Metrics for bug366, discussion (missed optimization)

start0.0ms (0%)

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

analyze42.0ms (2.4%)

Memory

-3.6MiB live, 39.9MiB allocated; 12ms 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)

sample1.2s (67.6%)

Memory

-148.2MiB live, 978.8MiB allocated; 985ms collecting garbage

Samples

865.0ms	8 256×	0	valid
31.0ms	631×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 630.0ms

ival-mult: 518.0ms (82.2% of total)

ival-sqrt: 68.0ms (10.8% of total)

ival-sub: 38.0ms (6% of total)

adjust: 3.0ms (0.5% of total)

ival-assert: 3.0ms (0.5% of total)

Bogosity

explain75.0ms (4.2%)

Memory

8.2MiB live, 108.2MiB allocated; 5ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
134	-	2	(-1.3698438633682287e-158 2.4000231773668236e-270)	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
13	-	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	110	0
↳	`(*.f64 b b)`	overflow	13
↳	`(-.f64 (.f64 a a) (.f64 b b))`	overflow	110
↳	`(*.f64 a a)`	overflow	110
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`	uflow-rescue	22	0
↳	`(*.f64 b b)`	underflow	122
↳	`(-.f64 (.f64 a a) (.f64 b b))`	underflow	22
↳	`(*.f64 a a)`	underflow	22
`-.f64`	`(-.f64 (.f64 a a) (.f64 b b))`	nan-rescue	13	0
↳	`(*.f64 a a)`	overflow	110
↳	`(*.f64 b b)`	overflow	13

Confusion

	Predicted +	Predicted -
+	132	2
-	0	122

Precision

1.0

Recall

0.9850746268656716

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	132	0	2
-	0	0	122

Precision?

1.0

Recall?

0.9850746268656716

Freqs

test

number	freq
0	124
1	119
2	13

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

31.0ms

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 (55.9% of total)

ival-sub: 3.0ms (16.8% of total)

ival-sqrt: 3.0ms (16.8% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess113.0ms (6.4%)

Memory

-11.8MiB live, 82.9MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	50
1	55	50
2	214	50
3	344	50
4	875	50
5	1839	50
6	3017	50
7	3359	50
8	3437	50
9	3437	50
10	3633	50
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 a b) (+.f64 b a)))

Symmetry

(abs a)

(abs b)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB 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
▶	51.1%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Compiler

Compiled 8 to 6 computations (25% saved)

series7.0ms (0.4%)

Memory

8.5MiB live, 8.5MiB 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	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	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	b	@	0	((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) a (* b b) b)

rewrite49.0ms (2.8%)

Memory

-5.7MiB live, 41.1MiB allocated; 2ms 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))) (+.f64 (pow.f64 a #s(literal 4 binary64)) (+.f64 (pow.f64 b #s(literal 4 binary64)) (.f64 (.f64 a a) (*.f64 b b)))))
(fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 a) (neg.f64 a) (*.f64 (neg.f64 b) b))
(fma.f64 (fabs.f64 a) (fabs.f64 a) (*.f64 (neg.f64 b) b))
(fma.f64 a a (*.f64 (neg.f64 b) b))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (.f64 a a) (.f64 (neg.f64 b) b))
(*.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)))
(*.f64 (neg.f64 a) (neg.f64 a))
(*.f64 (fabs.f64 a) (fabs.f64 a))
(*.f64 a a)
(pow.f64 a #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 a) #s(literal 2 binary64)))
a
(*.f64 (pow.f64 b #s(literal 1 binary64)) (pow.f64 b #s(literal 1 binary64)))
(*.f64 (neg.f64 b) (neg.f64 b))
(*.f64 (fabs.f64 b) (fabs.f64 b))
(*.f64 b b)
(pow.f64 b #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)))
b
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (/.f64 (.f64 a a) b) (sqrt.f64 #s(literal -1 binary64))) #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) (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) b) #s(literal 3 binary64))) #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) (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) b) #s(literal 3 binary64)))) (.f64 a a) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) b))) (.f64 a a) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b)))
#s(approx (- (* a a) (* b b)) (*.f64 (+.f64 a b) (-.f64 a b)))
#s(approx (* a a) (*.f64 a a))
#s(approx a a)
#s(approx (sqrt (- (* a a) (* b b))) a)
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (fma.f64 (/.f64 (.f64 b b) (*.f64 a a)) #s(literal -1/2 binary64) #s(literal 1 binary64)) a))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (+.f64 (fma.f64 (/.f64 (.f64 b b) (.f64 a a)) #s(literal -1/2 binary64) #s(literal 1 binary64)) (/.f64 (.f64 #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)) (.f64 (fma.f64 (/.f64 (.f64 b b) (.f64 a a)) #s(literal -1 binary64) #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) (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 (-.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 b b)) (pow.f64 a #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) a)) (*.f64 b b) a))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (-.f64 (.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 a #s(literal -3 binary64)))) (.f64 b b)) (/.f64 #s(literal 1/2 binary64) a)) (*.f64 b b) a))
#s(approx (- (* a a) (* b b)) (fma.f64 a a (neg.f64 (*.f64 b b))))
#s(approx (* b b) (*.f64 b b))
#s(approx b b)
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (fma.f64 (/.f64 (.f64 a a) (.f64 (.f64 b b) (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) b))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) #s(literal -1/8 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 a a)) (.f64 (.f64 b b) (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64))) b))
#s(approx (sqrt (- (* a a) (* b b))) (.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 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 (pow.f64 a #s(literal 4 binary64)) (.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) #s(literal -1/8 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 a a)) (.f64 (.f64 b b) (sqrt.f64 #s(literal -1 binary64))))) (sqrt.f64 #s(literal -1 binary64))) b)))
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 (.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 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)))

