Metrics for bug366, discussion (missed optimization)

start0.0ms (0%)

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

analyze40.0ms (2.7%)

Memory

4.2MiB live, 46.0MiB 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)

sample716.0ms (48.1%)

Memory

9.3MiB live, 626.9MiB allocated; 75ms collecting garbage

Samples

438.0ms	8 256×	0	valid
33.0ms	615×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 274.0ms

ival-mult: 131.0ms (47.7% of total)

ival-sqrt: 98.0ms (35.7% of total)

ival-sub: 39.0ms (14.2% of total)

adjust: 3.0ms (1.1% of total)

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

Bogosity

explain112.0ms (7.5%)

Memory

-20.0MiB live, 80.0MiB allocated; 10ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
123	-	-	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
21	-	-	`(-.f64 (.f64 a a) (.f64 b b))`
0	-	-	`(*.f64 a a)`
0	-	-	`a`
0	-	-	`b`
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	107	0
↳	`(*.f64 b b)`	overflow	21
↳	`(-.f64 (.f64 a a) (.f64 b b))`	overflow	107
↳	`(*.f64 a a)`	overflow	107
`-.f64`	`(-.f64 (.f64 a a) (.f64 b b))`	nan-rescue	21	0
↳	`(*.f64 a a)`	overflow	107
↳	`(*.f64 b b)`	overflow	21
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`	uflow-rescue	16	0
↳	`(*.f64 b b)`	underflow	109
↳	`(-.f64 (.f64 a a) (.f64 b b))`	underflow	16
↳	`(*.f64 a a)`	underflow	16

Confusion

	Predicted +	Predicted -
+	123	0
-	0	133

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	123	0	0
-	0	0	133

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	133
1	102
2	21

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

34.0ms

512×

valid

Compiler

Compiled 58 to 22 computations (62.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 7.0ms (49.9% of total)

ival-sqrt: 4.0ms (28.5% of total)

ival-sub: 2.0ms (14.3% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess124.0ms (8.3%)

Memory

24.8MiB live, 117.5MiB allocated; 5ms 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

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.6%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Compiler

Compiled 8 to 6 computations (25% saved)

series22.0ms (1.5%)

Memory

-33.5MiB live, 8.2MiB allocated; 15ms 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
14.0ms	b	@	inf	((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) a (* b b) b)
4.0ms	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)

rewrite49.0ms (3.3%)

Memory

34.7MiB live, 34.7MiB allocated; 0ms 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 (0.4%)

Memory: 6.9MiB live, 6.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 095 to 230 computations (79% saved)

prune30.0ms (2%)

Memory

-33.7MiB live, 14.8MiB allocated; 15ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	58	3	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	3	62

Accuracy

99.8%

Counts

62 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
	54.6%	(sqrt.f64 (fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 b) b)))
	91.1%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a))
▶	98.8%	#s(approx (sqrt (- (* a a) (* b b))) a)

Status

Accuracy

Program

54.6%

(sqrt.f64 (fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 b) b)))

91.1%

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

▶

98.8%

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

Compiler

Compiled 39 to 26 computations (33.3% saved)

series2.0ms (0.1%)

Memory

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

Counts

2 → 23

Calls

Call 1

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

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 (sqrt (- (* a a) (* b b))) #s(hole binary64 a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))))
#s(approx (sqrt (- (* a 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 (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))))
#s(approx (sqrt (- (* a 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
0.0ms	a	@	-inf	((sqrt (- (* a a) (* b b))) a)
0.0ms	a	@	inf	((sqrt (- (* a a) (* b b))) a)
0.0ms	a	@	0	((sqrt (- (* a a) (* b b))) a)
0.0ms	b	@	inf	((sqrt (- (* a a) (* b b))) a)
0.0ms	b	@	-inf	((sqrt (- (* a a) (* b b))) a)

rewrite40.0ms (2.7%)

Memory

26.4MiB live, 26.4MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	137	727
0	137	695
0	730	670

Stop Event

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

Counts

25 → 25

Calls

Call 1

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

eval2.0ms (0.2%)

Memory: 4.4MiB live, 4.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 678 to 123 computations (81.9% saved)

prune8.0ms (0.6%)

Memory

-38.6MiB live, 8.9MiB allocated; 4ms collecting garbage

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	24	3	27

Accuracy

99.8%

Counts

27 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
	54.6%	(sqrt.f64 (fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 b) b)))
▶	91.1%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64) a))
✓	98.8%	#s(approx (sqrt (- (* a a) (* b b))) a)

