Metrics for fabs fraction 2

start0.0ms (0%)

Memory: 0.1MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.6MiB live, 0.6MiB 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)

sample764.0ms (62.7%)

Memory

43.1MiB live, 586.0MiB allocated; 671ms collecting garbage

Samples

310.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 129.0ms

ival-fabs: 51.0ms (39.7% of total)

ival-div!: 43.0ms (33.4% of total)

ival-sub!: 33.0ms (25.7% of total)

adjust: 2.0ms (1.6% of total)

Bogosity

explain57.0ms (4.7%)

Memory

-6.5MiB live, 82.9MiB allocated; 21ms 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

24.0ms

512×

valid

Compiler

Compiled 42 to 22 computations (47.6% saved)

Precisions

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

ival-fabs: 3.0ms (39.9% of total)

ival-sub!: 2.0ms (26.6% of total)

ival-div!: 2.0ms (26.6% of total)

adjust: 0.0ms (0% of total)

preprocess79.0ms (6.5%)

Memory

-18.0MiB live, 27.1MiB allocated; 8ms 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	1469	40
7	4523	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

7.7MiB live, 7.7MiB 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)

rewrite79.0ms (6.5%)

Memory

6.2MiB live, 75.7MiB allocated; 76ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	52	178
0	55	161
1	206	158
0	1485	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 a b)))) #s(literal 2 binary64))
(/.f64 (neg.f64 (fabs.f64 (-.f64 a b))) #s(literal -2 binary64))
(/.f64 (fabs.f64 (-.f64 a b)) #s(literal 2 binary64))
(neg.f64 (/.f64 (neg.f64 (fabs.f64 (-.f64 a b))) #s(literal 2 binary64)))
(neg.f64 (/.f64 (fabs.f64 (-.f64 a b)) #s(literal -2 binary64)))
(pow.f64 (pow.f64 (-.f64 a b) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(/.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) (pow.f64 b #s(literal 2 binary64)))))
(/.f64 (fabs.f64 (-.f64 (pow.f64 a #s(literal 2 binary64)) (pow.f64 b #s(literal 2 binary64)))) (fabs.f64 (+.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) (pow.f64 a #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (-.f64 a b)))
(sqrt.f64 (pow.f64 (-.f64 a b) #s(literal 2 binary64)))
(fabs.f64 (-.f64 a b))
(fabs.f64 (-.f64 b a))
(/.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 (pow.f64 a #s(literal 2 binary64)) (pow.f64 b #s(literal 2 binary64)))) (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) (pow.f64 a #s(literal 2 binary64)))))
(/.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) (pow.f64 b #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 a #s(literal 2 binary64)) (pow.f64 b #s(literal 2 binary64))) (+.f64 b a))
(/.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) (pow.f64 b #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (fma.f64 b (+.f64 b a) (pow.f64 a #s(literal 2 binary64))))
(/.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) (pow.f64 b #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 a #s(literal 2 binary64)) (+.f64 b a)) (/.f64 (pow.f64 b #s(literal 2 binary64)) (+.f64 b a)))
(-.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 b (+.f64 b a) (pow.f64 a #s(literal 2 binary64)))) (/.f64 (pow.f64 b #s(literal 3 binary64)) (fma.f64 b (+.f64 b a) (pow.f64 a #s(literal 2 binary64)))))
(-.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) (pow.f64 a #s(literal 2 binary64)))) (/.f64 (pow.f64 (neg.f64 b) #s(literal 3 binary64)) (fma.f64 b (+.f64 b a) (pow.f64 a #s(literal 2 binary64)))))
(+.f64 (neg.f64 b) a)
(+.f64 a (neg.f64 b))
(fma.f64 #s(literal -1 binary64) b a)
(fma.f64 b #s(literal -1 binary64) a)
(neg.f64 (-.f64 b a))
a
b
#s(literal 2 binary64)
#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 a b))))
#s(approx (fabs (- a b)) (fabs.f64 (-.f64 a b)))
#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) (fma.f64 (/.f64 (neg.f64 b) a) a a))
#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 a b))))
#s(approx (fabs (- a b)) (fabs.f64 (-.f64 a b)))
#s(approx (- a b) (fma.f64 (/.f64 (neg.f64 b) a) 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 a b))))
#s(approx (fabs (- a b)) (fabs.f64 (-.f64 a b)))
#s(approx (- a b) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 a b)) (neg.f64 b)))

eval5.0ms (0.4%)