eval6.0ms (0.3%)

Memory: 9.5MiB live, 9.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 095 to 230 computations (79% saved)

prune13.0ms (0.7%)

Memory

16.6MiB live, 16.6MiB 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

99.5%

Counts

62 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.1%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
▶	79.8%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (-.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 b b)) (pow.f64 a #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) a)) (*.f64 b b) a))
▶	98.6%	#s(approx (sqrt (- (* a a) (* b b))) a)

Status

Accuracy

Program

✓

51.1%

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

▶

79.8%

#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 b b)) (pow.f64 a #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) a)) (*.f64 b b) a))

▶

98.6%

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

Compiler

Compiled 45 to 30 computations (33.3% saved)

series20.0ms (1.1%)

Memory

-26.0MiB live, 22.9MiB allocated; 3ms collecting garbage

Counts

14 → 48

Calls

Call 1

Inputs
#s(approx (sqrt (- (* a a) (* b b))) a)
a
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (-.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 b b)) (pow.f64 a #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) a)) (*.f64 b b) a))
(fma.f64 (-.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 b b)) (pow.f64 a #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) a)) (*.f64 b b) a)
(-.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 b b)) (pow.f64 a #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) a))
(/.f64 (.f64 #s(literal -1/8 binary64) (.f64 b b)) (pow.f64 a #s(literal 3 binary64)))
(.f64 #s(literal -1/8 binary64) (.f64 b b))
#s(literal -1/8 binary64)
(*.f64 b b)
b
(pow.f64 a #s(literal 3 binary64))
#s(literal 3 binary64)
(/.f64 #s(literal 1/2 binary64) a)
#s(literal 1/2 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 (+ (* (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (* b b)) a) #s(hole binary64 (* -1/8 (/ (pow b 4) (pow a 3)))))
#s(approx (+ (* (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (* b b)) a) #s(hole binary64 (/ (+ (* -1/2 (* (pow a 2) (pow b 2))) (* -1/8 (pow b 4))) (pow a 3))))
#s(approx (+ (* (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (* b b)) a) #s(hole binary64 (/ (+ (* -1/8 (pow b 4)) (* (pow a 2) (+ (* -1/2 (pow b 2)) (pow a 2)))) (pow a 3))))
#s(approx (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) #s(hole binary64 (* -1/8 (/ (pow b 2) (pow a 3)))))
#s(approx (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) #s(hole binary64 (/ (+ (* -1/2 (pow a 2)) (* -1/8 (pow b 2))) (pow a 3))))
#s(approx (/ (* -1/8 (* b b)) (pow a 3)) #s(hole binary64 (* -1/8 (/ (pow b 2) (pow a 3)))))
#s(approx (pow a 3) #s(hole binary64 (pow a 3)))
#s(approx (/ 1/2 a) #s(hole binary64 (/ 1/2 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 (+ (* (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (* b b)) a) #s(hole binary64 a))
#s(approx (+ (* (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (* b b)) a) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#s(approx (+ (* (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (* 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 (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) #s(hole binary64 (/ -1/2 a)))
#s(approx (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) #s(hole binary64 (/ (- (* -1/8 (/ (pow b 2) (pow a 2))) 1/2) a)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 a)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))))
#s(approx (+ (* (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (* b b)) a) #s(hole binary64 (* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))))
#s(approx (+ (* (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (* 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 (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) #s(hole binary64 (* -1 (/ (+ 1/2 (* 1/8 (/ (pow b 2) (pow a 2)))) a))))
#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 (+ (* (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (* b b)) a) #s(hole binary64 (+ a (* -1/2 (/ (pow b 2) a)))))
#s(approx (+ (* (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (* b b)) a) #s(hole binary64 (+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))))
#s(approx (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) #s(hole binary64 (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))
#s(approx (* -1/8 (* b b)) #s(hole binary64 (* -1/8 (pow b 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 (+ (* (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (* b b)) a) #s(hole binary64 (* -1 (* (pow b 4) (+ (* 1/8 (/ 1 (pow a 3))) (* 1/2 (/ 1 (* a (pow b 2)))))))))
#s(approx (+ (* (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (* b b)) a) #s(hole binary64 (* (pow b 4) (- (/ a (pow b 4)) (+ (* 1/8 (/ 1 (pow a 3))) (/ 1/2 (* a (pow b 2))))))))
#s(approx (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) #s(hole binary64 (* -1 (* (pow b 2) (+ (* 1/8 (/ 1 (pow a 3))) (* 1/2 (/ 1 (* a (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
8.0ms	b	@	inf	((sqrt (- (* a a) (* b b))) a (sqrt (- (* a a) (* b b))) (+ (* (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (* b b)) a) (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (/ (* -1/8 (* b b)) (pow a 3)) (* -1/8 (* b b)) -1/8 (* b b) b (pow a 3) 3 (/ 1/2 a) 1/2)
3.0ms	b	@	0	((sqrt (- (* a a) (* b b))) a (sqrt (- (* a a) (* b b))) (+ (* (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (* b b)) a) (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (/ (* -1/8 (* b b)) (pow a 3)) (* -1/8 (* b b)) -1/8 (* b b) b (pow a 3) 3 (/ 1/2 a) 1/2)
2.0ms	a	@	0	((sqrt (- (* a a) (* b b))) a (sqrt (- (* a a) (* b b))) (+ (* (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (* b b)) a) (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (/ (* -1/8 (* b b)) (pow a 3)) (* -1/8 (* b b)) -1/8 (* b b) b (pow a 3) 3 (/ 1/2 a) 1/2)
2.0ms	b	@	-inf	((sqrt (- (* a a) (* b b))) a (sqrt (- (* a a) (* b b))) (+ (* (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (* b b)) a) (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (/ (* -1/8 (* b b)) (pow a 3)) (* -1/8 (* b b)) -1/8 (* b b) b (pow a 3) 3 (/ 1/2 a) 1/2)
2.0ms	a	@	-inf	((sqrt (- (* a a) (* b b))) a (sqrt (- (* a a) (* b b))) (+ (* (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (* b b)) a) (- (/ (* -1/8 (* b b)) (pow a 3)) (/ 1/2 a)) (/ (* -1/8 (* b b)) (pow a 3)) (* -1/8 (* b b)) -1/8 (* b b) b (pow a 3) 3 (/ 1/2 a) 1/2)