Status

Accuracy

Program

54.6%

(sqrt.f64 (fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 b) b)))

▶

91.1%

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

✓

98.8%

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

Compiler

Compiled 39 to 26 computations (33.3% saved)

series7.0ms (0.5%)

Memory

11.2MiB live, 11.2MiB allocated; 0ms collecting garbage

Counts

7 → 33

Calls

Call 1

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

Calls

6 calls:

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

rewrite47.0ms (3.2%)

Memory

-0.1MiB live, 46.4MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	164	907
0	169	870
0	836	844

Stop Event

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

Counts

40 → 55

Calls

Call 1

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

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

eval6.0ms (0.4%)

Memory: 6.5MiB live, 6.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 490 to 237 computations (84.1% saved)

prune27.0ms (1.8%)

Memory

-14.6MiB live, 32.5MiB allocated; 2ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	0	1	1
Picked	1	0	1
Done	1	0	1
Total	59	2	61

Accuracy

100.0%

Counts

61 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
	54.6%	(sqrt.f64 (fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 b) b)))
▶	99.5%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 b (/.f64 b a)) #s(literal -1/2 binary64) a))

Status

Accuracy

Program

54.6%

(sqrt.f64 (fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 b) b)))

▶

99.5%

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

Compiler

Compiled 29 to 19 computations (34.5% saved)

series8.0ms (0.5%)

Memory

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

Counts

7 → 33

Calls

Call 1

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

Calls

6 calls:

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

rewrite45.0ms (3%)

Memory

20.3MiB live, 20.3MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	165	907
0	171	870
0	836	844

Stop Event

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

Counts

40 → 53

Calls

Call 1

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

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

eval5.0ms (0.3%)

Memory: 5.0MiB live, 5.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 448 to 222 computations (84.7% saved)

prune94.0ms (6.3%)

Memory

-45.8MiB live, 27.5MiB allocated; 67ms collecting garbage

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	56	2	58

Accuracy

100.0%

Counts

58 → 2

Alt Table

Click to see full alt table

Status

Accuracy

Program

54.6%

(sqrt.f64 (fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 b) b)))

✓

99.5%

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

Compiler

Compiled 93 to 44 computations (52.7% saved)

regimes12.0ms (0.8%)

Memory

17.8MiB live, 17.8MiB allocated; 0ms collecting garbage

Accuracy

Total -29.3b remaining (-9125%)

Threshold costs -29.3b (-9125%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
99.5%	1	`(*.f64 b b)`
99.5%	1	`(*.f64 a a)`
99.5%	1	`(-.f64 (.f64 a a) (.f64 b b))`
99.5%	1	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
99.5%	1	`a`
99.5%	1	`b`

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify60.0ms (4.1%)

Memory

-31.4MiB live, 18.1MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	24	17
2	84	17
3	226	17
4	404	17
5	835	17
6	1384	17
7	2068	17
8	2903	17
9	3213	17
10	3275	17
11	3275	17
12	3353	17

Stop Event

1×

saturated

Calls

Call 1

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

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

derivations5.0ms (0.3%)

Memory

4.7MiB live, 4.7MiB allocated; 0ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 17 to 11 computations (35.3% saved)

preprocess19.0ms (1.3%)

Memory: 30.4MiB live, 30.4MiB allocated; 0ms collecting garbage
Remove: (abs b)
Compiler: Compiled 178 to 118 computations (33.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze40.0ms (2.7%)

sample716.0ms (48.1%)

explain112.0ms (7.5%)

preprocess124.0ms (8.3%)

eval0.0ms (0%)

prune0.0ms (0%)

series22.0ms (1.5%)

rewrite49.0ms (3.3%)

eval6.0ms (0.4%)

prune30.0ms (2%)

series2.0ms (0.1%)

rewrite40.0ms (2.7%)

eval2.0ms (0.2%)

prune8.0ms (0.6%)

series7.0ms (0.5%)

rewrite47.0ms (3.2%)

eval6.0ms (0.4%)

prune27.0ms (1.8%)

series8.0ms (0.5%)

rewrite45.0ms (3%)

eval5.0ms (0.3%)

prune94.0ms (6.3%)

regimes12.0ms (0.8%)

simplify60.0ms (4.1%)

derivations5.0ms (0.3%)

preprocess19.0ms (1.3%)

end0.0ms (0%)

Profiling