Metrics for Complex division, real part

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze27.0ms (2%)

Memory

-8.1MiB live, 28.6MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.8%	0.2%	0%	0%	0%	0
0%	0%	99.8%	0.2%	0%	0%	0%	1
0%	0%	99.8%	0.2%	0%	0%	0%	2
0%	0%	99.8%	0.2%	0%	0%	0%	3
0%	0%	99.8%	0.2%	0%	0%	0%	4
75%	74.9%	25%	0.2%	0%	0%	0%	5
75%	74.9%	25%	0.2%	0%	0%	0%	6
75%	74.9%	25%	0.2%	0%	0%	0%	7
87.5%	87.3%	12.5%	0.2%	0%	0%	0%	8
93.8%	93.6%	6.2%	0.2%	0%	0%	0%	9
93.8%	93.6%	6.2%	0.2%	0%	0%	0%	10
93.8%	93.6%	6.2%	0.2%	0%	0%	0%	11
96.9%	96.7%	3.1%	0.2%	0%	0%	0%	12

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample839.0ms (63%)

Memory

25.8MiB live, 883.9MiB allocated

Samples

553.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 340.0ms

ival-mult: 212.0ms (62.3% of total)

ival-add: 68.0ms (20% of total)

ival-div: 50.0ms (14.7% of total)

ival-true: 6.0ms (1.8% of total)

ival-assert: 3.0ms (0.9% of total)

Bogosity

explain125.0ms (9.4%)

Memory

-4.5MiB live, 160.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
122	-	1	(1.4531434752169376e-266 -3.1883438220420717e-301 -2.0603569621327523e-113 -8.660947481383659e-24)	`(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))`
4	-	0	-	`(+.f64 (.f64 a c) (.f64 b d))`
0	-	0	-	`(+.f64 (.f64 c c) (.f64 d d))`
0	-	0	-	`a`
0	-	0	-	`d`
0	-	0	-	`(*.f64 d d)`
0	-	0	-	`(*.f64 c c)`
0	-	0	-	`(*.f64 a c)`
0	-	0	-	`c`
0	-	0	-	`b`
0	-	0	-	`(*.f64 b d)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))`	o/o	68	0
↳	`(+.f64 (.f64 a c) (.f64 b d))`	overflow	77
↳	`(*.f64 a c)`	overflow	42
↳	`(*.f64 b d)`	overflow	43
↳	`(+.f64 (.f64 c c) (.f64 d d))`	overflow	127
↳	`(*.f64 c c)`	overflow	79
↳	`(*.f64 d d)`	overflow	70
`/.f64`	`(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))`	n/o	33	0
↳	`(+.f64 (.f64 c c) (.f64 d d))`	overflow	127
↳	`(*.f64 c c)`	overflow	79
↳	`(*.f64 d d)`	overflow	70
`/.f64`	`(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))`	o/n	9	0
↳	`(+.f64 (.f64 a c) (.f64 b d))`	overflow	77
↳	`(*.f64 a c)`	overflow	42
↳	`(*.f64 b d)`	overflow	43
`/.f64`	`(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))`	n/u	7	0
↳	`(+.f64 (.f64 c c) (.f64 d d))`	underflow	15
↳	`(*.f64 c c)`	underflow	54
↳	`(*.f64 d d)`	underflow	54
`+.f64`	`(+.f64 (.f64 a c) (.f64 b d))`	nan-rescue	4	0
↳	`(*.f64 a c)`	overflow	42
↳	`(*.f64 b d)`	overflow	43
`/.f64`	`(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))`	u/u	3	0
↳	`(+.f64 (.f64 a c) (.f64 b d))`	underflow	4
↳	`(*.f64 a c)`	underflow	27
↳	`(*.f64 b d)`	underflow	27
↳	`(+.f64 (.f64 c c) (.f64 d d))`	underflow	15
↳	`(*.f64 c c)`	underflow	54
↳	`(*.f64 d d)`	underflow	54
`/.f64`	`(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))`	u/n	1	0
↳	`(+.f64 (.f64 a c) (.f64 b d))`	underflow	4
↳	`(*.f64 a c)`	underflow	27
↳	`(*.f64 b d)`	underflow	27

Confusion

	Predicted +	Predicted -
+	121	1
-	0	134

Precision

1.0

Recall

0.9918032786885246

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	121	0	1
-	0	0	134

Precision?

1.0

Recall?

0.9918032786885246

Freqs

test

number	freq
0	135
1	117
2	4

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

43.0ms

512×

valid

Compiler

Compiled 154 to 48 computations (68.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-mult: 14.0ms (64.8% of total)

ival-add: 4.0ms (18.5% of total)

ival-div: 3.0ms (13.9% of total)

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

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

preprocess4.0ms (0.3%)

Memory

6.8MiB live, 6.8MiB allocated

Algorithm

1×	egg-herbie

Calls

Call 1

Inputs
(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

Outputs
(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 15 to 11 computations (26.7% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 4 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.2%	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 b d)
cost-diff	0	(*.f64 a c)
cost-diff	0	(+.f64 (.f64 a c) (.f64 b d))
cost-diff	0	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

Calls

Call 1

Inputs
(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
(+.f64 (.f64 a c) (.f64 b d))
(*.f64 a c)
a
c
(*.f64 b d)
b
d
(+.f64 (.f64 c c) (.f64 d d))
(*.f64 c c)
(*.f64 d d)

Outputs
(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
(+.f64 (.f64 a c) (.f64 b d))
(*.f64 a c)
a
c
(*.f64 b d)
b
d
(+.f64 (.f64 c c) (.f64 d d))
(*.f64 c c)
(*.f64 d d)

localize32.0ms (2.4%)

Memory

-0.1MiB live, 37.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 a c)
accuracy	0.0078125	(+.f64 (.f64 c c) (.f64 d d))
accuracy	0.9648375574906174	(+.f64 (.f64 a c) (.f64 b d))
accuracy	29.03351335715648	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

Samples

25.0ms

256×

valid

Compiler

Compiled 92 to 24 computations (73.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-mult: 12.0ms (76.2% of total)

ival-add: 2.0ms (12.7% of total)

ival-div: 1.0ms (6.3% of total)

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

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

series20.0ms (1.5%)

Memory

-16.0MiB live, 21.2MiB allocated

Counts

5 → 43

Calls

Call 1

Inputs
(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
(+.f64 (.f64 a c) (.f64 b d))
(*.f64 a c)
(*.f64 b d)
(+.f64 (.f64 c c) (.f64 d d))

