Metrics for bug366, discussion (missed optimization)

start0.0ms (0%)

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

analyze37.0ms (2.2%)

Memory

2.0MiB live, 44.0MiB allocated; 9ms 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)

sample984.0ms (58.4%)

Memory

44.1MiB live, 690.4MiB allocated; 689ms collecting garbage

Samples

696.0ms	8 256×	0	valid
34.0ms	622×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 269.0ms

ival-mult: 147.0ms (54.7% of total)

ival-sqrt: 74.0ms (27.5% of total)

ival-sub: 42.0ms (15.6% of total)

adjust: 3.0ms (1.1% of total)

ival-assert: 3.0ms (1.1% of total)

Bogosity

explain120.0ms (7.1%)

Memory

-9.2MiB live, 94.9MiB allocated; 78ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
138	-	1	(3.724948312681563e-156 1.1184152781670311e-281)	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
14	-	0	-	`(-.f64 (.f64 a a) (.f64 b b))`
0	-	0	-	`(*.f64 a a)`
0	-	0	-	`a`
0	-	0	-	`b`
0	-	0	-	`(*.f64 b b)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`	oflow-rescue	129	0
↳	`(*.f64 b b)`	overflow	14
↳	`(-.f64 (.f64 a a) (.f64 b b))`	overflow	129
↳	`(*.f64 a a)`	overflow	129
`-.f64`	`(-.f64 (.f64 a a) (.f64 b b))`	nan-rescue	14	0
↳	`(*.f64 a a)`	overflow	129
↳	`(*.f64 b b)`	overflow	14
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`	uflow-rescue	8	0
↳	`(*.f64 b b)`	underflow	101
↳	`(-.f64 (.f64 a a) (.f64 b b))`	underflow	8
↳	`(*.f64 a a)`	underflow	8

Confusion

	Predicted +	Predicted -
+	137	1
-	0	118

Precision

1.0

Recall

0.9927536231884058

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	137	0	1
-	0	0	118

Precision?

1.0

Recall?

0.9927536231884058

Freqs

test

number	freq
0	119
1	123
2	14

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

36.0ms

512×

valid

Compiler

Compiled 58 to 22 computations (62.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-mult: 10.0ms (54.2% of total)

ival-sqrt: 5.0ms (27.1% of total)

ival-sub: 3.0ms (16.3% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess123.0ms (7.3%)

Memory

-16.8MiB live, 75.1MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	50
1	55	50
2	214	50
3	344	50
4	875	50
5	1839	50
6	3017	50
7	3359	50
8	3437	50
9	3437	50
10	3633	50
0	6	8
0	10	8
1	23	8
2	83	8
3	225	8
4	405	8
5	836	8
6	1387	8
7	2071	8
8	2896	8
9	3206	8
10	3268	8
11	3268	8
12	3346	8
0	3346	8

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs a)

(abs b)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.7%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Compiler

Compiled 8 to 6 computations (25% saved)

series7.0ms (0.4%)

Memory

7.5MiB live, 7.5MiB allocated; 0ms collecting garbage

Counts

6 → 32

Calls

Call 1

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

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

Calls

6 calls:

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

rewrite62.0ms (3.7%)

Memory

-8.4MiB live, 41.0MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

38 → 57

Calls

Call 1

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

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

eval7.0ms (0.4%)

Memory: 8.2MiB live, 8.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 171 to 229 computations (80.4% saved)

prune13.0ms (0.8%)

Memory

13.7MiB live, 13.7MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	3	62

Accuracy

99.9%

Counts

62 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.7%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
▶	81.8%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 b b) (pow.f64 a #s(literal 5 binary64))) #s(literal -1/16 binary64) (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (.f64 a a) a) #s(literal -1 binary64)))) (.f64 b b) (.f64 #s(literal -1/2 binary64) (pow.f64 a #s(literal -1 binary64)))) (*.f64 b b) a))
▶	99.1%	#s(approx (sqrt (- (* a a) (* b b))) a)

Status

Accuracy

Program

✓

49.7%

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

▶

81.8%

#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 b b) (pow.f64 a #s(literal 5 binary64))) #s(literal -1/16 binary64) (*.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (*.f64 a a) a) #s(literal -1 binary64)))) (*.f64 b b) (*.f64 #s(literal -1/2 binary64) (pow.f64 a #s(literal -1 binary64)))) (*.f64 b b) a))

▶

99.1%

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

Compiler

Compiled 59 to 37 computations (37.3% saved)

series25.0ms (1.5%)

