Metrics for fabs fraction 2

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB 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 8 to 8 computations (0% saved)

sample860.0ms (63.9%)

Memory

14.1MiB live, 640.6MiB allocated; 851ms collecting garbage

Samples

648.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 394.0ms

ival-fabs: 314.0ms (79.6% of total)

ival-div!: 44.0ms (11.2% of total)

ival-sub!: 35.0ms (8.9% of total)

adjust: 2.0ms (0.5% of total)

Bogosity

explain46.0ms (3.5%)

Memory

27.9MiB live, 73.6MiB allocated; 4ms collecting garbage

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`a`
-	-	`#s(literal 2 binary64)`
-	-	`(fabs.f64 (-.f64 a b))`
-	-	`(-.f64 a b)`
-	-	`b`
-	-	`(/.f64 (fabs.f64 (-.f64 a b)) #s(literal 2 binary64))`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

21.0ms

512×

valid

Compiler

Compiled 42 to 22 computations (47.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-fabs: 3.0ms (41.7% of total)

ival-sub!: 2.0ms (27.8% of total)

ival-div!: 2.0ms (27.8% of total)

adjust: 0.0ms (0% of total)

preprocess146.0ms (10.9%)

Memory

-42.6MiB live, 63.7MiB allocated; 91ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	40
1	41	40
2	62	40
3	120	40
4	240	40
5	419	40
6	1472	40
7	5212	40

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 (fabs.f64 (-.f64 a b)) #s(literal 2 binary64))

Symmetry

(sort a b)

Compiler

Compiled 12 to 12 computations (0% saved)

series4.0ms (0.3%)

Memory

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

Counts

6 → 16

Calls

Call 1

Inputs
(/.f64 (fabs.f64 (-.f64 a b)) #s(literal 2 binary64))
(fabs.f64 (-.f64 a b))
(-.f64 a b)
a
b
#s(literal 2 binary64)

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	a	@	inf	((/ (fabs (- a b)) 2) (fabs (- a b)) (- a b) a b 2)
1.0ms	a	@	-inf	((/ (fabs (- a b)) 2) (fabs (- a b)) (- a b) a b 2)
1.0ms	b	@	-inf	((/ (fabs (- a b)) 2) (fabs (- a b)) (- a b) a b 2)
1.0ms	b	@	inf	((/ (fabs (- a b)) 2) (fabs (- a b)) (- a b) a b 2)
1.0ms	b	@	0	((/ (fabs (- a b)) 2) (fabs (- a b)) (- a b) a b 2)

rewrite62.0ms (4.6%)

Memory

15.4MiB live, 62.1MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	52	178
0	55	161
1	206	158
0	1504	158

Stop Event

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

Counts

22 → 53

Calls

Call 1

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

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

eval5.0ms (0.4%)

Memory: 6.8MiB live, 6.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 584 to 174 computations (70.2% saved)

prune1.0ms (0.1%)

Memory

2.2MiB live, 2.2MiB allocated; 0ms collecting garbage

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	46	1	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	1	48

Accuracy

100.0%

Counts

48 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 b a))))

Compiler

Compiled 13 to 11 computations (15.4% saved)

series5.0ms (0.4%)

Memory

5.4MiB live, 5.4MiB allocated; 0ms collecting garbage

Counts

7 → 19

Calls

Call 1

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

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

Calls

6 calls:

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

rewrite59.0ms (4.4%)

Memory

-4.4MiB live, 41.4MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	64	235
0	68	215
1	238	210
0	1709	210

Stop Event

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

Counts

26 → 54

Calls

Call 1

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

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

eval5.0ms (0.4%)

Memory: 6.6MiB live, 6.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 872 to 205 computations (76.5% saved)

prune2.0ms (0.2%)

Memory

3.0MiB live, 3.0MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	3	46

Accuracy

100.0%

Counts

46 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 b a))))
▶	50.2%	#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- b a) (neg.f64 a)))))
▶	53.4%	#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- b a) b))))

Status

Accuracy

Program

✓

100.0%

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

▶

50.2%

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

▶

53.4%

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

Compiler

Compiled 44 to 36 computations (18.2% saved)

series4.0ms (0.3%)

Memory

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

Counts

12 → 20

Calls

Call 1

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

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

Calls

6 calls:

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

rewrite55.0ms (4.1%)