Memory: 8.5MiB live, 8.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 584 to 173 computations (70.4% saved)

prune6.0ms (0.5%)

Memory

-45.0MiB live, 2.9MiB allocated; 3ms 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 a b))))

Compiler

Compiled 13 to 11 computations (15.4% saved)

series3.0ms (0.3%)

Memory

6.2MiB live, 6.2MiB 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 a b))))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 a b)))
#s(literal 1/2 binary64)
(fabs.f64 (-.f64 a b))
(-.f64 a b)
a
b

Outputs
#s(approx (/ (fabs (- a b)) 2) #s(hole binary64 (* 1/2 (fabs (- a b)))))
#s(approx (* 1/2 (fabs (- a b))) #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 (* 1/2 (fabs (- a b))) #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 (* 1/2 (fabs (- a b))) #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) (* 1/2 (fabs (- a b))) 1/2 (fabs (- a b)) (- a b) a b)
0.0ms	a	@	-inf	((/ (fabs (- a b)) 2) (* 1/2 (fabs (- a b))) 1/2 (fabs (- a b)) (- a b) a b)
0.0ms	b	@	-inf	((/ (fabs (- a b)) 2) (* 1/2 (fabs (- a b))) 1/2 (fabs (- a b)) (- a b) a b)
0.0ms	b	@	inf	((/ (fabs (- a b)) 2) (* 1/2 (fabs (- a b))) 1/2 (fabs (- a b)) (- a b) a b)
0.0ms	a	@	0	((/ (fabs (- a b)) 2) (* 1/2 (fabs (- a b))) 1/2 (fabs (- a b)) (- a b) a b)

rewrite52.0ms (4.2%)

Memory

1.5MiB live, 46.9MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	56	235
0	59	213
1	210	210
0	1490	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 a b))))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 a b)))
#s(literal 1/2 binary64)
(fabs.f64 (-.f64 a b))
(-.f64 a b)
a
b
#s(approx (/ (fabs (- a b)) 2) #s(hole binary64 (* 1/2 (fabs (- a b)))))
#s(approx (* 1/2 (fabs (- a b))) #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 (* 1/2 (fabs (- a b))) #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 (* 1/2 (fabs (- a b))) #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
#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 a b))))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 a b)))
(*.f64 (fabs.f64 (-.f64 a b)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(pow.f64 (pow.f64 (-.f64 a b) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(/.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) (pow.f64 b #s(literal 2 binary64)))))
(/.f64 (fabs.f64 (-.f64 (pow.f64 a #s(literal 2 binary64)) (pow.f64 b #s(literal 2 binary64)))) (fabs.f64 (+.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) (pow.f64 a #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (-.f64 a b)))
(sqrt.f64 (pow.f64 (-.f64 a b) #s(literal 2 binary64)))
(fabs.f64 (-.f64 a b))
(fabs.f64 (-.f64 b a))
(/.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 (pow.f64 a #s(literal 2 binary64)) (pow.f64 b #s(literal 2 binary64)))) (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) (pow.f64 a #s(literal 2 binary64)))))
(/.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) (pow.f64 b #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 a #s(literal 2 binary64)) (pow.f64 b #s(literal 2 binary64))) (+.f64 b a))
(/.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) (pow.f64 b #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (fma.f64 b (+.f64 b a) (pow.f64 a #s(literal 2 binary64))))
(/.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) (pow.f64 b #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 a #s(literal 2 binary64)) (+.f64 b a)) (/.f64 (pow.f64 b #s(literal 2 binary64)) (+.f64 b a)))
(-.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 b (+.f64 b a) (pow.f64 a #s(literal 2 binary64)))) (/.f64 (pow.f64 b #s(literal 3 binary64)) (fma.f64 b (+.f64 b a) (pow.f64 a #s(literal 2 binary64)))))
(-.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) (pow.f64 a #s(literal 2 binary64)))) (/.f64 (pow.f64 (neg.f64 b) #s(literal 3 binary64)) (fma.f64 b (+.f64 b a) (pow.f64 a #s(literal 2 binary64)))))
(+.f64 (neg.f64 b) a)
(+.f64 a (neg.f64 b))
(fma.f64 #s(literal -1 binary64) b a)
(fma.f64 b #s(literal -1 binary64) a)
(neg.f64 (-.f64 b a))
a
b
#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 a b))))
#s(approx (* 1/2 (fabs (- a b))) (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 a b))))
#s(approx (fabs (- a b)) (fabs.f64 (-.f64 a b)))
#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) (fma.f64 (/.f64 (neg.f64 b) a) a a))
#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 a b))))
#s(approx (* 1/2 (fabs (- a b))) (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 a b))))
#s(approx (fabs (- a b)) (fabs.f64 (-.f64 a b)))
#s(approx (- a b) (fma.f64 (/.f64 (neg.f64 b) a) 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 a b))))
#s(approx (* 1/2 (fabs (- a b))) (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 a b))))
#s(approx (fabs (- a b)) (fabs.f64 (-.f64 a b)))
#s(approx (- a b) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 a b)) (neg.f64 b)))