Memory

-22.0MiB live, 24.1MiB allocated; 3ms collecting garbage

Counts

21 → 69

Calls

Call 1

Inputs
#s(approx (sqrt (- (* a a) (* b b))) a)
a
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 b b) (pow.f64 a #s(literal 5 binary64))) #s(literal -1/16 binary64) (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (.f64 a a) a) #s(literal -1 binary64)))) (.f64 b b) (.f64 #s(literal -1/2 binary64) (pow.f64 a #s(literal -1 binary64)))) (*.f64 b b) a))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 b b) (pow.f64 a #s(literal 5 binary64))) #s(literal -1/16 binary64) (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (.f64 a a) a) #s(literal -1 binary64)))) (.f64 b b) (.f64 #s(literal -1/2 binary64) (pow.f64 a #s(literal -1 binary64)))) (*.f64 b b) a)
(fma.f64 (fma.f64 (/.f64 (.f64 b b) (pow.f64 a #s(literal 5 binary64))) #s(literal -1/16 binary64) (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (.f64 a a) a) #s(literal -1 binary64)))) (.f64 b b) (.f64 #s(literal -1/2 binary64) (pow.f64 a #s(literal -1 binary64))))
(fma.f64 (/.f64 (.f64 b b) (pow.f64 a #s(literal 5 binary64))) #s(literal -1/16 binary64) (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (.f64 a a) a) #s(literal -1 binary64))))
(/.f64 (*.f64 b b) (pow.f64 a #s(literal 5 binary64)))
(*.f64 b b)
b
(pow.f64 a #s(literal 5 binary64))
#s(literal 5 binary64)
#s(literal -1/16 binary64)
(.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (*.f64 a a) a) #s(literal -1 binary64)))
#s(literal -1/8 binary64)
(pow.f64 (.f64 (.f64 a a) a) #s(literal -1 binary64))
(.f64 (.f64 a a) a)
(*.f64 a a)
#s(literal -1 binary64)
(*.f64 #s(literal -1/2 binary64) (pow.f64 a #s(literal -1 binary64)))
#s(literal -1/2 binary64)
(pow.f64 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 a #s(hole binary64 a))
#s(approx (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) #s(hole binary64 (* -1/16 (/ (pow b 6) (pow a 5)))))
#s(approx (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) #s(hole binary64 (/ (+ (* -1/8 (* (pow a 2) (pow b 4))) (* -1/16 (pow b 6))) (pow a 5))))
#s(approx (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) #s(hole binary64 (/ (+ (* -1/16 (pow b 6)) (* (pow a 2) (+ (* -1/2 (* (pow a 2) (pow b 2))) (* -1/8 (pow b 4))))) (pow a 5))))
#s(approx (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) #s(hole binary64 (/ (+ (* -1/16 (pow b 6)) (* (pow a 2) (+ (* -1/8 (pow b 4)) (* (pow a 2) (+ (* -1/2 (pow b 2)) (pow a 2)))))) (pow a 5))))
#s(approx (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) #s(hole binary64 (* -1/16 (/ (pow b 4) (pow a 5)))))
#s(approx (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) #s(hole binary64 (/ (+ (* -1/8 (* (pow a 2) (pow b 2))) (* -1/16 (pow b 4))) (pow a 5))))
#s(approx (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) #s(hole binary64 (/ (+ (* -1/16 (pow b 4)) (* (pow a 2) (+ (* -1/2 (pow a 2)) (* -1/8 (pow b 2))))) (pow a 5))))
#s(approx (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) #s(hole binary64 (* -1/16 (/ (pow b 2) (pow a 5)))))
#s(approx (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) #s(hole binary64 (/ (+ (* -1/8 (pow a 2)) (* -1/16 (pow b 2))) (pow a 5))))
#s(approx (/ (* b b) (pow a 5)) #s(hole binary64 (/ (pow b 2) (pow a 5))))
#s(approx (pow a 5) #s(hole binary64 (pow a 5)))
#s(approx (* -1/8 (pow (* (* a a) a) -1)) #s(hole binary64 (/ -1/8 (pow a 3))))
#s(approx (pow (* (* a a) a) -1) #s(hole binary64 (/ 1 (pow a 3))))
#s(approx (* (* a a) a) #s(hole binary64 (pow a 3)))
#s(approx (* a a) #s(hole binary64 (pow a 2)))
#s(approx (* -1/2 (pow a -1)) #s(hole binary64 (/ -1/2 a)))
#s(approx (pow a -1) #s(hole binary64 (/ 1 a)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))))
#s(approx (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) #s(hole binary64 a))
#s(approx (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#s(approx (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))))
#s(approx (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) #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 (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) #s(hole binary64 (/ -1/2 a)))
#s(approx (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) #s(hole binary64 (/ (- (* -1/8 (/ (pow b 2) (pow a 2))) 1/2) a)))
#s(approx (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) #s(hole binary64 (/ (- (+ (* -1/8 (/ (pow b 2) (pow a 2))) (* -1/16 (/ (pow b 4) (pow a 4)))) 1/2) a)))
#s(approx (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) #s(hole binary64 (/ -1/8 (pow a 3))))
#s(approx (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) #s(hole binary64 (/ (- (* -1/16 (/ (pow b 2) (pow a 2))) 1/8) (pow a 3))))
