Metrics for Difference of squares

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample880.0ms (64.4%)

Memory

31.9MiB live, 539.9MiB allocated; 838ms collecting garbage

Samples

647.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 371.0ms

ival-mult!: 351.0ms (94.6% of total)

ival-sub!: 18.0ms (4.9% of total)

adjust: 1.0ms (0.3% of total)

Bogosity

preprocess50.0ms (3.6%)

Memory

-25.3MiB live, 19.5MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	45
1	51	42
2	223	42
3	386	42
4	950	42
5	1955	42
6	2959	42
7	3299	42
8	3377	42
9	3377	42
10	3570	42

Stop Event

1×

saturated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	91.4%	(-.f64 (.f64 a a) (.f64 b b))

Symmetry

(abs a)

(abs b)

Compiler

Compiled 10 to 10 computations (0% saved)

series4.0ms (0.3%)

Memory

7.3MiB live, 7.3MiB allocated; 0ms collecting garbage

Counts

5 → 8

Calls

Call 1

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

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

Calls

6 calls:

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

rewrite65.0ms (4.8%)

Memory

41.5MiB live, 86.3MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	129
0	32	125
1	132	124
0	1187	123

Stop Event

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

Counts

13 → 127

Calls

Call 1

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

Outputs
(*.f64 (+.f64 (neg.f64 a) (neg.f64 b)) (-.f64 (neg.f64 a) (neg.f64 b)))
(*.f64 (+.f64 (neg.f64 a) (fabs.f64 b)) (-.f64 (neg.f64 a) (fabs.f64 b)))
(*.f64 (+.f64 (neg.f64 a) b) (-.f64 (neg.f64 a) b))
(*.f64 (+.f64 (fabs.f64 a) (neg.f64 b)) (-.f64 (fabs.f64 a) (neg.f64 b)))
(*.f64 (+.f64 (fabs.f64 a) (fabs.f64 b)) (-.f64 (fabs.f64 a) (fabs.f64 b)))
(*.f64 (+.f64 (fabs.f64 a) b) (-.f64 (fabs.f64 a) b))
(*.f64 (+.f64 a (neg.f64 b)) (-.f64 a (neg.f64 b)))
(*.f64 (+.f64 a (fabs.f64 b)) (-.f64 a (fabs.f64 b)))
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 (+.f64 b a) (-.f64 a b))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (.f64 b b) b) b) (.f64 (.f64 (.f64 a a) a) a))) (neg.f64 (-.f64 (.f64 (neg.f64 b) b) (.f64 a a))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 (.f64 b b) b) b) (.f64 (neg.f64 b) b) (.f64 (.f64 (.f64 (.f64 a a) a) a) (.f64 a a)))) (neg.f64 (fma.f64 (.f64 (.f64 b b) b) b (.f64 (.f64 a a) (fma.f64 b b (.f64 a a))))))
(/.f64 (neg.f64 (.f64 (fma.f64 b b (.f64 a a)) (.f64 (-.f64 a b) (+.f64 b a)))) (neg.f64 (fma.f64 b b (.f64 a a))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 a a) a) a) (.f64 a a)) (.f64 (.f64 (.f64 (.f64 b b) b) b) (.f64 b b)))) (neg.f64 (fma.f64 (.f64 (.f64 a a) a) a (.f64 (.f64 b b) (fma.f64 b b (*.f64 a a))))))
