Metrics for bug366, discussion (missed optimization)

start0.0ms (0%)

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

analyze33.0ms (1.2%)

Memory

-4.6MiB live, 42.1MiB allocated; 5ms 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)

sample769.0ms (29.1%)

Memory

29.4MiB live, 727.2MiB allocated; 165ms collecting garbage

Samples

443.0ms	8 256×	0	valid
30.0ms	640×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 268.0ms

ival-mult: 159.0ms (59.4% of total)

ival-sqrt: 58.0ms (21.7% of total)

ival-sub: 38.0ms (14.2% of total)

ival-true: 7.0ms (2.6% of total)

adjust: 3.0ms (1.1% of total)

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

Bogosity

explain83.0ms (3.1%)

Memory

8.5MiB live, 99.5MiB allocated; 18ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
129	-	-	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
18	-	-	`(-.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	115	0
↳	`(*.f64 b b)`	overflow	18
↳	`(-.f64 (.f64 a a) (.f64 b b))`	overflow	115
↳	`(*.f64 a a)`	overflow	115
`-.f64`	`(-.f64 (.f64 a a) (.f64 b b))`	nan-rescue	18	0
↳	`(*.f64 a a)`	overflow	115
↳	`(*.f64 b b)`	overflow	18
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`	uflow-rescue	14	0
↳	`(*.f64 b b)`	underflow	108
↳	`(-.f64 (.f64 a a) (.f64 b b))`	underflow	14
↳	`(*.f64 a a)`	underflow	14

Confusion

	Predicted +	Predicted -
+	129	0
-	0	127

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	129	0	0
-	0	0	127

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	127
1	111
2	18

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

32.0ms

512×

valid

Compiler

Compiled 58 to 22 computations (62.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-sqrt: 9.0ms (46.1% of total)

ival-mult: 7.0ms (35.9% of total)

ival-sub: 2.0ms (10.2% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess127.0ms (4.8%)

Memory

3.6MiB live, 102.5MiB allocated; 22ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	42
1	51	42
2	210	42
3	333	42
4	846	42
5	1830	42
6	3004	42
7	3347	42
8	3425	42
9	3425	42
10	3627	42
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 b)

(abs a)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.5%	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify72.0ms (2.7%)

Memory

-5.0MiB live, 41.7MiB allocated; 11ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 b b)
cost-diff	0	(*.f64 a a)
cost-diff	0	(-.f64 (.f64 a a) (.f64 b b))
cost-diff	0	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	23
0	10	23
1	23	23
2	83	23
3	225	23
4	405	23
5	836	23
6	1387	23
7	2071	23
8	2896	23
9	3206	23
10	3268	23
11	3268	23
12	3346	23
0	3346	23

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

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

localize18.0ms (0.7%)

Memory

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

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 b b)
accuracy	0.0	(*.f64 a a)
accuracy	3.5859375000000004	(-.f64 (.f64 a a) (.f64 b b))
accuracy	30.059792083774497	(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))

Samples

13.0ms

256×

valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-mult: 3.0ms (46.5% of total)

ival-sqrt: 2.0ms (31% of total)

ival-sub: 1.0ms (15.5% of total)

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

adjust: 0.0ms (0% of total)

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

series6.0ms (0.2%)

Memory

5.6MiB live, 5.6MiB allocated; 0ms collecting garbage

Counts

4 → 29

Calls

Call 1

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

Outputs
(* b (sqrt -1))
(+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(+ (* 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)))))))
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(pow a 2)
a
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))
(* 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)))))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* -1 a)
(* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))
(* -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))))))))
(+ a (* -1/2 (/ (pow b 2) a)))
(+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))
(+ 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)))))
(+ (* -1 (pow b 2)) (pow a 2))
(pow b 2)
(* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -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)))))))
(* 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))))))))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(* -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))))))))
(* -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) (* b b))
1.0ms	b	@	inf	((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) (* b b))
1.0ms	a	@	inf	((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) (* b b))
1.0ms	a	@	-inf	((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) (* b b))
1.0ms	b	@	0	((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) (* b b))

simplify180.0ms (6.8%)

Memory

-28.8MiB live, 131.5MiB allocated; 19ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	119	542
1	358	541
2	1418	530
3	7250	520
0	8174	489

Stop Event

1×	iter limit
1×	node limit

Counts

29 → 28

Calls

Call 1

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

rewrite123.0ms (4.7%)

Memory

0.2MiB live, 132.5MiB allocated; 17ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	41	21
2	352	21
3	4738	21
0	8743	15