#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 (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) #s(hole binary64 (* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))))
#s(approx (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) #s(hole binary64 (* -1 (* a (- (+ (* 1/8 (/ (pow b 4) (pow a 4))) (* 1/2 (/ (pow b 2) (pow a 2)))) 1)))))
#s(approx (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) #s(hole binary64 (* -1 (* a (- (+ (* 1/16 (/ (pow b 6) (pow a 6))) (+ (* 1/8 (/ (pow b 4) (pow a 4))) (* 1/2 (/ (pow b 2) (pow a 2))))) 1)))))
#s(approx (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) #s(hole binary64 (* -1 (/ (+ 1/2 (* 1/8 (/ (pow b 2) (pow a 2)))) a))))
#s(approx (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) #s(hole binary64 (* -1 (/ (+ 1/2 (+ (* 1/16 (/ (pow b 4) (pow a 4))) (* 1/8 (/ (pow b 2) (pow a 2))))) a))))
#s(approx (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) #s(hole binary64 (* -1 (/ (+ 1/8 (* 1/16 (/ (pow b 2) (pow a 2)))) (pow a 3)))))
#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) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) #s(hole binary64 (+ a (* -1/2 (/ (pow b 2) a)))))
#s(approx (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) #s(hole binary64 (+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))))
#s(approx (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) #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) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) #s(hole binary64 (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))
#s(approx (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) #s(hole binary64 (- (* (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) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) #s(hole binary64 (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))))
#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 (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) #s(hole binary64 (* -1 (* (pow b 6) (+ (* 1/16 (/ 1 (pow a 5))) (* 1/8 (/ 1 (* (pow a 3) (pow b 2)))))))))
#s(approx (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) #s(hole binary64 (* (pow b 6) (- (* -1 (/ (+ (* 1/8 (/ 1 (pow a 3))) (* 1/2 (/ 1 (* a (pow b 2))))) (pow b 2))) (* 1/16 (/ 1 (pow a 5)))))))
#s(approx (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) #s(hole binary64 (* (pow b 6) (- (/ a (pow b 6)) (+ (* 1/16 (/ 1 (pow a 5))) (+ (/ 1/8 (* (pow a 3) (pow b 2))) (* 1/2 (/ 1 (* a (pow b 4))))))))))
#s(approx (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) #s(hole binary64 (* -1 (* (pow b 4) (+ (* 1/16 (/ 1 (pow a 5))) (* 1/8 (/ 1 (* (pow a 3) (pow b 2)))))))))
#s(approx (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) #s(hole binary64 (* (pow b 4) (- (* -1 (/ (+ (* 1/8 (/ 1 (pow a 3))) (* 1/2 (/ 1 (* a (pow b 2))))) (pow b 2))) (* 1/16 (/ 1 (pow a 5)))))))
#s(approx (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) #s(hole binary64 (* -1 (* (pow b 2) (+ (* 1/16 (/ 1 (pow a 5))) (* 1/8 (/ 1 (* (pow a 3) (pow b 2)))))))))
#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
5.0ms	a	@	inf	((sqrt (- (* a a) (* b b))) a (sqrt (- (* a a) (* b b))) (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (/ (* b b) (pow a 5)) (* b b) b (pow a 5) 5 -1/16 (* -1/8 (pow (* (* a a) a) -1)) -1/8 (pow (* (* a a) a) -1) (* (* a a) a) (* a a) -1 (* -1/2 (pow a -1)) -1/2 (pow a -1))
5.0ms	a	@	-inf	((sqrt (- (* a a) (* b b))) a (sqrt (- (* a a) (* b b))) (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (/ (* b b) (pow a 5)) (* b b) b (pow a 5) 5 -1/16 (* -1/8 (pow (* (* a a) a) -1)) -1/8 (pow (* (* a a) a) -1) (* (* a a) a) (* a a) -1 (* -1/2 (pow a -1)) -1/2 (pow a -1))
4.0ms	a	@	0	((sqrt (- (* a a) (* b b))) a (sqrt (- (* a a) (* b b))) (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (/ (* b b) (pow a 5)) (* b b) b (pow a 5) 5 -1/16 (* -1/8 (pow (* (* a a) a) -1)) -1/8 (pow (* (* a a) a) -1) (* (* a a) a) (* a a) -1 (* -1/2 (pow a -1)) -1/2 (pow a -1))
3.0ms	b	@	inf	((sqrt (- (* a a) (* b b))) a (sqrt (- (* a a) (* b b))) (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (/ (* b b) (pow a 5)) (* b b) b (pow a 5) 5 -1/16 (* -1/8 (pow (* (* a a) a) -1)) -1/8 (pow (* (* a a) a) -1) (* (* a a) a) (* a a) -1 (* -1/2 (pow a -1)) -1/2 (pow a -1))
3.0ms	b	@	0	((sqrt (- (* a a) (* b b))) a (sqrt (- (* a a) (* b b))) (+ (* (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (* b b)) a) (+ (* (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (* b b)) (* -1/2 (pow a -1))) (+ (* (/ (* b b) (pow a 5)) -1/16) (* -1/8 (pow (* (* a a) a) -1))) (/ (* b b) (pow a 5)) (* b b) b (pow a 5) 5 -1/16 (* -1/8 (pow (* (* a a) a) -1)) -1/8 (pow (* (* a a) a) -1) (* (* a a) a) (* a a) -1 (* -1/2 (pow a -1)) -1/2 (pow a -1))