Outputs
(/ (* b d) (+ (pow c 2) (pow d 2)))
(+ (/ (* a c) (+ (pow c 2) (pow d 2))) (/ (* b d) (+ (pow c 2) (pow d 2))))
(* b d)
(+ (* a c) (* b d))
(* a c)
(/ (* a c) (+ (pow c 2) (pow d 2)))
(* a (+ (/ c (+ (pow c 2) (pow d 2))) (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))
(* a (+ c (/ (* b d) a)))
(* -1 (* a (+ (* -1 (/ c (+ (pow c 2) (pow d 2)))) (* -1 (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))))
(* -1 (* a (+ (* -1 c) (* -1 (/ (* b d) a)))))
(* b (+ (/ d (+ (pow c 2) (pow d 2))) (/ (* a c) (* b (+ (pow c 2) (pow d 2))))))
(* b (+ d (/ (* a c) b)))
(* -1 (* b (+ (* -1 (/ d (+ (pow c 2) (pow d 2)))) (* -1 (/ (* a c) (* b (+ (pow c 2) (pow d 2))))))))
(* -1 (* b (+ (* -1 d) (* -1 (/ (* a c) b)))))
(/ b d)
(+ (/ b d) (/ (* a c) (pow d 2)))
(+ (* c (+ (* -1 (/ (* b c) (pow d 3))) (/ a (pow d 2)))) (/ b d))
(+ (* c (+ (* c (- (* -1 (/ (* a c) (pow d 4))) (/ b (pow d 3)))) (/ a (pow d 2)))) (/ b d))
(pow d 2)
(+ (pow c 2) (pow d 2))
(/ a c)
(/ (+ a (/ (* b d) c)) c)
(/ (+ a (+ (* -1 (/ (* a (pow d 2)) (pow c 2))) (/ (* b d) c))) c)
(/ (- (+ a (+ (* -1 (/ (* b (pow d 3)) (pow c 3))) (/ (* b d) c))) (/ (* a (pow d 2)) (pow c 2))) c)
(* c (+ a (/ (* b d) c)))
(pow c 2)
(* (pow c 2) (+ 1 (/ (pow d 2) (pow c 2))))
(* -1 (/ (+ (* -1 a) (* -1 (/ (* b d) c))) c))
(* -1 (/ (+ (* -1 a) (* -1 (/ (+ (* -1 (/ (* a (pow d 2)) c)) (* b d)) c))) c))
(* -1 (/ (+ (* -1 a) (* -1 (/ (+ (* -1 (/ (- (/ (* b (pow d 3)) c) (* -1 (* a (pow d 2)))) c)) (* b d)) c))) c))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* b d) c)))))
(+ (/ a c) (/ (* b d) (pow c 2)))
(+ (* d (+ (* -1 (/ (* a d) (pow c 3))) (/ b (pow c 2)))) (/ a c))
(+ (* d (+ (* d (- (* -1 (/ (* b d) (pow c 4))) (/ a (pow c 3)))) (/ b (pow c 2)))) (/ a c))
(/ (+ b (/ (* a c) d)) d)
(/ (+ b (+ (* -1 (/ (* b (pow c 2)) (pow d 2))) (/ (* a c) d))) d)
(/ (- (+ b (+ (* -1 (/ (* a (pow c 3)) (pow d 3))) (/ (* a c) d))) (/ (* b (pow c 2)) (pow d 2))) d)
(* d (+ b (/ (* a c) d)))
(* (pow d 2) (+ 1 (/ (pow c 2) (pow d 2))))
(* -1 (/ (+ (* -1 b) (* -1 (/ (* a c) d))) d))
(* -1 (/ (+ (* -1 b) (* -1 (/ (+ (* -1 (/ (* b (pow c 2)) d)) (* a c)) d))) d))
(* -1 (/ (+ (* -1 b) (* -1 (/ (+ (* -1 (/ (- (/ (* a (pow c 3)) d) (* -1 (* b (pow c 2)))) d)) (* a c)) d))) d))
(* -1 (* d (+ (* -1 b) (* -1 (/ (* a c) d)))))

Calls

12 calls:

Time	Variable		Point	Expression
6.0ms	d	@	0	((/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* a c) (* b d) (+ (* c c) (* d d)))
2.0ms	d	@	-inf	((/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* a c) (* b d) (+ (* c c) (* d d)))
2.0ms	b	@	-inf	((/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* a c) (* b d) (+ (* c c) (* d d)))
1.0ms	a	@	-inf	((/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* a c) (* b d) (+ (* c c) (* d d)))
1.0ms	a	@	0	((/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* a c) (* b d) (+ (* c c) (* d d)))

simplify1.0ms (0%)

Memory

1.1MiB live, 1.0MiB allocated

Algorithm

1×	egg-herbie

Counts

43 → 5

Calls

Call 1

Inputs
(/ (* b d) (+ (pow c 2) (pow d 2)))
(+ (/ (* a c) (+ (pow c 2) (pow d 2))) (/ (* b d) (+ (pow c 2) (pow d 2))))
(* b d)
(+ (* a c) (* b d))
(* a c)
(/ (* a c) (+ (pow c 2) (pow d 2)))
(* a (+ (/ c (+ (pow c 2) (pow d 2))) (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))
(* a (+ c (/ (* b d) a)))
(* -1 (* a (+ (* -1 (/ c (+ (pow c 2) (pow d 2)))) (* -1 (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))))
(* -1 (* a (+ (* -1 c) (* -1 (/ (* b d) a)))))
(* b (+ (/ d (+ (pow c 2) (pow d 2))) (/ (* a c) (* b (+ (pow c 2) (pow d 2))))))
(* b (+ d (/ (* a c) b)))
(* -1 (* b (+ (* -1 (/ d (+ (pow c 2) (pow d 2)))) (* -1 (/ (* a c) (* b (+ (pow c 2) (pow d 2))))))))
(* -1 (* b (+ (* -1 d) (* -1 (/ (* a c) b)))))
(/ b d)
(+ (/ b d) (/ (* a c) (pow d 2)))
(+ (* c (+ (* -1 (/ (* b c) (pow d 3))) (/ a (pow d 2)))) (/ b d))
(+ (* c (+ (* c (- (* -1 (/ (* a c) (pow d 4))) (/ b (pow d 3)))) (/ a (pow d 2)))) (/ b d))
(pow d 2)
(+ (pow c 2) (pow d 2))
(/ a c)
(/ (+ a (/ (* b d) c)) c)
(/ (+ a (+ (* -1 (/ (* a (pow d 2)) (pow c 2))) (/ (* b d) c))) c)
(/ (- (+ a (+ (* -1 (/ (* b (pow d 3)) (pow c 3))) (/ (* b d) c))) (/ (* a (pow d 2)) (pow c 2))) c)
(* c (+ a (/ (* b d) c)))
(pow c 2)
(* (pow c 2) (+ 1 (/ (pow d 2) (pow c 2))))
(* -1 (/ (+ (* -1 a) (* -1 (/ (* b d) c))) c))
(* -1 (/ (+ (* -1 a) (* -1 (/ (+ (* -1 (/ (* a (pow d 2)) c)) (* b d)) c))) c))
(* -1 (/ (+ (* -1 a) (* -1 (/ (+ (* -1 (/ (- (/ (* b (pow d 3)) c) (* -1 (* a (pow d 2)))) c)) (* b d)) c))) c))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* b d) c)))))
(+ (/ a c) (/ (* b d) (pow c 2)))
(+ (* d (+ (* -1 (/ (* a d) (pow c 3))) (/ b (pow c 2)))) (/ a c))
(+ (* d (+ (* d (- (* -1 (/ (* b d) (pow c 4))) (/ a (pow c 3)))) (/ b (pow c 2)))) (/ a c))
(/ (+ b (/ (* a c) d)) d)
(/ (+ b (+ (* -1 (/ (* b (pow c 2)) (pow d 2))) (/ (* a c) d))) d)
(/ (- (+ b (+ (* -1 (/ (* a (pow c 3)) (pow d 3))) (/ (* a c) d))) (/ (* b (pow c 2)) (pow d 2))) d)
(* d (+ b (/ (* a c) d)))
(* (pow d 2) (+ 1 (/ (pow c 2) (pow d 2))))
(* -1 (/ (+ (* -1 b) (* -1 (/ (* a c) d))) d))
(* -1 (/ (+ (* -1 b) (* -1 (/ (+ (* -1 (/ (* b (pow c 2)) d)) (* a c)) d))) d))
(* -1 (/ (+ (* -1 b) (* -1 (/ (+ (* -1 (/ (- (/ (* a (pow c 3)) d) (* -1 (* b (pow c 2)))) d)) (* a c)) d))) d))
(* -1 (* d (+ (* -1 b) (* -1 (/ (* a c) d)))))

Outputs
(/ (* b d) (+ (pow c 2) (pow d 2)))
(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
(+ (/ (* a c) (+ (pow c 2) (pow d 2))) (/ (* b d) (+ (pow c 2) (pow d 2))))
(+.f64 (.f64 a c) (.f64 b d))
(* b d)
(*.f64 a c)
(+ (* a c) (* b d))
(*.f64 b d)
(* a c)
(+.f64 (.f64 c c) (.f64 d d))

rewrite0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Counts

5 → 5

Calls

Call 1

Inputs
(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
(+.f64 (.f64 a c) (.f64 b d))
(*.f64 a c)
(*.f64 b d)
(+.f64 (.f64 c c) (.f64 d d))

Outputs
(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
(+.f64 (.f64 a c) (.f64 b d))
(*.f64 a c)
(*.f64 b d)
(+.f64 (.f64 c c) (.f64 d d))

eval1.0ms (0.1%)

Memory: 1.7MiB live, 1.7MiB allocated
Compiler: Compiled 190 to 27 computations (85.8% saved)

prune1.0ms (0.1%)

Memory

2.9MiB live, 2.9MiB allocated

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	7	3	10
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	7	4	11