eval4.0ms (0.4%)

Memory: 5.8MiB live, 5.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 881 to 205 computations (76.7% saved)

prune2.0ms (0.2%)

Memory

2.4MiB live, 2.4MiB 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 a b))))
▶	52.8%	#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- a b) (neg.f64 b)))))
▶	51.0%	#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- a b) a))))

Status

Accuracy

Program

✓

100.0%

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

▶

52.8%

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

▶

51.0%

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

Compiler

Compiled 44 to 34 computations (22.7% saved)

series3.0ms (0.3%)

Memory

3.4MiB live, 3.4MiB 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 (- a b) a))))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- a b) a)))
#s(literal 1/2 binary64)
(fabs.f64 #s(approx (- a b) a))
#s(approx (- a b) a)
a
#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- a b) (neg.f64 b)))))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- a b) (neg.f64 b))))
(fabs.f64 #s(approx (- a b) (neg.f64 b)))
#s(approx (- a b) (neg.f64 b))
(neg.f64 b)
b

Outputs
#s(approx (/ (fabs (- a b)) 2) #s(hole binary64 (* 1/2 (fabs (- a b)))))
#s(approx (* 1/2 (fabs (- a b))) #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 (* 1/2 (fabs (- a b))) #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 (neg b) #s(hole binary64 (* -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 (* 1/2 (fabs (- a b))) #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	b	@	-inf	((/ (fabs (- a b)) 2) (* 1/2 (fabs (- a b))) 1/2 (fabs (- a b)) (- a b) a (/ (fabs (- a b)) 2) (* 1/2 (fabs (- a b))) (fabs (- a b)) (- a b) (neg b) b)
1.0ms	a	@	-inf	((/ (fabs (- a b)) 2) (* 1/2 (fabs (- a b))) 1/2 (fabs (- a b)) (- a b) a (/ (fabs (- a b)) 2) (* 1/2 (fabs (- a b))) (fabs (- a b)) (- a b) (neg b) b)
1.0ms	a	@	inf	((/ (fabs (- a b)) 2) (* 1/2 (fabs (- a b))) 1/2 (fabs (- a b)) (- a b) a (/ (fabs (- a b)) 2) (* 1/2 (fabs (- a b))) (fabs (- a b)) (- a b) (neg b) b)
0.0ms	b	@	inf	((/ (fabs (- a b)) 2) (* 1/2 (fabs (- a b))) 1/2 (fabs (- a b)) (- a b) a (/ (fabs (- a b)) 2) (* 1/2 (fabs (- a b))) (fabs (- a b)) (- a b) (neg b) b)
0.0ms	a	@	0	((/ (fabs (- a b)) 2) (* 1/2 (fabs (- a b))) 1/2 (fabs (- a b)) (- a b) a (/ (fabs (- a b)) 2) (* 1/2 (fabs (- a b))) (fabs (- a b)) (- a b) (neg b) b)