(/.f64 (.f64 (fma.f64 b b (.f64 a a)) (.f64 (-.f64 a b) (+.f64 b a))) (fma.f64 b b (.f64 a a)))
(/.f64 (-.f64 (.f64 (.f64 (.f64 b b) b) b) (.f64 (.f64 (.f64 a a) a) a)) (-.f64 (.f64 (neg.f64 b) b) (.f64 a a)))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 a a) a) a) (.f64 a a)) (.f64 (.f64 (.f64 (.f64 b b) b) b) (.f64 b b))) (fma.f64 (.f64 (.f64 a a) a) a (.f64 (.f64 b b) (fma.f64 b b (*.f64 a a)))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 b b) b) b) (.f64 (neg.f64 b) b) (.f64 (.f64 (.f64 (.f64 a a) a) a) (.f64 a a))) (fma.f64 (.f64 (.f64 a a) a) a (-.f64 (.f64 (.f64 (.f64 b b) b) b) (.f64 (.f64 a a) (*.f64 (neg.f64 b) b)))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 b b) b) b) (.f64 (neg.f64 b) b) (.f64 (.f64 (.f64 (.f64 a a) a) a) (.f64 a a))) (fma.f64 (.f64 (.f64 b b) b) b (.f64 (.f64 a a) (fma.f64 b b (.f64 a a)))))
(fma.f64 (.f64 #s(literal -1 binary64) (neg.f64 b)) (neg.f64 b) (.f64 a a))
(fma.f64 (.f64 #s(literal -1 binary64) (fabs.f64 b)) (fabs.f64 b) (.f64 a a))
(fma.f64 (.f64 #s(literal -1 binary64) b) b (.f64 a a))
(fma.f64 (.f64 (neg.f64 a) #s(literal 1 binary64)) (.f64 (neg.f64 a) #s(literal 1 binary64)) (*.f64 (neg.f64 b) b))
(fma.f64 (.f64 (fabs.f64 a) #s(literal 1 binary64)) (.f64 (fabs.f64 a) #s(literal 1 binary64)) (*.f64 (neg.f64 b) b))
(fma.f64 (.f64 a #s(literal 1 binary64)) (.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 b) b))
(fma.f64 (.f64 #s(literal 1 binary64) (neg.f64 a)) (.f64 #s(literal 1 binary64) (neg.f64 a)) (*.f64 (neg.f64 b) b))
(fma.f64 (.f64 #s(literal 1 binary64) (neg.f64 a)) (neg.f64 a) (.f64 (neg.f64 b) b))
(fma.f64 (.f64 #s(literal 1 binary64) (fabs.f64 a)) (.f64 #s(literal 1 binary64) (fabs.f64 a)) (*.f64 (neg.f64 b) b))
(fma.f64 (.f64 #s(literal 1 binary64) (fabs.f64 a)) (fabs.f64 a) (.f64 (neg.f64 b) b))
(fma.f64 (.f64 #s(literal 1 binary64) a) (.f64 #s(literal 1 binary64) a) (*.f64 (neg.f64 b) b))
(fma.f64 (.f64 #s(literal 1 binary64) a) a (.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 (neg.f64 b)) (neg.f64 b) (*.f64 a a))
(fma.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b) (*.f64 a a))
(fma.f64 (neg.f64 (neg.f64 a)) (neg.f64 (neg.f64 a)) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 (fabs.f64 a)) (neg.f64 (fabs.f64 a)) (*.f64 (neg.f64 b) b))
(fma.f64 (fabs.f64 (fabs.f64 a)) (fabs.f64 (fabs.f64 a)) (*.f64 (neg.f64 b) b))
(fma.f64 (exp.f64 (log.f64 a)) (exp.f64 (log.f64 a)) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 a) (.f64 (neg.f64 a) #s(literal 1 binary64)) (.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 a) (neg.f64 a) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 b) (.f64 (neg.f64 b) #s(literal -1 binary64)) (.f64 a a))