Accuracy

55.3%

Counts

11 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.2%	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
▶	36.6%	(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 b d)) (+.f64 (.f64 c c) (*.f64 d d)))
▶	35.7%	(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (*.f64 d d)))
▶	3.8%	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 a c) (.f64 b d)))

Compiler

Compiled 76 to 52 computations (31.6% saved)

simplify1.0ms (0.1%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(+.f64 (.f64 c c) (.f64 d d))
cost-diff	0	(*.f64 b d)
cost-diff	0	#s(approx (+ (* a c) (* b d)) (*.f64 b d))
cost-diff	0	(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 b d)) (+.f64 (.f64 c c) (*.f64 d d)))
cost-diff	0	(+.f64 (.f64 c c) (.f64 d d))
cost-diff	0	(*.f64 a c)
cost-diff	0	#s(approx (+ (* a c) (* b d)) (*.f64 a c))
cost-diff	0	(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (*.f64 d d)))
cost-diff	0	(*.f64 b d)
cost-diff	0	(*.f64 a c)
cost-diff	0	(+.f64 (.f64 a c) (.f64 b d))
cost-diff	0	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 a c) (.f64 b d)))

Calls

Call 1

Inputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 a c) (.f64 b d)))
(+.f64 (.f64 a c) (.f64 b d))
(*.f64 a c)
a
c
(*.f64 b d)
b
d
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (*.f64 d d)))
#s(approx (+ (* a c) (* b d)) (*.f64 a c))
(*.f64 a c)
a
c
(+.f64 (.f64 c c) (.f64 d d))
(*.f64 c c)
(*.f64 d d)
d
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 b d)) (+.f64 (.f64 c c) (*.f64 d d)))
#s(approx (+ (* a c) (* b d)) (*.f64 b d))
(*.f64 b d)
b
d
(+.f64 (.f64 c c) (.f64 d d))
(*.f64 c c)
c
(*.f64 d d)

Outputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 a c) (.f64 b d)))
(+.f64 (.f64 a c) (.f64 b d))
(*.f64 a c)
a
c
(*.f64 b d)
b
d
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (*.f64 d d)))
#s(approx (+ (* a c) (* b d)) (*.f64 a c))
(*.f64 a c)
a
c
(+.f64 (.f64 c c) (.f64 d d))
(*.f64 c c)
(*.f64 d d)
d
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 b d)) (+.f64 (.f64 c c) (*.f64 d d)))
#s(approx (+ (* a c) (* b d)) (*.f64 b d))
(*.f64 b d)
b
d
(+.f64 (.f64 c c) (.f64 d d))
(*.f64 c c)
c
(*.f64 d d)

localize38.0ms (2.9%)

Memory

4.5MiB live, 49.8MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 b d)
accuracy	0.0078125	(+.f64 (.f64 c c) (.f64 d d))
accuracy	29.03351335715648	(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 b d)) (+.f64 (.f64 c c) (*.f64 d d)))
accuracy	30.3268705063563	#s(approx (+ (* a c) (* b d)) (*.f64 b d))
accuracy	0.0	(*.f64 a c)
accuracy	0.0078125	(+.f64 (.f64 c c) (.f64 d d))
accuracy	29.03351335715648	(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (*.f64 d d)))
accuracy	29.92935627803062	#s(approx (+ (* a c) (* b d)) (*.f64 a c))
accuracy	0.0	(*.f64 b d)
accuracy	0.0	(*.f64 a c)
accuracy	0.9648375574906174	(+.f64 (.f64 a c) (.f64 b d))
accuracy	61.547380541327236	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 a c) (.f64 b d)))

Samples

28.0ms

256×

valid

Compiler

Compiled 254 to 35 computations (86.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 6.0ms (58.7% of total)

ival-add: 2.0ms (19.6% of total)

ival-div: 1.0ms (9.8% of total)

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

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

series8.0ms (0.6%)

Memory

12.9MiB live, 12.9MiB allocated

Counts

9 → 43

Calls

Call 1

Inputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 a c) (.f64 b d)))
(+.f64 (.f64 a c) (.f64 b d))
(*.f64 a c)
(*.f64 b d)
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (*.f64 d d)))
#s(approx (+ (* a c) (* b d)) (*.f64 a c))
(+.f64 (.f64 c c) (.f64 d d))
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 b d)) (+.f64 (.f64 c c) (*.f64 d d)))
#s(approx (+ (* a c) (* b d)) (*.f64 b d))

Outputs
(/ (* b d) (+ (pow c 2) (pow d 2)))
(+ (/ (* a c) (+ (pow c 2) (pow d 2))) (/ (* b d) (+ (pow c 2) (pow d 2))))
(* b d)
(+ (* a c) (* b d))
(* a c)
(/ (* a c) (+ (pow c 2) (pow d 2)))
(* a (+ (/ c (+ (pow c 2) (pow d 2))) (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))
(* a (+ c (/ (* b d) a)))
(* -1 (* a (+ (* -1 (/ c (+ (pow c 2) (pow d 2)))) (* -1 (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))))
(* -1 (* a (+ (* -1 c) (* -1 (/ (* b d) a)))))
(* b (+ (/ d (+ (pow c 2) (pow d 2))) (/ (* a c) (* b (+ (pow c 2) (pow d 2))))))
(* b (+ d (/ (* a c) b)))
(* -1 (* b (+ (* -1 (/ d (+ (pow c 2) (pow d 2)))) (* -1 (/ (* a c) (* b (+ (pow c 2) (pow d 2))))))))
(* -1 (* b (+ (* -1 d) (* -1 (/ (* a c) b)))))
(/ b d)
(+ (/ b d) (/ (* a c) (pow d 2)))
(+ (* c (+ (* -1 (/ (* b c) (pow d 3))) (/ a (pow d 2)))) (/ b d))
(+ (* c (+ (* c (- (* -1 (/ (* a c) (pow d 4))) (/ b (pow d 3)))) (/ a (pow d 2)))) (/ b d))
(pow d 2)
(+ (pow c 2) (pow d 2))
(/ a c)
(/ (+ a (/ (* b d) c)) c)
(/ (+ a (+ (* -1 (/ (* a (pow d 2)) (pow c 2))) (/ (* b d) c))) c)
(/ (- (+ a (+ (* -1 (/ (* b (pow d 3)) (pow c 3))) (/ (* b d) c))) (/ (* a (pow d 2)) (pow c 2))) c)
(* c (+ a (/ (* b d) c)))
(pow c 2)
(* (pow c 2) (+ 1 (/ (pow d 2) (pow c 2))))
(* -1 (/ (+ (* -1 a) (* -1 (/ (* b d) c))) c))
(* -1 (/ (+ (* -1 a) (* -1 (/ (+ (* -1 (/ (* a (pow d 2)) c)) (* b d)) c))) c))
(* -1 (/ (+ (* -1 a) (* -1 (/ (+ (* -1 (/ (- (/ (* b (pow d 3)) c) (* -1 (* a (pow d 2)))) c)) (* b d)) c))) c))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* b d) c)))))
(+ (/ a c) (/ (* b d) (pow c 2)))
(+ (* d (+ (* -1 (/ (* a d) (pow c 3))) (/ b (pow c 2)))) (/ a c))
(+ (* d (+ (* d (- (* -1 (/ (* b d) (pow c 4))) (/ a (pow c 3)))) (/ b (pow c 2)))) (/ a c))
(/ (+ b (/ (* a c) d)) d)
(/ (+ b (+ (* -1 (/ (* b (pow c 2)) (pow d 2))) (/ (* a c) d))) d)
(/ (- (+ b (+ (* -1 (/ (* a (pow c 3)) (pow d 3))) (/ (* a c) d))) (/ (* b (pow c 2)) (pow d 2))) d)
(* d (+ b (/ (* a c) d)))
(* (pow d 2) (+ 1 (/ (pow c 2) (pow d 2))))
(* -1 (/ (+ (* -1 b) (* -1 (/ (* a c) d))) d))
(* -1 (/ (+ (* -1 b) (* -1 (/ (+ (* -1 (/ (* b (pow c 2)) d)) (* a c)) d))) d))
(* -1 (/ (+ (* -1 b) (* -1 (/ (+ (* -1 (/ (- (/ (* a (pow c 3)) d) (* -1 (* b (pow c 2)))) d)) (* a c)) d))) d))
(* -1 (* d (+ (* -1 b) (* -1 (/ (* a c) d)))))