rewrite59.0ms (4.8%)

Memory

17.3MiB live, 62.7MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	62	289
0	67	266
1	228	263
0	1524	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 (- a b) a))))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- a b) a)))
#s(literal 1/2 binary64)
(fabs.f64 #s(approx (- a b) a))
#s(approx (- a b) a)
a
#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- a b) (neg.f64 b)))))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- a b) (neg.f64 b))))
(fabs.f64 #s(approx (- a b) (neg.f64 b)))
#s(approx (- a b) (neg.f64 b))
(neg.f64 b)
b
#s(approx (/ (fabs (- a b)) 2) #s(hole binary64 (* 1/2 (fabs (- a b)))))
#s(approx (* 1/2 (fabs (- a b))) #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 (* 1/2 (fabs (- a b))) #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 (neg b) #s(hole binary64 (* -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 (* 1/2 (fabs (- a b))) #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
#s(approx (/ (fabs (- a b)) 2) (*.f64 (fabs.f64 #s(approx (- a b) a)) #s(literal 1/2 binary64)))
(*.f64 (fabs.f64 #s(approx (- a b) a)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- a b) a)))
#s(literal 1/2 binary64)
(pow.f64 (pow.f64 #s(approx (- a b) a) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 #s(approx (- a b) a)) (sqrt.f64 #s(approx (- a b) a)))
(sqrt.f64 (pow.f64 #s(approx (- a b) a) #s(literal 2 binary64)))
(fabs.f64 (neg.f64 (neg.f64 #s(approx (- a b) a))))
(fabs.f64 (neg.f64 #s(approx (- a b) a)))
(fabs.f64 #s(approx (- a b) a))
#s(approx (- a b) a)
a
#s(approx (/ (fabs (- a b)) 2) (*.f64 (fabs.f64 #s(approx (- a b) (neg.f64 b))) #s(literal 1/2 binary64)))
(*.f64 (fabs.f64 #s(approx (- a b) (neg.f64 b))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- a b) (neg.f64 b))))
(pow.f64 (pow.f64 #s(approx (- a b) (neg.f64 b)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 #s(approx (- a b) (neg.f64 b))) (sqrt.f64 #s(approx (- a b) (neg.f64 b))))
(sqrt.f64 (pow.f64 #s(approx (- a b) (neg.f64 b)) #s(literal 2 binary64)))
(fabs.f64 (neg.f64 (neg.f64 #s(approx (- a b) (neg.f64 b)))))
(fabs.f64 (neg.f64 #s(approx (- a b) (neg.f64 b))))
(fabs.f64 #s(approx (- a b) (neg.f64 b)))
#s(approx (- a b) (neg.f64 b))
(*.f64 #s(literal -1 binary64) b)
(*.f64 b #s(literal -1 binary64))
(neg.f64 b)
b
#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 a b))))
#s(approx (* 1/2 (fabs (- a b))) (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 a b))))
#s(approx (fabs (- a b)) (fabs.f64 (-.f64 a b)))
#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) (fma.f64 (/.f64 (neg.f64 b) a) a a))
#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 a b))))
#s(approx (* 1/2 (fabs (- a b))) (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 a b))))
#s(approx (fabs (- a b)) (fabs.f64 (-.f64 a b)))
#s(approx (- a b) (fma.f64 (/.f64 (neg.f64 b) a) a a))
#s(approx (- a b) (-.f64 a b))
#s(approx (neg b) (neg.f64 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 a b))))
#s(approx (* 1/2 (fabs (- a b))) (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 a b))))
#s(approx (fabs (- a b)) (fabs.f64 (-.f64 a b)))
#s(approx (- a b) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 a b)) (neg.f64 b)))

eval3.0ms (0.3%)