(fma.f64 (neg.f64 b) (neg.f64 (neg.f64 b)) (*.f64 a a))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(fma.f64 (fabs.f64 a) (.f64 (fabs.f64 a) #s(literal 1 binary64)) (.f64 (neg.f64 b) b))
(fma.f64 (fabs.f64 a) (fabs.f64 a) (*.f64 (neg.f64 b) b))
(fma.f64 (fabs.f64 b) (.f64 (fabs.f64 b) #s(literal -1 binary64)) (.f64 a a))
(fma.f64 (fabs.f64 b) (neg.f64 (fabs.f64 b)) (*.f64 a a))
(fma.f64 #s(literal 1 binary64) (.f64 a a) (.f64 (neg.f64 b) b))
(fma.f64 (.f64 a a) #s(literal 1 binary64) (.f64 (neg.f64 b) b))
(fma.f64 (.f64 b b) #s(literal -1 binary64) (.f64 a a))
(fma.f64 #s(literal -1 binary64) (.f64 b b) (.f64 a a))
(fma.f64 b (.f64 b #s(literal -1 binary64)) (.f64 a a))
(fma.f64 b (neg.f64 b) (*.f64 a a))
(fma.f64 a (.f64 a #s(literal 1 binary64)) (.f64 (neg.f64 b) b))
(fma.f64 a a (*.f64 (neg.f64 b) b))
(-.f64 (/.f64 (.f64 (.f64 (.f64 b b) b) b) (-.f64 (.f64 (neg.f64 b) b) (.f64 a a))) (/.f64 (.f64 (.f64 (.f64 a a) a) a) (-.f64 (.f64 (neg.f64 b) b) (.f64 a a))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 a a) a) a) (fma.f64 b b (.f64 a a))) (/.f64 (.f64 (.f64 (.f64 b b) b) b) (fma.f64 b b (.f64 a a))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 a a) a) a) (.f64 a a)) (fma.f64 (.f64 (.f64 a a) a) a (.f64 (.f64 b b) (fma.f64 b b (.f64 a a))))) (/.f64 (.f64 (.f64 (.f64 (.f64 b b) b) b) (.f64 b b)) (fma.f64 (.f64 (.f64 a a) a) a (.f64 (.f64 b b) (fma.f64 b b (.f64 a a))))))
(-.f64 (.f64 a a) (.f64 (*.f64 (neg.f64 b) b) #s(literal -1 binary64)))
(-.f64 (.f64 a a) (.f64 #s(literal 1 binary64) (*.f64 b b)))
(-.f64 (.f64 a a) (.f64 (neg.f64 (neg.f64 b)) b))
(-.f64 (.f64 a a) (.f64 b b))
(-.f64 (.f64 (neg.f64 b) b) (.f64 (neg.f64 a) a))
(+.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 b b) b) b) (.f64 (neg.f64 b) b)) (fma.f64 (.f64 (.f64 b b) b) b (.f64 (.f64 a a) (fma.f64 b b (.f64 a a))))) (/.f64 (.f64 (.f64 (.f64 (.f64 a a) a) a) (.f64 a a)) (fma.f64 (.f64 (.f64 b b) b) b (.f64 (.f64 a a) (fma.f64 b b (.f64 a a))))))
(+.f64 (.f64 a a) (.f64 (neg.f64 b) b))
(+.f64 (.f64 (neg.f64 b) b) (.f64 a a))
(.f64 (.f64 (neg.f64 a) #s(literal 1 binary64)) (*.f64 (neg.f64 a) #s(literal 1 binary64)))
(.f64 (.f64 (fabs.f64 a) #s(literal 1 binary64)) (*.f64 (fabs.f64 a) #s(literal 1 binary64)))
(.f64 (.f64 a #s(literal 1 binary64)) (*.f64 a #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 a)) (*.f64 #s(literal 1 binary64) (neg.f64 a)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 a)) (neg.f64 a))
(.f64 (.f64 #s(literal 1 binary64) (fabs.f64 a)) (*.f64 #s(literal 1 binary64) (fabs.f64 a)))