Calls

12 calls:

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

simplify1.0ms (0.1%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×	egg-herbie

Counts

43 → 9

Calls

Call 1

Inputs
(/ (* b d) (+ (pow c 2) (pow d 2)))
(+ (/ (* a c) (+ (pow c 2) (pow d 2))) (/ (* b d) (+ (pow c 2) (pow d 2))))
(* b d)
(+ (* a c) (* b d))
(* a c)
(/ (* a c) (+ (pow c 2) (pow d 2)))
(* a (+ (/ c (+ (pow c 2) (pow d 2))) (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))
(* a (+ c (/ (* b d) a)))
(* -1 (* a (+ (* -1 (/ c (+ (pow c 2) (pow d 2)))) (* -1 (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))))
(* -1 (* a (+ (* -1 c) (* -1 (/ (* b d) a)))))
(* b (+ (/ d (+ (pow c 2) (pow d 2))) (/ (* a c) (* b (+ (pow c 2) (pow d 2))))))
(* b (+ d (/ (* a c) b)))
(* -1 (* b (+ (* -1 (/ d (+ (pow c 2) (pow d 2)))) (* -1 (/ (* a c) (* b (+ (pow c 2) (pow d 2))))))))
(* -1 (* b (+ (* -1 d) (* -1 (/ (* a c) b)))))
(/ b d)
(+ (/ b d) (/ (* a c) (pow d 2)))
(+ (* c (+ (* -1 (/ (* b c) (pow d 3))) (/ a (pow d 2)))) (/ b d))
(+ (* c (+ (* c (- (* -1 (/ (* a c) (pow d 4))) (/ b (pow d 3)))) (/ a (pow d 2)))) (/ b d))
(pow d 2)
(+ (pow c 2) (pow d 2))
(/ a c)
(/ (+ a (/ (* b d) c)) c)
(/ (+ a (+ (* -1 (/ (* a (pow d 2)) (pow c 2))) (/ (* b d) c))) c)
(/ (- (+ a (+ (* -1 (/ (* b (pow d 3)) (pow c 3))) (/ (* b d) c))) (/ (* a (pow d 2)) (pow c 2))) c)
(* c (+ a (/ (* b d) c)))
(pow c 2)
(* (pow c 2) (+ 1 (/ (pow d 2) (pow c 2))))
(* -1 (/ (+ (* -1 a) (* -1 (/ (* b d) c))) c))
(* -1 (/ (+ (* -1 a) (* -1 (/ (+ (* -1 (/ (* a (pow d 2)) c)) (* b d)) c))) c))
(* -1 (/ (+ (* -1 a) (* -1 (/ (+ (* -1 (/ (- (/ (* b (pow d 3)) c) (* -1 (* a (pow d 2)))) c)) (* b d)) c))) c))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* b d) c)))))
(+ (/ a c) (/ (* b d) (pow c 2)))
(+ (* d (+ (* -1 (/ (* a d) (pow c 3))) (/ b (pow c 2)))) (/ a c))
(+ (* d (+ (* d (- (* -1 (/ (* b d) (pow c 4))) (/ a (pow c 3)))) (/ b (pow c 2)))) (/ a c))
(/ (+ b (/ (* a c) d)) d)
(/ (+ b (+ (* -1 (/ (* b (pow c 2)) (pow d 2))) (/ (* a c) d))) d)
(/ (- (+ b (+ (* -1 (/ (* a (pow c 3)) (pow d 3))) (/ (* a c) d))) (/ (* b (pow c 2)) (pow d 2))) d)
(* d (+ b (/ (* a c) d)))
(* (pow d 2) (+ 1 (/ (pow c 2) (pow d 2))))
(* -1 (/ (+ (* -1 b) (* -1 (/ (* a c) d))) d))
(* -1 (/ (+ (* -1 b) (* -1 (/ (+ (* -1 (/ (* b (pow c 2)) d)) (* a c)) d))) d))
(* -1 (/ (+ (* -1 b) (* -1 (/ (+ (* -1 (/ (- (/ (* a (pow c 3)) d) (* -1 (* b (pow c 2)))) d)) (* a c)) d))) d))
(* -1 (* d (+ (* -1 b) (* -1 (/ (* a c) d)))))

Outputs
(/ (* b d) (+ (pow c 2) (pow d 2)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 a c) (.f64 b d)))
(+ (/ (* a c) (+ (pow c 2) (pow d 2))) (/ (* b d) (+ (pow c 2) (pow d 2))))
(+.f64 (.f64 a c) (.f64 b d))
(* b d)
(*.f64 a c)
(+ (* a c) (* b d))
(*.f64 b d)
(* a c)
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (*.f64 d d)))
(/ (* a c) (+ (pow c 2) (pow d 2)))
#s(approx (+ (* a c) (* b d)) (*.f64 a c))
(* a (+ (/ c (+ (pow c 2) (pow d 2))) (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))
(+.f64 (.f64 c c) (.f64 d d))
(* a (+ c (/ (* b d) a)))
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 b d)) (+.f64 (.f64 c c) (*.f64 d d)))
(* -1 (* a (+ (* -1 (/ c (+ (pow c 2) (pow d 2)))) (* -1 (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))))
#s(approx (+ (* a c) (* b d)) (*.f64 b d))

rewrite0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Counts

9 → 9

Calls

Call 1

Inputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 a c) (.f64 b d)))
(+.f64 (.f64 a c) (.f64 b d))
(*.f64 a c)
(*.f64 b d)
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (*.f64 d d)))
#s(approx (+ (* a c) (* b d)) (*.f64 a c))
(+.f64 (.f64 c c) (.f64 d d))
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 b d)) (+.f64 (.f64 c c) (*.f64 d d)))
#s(approx (+ (* a c) (* b d)) (*.f64 b d))

Outputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 a c) (.f64 b d)))
(+.f64 (.f64 a c) (.f64 b d))
(*.f64 a c)
(*.f64 b d)
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (*.f64 d d)))
#s(approx (+ (* a c) (* b d)) (*.f64 a c))
(+.f64 (.f64 c c) (.f64 d d))
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 b d)) (+.f64 (.f64 c c) (*.f64 d d)))
#s(approx (+ (* a c) (* b d)) (*.f64 b d))

eval5.0ms (0.4%)

Memory: -35.4MiB live, 2.8MiB allocated
Compiler: Compiled 501 to 33 computations (93.4% saved)

prune3.0ms (0.2%)

Memory

4.9MiB live, 4.9MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	16	3	19
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	16	7	23

Accuracy

55.6%

Counts

23 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.2%	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
✓	36.6%	(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 b d)) (+.f64 (.f64 c c) (*.f64 d d)))
✓	35.7%	(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (*.f64 d d)))
▶	2.1%	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 c c) (.f64 d d)))
✓	3.8%	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 a c) (.f64 b d)))
▶	4.6%	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 b d)))
▶	4.9%	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 a c)))

Compiler

Compiled 153 to 95 computations (37.9% saved)

simplify1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 d d)
cost-diff	0	(*.f64 c c)
cost-diff	0	(+.f64 (.f64 c c) (.f64 d d))
cost-diff	0	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 c c) (.f64 d d)))
cost-diff	0	(*.f64 b d)
cost-diff	0	#s(approx (+ (* a c) (* b d)) (*.f64 b d))
cost-diff	0	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 b d)))
cost-diff	0	(*.f64 a c)
cost-diff	0	#s(approx (+ (* a c) (* b d)) (*.f64 a c))
cost-diff	0	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 a c)))

Calls

Call 1

Inputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 a c)))
#s(approx (+ (* a c) (* b d)) (*.f64 a c))
(*.f64 a c)
a
c
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 b d)))
#s(approx (+ (* a c) (* b d)) (*.f64 b d))
(*.f64 b d)
b
d
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 c c) (.f64 d d)))
(+.f64 (.f64 c c) (.f64 d d))
(*.f64 c c)
c
(*.f64 d d)
d

Outputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 a c)))
#s(approx (+ (* a c) (* b d)) (*.f64 a c))
(*.f64 a c)
a
c
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 b d)))
#s(approx (+ (* a c) (* b d)) (*.f64 b d))
(*.f64 b d)
b
d
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 c c) (.f64 d d)))
(+.f64 (.f64 c c) (.f64 d d))
(*.f64 c c)
c
(*.f64 d d)
d

localize29.0ms (2.2%)

Memory

-3.7MiB live, 35.0MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 d d)
accuracy	0.0	(*.f64 c c)
accuracy	0.0078125	(+.f64 (.f64 c c) (.f64 d d))
accuracy	62.63478116152093	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 c c) (.f64 d d)))
accuracy	0.0	(*.f64 b d)
accuracy	30.3268705063563	#s(approx (+ (* a c) (* b d)) (*.f64 b d))
accuracy	61.547380541327236	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 b d)))
accuracy	0.0	(*.f64 a c)
accuracy	29.92935627803062	#s(approx (+ (* a c) (* b d)) (*.f64 a c))
accuracy	61.547380541327236	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 a c)))

Samples

20.0ms

256×

valid

Compiler

Compiled 210 to 34 computations (83.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 6.0ms (58.7% of total)

ival-add: 2.0ms (19.6% of total)

ival-div: 1.0ms (9.8% of total)

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

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

series9.0ms (0.7%)

Memory

13.0MiB live, 13.0MiB allocated

Counts

10 → 43

Calls

Call 1

Inputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 a c)))
#s(approx (+ (* a c) (* b d)) (*.f64 a c))
(*.f64 a c)
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 b d)))
#s(approx (+ (* a c) (* b d)) (*.f64 b d))
(*.f64 b d)
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 c c) (.f64 d d)))
(+.f64 (.f64 c c) (.f64 d d))
(*.f64 c c)
(*.f64 d d)

Outputs
(/ (* b d) (+ (pow c 2) (pow d 2)))
(+ (/ (* a c) (+ (pow c 2) (pow d 2))) (/ (* b d) (+ (pow c 2) (pow d 2))))
(* b d)
(+ (* a c) (* b d))
(* a c)
(/ (* a c) (+ (pow c 2) (pow d 2)))
(* a (+ (/ c (+ (pow c 2) (pow d 2))) (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))
(* a (+ c (/ (* b d) a)))
(* -1 (* a (+ (* -1 (/ c (+ (pow c 2) (pow d 2)))) (* -1 (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))))
(* -1 (* a (+ (* -1 c) (* -1 (/ (* b d) a)))))
(* b (+ (/ d (+ (pow c 2) (pow d 2))) (/ (* a c) (* b (+ (pow c 2) (pow d 2))))))
(* b (+ d (/ (* a c) b)))
(* -1 (* b (+ (* -1 (/ d (+ (pow c 2) (pow d 2)))) (* -1 (/ (* a c) (* b (+ (pow c 2) (pow d 2))))))))
(* -1 (* b (+ (* -1 d) (* -1 (/ (* a c) b)))))
(/ b d)
(+ (/ b d) (/ (* a c) (pow d 2)))
(+ (* c (+ (* -1 (/ (* b c) (pow d 3))) (/ a (pow d 2)))) (/ b d))
(+ (* c (+ (* c (- (* -1 (/ (* a c) (pow d 4))) (/ b (pow d 3)))) (/ a (pow d 2)))) (/ b d))
(pow d 2)
(+ (pow c 2) (pow d 2))
(pow c 2)
(/ a c)
(/ (+ a (/ (* b d) c)) c)
(/ (+ a (+ (* -1 (/ (* a (pow d 2)) (pow c 2))) (/ (* b d) c))) c)
(/ (- (+ a (+ (* -1 (/ (* b (pow d 3)) (pow c 3))) (/ (* b d) c))) (/ (* a (pow d 2)) (pow c 2))) c)
(* c (+ a (/ (* b d) c)))
(* (pow c 2) (+ 1 (/ (pow d 2) (pow c 2))))
(* -1 (/ (+ (* -1 a) (* -1 (/ (* b d) c))) c))
(* -1 (/ (+ (* -1 a) (* -1 (/ (+ (* -1 (/ (* a (pow d 2)) c)) (* b d)) c))) c))
(* -1 (/ (+ (* -1 a) (* -1 (/ (+ (* -1 (/ (- (/ (* b (pow d 3)) c) (* -1 (* a (pow d 2)))) c)) (* b d)) c))) c))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* b d) c)))))
(+ (/ a c) (/ (* b d) (pow c 2)))
(+ (* d (+ (* -1 (/ (* a d) (pow c 3))) (/ b (pow c 2)))) (/ a c))
(+ (* d (+ (* d (- (* -1 (/ (* b d) (pow c 4))) (/ a (pow c 3)))) (/ b (pow c 2)))) (/ a c))
(/ (+ b (/ (* a c) d)) d)
(/ (+ b (+ (* -1 (/ (* b (pow c 2)) (pow d 2))) (/ (* a c) d))) d)
(/ (- (+ b (+ (* -1 (/ (* a (pow c 3)) (pow d 3))) (/ (* a c) d))) (/ (* b (pow c 2)) (pow d 2))) d)
(* d (+ b (/ (* a c) d)))
(* (pow d 2) (+ 1 (/ (pow c 2) (pow d 2))))
(* -1 (/ (+ (* -1 b) (* -1 (/ (* a c) d))) d))
(* -1 (/ (+ (* -1 b) (* -1 (/ (+ (* -1 (/ (* b (pow c 2)) d)) (* a c)) d))) d))
(* -1 (/ (+ (* -1 b) (* -1 (/ (+ (* -1 (/ (- (/ (* a (pow c 3)) d) (* -1 (* b (pow c 2)))) d)) (* a c)) d))) d))
(* -1 (* d (+ (* -1 b) (* -1 (/ (* a c) d)))))

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	c	@	-inf	((/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* a c) (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* b d) (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* c c) (* d d)) (* c c) (* d d))
1.0ms	d	@	-inf	((/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* a c) (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* b d) (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* c c) (* d d)) (* c c) (* d d))
1.0ms	c	@	inf	((/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* a c) (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* b d) (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* c c) (* d d)) (* c c) (* d d))
1.0ms	b	@	-inf	((/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* a c) (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* b d) (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* c c) (* d d)) (* c c) (* d d))
1.0ms	a	@	-inf	((/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* a c) (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* b d) (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* c c) (* d d)) (* c c) (* d d))

simplify1.0ms (0.1%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	egg-herbie