Memory: 7.1MiB live, 7.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 639 to 122 computations (80.9% saved)

prune4.0ms (0.3%)

Memory

7.3MiB live, 7.3MiB 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 a b))))
✓	52.8%	#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- a b) (neg.f64 b)))))
✓	51.0%	#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- a b) a))))

Status

Accuracy

Program

✓

100.0%

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

✓

52.8%

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

✓

51.0%

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

Compiler

Compiled 94 to 56 computations (40.4% saved)

regimes44.0ms (3.6%)

Memory

-27.1MiB live, 20.6MiB allocated; 15ms 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 (- a b) a))))
#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 #s(approx (- a b) (neg.f64 b)))))
#s(approx (/ (fabs (- a b)) 2) (*.f64 #s(literal 1/2 binary64) (fabs.f64 (-.f64 a b))))
(/.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 a b))))

Calls

5 calls:

36.0ms	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

14.2MiB live, 14.2MiB 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 (- a b) a))))

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

Outputs

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
64.4%	6	`(-.f64 a b)`
64.4%	6	`(fabs.f64 (-.f64 a b))`
64.4%	6	`(/.f64 (fabs.f64 (-.f64 a b)) #s(literal 2 binary64))`
88.3%	2	`a`
84.1%	2	`b`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

regimes9.0ms (0.7%)

Memory

-29.4MiB live, 15.7MiB allocated; 5ms 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 (- a b) a))))

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
51.0%	1	`(fabs.f64 (-.f64 a b))`
51.0%	1	`(/.f64 (fabs.f64 (-.f64 a b)) #s(literal 2 binary64))`
51.0%	1	`(-.f64 a b)`
51.0%	1	`b`
51.0%	1	`a`

Compiler

Compiled 15 to 17 computations (-13.3% saved)

bsearch13.0ms (1%)

Memory

25.5MiB live, 25.5MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	-1.5569685832611368e-123	-1.9942548296019503e-134

Samples

6.0ms

160×

valid

Compiler

Compiled 319 to 261 computations (18.2% saved)

Precisions

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

ival-sub!: 1.0ms (42.5% of total)

ival-fabs: 1.0ms (42.5% of total)

ival-div!: 1.0ms (42.5% of total)

adjust: 0.0ms (0% of total)

derivations1.0ms (0.1%)

Memory

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

Stop Event

1×

done

Compiler

Compiled 63 to 23 computations (63.5% saved)

preprocess21.0ms (1.7%)

Memory: 8.7MiB live, 52.5MiB allocated; 8ms collecting garbage
Compiler: Compiled 264 to 140 computations (47% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.1MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze0.0ms (0%)

sample764.0ms (62.7%)

explain57.0ms (4.7%)

preprocess79.0ms (6.5%)

series4.0ms (0.3%)

rewrite79.0ms (6.5%)

eval5.0ms (0.4%)

prune6.0ms (0.5%)

series3.0ms (0.3%)

rewrite52.0ms (4.2%)

eval4.0ms (0.4%)

prune2.0ms (0.2%)

series3.0ms (0.3%)

rewrite59.0ms (4.8%)

eval3.0ms (0.3%)

prune4.0ms (0.3%)

regimes44.0ms (3.6%)

regimes7.0ms (0.5%)

regimes9.0ms (0.7%)

bsearch13.0ms (1%)

derivations1.0ms (0.1%)

preprocess21.0ms (1.7%)

end0.0ms (0%)

Profiling