Memory

-12.9MiB live, 32.9MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	70	289
0	75	268
1	256	263
0	1744	263

Stop Event

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

Counts

32 → 46

Calls

Call 1

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

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

eval4.0ms (0.3%)

Memory: 8.2MiB live, 8.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 639 to 126 computations (80.3% saved)

prune4.0ms (0.3%)

Memory

7.8MiB live, 7.8MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	37	0	37
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	37	3	40

Accuracy

100.0%

Counts

40 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 b a))))
✓	50.2%	#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- b a) (neg.f64 a)))))
✓	53.4%	#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- b a) b))))

Status

Accuracy

Program

✓

100.0%

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

✓

50.2%

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

✓

53.4%

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

Compiler

Compiled 94 to 61 computations (35.1% saved)

regimes24.0ms (1.8%)

Memory

-27.2MiB live, 20.9MiB allocated; 10ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

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

Calls

5 calls:

17.0ms	b
2.0ms	(/.f64 (fabs.f64 (-.f64 a b)) #s(literal 2 binary64))
2.0ms	a
2.0ms	(fabs.f64 (-.f64 a b))
2.0ms	(-.f64 a b)

Results

Accuracy	Segments	Branch
100.0%	1	`(-.f64 a b)`
100.0%	1	`(fabs.f64 (-.f64 a b))`
100.0%	1	`(/.f64 (fabs.f64 (-.f64 a b)) #s(literal 2 binary64))`
100.0%	1	`a`
100.0%	1	`b`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes7.0ms (0.5%)

Memory

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

Counts

2 → 2

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

Calls

5 calls:

1.0ms	(/.f64 (fabs.f64 (-.f64 a b)) #s(literal 2 binary64))
1.0ms	b
1.0ms	a
1.0ms	(-.f64 a b)
1.0ms	(fabs.f64 (-.f64 a b))

Results

Accuracy	Segments	Branch
59.3%	3	`(-.f64 a b)`
59.3%	3	`(fabs.f64 (-.f64 a b))`
59.3%	3	`(/.f64 (fabs.f64 (-.f64 a b)) #s(literal 2 binary64))`
82.9%	2	`a`
85.1%	2	`b`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes5.0ms (0.4%)

Memory

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

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

5 calls:

1.0ms	a
1.0ms	(/.f64 (fabs.f64 (-.f64 a b)) #s(literal 2 binary64))
1.0ms	(-.f64 a b)
1.0ms	(fabs.f64 (-.f64 a b))
1.0ms	b

Results

Accuracy	Segments	Branch
53.4%	1	`(fabs.f64 (-.f64 a b))`
53.4%	1	`(/.f64 (fabs.f64 (-.f64 a b)) #s(literal 2 binary64))`
53.4%	1	`(-.f64 a b)`
53.4%	1	`a`
53.4%	1	`b`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

bsearch10.0ms (0.8%)

Memory

-37.6MiB live, 9.0MiB allocated; 2ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
9.0ms	9.699963326376298e-151	2.4703599112549005e-148

Samples

4.0ms

112×

valid

Compiler

Compiled 226 to 200 computations (11.5% saved)

Precisions

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

ival-fabs: 1.0ms (64.7% of total)

ival-div!: 1.0ms (64.7% of total)

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

adjust: 0.0ms (0% of total)

derivations15.0ms (1.1%)

Memory

21.9MiB live, 21.8MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 63 to 24 computations (61.9% saved)

preprocess21.0ms (1.6%)

Memory: -12.4MiB live, 33.7MiB allocated; 3ms collecting garbage
Compiler: Compiled 264 to 146 computations (44.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample860.0ms (63.9%)

explain46.0ms (3.5%)

preprocess146.0ms (10.9%)

series4.0ms (0.3%)

rewrite62.0ms (4.6%)

eval5.0ms (0.4%)

prune1.0ms (0.1%)

series5.0ms (0.4%)

rewrite59.0ms (4.4%)

eval5.0ms (0.4%)

prune2.0ms (0.2%)

series4.0ms (0.3%)

rewrite55.0ms (4.1%)

eval4.0ms (0.3%)

prune4.0ms (0.3%)

regimes24.0ms (1.8%)

regimes7.0ms (0.5%)

regimes5.0ms (0.4%)

bsearch10.0ms (0.8%)

derivations15.0ms (1.1%)

preprocess21.0ms (1.6%)

end0.0ms (0%)

Profiling