Counts

43 → 10

Calls

Call 1

Inputs
(/ (* b d) (+ (pow c 2) (pow d 2)))
(+ (/ (* a c) (+ (pow c 2) (pow d 2))) (/ (* b d) (+ (pow c 2) (pow d 2))))
(* b d)
(+ (* a c) (* b d))
(* a c)
(/ (* a c) (+ (pow c 2) (pow d 2)))
(* a (+ (/ c (+ (pow c 2) (pow d 2))) (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))
(* a (+ c (/ (* b d) a)))
(* -1 (* a (+ (* -1 (/ c (+ (pow c 2) (pow d 2)))) (* -1 (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))))
(* -1 (* a (+ (* -1 c) (* -1 (/ (* b d) a)))))
(* b (+ (/ d (+ (pow c 2) (pow d 2))) (/ (* a c) (* b (+ (pow c 2) (pow d 2))))))
(* b (+ d (/ (* a c) b)))
(* -1 (* b (+ (* -1 (/ d (+ (pow c 2) (pow d 2)))) (* -1 (/ (* a c) (* b (+ (pow c 2) (pow d 2))))))))
(* -1 (* b (+ (* -1 d) (* -1 (/ (* a c) b)))))
(/ b d)
(+ (/ b d) (/ (* a c) (pow d 2)))
(+ (* c (+ (* -1 (/ (* b c) (pow d 3))) (/ a (pow d 2)))) (/ b d))
(+ (* c (+ (* c (- (* -1 (/ (* a c) (pow d 4))) (/ b (pow d 3)))) (/ a (pow d 2)))) (/ b d))
(pow d 2)
(+ (pow c 2) (pow d 2))
(pow c 2)
(/ a c)
(/ (+ a (/ (* b d) c)) c)
(/ (+ a (+ (* -1 (/ (* a (pow d 2)) (pow c 2))) (/ (* b d) c))) c)
(/ (- (+ a (+ (* -1 (/ (* b (pow d 3)) (pow c 3))) (/ (* b d) c))) (/ (* a (pow d 2)) (pow c 2))) c)
(* c (+ a (/ (* b d) c)))
(* (pow c 2) (+ 1 (/ (pow d 2) (pow c 2))))
(* -1 (/ (+ (* -1 a) (* -1 (/ (* b d) c))) c))
(* -1 (/ (+ (* -1 a) (* -1 (/ (+ (* -1 (/ (* a (pow d 2)) c)) (* b d)) c))) c))
(* -1 (/ (+ (* -1 a) (* -1 (/ (+ (* -1 (/ (- (/ (* b (pow d 3)) c) (* -1 (* a (pow d 2)))) c)) (* b d)) c))) c))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* b d) c)))))
(+ (/ a c) (/ (* b d) (pow c 2)))
(+ (* d (+ (* -1 (/ (* a d) (pow c 3))) (/ b (pow c 2)))) (/ a c))
(+ (* d (+ (* d (- (* -1 (/ (* b d) (pow c 4))) (/ a (pow c 3)))) (/ b (pow c 2)))) (/ a c))
(/ (+ b (/ (* a c) d)) d)
(/ (+ b (+ (* -1 (/ (* b (pow c 2)) (pow d 2))) (/ (* a c) d))) d)
(/ (- (+ b (+ (* -1 (/ (* a (pow c 3)) (pow d 3))) (/ (* a c) d))) (/ (* b (pow c 2)) (pow d 2))) d)
(* d (+ b (/ (* a c) d)))
(* (pow d 2) (+ 1 (/ (pow c 2) (pow d 2))))
(* -1 (/ (+ (* -1 b) (* -1 (/ (* a c) d))) d))
(* -1 (/ (+ (* -1 b) (* -1 (/ (+ (* -1 (/ (* b (pow c 2)) d)) (* a c)) d))) d))
(* -1 (/ (+ (* -1 b) (* -1 (/ (+ (* -1 (/ (- (/ (* a (pow c 3)) d) (* -1 (* b (pow c 2)))) d)) (* a c)) d))) d))
(* -1 (* d (+ (* -1 b) (* -1 (/ (* a c) d)))))

Outputs
(/ (* b d) (+ (pow c 2) (pow d 2)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 a c)))
(+ (/ (* a c) (+ (pow c 2) (pow d 2))) (/ (* b d) (+ (pow c 2) (pow d 2))))
#s(approx (+ (* a c) (* b d)) (*.f64 a c))
(* b d)
(*.f64 a c)
(+ (* a c) (* b d))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 b d)))
(* a c)
#s(approx (+ (* a c) (* b d)) (*.f64 b d))
(/ (* a c) (+ (pow c 2) (pow d 2)))
(*.f64 b d)
(* a (+ (/ c (+ (pow c 2) (pow d 2))) (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 c c) (.f64 d d)))
(* a (+ c (/ (* b d) a)))
(+.f64 (.f64 c c) (.f64 d d))
(* -1 (* a (+ (* -1 (/ c (+ (pow c 2) (pow d 2)))) (* -1 (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))))
(*.f64 c c)
(* -1 (* a (+ (* -1 c) (* -1 (/ (* b d) a)))))
(*.f64 d d)

rewrite0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Counts

10 → 10

Calls

Call 1

Inputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 a c)))
#s(approx (+ (* a c) (* b d)) (*.f64 a c))
(*.f64 a c)
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 b d)))
#s(approx (+ (* a c) (* b d)) (*.f64 b d))
(*.f64 b d)
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 c c) (.f64 d d)))
(+.f64 (.f64 c c) (.f64 d d))
(*.f64 c c)
(*.f64 d d)

Outputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 a c)))
#s(approx (+ (* a c) (* b d)) (*.f64 a c))
(*.f64 a c)
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 b d)))
#s(approx (+ (* a c) (* b d)) (*.f64 b d))
(*.f64 b d)
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 c c) (.f64 d d)))
(+.f64 (.f64 c c) (.f64 d d))
(*.f64 c c)
(*.f64 d d)

eval2.0ms (0.1%)

Memory: 2.9MiB live, 2.9MiB allocated
Compiler: Compiled 522 to 34 computations (93.5% saved)

prune4.0ms (0.3%)

Memory

6.5MiB live, 6.5MiB allocated

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	16	2	18
Fresh	0	0	0
Picked	0	3	3
Done	0	4	4
Total	16	9	25

Accuracy

55.7%

Counts

25 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.2%	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
✓	36.6%	(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 b d)) (+.f64 (.f64 c c) (*.f64 d d)))
✓	35.7%	(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (*.f64 d d)))
✓	2.1%	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 c c) (.f64 d d)))
✓	3.8%	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 a c) (.f64 b d)))
▶	5.0%	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (*.f64 c c))
▶	4.5%	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 d d)))
✓	4.6%	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 b d)))
✓	4.9%	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 a c)))

Compiler

Compiled 199 to 122 computations (38.7% saved)

simplify0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 c c)
cost-diff	0	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (*.f64 c c))
cost-diff	0	(*.f64 d d)
cost-diff	0	#s(approx (+ (* a c) (* b d)) (*.f64 d d))
cost-diff	0	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 d d)))

Calls

Call 1

Inputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 d d)))
#s(approx (+ (* a c) (* b d)) (*.f64 d d))
(*.f64 d d)
d
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (*.f64 c c))
(*.f64 c c)
c

Outputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 d d)))
#s(approx (+ (* a c) (* b d)) (*.f64 d d))
(*.f64 d d)
d
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (*.f64 c c))
(*.f64 c c)
c

localize25.0ms (1.9%)

Memory

-7.9MiB live, 30.7MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 c c)
accuracy	60.80629460662306	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (*.f64 c c))
accuracy	0.0	(*.f64 d d)
accuracy	56.79814510180251	#s(approx (+ (* a c) (* b d)) (*.f64 d d))
accuracy	61.547380541327236	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 d d)))

Samples

19.0ms

256×

valid

Compiler

Compiled 112 to 29 computations (74.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 6.0ms (59.3% of total)

ival-add: 2.0ms (19.8% of total)

ival-div: 1.0ms (9.9% of total)

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

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

series6.0ms (0.5%)

Memory

8.8MiB live, 8.8MiB allocated

Counts

5 → 40

Calls

Call 1

Inputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 d d)))
#s(approx (+ (* a c) (* b d)) (*.f64 d d))
(*.f64 d d)
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (*.f64 c c))
(*.f64 c c)