Stop Event

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

Counts

4 → 155

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 (.f64 b (+.f64 b a)) (*.f64 a a)))
(*.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (hypot.f64 b a))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (-.f64 (pow.f64 a #s(literal 8 binary64)) (-.f64 (pow.f64 b #s(literal 8 binary64)) (pow.f64 (.f64 b a) #s(literal 4 binary64))))) #s(literal 1/2 binary64)) (hypot.f64 (.f64 b (+.f64 b a)) (.f64 a a)))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (+.f64 (pow.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 a #s(literal 12 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) (pow.f64 a #s(literal 8 binary64)))))
(.f64 (pow.f64 (.f64 (fma.f64 b b (*.f64 a a)) (-.f64 a b)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 b a) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 (fma.f64 b b (*.f64 a a)) (+.f64 b a)) #s(literal 1/4 binary64)) (pow.f64 (-.f64 a b) #s(literal 1/4 binary64)))
(.f64 (neg.f64 (pow.f64 (fma.f64 b b (.f64 a a)) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal 1/4 binary64))))
(.f64 (fabs.f64 (pow.f64 (fma.f64 b b (.f64 a a)) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal 1/4 binary64))))
(.f64 (pow.f64 (fma.f64 b b (.f64 a a)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal 1/4 binary64)))
(.f64 (hypot.f64 (.f64 b (+.f64 b a)) (.f64 a a)) (pow.f64 (/.f64 (fma.f64 b b (.f64 a a)) (-.f64 (pow.f64 (*.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a)))
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
(.f64 (hypot.f64 b a) (pow.f64 (/.f64 (fma.f64 b b (.f64 a a)) (fma.f64 b b (*.f64 a a))) #s(literal 1/2 binary64)))
(pow.f64 (neg.f64 (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (fabs.f64 (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 (fma.f64 b b (*.f64 a a)))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal 1/2 binary64))
(pow.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) #s(literal 1/4 binary64))
(/.f64 (neg.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64))) (neg.f64 (hypot.f64 b a)))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))) (neg.f64 (hypot.f64 (.f64 b (+.f64 b a)) (.f64 a a))))
(/.f64 (pow.f64 (hypot.f64 b a) #s(literal 2 binary64)) (hypot.f64 b a))
(/.f64 (hypot.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (hypot.f64 (.f64 b (+.f64 b a)) (.f64 a a)))
(sqrt.f64 (exp.f64 (log.f64 (fma.f64 b b (*.f64 a a)))))
(sqrt.f64 (fma.f64 b b (*.f64 a a)))
(hypot.f64 (exp.f64 (log.f64 b)) (exp.f64 (log.f64 a)))
(hypot.f64 (exp.f64 (log.f64 b)) a)
(hypot.f64 (exp.f64 (log.f64 a)) (exp.f64 (log.f64 b)))
(hypot.f64 (exp.f64 (log.f64 a)) b)
(hypot.f64 b (exp.f64 (log.f64 a)))
(hypot.f64 b a)
(hypot.f64 a (exp.f64 (log.f64 b)))
(hypot.f64 a b)
(exp.f64 (fma.f64 (log.f64 (fma.f64 b b (.f64 a a))) #s(literal 1/4 binary64) (.f64 (log.f64 (fma.f64 b b (*.f64 a a))) #s(literal 1/4 binary64))))
(exp.f64 (fma.f64 (log.f64 (-.f64 a b)) #s(literal 1/2 binary64) (*.f64 (log.f64 (+.f64 b a)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 (+.f64 b a)) #s(literal 1/2 binary64) (*.f64 (log.f64 (-.f64 a b)) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (fma.f64 b b (*.f64 a a))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (exp.f64 (log.f64 (fma.f64 b b (.f64 a a))))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 b b (.f64 a a)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) #s(literal 1/4 binary64)))
(exp.f64 (log.f64 (hypot.f64 b a)))
(+.f64 (cosh.f64 (log.f64 (hypot.f64 b a))) (sinh.f64 (log.f64 (hypot.f64 b a))))
(.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (fma.f64 b b (.f64 a a)))
(.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (-.f64 (pow.f64 a #s(literal 8 binary64)) (-.f64 (pow.f64 b #s(literal 8 binary64)) (pow.f64 (.f64 b a) #s(literal 4 binary64))))) (-.f64 (pow.f64 (*.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (+.f64 (pow.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 a #s(literal 12 binary64)))) (fma.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) (pow.f64 a #s(literal 8 binary64))))
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 (+.f64 b a) (-.f64 a b))
(.f64 (fma.f64 b b (.f64 a a)) (/.f64 (fma.f64 b b (.f64 a a)) (fma.f64 b b (.f64 a a))))
(.f64 (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) (/.f64 (fma.f64 b b (.f64 a a)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (-.f64 a b)) (+.f64 b a))
(/.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (+.f64 b a)) (-.f64 a b))
(/.f64 (.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (+.f64 b a)) (fma.f64 b (+.f64 b a) (.f64 a a)))
(/.f64 (.f64 (+.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (-.f64 a b)) (fma.f64 b (+.f64 b a) (.f64 a a)))
(/.f64 (.f64 (-.f64 a b) (+.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))) (fma.f64 b (+.f64 b a) (.f64 a a)))
(/.f64 (.f64 (-.f64 a b) (fma.f64 b b (.f64 a a))) (-.f64 a b))
(/.f64 (.f64 (+.f64 b a) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (fma.f64 b (+.f64 b a) (.f64 a a)))
(/.f64 (.f64 (+.f64 b a) (fma.f64 b b (.f64 a a))) (+.f64 b a))
(/.f64 (.f64 (fma.f64 b b (.f64 a a)) (-.f64 a b)) (-.f64 a b))
(/.f64 (.f64 (fma.f64 b b (.f64 a a)) (+.f64 b a)) (+.f64 b a))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) #s(literal 2 binary64))) (fma.f64 b b (*.f64 a a)))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 2 binary64))) (fma.f64 b b (*.f64 a a)))
(/.f64 (-.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) (fma.f64 b b (*.f64 a a)))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (*.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))))))))
(/.f64 (.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (+.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))) (.f64 (fma.f64 b (+.f64 b a) (.f64 a a)) (fma.f64 b (+.f64 b a) (.f64 a a))))
(/.f64 (.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (fma.f64 b b (.f64 a a))) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))))
(/.f64 (.f64 (fma.f64 b b (.f64 a a)) (+.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))) (.f64 (+.f64 b a) (fma.f64 b (+.f64 b a) (.f64 a a))))
(/.f64 (.f64 (+.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (fma.f64 b b (.f64 a a))) (+.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))))
(/.f64 (.f64 (fma.f64 b b (.f64 a a)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (.f64 (-.f64 a b) (fma.f64 b (+.f64 b a) (.f64 a a))))
(/.f64 (-.f64 (.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) (.f64 (fma.f64 b b (.f64 a a)) (pow.f64 b #s(literal 4 binary64)))) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))))