(.f64 (.f64 #s(literal 1 binary64) (fabs.f64 a)) (fabs.f64 a))
(.f64 (.f64 #s(literal 1 binary64) a) (*.f64 #s(literal 1 binary64) a))
(.f64 (.f64 #s(literal 1 binary64) a) a)
(*.f64 (neg.f64 (neg.f64 a)) (neg.f64 (neg.f64 a)))
(*.f64 (neg.f64 (fabs.f64 a)) (neg.f64 (fabs.f64 a)))
(*.f64 (fabs.f64 (fabs.f64 a)) (fabs.f64 (fabs.f64 a)))
(*.f64 (exp.f64 (log.f64 a)) (exp.f64 (log.f64 a)))
(.f64 (neg.f64 a) (.f64 (neg.f64 a) #s(literal 1 binary64)))
(*.f64 (neg.f64 a) (neg.f64 a))
(.f64 (fabs.f64 a) (.f64 (fabs.f64 a) #s(literal 1 binary64)))
(*.f64 (fabs.f64 a) (fabs.f64 a))
(.f64 #s(literal 1 binary64) (.f64 a a))
(.f64 (.f64 a a) #s(literal 1 binary64))
(.f64 a (.f64 a #s(literal 1 binary64)))
(*.f64 a a)
(pow.f64 (exp.f64 (log.f64 a)) #s(literal 2 binary64))
(pow.f64 (neg.f64 a) #s(literal 2 binary64))
(pow.f64 (fabs.f64 a) #s(literal 2 binary64))
(pow.f64 (*.f64 a a) #s(literal 1 binary64))
(pow.f64 a #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 a a)) #s(literal 2 binary64))
(/.f64 (.f64 (.f64 a a) #s(literal 2 binary64)) #s(literal 2 binary64))
(neg.f64 (.f64 (.f64 a a) #s(literal -1 binary64)))
(neg.f64 (.f64 #s(literal -1 binary64) (.f64 a a)))
(neg.f64 (*.f64 (neg.f64 a) a))
(fabs.f64 (*.f64 a a))
(exp.f64 (fma.f64 (log.f64 a) #s(literal 2 binary64) #s(literal 0 binary64)))
(exp.f64 (+.f64 #s(literal 0 binary64) (*.f64 (log.f64 a) #s(literal 2 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))))
a
(*.f64 (neg.f64 (neg.f64 b)) (neg.f64 (neg.f64 b)))
(*.f64 (neg.f64 (fabs.f64 b)) (neg.f64 (fabs.f64 b)))
(*.f64 (fabs.f64 (fabs.f64 b)) (fabs.f64 (fabs.f64 b)))
(*.f64 (exp.f64 (log.f64 b)) (exp.f64 (log.f64 b)))
(*.f64 (neg.f64 b) (neg.f64 b))
(*.f64 (fabs.f64 b) (fabs.f64 b))
(*.f64 b b)
(pow.f64 (exp.f64 (log.f64 b)) #s(literal 2 binary64))
(pow.f64 (neg.f64 b) #s(literal 2 binary64))
(pow.f64 (fabs.f64 b) #s(literal 2 binary64))
(pow.f64 (*.f64 b b) #s(literal 1 binary64))
(pow.f64 b #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 b) b))
(fabs.f64 (*.f64 b b))
(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))))
b
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
#s(approx (- (* a a) (* b b)) (*.f64 (-.f64 a b) (+.f64 b a)))
#s(approx (* a a) (*.f64 a a))
#s(approx (- (* a a) (* b b)) (*.f64 a a))
#s(approx (- (* a a) (* b b)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 b (/.f64 b (.f64 a a)))) (.f64 a a)))
#s(approx (- (* a a) (* b b)) (*.f64 (-.f64 a b) (+.f64 b a)))
#s(approx (* b b) (*.f64 b b))
#s(approx (- (* a a) (* b b)) (.f64 (.f64 (fma.f64 a (/.f64 a (*.f64 b b)) #s(literal -1 binary64)) b) b))

