Metrics for Difference of squares

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB 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)

sample1.5s (75.9%)

Memory

-118.2MiB live, 985.3MiB allocated; 1.3s collecting garbage

Samples

1.1s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 891.0ms

ival-mult: 833.0ms (93.5% of total)

ival-sub: 54.0ms (6.1% of total)

ival-assert: 3.0ms (0.3% of total)

adjust: 2.0ms (0.2% of total)

Bogosity

explain70.0ms (3.6%)

Memory

6.4MiB live, 53.4MiB allocated; 3ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
13	-	-	`(-.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
`-.f64`	`(-.f64 (.f64 a a) (.f64 b b))`	nan-rescue	13	0
↳	`(*.f64 a a)`	overflow	51
↳	`(*.f64 b b)`	overflow	62

Confusion

	Predicted +	Predicted -
+	13	0
-	0	243

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	13	0	0
-	0	0	243

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	243
1	13

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

37.0ms

512×

valid

Compiler

Compiled 41 to 19 computations (53.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-mult: 23.0ms (90.4% of total)

ival-sub: 2.0ms (7.9% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess115.0ms (5.9%)

Memory

10.1MiB live, 55.9MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (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
0	5	7
0	8	7
1	21	7
2	81	7
3	223	7
4	403	7
5	836	7
6	1385	7
7	2069	7
8	2898	7
9	3208	7
10	3270	7
11	3270	7
12	3348	7
0	3348	7

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs a)

(abs b)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	94.9%	(-.f64 (.f64 a a) (.f64 b b))

Compiler

Compiled 7 to 5 computations (28.6% saved)

series4.0ms (0.2%)

Memory

3.7MiB live, 3.7MiB allocated; 0ms collecting garbage

Counts

5 → 10

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)))
#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)

rewrite66.0ms (3.4%)

Memory

-7.2MiB live, 38.6MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	135
0	36	131
1	136	130
0	1191	129

Stop Event

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

Counts

15 → 129

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

eval13.0ms (0.7%)

Memory: 15.4MiB live, 15.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 477 to 299 computations (79.8% saved)

prune4.0ms (0.2%)

Memory

10.6MiB live, 10.6MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	131	2	133

Accuracy

100.0%

Counts

133 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.1%	#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
▶	54.3%	#s(approx (- (* a a) (* b b)) (*.f64 a a))

Compiler

Compiled 23 to 15 computations (34.8% saved)

series4.0ms (0.2%)

Memory

5.2MiB live, 5.2MiB allocated; 0ms collecting garbage

Counts

7 → 11

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 #s(hole binary64 a))
#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 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	b	@	-inf	((- (* 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	b	@	0	((- (* 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)

rewrite56.0ms (2.8%)

Memory

-9.3MiB live, 40.1MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	163
0	42	157
1	142	156
0	1200	155

Stop Event

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

Counts

18 → 67

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

eval12.0ms (0.6%)

Memory: -31.5MiB live, 13.1MiB allocated; 9ms collecting garbage
Compiler: Compiled 954 to 178 computations (81.3% saved)

prune4.0ms (0.2%)

Memory

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

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	68	2	70

Accuracy

100.0%

Counts

70 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.1%	#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
✓	54.3%	#s(approx (- (* a a) (* b b)) (*.f64 a a))

Compiler

Compiled 53 to 27 computations (49.1% saved)

regimes8.0ms (0.4%)

Memory

17.0MiB live, 17.0MiB allocated; 0ms 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:

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
97.3%	2	`(*.f64 b b)`
97.7%	2	`(*.f64 a a)`
97.7%	2	`(-.f64 (.f64 a a) (.f64 b b))`
97.7%	2	`a`
97.3%	2	`b`

Compiler

Compiled 15 to 15 computations (0% saved)

regimes4.0ms (0.2%)

Memory

9.0MiB live, 9.0MiB 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
82.9%	2	`(*.f64 a a)`
97.7%	2	`(-.f64 (.f64 a a) (.f64 b b))`
82.9%	2	`a`

Compiler

Compiled 11 to 10 computations (9.1% saved)

regimes9.0ms (0.4%)

Memory

-32.7MiB live, 13.3MiB allocated; 6ms 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:

4.0ms	(*.f64 a a)
1.0ms	a
1.0ms	b
1.0ms	(-.f64 (.f64 a a) (.f64 b b))
1.0ms	(*.f64 b b)

Results

Accuracy	Segments	Branch
54.3%	1	`(*.f64 a a)`
54.3%	1	`a`
54.3%	1	`(*.f64 b b)`
54.3%	1	`b`
54.3%	1	`(-.f64 (.f64 a a) (.f64 b b))`

Compiler

Compiled 15 to 15 computations (0% saved)

bsearch9.0ms (0.5%)

Memory

15.6MiB live, 15.6MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
8.0ms	1.3800870199187034e+151	3.208865680725636e+153

Samples

4.0ms

112×

valid

Compiler

Compiled 136 to 108 computations (20.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-mult: 1.0ms (50.3% of total)

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

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

adjust: 0.0ms (0% of total)

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

bsearch0.0ms (0%)

Memory

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

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.29241e-318	0.0

Compiler

Compiled 10 to 10 computations (0% saved)

simplify56.0ms (2.8%)

Memory

-8.5MiB live, 38.3MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	66
1	38	66
2	103	66
3	246	66
4	426	66
5	855	66
6	1406	66
7	2090	66
8	2929	66
9	3239	66
10	3301	66
11	3301	66
12	3379	66

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 a #s(literal 3200000000000000148003460348934383168039240716642326031740439270440721720120948829548269436230509604223669198415670098909420726064526137492312064291504128 binary64)) (-.f64 (*.f64 a a) (*.f64 b b)) #s(approx (- (* a a) (* b b)) (*.f64 a a)))

(if (<=.f64 (-.f64 (*.f64 a a) (*.f64 b b)) #s(literal -101201/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b)) #s(approx (- (* a a) (* b b)) (*.f64 a a)))

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

Outputs

(if (<=.f64 a #s(literal 3200000000000000148003460348934383168039240716642326031740439270440721720120948829548269436230509604223669198415670098909420726064526137492312064291504128 binary64)) (-.f64 (*.f64 a a) (*.f64 b b)) #s(approx (- (* a a) (* b b)) (*.f64 a a)))

(if (<=.f64 (-.f64 (*.f64 a a) (*.f64 b b)) #s(literal -101201/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b)) #s(approx (- (* a a) (* b b)) (*.f64 a a)))

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

derivations9.0ms (0.4%)

Memory

11.6MiB live, 11.6MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 66 to 18 computations (72.7% saved)

preprocess30.0ms (1.5%)

Memory: -15.0MiB live, 46.8MiB allocated; 9ms collecting garbage
Remove: (abs b)
Compiler: Compiled 292 to 128 computations (56.2% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample1.5s (75.9%)

explain70.0ms (3.6%)

preprocess115.0ms (5.9%)

eval0.0ms (0%)

prune0.0ms (0%)

series4.0ms (0.2%)

rewrite66.0ms (3.4%)

eval13.0ms (0.7%)

prune4.0ms (0.2%)

series4.0ms (0.2%)

rewrite56.0ms (2.8%)

eval12.0ms (0.6%)

prune4.0ms (0.2%)

regimes8.0ms (0.4%)

regimes4.0ms (0.2%)

regimes9.0ms (0.4%)

bsearch9.0ms (0.5%)

bsearch0.0ms (0%)

simplify56.0ms (2.8%)

derivations9.0ms (0.4%)

preprocess30.0ms (1.5%)

end0.0ms (0%)

Profiling