(/.f64 (-.f64 (.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) (.f64 (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) (pow.f64 b #s(literal 6 binary64)))) (-.f64 (pow.f64 a #s(literal 8 binary64)) (-.f64 (pow.f64 b #s(literal 8 binary64)) (pow.f64 (*.f64 b a) #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 a #s(literal 8 binary64)) (pow.f64 b #s(literal 8 binary64))) (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal 3 binary64)))
(/.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (.f64 (-.f64 (pow.f64 a #s(literal 8 binary64)) (-.f64 (pow.f64 b #s(literal 8 binary64)) (pow.f64 (.f64 b a) #s(literal 4 binary64)))) (fma.f64 b b (*.f64 a a))))
(/.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 a #s(literal 18 binary64)) (pow.f64 b #s(literal 18 binary64))) (.f64 (+.f64 (-.f64 (pow.f64 b #s(literal 12 binary64)) (pow.f64 (.f64 b a) #s(literal 6 binary64))) (pow.f64 a #s(literal 12 binary64))) (-.f64 (pow.f64 (*.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (fma.f64 b b (*.f64 a a)))
(/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (+.f64 (pow.f64 b #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (.f64 (fma.f64 b (+.f64 b a) (.f64 a a)) (fma.f64 b (+.f64 b a) (*.f64 a a))))
(/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (-.f64 (pow.f64 (*.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))))
(neg.f64 (fma.f64 b b (*.f64 a a)))
(fma.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 a #s(literal 8 binary64)) (-.f64 (pow.f64 b #s(literal 8 binary64)) (pow.f64 (.f64 b a) #s(literal 4 binary64))))) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (*.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(fma.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (+.f64 (pow.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 a #s(literal 12 binary64)))) (fma.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) (pow.f64 a #s(literal 8 binary64))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(fma.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))))
(fma.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (fma.f64 b b (.f64 a a)) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))))
(fma.f64 (exp.f64 (log.f64 b)) (exp.f64 (log.f64 b)) (*.f64 a a))
(fma.f64 (exp.f64 (log.f64 a)) (exp.f64 (log.f64 a)) (*.f64 b b))
(fma.f64 (pow.f64 a #s(literal 3 binary64)) (/.f64 (pow.f64 a #s(literal 3 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(fma.f64 (pow.f64 a #s(literal 3 binary64)) (/.f64 a (fma.f64 b b (.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))))
(fma.f64 (-.f64 a b) b (*.f64 (-.f64 a b) a))
(fma.f64 (-.f64 a b) a (*.f64 (-.f64 a b) b))
(fma.f64 (pow.f64 a #s(literal 4 binary64)) (/.f64 (.f64 a a) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (*.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(fma.f64 b (-.f64 a b) (*.f64 a (-.f64 a b)))
(fma.f64 b b (*.f64 a a))
(fma.f64 (.f64 a a) (/.f64 (pow.f64 a #s(literal 4 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (*.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(fma.f64 (.f64 a a) (/.f64 (.f64 a a) (fma.f64 b b (.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))))
(fma.f64 a (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 b b (.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))))
(fma.f64 a (-.f64 a b) (*.f64 b (-.f64 a b)))
(fma.f64 a a (*.f64 b b))
(-.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))))
(-.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(-.f64 (.f64 b b) (.f64 a a))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (.f64 b (-.f64 a b)) (.f64 a (-.f64 a b)))
(+.f64 (.f64 a (-.f64 a b)) (.f64 b (-.f64 a b)))
(+.f64 (.f64 (-.f64 a b) b) (.f64 (-.f64 a b) a))
(+.f64 (.f64 (-.f64 a b) a) (.f64 (-.f64 a b) b))
(+.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))))
(+.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(+.f64 (.f64 b b) (.f64 a a))
(+.f64 (.f64 a a) (.f64 b b))
(*.f64 (exp.f64 (log.f64 a)) (exp.f64 (log.f64 a)))
(*.f64 a a)
(pow.f64 (exp.f64 (log.f64 a)) #s(literal 2 binary64))
(pow.f64 (pow.f64 a #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 a a) #s(literal 1 binary64))
(pow.f64 a #s(literal 2 binary64))
(neg.f64 (*.f64 a a))
(sqrt.f64 (pow.f64 a #s(literal 4 binary64)))
(fabs.f64 (*.f64 a a))
(exp.f64 (+.f64 (/.f64 (.f64 (log.f64 a) #s(literal 2 binary64)) #s(literal 2 binary64)) (/.f64 (.f64 (log.f64 a) #s(literal 2 binary64)) #s(literal 2 binary64))))
(exp.f64 (+.f64 (/.f64 (.f64 (log.f64 a) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (log.f64 a) #s(literal 1 binary64))))
(exp.f64 (fma.f64 (log.f64 a) #s(literal 1 binary64) (/.f64 (*.f64 (log.f64 a) #s(literal 2 binary64)) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (log.f64 a) #s(literal 1 binary64) (*.f64 (log.f64 a) #s(literal 1 binary64))))
(exp.f64 (/.f64 (*.f64 #s(literal 4 binary64) (log.f64 a)) #s(literal 2 binary64)))
(exp.f64 (/.f64 (.f64 (.f64 (log.f64 a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (/.f64 (*.f64 (log.f64 a) #s(literal 4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (/.f64 (.f64 (log.f64 a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 a) #s(literal 1 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 a))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 a) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 a) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 a) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 a) #s(literal 2 binary64))))
(*.f64 (exp.f64 (log.f64 b)) (exp.f64 (log.f64 b)))
(*.f64 b b)
(pow.f64 (exp.f64 (log.f64 b)) #s(literal 2 binary64))
(pow.f64 (pow.f64 b #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 b b) #s(literal 1 binary64))
(pow.f64 b #s(literal 2 binary64))
(neg.f64 (*.f64 b b))
(sqrt.f64 (pow.f64 b #s(literal 4 binary64)))
(fabs.f64 (*.f64 b b))
(exp.f64 (+.f64 (/.f64 (.f64 (log.f64 b) #s(literal 2 binary64)) #s(literal 2 binary64)) (/.f64 (.f64 (log.f64 b) #s(literal 2 binary64)) #s(literal 2 binary64))))
(exp.f64 (+.f64 (/.f64 (.f64 (log.f64 b) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (log.f64 b) #s(literal 1 binary64))))
(exp.f64 (fma.f64 (log.f64 b) #s(literal 1 binary64) (/.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)) #s(literal 2 binary64))))
(exp.f64 (fma.f64 (log.f64 b) #s(literal 1 binary64) (*.f64 (log.f64 b) #s(literal 1 binary64))))
(exp.f64 (/.f64 (*.f64 #s(literal 4 binary64) (log.f64 b)) #s(literal 2 binary64)))
(exp.f64 (/.f64 (.f64 (.f64 (log.f64 b) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (/.f64 (*.f64 (log.f64 b) #s(literal 4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (/.f64 (.f64 (log.f64 b) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 b) #s(literal 1 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 b))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 b) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 b) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 b) #s(literal 2 binary64))))