eval12.0ms (0.9%)

Memory: -27.4MiB live, 18.2MiB allocated; 2ms collecting garbage
Compiler: Compiled 766 to 289 computations (62.3% saved)

prune3.0ms (0.2%)

Memory

4.8MiB live, 4.8MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	2	122

Accuracy

100.0%

Counts

122 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.5%	#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
▶	56.3%	#s(approx (- (* a a) (* b b)) (*.f64 a a))

Compiler

Compiled 15 to 15 computations (0% saved)

series4.0ms (0.3%)

Memory

5.1MiB live, 5.1MiB allocated; 0ms collecting garbage

Counts

7 → 9

Calls

Call 1

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

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

Calls

6 calls:

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

rewrite91.0ms (6.7%)

Memory

-11.9MiB live, 40.6MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	157
0	41	151
1	141	150
0	1199	149

Stop Event

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

Counts

16 → 65

Calls

Call 1

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

Outputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(.f64 (.f64 (neg.f64 a) #s(literal 1 binary64)) (*.f64 (neg.f64 a) #s(literal 1 binary64)))
(.f64 (.f64 (fabs.f64 a) #s(literal 1 binary64)) (*.f64 (fabs.f64 a) #s(literal 1 binary64)))
(.f64 (.f64 a #s(literal 1 binary64)) (*.f64 a #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 a)) (*.f64 #s(literal 1 binary64) (neg.f64 a)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 a)) (neg.f64 a))
(.f64 (.f64 #s(literal 1 binary64) (fabs.f64 a)) (*.f64 #s(literal 1 binary64) (fabs.f64 a)))
(.f64 (.f64 #s(literal 1 binary64) (fabs.f64 a)) (fabs.f64 a))
(.f64 (.f64 #s(literal 1 binary64) a) (*.f64 #s(literal 1 binary64) a))
(.f64 (.f64 #s(literal 1 binary64) a) a)
(*.f64 (neg.f64 (neg.f64 a)) (neg.f64 (neg.f64 a)))
(*.f64 (neg.f64 (fabs.f64 a)) (neg.f64 (fabs.f64 a)))
(*.f64 (fabs.f64 (fabs.f64 a)) (fabs.f64 (fabs.f64 a)))
(*.f64 (exp.f64 (log.f64 a)) (exp.f64 (log.f64 a)))
(.f64 (neg.f64 a) (.f64 (neg.f64 a) #s(literal 1 binary64)))
(*.f64 (neg.f64 a) (neg.f64 a))
(.f64 (fabs.f64 a) (.f64 (fabs.f64 a) #s(literal 1 binary64)))
(*.f64 (fabs.f64 a) (fabs.f64 a))
(.f64 #s(literal 1 binary64) (.f64 a a))
(.f64 (.f64 a a) #s(literal 1 binary64))
(.f64 a (.f64 a #s(literal 1 binary64)))
(*.f64 a a)
(pow.f64 (exp.f64 (log.f64 a)) #s(literal 2 binary64))
(pow.f64 (neg.f64 a) #s(literal 2 binary64))
(pow.f64 (fabs.f64 a) #s(literal 2 binary64))
(pow.f64 (*.f64 a a) #s(literal 1 binary64))
(pow.f64 a #s(literal 2 binary64))
(/.f64 (.f64 (.f64 a a) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 a a)) #s(literal 2 binary64))
(neg.f64 (.f64 (.f64 a a) #s(literal -1 binary64)))
(neg.f64 (.f64 #s(literal -1 binary64) (.f64 a a)))
(neg.f64 (*.f64 (neg.f64 a) a))
(fabs.f64 (*.f64 a a))
(exp.f64 (fma.f64 (log.f64 a) #s(literal 2 binary64) #s(literal 0 binary64)))
(exp.f64 (+.f64 #s(literal 0 binary64) (*.f64 (log.f64 a) #s(literal 2 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))))
a
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
(.f64 (.f64 #s(literal -1 binary64) (fabs.f64 b)) (fabs.f64 b))
(.f64 (.f64 #s(literal -1 binary64) (neg.f64 b)) (neg.f64 b))
(*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b))
(*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b))
(.f64 (fabs.f64 b) (.f64 (fabs.f64 b) #s(literal -1 binary64)))
(*.f64 (fabs.f64 b) (neg.f64 (fabs.f64 b)))
(.f64 (.f64 b b) #s(literal -1 binary64))
(.f64 #s(literal -1 binary64) (.f64 b b))
(.f64 (neg.f64 b) (.f64 (neg.f64 b) #s(literal -1 binary64)))
(*.f64 (neg.f64 b) (neg.f64 (neg.f64 b)))
(*.f64 (neg.f64 b) b)
(*.f64 b (neg.f64 b))
(neg.f64 (*.f64 b b))
(*.f64 #s(literal -1 binary64) b)
(*.f64 b #s(literal -1 binary64))
(neg.f64 b)
b
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
#s(approx (- (* a a) (* b b)) (*.f64 (-.f64 a b) (+.f64 b a)))
#s(approx (* a a) (*.f64 a a))
#s(approx (- (* a a) (* b b)) (*.f64 a a))
#s(approx (- (* a a) (* b b)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 b (/.f64 b (.f64 a a)))) (.f64 a a)))
#s(approx (- (* a a) (* b b)) (*.f64 (-.f64 a b) (+.f64 b a)))
#s(approx (* (neg b) b) (*.f64 (neg.f64 b) b))
#s(approx (neg b) (neg.f64 b))
#s(approx (- (* a a) (* b b)) (.f64 (.f64 (fma.f64 a (/.f64 a (*.f64 b b)) #s(literal -1 binary64)) b) b))

eval5.0ms (0.3%)