rewrite52.0ms (2.9%)

Memory

10.8MiB live, 57.5MiB allocated; 1ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	222	1491
0	236	1436
0	1143	1400

Stop Event

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

Counts

62 → 94

Calls

Call 1

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

eval11.0ms (0.6%)

Memory: 13.6MiB live, 13.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 3 701 to 444 computations (88% saved)

prune108.0ms (6.1%)

Memory

-0.8MiB live, 94.2MiB allocated; 3ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	111	3	114

Accuracy

99.5%

Counts

114 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	51.1%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))
✓	79.8%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (-.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 b b)) (pow.f64 a #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) a)) (*.f64 b b) a))
✓	98.6%	#s(approx (sqrt (- (* a a) (* b b))) a)

Status

Accuracy

Program

✓

51.1%

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

✓

79.8%

#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 b b)) (pow.f64 a #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) a)) (*.f64 b b) a))

✓

98.6%

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

Compiler

Compiled 90 to 51 computations (43.3% saved)

regimes9.0ms (0.5%)

Memory

12.5MiB live, 12.5MiB allocated; 0ms collecting garbage

Accuracy

Total -35.0b remaining (-3909.3%)

Threshold costs -35b (-3909.3%)

Counts

3 → 1

Calls

Call 1

Inputs

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

#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (-.f64 (/.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 b b)) (pow.f64 a #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) a)) (*.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:

1.0ms	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
98.6%	1	`(*.f64 b b)`
98.6%	1	`(*.f64 a a)`
98.6%	1	`(-.f64 (.f64 a a) (.f64 b b))`
98.6%	1	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
98.6%	1	`a`
98.6%	1	`b`

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify56.0ms (3.2%)

Memory

-20.1MiB live, 28.9MiB allocated; 2ms 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

1.3MiB live, 1.3MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 10 to 7 computations (30% saved)

preprocess11.0ms (0.6%)

Memory: 13.6MiB live, 13.6MiB 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%)

analyze42.0ms (2.4%)

sample1.2s (67.6%)

explain75.0ms (4.2%)

preprocess113.0ms (6.4%)

eval0.0ms (0%)

prune0.0ms (0%)

series7.0ms (0.4%)

rewrite49.0ms (2.8%)

eval6.0ms (0.3%)

prune13.0ms (0.7%)

series20.0ms (1.1%)

rewrite52.0ms (2.9%)

eval11.0ms (0.6%)

prune108.0ms (6.1%)

regimes9.0ms (0.5%)

simplify56.0ms (3.2%)

derivations2.0ms (0.1%)

preprocess11.0ms (0.6%)

end0.0ms (0%)

Profiling