eval19.0ms (0.7%)

Memory: 25.3MiB live, 25.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 3 481 to 647 computations (81.4% saved)

prune7.0ms (0.3%)

Memory

9.1MiB live, 9.1MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	177	5	182
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	178	5	183

Accuracy

100.0%

Counts

183 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a)))
▶	53.0%	(sqrt.f64 (fma.f64 b b (*.f64 a a)))
▶	1.4%	(sqrt.f64 #s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b)))
▶	99.9%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))
▶	1.1%	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))

Compiler

Compiled 114 to 80 computations (29.8% saved)

simplify104.0ms (4%)

Memory

-39.0MiB live, 21.6MiB allocated; 5ms collecting garbage

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (+.f64 b a))
cost-diff	0	(-.f64 a b)
cost-diff	0	(sqrt.f64 (-.f64 a b))
cost-diff	0	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a)))
cost-diff	0	(*.f64 a a)
cost-diff	0	(fma.f64 b b (*.f64 a a))
cost-diff	4	(sqrt.f64 (fma.f64 b b (*.f64 a a)))
cost-diff	0	(neg.f64 b)
cost-diff	0	(*.f64 (neg.f64 b) b)
cost-diff	0	#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
cost-diff	0	(sqrt.f64 #s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b)))
cost-diff	0	(neg.f64 a)
cost-diff	0	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
cost-diff	0	(/.f64 #s(literal -1/2 binary64) a)
cost-diff	0	(*.f64 (/.f64 #s(literal -1/2 binary64) a) b)
cost-diff	0	(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)
cost-diff	0	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	125
0	41	125
1	63	125
2	153	125
3	383	125
4	740	125
5	1280	125
6	1869	125
7	2553	125
8	3388	125
9	4058	125
10	4522	125
11	5025	125
12	5377	125
13	5473	125
14	5662	125
0	5662	121

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize62.0ms (2.4%)

Memory

-1.6MiB live, 88.4MiB allocated; 9ms collecting garbage

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 b a)
accuracy	0.0	(sqrt.f64 (+.f64 b a))
accuracy	0.00390625	(sqrt.f64 (-.f64 a b))
accuracy	0.46875	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a)))
accuracy	0.0	(fma.f64 b b (*.f64 a a))
accuracy	0.0	(*.f64 a a)
accuracy	30.059792083787244	(sqrt.f64 (fma.f64 b b (*.f64 a a)))
accuracy	0.0	(*.f64 (neg.f64 b) b)
accuracy	0.0	(neg.f64 b)
accuracy	30.059792083774497	(sqrt.f64 #s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b)))
accuracy	59.317585877554606	#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
accuracy	0.0	(neg.f64 a)
accuracy	63.2746531684847	#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
accuracy	0.0	(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a)
accuracy	0.0	(/.f64 #s(literal -1/2 binary64) a)
accuracy	0.06979876947798899	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))
accuracy	0.2109375	(*.f64 (/.f64 #s(literal -1/2 binary64) a) b)

Samples

46.0ms

256×

valid

Compiler

Compiled 108 to 23 computations (78.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-mult: 11.0ms (36.9% of total)

ival-sqrt: 5.0ms (16.8% of total)

ival-hypot: 4.0ms (13.4% of total)

ival-add: 3.0ms (10.1% of total)

ival-div: 2.0ms (6.7% of total)

ival-sub: 2.0ms (6.7% of total)

ival-neg: 2.0ms (6.7% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series27.0ms (1%)

Memory

24.6MiB live, 24.6MiB allocated; 0ms collecting garbage

Counts

18 → 130

Calls

Call 1

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

Outputs
(* b (sqrt -1))
(+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(+ (* 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)))))))
(* -1/2 (/ (pow b 2) a))
(/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)
(* -1/2 (/ b a))
(/ -1/2 a)
(* -1 a)
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
b
(+ b (* 1/2 (/ (pow a 2) b)))
(+ b (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (pow b 3))) (* 1/2 (/ 1 b)))))
(+ b (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (pow b 5))) (* 1/8 (/ 1 (pow b 3))))) (* 1/2 (/ 1 b)))))
(pow b 2)
(+ (pow a 2) (pow b 2))
(pow a 2)
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
(* (sqrt b) (sqrt -1))
(+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))
(+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))
(+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))
(* -1 b)
(- a b)
(sqrt b)
(+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))
(+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))
(+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))
(+ a b)
a
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))
(* 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)))))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (* 1/2 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* 1/2 (/ (pow b 2) (pow a 2))))))
(* a (+ 1 (+ (* -1/8 (/ (pow b 4) (pow a 4))) (+ (* 1/16 (/ (pow b 6) (pow a 6))) (* 1/2 (/ (pow b 2) (pow a 2)))))))
(* (pow a 2) (+ 1 (/ (pow b 2) (pow a 2))))
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(sqrt a)
(* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))
(* a (+ 1 (* -1 (/ b a))))
(* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
(* a (+ 1 (/ b a)))
(* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))
(* -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))))))))
(* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))
(* -1 (* a (+ 1 (* 1/2 (/ (pow b 2) (pow a 2))))))
(* -1 (* a (+ 1 (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* 1/2 (/ (pow b 2) (pow a 2)))))))
(* -1 (* a (+ 1 (+ (* -1/8 (/ (pow b 4) (pow a 4))) (+ (* 1/16 (/ (pow b 6) (pow a 6))) (* 1/2 (/ (pow b 2) (pow a 2))))))))
(* -1 (* a (pow (sqrt -1) 2)))
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (* (pow b 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(+ a (* -1/2 (/ (pow b 2) a)))
(+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))
(+ 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)))))
(+ (* -1 (pow b 2)) (pow a 2))
(+ a (* 1/2 (/ (pow b 2) a)))
(+ a (* (pow b 2) (+ (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))
(+ 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)))))
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b)))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)))))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(+ a (* -1 b))
(+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b)))
(+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a))))))
(+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -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)))))))
(* 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))))))))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* b (+ 1 (* 1/2 (/ (pow a 2) (pow b 2)))))
(* b (+ 1 (+ (* -1/8 (/ (pow a 4) (pow b 4))) (* 1/2 (/ (pow a 2) (pow b 2))))))
(* b (+ 1 (+ (* -1/8 (/ (pow a 4) (pow b 4))) (+ (* 1/16 (/ (pow a 6) (pow b 6))) (* 1/2 (/ (pow a 2) (pow b 2)))))))
(* (pow b 2) (+ 1 (/ (pow a 2) (pow b 2))))
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
(* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(* b (- (/ a b) 1))
(* b (+ (sqrt (/ 1 b)) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (pow a 3) (sqrt (/ 1 (pow b 7))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))
(* b (+ 1 (/ a b)))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(* -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))))))))
(* -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)))))))))
(* -1 (* b (+ 1 (* 1/2 (/ (pow a 2) (pow b 2))))))
(* -1 (* b (+ 1 (+ (* -1/8 (/ (pow a 4) (pow b 4))) (* 1/2 (/ (pow a 2) (pow b 2)))))))
(* -1 (* b (+ 1 (+ (* -1/8 (/ (pow a 4) (pow b 4))) (+ (* 1/16 (/ (pow a 6) (pow b 6))) (* 1/2 (/ (pow a 2) (pow b 2))))))))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* -1 (* (sqrt b) (sqrt -1)))
(* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* (sqrt b) (pow (sqrt -1) 2)))
(* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))
(* -1 (* b (- (* -1 (/ a b)) 1)))