Outputs
(/ (* b d) (+ (pow c 2) (pow d 2)))
(+ (/ (* a c) (+ (pow c 2) (pow d 2))) (/ (* b d) (+ (pow c 2) (pow d 2))))
(* b d)
(+ (* a c) (* b d))
(/ (* a c) (+ (pow c 2) (pow d 2)))
(* a (+ (/ c (+ (pow c 2) (pow d 2))) (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))
(* a c)
(* a (+ c (/ (* b d) a)))
(* -1 (* a (+ (* -1 (/ c (+ (pow c 2) (pow d 2)))) (* -1 (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))))
(* -1 (* a (+ (* -1 c) (* -1 (/ (* b d) a)))))
(* b (+ (/ d (+ (pow c 2) (pow d 2))) (/ (* a c) (* b (+ (pow c 2) (pow d 2))))))
(* b (+ d (/ (* a c) b)))
(* -1 (* b (+ (* -1 (/ d (+ (pow c 2) (pow d 2)))) (* -1 (/ (* a c) (* b (+ (pow c 2) (pow d 2))))))))
(* -1 (* b (+ (* -1 d) (* -1 (/ (* a c) b)))))
(/ b d)
(+ (/ b d) (/ (* a c) (pow d 2)))
(+ (* c (+ (* -1 (/ (* b c) (pow d 3))) (/ a (pow d 2)))) (/ b d))
(+ (* c (+ (* c (- (* -1 (/ (* a c) (pow d 4))) (/ b (pow d 3)))) (/ a (pow d 2)))) (/ b d))
(pow c 2)
(/ a c)
(/ (+ a (/ (* b d) c)) c)
(/ (+ a (+ (* -1 (/ (* a (pow d 2)) (pow c 2))) (/ (* b d) c))) c)
(/ (- (+ a (+ (* -1 (/ (* b (pow d 3)) (pow c 3))) (/ (* b d) c))) (/ (* a (pow d 2)) (pow c 2))) c)
(* c (+ a (/ (* b d) c)))
(* -1 (/ (+ (* -1 a) (* -1 (/ (* b d) c))) c))
(* -1 (/ (+ (* -1 a) (* -1 (/ (+ (* -1 (/ (* a (pow d 2)) c)) (* b d)) c))) c))
(* -1 (/ (+ (* -1 a) (* -1 (/ (+ (* -1 (/ (- (/ (* b (pow d 3)) c) (* -1 (* a (pow d 2)))) c)) (* b d)) c))) c))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* b d) c)))))
(+ (/ a c) (/ (* b d) (pow c 2)))
(+ (* d (+ (* -1 (/ (* a d) (pow c 3))) (/ b (pow c 2)))) (/ a c))
(+ (* d (+ (* d (- (* -1 (/ (* b d) (pow c 4))) (/ a (pow c 3)))) (/ b (pow c 2)))) (/ a c))
(pow d 2)
(/ (+ b (/ (* a c) d)) d)
(/ (+ b (+ (* -1 (/ (* b (pow c 2)) (pow d 2))) (/ (* a c) d))) d)
(/ (- (+ b (+ (* -1 (/ (* a (pow c 3)) (pow d 3))) (/ (* a c) d))) (/ (* b (pow c 2)) (pow d 2))) d)
(* d (+ b (/ (* a c) d)))
(* -1 (/ (+ (* -1 b) (* -1 (/ (* a c) d))) d))
(* -1 (/ (+ (* -1 b) (* -1 (/ (+ (* -1 (/ (* b (pow c 2)) d)) (* a c)) d))) d))
(* -1 (/ (+ (* -1 b) (* -1 (/ (+ (* -1 (/ (- (/ (* a (pow c 3)) d) (* -1 (* b (pow c 2)))) d)) (* a c)) d))) d))
(* -1 (* d (+ (* -1 b) (* -1 (/ (* a c) d)))))

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	d	@	-inf	((/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* d d) (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (* c c))
1.0ms	c	@	-inf	((/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* d d) (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (* c c))
1.0ms	c	@	inf	((/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* d d) (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (* c c))
1.0ms	a	@	-inf	((/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* d d) (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (* c c))
1.0ms	b	@	-inf	((/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+ (* a c) (* b d)) (* d d) (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (* c c))

simplify1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	egg-herbie

Counts

40 → 5

Calls

Call 1

Inputs
(/ (* b d) (+ (pow c 2) (pow d 2)))
(+ (/ (* a c) (+ (pow c 2) (pow d 2))) (/ (* b d) (+ (pow c 2) (pow d 2))))
(* b d)
(+ (* a c) (* b d))
(/ (* a c) (+ (pow c 2) (pow d 2)))
(* a (+ (/ c (+ (pow c 2) (pow d 2))) (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))
(* a c)
(* a (+ c (/ (* b d) a)))
(* -1 (* a (+ (* -1 (/ c (+ (pow c 2) (pow d 2)))) (* -1 (/ (* b d) (* a (+ (pow c 2) (pow d 2))))))))
(* -1 (* a (+ (* -1 c) (* -1 (/ (* b d) a)))))
(* b (+ (/ d (+ (pow c 2) (pow d 2))) (/ (* a c) (* b (+ (pow c 2) (pow d 2))))))
(* b (+ d (/ (* a c) b)))
(* -1 (* b (+ (* -1 (/ d (+ (pow c 2) (pow d 2)))) (* -1 (/ (* a c) (* b (+ (pow c 2) (pow d 2))))))))
(* -1 (* b (+ (* -1 d) (* -1 (/ (* a c) b)))))
(/ b d)
(+ (/ b d) (/ (* a c) (pow d 2)))
(+ (* c (+ (* -1 (/ (* b c) (pow d 3))) (/ a (pow d 2)))) (/ b d))
(+ (* c (+ (* c (- (* -1 (/ (* a c) (pow d 4))) (/ b (pow d 3)))) (/ a (pow d 2)))) (/ b d))
(pow c 2)
(/ a c)
(/ (+ a (/ (* b d) c)) c)
(/ (+ a (+ (* -1 (/ (* a (pow d 2)) (pow c 2))) (/ (* b d) c))) c)
(/ (- (+ a (+ (* -1 (/ (* b (pow d 3)) (pow c 3))) (/ (* b d) c))) (/ (* a (pow d 2)) (pow c 2))) c)
(* c (+ a (/ (* b d) c)))
(* -1 (/ (+ (* -1 a) (* -1 (/ (* b d) c))) c))
(* -1 (/ (+ (* -1 a) (* -1 (/ (+ (* -1 (/ (* a (pow d 2)) c)) (* b d)) c))) c))
(* -1 (/ (+ (* -1 a) (* -1 (/ (+ (* -1 (/ (- (/ (* b (pow d 3)) c) (* -1 (* a (pow d 2)))) c)) (* b d)) c))) c))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* b d) c)))))
(+ (/ a c) (/ (* b d) (pow c 2)))
(+ (* d (+ (* -1 (/ (* a d) (pow c 3))) (/ b (pow c 2)))) (/ a c))
(+ (* d (+ (* d (- (* -1 (/ (* b d) (pow c 4))) (/ a (pow c 3)))) (/ b (pow c 2)))) (/ a c))
(pow d 2)
(/ (+ b (/ (* a c) d)) d)
(/ (+ b (+ (* -1 (/ (* b (pow c 2)) (pow d 2))) (/ (* a c) d))) d)
(/ (- (+ b (+ (* -1 (/ (* a (pow c 3)) (pow d 3))) (/ (* a c) d))) (/ (* b (pow c 2)) (pow d 2))) d)
(* d (+ b (/ (* a c) d)))
(* -1 (/ (+ (* -1 b) (* -1 (/ (* a c) d))) d))
(* -1 (/ (+ (* -1 b) (* -1 (/ (+ (* -1 (/ (* b (pow c 2)) d)) (* a c)) d))) d))
(* -1 (/ (+ (* -1 b) (* -1 (/ (+ (* -1 (/ (- (/ (* a (pow c 3)) d) (* -1 (* b (pow c 2)))) d)) (* a c)) d))) d))
(* -1 (* d (+ (* -1 b) (* -1 (/ (* a c) d)))))

Outputs
(/ (* b d) (+ (pow c 2) (pow d 2)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 d d)))
(+ (/ (* a c) (+ (pow c 2) (pow d 2))) (/ (* b d) (+ (pow c 2) (pow d 2))))
#s(approx (+ (* a c) (* b d)) (*.f64 d d))
(* b d)
(*.f64 d d)
(+ (* a c) (* b d))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (*.f64 c c))
(/ (* a c) (+ (pow c 2) (pow d 2)))
(*.f64 c c)

rewrite0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Counts

5 → 5

Calls

Call 1

Inputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 d d)))
#s(approx (+ (* a c) (* b d)) (*.f64 d d))
(*.f64 d d)
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (*.f64 c c))
(*.f64 c c)

Outputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 d d)))
#s(approx (+ (* a c) (* b d)) (*.f64 d d))
(*.f64 d d)
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (*.f64 c c))
(*.f64 c c)

eval1.0ms (0.1%)

Memory: 1.3MiB live, 1.3MiB allocated
Compiler: Compiled 205 to 19 computations (90.7% saved)

prune4.0ms (0.3%)

Memory

5.9MiB live, 5.9MiB allocated

Pruning

9 alts after pruning (0 fresh and 9 done)

	Pruned	Kept	Total
New	7	0	7
Fresh	0	0	0
Picked	0	2	2
Done	0	7	7
Total	7	9	16

Accuracy

55.7%

Counts

16 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	54.2%	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
✓	36.6%	(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 b d)) (+.f64 (.f64 c c) (*.f64 d d)))
✓	35.7%	(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (*.f64 d d)))
✓	2.1%	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 c c) (.f64 d d)))
✓	3.8%	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 a c) (.f64 b d)))
✓	5.0%	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (*.f64 c c))
✓	4.5%	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 d d)))
✓	4.6%	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 b d)))
✓	4.9%	#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 a c)))

