ms (0%)

Profiling