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	b	@	inf	((sqrt (- (* a a) (* b b))) (+ (* (* (/ -1/2 a) b) b) a) (* (/ -1/2 a) b) (/ -1/2 a) (sqrt (- (* a a) (* b b))) (neg a) (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* (neg b) b) (neg b) (sqrt (+ (* b b) (* a a))) (+ (* b b) (* a a)) (* a a) (* (sqrt (- a b)) (sqrt (+ b a))) (sqrt (- a b)) (- a b) (sqrt (+ b a)) (+ b a))
5.0ms	a	@	inf	((sqrt (- (* a a) (* b b))) (+ (* (* (/ -1/2 a) b) b) a) (* (/ -1/2 a) b) (/ -1/2 a) (sqrt (- (* a a) (* b b))) (neg a) (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* (neg b) b) (neg b) (sqrt (+ (* b b) (* a a))) (+ (* b b) (* a a)) (* a a) (* (sqrt (- a b)) (sqrt (+ b a))) (sqrt (- a b)) (- a b) (sqrt (+ b a)) (+ b a))
4.0ms	a	@	0	((sqrt (- (* a a) (* b b))) (+ (* (* (/ -1/2 a) b) b) a) (* (/ -1/2 a) b) (/ -1/2 a) (sqrt (- (* a a) (* b b))) (neg a) (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* (neg b) b) (neg b) (sqrt (+ (* b b) (* a a))) (+ (* b b) (* a a)) (* a a) (* (sqrt (- a b)) (sqrt (+ b a))) (sqrt (- a b)) (- a b) (sqrt (+ b a)) (+ b a))
4.0ms	a	@	-inf	((sqrt (- (* a a) (* b b))) (+ (* (* (/ -1/2 a) b) b) a) (* (/ -1/2 a) b) (/ -1/2 a) (sqrt (- (* a a) (* b b))) (neg a) (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* (neg b) b) (neg b) (sqrt (+ (* b b) (* a a))) (+ (* b b) (* a a)) (* a a) (* (sqrt (- a b)) (sqrt (+ b a))) (sqrt (- a b)) (- a b) (sqrt (+ b a)) (+ b a))
3.0ms	b	@	-inf	((sqrt (- (* a a) (* b b))) (+ (* (* (/ -1/2 a) b) b) a) (* (/ -1/2 a) b) (/ -1/2 a) (sqrt (- (* a a) (* b b))) (neg a) (sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* (neg b) b) (neg b) (sqrt (+ (* b b) (* a a))) (+ (* b b) (* a a)) (* a a) (* (sqrt (- a b)) (sqrt (+ b a))) (sqrt (- a b)) (- a b) (sqrt (+ b a)) (+ b a))

simplify195.0ms (7.4%)

Memory

-0.6MiB live, 137.8MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	598	2974
1	2145	2569
0	9492	2395