Memory: 9.1MiB live, 9.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 266 to 166 computations (37.6% saved)

prune2.0ms (0.2%)

Memory

5.7MiB live, 5.7MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	55	2	57

Accuracy

100.0%

Counts

57 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	50.5%	#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
✓	56.3%	#s(approx (- (* a a) (* b b)) (*.f64 a a))

Compiler

Compiled 31 to 27 computations (12.9% saved)

regimes9.0ms (0.6%)

Memory

-27.6MiB live, 18.6MiB allocated; 3ms collecting garbage

Counts

3 → 2

Calls

Call 1

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

Outputs
(-.f64 (.f64 a a) (.f64 b b))
#s(approx (- (* a a) (* b b)) (*.f64 a a))

Calls

5 calls:

3.0ms	(*.f64 a a)
2.0ms	b
2.0ms	a
1.0ms	(*.f64 b b)
1.0ms	(-.f64 (.f64 a a) (.f64 b b))

Results

Accuracy	Segments	Branch
94.9%	2	`(*.f64 b b)`
96.5%	2	`(*.f64 a a)`
96.5%	2	`(-.f64 (.f64 a a) (.f64 b b))`
96.5%	2	`a`
94.9%	2	`b`

Compiler

Compiled 11 to 15 computations (-36.4% saved)

regimes4.0ms (0.3%)

Memory

10.0MiB live, 10.0MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

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

Outputs
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
#s(approx (- (* a a) (* b b)) (*.f64 a a))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
79.3%	2	`(*.f64 a a)`
96.5%	2	`(-.f64 (.f64 a a) (.f64 b b))`
79.3%	2	`a`

Compiler

Compiled 8 to 10 computations (-25% saved)

regimes5.0ms (0.4%)

Memory

12.3MiB live, 12.3MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))

Outputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
56.3%	1	`(*.f64 a a)`
56.3%	1	`a`
56.3%	1	`(*.f64 b b)`
56.3%	1	`b`
56.3%	1	`(-.f64 (.f64 a a) (.f64 b b))`

Compiler

Compiled 11 to 15 computations (-36.4% saved)

bsearch8.0ms (0.6%)

Memory

10.4MiB live, 10.4MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
7.0ms	2.3701320649318564e+149	8.549455269103664e+150

Samples

3.0ms

112×

valid

Compiler

Compiled 94 to 108 computations (-14.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-mult!: 1.0ms (78.4% of total)

ival-sub!: 0.0ms (0% of total)

adjust: 0.0ms (0% of total)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-7.158130232355736e-260	0.0

Compiler

Compiled 8 to 10 computations (-25% saved)

derivations9.0ms (0.7%)

Memory

6.4MiB live, 6.4MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 22 to 18 computations (18.2% saved)

preprocess216.0ms (15.8%)

Memory

-4.7MiB live, 41.7MiB allocated; 3ms collecting garbage

Remove

(abs b)

(abs a)

Compiler

Compiled 214 to 188 computations (12.1% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample880.0ms (64.4%)

preprocess50.0ms (3.6%)

series4.0ms (0.3%)

rewrite65.0ms (4.8%)

eval12.0ms (0.9%)

prune3.0ms (0.2%)

series4.0ms (0.3%)

rewrite91.0ms (6.7%)

eval5.0ms (0.3%)

prune2.0ms (0.2%)

regimes9.0ms (0.6%)

regimes4.0ms (0.3%)

regimes5.0ms (0.4%)

bsearch8.0ms (0.6%)

bsearch0.0ms (0%)

derivations9.0ms (0.7%)

preprocess216.0ms (15.8%)

end0.0ms (0%)

Profiling