rewrite71.0ms (4.2%)

Memory

7.2MiB live, 52.3MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	314	2750
0	340	2441
0	1649	2388

Stop Event

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

Counts

90 → 150

Calls

Call 1

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

eval22.0ms (1.3%)

Memory: 27.1MiB live, 27.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 8 909 to 833 computations (90.6% saved)

prune137.0ms (8.1%)

Memory

-19.7MiB live, 120.3MiB allocated; 15ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	185	3	188

Accuracy

99.9%

Counts

188 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.7%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
✓	81.8%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 b b) (pow.f64 a #s(literal 5 binary64))) #s(literal -1/16 binary64) (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (.f64 a a) a) #s(literal -1 binary64)))) (.f64 b b) (.f64 #s(literal -1/2 binary64) (pow.f64 a #s(literal -1 binary64)))) (*.f64 b b) a))
✓	99.1%	#s(approx (sqrt (- (* a a) (* b b))) a)

Status

Accuracy

Program

✓

49.7%

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

✓

81.8%

#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 b b) (pow.f64 a #s(literal 5 binary64))) #s(literal -1/16 binary64) (*.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (*.f64 a a) a) #s(literal -1 binary64)))) (*.f64 b b) (*.f64 #s(literal -1/2 binary64) (pow.f64 a #s(literal -1 binary64)))) (*.f64 b b) a))

✓

99.1%

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

Compiler

Compiled 118 to 64 computations (45.8% saved)

regimes9.0ms (0.5%)

Memory

13.9MiB live, 13.9MiB allocated; 0ms collecting garbage

Accuracy

Total -38.2b remaining (-6283.3%)

Threshold costs -38.2b (-6283.3%)

Counts

3 → 1

Calls

Call 1

Inputs

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

#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (*.f64 b b) (pow.f64 a #s(literal 5 binary64))) #s(literal -1/16 binary64) (*.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (*.f64 a a) a) #s(literal -1 binary64)))) (*.f64 b b) (*.f64 #s(literal -1/2 binary64) (pow.f64 a #s(literal -1 binary64)))) (*.f64 b b) a))

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
99.1%	1	`(*.f64 b b)`
99.1%	1	`(*.f64 a a)`
99.1%	1	`(-.f64 (.f64 a a) (.f64 b b))`
99.1%	1	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
99.1%	1	`a`
99.1%	1	`b`

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify55.0ms (3.3%)

Memory

-32.7MiB live, 13.9MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	20	10
2	80	10
3	222	10
4	402	10
5	831	10
6	1382	10
7	2066	10
8	2891	10
9	3201	10
10	3263	10
11	3263	10
12	3341	10

Stop Event

1×

saturated

Calls

Call 1

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

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

derivations2.0ms (0.1%)

Memory

1.1MiB live, 1.1MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 10 to 7 computations (30% saved)

preprocess11.0ms (0.7%)

Memory: 14.5MiB live, 14.5MiB allocated; 0ms collecting garbage
Remove: (abs b)
Compiler: Compiled 96 to 68 computations (29.2% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze37.0ms (2.2%)

sample984.0ms (58.4%)

explain120.0ms (7.1%)

preprocess123.0ms (7.3%)

eval0.0ms (0%)

prune0.0ms (0%)

series7.0ms (0.4%)

rewrite62.0ms (3.7%)

eval7.0ms (0.4%)

prune13.0ms (0.8%)

series25.0ms (1.5%)

rewrite71.0ms (4.2%)

eval22.0ms (1.3%)

prune137.0ms (8.1%)

regimes9.0ms (0.5%)

simplify55.0ms (3.3%)

derivations2.0ms (0.1%)

preprocess11.0ms (0.7%)

end0.0ms (0%)

Profiling