Stop Event

1×	iter limit
1×	node limit

Counts

130 → 128

Calls

Call 1

Inputs
(* b (sqrt -1))
(+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(+ (* 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)))))))
(* -1/2 (/ (pow b 2) a))
(/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)
(* -1/2 (/ b a))
(/ -1/2 a)
(* -1 a)
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
b
(+ b (* 1/2 (/ (pow a 2) b)))
(+ b (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (pow b 3))) (* 1/2 (/ 1 b)))))
(+ b (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (pow b 5))) (* 1/8 (/ 1 (pow b 3))))) (* 1/2 (/ 1 b)))))
(pow b 2)
(+ (pow a 2) (pow b 2))
(pow a 2)
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
(* (sqrt b) (sqrt -1))
(+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))
(+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))
(+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))
(* -1 b)
(- a b)
(sqrt b)
(+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))
(+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))
(+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))
(+ a b)
a
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))
(* 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)))))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (* 1/2 (/ (pow b 2) (pow a 2)))))
(* a (+ 1 (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* 1/2 (/ (pow b 2) (pow a 2))))))
(* a (+ 1 (+ (* -1/8 (/ (pow b 4) (pow a 4))) (+ (* 1/16 (/ (pow b 6) (pow a 6))) (* 1/2 (/ (pow b 2) (pow a 2)))))))
(* (pow a 2) (+ 1 (/ (pow b 2) (pow a 2))))
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(sqrt a)
(* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))
(* a (+ 1 (* -1 (/ b a))))
(* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
(* a (+ 1 (/ b a)))
(* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))
(* -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))))))))
(* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))
(* -1 (* a (+ 1 (* 1/2 (/ (pow b 2) (pow a 2))))))
(* -1 (* a (+ 1 (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* 1/2 (/ (pow b 2) (pow a 2)))))))
(* -1 (* a (+ 1 (+ (* -1/8 (/ (pow b 4) (pow a 4))) (+ (* 1/16 (/ (pow b 6) (pow a 6))) (* 1/2 (/ (pow b 2) (pow a 2))))))))
(* -1 (* a (pow (sqrt -1) 2)))
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt a) (pow (sqrt -1) 2)))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (* (pow b 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))
(* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(+ a (* -1/2 (/ (pow b 2) a)))
(+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))
(+ 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)))))
(+ (* -1 (pow b 2)) (pow a 2))
(+ a (* 1/2 (/ (pow b 2) a)))
(+ a (* (pow b 2) (+ (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))
(+ 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)))))
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b)))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)))))
(+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(+ a (* -1 b))
(+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b)))
(+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a))))))
(+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))
(* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -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)))))))
(* 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))))))))
(* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* b (+ 1 (* 1/2 (/ (pow a 2) (pow b 2)))))
(* b (+ 1 (+ (* -1/8 (/ (pow a 4) (pow b 4))) (* 1/2 (/ (pow a 2) (pow b 2))))))
(* b (+ 1 (+ (* -1/8 (/ (pow a 4) (pow b 4))) (+ (* 1/16 (/ (pow a 6) (pow b 6))) (* 1/2 (/ (pow a 2) (pow b 2)))))))
(* (pow b 2) (+ 1 (/ (pow a 2) (pow b 2))))
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
(* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(* b (- (/ a b) 1))
(* b (+ (sqrt (/ 1 b)) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))))
(* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (pow a 3) (sqrt (/ 1 (pow b 7))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))
(* b (+ 1 (/ a b)))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))
(* -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))))))))
(* -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)))))))))
(* -1 (* b (+ 1 (* 1/2 (/ (pow a 2) (pow b 2))))))
(* -1 (* b (+ 1 (+ (* -1/8 (/ (pow a 4) (pow b 4))) (* 1/2 (/ (pow a 2) (pow b 2)))))))
(* -1 (* b (+ 1 (+ (* -1/8 (/ (pow a 4) (pow b 4))) (+ (* 1/16 (/ (pow a 6) (pow b 6))) (* 1/2 (/ (pow a 2) (pow b 2))))))))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* -1 (* (sqrt b) (sqrt -1)))
(* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* (sqrt b) (pow (sqrt -1) 2)))
(* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))
(* -1 (* b (- (* -1 (/ a b)) 1)))