Compiler

Compiled 398 to 151 computations (62.1% saved)

regimes19.0ms (1.4%)

Memory

-20.9MiB live, 22.1MiB allocated

Counts

9 → 1

Calls

Call 1

Inputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 a c)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 b d)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 d d)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (*.f64 c c))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 a c) (.f64 b d)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 c c) (.f64 d d)))
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (*.f64 d d)))
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 b d)) (+.f64 (.f64 c c) (*.f64 d d)))
(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

Outputs
(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

Calls

5 calls:

5.0ms	d
3.0ms	c
3.0ms	a
3.0ms	b
3.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

Results

Accuracy	Segments	Branch
54.2%	1	`a`
54.2%	1	`b`
54.2%	1	`c`
54.2%	1	`d`
54.2%	1	`(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))`

Compiler

Compiled 19 to 27 computations (-42.1% saved)

regimes15.0ms (1.2%)

Memory

20.6MiB live, 20.6MiB allocated

Counts

8 → 3

Calls

Call 1

Inputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 a c)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 b d)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 d d)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (*.f64 c c))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 a c) (.f64 b d)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 c c) (.f64 d d)))
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (*.f64 d d)))
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 b d)) (+.f64 (.f64 c c) (*.f64 d d)))

Outputs

(/.f64 #s(approx (+ (* a c) (* b d)) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d)))

(/.f64 #s(approx (+ (* a c) (* b d)) (*.f64 a c)) (+.f64 (*.f64 c c) (*.f64 d d)))

(/.f64 #s(approx (+ (* a c) (* b d)) (*.f64 b d)) (+.f64 (*.f64 c c) (*.f64 d d)))

Calls

5 calls:

3.0ms	d
3.0ms	a
3.0ms	b
3.0ms	c
3.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

Results

Accuracy	Segments	Branch
43.3%	3	`a`
46.4%	3	`c`
38.4%	2	`(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))`
42.7%	3	`d`
47.3%	3	`b`

Compiler

Compiled 19 to 27 computations (-42.1% saved)

regimes15.0ms (1.1%)

Memory

-19.4MiB live, 19.4MiB allocated

Counts

7 → 1

Calls

Call 1

Inputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 a c)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 b d)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 d d)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (*.f64 c c))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 a c) (.f64 b d)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 c c) (.f64 d d)))
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (*.f64 d d)))

Outputs
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (*.f64 d d)))

Calls

5 calls:

4.0ms	b
3.0ms	d
3.0ms	a
3.0ms	c
2.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

Results

Accuracy	Segments	Branch
35.7%	1	`(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))`
35.7%	1	`d`
35.7%	1	`a`
35.7%	1	`c`
35.7%	1	`b`

Compiler

Compiled 19 to 27 computations (-42.1% saved)

regimes12.0ms (0.9%)

Memory

19.2MiB live, 19.2MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 a c)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 b d)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 d d)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (*.f64 c c))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 a c) (.f64 b d)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (+.f64 (.f64 c c) (.f64 d d)))

Outputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (*.f64 c c))

Calls

5 calls:

2.0ms	d
2.0ms	b
2.0ms	c
2.0ms	a
2.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

Results

Accuracy	Segments	Branch
5.0%	1	`b`
5.0%	1	`a`
5.0%	1	`d`
5.0%	1	`(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))`
5.0%	1	`c`

Compiler

Compiled 19 to 27 computations (-42.1% saved)

regimes10.0ms (0.7%)

Memory

-20.9MiB live, 17.8MiB allocated

Accuracy

Total -1.8b remaining (-3%)

Threshold costs -1.8b (-3%)

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 a c)))

#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 b d)))

#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 d d)))

Outputs
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 a c)))

Calls

5 calls:

3.0ms	b
2.0ms	d
2.0ms	a
2.0ms	c
1.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

Results

Accuracy	Segments	Branch
4.9%	1	`a`
4.9%	1	`d`
4.9%	1	`c`
4.9%	1	`b`
4.9%	1	`(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))`

Compiler

Compiled 19 to 27 computations (-42.1% saved)

bsearch24.0ms (1.8%)

Memory

23.3MiB live, 23.3MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	9.68220653894404e-7	0.0018845972645716504
8.0ms	-2.1644377257659007e-56	-8.714970429903669e-57

Samples

13.0ms

208×

valid

Compiler

Compiled 512 to 382 computations (25.4% saved)

Precisions

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

ival-mult: 5.0ms (60.9% of total)

ival-add: 2.0ms (24.4% of total)

ival-div: 1.0ms (12.2% of total)

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

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

simplify7.0ms (0.5%)

Memory

-30.9MiB live, 7.5MiB allocated

Algorithm

1×	egg-herbie

Calls

Call 1

Inputs
(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
(if (<=.f64 b #s(literal -4196261778848663/220855883097298041197912187592864814478435487109452369765200775161577472 binary64)) (/.f64 #s(approx (+ (* a c) (* b d)) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d))) (if (<=.f64 b #s(literal 5072854620270127/9223372036854775808 binary64)) (/.f64 #s(approx (+ ( a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (.f64 d d))) (/.f64 #s(approx (+ ( a c) (* b d)) (.f64 b d)) (+.f64 (.f64 c c) (*.f64 d d)))))
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (*.f64 d d)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (*.f64 c c))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 a c)))

Outputs
(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
(if (<=.f64 b #s(literal -4196261778848663/220855883097298041197912187592864814478435487109452369765200775161577472 binary64)) (/.f64 #s(approx (+ (* a c) (* b d)) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d))) (if (<=.f64 b #s(literal 5072854620270127/9223372036854775808 binary64)) (/.f64 #s(approx (+ ( a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (.f64 d d))) (/.f64 #s(approx (+ ( a c) (* b d)) (.f64 b d)) (+.f64 (.f64 c c) (*.f64 d d)))))
(/.f64 #s(approx (+ (* a c) (* b d)) (.f64 a c)) (+.f64 (.f64 c c) (*.f64 d d)))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) (*.f64 c c))
#s(approx (/ (+ (* a c) (* b d)) (+ (* c c) (* d d))) #s(approx (+ (* a c) (* b d)) (*.f64 a c)))

soundness1.0ms (0.1%)

Memory

1.4MiB live, 1.4MiB allocated

Stop Event

1×

done

Compiler

Compiled 145 to 30 computations (79.3% saved)

preprocess37.0ms (2.8%)

Memory: 9.6MiB live, 49.7MiB allocated
Compiler: Compiled 392 to 122 computations (68.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze27.0ms (2%)

sample839.0ms (63%)

explain125.0ms (9.4%)

preprocess4.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify0.0ms (0%)

localize32.0ms (2.4%)

series20.0ms (1.5%)

simplify1.0ms (0%)

rewrite0.0ms (0%)

eval1.0ms (0.1%)

prune1.0ms (0.1%)

simplify1.0ms (0.1%)

localize38.0ms (2.9%)

series8.0ms (0.6%)

simplify1.0ms (0.1%)

rewrite0.0ms (0%)

eval5.0ms (0.4%)

prune3.0ms (0.2%)

simplify1.0ms (0%)

localize29.0ms (2.2%)

series9.0ms (0.7%)

simplify1.0ms (0.1%)

rewrite0.0ms (0%)

eval2.0ms (0.1%)

prune4.0ms (0.3%)

simplify0.0ms (0%)

localize25.0ms (1.9%)

series6.0ms (0.5%)

simplify1.0ms (0%)

rewrite0.0ms (0%)

eval1.0ms (0.1%)

prune4.0ms (0.3%)

regimes19.0ms (1.4%)

regimes15.0ms (1.2%)

regimes15.0ms (1.1%)

regimes12.0ms (0.9%)

regimes10.0ms (0.7%)

bsearch24.0ms (1.8%)

simplify7.0ms (0.5%)

soundness1.0ms (0.1%)

preprocess37.0ms (2.8%)

end0.0ms (0%)

Profiling