Metrics for Difference of squares

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB 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)

sample839.0ms (61.5%)

Memory

10.2MiB live, 959.5MiB allocated; 264ms collecting garbage

Samples

565.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 247.0ms

ival-mult!: 228.0ms (92.2% of total)

ival-sub!: 18.0ms (7.3% of total)

adjust: 1.0ms (0.4% of total)

Bogosity

preprocess55.0ms (4%)

Memory

-17.0MiB live, 29.6MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	42
1	62	42
2	273	42
3	477	42
4	1202	42
5	4632	42

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	94.9%	(-.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

8.3MiB live, 8.3MiB allocated; 0ms collecting garbage

Counts

5 → 9

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 #s(hole binary64 a))
#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 b #s(hole binary64 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	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)

rewrite94.0ms (6.9%)

Memory

-9.4MiB live, 88.1MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	124
0	33	120
1	157	119
0	1645	118
1	5850	118

Stop Event

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

Counts

14 → 113

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

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

eval17.0ms (1.3%)

Memory: 18.2MiB live, 18.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 515 to 233 computations (54.8% saved)

prune4.0ms (0.3%)

Memory

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

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	2	108

Accuracy

100.0%

Counts

108 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 (-.f64 a b) (+.f64 b a))
▶	57.8%	#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))

Compiler

Compiled 13 to 13 computations (0% saved)

series6.0ms (0.5%)

Memory

7.9MiB live, 7.9MiB allocated; 0ms collecting garbage

Counts

8 → 31

Calls

Call 1

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

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

Calls

6 calls:

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

rewrite71.0ms (5.2%)

Memory

-7.2MiB live, 39.3MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	134	556
0	138	505
0	930	495
1	2769	495

Stop Event

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

Counts

39 → 72

Calls

Call 1

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

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

eval5.0ms (0.4%)

Memory: 9.6MiB live, 9.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 349 to 188 computations (46.1% saved)

prune2.0ms (0.2%)

Memory

3.9MiB live, 3.9MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	61	3	64

Accuracy

100.0%

Counts

64 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (-.f64 a b) (+.f64 b a))
✓	57.8%	#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
▶	50.3%	#s(approx (* (- a b) (+ b a)) (*.f64 a a))

Compiler

Compiled 20 to 20 computations (0% saved)

series2.0ms (0.1%)

Memory

3.4MiB live, 3.4MiB allocated; 0ms collecting garbage

Counts

3 → 14

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	a	@	-inf	((* (- a b) (+ b a)) (* a a) a)
1.0ms	a	@	inf	((* (- a b) (+ b a)) (* a a) a)
0.0ms	a	@	0	((* (- a b) (+ b a)) (* a a) a)
0.0ms	b	@	inf	((* (- a b) (+ b a)) (* a a) a)
0.0ms	b	@	-inf	((* (- a b) (+ b a)) (* a a) a)

rewrite51.0ms (3.7%)

Memory

-23.9MiB live, 21.1MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	83	319
0	84	282
0	666	272
1	2023	272

Stop Event

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

Counts

17 → 23

Calls

Call 1

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

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

eval2.0ms (0.2%)

Memory: 2.9MiB live, 2.9MiB allocated; 0ms collecting garbage
Compiler: Compiled 154 to 87 computations (43.5% saved)

prune2.0ms (0.1%)

Memory

2.8MiB live, 2.8MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	20	0	20
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	20	3	23

Accuracy

100.0%

Counts

23 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (-.f64 a b) (+.f64 b a))
✓	57.8%	#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
✓	50.3%	#s(approx (* (- a b) (+ b a)) (*.f64 a a))

Compiler

Compiled 39 to 38 computations (2.6% saved)

regimes9.0ms (0.6%)

Memory

13.5MiB live, 13.5MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
100.0%	1	`(*.f64 b b)`
100.0%	1	`(*.f64 a a)`
100.0%	1	`(-.f64 (.f64 a a) (.f64 b b))`
100.0%	1	`a`
100.0%	1	`b`

Compiler

Compiled 11 to 15 computations (-36.4% saved)

regimes6.0ms (0.5%)

Memory

8.1MiB live, 8.1MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
81.3%	2	`(*.f64 b b)`
78.0%	2	`(*.f64 a a)`
96.7%	2	`(-.f64 (.f64 a a) (.f64 b b))`
78.0%	2	`a`
81.3%	2	`b`

Compiler

Compiled 11 to 15 computations (-36.4% saved)

regimes5.0ms (0.4%)

Memory

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

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

Outputs
#s(approx (* (- a b) (+ b a)) (*.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
50.3%	1	`(*.f64 a a)`
50.3%	1	`a`
50.3%	1	`(*.f64 b b)`
50.3%	1	`b`
50.3%	1	`(-.f64 (.f64 a a) (.f64 b b))`

Compiler

Compiled 11 to 15 computations (-36.4% saved)

bsearch0.0ms (0%)

Memory

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

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.5240841687700152e-289	0.0

Compiler

Compiled 8 to 10 computations (-25% saved)

derivations166.0ms (12.1%)

Memory

-43.3MiB live, 8.7MiB allocated; 7ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 22 to 21 computations (4.5% saved)

preprocess23.0ms (1.7%)

Memory

23.8MiB live, 23.8MiB allocated; 0ms collecting garbage

Remove

(abs b)

(abs a)

Compiler

Compiled 156 to 151 computations (3.2% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample839.0ms (61.5%)

preprocess55.0ms (4%)

series4.0ms (0.3%)

rewrite94.0ms (6.9%)

eval17.0ms (1.3%)

prune4.0ms (0.3%)

series6.0ms (0.5%)

rewrite71.0ms (5.2%)

eval5.0ms (0.4%)

prune2.0ms (0.2%)

series2.0ms (0.1%)

rewrite51.0ms (3.7%)

eval2.0ms (0.2%)

prune2.0ms (0.1%)

regimes9.0ms (0.6%)

regimes6.0ms (0.5%)

regimes5.0ms (0.4%)

bsearch0.0ms (0%)

derivations166.0ms (12.1%)

preprocess23.0ms (1.7%)

end0.0ms (0%)

Profiling