Outputs
(* b (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) b)
(+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (.f64 a a) b) (.f64 (sqrt.f64 #s(literal -1 binary64)) b))
(+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))
(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))
(+ (* 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)))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (/.f64 a (pow.f64 b #s(literal 5 binary64))) (/.f64 a (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) #s(literal 1/16 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))
(* -1/2 (/ (pow b 2) a))
(.f64 (/.f64 (.f64 b b) a) #s(literal -1/2 binary64))
(/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)
(/.f64 (fma.f64 (.f64 b b) #s(literal -1/2 binary64) (.f64 a a)) a)
(* -1/2 (/ b a))
(*.f64 (/.f64 b a) #s(literal -1/2 binary64))
(/ -1/2 a)
(/.f64 #s(literal -1/2 binary64) a)
(* -1 a)
(neg.f64 a)
(* -1 (pow b 2))
(*.f64 (neg.f64 b) b)
(- (pow a 2) (pow b 2))
(*.f64 (+.f64 b a) (-.f64 a b))
b
(+ b (* 1/2 (/ (pow a 2) b)))
(fma.f64 (/.f64 (*.f64 a a) b) #s(literal 1/2 binary64) b)
(+ b (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (pow b 3))) (* 1/2 (/ 1 b)))))
(fma.f64 (fma.f64 (/.f64 (.f64 a a) (pow.f64 b #s(literal 3 binary64))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) b)) (.f64 a a) b)
(+ b (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (pow b 5))) (* 1/8 (/ 1 (pow b 3))))) (* 1/2 (/ 1 b)))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 a a) (pow.f64 b #s(literal 5 binary64))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 b #s(literal 3 binary64)))) (.f64 a a) (/.f64 #s(literal 1/2 binary64) b)) (*.f64 a a) b)
(pow b 2)
(*.f64 b b)
(+ (pow a 2) (pow b 2))
(fma.f64 b b (*.f64 a a))
(pow a 2)
(*.f64 a a)
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) b (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(fma.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) (.f64 (neg.f64 b) b)))) a #s(literal 0 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) b)) a (.f64 (sqrt.f64 #s(literal -1 binary64)) b))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
(fma.f64 (+.f64 (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) (.f64 (neg.f64 b) b))) #s(literal 0 binary64)) (pow.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) b) #s(literal 3 binary64))) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 0 binary64) (.f64 (neg.f64 b) b)))) a #s(literal 0 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) b))) a (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))
(* (sqrt b) (sqrt -1))
(*.f64 (sqrt.f64 b) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (/.f64 a (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (.f64 (sqrt.f64 b) (sqrt.f64 #s(literal -1 binary64))))
(+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 a (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 3 binary64)))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) a (.f64 (sqrt.f64 b) (sqrt.f64 #s(literal -1 binary64))))
(+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (/.f64 a (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 3 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) #s(literal -1/8 binary64))) a (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) a (*.f64 (sqrt.f64 b) (sqrt.f64 #s(literal -1 binary64))))
(* -1 b)
(neg.f64 b)
(- a b)
(-.f64 a b)
(sqrt b)
(sqrt.f64 b)
(+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))
(fma.f64 (*.f64 a #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (sqrt.f64 b))
(+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))
(fma.f64 (fma.f64 (.f64 a #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) #s(literal 1/2 binary64))) a (sqrt.f64 b))
(+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 3 binary64)))) #s(literal -1/8 binary64))) a (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) #s(literal 1/2 binary64))) a (sqrt.f64 b))
(+ a b)
(+.f64 b a)
a
(* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))
(fma.f64 (.f64 a #s(literal -1/2 binary64)) (.f64 (/.f64 b a) (/.f64 b a)) a)
(* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))
(fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) a) (/.f64 (.f64 b b) a) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 b #s(literal 4 binary64))) (pow.f64 a #s(literal 4 binary64)))) a a)
(* 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)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))) #s(literal -1/16 binary64) (fma.f64 (/.f64 #s(literal -1/2 binary64) a) (/.f64 (.f64 b b) a) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 b #s(literal 4 binary64))) (pow.f64 a #s(literal 4 binary64))))) a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (/.f64 b a) (/.f64 b a))) (*.f64 a a))
(* a (+ 1 (* 1/2 (/ (pow b 2) (pow a 2)))))
(fma.f64 (.f64 a #s(literal 1/2 binary64)) (.f64 (/.f64 b a) (/.f64 b a)) a)
(* a (+ 1 (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* 1/2 (/ (pow b 2) (pow a 2))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) a) (/.f64 (.f64 b b) a) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 b #s(literal 4 binary64))) (pow.f64 a #s(literal 4 binary64)))) a a)
(* a (+ 1 (+ (* -1/8 (/ (pow b 4) (pow a 4))) (+ (* 1/16 (/ (pow b 6) (pow a 6))) (* 1/2 (/ (pow b 2) (pow a 2)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) a) (/.f64 (.f64 b b) a) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 b #s(literal 4 binary64))) (pow.f64 a #s(literal 4 binary64))))) a a)
(* (pow a 2) (+ 1 (/ (pow b 2) (pow a 2))))
(.f64 (.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal 1 binary64)) a) a)
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
a
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) a) (/.f64 (fma.f64 (neg.f64 b) b #s(literal 0 binary64)) a) #s(literal 1 binary64)) a)
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(*.f64 (fma.f64 (/.f64 (fma.f64 (neg.f64 b) b #s(literal 0 binary64)) a) #s(literal 0 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) a) (/.f64 (fma.f64 (neg.f64 b) b #s(literal 0 binary64)) a) #s(literal 1 binary64))) a)
(sqrt a)
(sqrt.f64 a)
(* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) b) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) a)
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 b b)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal -1/2 binary64) b) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))) a)
(* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))
(.f64 (-.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 b b)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal -1/2 binary64) b) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))) (.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 b #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))))) a)
(* a (+ 1 (* -1 (/ b a))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 b a)) a)
(* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) b) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a))) a)
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))
(.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 b b)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) b) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))) a)
(* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
(.f64 (+.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 b b)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 b #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 7 binary64)))))) (fma.f64 (.f64 #s(literal 1/2 binary64) b) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 a #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) a)))) a)
(* a (+ 1 (/ b a)))
(fma.f64 (/.f64 b a) a a)
(* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))
(.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) a) (/.f64 (.f64 b b) a) #s(literal 1 binary64)) (neg.f64 a))
(* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))
(.f64 (fma.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal -1/2 binary64) a) (/.f64 (.f64 b b) a) #s(literal 1 binary64))) (neg.f64 a))
(* -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))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))) #s(literal -1/16 binary64) (fma.f64 (/.f64 #s(literal -1/2 binary64) a) (/.f64 (.f64 b b) a) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 b #s(literal 4 binary64))) (pow.f64 a #s(literal 4 binary64))))) a a))
(* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))
(.f64 (-.f64 (.f64 (/.f64 #s(literal 1/2 binary64) a) (/.f64 (*.f64 b b) a)) #s(literal 1 binary64)) (neg.f64 a))
(* -1 (* a (+ 1 (* 1/2 (/ (pow b 2) (pow a 2))))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) a) (/.f64 (.f64 b b) a) #s(literal 1 binary64)) (neg.f64 a))
(* -1 (* a (+ 1 (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* 1/2 (/ (pow b 2) (pow a 2)))))))
(.f64 (fma.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) a) (/.f64 (.f64 b b) a) #s(literal 1 binary64))) (neg.f64 a))
(* -1 (* a (+ 1 (+ (* -1/8 (/ (pow b 4) (pow a 4))) (+ (* 1/16 (/ (pow b 6) (pow a 6))) (* 1/2 (/ (pow b 2) (pow a 2))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) a) (/.f64 (.f64 b b) a) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 b #s(literal 4 binary64))) (pow.f64 a #s(literal 4 binary64))))) a a))
(* -1 (* a (pow (sqrt -1) 2)))
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(.f64 (neg.f64 b) (fma.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 (.f64 a a) b) #s(literal 1 binary64))))
(* -1 (* b (+ 1 (+ (* -1/8 (/ (pow a 4) (pow b 4))) (+ (* 1/16 (/ (pow a 6) (pow b 6))) (* 1/2 (/ (pow a 2) (pow b 2))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) b) (/.f64 (.f64 a a) b) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 a #s(literal 4 binary64))) (pow.f64 b #s(literal 4 binary64))))) b b))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) b (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(*.f64 (neg.f64 b) (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 a a #s(literal 0 binary64)) b) (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) b)))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(.f64 (neg.f64 b) (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 (fma.f64 (/.f64 (fma.f64 a a #s(literal 0 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) (.f64 (neg.f64 b) (sqrt.f64 #s(literal -1 binary64))))) (neg.f64 b)) (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) b)))
(* -1 (* (sqrt b) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 b))
(* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))
(.f64 (neg.f64 b) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) a)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
(.f64 (neg.f64 b) (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) a) a)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) a)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (sqrt.f64 #s(literal -1 binary64))))))
(* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
(.f64 (neg.f64 b) (fma.f64 (.f64 (.f64 #s(literal -1/8 binary64) a) a) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64))))) (fma.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 a #s(literal 3 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64))))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) a)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (sqrt.f64 #s(literal -1 binary64)))))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(*.f64 (neg.f64 b) (-.f64 #s(literal 1 binary64) (/.f64 a b)))
(* -1 (* (sqrt b) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 b) #s(literal 1 binary64))
(* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))
(.f64 (neg.f64 b) (fma.f64 (.f64 #s(literal 1/2 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) #s(literal -1 binary64))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))
(.f64 (neg.f64 b) (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 a a) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) #s(literal -1 binary64)))))
(* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))
(.f64 (neg.f64 b) (fma.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 a a) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (fma.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 a #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) #s(literal -1 binary64))))))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(*.f64 (neg.f64 b) (-.f64 (/.f64 (neg.f64 a) b) #s(literal 1 binary64)))

rewrite141.0ms (5.3%)

Memory

18.6MiB live, 109.3MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	116
0	41	114
1	123	114
2	916	106
0	9579	94

Stop Event

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

Counts

18 → 813

Calls

Call 1

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

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

eval95.0ms (3.6%)

Memory: -21.4MiB live, 116.7MiB allocated; 27ms collecting garbage
Compiler: Compiled 16 059 to 2 201 computations (86.3% saved)

prune35.0ms (1.3%)

Memory

-11.3MiB live, 35.8MiB allocated; 2ms collecting garbage

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	683	1	684
Fresh	0	0	0
Picked	3	2	5
Done	0	0	0
Total	686	3	689

Accuracy

100.0%

Counts

689 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a)))
▶	99.5%	#s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a)
✓	99.9%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))

Compiler

Compiled 37 to 26 computations (29.7% saved)

simplify4.0ms (0.1%)

Memory

6.5MiB live, 6.5MiB allocated; 0ms collecting garbage

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
0	8	12
1	10	12
0	10	12

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

localize17.0ms (0.7%)

Memory

33.6MiB live, 33.6MiB allocated; 0ms collecting garbage

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
accuracy	0.29843597346232437	#s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a)

Samples

13.0ms

256×

valid

Compiler

Compiled 12 to 9 computations (25% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-sqrt: 3.0ms (39% of total)

ival-sub: 1.0ms (13% of total)

ival-add: 1.0ms (13% of total)

ival-mult: 1.0ms (13% of total)

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

adjust: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

3.3MiB live, 3.3MiB allocated; 0ms collecting garbage

Counts

1 → 22

Calls

Call 1

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

Outputs
(* b (sqrt -1))
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
a
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(* -1 (* a (pow (sqrt -1) 2)))
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	a	@	0	((* (sqrt (- a b)) (sqrt (+ b a))))
0.0ms	a	@	-inf	((* (sqrt (- a b)) (sqrt (+ b a))))
0.0ms	b	@	inf	((* (sqrt (- a b)) (sqrt (+ b a))))
0.0ms	a	@	inf	((* (sqrt (- a b)) (sqrt (+ b a))))
0.0ms	b	@	-inf	((* (sqrt (- a b)) (sqrt (+ b a))))

simplify143.0ms (5.4%)

Memory

-27.8MiB live, 166.0MiB allocated; 33ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	175	581
1	703	308
2	4482	277
0	8344	261

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 21

Calls

Call 1

Inputs
(* b (sqrt -1))
(+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))
(+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))
a
(* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))
(* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))
(* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))
(* -1 (* a (pow (sqrt -1) 2)))
(* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))
(+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))
(+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))
(+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))
(* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))
(* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))
(* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))
(* -1 (* b (sqrt -1)))
(* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))
(* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))

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

rewrite120.0ms (4.6%)

Memory

3.0MiB live, 109.0MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
0	8	10
1	36	10
2	262	10
3	3686	10
0	9401	10

Stop Event

1×	iter limit
1×	node limit
1×	saturated

Counts

1 → 1

Calls

Call 1

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

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

eval1.0ms (0%)

Memory: 1.2MiB live, 1.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 333 to 79 computations (76.3% saved)

prune2.0ms (0.1%)

Memory

2.4MiB live, 2.4MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	13	3	16

Accuracy

100.0%

Counts

16 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a)))
✓	99.5%	#s(approx (* (sqrt (- a b)) (sqrt (+ b a))) a)
✓	99.9%	#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) a) b) b a))

Compiler

Compiled 113 to 60 computations (46.9% saved)

regimes17.0ms (0.7%)

Memory

-27.8MiB live, 18.5MiB allocated; 4ms collecting garbage

Counts

7 → 1

Calls

Call 1

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

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

Calls

6 calls:

6.0ms	(*.f64 a a)
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))

Results

Accuracy	Segments	Branch
99.9%	1	`(*.f64 b b)`
99.9%	1	`(*.f64 a a)`
99.9%	1	`(-.f64 (.f64 a a) (.f64 b b))`
99.9%	1	`(sqrt.f64 (-.f64 (.f64 a a) (.f64 b b)))`
99.9%	1	`a`
99.9%	1	`b`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes10.0ms (0.4%)

Memory

18.2MiB live, 18.2MiB allocated; 0ms collecting garbage

Accuracy

Total -63.2b remaining (-21192.6%)

Threshold costs -63.2b (-21192.6%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Accuracy	Segments	Branch
99.5%	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)

simplify58.0ms (2.2%)

Memory

-19.9MiB live, 26.7MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	28
1	31	28
2	90	28
3	232	28
4	410	28
5	845	28
6	1396	28
7	2080	28
8	2915	28
9	3225	28
10	3287	28
11	3287	28
12	3365	28

Stop Event

1×

saturated

Calls

Call 1

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

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

derivations152.0ms (5.7%)

Memory

1.8MiB live, 53.3MiB allocated; 5ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 28 to 17 computations (39.3% saved)

preprocess20.0ms (0.8%)

Memory: 28.1MiB live, 28.1MiB allocated; 0ms collecting garbage
Remove: (abs b)
Compiler: Compiled 200 to 130 computations (35% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze33.0ms (1.2%)

sample769.0ms (29.1%)

explain83.0ms (3.1%)

preprocess127.0ms (4.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify72.0ms (2.7%)

localize18.0ms (0.7%)

series6.0ms (0.2%)

simplify180.0ms (6.8%)

rewrite123.0ms (4.7%)

eval19.0ms (0.7%)

prune7.0ms (0.3%)

simplify104.0ms (4%)

localize62.0ms (2.4%)

series27.0ms (1%)

simplify195.0ms (7.4%)

rewrite141.0ms (5.3%)

eval95.0ms (3.6%)

prune35.0ms (1.3%)

simplify4.0ms (0.1%)

localize17.0ms (0.7%)

series1.0ms (0%)

simplify143.0ms (5.4%)

rewrite120.0ms (4.6%)

eval1.0ms (0%)

prune2.0ms (0.1%)

regimes17.0ms (0.7%)

regimes10.0ms (0.4%)

simplify58.0ms (2.2%)

derivations152.0ms (5.7%)

preprocess20.0ms (0.8%)

end0.0ms (0%)

Profiling